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diff --git a/.ipynb_checkpoints/debinningFunction-checkpoint.ipynb b/.ipynb_checkpoints/debinningFunction-checkpoint.ipynb
index cb82baf..9ba47fa 100644
--- a/.ipynb_checkpoints/debinningFunction-checkpoint.ipynb
+++ b/.ipynb_checkpoints/debinningFunction-checkpoint.ipynb
@@ -1,631 +1,630 @@
{
"metadata": {
"name": "",
- "signature": "sha256:c791533364436ab31de625cd03cf5b716781a9c09b1e17428da1b3a78e4ef859"
+ "signature": "sha256:f9ecdcb2035923432ee32d967e3c0f105cc4b8a80c7046991c18f2b1f9639f45"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
- "from os import listdir as ls\n",
"from __future__ import division\n",
"import numpy as np\n",
"from time import time\n",
"import bisect\n",
"import operator as op\n",
"\n",
"import utilities.sampleFunctions as funcs\n",
"import utilities.probCalc as pc\n",
"import utilities.plotting as debinPlot\n",
"reload(funcs)\n",
"reload(pc)\n",
"reload(debinPlot)\n",
"\n",
"%matplotlib inline\n",
"from matplotlib import pyplot as plt\n",
"from IPython.html.widgets import interact, interactive, fixed\n",
"from IPython.html import widgets\n",
"from IPython.display import clear_output, display, HTML\n",
"\n",
"def quickData():\n",
" ''' Shorthand for getting easyEndpoint data (384 x values in [8.5,200])\n",
" - set nPulls before calling\n",
" - see utilities.sampleFunctions.functionToData for more details\n",
" '''\n",
" return funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n",
"\n",
"\n",
"def quickBG():\n",
" ''' Shorthand for getting endpointBG data (384 x values in [8.5,200])\n",
" - set nPulls before calling\n",
" - see utilities.sampleFunctions.functionToData for more details\n",
" '''\n",
- " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n"
+ " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"nPulls = 20\n",
"pullData = {index:[] for index in xrange(nPulls)}\n",
"funcs.settings['simpleSortedOutput'] = True\n",
"for iteration in xrange(2000):\n",
" for i,v in enumerate(quickData()):\n",
" pullData[i].append(v)\n",
"\n",
"funcs.settings['simpleSortedOutput'] = False\n",
"x, f, F, data = quickData()\n",
"f = f / F[-1]\n",
"F = F / F[-1]\n",
"\n",
"ithPDF = {}\n",
"for i in xrange(1, nPulls+1):\n",
" ithPDF[i-1] = np.array([f[j] * F[j]**(i-1) * (1 - F[j])**(nPulls-i) * pc.nKr(nPulls, i) for j in xrange(len(x))])\n",
"\n",
"def makeHist(i=0):\n",
" histogramRange = np.arange(0, 201, 5)\n",
" plt.hist(pullData[i], bins=histogramRange, alpha=0.4, normed=True)\n",
" plt.plot(x, ithPDF[i])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"interact(makeHist, i=(0,nPulls-1))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"<function __main__.makeHist>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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3HKEkMkXPPUqgyMYzd9x17IroJzpF8l1efEv2dh1NCzuMrFZb/CnejGwMOwwR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\nAABJRU5ErkJggg==\n",
"text": [
- "<matplotlib.figure.Figure at 0x7fb124123a90>"
+ "<matplotlib.figure.Figure at 0x7f57ec05d750>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"### The formula looks insane....\n",
"zero = np.around(np.array([sum([(pc.nKr(nPulls, i) // nPulls) * Fx**(i-1) * (1 - Fx)**(nPulls-i) \n",
" for i in xrange(1, nPulls+1)]) for Fx in F]) - 1, decimals=14)\n",
"\n",
"np.linalg.norm(zero)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"0.0"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"The new binfull algorithm $\\Rightarrow$ debinning function"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"funcs.settings['simpleSortedOutput'] = False\n",
"nPulls = 96\n",
"nFictitious=96\n",
"\n",
"x, f, F, data = quickData()\n",
"x, bgf, bgF, bgData = quickBG()\n",
"f = f / F[-1]\n",
"F = F / F[-1]\n",
"bgf = bgf / bgF[-1]\n",
"bgF = bgF / bgF[-1]\n",
"\n",
" \n",
"def mapDataToX(dindex):\n",
" # maps elements of data to elements of x\n",
" # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
" xindex = bisect.bisect_left(x, data[dindex])\n",
" if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
" return xindex - 1\n",
" return xindex\n",
"dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
"\n",
"\n",
"def vecG_rth(rindex, xindex):\n",
" r = rindex+1\n",
" return pc.nKr(nFictitious, r) * bgF[xindex]**(r-1) * (1 - bgF[xindex])**(nFictitious - r)\n",
"\n",
"\n",
"vecG_rx = np.array([[vecG_rth(rindex, xindex) for xindex in xrange(len(x))]\n",
" for rindex in xrange(nFictitious)])\n",
"sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
"debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
"\n",
"# Discard trivial data\n",
"x = x.compress(bgf > 0)\n",
"debinningData = debinningData.compress(bgf > 0)\n",
"f = f.compress(bgf > 0)\n",
"bgf = bgf.compress(bgf > 0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Pretty plot\n",
"fig, axes = plt.subplots(figsize=(11,7))\n",
"plt.plot(x, debinningData)\n",
"histogramRange = np.arange(0, 201, 5)\n",
"plt.hist(data, bins=histogramRange, alpha=0.4, normed=True)\n",
"plt.plot(x, f)\n",
"plt.plot(x, bgf)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
- "[<matplotlib.lines.Line2D at 0x7fb11cfabb10>]"
+ "[<matplotlib.lines.Line2D at 0x7f57cbae6b10>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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4xBCWDBuIFaiFuyUXxuS5EDxAeKkMel+3julj23moMBHxBQqcIvIPIYlJXPrE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\nAABJRU5ErkJggg==\n",
"text": [
- "<matplotlib.figure.Figure at 0x7fb11d0ca290>"
+ "<matplotlib.figure.Figure at 0x7f57cbc07f90>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Residual Plot\n",
"fig, axes = plt.subplots(figsize=(11,7))\n",
"plt.plot(x, (f - debinningData)**2 / f)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
- "[<matplotlib.lines.Line2D at 0x7fe06541da90>]"
+ "[<matplotlib.lines.Line2D at 0x7f57cbbbb9d0>]"
]
},
{
"metadata": {},
"output_type": "display_data",
- "png": 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rCAYTlsJzzz3uT5062R1///3So4+61ijApzgt3ZTWpo37vzR/vu9KgKohiCJQ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\ndQtDOogiWnHpnp8xQ2rbVmrc2G8dPpx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AQPIdIyr5FlGCKMoFQRQAgIAE1TW/cGEw9QBxRxAFACAgQQTRnj0JoigfBFEAAAKwZYtU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\n",
"text": [
- "<matplotlib.figure.Figure at 0x7fe06541d410>"
+ "<matplotlib.figure.Figure at 0x7f57cbbbb510>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print sum((f - debinningData)**2 / f)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "0.168808848476\n"
+ "0.130624657206\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Constructive Comments from Awesome People"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Greg says, try a KS test. \n",
" - If I have f(x), how likely will I draw a sample which looks like g(x).\n",
" - Related to Wilks' Theorem\n",
" - Also, check out rank statistics\n",
" \n",
"Christoph mentioned \"max gap method\" for when you have no idea whatsoever what your background is."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Test Suite"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Let's try some GPU programming:\n",
"import pycuda.driver as cuda\n",
"import pycuda.autoinit\n",
"from pycuda.compiler import SourceModule\n",
"from string import Template\n",
"\n",
"funcs.settings['simpleSortedOutput'] = False\n",
"nPulls = 96\n",
"nFictitious = 96 # Multiple of 32 for GPU programming ease.\n",
"lenXdomain = len(np.arange(8.5, 200.2, 0.5))\n",
"\n",
"mod_template = Template(\"\"\"\n",
" __global__ void vecG(double *vecG_rx, double *bgF, double *nKr) {\n",
" const int idr = threadIdx.y + blockDim.y * blockIdx.y;\n",
" const int idx = threadIdx.x + blockDim.x * blockIdx.x;\n",
" const int idrx = idx + idr*${lenX};\n",
" const int r = (idr + 1) < (${nFic} - idr) ? (idr + 1) : ${nFic} - idr;\n",
" vecG_rx[idrx] = nKr[r-1] * pow(bgF[idx], idr) * pow(1 - bgF[idx], ${nFic} - idr - 1);\n",
" }\n",
" \"\"\")\n",
"\n",
"mod = SourceModule(mod_template.substitute(nFic=nFictitious, lenX=lenXdomain))\n",
"\n",
"timer = time()\n",
"\n",
"# initialize the loop\n",
"nKr = pc.get_nKrArray(nFictitious)\n",
"chisq = []\n",
"bgchisq = []\n",
"ks = []\n",
"bgks = []\n",
"\n",
"for trial in xrange(100000):\n",
"\n",
" x, f, F, data = quickData()\n",
" x, bgf, bgF, bgData = quickBG()\n",
" f = f / F[-1]\n",
" F = F / F[-1]\n",
" bgf = bgf / bgF[-1]\n",
" bgF = bgF / bgF[-1]\n",
"\n",
" def mapDataToX(dindex):\n",
" # maps elements of data to elements of x\n",
" # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
" xindex = bisect.bisect_left(x, data[dindex])\n",
" if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
" return xindex - 1\n",
" return xindex\n",
" dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
"\n",
" # Use the GPU for the most expensive / paralellizable part of the calculation:\n",
" # =====\n",
" \n",
" # Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n",
" vecG_rx = np.empty([nFictitious, len(x)])\n",
" \n",
" # Allocate memory on the GPU for vecG calculation\n",
" vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n",
" bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n",
" nKr_gpu = cuda.mem_alloc(nKr.nbytes)\n",
" \n",
" # Transfer data to the GPU\n",
" cuda.memcpy_htod(bgF_gpu, bgF)\n",
" cuda.memcpy_htod(nKr_gpu, nKr)\n",
" \n",
" # Get a reference to the GPU module function and do the calculation\n",
" # NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n",
" vecG_func = mod.get_function('vecG')\n",
" vecG_func(vecG_rx_gpu, bgF_gpu, nKr_gpu, block=(16, 4, 1), grid=(24, 24))\n",
"\n",
" # Get the result back from the GPU and use it!\n",
" cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n",
" sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
" debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
" \n",
" x = x.compress(bgf > 0)\n",
" debinningData = debinningData.compress(bgf > 0)\n",
" f = f.compress(bgf > 0)\n",
" bgf = bgf.compress(bgf > 0)\n",
" F = F.compress(bgf > 0)\n",
" bgF = bgF.compress(bgf > 0)\n",
" \n",
" # Chisq test....\n",
" chisq.append(sum((debinningData - f)**2 / f))\n",
" bgchisq.append(sum((debinningData - bgf)**2 / bgf))\n",
" \n",
" # KS test...\n",
" debinningCDF = pc.A(debinningData, 0.5)\n",
" ks.append(max(abs(debinningCDF - F)))\n",
" bgks.append(max(abs(debinningCDF - bgF)))\n",
" \n",
" if trial == 0:\n",
" # Infinity sigma upper and lower bands...\n",
" debinningUpper = debinningData.copy()\n",
" debinningLower = debinningData.copy()\n",
" # Uncertainty PDFs for each x value...\n",
" uncertaintyHistos = [debinPlot.HistoContainer(np.arange(0., 0.024, 0.0002), debinningData[i])\n",
" for i in xrange(len(x))]\n",
" else:\n",
" debinningUpper = np.clip(debinningData, debinningUpper, 20.)\n",
" debinningLower = np.clip(debinningData, -1., debinningLower)\n",
" for i in xrange(len(x)):\n",
" try:\n",
" uncertaintyHistos[i].addValue(debinningData[i])\n",
" except ValueError as e:\n",
" print e.message\n",
" print 'xindex = ' + str(i) + ', debinningData[xindex] = ' + str(debinningData[i])\n",
" \n",
"print time() - timer"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "348.400629997\n"
+ "255.336770058\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Try with a HUGE data set:\n",
"nPulls = 10000\n",
"\n",
"timer = time()\n",
"x, f, F, data = quickData()\n",
"x, bgf, bgF, bgData = quickBG()\n",
"f = f / F[-1]\n",
"F = F / F[-1]\n",
"bgf = bgf / bgF[-1]\n",
"bgF = bgF / bgF[-1]\n",
"\n",
"def mapDataToX(dindex):\n",
" # maps elements of data to elements of x\n",
" # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
" xindex = bisect.bisect_left(x, data[dindex])\n",
" if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
" return xindex - 1\n",
" return xindex\n",
"dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
"\n",
"# Use the GPU for the most expensive / paralellizable part of the calculation:\n",
"# =====\n",
"\n",
"# Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n",
"vecG_rx = np.empty([nFictitious, len(x)])\n",
"\n",
"# Allocate memory on the GPU for vecG calculation\n",
"vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n",
"bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n",
"nKr_gpu = cuda.mem_alloc(nKr.nbytes)\n",
"\n",
"# Transfer data to the GPU\n",
"cuda.memcpy_htod(bgF_gpu, bgF)\n",
"cuda.memcpy_htod(nKr_gpu, nKr)\n",
"\n",
"# Get a reference to the GPU module function and do the calculation\n",
"# NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n",
"vecG_func = mod.get_function('vecG')\n",
"vecG_func(vecG_rx_gpu, bgF_gpu, nKr_gpu, block=(16, 4, 1), grid=(24, 24))\n",
"\n",
"# Get the result back from the GPU and use it!\n",
"cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n",
"sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
"BIGdebinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
"\n",
"x = x.compress(bgf > 0)\n",
"BIGdebinningData = BIGdebinningData.compress(bgf > 0)\n",
"f = f.compress(bgf > 0)\n",
"bgf = bgf.compress(bgf > 0)\n",
"F = F.compress(bgf > 0)\n",
"bgF = bgF.compress(bgf > 0)\n",
" \n",
"print time() - timer"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "0.0659880638123\n"
+ "0.0508160591125\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"timer = time()\n",
"# Pretty plot\n",
"fig, axes = plt.subplots(figsize=(11,7))\n",
"plt.fill_between(x, debinningUpper, debinningLower, alpha=0.4, zorder=1)\n",
"plt.plot(x, f, color='#880088', zorder=3)\n",
"plt.plot(x, BIGdebinningData, color='black', linestyle='--', linewidth=2, zorder=4)\n",
"for i, v in enumerate(x):\n",
" debinPlot.verticalColorBand(uncertaintyHistos[i], v, 0.5)\n",
"print time() - timer"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "12.6747150421\n"
+ "9.35061311722\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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Z0pJ4Dfc8LjdF7saYvL+lJTGlbpdFslPw7nXslHuqFD3AyA5YECsajbB79/N8\n+ct3U15env4LishFu9iUulYakm5v2rT5NDWNVGdTpIMEAkFycsbw+usLiNi9XRHpstThlG5t165d\nLFtWR2Xl1X6HItKt9OlzGZs392TGjAV+hyIiHaCtSUMiXZbjOEydWk1x8XUEknOl0i7skjtuWtle\nuSdV6vpsKXU3fWyXR0pOr7vnt9Pa9jXstqlmmCfHl+p8raXz3bjsdL49k9yejQ6Qba14mmp2up1e\nd7eTU+tuurylJXFGuj1cwL0Hu637fkuLF1MkAuvWecele9b6gAG3MXfuZIYM2cwllwxP78VExFf6\nV1a6rY0bN7FzZx6lpQP9DkWkWwoGs+jd+w5eeum9c15cQUQ6J3U4pVtyHIeZM1dSUjLG71BEurXC\nwlKamq7grbeUWhfpypRSl25p+/bt7NuXy6BBlX6H0qXYKXQ7fZ1cFD3VLHV7O1Xa3U6X26npYLD1\nc9sF3N199qxzt21WVuI1UxWED6aogGXPXE8u9m6fw06N2wXe7aLydlF297hUM9OjUS8WezZ6JOKl\n1MNh75rNzYkz891ruNcJBhOvaZ/PLcY/KuWyHe2nsvIqli59ibFjdzJwoDIOIl2RnnBKtzR37ioK\nC6/yOwwRAQKBAD173szkyQtpcXu/ItKlqMMp3c7BgwfZurVZYzdFMkivXv04eLCM1avX+R2KiKSB\nUurS7Sxfvp5QaAQmVTVuOWdu+tyeCW6nqZPXPk+VeralKrCenJpuba3yVDPc7fOkmj0eCEAo1PY9\npErp2+l1+xz2canWrLD3B4OJM8+TZ9Q3NyfGahd1dx8C2mumt5ZSD4W89u779uz75ubWP2P3HOvW\ndUxB+IqK63jrrSmMHHkZOTmtr/glIp2PnnBKt9LU1ER19Q7Kyy/xOxQRSZKX14P6+sEsWbLS71BE\npJ2pwyndysaNmwiHBxIK5fodioik0KfPNcyevYHGxka/QxGRdqSUunQr1dWb6dHjBr/D6FTstc/t\ntK9dfD3VLHG7fWtrore2ZnmqFG8g0Po13fRwaynwVMXWk2elu/uT08qtzZh3PwP7/QkfjL8RBtyi\n7lHA/fsmB3DbBwG39GQu4K7w2OxeDGiIbc54zTmTFrczzeFw6jXRm5q8NHoo5KXS7QLwbro8GIyl\n1d37sock2IXka2piXy+/nLTKySmguXkoK1as4aabrkvvxUSkw+gJp3Qbx48fZ+fO0/TooVJIIpms\nd++rmT0x0vabAAAgAElEQVR7A01NTX6HIiLtRB1O6TbWr98MDNNkIZEMl5tbSGPjQNasqfE7FBFp\nJ8ZJNZUyQxhjnEyOTzoPx3H4yU+ew5h7KSjo5Xc4GW/t2tbT2pBYqDzV+/D+lLWdpnZT4/Z+eya5\nfaydLrev6bZPXlfdfZ0qFZ6Vlbidqm3yLPkJE90cM1Do3lD8aw7ewKRA0n73nIV46fUmID++3YKX\nPg8SS70DnLauEU+pUwC4QxqPWdtNMPPN2IcSjXpp8qamxPS6mxpPte66PaO9sdFLr0ejXvvkmfHu\nudO51np9/XFaWt7kq1/9JMFUVfdFpEMZY3Ac54Kf2OgJp3QLBw8e5OjRbHU2RTqJgoJenDhRxubN\nW/wORUTagTqc0i1s2LCNQGCI32GIyHkoLh7FnDmr/Q5DRNqBZqlLl+c4DkuXbqe09D6/Q8k49trn\nkHp9cnvmt81OZdtp71Sz0e329hBaO8VtF1W347ALpbtt7HR48hrs9nmSC7vbKXz7vu6613ip7ny8\n34xFwJXW/vj5zvypngXkxbcjgDsCKJdYWh1i6XI3xhZiaXX33G5K3bHauDPXc4ilzyE26929di8r\nvmMw4W/jB9bhpeDr4K03YsHk5MRS5eClxZubE4ckuHNzCgvhdDyl39SUuuJAOOx9T9auTW9avVev\nfuzcCfv27aNv377pu5CIpJ2ecEqXd+jQIU6cyCE/v6ffoYjIeQqFRrJ4sZa7FOns1OGULm/Tpu0Y\nM9jvMETkAlRUDGfZsn3U19e33VhEMpZS6tKlOY7DkiXbKCm51+9QfOemz5OLe7vaKnJut0+emZ6q\ngLu9nTzz207Hp0qpu6lwe78x3v7k89nnSLVuunvc+A+YxHS4O4dsOF7h9V546e1cvFR7kbXtFnJv\nwUudNwE93Jvy4sexzh3CS7sHgVPWud1Z6u6xTYBbMjYPOBnfDuOl5ftZ+xuBQ/HtWpj4+fhNHICZ\n02IXdfts9jruzc3e59PUlPi52gXh3Znp7nsQS9G7P1fpSq0HgyEcZxjr1m3guuvGpOciIpJ2esIp\nXZpmp4t0fqWlI3jnnY2oTJ5I56UOp3RpGzZsIxgc6ncYInIRCgpKOHo0n927d/sdiohcIHU4pcty\n0+mlpSqHJNLZ5eSMYMmS9X6HISIXSGM4pcvas2cPJ04UMHBgj7YbdzFr1sS+pipRlLzqT2slg1pb\n7cdtmzz+024HiSWP7HGW9nZWlndsdnbqmNzt7OzUY0xDIWuM5n0GSuMNHLwxl+6f1v2sffYKQPl4\nqwiF8MZo5lj7sbbdzG6Wtc8ukZSDN84yijeGs9m6psErixSy9rvjOnOIjRGF2HhPd85ME94qRqes\n6xyN3x/AHmt/T5jw2fiHHB/v+fZLTsL4THvcq7s/+Xtmt7d/ftztdfGJ5CNHkhbl5UNYuXIRkyY1\nkpeX1/YBIpJR9IRTuqz33ltHTs7lfochIu0gGAwRjQ5m06bNfociIhdAHU7pkmpra1m16hC9ew/z\nOxQRaSc9e17CokWb/A5DRC6AUurS6TmOw8mTJ2lqaqKoqAhjDAsXLgEuJRAItnl8V7BmTep0uJ36\nDKb4KJLLG9nHufvttHeqEkl2iSL7OskpWTdlnly6KDkdn7zSkJsut899973GW3knDy8dXY6X4s4n\nVm4IvBR5yHo/By8FXoiXvu5JrPSQe5w7IiOI9ye6+zkU45VWiuL9Rj0N9IlvR/BijcTfc8/RaMXq\nlldy0/UtVtsAXorcWPGdtLargEOxUlAHG/uydv015OU0cvOgWV6M8bJJ93zGnEmvvzXFObMSkf0z\n0FopqwZ3NSMSfx5c69alL61eXNyHXbtaOHz4MOXl5em5iIikhTqc0mm1tLSwdOlK3nlnIydOBDEm\nF8epxZgI0ehQ+va9yu8QRTpM3cki1r13NWvXjCF8OpvLB69g+YYbGF68jt4c8Du8dmGMIRAYzrp1\nmxk3Th1Okc5EHU7plI4ePcrzz89k795yeve+jwEDvGUro9FIt3myKd1buDmLzcsvZ+3iMezbMYBL\nLlnL3fdMoSpvBybsUJBXx5yaSfzFZU+nfBrZGZWVDae6egq33XYDgYBGhYl0FiaTC+kaY5xMjk/8\ncejQIZ566m2i0ZsoL+++NTbdFV6g9ZnDybPL3e1UKXA7lW3vT3W+5JnkbrrVTr9nZXnp8NZmpttp\nW/ccwaCXfh//gPFW4MkmcUa4XXzATVkXk5gmd7mp9QK89LLBm+2dk3S+fOur21HLJjF9Tvx498/2\nBuu4bLwUfQFe6jybxJWG7P1uyvy4FdOx+HYPzsxSd4ADG6pYPWMsGxaMos+gvYy6ZRnDr6ghlBXP\nr9cBpyESCfD0f3+Z8Te8wZD+m7wZ8PvibQC2wcwXY0E1NXmrEUUinEm1NzfH3oPY6kL2fncFopYW\n76u7na7U+s6dk/niF8fQv3//9FxARN7HGIPjOBf8p6uecEqncvLkSZ566m2MuZ3y8gF+hyPSYRpO\nFrBu9mhWzxhLS1MWV961lEe+/z8UF9bGGjTjlV+KCwajjLttGnPmT2JQvy0EzvSUO7dQaDirV29W\nh1OkE1GHUzqNcDjM889PJxweS58+6mxK1xeNBNi+Yjir517LzmVDGX5DDXf9zRT6X7499pS4Du/J\naCuGDVnPksW3snrjWK6uWtwRYaddeflQli1bwj33tJCVpX/GRDoDpdSl05g5cwFz5kQZOPB2v0Px\nzdq1rRdwd9npbjsFnmq7tQLvdtH2YDA28xm8FLnjJKbA7bZ2St0+n3ts8ix199x3T4of2AMvvZ2N\nly7PBcri26eJpc/d/e6QgRa8wu9ZeDPF3T5JDt7M7954KfBcvNnepSSmvXOsNu513BR9C17KHet8\ndiH3ZqtNHd6M+WzOzBQnYu1vgWPbS1nz8ljWvnwNxZUnGPXRpYy4dTU5hU2xdL57PoP3VPM0Xgr+\nFF7avwEOrOjHS889zOc/+kNysptj9+oetz/+H8AhmPnH2M3X13tp9IYGL03e2OgVgQ+H4XT883Tf\nD4e9NHs4nM60+jQeffQShg7tvsNqRDqSUurSLezfv585c3bTr99H/Q5FJC2aG0JsnDqK1c9fy7Ft\nZYx8YAUff/IpyoYdiv2mrr3wc/fpu5dBQ7ZQvep2brt2RrvF7Kfc3KGsXLlVHU6RTkIdTsl40WiU\nV16ZT2HhzWRlZbd9gEgncnhjBSv/dD01b15FvzG7uPbRBQy9YwPB7Kj3NLYd3Hbn2zzzy7/n6hHV\nFOdcRO81Q5SWDmL16oV84ANN5OTktH2AiPhKHU7JeDU169mzp5jBgwf6HUqHcmehJxdhd9lF01tb\nBz3VrPPkgt522jtVqt1xEouvQ+y1fb5UxyXPRr/XTZnn4KWP8/DS11fGv+bjpaPt9ckL8VLaedY5\n7ALvIbwUeD7vT4E3kTjTvchqW4KnwTrOTekbEgu7u8dVWse5650HSZxd78ZaCkQg3JjFhslXsvLn\n11O7pydXPryERxb/lOL+J71Z6gHr2iFis93dz8H9TA7grceeTWyYgLvfvf7xWJzFnGT07dUs2HIP\n9935Z28WfT6xgvkAO2HCF+Lfp2Mw7U+xb05Wlpc6Dwa94u/2cIzTrXSOa2piXy9v51Vms7KyaWnp\nx44dO7j00kvb9+Qi0u7U4ZSMFg6HefPNFfTuPcnvUEQu2pGa3qx84npqnr+ayut2c8OX5jH0rg0E\niqJeiaY0uv6uufzmu1/nwOV96VO2L/0XTLP8/CGsXLlJHU6RTkAdTsloK1aspra2ioEDS9puLJKB\nWk5nsfHlK1j56+s5sa2UUQ8v5eGFP6PHJcfhSMfGkpPbzC33zmTO7Pv4xMd+0+mLwZeUDKCmZgFN\nTUqri2Q6zVKXjBUOh/nhD58nP/9+8vJ6tH1AF+Cm0ZPT5cmF2939dsraTnfb6XX3a6pZ6nY63J6Z\nnlyo3d3OtobQ2sXeU6XU75lkYuuSQywFnGrt8yxrv9s2H6/Aul14PWTtt1PtRVYbO01uPzG011J3\nZ7fnWMcVWtsFeGl+h8RZ5e7MbnutdTc1fdqKDzi2qYyVT1zP2t+PZmufd9hfsYoTgePs2gWHD8fS\n0j//OTz6qHU8sfPNmA07dsOtI+HSoWCK8Yq2h/Fm8fewjqvDKyRfZ91/BG+IwKFYqaWnH/sHxn3w\nLYZduR52W+c+DeyMb+/jzOz1t//oEI7fc0ODVxz+9GnO7E81oz0c9t5vaUnPjPWdO2fy0EP99ZRT\nJM0udpa61gWTjFVTs4FTpyq7TWdTOr9oxLDljct4ceIj/PGWLxIIRfjMe78gcutc/jzrODNmwMaN\ncOxYrLPmdtyS/eF5+OvHYMQdUDkGPvk5eGWa16m7GIFglDs+PZU5r9xLJNL5/wnIzx/CihXb/A5D\nRNqglLpkpGg0yqxZaygru9vvUETOav9+eOH5EM8+mc/gk9fwgSGXM+ZLi3hw8h/Iyo096vvUJ2DE\nZTBwCAwaBBUVUJANecWpz3n3ndAchnnz4cAheP7l2H8v/hI+ds/Fxzxk9EaWTL6FVQuu45qh7138\nCX0US6vPV1pdJMMppS4ZaevWrTz99HoGDvyA36Gkjb0WOiSm0VtLqduzgu02ycXUU61Pbp+jtfXT\n7TR5qu3WZrRPuC9+kiK8VHcoabsoxXYhXkrYne2dT+K65m6nrCfeDHMHLxWfjTczPdu6ZtA6j5Wu\nPpPXKbDiyMVLl9trsNtOeuerPQTPvQi/fTKb6lXNZzLw147KZvHy5tif8u7OCN6f9vYTzSBwNL5d\nipe6tzgObNoEb7wBkyfD9OmQl4c3M/0E3lAEx7qHE3iz2o/y/qEAp+DQ+kpe+Oqj/PV//ZCchvij\n02PAoXibQ8TS6hBLsx+ObU59zTmzlnpDgzc73f3a1OSttW6n1O1119t7xvrOnTN46KEBSquLpJFS\n6tIlLVxYQ0FBmpYoEbkIkXCA1382hC9+Cd5b1UwoK8B9dwX5/VMwfXZz2yc4D8bApZfC174GCxbE\nO5vJ8URg+/bzP3fvYfsZeuNGFr1+x8UH6rO8vMGsXn0BH4KIdBh1OCXjHDt2jA0baikp6V51NyWz\nNRzNZ+H37uBXg74Jc8bzwG09+d0vDEcORnnjzQif+RT07Nn2edrbb56Cy66Eb/9L62NCW3Pr599m\n1dxrOXmsV9uNM1hp6UDWrTtAc3P7dvhFpP1oDKdknBUraggGRxAIdI2/h9as8bbtMjT2bHP3tb0v\n1bY9CzwQSEyj22lye7/71S7e7m677d2v7rZd2D0U8s531wfd/DtekfFcwM1kFuHN2i4icW3xAmu/\nPWvc5XbWcvHWQ8/Gm21tF4zPwZsRHsRLFTfjpcnd1+ClyQtIXFfdvX4LXiq+IfZ67z74xVPwyXtL\n2PvCbax/8Sou+fA6Pjb1GXpfdYC/dK/hps7D1vUarZiCeJ9Jo3XNHLzZ+g3Wse766uV4y1mWEJt5\nDrHP3pqhv2ljLF39Xz+El6fAs8/CdaOtzyCAN3vdPV/P2LWL+p1izKcWMX/R3Xzw/7yQmEYvxRvO\nUMiZEk6THjBMfTV206n+FzUmNhTAfd/+mXf7gzU17ZtWDwZDhMN92LVrF8OGDWu/E4tIu+ka/6JL\nlxGJRKiu3kZ5ucZiiT/Wb4CH/hoGXQH/8UP42gcvI793HZ/f8CMmPf0Sva884HeICX78X/DeHLji\nCti8GW66Cb7zXa80UVuue3geu1YOYd/6qvQGmma5uUNYtUqz1UUylTqcklF27NhBfX0ZOTkFbTcW\naUdbtsDHPmoYORb+8AJEIoa7RvfiX9+s5tbHZ1JQUdf2SXxy/bWwZAl89auxMZ1vTPWeMrYlOy/M\nLY/OYM7P7zvnYzJRWdlgVq/eR1N71I4SkXanDqdklMWLN5Kfr6eb0rEaDhew6L+v46WXHYIE+NTd\nPdiy0mH6guPcdGuk7RNkgNxc+NGPYNYs+MMzicMm2jJq4jKaGnLZtLjzTtSLpdVja6uLSObRGE7J\nGPX19dTUHKFfv3YoNOgzd9zm2VYJssdiul/tsW/22MpUq/60VurIPtYey2mXOWqtRJJ93MQPxAff\n9cAbyzc8xc32xBtPaa8oVIy3ek9eUht3TGU+3hhIt4RRAYl/CrsPu6PWtj2eM4D3myxoXTOIN9bR\nbWuPocyCE+tLWPw/t1LzwtVcev9afvLPG/joF2qpKj3pXccdW+lY53PHQobxSjI14ZUfisTjdY9z\nx3PmWPub8Ja2tFc3cuPbbX0OEevcRXhjP20R4DTceT2xlYPclLrBG9fqXqMZ7/OOQiDgcMfX32TG\n9z7MsB9sIBiKxL6v9lhb9xw9YNJfxT7kmb93En5+3K/JK1253P1NTbFxnNC+YzkLC4exfPl6lUcS\nyUDqcErG2LJlK9HoIAKBYNuNRS5QdTUEj5Wz70/j2TFjOFc9upjPb/gRBQV13Auxzl9jGyfphBzH\n64unMvjGLfTqf4QV029g7H3vdlhc7amkZABr177DwYMHqaio8DscEbEopS4ZY/HiLRQXD/U7DOmi\nVq+Gu8fnc8Mt8Hcfr6BizF6+sP4H3P7dtzN6fGZ7iETgLx+BH//q7O3GPTaVRa/cwem6FAU/O4FA\nIEhR0e388Y+zaGzsgn81iHRiesIpGeHkyZPs2NHAgAF9/Q7loq1b56UXjWl9xaDkskh2mj35fft8\nra0AZKfd7TbuV/vcdokk97iJHzZeyrgQr9RRAO9P07L41yxgUHw7ivebJBcv9doTLz1ciJcOz8Ur\ndRS0zu2WRSogMWXspqDziZUHAm/lIJf76K4Rb8Wi+Hk3bYSv/1UP3njnJA4N5GYHmPAP67jurx2M\nG+tpvPRxi3X+E9Y9BPFKFjVZ+9xU9ylru9GKqQUvld2El17Psu6tFu+zd/tJZVYc2Xipffsx5Wm8\nlH4+XhmqpDl382bHVkZ6DqhtgMe/RGL5qnj78rxDDL9zHQun38mdn3nTu58AXqmqPd59Tviigfik\n/akvxm7y1CnvulnWvzDJ/y+4c3vWr4cRI2g3JSUD2LPnUl57bTZ/8ReTMOZsz3VFpKPoCadkhI0b\nt2DMUP3jIO2mpSnIgv8ZzagRWbz+zkmysgxf+hLs2BXle//p0J1+1O68E373u9gfG9/5AfzH/7be\n9pbPz2DNm9dwYn9J640yXL9+17ByZYRVq9a23VhEOoQ6nOI7x3FYuHATJSWpZqSInJ9wQ4ilP72Z\nJ4b8I/vfuppPP5jPI5+FzesdfvpT6K5D+x56CH7/y9jTxX/+Afzkl6nbFZbWce0n3mXuMxM7NsB2\nZIyhsvIOJk9ewfHjx/0OR0QA42Rw4TVjjJPJ8Un72Lt3L7/4RTUDBz7odygXbO3a1DNz7dWD7Nnj\nqWapZ2UlphxTrSKUnZ2YJnfbB4Ox99z2qVLqbho9EIAJd8UPzAX6xIMN4c1ctmem26la96lgEd6f\nq6V4KfVSwF1eMYSX3s6yzhEkcca6m6Z2H6gZwO0U2isABfDSymG8NLWJ7W+uy2bFC9ez5Ee30u/G\nXdz4rdn0GbsvcbLMMbw0dZZ1DofEWeXutj0Lvdna32K9785YP4k3nCBktYlY93jS2g+xNDzxz8M9\n1n4M4Abe09qfhZfmz8X7fIy1vxHv+2rP4s+Fp5+Gz30Orrsutj579qmka56EcGOI39z5Ne7/lz9R\ndcWu2Ix5N9W/nTNpdI4AG+Pbu2Jf3nzJoaEhtl1f76XOGxrAHVbZ3OytOhQOe0Xq2zO1DrB/fw1D\nh27hL//yg8qeiFwkYwyO41zw/0h6wim+W758A6HQZX6HIZ3U8QPZPPaxIdw6/FIOLKni49Of4oFX\nnqXP6NgajepnJHr0UXjpJZgxw/sjJVkoL8xtX57OnF907mLwffqMYN06WL9+g9+hiHR76nCKrxoa\nGli6dDe9e2v9Yzk/tQdz+dpHL2XQ8Gx+Pmsbi5vWMPDbz1E+6qDfoWW8j3wEiovP3mbk/SuIhLPY\nMHdUxwSVBsYYeve+lSlTlmoFIhGfaZa6+CYajTJ58izgSrKyWnnUkoHWxuch2LNuk4td29v2zHS7\nvZvuTrUvuSC7mw4Phbxt+3yhkFc0PifHO9Zte9f9JnE2s/tAuRdeWrkUL9VdjDdr3C6y7qa660ko\nHH4mHRy12pTipY+z8FL02dZ+By8N7MZXiDdL3d0HUAfkQePRfL7/uWH8bOoujkZj+dzRo+E//gOu\nGgzE07lE8FLwbuq6BW/mtYOXXs8nNiPdvQd7Fro7ROA03p/o7r4GvKEALXip82ZrO2odZ997CO83\ncIN1fffcvfBmtJ+wPos8vM/7ON6M9CK8lH/UOo89RMAtuA/e97cU72fA+sxMxOGOb7/JtP/7EYY/\nU0OWE//g8vG+Pylmxt/3l4bX/xA7YVYW1MaHHCT/f5FKTU2shBPAqHbq5xYU9OLo0aG8884Sxo+/\npX1OKiLnTU84xTeLFi1l9eoQffuO9jsU6QQaj+Ux75/u4dcjvsaW3c0cjZ7gskvhz8/D0qUwcaLS\n5xfDcTgz9tI18LptlA87yLJXbvInqHZSWTmGOXO2c+zYMb9DEem21OEUXxw+fJi33tpE//7jNJhf\nzqqpNod3/208vxn9dRqP5/PI0p/yi9c38NsnYc1y+OhHWn9iJuemrg4+9hfwF5/0njC6xn11GtV/\nup2Gk/mpD+4EQqEcQqHRzJmz2O9QRLotzVKXDheNRnn66VfZv/9KKioyuxSSuya6y04L2kXTWyvO\nnpxGTF7jHBLT5fb7qYq2Z2cnznq3Z57b7cd/PH5RN40dxEv95uIV8a7DS4H3wkuTF+OlunvipW3d\nr014afaipG03lZuPlzIOW7HYKfowsbQweDPa47Oum+tDPP+NUZx48V6G3r2Jm/55Fr1GtvKEyr1m\nHd6f0c0kzmSHWJo7bB3nLjDUaLUFL9VuF3Nvtva71zPW+Vqs+3Ws4+wi9RES0+tu2t3gpaajVlv3\nfOV4QwXy8WagZ5M4697+fruz13Pwhkq4sRZb5zgN2w/D2LFw7Bj88zfh378Tfy8+G33Gt+7H4DDh\n66/HPqs91vs749v7rH1bYptTf+OcmaVeWwun47E2Nnqz10+f9vZHIt7s9Wj8c7jiCtpFNBph164X\n+dKXxlFZWdn2ASKSQLPUpdNZv34DW7fmZHxnU/zRcjqLP/7jVVxTOpCHf7mcsn/6X+771Z/pNUTp\n0HQZPBheeCH2h8v3vg8vvZL4/s1fnEXNtKs5trMs9Qk6gUAgSH7+tUyfrqecIn5Qh1M6VEtLC1On\nLqe8/Aa/Q5EMEwkHmPKfo7ihZDif/n+rWNe0hYICOBWobftguWgTJsAPfxjb/uznYcNG7738knqu\n+8x85v7vvf4E107Ky4eyYUMzu3fv9jsUkW5Hs9SlQ61cuYbjxysZNChzn5S4afTklHnyPnsGelZW\n6v12et2ehR4IeDUQ7bS4e1wolJgid9va6fWJHzben4z5eDOQ8wC3ypT7f3gvElPa7izjoXizlbOt\nNqXW/gBemjfX2lce347ipY+jeOutG7yZ1dlWfPas7UKIFhtq/jiap741jJ8e+DNRxyEnB/72i/Ct\nr0FvuyC8e50jeE7hzfyuJzGNX2/td7n3YqfRm/FmtNuzzSNW+yarfb11nLsufAOJa6nbYyHDVnt3\nf5a1P986t3u9kBVTNt5nX4yXxg4Cfa39bkUou3h+Ad6wBXd2uz30INuL6ctfhiVL4Lnn4N9/AM8+\n7Z1jzFfeZcVtN7B7/SD6X7ojtj8Pb5iFm8K3CupPesww/VexF8n/76Ry+rT3sx4Op25zMYwxFBaO\nYdasZXz2s/3b/wIi0io94ZQOEw6HmT59DRUVY/0ORTKA48CWNy7jmav+gVW/uZa/+/1iBg9x+Pyj\nsLkGfvz/oHdvv6PsXoyBJ56Axx+HJ59MfC+U18Jt33qbOT+d1KmLwZeVDWbTphY95RTpYHrCKR2m\npmYDdXV9KSvr0XZj6dL2Vfdn7rfvpfFYPrf/11sMvW8DxsRqnOaC99RQOlxREfzrv8ZfNCe+d/kD\nq1jy81vYMGcUI+5c875jOwNjDAUFo5k3byWf/rSecop0FHU4pUNEo1FmzVpDaeldfoeSUmtp9ORC\n1cFgYlrQLt6eqsC7PdvcLuaenZ2YSofEWeqBQKyAu7vfPcfdHzHejONyvJnNhXj7S/FmmLtPCIMk\nrKedMMvZ7dxVklic3X2KVYKXC3HTulHr/WwSi7YfjW/n4KVZg8BpWDa7F9/82xIqay/lGz9YzhV/\nuYzAUQf2Aj3jpw9Y8dvF1hvxUsb2jHEHbwZ3I15KugFvdrqbcj+Cl45vsa7ThLdWeAteofgIiWl0\nNx3upnuj1vWOt7I/itdxO433GTbjzZLPtmJxFZC4fnqTtd3ParM/vt0TL2Ue/7yB2PfErUrgDhUo\nJnE4hvtz1IQ33KLI2gaoAIPDHd+fxlt/9yDD768hqzDi/Vy5P0d2sf6ecPfnY9+E6b9xUi6OkFwV\nzZ2x7j5FXb++/ddYLysbQk3NEg4cOECfPn3aPkBELppS6tIhtm3bxuHDxRQVlbfdWLqcFe/mc9eV\n/bnuvhPM2rmV90qmMuqRpQSCnTg3200NvH0rJYMPs+KFzjvxzxhDTs5VLFiw0u9QRLoNdTilQ7z7\n7jqKitqpoJ50Gof3hrjrqj6MuaWRmZt3Y4IOn30Ipr6pVYE6k5O1MGWK93rcV6fy3pN3cLo2r/WD\nMlxFxSWsXHmE48ePt91YRC5amyl1Y8xE4L+JJUyedBzn+yna/BS4l1gS67OO46yI738auA845DjO\nKKt9CfACMBDYAfyF4zgnks8rXcPRo0fZtKmeAQMG+h1KSmvXpk6jJ6+P7u6zi7On2m+n2u110O2Z\n6XYBd3ttdDvlPnFS/OJ5eAXZe+OlZAvwZpL3wEuH5+HNIHffD1r77BnmBi/dGsRLPedbx7rvgZey\nPWTOnjYAACAASURBVGXFZHccw7HzRSOGNc+MZf7/mcDm078gK8vhs4/At74FQ4ZY7ZtILHQOsdR1\ng3W+Q9a2PSO8ydp2f3s0W/fQgJdCDltf3ZTvcbzUucFLqTfiDQtoJjFN7t5rk9XW1WDFbc+ob7Hu\n0YHp07xZ227a2Bi46+7YyWfOiO10HO/9uz9svN/WhXizzkN4379ivO9ZjnUPuXgpc/d/wXrrXo7i\npegDJBaqj0J9PYyeALt2wbvvwvVXQvn4Qwy/fx2LXhzHHV+Z5sXlxuSm4vdx5nt292OGmb+I3ZBd\nkcF9bX8FrwA8xNLqECsM316F4AOBIFlZI1myZA13331b+5xURFp11iecxpgg8DNgInA58EljzIik\nNpOAYY7jDAf+Gvil9fYz8WOTfQuY4TjOJcCs+GvpolasqCEra4SWsOwmds4eyu/GfIm1v7uGj77+\ne16acZLNK+DXv07qbEqnUFAADzwQ6+x95jOxDijALf80k9XPj+Xknl5nP0EG6937ct59dzsNyYvI\ni0i7ayulfh2wxXGcHY7jhIHngQ8ltbkf+B2A4zjVQE9jTJ/46wV4f4unPCb+9cMXFr5kunA4zKJF\n2ygvv9TvUCSNFi+G3/6skJcffIhpn/sIN/7LbD41/wkqx+5l7FgYOMDvCOVifO97MGoUbN4MX/92\nbF9hn1OMeXQR839yt7/BXYRQKIdIZBirV9f4HYpIl9dWh7MfYBcr24OXfDmfNskqHMdx55sexCtR\nLF3Mjh07OH26guzs/LYbS6ezcCHcPT7A9dfDY38fodc12/ir9T/mso+u1RjNLiQ3F559NjbU41dP\nwptvxfZf9zfz2VU9lP1r2vqVn7nKy69g3rz1RCKRthuLyAVrawznuU4hTf6n5ZynnjqO4xhjWm3/\n+OOPn9keN24c48aNO9dTSwZYvHgjBQUj/Q7jDLv8Uaqxmsllj9wxlfb4zLZKHtljOLOzvf12eaNg\nMPaPuH3unBwYPzF+8iJiqwBBbAyeOzejDG+sXBHeOMoeeGMGy/HGKbpfe+ONv8zGG+tn8P5vDVr7\ni61r2uKfzbxV8G//BrNnA0TJC2Xxxc+3MObL75B1ktjYyWy8ckB5eKvzOHhjKx28UkduLiQbb4zk\nUbwxhafxxmfaK/ZE8MZOHsUbc1mPN3bSXYa9DnBXygxZ57b3N3n3iSFxlaAGqw0wc5pDNH6NSMQb\nc+k4nNnf0pI4QcrEx30GAl4bgFdfiR0cjX829hjhN/+cWFLI/TmacJfxyjz1IrGkkbsCUYhYaSuA\nw/Gv/a1772XdY1/rHEG8n59dcOUI+N6/wTe+BQvegfvuhOwBzdz8rZnM/ckkPvH0b2Ix2o8xChNf\nT/j7+E1sgDdei92v/f9fKslF5teujX1tr7GceXk9OHSojK1bt3LJJZe0z0lFuoC5c+cyd+7cdjtf\nWx3OvcR+Nbn6E3uCebY2VfF9Z3PQGNPHcZwDxphKvGkB72N3OKVzOXXqFOvXH6OqSvnUruafvpzH\nwpWN5AVD/M3D2fzTv9dTWkrsN8rhto6Wzuor/wA33Ay3WCP5r/z0Upb+6ma2zh7BsPHr/QvuIhQV\nXcG8eUvU4RSxJD/k+853vnNR52srpb4UGG6MGWSMyQY+DryW1OY14CEAY8wNwAkrXd6a14CH49sP\nA5PPK2rJeLt37+bpp98gFBpFIKBlY7qK2l09mPyxT3HjgQf40ifK2Xs4zI/+N97ZlC4vGIRbbknc\nF8iKMu4705jzg3uJtnTOSnu9elWxfXuYgwfb+qdLRC6UcdpYFNcYcy9eWaSnHMf5T2PMFwAcx3ki\n3sadyV4PPOI4zvL4/ueA24kV7jgE/F/HcZ6Jl0V6ERjAWcoiGWOctuKTzNLS0sK8ee8xa9ZuevS4\nlV69qvwO6Yzk8kepUueQOk1uf83OTt3WTQvm5CSWOnK37dWFcnJgwofiB9ilbAri2/l46cwCvFWE\niqztnlb7ALF0O8RSoj2s9hBLq7rbuXip5iYSSx65qdf4Z7NzJwysgpbaLBb/z60s+d9bGPPYIq7/\n/FxCPVu887np2TBeGj0bL1Vbi5e6P42XW2nAS7W7cdip8Hrr3Kes/Xut/c145Y3CeKWKHLynrW4q\n/lTScW5MjdZ2gDMp+Leneb9/otHENHnyPsfxfk4ikcR0uTs80C51ZG/D+0sDGeOdw06vJw/1cM9h\nr0414V7jrTLVC68skvuzkw8Mi28X4pXJKra2i/B+Novwyi/lkTiIKj6U4Pk7P8+IB1dx9UcWezmu\nQ8RKIwFsB9y5Obu87TdedXAnidfXw6n497IpPmyhocErkdTU5H2W7VkiCWDv3jVcf/0RJk26o/1O\nKtKFGGNwHOeCR+e3WYfTcZxpwLSkfU8kvX6slWM/2cr+Y8CEcw9TOoPm5mZeeGEaNTVF9O//EbKy\nsts+SDLSO+/E1tNetAhm/WIYq7/7YcpHHuThJT+j5+Dj3phIEWKd4zu+O5WXP/EwI+5ZSU7yIuyd\nQO/el7B48XLuuKORvLzOW9BeJFN1zvyHZJyWlhaee24qGzeWM3jwnepsdlJr18J9H4Bbb41NCDLh\nEC/8y1Xc9ZMpPPjCH2KdTRHLihWwbBn0uXovA27byuInOmcR9VAoh3B4MOvXb/Q7FJEuqc2Uup+U\nUu883nxzNgsXBhg4cJzfoSRYty5xBmyqlYGM8VLjyalLO2Xuvm/vs1cLctOZWVle2t1OcwYCcPcH\n48EU46Wv3bR4EV7aOwcvhdkLb3WhfnjpUbvSVA5emrMnibPTIXG1mXq8lHs9Z2Yl//wp+PuvxtK4\nedlBbgvexNf/McId36rm/7N33vFRVen/f9+Z9F4ICakg0osCCgqIdCnSREB0BV3Z1XXd3rvbvvtz\nV911XXVdFVSsCAgKoQsCUgRsEKkCgYQQQnrPZGZ+f9w5OWfGCUMgMCnn/XrxumfunHPnkNx7c+Z+\nnufzWENcOqaQiUuR+kiB8tlqhnmtMu9SpLxeipS4K5BPSwOVcWpfIYFXK+0ypU8hMnu8AimNlyh9\n1Oxy139lQ6bTTQ4XtxqHw71tcx1DbEV/MKV1VUb35qyjZqyrErxaaUh1PxB4O2/BPL9URwS1kpVA\nDf2YMMWQMrn4fUQizejiMIObwN0FoQsyYz0UeS5FyeOs3w6TpkK3bvDpTqjNj+Hlod/jm5n/IjKx\n3Py5n3SNO4GsCPUlcNTVPgKrXzd/EDU1UOZyCxAG81VVNEjuNpuU1+vrZWhDv4Y6dpdHeXkBAQGb\n+P735+hCFRqNB5crqesnnJrLZvfufWzbVkpa2i3+normMhg1EgKsBrdGDuC58VN55/DnjP39DqxB\n2p9Q450Rt5iLzUOH4LEnIDqjhP737WX7k63TDD4yMoFz54LIzfVltKLRaJqKXnBqLhmHw8GWLTt4\n992TpKZO0NnorZiKs5Ec/ctc/q/Twyx8vZL5y94lMqXM90BNuyYkBJ53RfT/39/hyFG4+eebObap\nFwWHW2c9j6CgXuzd2zrtnTSaloyW1DWXRH5+PitWbOXkyUjS0lpWzOaBA7iZZKtG7d4kdc+2KpN7\nZqmrcmZgoHsGutjvafY+dqqSja4atYsMYCFVxiMztYORkqehjEtAfk0MRsraFqREH4DphgtSUg6U\n43bvhpQukJoKjiqDzxYNYfujY7nuW3sY+sMPCAyzmZKpmIuBNGoX8n8ZMhvdgZTRS5W+dmT2eIUy\n71pMGVyMFcblNmWcU+kr5PcqpDm7KsXbcDd+d81lwxqnmzQOpiTbWMa4mnle5yXnxeFwz5AG90xy\nVU5X2w6Hh/G7IT9TjFXPU7FPdT5QCxWoWepqOyBAno/itTiO2C+242cY0MnVMRR5LnZGnkcdkedR\nBLIQQRgy/CEJsMI3vw2LXoHRo2HjO7DvxWGc2NSNWUteNjPSAc4CIjyyAjjuah8Cssxm5mKZsV5R\nYW5VSb2yUoY21NXJ35nN1nyyut1uIy/vDX71q9k6eUijUdCSuuaqc/z4CZ57bj2FhTfQpcuEFrXY\n1DROQQEseAhuGgE//jHkf5rMa7c+zMG3r2Pulv9x6/+tMxebGk0T+fv/QXy8mTx07DgM+NYuio51\n4OSHXX0PbmFYrYHY7V04dOiIv6ei0bQp9IJT0ySys7NZuPAjoqIm0aFDF39PR3MR2O3wzH+he194\naZHrye3Jrrx1231cv2A3d2/5Hwl9Gi32pdH4pEMHWLrUjOXs1hWsQXZufXQdm387Gaej9SXfxMb2\n4KOPDvl7GhpNm8KnD6dGIygsLOTVV7cSGzuBiIiWV1omyyXLedZDF9KiYXiXzj2zfkV/tfa5mnUu\n2mo9dFVeHzfRkNJzR0BUy4tAZqF3QEqXIns8HJldHo+sZR6MNHX3NHBXs4hFBnkiDXJ3fSiMGGH6\naQIMHxDG6Lx7GNy7hFGrniKsY6U0SrciM5RrcDdFF7K2MFIvQtYyV43Xa5C10e3IrHKLMrYCeecp\nBPKU/z+Y8riQtMuU49Uqx6uXfTa953STwBvM2auk5CokbjUDvb7eXSL3lMtFf1WCF3irma5K9KrU\nrs7J8xiqZC7eE+ei2jdAuVNbLO7nd2NhImr2uhgvHBNWve1saI+basgs9VrkeVmBLDqchnQiSMTd\nTcEV7jFymGtfoDmux/j97Hl2OFm7BtD37k/k+QRmgWSH0t91Hk+632DNy42HUTmdUl6/kjXWo6IS\nyc62kJeXR6dOnXwP0Gg0PtELTs1FUV1dzeLF67BYhhIZmeB7gKZFEBBgLjhPZRvc2/VmMnKGMvH1\nd8kY9ZW/p6Zp4xgGjHo8k/fumkuPGV8Q2PCtpXUQENCTzz47rBecGk0zoRecmq9RUVFBbm4uBQXF\n1NbWExUVysGDpykq6kFqauuLyWrPOJ0wp3df4m0TGHTjQW5Z+5QZp6lz8TRXgdRh2XQakMO+54Zx\n04wP/T2dJtGxYzc+/ngfY8faCFSzsTQazSWhs9Q1DZSWlvLhh3vYu/cMDkcqhhGP1RpIfX0VVquV\n5OTrW5wZclaWe+1p+LrMqGapezN498w8VyVzVUoH87Vq5N4gS043ZCZ5LDLrNxQpmXfEvU61kMzF\nuCCkpB6h7A9GytcJyrEtyv5gqA92/f/sQB2U50ax/sfTKTkex8SXlpE86LTZtxKZZVyDex10sT9U\n2V+JlMyF/H4WSQUyS92m9K1HZpXnK/83tU8Z0gzcqYwT9dXL5TE2vOtk3G3mLzNzldOrHO6Zhe6Z\nQW63e6+Dbre7Z5I3Jq97Zr2r4zzldYHnLczbe4bhbtwO7q89jeE9jeDFPlVqV89jtcgBmOetSMBW\nw0Fuu8uQ7ghJyNrrMcja64mYBQjAlOJFGEaUaxsJBJg/i6NHIaG2A6+N/g4Ldj5JmMX1iz2JdCrI\nxcxUBzgN7DOb6141fziVldIMvrpaGsJXV5tG8WD+3sXvtb6++Wqsnzy5gXnz0ujZs2fzHFCjacXo\nLHVNs3DgwJf8618r2bcvgU6d5pKePpq0tOtITu5NevoNpKQMaHGLTY1k36fQvz9s2GAuYj5beCOL\nbv4+iQPOcN/ep0kectrfU9S0I8rKzPKoQ4ZAffR5es36nB2Pj/b3tJpMVFQPdu7UpS41muZALzjb\nOU6nk23bdvHaa18SEzONlJTrsFq1fNRaqK+Hvz4BN42Cgwfhsb8E8ta4b/HFosHMzXyB4X/YqCsF\naa46kZEQFQWlpfCr38OwX23iy6XXU3Sy5SUbXojY2DSOHSunpKTEd2eNRnNBtKTeztmyZQdr1hSQ\nnj6BwMBg3wNaAAcOeM/S9WXqrppkqzKiWvtcNXsPDnbvL7ai75jZSjZ6KDKTPAopH4cj5ccApOwY\ni5TXRbZuR2WcFVn3Gkx5E8zsdZeM+NUJmPcA7Nhlvp5zUyduODSfET/9iBt+8RGWAIc8dpVybDtS\nilcr+BlI8/V6pHxux5TNQUrdBcjM9WqP94UJuyqXVyufWYGU2muR8rrIOn/X6SaRC1RDdru98Xrn\nqoG6mp0O7pnpqkTudLrv95Z57llv3dv7AnW/+l5jsri321xjtdVVtwXVEF6V5a1W78bv6nUhwkGC\nguQ5HRSkyOuzDDM7HUwZXZyDycjzuBvQy9VWQ0NC4cgx6Dvc/J3s3AnOtSM5uyeVGS++Zp6X4sFh\nETJE4wggivy4aq1vfNFJuescKSszpXQwpXXRrqnxXmO9OaT1U6d2M2mSwdChgy//YBpNK0ZL6ppL\n5rPP9rN27RkyMia2msWmxsRuh0nTzcVmp44Gv+ozkdvt0/jm6hcY/L1t5mJTo/Ej3a+Fn/7UbD/y\nCAx4cBt5n6WS83GGfyfWROLju7Njx1H0ww+N5vLQC852Sl5eHu+88zkpKRN1paBWiNUKTz0Otw2K\n43v1P2barErufvd54q4p9D1Yo7lK/OY3ZgnVfftgeaadW36+ns1/nuT1iW5LJTw8luLicHJzc313\n1mg0jaJtkdohNTU1vPnmZqKiRhIcHO57QAtAldEbq4nuS1JXa00HB7tn7ApJ0TCkmbsqtYtjjJ1p\nyNrnnZAyejJSjg5GZqZnILPRI5AZvRFIyVyYbluQ0nQw8nNU21OHebzyM5GUPz+TuxyRTP7wNRL6\n5kuz9DqkmbqadS7WoiXIrPI6ZDZ6De6yd63SFhI4yj41k7xKaYvPrsbdPF70r5L/z43rnA2Zxg2Z\n32Xu5uye5u2iLV7X1blL0qp87i1L3ZtErvZRJXXRT7zv8PLgWJXLGzu22lfNaheo8rm3cZ5Z6up+\n9fxvzKlB9FFdF8TPtaZGyuvqtbDmbWeDLD/uLkOGWFRhnu9ghlWImvbiPO5Gw3kUHgn/+ReczoHZ\ns8AS/Cl7Fw3n8Ma+9JzgcmrPRRYwsCPPGdfPeuwCg40vOht+TuL/Il6D+89V5cCB5pHVAwO78dln\nR0hNTfXdWaPReEU/4WyHbNz4EcXF1xAbq2+erQF1ceV0wpdvXMfLA75PpxtzuHf3M+ZiU6NpoUyb\nCo887PqiaHUy6rFMPvzTBOx1Vt+DWwgJCdeyd+8p6tSSVhqNpknoBWc74/Tp0+zYUUBy8g3+norm\nIjhzFsaNgz/9CaoKwlkx+x52/HU0szJfZvijG7EG6lhNTeui85hjxF5TyKev3OTvqVw0gYHB2Gwp\nHD9+3N9T0WhaLXrB2Y6oq6tj+fLtREcPx2rV0RQtncyNcN0o2LwZ/vufAJ7t+xAxXYq4b9/TJA3S\n8WSa1suoP2ay86lR1JSG+O7cQoiI6M7HHx/x9zQ0mlaLXnW0IzIzt1BQkE56euuQ0g8ccK8SpNof\nebM6UiuuqBWFRFu1NAoIkHFr6v6gIPk5t81QbI8iXdtuQJyrHYYZxwlmrKSwhYlX2jHIGE7V6igE\nGQcnvva5PqOuDn79B3jiP+brgckJzDZmcdcLS0mdmG3GXdZhXr0ibrQaGcNpU+YrYi/zkPGchcpn\nnkXGatYjY0hrkTF7pcpxxL4y5fOKkHF8qs2RXbbXr3I2xD+qMZJ1ZVDr+nzVckiNvRSxhk6nezyn\nZxUgb/09Yy49rZC8xWd6xoM2ZnsktuIcVedzsUkxjcVxCsS5qFY0UmM1VTsndb9hyPO+vl5eI8I+\nKiBA/pzUdl2dvBbq6mQ1olWvOLl9ruvghcjzoRvSHkucD9XI68KJjFuOp8Emq8NN+XSdcpBdL4xk\n5G/WyhjOYOS5Kf46BcLYb5mfvfEFp9efg/g/i604p8C8j8Dlx3LGxqZx+PBWSkpKiImJ8T1Ao9G4\noRecbRSn00lOTg7Z2bnk5BRTVVXL4cPQpcsYf09N44Of/w6eetZcJEyLHc78YZ247R8vERxd63uw\nRtOCcTjg5TfgqRcgc/F6lo76IQPm7SLaaPnG6haLBau1F/v2HWDMmOH+no5G0+rQC842yLFjx1i1\nag8FBSFYLJ0JD++DYVjJyEjAYmk9gfrtlV/8EDasjOS2ypkseOJTek/bLjN3NZpWjGHAi6/CF1/A\nv14uZ+pDu9j21/Hc/tsl/p7aRdGxY28++ugdhg+/keBg7V2s0TQFXWmoDVFbW8v773/Avn3VxMUN\nJTo6yfegFkhWlrlV5XLP6ipqFRVVPgdTIlf3CSskz4oqanUh0WfsVENaHYVgyoBgVgYCU6oWP1a1\nolAiUmqPRMroIK2GIpFSdzJS4lYqiZYdiSLzodnU11uY8to7RHcuNuVLITOGIRefZUgJvAIpaQYD\nxa62kBxrMKVxMG1thI2RaoukWh1V414xyKmMBTinHK9Ueb8ENqwyX6iWRjablI9tNintqtK4kEQ9\n7YzE+2qVIE97I0/7I3CXw1VpXZX2vcnrnlK8N0ldfc+bLO7ZV7zu1+/rxwAp+14Ib/Kx2latkNT3\nAwLka9UuTJzzhuFuF6ZaKIlrJCRE2oWFhMB4Ia93Abq6PkjYIsUgr5uByHM+EnB5ct54o/k5+7YE\nsvXOn3Hnay+TdN0Z81wTeTmnXduDwH5X+zANtlvvL5EViCoqzH9gVh8Sknptrfu51qcPl0129hZm\nzoxh4MDrL/9gGk0rQlca0gBQWlrKCy+8y+efx9K584xWu9hsb6gLk8PL+vLKiO+RPuIr7v7wBXOx\nqdG0MQYNggXzzS8QP3vUxtDfbWTzo5NbjRl8QsL1rFnzBdWirqZGo7ko9IKzDVBaWsrChaspKrqO\ntLSbMLxlH2haFE4nPPs8TJoG1aWBZC6YyZZfTWDmW68y9GebsVhbyV9fjeYS+OsfICYG1m+E7MQ9\nVORHcnxDD39P66IIC4uhpqY727fv8fdUNJpWhZbUWznV1dW88MIKSkquJympl7+nc8kISVGV0a1W\nd7lQ3a/K50IO9CazBwW5y4VqRRVxvHFTDFnNJx4zmxxMuVBIgyLauQNSUgc5LhaZaRuJ/CpnQWbp\nBpn9iothwSOw/F1z98OdpjN5QgBjnnqP4EiXLq7mUAQgpfFapJRdj5TAa5HSeDUNVVoaMojLkBnm\nxUiZvxxZgagGmbGuSuoGZja7Mq9Ni5yMGWdOasM6Z4OE6XCY2c3gLoE7HN4zzD3bAm+Supq97imH\nqxnmqozueftwOLx/jqekLvBsNyaJX21UCV7Nzlb3qSEo6nUktmrYiTepXQ1NCQqSGethYVJqnzzH\ngDTXh6a4tl0AYYSRBHR3tdWQkh7w9JOw8FX4738grqgXH/5qAt/c/BSWfNcvRZznJ4FDrvZnmLI6\nQB6sftv8BZWXS0m9rIyG6lV1de5t8bu/XGm9vr6O3Nwl/PCHt5GQkOB7gEbTBtCSejvGbrezbNkG\nzp/v1qoXm+2JHbvg+pvMxWZ4iJX5kTP47hMnmLRwqVxsajTtgO98G/Z+BEMGw7VTDhLWoZL9bw30\n97QuioCAIIKDbyQz8yP0QxGN5uLQC85WzLZtu8nKCiUlZZC/p6K5CD7aAyPGwanTcG1sHL/r8g2e\n3LuN3nM/9/fUNJqrjvpk1TBg5D8y2f7/xlFXFXjhgS2ExMTuHDoER44c9fdUNJpWgZbUrzJ2u52s\nrIMUFJQQGGilT5/uxMfH+x7oQXZ2Ns8/v4OUlDsIDGyd9hyqjK5KfaLtmYGuyn5qhrkqpYutkAVD\nQtwz0yff7lIDYpDy3jXIrPIQpBwYgpTMxY+4I2Z2OpjZ5bFKX9WwWpy2YTRI8HYLjLw5mNCj/fnB\nXUnc9sQaAkLqZV8DKYvblOOVIbPOg5DyfjnScL0G94x1cRwhS1Yi5fIypESfo/StRMroDqV/Hqxf\nZk6ysUxzVS4X+1UJ3DPDXK0Nr/YX+xozZFdlb1Vqv1A2emPHbuzWcrkG4S0BtWiCYXw9e72x68wz\nXEUtlCCy1NX94eEwdbrroCLUpDPS+L078hrpgenmAOa1J2TtOhpCPFbOn0tC97MM/elmyHa9b0NK\n6keBY0rbtdZb/ZqTMpcZfWUlDdnr1dUyxKOuTmavi/P1cqX18vICHI51/OAHswkSPxSNpo1yuZK6\n9uG8ihQWFrJ48TrOnetAUFAqdns169atZeTINEaPHobVenEembW1tSxZso3Y2LGtdrHZ3nA64dP/\nDGPmyRFMePF9et75voyj1Gg0AIz48zoWD/0u183/mPCGAOWWS2RkAtnZ6eze/Qm33NJ6asNrNP5A\nS+pXibKyMhYuXENl5U107jye5OTepKUNIjV1Nps21fD225nY7Re3Atm8eSelpV219VEroboolHdn\n3UvW69dz3+7n6XnnRZguajTtjKIieObtInrM/IQd/2g9FdE6dbqRDRuOUFysbcw0mguhJfWrgMPh\n4KWXlpOX15ukpN5fe9/pdHLy5GaGDXNy++0XvtEePXqMhQv3kJ5+J1Zr64h1UlGlPlXSU42phRyu\nZqar2eiqpKdK6uJ9q1Vmo4eEyGOMn2NIc/ZEpAQYgSmVgyn/iazyKGTmeZhrG44px4OpD4h2IA2y\n+7lz8KM/whN/AntJGu/NvZvu07O49bE1BAS6vlTUIOuqC+naBuS72lXIDPNqpDl8Pe51y0WfImQN\n81pkrWuxrwqZpV6OlOiLkDJ6veyzaYXTrb62ar4utmKfzeYul6u1zNVx3rLHVXN4gfq+Kql7Sufi\nnFGle08jdk/5vC3I5ZeCCF9pzCRetAMCZDswUF47wcHuBRRUtwchtYeHm9uJsw1TVgez1vo1rnYE\n0iS+GzI0pTc4bTBkKOzZC0/+Pgjrf37BNzY9S9y1hWbYhzifVUn9BA2SOgdhzevmL7m0VGasl5dL\nGb26WoZvqE4Kvb9+S24yeXkH6NXrFLNnT7r8g2k0LRSdpd4K2L8/i+PHw7wuNsH8JWZk3Mr27RV8\n8knjCSRffJHFokW76djxtla52GwPfLgDrh8LbyyFe2fHs3zafMb+633G/HMVAcFaQ9dovGEY8Otf\nmu0//7uObvdvYusfb/PvpJpAYmJvPv20ipMnT/p7KhpNi0UvOK8w1dXVrFr1KYmJQy/Yz2Kx1/rZ\n+QAAIABJREFUkpw8hpUrP6eoqOhr73/yyee88cZ+kpKmEh4e5+UIGn9it8NfnoTRMyEvH3p3SGBi\n/TTu3fks3aZ96e/paTQtnmlTYdw4KC6Bd/N3cWZPOrkfp/ke2AKwWCzExg5l5cqdFx0apdG0N7Sk\nfoXZuXMPq1fXkZ4+7KL6nz17iNTUL7n//hkNFYOysg6yePEXpKTcTnBw+JWc7hXhwAF3+U7IdGpm\nutjnKek1ZvAuJL2AANlHSHuq5Dd2tmHWLQdTwhZ10lORmeddcDdnF1J3NDLDVnw1C0bK71Yg0Fxs\nTp4H69aZuyd3GMy3J6Yy8bn3CAxX9OIyZL3zMKQ5u5olXuBqVynvlyMz0K24Z6OL/iW4Z7gLKV18\nXiFSOs/HrU76+nXmNeZwSMnRZnOXz8V+NUvdmzl7Y5K6p+ytyuieGeae5uxq25ss7ymht1fZvKl4\nc4mwWt2titTwFm9Z6iEh7uErYBrEi/a47xoyM707MowlHVNWB9Mw3uUMcfAr6D/I/J2/+ete1G8e\nwd1rnsfIdfWtw5TYwcxcP+lqZ2HWXAfWv+KkxFWgoKJCZqzX1pqyumiDKa2Lc7E5pPWTJzcybVos\nQ4ZoqzpN20NL6i0Yu93O1q2HSEi4+L+ASUk9OXo0iIMHTR+Q4uJili7dQ6dOE1rlYrM9YLXCTTdB\nbJSV70TP5S9/himLlhMYWu97sEajaaBXL/j+980vDtmhB6kpDeVYZjOsBK8SSUk3sXZtFuVilavR\naBrQtkhXkGPHjlFWlkBsbHSTxiUk3Mz772cSGRnBqlU7sViGEBratGNorh6Oegu3VI4jJOpa5i9f\nSadBOb4HaTQar/zhDzB7Ngy5Hr7ql8kHP72drssOYQlw+B7sZ0JCInA4+vHBB7uYNm2cv6ej0bQo\ntKR+BXnhheUUFQ0mNjbVd2cPTp3ajsNxmtDQQSQmdvc9oAWSlWVuLRb3LHRPSV2VxS0Wd6N2VWpX\ns2TVLHVPSW/sDENK5wlIU/cUZJZsJO7Z5t4y08UxQGaJxyn7q6CyIoL37pmLxWJnyqK3COtQJT8P\n3A3Zy5B12sE9a1y8X6/sq1L6iXat0v880ti9GpnJex5TVlePXSnnsW61000OF7Wma2vdjdpV2duz\n3rnN5p5prmaVq21vkrqKmu0uaMyc3W53z0zX0nnzoWaxqwUUvEntISH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ETOX114/xxhur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\n/euYNy+TadMmBFWVIhnD2Qk//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449P1dmo/HPbahsPez8lxum+apOLii1iy5HmuvfZyMjMzu+eiItKtdMtGpAPL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\nXSJ9XqmuAAAAAElFTkSuQmCC\n",
"text": [
- "<matplotlib.figure.Figure at 0x7fe0651aa490>"
+ "<matplotlib.figure.Figure at 0x7f57cb9f0150>"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, axes = plt.subplots(figsize=(11,7))\n",
"histogramRange = np.arange(0, 1, .005)\n",
"plt.hist(chisq, bins=histogramRange)\n",
"plt.hist(bgchisq, bins=histogramRange, alpha=0.4)\n",
"print"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Je3f7mYeaofAtmX/JLEwOhU8zdA5wGDihhyVh/iUHY/1czBtuvSHJdEPnAIfB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\nvdjCDGa94wAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7fe04ddc3790>"
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, axes = plt.subplots(figsize=(11,7))\n",
"histogramRange = np.arange(0, 0.3, .002)\n",
"plt.hist(ks, bins=histogramRange)\n",
"plt.hist(bgks, bins=histogramRange, alpha=0.4)\n",
"print"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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yniRprR2qqvuSHEryYpLru671JLk+yUeTnJPkQTPOYfqdyIlcfPnaJKvDDx+eYG0AmDUb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\nAEAvBE0AAHohaAIA0Iv/D382UsP4CSbiAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7fe04d9217d0>"
]
}
],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"q = np.arange(8.1, 200.05, 0.1)\n",
"len(q)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 16,
"text": [
"1920"
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
\ No newline at end of file
diff --git a/binDilemmaDemo.ipynb b/binDilemmaDemo.ipynb
index cb97820..81b4b1a 100644
--- a/binDilemmaDemo.ipynb
+++ b/binDilemmaDemo.ipynb
@@ -1,163 +1,260 @@
{
"metadata": {
"name": "",
- "signature": "sha256:081f96228ccfc58238ec3e8d324c8e8cd8adb40d27bdc09f38a88ea0f597e230"
+ "signature": "sha256:9ed1c02fa5fec38c392a108dda0d0220c35fefe5354568be75bfc77edfb54763"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
- "from os import listdir as ls\n",
- "from __future__ import division\n",
"from time import time\n",
- "import bisect\n",
"import numpy as np\n",
"import utilities.sampleFunctions as funcs\n",
"import utilities.minimizers as miniz\n",
"reload(funcs)\n",
- "\n",
- "funcs.randomGenerator.setSeed('seedOne')\n",
- "funcs.settings['simpleSortedOutput'] = True\n",
+ "reload(miniz)\n",
"\n",
"%matplotlib inline\n",
"from matplotlib import pyplot as plt"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
+ "funcs.randomGenerator.setSeed('seedOne')\n",
+ "funcs.settings['simpleSortedOutput'] = True\n",
+ "\n",
"nPulls = 400\n",
"nTrials = 1000\n",
"basePars = (0.00006, 10., 200., 110., 1.5, 50., 140.)\n",
"baseGuess = (140., -2., -0.1, 10.)\n",
"\n",
- "def fitTwoHistograms():\n",
+ "def fitTwoHistograms(percentile):\n",
" data = funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, (0,200), basePars)\n",
+ " percentieth = data[data > np.percentile(data, percentile)]\n",
"\n",
" # The histograms are filled with the same data, only different binning.\n",
- " binContentsOne, binEdgesOne = np.histogram(data, np.arange(3., 204., 10.))\n",
- " binContentsTwo, binEdgesTwo = np.histogram(data, np.arange(0., 201., 5.))\n",
+ " binContentsOne, binEdgesOne = np.histogram(percentieth, np.arange(3., 204., 10.))\n",
+ " binContentsTwo, binEdgesTwo = np.histogram(percentieth, np.arange(0., 201., 5.))\n",
" \n",
- " # The fit ranges are defined to be from \"the peak\" to \"the last non-zero bin\", blindly.\n",
+ " # The fit ranges are defined to be from the value of the 70th percentile data point\n",
+ " # to \"the last non-zero bin\", blindly.\n",
" fitBinsOne = np.flatnonzero(binContentsOne[binContentsOne.argmax():]) + binContentsOne.argmax()\n",
" fitBinsTwo = np.flatnonzero(binContentsTwo[binContentsTwo.argmax():]) + binContentsTwo.argmax()\n",
" \n",
" ### FITTING METHOD: Binned Maximum Likelihood ###\n",
" fitGuessOne = np.array([value * funcs.randomGenerator.normal(1., 0.1) for value in baseGuess])\n",
" fitGuessTwo = fitGuessOne.copy()\n",
"\n",
" def chiSqOne(pars):\n",
"# return funcs.chiSqSimple(binContentsOne, binEdgesOne, fitBinsOne, funcs.theKink, pars)\n",
" return -2. * funcs.theKink_BinnedLikelihood(binContentsOne, binEdgesOne, fitBinsOne, pars)\n",
" def chiSqTwo(pars):\n",
"# return funcs.chiSqSimple(binContentsTwo, binEdgesTwo, fitBinsTwo, funcs.theKink, pars)\n",
" return -2. * funcs.theKink_BinnedLikelihood(binContentsTwo, binEdgesTwo, fitBinsTwo, pars)\n",
"\n",
" fitOne = miniz.nelderMead(chiSqOne, fitGuessOne, xtol=0.01, ftol=0.05, disp=0)\n",
" fitTwo = miniz.nelderMead(chiSqTwo, fitGuessTwo, xtol=0.01, ftol=0.05, disp=0)\n",
" return (data, fitOne, fitTwo)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"totalTime = 0\n",
- "xKinkOne = []\n",
- "xKinkTwo = []\n",
- "for i in xrange(nTrials):\n",
- " timer = time()\n",
- " data, fitOne, fitTwo = fitTwoHistograms()\n",
- " totalTime += time() - timer\n",
- " \n",
- " if nTrials == 1:\n",
- " # What the heck is going on with this fit?!\n",
- " fig, axes = plt.subplots(figsize=(9,5), facecolor='#ffffff')\n",
- " plt.hist(data, bins=np.arange(3., 204., 10.))\n",
- " plt.hist(data, bins=np.arange(0., 201., 5.))\n",
- " ylim = axes.get_ylim()\n",
- " x = np.arange(40., 200.1, 0.1)\n",
- " yFitOne = funcs.theKink(x, fitOne)\n",
- " yFitTwo = funcs.theKink(x, fitTwo)\n",
- " plt.plot(x, yFitOne)\n",
- " plt.plot(x, yFitTwo)\n",
- " axes.set_ylim(ylim)\n",
- " elif i + 1 == nTrials:\n",
- " print 'Elapsed', totalTime\n",
- " xKinkOne.append(fitOne[0])\n",
- " xKinkTwo.append(fitTwo[0])"
+ "xKinkOne = {}\n",
+ "xKinkTwo = {}\n",
+ "xKinkDiff = {}\n",
+ "percentiles = np.arange(50, 71, 5)\n",
+ "\n",
+ "for percentile in percentiles:\n",
+ " xKinkOne[percentile] = []\n",
+ " xKinkTwo[percentile] = []\n",
+ " xKinkDiff[percentile] = []\n",
+ " for i in xrange(nTrials):\n",
+ " timer = time()\n",
+ " data, fitOne, fitTwo = fitTwoHistograms(percentile)\n",
+ " totalTime += time() - timer\n",
+ "\n",
+ " xKinkOne[percentile].append(fitOne[0])\n",
+ " xKinkTwo[percentile].append(fitTwo[0])\n",
+ " xKinkDiff[percentile].append(baseGuess[0] + fitTwo[0] - fitOne[0])\n",
+ "\n",
+ "def plotFitCompare(percentile):\n",
+ " # 400 data points generated\n",
+ " fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ " plt.hist(xKinkOne[percentile], range=(80,180), color='#66a61e', bins=np.arange(80., 181., 2.), alpha=0.6, zorder=2)\n",
+ " plt.hist(xKinkTwo[percentile], range=(80,180), color='#0088ff', bins=np.arange(80., 181., 2.), alpha=0.6, zorder=2)\n",
+ " plt.hist(xKinkDiff[percentile], range=(80,180), color='#000000', bins=np.arange(80., 181., 2.), alpha=0.8, zorder=1)\n",
+ " print 'percentile:', percentile\n",
+ "\n",
+ "print 'len(percentiles)', len(percentiles), 'Elapsed', totalTime"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "Elapsed 67.2579071522\n"
+ "len(percentiles) 5 Elapsed 233.278993368\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "# 400 data points generated\n",
- "plt.hist(xKinkOne, range=(100,200), bins=50, alpha=0.4)\n",
- "plt.hist(xKinkTwo, range=(100,200), bins=50, alpha=0.4)"
+ "plotFitCompare(percentiles[0])"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percentile: 50\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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6JFqzZk1Pn91xxx2xevXqiEjb60JD8te//nX84z/+Y+zevTv2798fJ06ciEce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\nJEISAIAkQhIAgCRCEgCAJEISAIAk/w/4fz59kRliZgAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fb2d3014750>"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "plotFitCompare(percentiles[1])"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percentile: 55\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fb2d3251b90>"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "plotFitCompare(percentiles[2])"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percentile: 60\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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hlmX2ebDrba9fffXV7Jprrsk6OzuzLMuyDz74IMsyez3Y9bbXf/iHf5ht2LAh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\n2Py1GpG9lj0AAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fb2d37824d0>"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "plotFitCompare(percentiles[3])"
],
"language": "python",
"metadata": {},
"outputs": [
{
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percentile: 65\n"
+ ]
+ },
+ {
"metadata": {},
- "output_type": "pyout",
- "prompt_number": 4,
+ "output_type": "display_data",
+ "png": 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AIIkHkgNQ0Q6/dzhuvf3zZdefXz0tvvfEMwV2BBOHIAlAZStl0XLvorLLNz78RoHNwMTi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\nAEgiSAIAkOT/AU17JHRKIUzUAAAAAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fb2d2d55fd0>"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "plotFitCompare(percentiles[4])"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
"text": [
- "(array([ 5., 6., 4., 1., 2., 6., 5., 7., 5.,\n",
- " 16., 6., 15., 18., 18., 23., 12., 38., 41.,\n",
- " 80., 86., 100., 129., 105., 51., 42., 20., 13.,\n",
- " 10., 7., 4., 0., 1., 0., 0., 0., 0.,\n",
- " 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
- " 0., 0., 0., 0., 0.]),\n",
- " array([ 100., 102., 104., 106., 108., 110., 112., 114., 116.,\n",
- " 118., 120., 122., 124., 126., 128., 130., 132., 134.,\n",
- " 136., 138., 140., 142., 144., 146., 148., 150., 152.,\n",
- " 154., 156., 158., 160., 162., 164., 166., 168., 170.,\n",
- " 172., 174., 176., 178., 180., 182., 184., 186., 188.,\n",
- " 190., 192., 194., 196., 198., 200.]),\n",
- " <a list of 50 Patch objects>)"
+ "percentile: 70\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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BYNBpGwAAAHCoqqpKVVVVEbue4yC5ZMkSlZWVqaioSGVlZcrJyQkfz8/P1yOPPKLm5mYd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\nAAAw8v8B2DgHDHepRs0AAAAASUVORK5CYII=\n",
"text": [
- "<matplotlib.figure.Figure at 0x7f8e30517750>"
+ "<matplotlib.figure.Figure at 0x7fb2d332c410>"
]
}
],
- "prompt_number": 4
+ "prompt_number": 11
}
],
"metadata": {}
}
]
}
\ No newline at end of file
diff --git a/debinningFunction.ipynb b/debinningFunction.ipynb
index cb82baf..9ba47fa 100644
--- a/debinningFunction.ipynb
+++ b/debinningFunction.ipynb
@@ -1,631 +1,630 @@
{
"metadata": {
"name": "",
- "signature": "sha256:c791533364436ab31de625cd03cf5b716781a9c09b1e17428da1b3a78e4ef859"
+ "signature": "sha256:f9ecdcb2035923432ee32d967e3c0f105cc4b8a80c7046991c18f2b1f9639f45"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
- "from os import listdir as ls\n",
"from __future__ import division\n",
"import numpy as np\n",
"from time import time\n",
"import bisect\n",
"import operator as op\n",
"\n",
"import utilities.sampleFunctions as funcs\n",
"import utilities.probCalc as pc\n",
"import utilities.plotting as debinPlot\n",
"reload(funcs)\n",
"reload(pc)\n",
"reload(debinPlot)\n",
"\n",
"%matplotlib inline\n",
"from matplotlib import pyplot as plt\n",
"from IPython.html.widgets import interact, interactive, fixed\n",
"from IPython.html import widgets\n",
"from IPython.display import clear_output, display, HTML\n",
"\n",
"def quickData():\n",
" ''' Shorthand for getting easyEndpoint data (384 x values in [8.5,200])\n",
" - set nPulls before calling\n",
" - see utilities.sampleFunctions.functionToData for more details\n",
" '''\n",
" return funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n",
"\n",
"\n",
"def quickBG():\n",
" ''' Shorthand for getting endpointBG data (384 x values in [8.5,200])\n",
" - set nPulls before calling\n",
" - see utilities.sampleFunctions.functionToData for more details\n",
" '''\n",
- " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n"
+ " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"nPulls = 20\n",
"pullData = {index:[] for index in xrange(nPulls)}\n",
"funcs.settings['simpleSortedOutput'] = True\n",
"for iteration in xrange(2000):\n",
" for i,v in enumerate(quickData()):\n",
" pullData[i].append(v)\n",
"\n",
"funcs.settings['simpleSortedOutput'] = False\n",
"x, f, F, data = quickData()\n",
"f = f / F[-1]\n",
"F = F / F[-1]\n",
"\n",
"ithPDF = {}\n",
"for i in xrange(1, nPulls+1):\n",
" ithPDF[i-1] = np.array([f[j] * F[j]**(i-1) * (1 - F[j])**(nPulls-i) * pc.nKr(nPulls, i) for j in xrange(len(x))])\n",
"\n",
"def makeHist(i=0):\n",
" histogramRange = np.arange(0, 201, 5)\n",
" plt.hist(pullData[i], bins=histogramRange, alpha=0.4, normed=True)\n",
" plt.plot(x, ithPDF[i])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"interact(makeHist, i=(0,nPulls-1))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"<function __main__.makeHist>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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3HKEkMkXPPUqgyMYzd9x17IroJzpF8l1efEv2dh1NCzuMrFZb/CnejGwMOwwR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\nAABJRU5ErkJggg==\n",
"text": [
- "<matplotlib.figure.Figure at 0x7fb124123a90>"
+ "<matplotlib.figure.Figure at 0x7f57ec05d750>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"### The formula looks insane....\n",
"zero = np.around(np.array([sum([(pc.nKr(nPulls, i) // nPulls) * Fx**(i-1) * (1 - Fx)**(nPulls-i) \n",
" for i in xrange(1, nPulls+1)]) for Fx in F]) - 1, decimals=14)\n",
"\n",
"np.linalg.norm(zero)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"0.0"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"The new binfull algorithm $\\Rightarrow$ debinning function"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"funcs.settings['simpleSortedOutput'] = False\n",
"nPulls = 96\n",
"nFictitious=96\n",
"\n",
"x, f, F, data = quickData()\n",
"x, bgf, bgF, bgData = quickBG()\n",
"f = f / F[-1]\n",
"F = F / F[-1]\n",
"bgf = bgf / bgF[-1]\n",
"bgF = bgF / bgF[-1]\n",
"\n",
" \n",
"def mapDataToX(dindex):\n",
" # maps elements of data to elements of x\n",
" # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
" xindex = bisect.bisect_left(x, data[dindex])\n",
" if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
" return xindex - 1\n",
" return xindex\n",
"dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
"\n",
"\n",
"def vecG_rth(rindex, xindex):\n",
" r = rindex+1\n",
" return pc.nKr(nFictitious, r) * bgF[xindex]**(r-1) * (1 - bgF[xindex])**(nFictitious - r)\n",
"\n",
"\n",
"vecG_rx = np.array([[vecG_rth(rindex, xindex) for xindex in xrange(len(x))]\n",
" for rindex in xrange(nFictitious)])\n",
"sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
"debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
"\n",
"# Discard trivial data\n",
"x = x.compress(bgf > 0)\n",
"debinningData = debinningData.compress(bgf > 0)\n",
"f = f.compress(bgf > 0)\n",
"bgf = bgf.compress(bgf > 0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Pretty plot\n",
"fig, axes = plt.subplots(figsize=(11,7))\n",
"plt.plot(x, debinningData)\n",
"histogramRange = np.arange(0, 201, 5)\n",
"plt.hist(data, bins=histogramRange, alpha=0.4, normed=True)\n",
"plt.plot(x, f)\n",
"plt.plot(x, bgf)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
- "[<matplotlib.lines.Line2D at 0x7fb11cfabb10>]"
+ "[<matplotlib.lines.Line2D at 0x7f57cbae6b10>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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4xBCWDBuIFaiFuyUXxuS5EDxAeKkMel+3julj23moMBHxBQqcIvIPIYlJXPrE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\nAABJRU5ErkJggg==\n",
"text": [
- "<matplotlib.figure.Figure at 0x7fb11d0ca290>"
+ "<matplotlib.figure.Figure at 0x7f57cbc07f90>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Residual Plot\n",
"fig, axes = plt.subplots(figsize=(11,7))\n",
"plt.plot(x, (f - debinningData)**2 / f)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
- "[<matplotlib.lines.Line2D at 0x7fe06541da90>]"
+ "[<matplotlib.lines.Line2D at 0x7f57cbbbb9d0>]"
]
},
{
"metadata": {},
"output_type": "display_data",
- "png": 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rCAYTlsJzzz3uT5062R1///3So4+61ijApzgt3ZTWpo37vzR/vu9KgKohiCJQ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\ndQtDOogiWnHpnp8xQ2rbVmrc2G8dPpx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AQPIdIyr5FlGCKMoFQRQAgIAE1TW/cGEw9QBxRxAFACAgQQTRnj0JoigfBFEAAAKwZYtU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\n",
"text": [
- "<matplotlib.figure.Figure at 0x7fe06541d410>"
+ "<matplotlib.figure.Figure at 0x7f57cbbbb510>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print sum((f - debinningData)**2 / f)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "0.168808848476\n"
+ "0.130624657206\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Constructive Comments from Awesome People"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Greg says, try a KS test. \n",
" - If I have f(x), how likely will I draw a sample which looks like g(x).\n",
" - Related to Wilks' Theorem\n",
" - Also, check out rank statistics\n",
" \n",
"Christoph mentioned \"max gap method\" for when you have no idea whatsoever what your background is."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Test Suite"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Let's try some GPU programming:\n",
"import pycuda.driver as cuda\n",
"import pycuda.autoinit\n",
"from pycuda.compiler import SourceModule\n",
"from string import Template\n",
"\n",
"funcs.settings['simpleSortedOutput'] = False\n",
"nPulls = 96\n",
"nFictitious = 96 # Multiple of 32 for GPU programming ease.\n",
"lenXdomain = len(np.arange(8.5, 200.2, 0.5))\n",
"\n",
"mod_template = Template(\"\"\"\n",
" __global__ void vecG(double *vecG_rx, double *bgF, double *nKr) {\n",
" const int idr = threadIdx.y + blockDim.y * blockIdx.y;\n",
" const int idx = threadIdx.x + blockDim.x * blockIdx.x;\n",
" const int idrx = idx + idr*${lenX};\n",
" const int r = (idr + 1) < (${nFic} - idr) ? (idr + 1) : ${nFic} - idr;\n",
" vecG_rx[idrx] = nKr[r-1] * pow(bgF[idx], idr) * pow(1 - bgF[idx], ${nFic} - idr - 1);\n",
" }\n",
" \"\"\")\n",
"\n",
"mod = SourceModule(mod_template.substitute(nFic=nFictitious, lenX=lenXdomain))\n",
"\n",
"timer = time()\n",
"\n",
"# initialize the loop\n",
"nKr = pc.get_nKrArray(nFictitious)\n",
"chisq = []\n",
"bgchisq = []\n",
"ks = []\n",
"bgks = []\n",
"\n",
"for trial in xrange(100000):\n",
"\n",
" x, f, F, data = quickData()\n",
" x, bgf, bgF, bgData = quickBG()\n",
" f = f / F[-1]\n",
" F = F / F[-1]\n",
" bgf = bgf / bgF[-1]\n",
" bgF = bgF / bgF[-1]\n",
"\n",
" def mapDataToX(dindex):\n",
" # maps elements of data to elements of x\n",
" # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
" xindex = bisect.bisect_left(x, data[dindex])\n",
" if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
" return xindex - 1\n",
" return xindex\n",
" dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
"\n",
" # Use the GPU for the most expensive / paralellizable part of the calculation:\n",
" # =====\n",
" \n",
" # Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n",
" vecG_rx = np.empty([nFictitious, len(x)])\n",
" \n",
" # Allocate memory on the GPU for vecG calculation\n",
" vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n",
" bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n",
" nKr_gpu = cuda.mem_alloc(nKr.nbytes)\n",
" \n",
" # Transfer data to the GPU\n",
" cuda.memcpy_htod(bgF_gpu, bgF)\n",
" cuda.memcpy_htod(nKr_gpu, nKr)\n",
" \n",
" # Get a reference to the GPU module function and do the calculation\n",
" # NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n",
" vecG_func = mod.get_function('vecG')\n",
" vecG_func(vecG_rx_gpu, bgF_gpu, nKr_gpu, block=(16, 4, 1), grid=(24, 24))\n",
"\n",
" # Get the result back from the GPU and use it!\n",
" cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n",
" sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
" debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
" \n",
" x = x.compress(bgf > 0)\n",
" debinningData = debinningData.compress(bgf > 0)\n",
" f = f.compress(bgf > 0)\n",
" bgf = bgf.compress(bgf > 0)\n",
" F = F.compress(bgf > 0)\n",
" bgF = bgF.compress(bgf > 0)\n",
" \n",
" # Chisq test....\n",
" chisq.append(sum((debinningData - f)**2 / f))\n",
" bgchisq.append(sum((debinningData - bgf)**2 / bgf))\n",
" \n",
" # KS test...\n",
" debinningCDF = pc.A(debinningData, 0.5)\n",
" ks.append(max(abs(debinningCDF - F)))\n",
" bgks.append(max(abs(debinningCDF - bgF)))\n",
" \n",
" if trial == 0:\n",
" # Infinity sigma upper and lower bands...\n",
" debinningUpper = debinningData.copy()\n",
" debinningLower = debinningData.copy()\n",
" # Uncertainty PDFs for each x value...\n",
" uncertaintyHistos = [debinPlot.HistoContainer(np.arange(0., 0.024, 0.0002), debinningData[i])\n",
" for i in xrange(len(x))]\n",
" else:\n",
" debinningUpper = np.clip(debinningData, debinningUpper, 20.)\n",
" debinningLower = np.clip(debinningData, -1., debinningLower)\n",
" for i in xrange(len(x)):\n",
" try:\n",
" uncertaintyHistos[i].addValue(debinningData[i])\n",
" except ValueError as e:\n",
" print e.message\n",
" print 'xindex = ' + str(i) + ', debinningData[xindex] = ' + str(debinningData[i])\n",
" \n",
"print time() - timer"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "348.400629997\n"
+ "255.336770058\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Try with a HUGE data set:\n",
"nPulls = 10000\n",
"\n",
"timer = time()\n",
"x, f, F, data = quickData()\n",
"x, bgf, bgF, bgData = quickBG()\n",
"f = f / F[-1]\n",
"F = F / F[-1]\n",
"bgf = bgf / bgF[-1]\n",
"bgF = bgF / bgF[-1]\n",
"\n",
"def mapDataToX(dindex):\n",
" # maps elements of data to elements of x\n",
" # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
" xindex = bisect.bisect_left(x, data[dindex])\n",
" if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
" return xindex - 1\n",
" return xindex\n",
"dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
"\n",
"# Use the GPU for the most expensive / paralellizable part of the calculation:\n",
"# =====\n",
"\n",
"# Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n",
"vecG_rx = np.empty([nFictitious, len(x)])\n",
"\n",
"# Allocate memory on the GPU for vecG calculation\n",
"vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n",
"bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n",
"nKr_gpu = cuda.mem_alloc(nKr.nbytes)\n",
"\n",
"# Transfer data to the GPU\n",
"cuda.memcpy_htod(bgF_gpu, bgF)\n",
"cuda.memcpy_htod(nKr_gpu, nKr)\n",
"\n",
"# Get a reference to the GPU module function and do the calculation\n",
"# NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n",
"vecG_func = mod.get_function('vecG')\n",
"vecG_func(vecG_rx_gpu, bgF_gpu, nKr_gpu, block=(16, 4, 1), grid=(24, 24))\n",
"\n",
"# Get the result back from the GPU and use it!\n",
"cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n",
"sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
"BIGdebinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
"\n",
"x = x.compress(bgf > 0)\n",
"BIGdebinningData = BIGdebinningData.compress(bgf > 0)\n",
"f = f.compress(bgf > 0)\n",
"bgf = bgf.compress(bgf > 0)\n",
"F = F.compress(bgf > 0)\n",
"bgF = bgF.compress(bgf > 0)\n",
" \n",
"print time() - timer"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "0.0659880638123\n"
+ "0.0508160591125\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"timer = time()\n",
"# Pretty plot\n",
"fig, axes = plt.subplots(figsize=(11,7))\n",
"plt.fill_between(x, debinningUpper, debinningLower, alpha=0.4, zorder=1)\n",
"plt.plot(x, f, color='#880088', zorder=3)\n",
"plt.plot(x, BIGdebinningData, color='black', linestyle='--', linewidth=2, zorder=4)\n",
"for i, v in enumerate(x):\n",
" debinPlot.verticalColorBand(uncertaintyHistos[i], v, 0.5)\n",
"print time() - timer"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
- "12.6747150421\n"
+ "9.35061311722\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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Z0pJ4Dfc8LjdF7saYvL+lJTGlbpdFslPw7nXslHuqFD3AyA5YECsajbB79/N8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\n3rnN5p5prmaVq21vkrqKmu0uaMyc3W53z0zX0nnzoWaxqwUUvEntISH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ETOX114/xxhur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\n/euYNy+TadMmBFWVIhnD2Qk//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449P1dmo/HPbahsPez8lxum+apOLii1iy5HmuvfZyMjMzu+eiItKtdMtGpAPL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\nXSJ9XqmuAAAAAElFTkSuQmCC\n",
"text": [
- "<matplotlib.figure.Figure at 0x7fe0651aa490>"
+ "<matplotlib.figure.Figure at 0x7f57cb9f0150>"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, axes = plt.subplots(figsize=(11,7))\n",
"histogramRange = np.arange(0, 1, .005)\n",
"plt.hist(chisq, bins=histogramRange)\n",
"plt.hist(bgchisq, bins=histogramRange, alpha=0.4)\n",
"print"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Je3f7mYeaofAtmX/JLEwOhU8zdA5wGDihhyVh/iUHY/1czBtuvSHJdEPnAIfB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\nvdjCDGa94wAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7fe04ddc3790>"
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, axes = plt.subplots(figsize=(11,7))\n",
"histogramRange = np.arange(0, 0.3, .002)\n",
"plt.hist(ks, bins=histogramRange)\n",
"plt.hist(bgks, bins=histogramRange, alpha=0.4)\n",
"print"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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8fAml07d4CqI7w6x1mD0LEjRnjDGYMAO22pWu631UZq3D7BE0AXpg0fj+CZ4w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\nAEAvBE0AAHohaAIA0Iv/D382UsP4CSbiAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7fe04d9217d0>"
]
}
],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"q = np.arange(8.1, 200.05, 0.1)\n",
"len(q)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 16,
"text": [
"1920"
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
\ No newline at end of file
diff --git a/legacy/runBinfull.py b/legacy/runBinfull.py
index 36d7dbb..299aaa2 100644
--- a/legacy/runBinfull.py
+++ b/legacy/runBinfull.py
@@ -1,381 +1,384 @@
'''
runBinfull.py
A script testing the binfull algorithm on some sample functions.
Copyright (C) 2014 Abram Krislock and Nathan Krislock
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see http://www.gnu.org/licenses/gpl-3.0.txt.
'''
###### IMPORTS ######
+import sys
+sys.path[0] = '..'
+
from time import time
totalTimer = time()
import utilities.sampleFunctions as funcs
import utilities.minimizers as minis
import binfull
import numpy as np
import bisect
from matplotlib import pyplot as plt
plt.rc('mathtext', fontset='stix')
import sys, getopt, os
setup = {'xlow':0, 'xhigh':200, 'binWidth':5, 'step':0.0001, 'npoints':1000,
'func':'all', 'dataDir':'dataSet_a', 'seed':'seed_a',
'nbinfull':100000, 'binfullWidth':0.75, 'smoother':'all'}
###### COMMAND LINE ARGS AND SETUP ######
try:
opts, args = getopt.getopt(sys.argv[1:], '',
[key + '=' for key in setup])
except getopt.GetoptError:
print 'runBinfull.py may be run with the following options:'
print ' DATA OPTIONS:'
print ' --xlow=[a], --xhigh=[b]: Set the x-axis range to [a,b]'
print ' --binWidth=[#]: Set the width of the bins for the histogram'
print ' --step=[#]: Set the step-size for fake data generation'
print ' --npoints=[#]: Set the number of points for fake data generation'
print ' --func=[#/all]: Choose the function by int from 0 to 4'
print ' --dataDir=[None/directory]: Data to or from ./savedData/directory'
print ' --seed=[string]: Set the random seed (uses hash value)'
print ' BINFULL OPTIONS:'
print ' --nbinfull=[#]: Set the number of points for binfull'
print ' --binfullWidth=[#]: Set the width of the bins for binfull'
print ' --smoother=[#/all]: Choose the smoothing function by int from 0 to 2'
print '### DEFAULTS:'
for key, value in setup.iteritems():
print ' ' + key + '=' + str(value)
print
sys.exit(2)
for opt, arg in opts:
if arg.isdigit():
setup[opt.strip('-')] = int(arg)
elif arg.replace('.', '', 1).isdigit():
setup[opt.strip('-')] = float(arg)
else:
setup[opt.strip('-')] = arg
# saving, loading, and plotting settings, creating directories as necessary.
if setup['dataDir']:
dataDir = 'savedData/' + setup['dataDir'] + '/'
plotDir = 'resultPlots/' + setup['dataDir'] + '/'
setupFileName = dataDir.partition(setup['dataDir'])
setupFileName = setupFileName[0] + 'setup_' + setupFileName[1] + '.txt'
# create the data directory, if necessary
if not os.path.isdir(dataDir):
os.mkdir(dataDir)
# load the settings, if the settings file exists
if os.path.exists(setupFileName):
setupFile = open(setupFileName, 'r')
line = (setupFile.readline().strip('\n')).partition(' = ')
while not line == ('', '', ''):
if line[2].isdigit():
setup[line[0]] = int(line[2])
elif line[2].replace('.', '', 1).isdigit():
setup[line[0]] = float(line[2])
else:
setup[line[0]] = line[2]
line = (setupFile.readline().strip('\n')).partition(' = ')
setupFile.close()
else:
plotDir = 'resultPlots/' + S['seed'] + 'N' + str(S['npoints']) + '/'
# make the plotting directory, if necessary
if not os.path.isdir(plotDir):
os.mkdir(plotDir)
# shorthand for the setup dict
S = setup
# list of functions to test
if S['func'] == 'all':
funcList = range(len(funcs.allFunctions))
else:
funcList = [S['func']]
# list of smoothing functions to test for each function
if S['smoother'] == 'all':
smoothList = range(len(binfull.smootherTuple))
else:
smoothList = [S['smoother']]
# names of the data arrays to be saved or loaded
dataNames = ['x', 'y', 'cdf', 'pdf', 'bgX', 'bgY', 'bgCdf', 'bgPdf']
###### BIG FUNC LOOP ######
for f in funcList:
# convert func int choice to actual function
func = funcs.allFunctions[f]
# filename prefix for this function
prefix = funcs.nameMap[func]
# init random number generator with S['seed'] and the function string.
funcs.randomGenerator.setSeed(S['seed'] + prefix)
###### FAKE DATA SETUP ######
t = time()
if S['dataDir'] and all(
[os.path.exists(dataDir + prefix + '_' + name + '.npy')
for name in dataNames]):
# fake data exists; load it!
print '\n ~~~~~~ Now loading function data: '
print prefix
print ' with', S['npoints'], 'points ~~~~~~ \n'
for name in dataNames:
exec(name + ' = np.load(dataDir + prefix + "_' + name + '.npy")')
else:
# generate fake data!
print '\n ###### Now generating data for function: '
print prefix
print ' with ', S['npoints'], 'points ###### \n'
x, y, cdf, pdf = funcs.functionToData(func, S['npoints'], S['step'])
bgNpoints = [S['npoints'], cdf[-1]]
bgX, bgY, bgCdf, bgPdf = funcs.functionToData(funcs.bgMap[func],
bgNpoints, S['step'])
setLog = True if funcs.bgMap[func] == funcs.exponentialBG else False
histogramRange = np.arange(S['xlow'], 0.5*S['binWidth'] + S['xhigh'],
S['binWidth'])
yNormed = y / cdf[-1]
bgYNormed = bgY / cdf[-1]
bgNpoints = len(bgPdf)
###### PLOTTING ######
fig, axes = plt.subplots(figsize=(11,7))
fig.subplots_adjust(left=0.14, right=0.95, top=0.95, bottom=0.125)
# save the plot painters as pXxxx
# the histogram painter is a list of "patches". grab any patch with [2][0]
pHist = (plt.hist(pdf, bins=histogramRange, log=setLog,
normed=True, alpha=0.4, color='#66a61e',
label=r'$%i$ Points' % S['npoints'], zorder=0))[2][0]
pBG, = plt.plot(bgX, bgYNormed, '--', color='#964a01', linewidth=4,
label='BG only PDF', zorder=1)
pTrue, = plt.plot(x, yNormed, '#964a01', linewidth=4,
label='True PDF', zorder=2)
xwidth = S['xhigh'] - S['xlow']
xdiv = xwidth / 4.
axes.set_xlim(S['xlow'] - 0.002*xwidth, S['xhigh'] + 0.001*xwidth)
axes.set_xticks(np.arange(S['xlow'], S['xhigh'] + 0.001*xwidth, xdiv))
axes.set_xticklabels([r'$%i$' % int(num) for num in
np.arange(S['xlow'], S['xhigh'] + 0.001*xwidth, xdiv)],
fontsize=30)
axes.set_xticks(np.arange(S['xlow'], S['xhigh'] + 0.001*xwidth, xdiv/5.),
minor=True)
if setLog:
axes.set_ylim(bottom=0.97e-4, top=0.101)
axes.set_yticklabels([r'$10^{%i}$' % int(num) for num in
np.arange(-5,1,1)], fontsize=30)
else:
# This is a bit of a pain in the ass... but makes a pretty yaxis:
ymaxx = 1.6 * plt.axis()[3]
ydiv = 10**(np.log10(ymaxx) // 1)
if ydiv * 3. > ymaxx:
ydiv /= 2.
elif ydiv * 5. <= ymaxx:
ydiv *= 2.
axes.set_ylim(bottom=-0.0001, top=ymaxx)
axes.set_yticks(np.arange(0, ymaxx*1.01, ydiv))
axes.set_yticklabels([r'$%0.3f$' % num for num
in np.arange(0, ymaxx*1.01, ydiv)], fontsize=30)
axes.set_yticks(np.arange(0, ymaxx*1.01, ydiv/5.), minor=True)
axes.set_xlabel('Arbitrary Units', labelpad=5, fontsize=28)
axes.set_ylabel('Probability', labelpad=5, fontsize=28)
axes.tick_params(length=10, width=2, labelsize=28, zorder=10, pad=10)
axes.tick_params(which='minor', length=5, width=2, zorder=11)
axes.minorticks_on()
plt.legend((pTrue, pBG, pHist),
(pTrue.get_label(), pBG.get_label(), pHist.get_label()),
shadow=True, loc='upper right', prop={'size':26},
labelspacing=0.25, handlelength=1.2, handletextpad=0.35)
filename = plotDir + prefix + '_data.pdf'
plt.savefig(filename)
plt.close()
print 'Time after fake data setup: ' + str(time() - t)
###### FAKE DATA SAVING TO FILES ######
if S['dataDir']:
t = time()
for name in dataNames:
if not os.path.exists(dataDir + prefix + '_' + name + '.npy'):
eval('np.save(dataDir + prefix + "_' + name + '", ' + name + ')')
print 'Time after fake data saving: ' + str(time() - t)
###### BINFULL ARRAY SET UP ######
binfullRange = np.arange(S['xlow'], 0.5*S['binfullWidth'] + S['xhigh'],
S['binfullWidth'])
bgBinfullCenters = np.arange(S['xlow'] + 0.5*S['binfullWidth'], S['xhigh'],
S['binfullWidth'])
# left-most entry in bgX which is >= bgBinfullCenters[i]
bgXindices = [bisect.bisect_left(bgX, value) for value in bgBinfullCenters]
###### BINFULL PARAMETER FINDING FOR EACH SMOOTHER ######
for s in smoothList:
# convert smoother int choice to actual smoother
smoother = binfull.smootherTuple[s]
smootherInstance = smoother(1.)
# filename prefix for this smoother and function
binfullPrefix = prefix + '_binfull' + str(smootherInstance)
###### BINFULL GENERATION ######
t = time()
if all([S['dataDir'], binfullPrefix + 'Sigma' in setup,
os.path.exists(dataDir + binfullPrefix + 'Edges.npy'),
os.path.exists(dataDir + binfullPrefix + 'Histo.npy')]):
# binfull data exists; load it!
print '\n ~~~~~~ Now loading binfull data from: '
print binfullPrefix + 'Smoother'
print ' ~~~~~~ \n'
binfullPdf = binfull.binfullFactory(
np.load(dataDir + binfullPrefix + 'Edges.npy'),
np.load(dataDir + binfullPrefix + 'Histo.npy'))
sigma = setup[binfullPrefix + 'Sigma']
else:
# binfull gets its own random number generator and seed
binfull.randomGenerator.setSeed(S['seed'] + str(smootherInstance))
# Use a chisq fit to find the best smoothing parameter
def minimizeMe(sigma):
ti = time()
localSmoother = smoother(sigma)
bgBinfullPdf = binfull.binfullHistogram(binfullRange, bgPdf, S['nbinfull'],
localSmoother)
# Normalize the true function -up- to the huge size of the binfull cdf
# NOTE: normalizing up to avoid possible machine epsilon problems
normalization = bgBinfullPdf.integral() / bgCdf[-1]
bgYscaled = bgY * normalization
# Calculate the chisq for this to match the true function
chisq = 0
for i, value in enumerate(bgBinfullPdf.histo):
chisq += (bgYscaled[bgXindices[i]] - value) ** 2
print 'This evaluation:'
print ' ' + str(localSmoother),
print 'smoother with sigma:', sigma
print ' chisq:', chisq
print 'Time after mimimizeMe evaluation: ' + str(time() - ti)
del localSmoother, bgBinfullPdf
return chisq
print '\n ###### Now running binfull algorithm with:'
print binfullPrefix + 'Smoother'
print ' ###### \n'
sigma = minis.goldenSectionSearch(minimizeMe,
smootherInstance['range'], 0.001)
print
print 'Minimization complete!! Best smoothing sigma:', sigma
setup[binfullPrefix + 'Sigma'] = sigma
smootherInstance = smoother(sigma)
binfullPdf = binfull.binfullHistogram(binfullRange, pdf, S['nbinfull'],
smootherInstance)
print 'Time after binfull setup: ' + str(time() - t)
print
t = time()
###### PLOTTING ######
fig, axes = plt.subplots(figsize=(11,7))
fig.subplots_adjust(left=0.14, right=0.95, top=0.95, bottom=0.125)
# save the plot painters as pXxxx, or use proxy painters:
# the histogram painter is a list of "patches". grab any patch with [2][0]
pHist = (plt.hist(pdf, bins=histogramRange, log=setLog,
normed=True, alpha=0.4, color='#66a61e',
label=r'$%i$ Points' % S['npoints'], zorder=0))[2][0]
pTrue, = plt.plot(x, yNormed, '#964a01', linewidth=4,
label='True PDF', zorder=3)
ex = int(np.log10(sigma) // 1)
if ex:
sigma *= 10**-ex
sigma = r'$\sigma = %0.3f \times 10^{%i}$' % (sigma, ex)
else:
sigma = r'$\sigma = %0.3f$' % sigma
proxySigma, = plt.plot(x[:1], yNormed[:1], 'w', linewidth=0, zorder=1,
label=sigma)
proxyBinfull = binfullPdf.fillPlot(color='#a41666', alpha=0.55, zorder=2,
label=str(smootherInstance)+' Binfull')
axes.set_xlim(S['xlow'] - 0.002*xwidth, S['xhigh'] + 0.001*xwidth)
axes.set_xticks(np.arange(S['xlow'], S['xhigh'] + 0.001*xwidth, xdiv))
axes.set_xticklabels([r'$%i$' % int(num) for num in
np.arange(S['xlow'], S['xhigh'] + 0.001*xwidth, xdiv)],
fontsize=30)
axes.set_xticks(np.arange(S['xlow'], S['xhigh'] + 0.001*xwidth, xdiv/5.),
minor=True)
if setLog:
axes.set_ylim(bottom=0.97e-4, top=0.101)
axes.set_yticklabels([r'$10^{%i}$' % int(num) for num in
np.arange(-5,1,1)], fontsize=30)
else:
axes.set_ylim(bottom=-0.0001, top=ymaxx)
axes.set_yticks(np.arange(0, ymaxx*1.01, ydiv))
axes.set_yticklabels([r'$%0.3f$' % num for num
in np.arange(0, ymaxx*1.01, ydiv)], fontsize=30)
axes.set_yticks(np.arange(0, ymaxx*1.01, ydiv/5.), minor=True)
axes.set_xlabel('Arbitrary Units', labelpad=5, fontsize=28)
axes.set_ylabel('Probability', labelpad=5, fontsize=28)
axes.tick_params(length=10, width=2, labelsize=28, zorder=10, pad=10)
axes.tick_params(which='minor', length=5, width=2, zorder=11)
axes.minorticks_on()
plt.legend((pTrue, pHist, proxyBinfull, proxySigma),
(pTrue.get_label(), pHist.get_label(),
proxyBinfull.get_label(), proxySigma.get_label()),
shadow=True, loc='upper right', prop={'size':26},
labelspacing=0.25, handlelength=1.2, handletextpad=0.35)
filename = plotDir + binfullPrefix + '.pdf'
plt.savefig(filename)
plt.close()
print 'Time after plotting: ' + str(time() - t)
print
###### BINFULL SAVING TO A FILE ######
if S['dataDir']:
t = time()
if not os.path.exists(dataDir + binfullPrefix + 'Edges.npy'):
np.save(dataDir + binfullPrefix + 'Edges', binfullPdf.binEdges)
if not os.path.exists(dataDir + binfullPrefix + 'Histo.npy'):
np.save(dataDir + binfullPrefix + 'Histo', binfullPdf.histo)
print 'Time after binfull saving: ' + str(time() - t)
print
###### FINALIZATIONS ######
# save the settings, and the sigma results:
if S['dataDir']:
setupFile = open(setupFileName, 'w')
for key, value in setup.iteritems():
setupFile.write(key + ' = ' + str(value) + '\n')
setupFile.close()
print 'Time after everything: ' + str(time() - totalTimer)
diff --git a/slides/.ipynb_checkpoints/NewStatistics-checkpoint.ipynb b/slides/.ipynb_checkpoints/NewStatistics-checkpoint.ipynb
index aa9a5fd..65fbaff 100644
--- a/slides/.ipynb_checkpoints/NewStatistics-checkpoint.ipynb
+++ b/slides/.ipynb_checkpoints/NewStatistics-checkpoint.ipynb
@@ -1,1328 +1,2490 @@
{
"metadata": {
"celltoolbar": "Slideshow",
"name": "",
- "signature": "sha256:2bce91243675c2ebc3aedc4b2f7015599bac408ed281212c97958575a1a2ccbf"
+ "signature": "sha256:c94e26b181dc86a4f55663831151d0f22921545ad617cd94c6a17b51f70ae569"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
- "cell_type": "heading",
- "level": 1,
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import sys\n",
+ "sys.path[0] = '..'\n",
+ "from __future__ import division\n",
+ "import numpy as np\n",
+ "from time import time\n",
+ "import bisect\n",
+ "import operator as op\n",
+ "\n",
+ "from utilities import settings\n",
+ "import utilities.sampleFunctions as funcs\n",
+ "import utilities.probCalc as pc\n",
+ "import utilities.plotting as debinPlot\n",
+ "import utilities.minimizers as miniz\n",
+ "reload(funcs)\n",
+ "reload(pc)\n",
+ "reload(debinPlot)\n",
+ "reload(miniz)\n",
+ "\n",
+ "%matplotlib inline\n",
+ "from matplotlib import pyplot as plt\n",
+ "from IPython.display import HTML"
+ ],
+ "language": "python",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
}
},
- "source": [
- "<center> Data Smoothing with a New Probability Calculus </center>"
- ]
+ "outputs": [],
+ "prompt_number": 1
},
{
- "cell_type": "heading",
- "level": 3,
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "slide"
}
},
"source": [
- "<center> Abram Krislock$^{[1]}$ and Nathan Krislock$^{[2]}$ </center>"
+ "# <center> debinning: Data Smoothing with a New Probability Calculus </center>"
]
},
{
- "cell_type": "heading",
- "level": 4,
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "cell_type": "markdown",
+ "metadata": {},
"source": [
- "<center> $^{[1]}$ Fysisk institutt, Universitetet i Oslo. </center> \n",
- "\n",
- "<center> [a.m.b.krislock@fys.uio.no](mailto:a.m.b.krislock@fys.uio.no \"Email Abram\") </center>"
+ "## <center> Abram Krislock </center>"
]
},
{
- "cell_type": "heading",
- "level": 4,
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "cell_type": "markdown",
+ "metadata": {},
"source": [
- "<center> $^{[2]}$ Department of Mathematical Sciences, Northern Illinois University. </center> \n",
+ "### <center> Fysisk institutt, Universitetet i Oslo. </center> \n",
"\n",
- "<center> [krislock@math.niu.edu](mailto:krislock@math.niu.edu \"Email Nathan\") </center>"
+ "### <center> [a.m.b.krislock@fys.uio.no](mailto:a.m.b.krislock@fys.uio.no \"Email Abram\") </center>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"Set some useful LaTeX commands for later in the document:\n",
"$ \\newcommand{\\Int}[2] {\\displaystyle \\int\\limits_{#1}^{#2}} $\n",
"$ \\newcommand{\\Prod}[2] {\\displaystyle \\prod\\limits_{#1}^{#2}} $\n",
"$ \\newcommand{\\Sum}[2] {\\displaystyle \\sum\\limits_{#1}^{#2}} $ \n",
"\n",
"### \\Int{lower}{upper} : $ \\Int{lower}{upper},\\qquad $ \\Prod{lower}{upper} : $ \\Prod{lower}{upper},\\qquad $ \\Sum{lower}{upper} : $ \\Sum{lower}{upper} $ ###\n",
"\n",
- "$ \\newcommand{subNsubR}[3] {{}_{#1} {#2}_{#3}} $\n",
+ "$ \\newcommand{subNsubR}[3] {{}_{#1} #2_{#3}} $\n",
+ "$ \\newcommand{rust}[1] {{\\require{color}\\color{Bittersweet}#1}} $\n",
+ "$ \\newcommand{sky}[1] {{\\require{color}\\color{SkyBlue}#1}} $\n",
"\n",
- "### \\subNsubR{n}{K}{r} : $ \\subNsubR{n}{K}{r} $"
+ "### \\subNsubR{n}{K}{r} : $ \\subNsubR{n}{K}{r},\\qquad $ \\rust{q} : $ \\rust{q},\\qquad $ \\sky{q} : $ \\sky{q} $"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
- "Motivation"
+ "Once Upon A Time..."
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "subslide"
}
},
"source": [
- "## Histogram Bin Dilemmas ##\n",
- "\n",
- "Suppose we draw some (experimental or simulated) data for some physical observable, $x$. \n",
- "\n",
- "This data will follow some probability distribution function (PDF), which we will call $f(x)$."
+ "We knew all the stuff!"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "-"
}
},
"source": [
- "The easiest way to empirically determine the shape of $f(x)$ is to repeatedly measure $x$, and throw the results into a histogram."
+ "### \"At the end of the 19th century... it was generally accepted that all the important laws of physics had been discovered...\" ([Source](http://en.wikipedia.org/wiki/History_of_physics \"http://en.wikipedia.org/wiki/History_of_physics\"))"
]
},
{
- "cell_type": "heading",
- "level": 2,
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "Probability of Datum and Data Samples"
+ "### Then this stuff happened:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "## Basic Datum Probability ##\n",
+ "$${\\huge{\\rm He}^{++},~{\\rm e}^-,~\\gamma \\qquad\\qquad \\hbar \\qquad\\qquad g^{\\mu\\nu}}$$\n",
"\n",
- "Suppose we draw some data (experimental or simulated) for some physical observable, $x$. \n",
- "\n",
- "This data will follow some probability distribution function (PDF)."
+ "$${\\huge E^2 = (mc^2)^2 + (pc)^2}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "The PDF, which we will call $f(x)$, gives the probability for a datum to lie between $x$ and $x + dx$. Thus,\n",
- "\n",
- "$$ P(\\tilde{x}\\in[x,x+dx]) = f(x) dx \\qquad {\\rm and} \\qquad \\Int{-\\infty}{\\infty} f(x) dx = 1~. $$"
+ "$${\\Large \\cdots {\\rm SU}(3)_C \\times {\\rm SU}(2)_L \\times {\\rm U}(1)_Y}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "--- \n",
- "\n",
- "The cumulative distribution function (CDF) is the anti-derivative of the PDF: \n",
- "\n",
- "$$ \\Int{-\\infty}{x} f(\\tilde{x}) d\\tilde{x} \\equiv F(x)~. $$\n",
- "\n",
- "It represents the probability to draw some value less than or equal to $x$."
+ "### Okay... But after that... Surely, we knew all the stuff!"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Well, actually...."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "notes"
+ "slide_type": "-"
}
},
"source": [
- "$$ \\Int{x}{\\infty} f(\\tilde{x}) d\\tilde{x} \\equiv 1 - F(x)~. $$"
+ "### Then this stuff happened:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "-"
}
},
"source": [
- "## Samples - I: Probability Density ## \n",
- "\n",
- "Let us define a sample of data as $\\{x_1, x_2, x_3 \\cdots\\}$, or just $\\{x_i\\}_{i=1}^n$ for a general sample with n data points."
+ "![We know almost nothing.](stuffWeKnow.png \"We know almost nothing.\")"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Let's face it."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "-"
}
},
"source": [
- "WLOG, let us take $x_i > x_j$ for any $i > j$."
+ "### Large Hadron Collider: A \"New Stuff\" Experiment"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "-"
}
},
"source": [
- "\\begin{align} \n",
- " P(\\{x_1\\}\\ d\\{x_1\\} &= f(x_1) dx_1 \\\\\n",
- " P(\\{x_1, x_2\\})\\ d\\{x_1, x_2\\} &= 2 \\times f(x_1) dx_1 f(x_2) dx_2 \\\\\n",
- " P(\\{x_1, x_2, x_3\\})\\ d\\{x_1, x_2, x_3\\} &= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3\n",
- "\\end{align}"
+ "![New stuff experiment!](epicLHCHighFive.png \"New stuff experiment!\")"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Dark Matter @ Large Hadron Collider\n",
+ "\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"\\begin{align}\n",
- " &{\\phantom=}\\mkern-17mu\\vdots \\\\\n",
- " P(\\{x_i\\}_{i=1}^n) d\\{x_i\\}_{i=1}^n &= n! \\Prod{i = 1}{n} f(x_i) dx_i \\\\\n",
- " \\phantom{d^3P(\\{x_1, x_2, x_3\\} \\equiv \\{x_1, x_3, x_2\\}\\cdots)} &\\phantom{= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}\n",
+ " {\\Huge \\widetilde{q_L}} & {\\Huge\\rightarrow} & {\\Huge \\rust{q}} \\\\\n",
+ " & {\\Huge\\searrow} \\\\\n",
+ " & & {\\Huge\\widetilde{\\chi}^0_2} & {\\Huge\\rightarrow} & {\\Huge h^0} & {\\Huge\\rightarrow} & {\\Huge \\rust{b}}\\\\\n",
+ " & & & {\\Huge\\searrow} & & {\\Huge \\hookrightarrow} & {\\Huge \\rust{b}} \\\\\n",
+ " & & & & {\\Huge \\color{Gray}{\\widetilde{\\chi}^0_1}}\n",
"\\end{align}"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "## Samples - II: Integration ## \n",
+ "### Calculate as one particle, the mass:\n",
"\n",
- "Since the sorted data is the most general, we must have care with integration limits:"
+ "$${\\huge m_{\\rust{q h^0}} \\qquad {\\rm using} \\qquad E^2 = (mc^2)^2 + (pc)^2}$$"
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "subslide"
}
},
"source": [
- "$$ \\Int{\\{x_1\\}_1}{} dP(\\{x_1\\}_1) = \\Int{-\\infty}{\\infty} f(x_1) dx_1 = 1 $$"
+ "The $m_{\\rust{qh^0}}$ Maximum Measurement"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ \\Int{\\{x_2\\}_2}{} dP(\\{x_1, x_2\\}_2) = 2 \\times \\Int{-\\infty}{\\infty} f(x_2) \\left[ \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right] dx_2, $$"
+ "![You want me to try.... What?!](tryChangingTheBins.png \"You want me to try.... What?!\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ \\Int{\\{x_3\\}_3}{} dP(\\{x_1, x_2, x_3\\}_3) = 3! \\times \\Int{-\\infty}{\\infty} f(x_3) \\left[ \\Int{-\\infty}{x_3} f(x_2) \\left( \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right) dx_2 \\right] dx_3 $$\n",
- "$$ \\vdots $$"
+ "### Change the... bins? Seriously?!"
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "subslide"
}
},
"source": [
- "## Samples - III: To be $r$th out of $n$... ## \n",
- "\n",
- "Let us define a new notation:"
+ "Change the bins! How bad could it be?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ {\\Large \\subNsubR{n}{f}{r} \\left[g\\left(\\{x_i\\}_n\\right)\\right] dx_r \\equiv \\Int{\\{x_{i \\neq r}\\}_n}{} g\\left(\\{x_i\\}_n\\right) dP(\\{x_i\\}_n) } $$ \n",
- "\n",
- "Interpretation: The expectation value of the function $g(\\{x_i\\}_n)$ as a function of the $r$th point of the sorted sample."
+ "![It could be very bad...](binningDilemma_final_orig.png \"It could be very bad...\")"
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "subslide"
}
},
"source": [
- "Then, $\\subNsubR{n}{f}{r} \\left[1\\right]$ is just the PDF of the $r$th data point for any sample of $n$ data points. Let us call it $\\subNsubR{n}{f}{r}(x_r)$.\n",
+ "Okay, that's bad, but how often...?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "funcs.randomGenerator.setSeed('seedOne')\n",
+ "funcs.settings['simpleSortedOutput'] = True\n",
"\n",
- "Theorem:\n",
+ "nPulls = 400\n",
+ "basePars = (0.00006, 10., 200., 110., 1.5, 50., 140.)\n",
+ "baseGuess = (140., -2., -0.1, 10.)\n",
"\n",
- "$$ {\\Large \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r}\\ f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. $$"
+ "def fitTwoHistograms(percentile):\n",
+ " data = funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, (0,200), basePars)\n",
+ " percentieth = data[data > np.percentile(data, percentile)]\n",
+ "\n",
+ " # The histograms are filled with the same data, only different binning.\n",
+ " binContentsOne, binEdgesOne = np.histogram(percentieth, np.arange(3., 204., 10.))\n",
+ " binContentsTwo, binEdgesTwo = np.histogram(percentieth, np.arange(0., 201., 5.))\n",
+ " \n",
+ " # The fit ranges are defined to be from the value of the 70th percentile data point\n",
+ " # to \"the last non-zero bin\", blindly.\n",
+ " fitBinsOne = np.flatnonzero(binContentsOne[binContentsOne.argmax():]) + binContentsOne.argmax()\n",
+ " fitBinsTwo = np.flatnonzero(binContentsTwo[binContentsTwo.argmax():]) + binContentsTwo.argmax()\n",
+ " \n",
+ " ### FITTING METHOD: Binned Maximum Likelihood ###\n",
+ " fitGuessOne = np.array([value * funcs.randomGenerator.normal(1., 0.1) for value in baseGuess])\n",
+ " fitGuessTwo = fitGuessOne.copy()\n",
+ "\n",
+ " def chiSqOne(pars):\n",
+ "# return funcs.chiSqSimple(binContentsOne, binEdgesOne, fitBinsOne, funcs.theKink, pars)\n",
+ " return -2. * funcs.theKink_BinnedLikelihood(binContentsOne, binEdgesOne, fitBinsOne, pars)\n",
+ " def chiSqTwo(pars):\n",
+ "# return funcs.chiSqSimple(binContentsTwo, binEdgesTwo, fitBinsTwo, funcs.theKink, pars)\n",
+ " return -2. * funcs.theKink_BinnedLikelihood(binContentsTwo, binEdgesTwo, fitBinsTwo, pars)\n",
+ "\n",
+ " fitOne = miniz.nelderMead(chiSqOne, fitGuessOne, xtol=0.01, ftol=0.05, disp=0)\n",
+ " fitTwo = miniz.nelderMead(chiSqTwo, fitGuessTwo, xtol=0.01, ftol=0.05, disp=0)\n",
+ " return (data, fitOne, fitTwo)\n",
+ "\n",
+ "xKinkOne = []\n",
+ "xKinkTwo = []\n",
+ "xKinkDiff = []\n",
+ "percentile = 60\n",
+ "nTrials = 1000\n",
+ "\n",
+ "for i in xrange(nTrials):\n",
+ " data, fitOne, fitTwo = fitTwoHistograms(percentile)\n",
+ " xKinkOne.append(fitOne[0])\n",
+ " xKinkTwo.append(fitTwo[0])\n",
+ " xKinkDiff.append(baseGuess[0] + fitTwo[0] - fitOne[0])"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def plotHistoFitCompare():\n",
+ " fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ " plt.hist(xKinkOne, range=(80,180), color='#66a61e', bins=np.arange(80, 181, 2), alpha=0.6, zorder=2)\n",
+ " plt.hist(xKinkTwo, range=(80,180), color='#0088ff', bins=np.arange(80, 181, 2), alpha=0.6, zorder=2)\n",
+ " plt.hist(xKinkDiff, range=(80,180), color='#000000', bins=np.arange(80, 181, 2), alpha=0.8, zorder=1)\n",
+ "\n",
+ " axes.set_xticks(np.arange(80, 181, 10))\n",
+ " axes.set_xticks(np.arange(80, 181, 2), minor=True)\n",
+ " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(80., 181., 10.)], fontsize=20)\n",
+ "\n",
+ " axes.set_yticks(np.arange(0, 250, 50))\n",
+ " axes.set_yticks(np.arange(0, 250, 10), minor=True)\n",
+ " axes.set_yticklabels([r'$%i$' % num for num in np.arange(0, 250, 50)], fontsize=20)\n",
+ "\n",
+ " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ " axes.minorticks_on() \n",
+ " axes.set_xlabel('Kink Fit Result', labelpad=5, fontsize=22)\n",
+ " axes.set_ylabel('Number of Counts (400 total)', labelpad=5, fontsize=22)\n",
+ "\n",
+ " print"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "plotHistoFitCompare()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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79+7V0aNHzUkcYDTKABAcaJQBmN2XGZ564XK5dO7cuYrjoqIi7du3T3379q1o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\nKBNCCCGEECKACmVCCCGEEEIE/A+gOP4Tl4r+OwAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa19505f290>"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "The debinning Project: Data Smoothing without Bins"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "## Samples - IV: To be $r$th out of $n$ (cont'd)... ## \n",
+ "### Histograms \"smooth\" the data in this way:\n",
"\n",
- "Suppose $n$ identical siblings have a race. Suppose we only care about who came in $r$th place.\n",
- "If we sorted them all: $n!$ But then we've overcounted, since we don't care who is 1st through $(r-1)$th, or who is $(r+1)$th through Nth.\n",
+ "![Let's try to find other shapes!](notTheOnlyShape.png \"Let's try to find other shapes!\")\n",
"\n",
- "$$ {}_nK_r \\equiv \\frac{n!}{(n-r)!(r-1)!} $$"
+ "### Is there a more appropriate smoothing shape?"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Gaussian Smoothing: binfull Histogram"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "Our sample is just like this, except that there is a certain probability to get $x_r$, as well as the probability to get $r-1$ points less than $x_r$ and $n-r$ points greater than $x_r$ in the sample. \n",
+ "### aka \"Kernel Density Estimation\":\n",
"\n",
- "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. $$"
+ "![Gaussian Smoothing](GaussianSmoothing.png \"Gaussian Smoothing\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "notes"
+ "slide_type": "fragment"
}
},
"source": [
- "If that was too much magic for anyone, the proof is down on sub-slides."
+ "### Select a point from our data..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
"source": [
- "Proof:\n",
- "\n",
- "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_2} f(x_1) \\Prod{i=1}{r-1} dx_i $$\n",
- "\n",
- "$$ \\times f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-1}}{\\infty} f(x_n) \\Prod{j=r+1}{n} dx_j $$"
+ "### Add a random deviate from a Gaussian distribution..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
"source": [
- "$\\phantom{Integration by parts:}$\n",
- "\n",
- "$$ \\phantom{\\Int{-\\infty}{x} f(\\widetilde{x}) F^{a-1}(\\widetilde{x}) d\\widetilde{x} = \\frac{1}{a} F^a(x) \\qquad {\\rm and} \\qquad \n",
- "\\Int{x}{\\infty} f(\\widetilde{x}) \\left(1 - F(\\widetilde{x})\\right)^{a-1} d\\widetilde{x} = \\frac{1}{a} \\left(1 - F(\\widetilde{x})\\right)^a } $$"
+ "### And repeat ad nauseam.\n",
+ "### Put all results into a binfull Histogram (\"full\" of arbitrarily small bins)."
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Proof:\n",
- "\n",
- "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_3} f(x_2) F(x_2) \\Prod{i=2}{r-1} dx_i $$\n",
- "\n",
- "$$ \\times f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-2}}{\\infty} f(x_{n-1}) \\left(1 - F(x_{n-1})\\right) \\Prod{j=r+1}{n-1} dx_j $$"
+ "binfull Histogram Demo"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
"source": [
- "Integration by parts:\n",
+ "![Linearly Increasing Gaussian Smoothing](easyEndpoint_binfullLinearExpanding_final.png \"Linearly Increasing Gaussian Smoothing\")\n",
"\n",
- "$$ \\Int{-\\infty}{x} f(\\widetilde{x}) F^{a-1}(\\widetilde{x}) d\\widetilde{x} = \\frac{1}{a} F^a(x) \\qquad {\\rm and} \\qquad \n",
- "\\Int{x}{\\infty} f(\\widetilde{x}) \\left(1 - F(\\widetilde{x})\\right)^{a-1} d\\widetilde{x} = \\frac{1}{a} \\left(1 - F(\\widetilde{x})\\right)^a $$"
+ "### Algorithm issues: Speed, choosing $\\sigma$, over/underflow, \"LinearExpanding\" - Kernel depends on \"time\"..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "slide"
}
},
"source": [
- "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\frac{1}{2} \\Int{-\\infty}{x_4} f(x_3) F^2 (x_3) \\Prod{i=3}{r-1} dx_i $$\n",
+ "## 1) New Probability Calculus:\n",
"\n",
- "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\frac{1}{2} \\Int{x_{n-2}}{\\infty} f(x_{n-2}) \\left(1 - F(x_{n-2})\\right)^2 \\Prod{j=r+1}{n-2} dx_j $$"
+ "### $\\qquad$ \"Can't I just calculate that thing?\""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ \\vdots $$\n",
+ "## 2) The debinning Calculation:\n",
"\n",
- "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = n! \\left(\\frac{1}{(r-1)!} F^{r-1}(x_r)\\right) f(x_r) dx_r \\left(\\frac{1}{(n-r)!} \\left(1 - F(x_r)\\right)^{n-r}\\right) $$"
+ "### $\\qquad$ \"Whoa, I can calculate something else!\""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. \\quad {}_\\blacksquare$$"
+ "## 3) The Future, and Shameless Advertising:\n",
+ "\n",
+ "### $\\qquad$ \"Yikes.... There is so much more!\""
]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import sys\n",
- "sys.path[0] = '..'"
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "slide"
}
},
- "outputs": [],
- "prompt_number": 1
+ "source": [
+ "# New Probability Calculus:\n",
+ "\n",
+ "## \"Can't I just calculate that thing?\""
+ ]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\" Presumably, skip slides are for non-output code blocks. \n",
- " Here, just import and define a few functions. \"\"\"\n",
- "from os import listdir as ls\n",
- "from __future__ import division\n",
- "import numpy as np\n",
- "import bisect\n",
- "import utilities.sampleFunctions as funcs\n",
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Datum Probability"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "### What's the probability to get some datum, $x$?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ {\\large P(\\widetilde{x}\\in[x,x+dx]) = f(x) dx \\quad {\\rm and} \\quad \\Int{-\\infty}{\\infty} f(x) dx = 1~.} $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "#### $f(x)$ is the Probability Distribution Function (PDF). \n",
+ "#### Its anti-derivative is the Cumulative Distribution Function (CDF):\n",
+ "\n",
+ "$$ F(x) = \\Int{-\\infty}{x} f(x') dx' = P(\\tilde{x} \\le x)$$\n",
+ "$$ 1 - F(x) = \\Int{x}{\\infty} f(x') dx' = P(\\tilde{x} > x) $$"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Sample Probability"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "### Probability to get a sample of data points, $\\{x_i\\}_{i=1}^n$?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\\begin{align} \n",
+ " dP(\\{x_1\\}) &= \\phantom{3!} \\phantom{\\times!!} f(x_1) dx_1 \\\\\n",
+ " dP(\\{x_1, x_2\\}) &= \\rust{2}\\phantom{!} \\rust{\\times} f(x_1) dx_1 f(x_2) dx_2 \\\\\n",
+ " dP(\\{x_1, x_2, x_3\\}) &= \\rust{3!} \\rust{\\times} f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Order doesn't matter... WLOG, sort:\n",
+ "\\begin{align}\n",
+ " \\{x_1, x_2\\} &\\equiv \\{x_2, x_1\\} \\\\\n",
+ " \\{x_1, x_2, x_3\\} &\\equiv \\{x_2, x_3, x_1\\} \\equiv \\cdots \\\\\n",
+ " \\phantom{dP(\\{x_1, x_2, x_3\\})} &\\phantom{= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}\n",
+ "\\end{align}\n",
+ "\n",
+ "$$ \\Rightarrow\\ {\\rm WLOG}\\ x_j < x_k\\ {\\rm for}\\ j < k\\ {\\rm for\\ all}\\ x_j, x_k \\in \\{x_i\\}_{i=1}^n$$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\\begin{align}\n",
+ " \\therefore dP(\\{x_i\\}_{i=1}^n) &= \\rust{n!} \\Prod{i = 1}{n} f(x_i) dx_i \\\\\n",
+ " \\phantom{dP(\\{x_1, x_2, x_3\\})} &\\phantom{= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Probability Calculus: Integration"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "### The data is all sorted... Careful with those integration limits!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ \\Int{\\{x_1, x_2\\}}{} dP(\\{x_1, x_2\\}) = 2 \\Int{-\\infty}{\\infty} f(x_2) \\left[ \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right] dx_2, $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$\\Int{\\{x_1, x_2, x_3\\}}{} dP(\\{x_1, x_2, x_3\\}) = 3!\\Int{-\\infty}{\\infty} f(x_3) \\left[ \\Int{-\\infty}{x_3} f(x_2) \\left( \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right) dx_2 \\right] dx_3$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$\\vdots$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Limits of inner integrals are *also* integration variables...\n",
+ "### Thus, integrals are \"chained\" together... Chain Integrals."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Probability Calculus: Being $r$th of $n$ ##"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\\begin{align}\n",
+ " \\subNsubR{n}{f}{r} (x_r)\\ dx_r &\\equiv\\ \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_{i=1}^n) \\\\\n",
+ " \\quad = n!\\ f(x_r)\\ dx_r\n",
+ " &\\phantom\\times\\ \\Int{-\\infty}{\\infty} f(x_n) \\Int{-\\infty}{x_n} f(x_{n-1}) \\cdots \\Int{-\\infty}{x_{r+2}} f(x_{r+1}) \\Prod{i=r+1}{n} dx_i \\\\\n",
+ " &\\times\\ \\Int{-\\infty}{\\infty} f(x_1) \\Int{x_1}{\\infty} f(x_2) \\cdots \\Int{x_{r-2}}{\\infty} f(x_{r-1}) \\Prod{i'=1}{r-1} dx_{i'}\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### $\\subNsubR{n}{f}{r}$ Theorem:\n",
+ "\n",
+ "$$ {\\Large \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r}\\ f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Probability Calculus: Being $r$th of $n$ ##"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### $n$ identical siblings: Race! $\\quad$ ... Outcomes? $n!$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Only care about $r$th place. $\\quad$ ... $n!$ is overcounting.\n",
+ "### $\\quad$ ... $(r-1)$ faster... who cares what order...\n",
+ "### $\\quad$ ... $(n-r)$ slower... who cares what order...\n",
+ "\n",
+ "### $$ \\Rightarrow \\subNsubR{n}{K}{r} \\equiv \\frac{n!}{(n-r)!(r-1)!} $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r}\\ f(x_r)\\ F^{r-1}(x_r)\\ \\left(1 - F(x_r)\\right)^{n-r} } $$\n",
+ "\n",
+ "$ {\\Large ({\\rm HW}-1)}$\n",
+ "$${\\large {\\rm Prove\\ the}\\ \\subNsubR{n}{f}{r}\\ {\\rm Theorem\\ by\\ computing\\ the\\ chain\\ integral.} }$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Proof:\n",
+ "\n",
+ "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_2} f(x_1) \\Prod{i=1}{r-1} dx_i $$\n",
+ "\n",
+ "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-1}}{\\infty} f(x_n) \\Prod{j=r+1}{n} dx_j $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_3} f(x_2) F(x_2) \\Prod{i=2}{r-1} dx_i $$\n",
+ "\n",
+ "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-2}}{\\infty} f(x_{n-1}) \\left(1 - F(x_{n-1})\\right) \\Prod{j=r+1}{n-1} dx_j $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Integration by parts:\n",
+ "\n",
+ "$$ \\Int{-\\infty}{x} f(\\widetilde{x}) F^{a-1}(\\widetilde{x}) d\\widetilde{x} = \\frac{1}{a} F^a(x) \\qquad {\\rm and} \\qquad \n",
+ "\\Int{x}{\\infty} f(\\widetilde{x}) \\left(1 - F(\\widetilde{x})\\right)^{a-1} d\\widetilde{x} = \\frac{1}{a} \\left(1 - F(x)\\right)^a $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\frac{1}{2} \\Int{-\\infty}{x_4} f(x_3) F^2 (x_3) \\Prod{i=3}{r-1} dx_i $$\n",
+ "\n",
+ "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\frac{1}{2} \\Int{x_{n-2}}{\\infty} f(x_{n-2}) \\left(1 - F(x_{n-2})\\right)^2 \\Prod{j=r+1}{n-2} dx_j $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ \\cdots\\ = n! \\left(\\frac{1}{(r-1)!} F^{r-1}(x_r)\\right) f(x_r) dx_r \\left(\\frac{1}{(n-r)!} \\left(1 - F(x_r)\\right)^{n-r}\\right) $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. \\quad {}_\\blacksquare$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
"reload(funcs)\n",
+ "def quickData():\n",
+ " ''' Shorthand for getting easyEndpoint data (384 x values in [8.5,200])\n",
+ " - set nPulls before calling\n",
+ " - see utilities.sampleFunctions.functionToData for more details\n",
+ " '''\n",
+ " return funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n",
+ "\n",
+ "\n",
+ "def quickBG():\n",
+ " ''' Shorthand for getting endpointBG data (384 x values in [8.5,200])\n",
+ " - set nPulls before calling\n",
+ " - see utilities.sampleFunctions.functionToData for more details\n",
+ " '''\n",
+ " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "nPulls = 10\n",
+ "pullData = {index:[] for index in xrange(nPulls)}\n",
+ "settings['simpleSortedOutput'] = True\n",
+ "for iteration in xrange(2000):\n",
+ " for i,v in enumerate(quickData()):\n",
+ " pullData[i].append(v)\n",
+ "\n",
+ "settings['simpleSortedOutput'] = False\n",
+ "x, f, F, data = quickData()\n",
+ "bgx, bgf, bgF, bgdata = quickBG()\n",
+ "f /= F[-1]\n",
+ "bgf /= F[-1]\n",
+ "bgF /= bgF[-1]\n",
+ "F /= F[-1]\n",
+ "\n",
+ "ithPDF = {}\n",
+ "for i in xrange(1, nPulls+1):\n",
+ " ithPDF[i-1] = np.array([f[j] * F[j]**(i-1) * (1 - F[j])**(nPulls-i) * pc.nKr(nPulls, i) for j in xrange(len(x))])"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def makeHist(i=0):\n",
+ " fig, axes = plt.subplots(figsize=(9,5), facecolor='#ffffff')\n",
+ " plt.plot(x, f, '--', color='#0088ff', alpha=0.6, linewidth=3)\n",
+ " plt.plot(x, bgf, '-.', color='#0088ff', alpha=0.6, linewidth=3)\n",
+ " plt.hist(pullData[i], bins=np.arange(0, 201, 5), alpha=0.4, color='#66a61e', normed=True)\n",
+ " plt.plot(x, ithPDF[i], '#964a01', linewidth=3)\n",
+ " \n",
+ " axes.set_xticks(np.arange(0, 201, 50))\n",
+ " axes.set_xticks(np.arange(0, 201, 10), minor=True)\n",
+ " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n",
+ " \n",
+ " axes.set_ylim(bottom=-0.0001, top=0.0401)\n",
+ " axes.set_yticks(np.arange(0, 0.04, 0.01))\n",
+ " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.04, 0.01)], fontsize=20)\n",
+ " axes.set_yticks(np.arange(0, 0.04, 0.01/5), minor=True)\n",
+ "\n",
+ " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
+ " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
+ "\n",
+ " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ " axes.minorticks_on()"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{1}(x)$ compared with the histogram of the 1st smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(0)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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48cUX3RYwtU17Vsy37rkW0isVob1SJY5IWjGjJ1nfl+3aBNOlovdERESOON3F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\n+qJr164AgGvXrjnNc+zYMTz66KMIDAyEQqFAz5498emnnzrk69KlC0Q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DBw/mwcHBXCaT\n8dDQUN6rVy8+Z84c/tNPPzXqsxPSkhjnzfxYDiGkzRs7diw2bdqEDz74ALNmzWrt6hBCyB2HAjZC\nSL2OHz+O++67D4GBgcjMzKx3uAdCCCHNg4b1IIQ49cwzz6C8vNw2Ovzrr79OwRohhLQSamEjhDgl\nEokgFosRFRWF2bNn469//WtrV4kQQu5YFLARQgghhHg4GoeNEEIIIcTDUcBGCCGEEOLhKGAjhBBC\nCPFwFLARQgghhHg4CtgIIYQQQjwcBWyEEEIIIR7u/wEDekbHW2M/kQAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181c0eed0>"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{2}(x)$ compared with the histogram of the 2nd smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(1)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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KSkoAALfffju8vLzw8ssv489//jPee+89TJkyBSUlJbjlllscFjCRM+Uc+A/0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\nRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181be8ad0>"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{3}(x)$ compared with the histogram of the 3rd smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(2)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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JrKXw6FbINPplZeSBwfCIiZM4IvtRDxgFxfldAIALhzajsaYMnv6hXdxFRNR/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\nzv1/9nTkgTneT+QAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa18192fe50>"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{4}(x)$ compared with the histogram of the 4th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(3)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
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Ehx56CBs2bED//v1tHkOGDEH//v3b1S5Rl2M2QX/ixnBowLDuvTq0qfhbZ1uf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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181785550>"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{5}(x)$ compared with the histogram of the 5th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(4)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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1+PTTTzF27FgIgoBXXnkFX3zxBXJycnDnnXdi48aNePrpp7sdyJw5cyCKItat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\nIAiCIAgrhwQbQRAEQRCElUOCjSAIgiAIwsohwUYQBEEQBGHlkGAjCII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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa18148c810>"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{6}(x)$ compared with the histogram of the 6th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(5)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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zCGZpWEdgQl8Ep/aXLZa2rWyq8u9ki4OIvFeP1mEbMGAAVq5cCa1Wi5/97GcAgCtXruCn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\nJgwdOtT4vTbvdRJsBEEQBEEQdg7ZsBEEQRAEQdg5JNgIgiAIgiDsHBJ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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa1811e53d0>"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{7}(x)$ compared with the histogram of the 7th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(6)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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BRK7FhI2IaJhaGypRf+k4AEAVEIjkyfLtzRgUlwhBLQ2emC43wtzWKlssROQ6HBKVUUVF\nhc25UspfENHglH2303qcNGEuAoPD+rnbvQS1GkEJI9BZKc1d66wuR0jmWNniIfJFer0eer3eo890\nuofNUfFzGh6dTmfzlZeXJ3dIRDQEZUd7DId6eP6aI5oRHBYlcqe8vDy7n+Hu5nQPm06nw9KlS/HY\nY4+xaLmLlJfbfpCyd43I+4gWC0oVMn+tizYpBc1XjjsqmbARuVpOTg6ys203uHZ30uZ0wmaxWPD2\n22/jnXfewcyZM/HYY4/h/vvvR1BQkDvj82nJyclyh0BEw1RfdALtTdUAAG1ELOJGTZM5ol4LD6qZ\nsBG5mhxTmJweEi0rK8Pzzz+PtLQ0HDx4EA899BBSUlKwatUqFBcXuzNGIiLFKv22ezuPlKk3QlDJ\nv5arZ8JmqKro504i8hZOf7LExcVh1apVuHjxIj766CPcfPPNqKurw+9+9zuMHj0ad9xxBz799FN3\nxkpEpDhKm78GAEFxCRDUagCAsake5o42mSMiouEa9K+CKpUKixcvxo4dO1BQUIAnn3wSERER+Oc/\n/4lbb70VY8aMwYsvvoimpiZ3xEtEpBimznZUnvrKei5XOareBHUAguKTrOed1ZUyRkNErjCsbT1G\njRqF9evX47nnnsPq1avx+9//HhcvXsRTTz2F1atX46GHHsJ///d/IykpaeDGiIgU7uWN69Fm7F7K\nH9BwCWHGTgCAOSQWr2z+s917Dh0+YK1C4EmaJJ11hWhnVTlC0kd5PAYicp1hJWxmsxkffvghXn31\nVezevRsAEB0dje9///vYuXMnXnvtNfz1r3/Fp59+ilmzZrkkYCIiubQZ9TbJV80nJ1B75Thu2lRM\ncZCYff1Nvoeis6VJ5NYeRL5kSLNjKysrsXbtWqSnp+Pee+/F7t27MWnSJPzxj39EWVkZ/vnPf6K0\ntBRPPPEEmpqa8PTTT7s6biIi2bVeOGs9Dh0zQcZI7NmuFOXCAyJvN6gett27d+PVV1/FRx99BJPJ\nBLVajbvuuguPP/44rr32Wpt74+PjsWHDBhw/fhwHDx50ZcxERLKzGAxoL7pgPQ8dpeCEjT1sRF7P\n6YTtqquuwtmz0m+TMTExePjhh/HYY48hNTW13/dlZmZah0uJiHxFe/EFiGYTACAoMRkBEZEyR2Qr\nKCEJEARAFGFsqIXF0AlVkEbusIhoiJxO2M6ePYusrCw8/vjjeOCBB6DVap1634oVKzB//vwhB0hE\npEStBWesx6GjldW7BkhF6IPiEmGorQJEEZ01lQhOyZA7LCIaIqcTti+//BLz5s0b9APmzJmDOXPm\nDPp9RERK1npR2QkbIA2LGmqrAEjDokzYiLyX0wnbxYsXoVKpBky+9u/fj4KCAvz4xz8ednC+rqLC\ndiKwHKUuiGjwLEYD2osuWs9DRo+XMZq+aRKToT9xBADnsRG5kl6vh16vH/hGF3J6lejy5cvxxhtv\nDHjfm2++ieXLlw8rKH+h0+lsvvLy8uQOiYic0F50AaLJCAAIShiBwIgomSNyjCtFidwjLy/P7me4\nuw1rHzZHRFGEKIqubtYnlZfb/sbL3jUi79B6QfnDoQBXihK5S05ODrKzs22uuTtpc3nCVlZWxsTD\nScnJyXKHQERDoOT913rSJIywHhvqqmExGaEKCJQxIiLfIMcUpn4TtnfffReCIFh7zC5cuIBNmzY5\nvNdkMuH06dPYtWsXZs6c6fpIiYgUQJq/1r3/WsgoZc5fAwCVRovAmHgYG2oBiwWGmipok/vfiomI\nlKnfhK33XLS9e/di7969/TaoUqnw1FNPDT8yIiIFai++2GP+WhICI6Nljqh/mqRkKWED0FldzoSN\nyEv1m7D1XOm5adMmjBo1CnPnznV4b1BQEFJSUrBkyRJkZWW5NkoiIoVQ+v5rvWmSdGg5fQwA0FnF\nhQdE3qrfhO2dd96xHm/atAnz5s3D22+/7e6YiIgUq+1ij/lr3pCw9SwCX82FB0TeyulFB4WFhVxM\nQET+zWxCW1GB9TTEGxI2rhQl8glOJ2wZGRluDIOISPnUzeUQjVfmr8Urf/4aIG2e28VQUwnRbJYx\nGiIaqj4TtpKSEgDS1hMBAQHWc2elpaUNLzIiIoUJaCy2HnvDcCgAqINDEBAZDdPlRohmMwx11XKH\nRERD0GfClpGRAUEQcObMGYwdO9Z6PhBRFCEIAsz8LY6IfEzPhM0bhkO7aJJ0MF1uBNBV8YDTW4i8\nTZ8JW1paGgRBQGBgoPXcWc4kdkRE3sRs7ETA5TLreahC64c6oknSofXcSQBd89i8J3YikvSZsBUV\nFfV7TkTkT6rPHYRgMQEAguISERgVI3NEzrNbeBDNhI3I27i8NBU5r6LCdk8kOUpdEJFzKk7ssR6H\nKLgclSM9Fx50VpcDyl8rQaRoer0eer3eo89UefRpZEOn09l85eXlyR0SEfWh4sSX1mNvWXDQxaaH\nrboSuFJukIiGJi8vz+5nuLuxh01G5eW2eyKxd41ImczGTlSf/dp67k3z1wAgIDQc6rAImFuaIRoN\nUHU0yR0SkVfLyclBdna2zTV3J219JmyZmZnDWjxQWFg45Pf6i+Tk5IFvIiLZ1Zw/BFNnOwAgKC4B\ngVGxMkc0eJokHdouNAMAVK11MkdD5N3kmMLUZ8JWXFzc10tERH7FZv6alw2HdpESNqkOqrqlVuZo\niGiw+kzY2ENGRCTx5vlrXXouPGAPG5H36XfjXCIif2c2GlB1Zp/13GsTth4LD9St7GEj8jZcJUpE\n1I+agu75a+bgaARGe9/8NaB3wlYHkStFibwKEzYion5UHN9jPTZFp8sXyDAFhEdCHRIKABDMBrTW\nlw/wDiJSkj6HRJcvXw5BELBu3TokJiZaz5311ltvuSRAIiI5VZzsnr/mzQmbIAjQJOrQduk8AKCx\n5DTC4lJkjoqInNVnwvbuu+8CAFatWoXExETrubOYsBGRtzMbDag63T1/zZsTNuDKStErCVtDyWmk\nTr9J5oiIyFl9JmxvvfUWBEFAUlKS9dxZLP5ORL6gtuAwTJ1tAIDwxEw0aSNljmh4gnqsFG0sOS1j\nJEQ0WH0mbD/5yU/6PSci8nXlPfZf001ZgFIvn6ev7bHwoLH0jIyRENFgsTSVjFj8nUjZKk7kW4+T\nJ18LHL8oXzAu0HOlaGPJaYiiyBERoiHwquLvFRUVOHToEA4dOmSXeJBzWPydSLnMJqPN/LXkyQtk\njMY1AqJioNJoAQCdLY1ob6qROSIi76T44u+iKOKPf/wjNmzYgIsXbX/THDVqFJ544gk89thjLg3Q\nl7H4O5Fy2c5fy0B4gncvOACurBRN0qG9WPr8biw5jZDoRJmjIvI+iir+3pvZbMa9996LDz/8EID0\nD3/EiBEAgMrKSly4cAGPP/44vvjiC2zduhVqtdo9EfsQFn8nUq6e9UOTJ18rWxyupklM7k7YSk9D\nl7VQ5oiIvI8cU5icHhJ9+eWX8eGHH0Kn0+Gtt95Ce3s7ysrKUFZWhvb2drz99ttISUnB9u3b8dJL\nL7kzZiIit7Odv+b9w6Fdes5ja+BKUSKv4XTC9tZbb0Gr1WL37t34yU9+gqCgIOtrQUFBeOihh7B7\n925oNBruwUZEXs1sMqLSx+avddEk9lwpelbGSIhoMJxO2C5cuICFCxdi9OjRfd4zatQoLFy4EIWF\nhS4JjohIDrUXjsDU0QoACE9IR0RihrwBuVDvlaJE5B2cTtgiIyMREREx4H3h4eFO3eeIyWRCbm4u\nsrKysHDhQsyYMQPPPvsszGazW9qorq5GdnY2brzxRmRlZWHGjBnYuHEjLBaLW2IjIu/Qs36oL81f\nA4DAmDiIKmn6cntTNTqa62WOiIic4fSigxtvvBH5+fkwGAw2w6E9GQwGfP3117juuuuGFMzKlSux\nc+dOHDx4EHFxcairq8Ps2bNRUFDgdGksZ9uora3FXXfdhddeew1ZWVkApHJcK1aswI4dO/Dxxx9D\npVINul0i8n6+On8NAASVCubQOAToqwBIG+iOmDhP5qiIaCBO97D95je/QVtbGx588EHU1dXZvV5f\nX48f//jHaG9vx/PPPz/oQPbt24c33ngDzzzzDOLi4gAAcXFxWLVqFTZv3oy9e/e6tI3nnnsOOTk5\n1mQNAB566CHcd9992LFjB15//XWXxkZE3sFsMqLqjG/OX+tiCY2zHnNYlMg79JmwrV27Fv/zP/9j\n/dq8eTMWL16MLVu2IDMzE3fffTdycnKQk5ODu+++G+np6fjggw9w2223YfPmzYMO5J133gEALFmy\nxOb6HXfcYfO6q9rYtWsXli9fjl27djm894MPPnBpbETkHeouHIWxvQUAEBafhnAfmr/WxdwzYWOJ\nKiKv0OeQ6Nq1a/t8U2trq3U/tt42b94MQRCwevXqQQWSn5+P2NhYJCQk2FxPTExEdHS0U71Yg2lj\n/PjxOH36NBobG23ujY2NBSDNb3NlbESkPC9vXI82o215GU3RPgRfOW4IiMJvX1pjfe3Q4QOYu3ic\nx+JzF0tovPWYCRuRd+gzYRtswtXTYGvTmUwmXLp0qc8VqHFxcSguLnZpG3/7299QW1uLxETbXb67\n7ulqxxWxEZEytRn1dglY8R8/QsuV44xrZyP6e92vf/1NPnxBzx427sVG5B36TNjWrFnjsSCamppg\nNpsRHBzs8HWtVguDwYC2tjaEhIS4pA2VSmWXrAHAX//6VwDAww8/7LLYiMg7iGYz2grPW89DR0+Q\nMRr3sQTHQBUQCIvJiNa6MhjamhEUMrTV/UTkGYOqJeouHR0dAICAAMfhdK3WvHz5cp9JkSva2Ldv\nH/bs2YP77rvPOj/NFe32paKiYsB75Ch/QeSv2suKYOmU/s0HRsUiMDZ+gHd4KZUKkbqxaCw+BQBo\nLDmDxPGzZQ6KSJn0ej30ev3AN7qZIhK2qKiofl9vaZEGKLRardvaaG1txfLly3HzzTdj06ZNLo2t\nL84Uis3NzfVobyeRP2u70D2fK2TMhEFP7/AmMalXdSdspaeZsBH1IS8vr995/Z4y6IStvb0du3fv\nRkFBAZqbmyGKosP7BjMHLiwsDMHBwQ43rAWkZEqtVve7Ie9w2hBFEQ899BCmTZuG9957z6Y3zRWx\n9aW8vHzAe9i7RuQ5rQXdCVvoqPEyRuJ+0Wndw71ceEDUt5ycHGRnZw94nzOdMMMxqIRty5YtePTR\nR9HQ0NDvfUNZJZqZmWm3YhMALBYLmpqakJmZCbVa7ZY2nn76acTHx+O1116zXmtvb7fOW3NFbI4k\nJycP+j1E5B6i2YS2wnPW89AxV8kYjftFp3X/+RpLmLAR9UUpU5Oc3jj3m2++wdKlS6HX67F06VJM\nnjwZAPDMM8/gnnvuQWRkJABgxYoVQ1phesstt6CoqMg6xNiloKAAHR0dmD9/vlva+MMf/gCTyWST\nrHX9OVwZGxEpW3upn8xfuyI6tTth40pRIuVzOmFbv349zGYztm7divfeew/Tpk2DIAh47rnn8MEH\nH+D8+fO47bbbsGPHDjz66KODDmTJkiUQRRHbtm2zub5lyxYAwLJly2yu79q1C9u3bx9WGx9//DFK\nSkrw0ksv2Vyvra2FRqMZcrtE5H1aC7qTFl+fvwYAUboxEK4smtLXFMF4pdg9ESmT0wnbvn37MGnS\nJNx+++3Waz3nr8XHx+Mvf/kLOjo6htTDNm/ePNx6661YvXo1KisrAQAlJSV45ZVXsGzZMixY0F0e\npqmpCYsWLcKdd96Js2fPDqmNw4cP44EHHsD27dsxfvx4m68pU6Zg/PjxQ2qXiLxTa48FB74+HAoA\n6kANIkZc2V9SFNFUdq7/NxCRrJyew1ZXV4d587oLBHdNzO851ys8PBzXXHMNPv300yEFs3XrVqxe\nvRo33XQToqKiUFdXhxUrVtitzoiIiMCcOXNQX19vN8nP2TaWL1+OtrY2nD9/Ho6MG2e7maaz7RKR\n95Hmr/n+/mu9xaRdhcvl0p+7sfQM4kdPlzkiIuqL0wlbdHQ0Ojs7redd212UlZVhzJgx1uuCIKCm\npmZIwWg0Grzwwgt44YUX+r1PpVIhP9/xjuPOtnHixAm3xEZE3qe9pBCiQfp8C4yJR5CPz1/rEp06\nAZf2S2XFILEnAAAgAElEQVQGG0pOyRwNEfXH6SHR1NRUlJSUWM8nTZoEQJoH1qW1tRX79u1z+9JW\nIiJXstnOY7Rvb+fRU8+Vog1FTNiIlMzpHraFCxfipZdeQm1tLeLj43H77bcjODgYv/rVr1BVVYWU\nlBRs2rQJtbW1uOuuu9wZMxGRS9kkbH4wf61LbMZk63FD8eBGHYjIs5zuYbvnnnuwYMECHD16FIBU\n9PzFF1+EwWDA+vXr8Ytf/AJHjx5FamoqfvOb37gtYCIiV7KYjGi71D1/LcRP5q8BQFTKeKjU0u/t\n+uoiGNrkL79DRI453cM2e/Zs7Ny50+baT3/6U0yfPh1bt25FQ0MDJkyYgOXLlw9YzomISCnaiwsh\nGg0AgMDYBATFxMkckeeoA4MQlTIeDcUnAQANxSeRNOH7MkdFRI4Mu5bozJkzMXPmTFfEQkTkca0X\nuvdfCx3jP71rXWIyJlsTtvqi40zYiBRKEcXf/VVFRYXNuVLKXxD5kzabBQf+l7DFZkzChSuL7huK\nOI+NyBl6vR56vWenEAw6Yevs7MTWrVuRn5+PsrIyAFLB02uvvRY/+MEPbCoEUP96r6bNzc3FmjVr\n5AmGyB+ZTWgrKrCe+tOCgy6xGVOsx/VFJ2WMhMh75OXleXwf1kElbPv27cMDDzyA0tJSu9feeOMN\nrFq1Cu+99x5razqpvLzc5py9a0SepW4uh2g0AgCC4pMQGBUjc0SeF9NzpWjRCYii6PNluYiGKycn\nB9nZ2TbX3L2lmdMJ26lTp3DzzTejra0NI0eOxNKlS5Geng4AKCoqwvvvv4/CwkLccsst+OabbzBx\n4kS3Be0rkpOT5Q6ByK8FNBZZj/1xOBQAwuJTERQaCUPrZXS2NKK1vhxhcSlyh0WkaHJMYXI6YVu9\nejXa2tqwatUqPPvss1CpbHcEWbt2LXJzc/H8889j9erV2Lp1q8uDJSJypcCGYuuxPy44AKTqNDHp\nk1B1eh8AoL7oBBM2IgVyeh+2PXv2YOzYsXj++eftkjUAUKvV+M1vfoOxY8f2WTaKiEgpTJ3tUF8u\ns5770/5rvcX2GhYlIuVxOmFrb2/HjBkz+r1HEARMnz4d7e3tww6MiMidqs8egCCaAQBBCSMQGBkt\nc0TysZ3HxoUHRErkdMI2btw4VFZWDnhfVVWVTTF4IiIlKj++23rsj6tDe+rZw1ZfdFzGSIioL07P\nYfvZz36GlStXYu/evZg3b57De/bt24cvv/wSr7zyissCJCJyB5uEzc+GQw8c2I91G3Kt54KxA5FX\njuuKTmJd3q8BldrmPSGB4Xji5095MEoi6snphC07OxtnzpzBokWLsHLlSjz44IPIzMwEAFy6dAnv\nvfceXn31VTzxxBP42c9+5raAiYiGy9DWjOqzB6znoWP9q4fNIhgwd/E4m2vnj8fC2FgPQbRgxqwI\naEfYLjzY9/E5T4ZIRL30mbCpVCq7vXhEUQQArF+/Hnl5eQ5f27BhA1566SWYzWZXx0pE5BIVJ7+E\naJE+o7S6NASERcgckfw0I1JhbKwHAHRWltolbEQkr37nsImiaPM1mNeIiJSq7Lud1uPQsZNkjEQ5\ntMmp1uOO8hIZIyEiR/rsYbNYLJ6Mg4jIY8q+22U9Dh3HTb4BqYetS0dlWT93EpEcnF4lSkTkC1ob\nKtFYfAoAIAoqhI4cN8A7/EPPHrbOSvvyg0Qkr0EXfyfXqaiosDmXo9QFkb8pP/Z/1mNzZCpUGq2M\n0SiHJnEEBLUaotkMY0MdzB1tUGtD5A6LSJH0ej30er1HnznohM1gMGDLli3Iz8+3Fi/X6XS49tpr\ncc899yAwMNDlQfqq3oVic3NzsWbNGnmCIfITPYdDjTGZMkaiLII6AEEJydbetc7KMoRkjpU5KiJl\nysvLw9q1az36zEElbIcPH8a9996L4uJiu9f+/Oc/47/+67/w97//fcCKCCTpSni7sHeNyL1EUbRZ\ncGCKZcLWkzY51ZqwdZSXMGEj6kNOTg6ys7NtrvXuhHE1pxO2srIyLFq0CA0NDUhLS8OPfvQj6z5s\nhYWFeO+991BUVISbb74Zx44dc3vgviA5OVnuEIj8SlP5ebTWSRPqg0IiYA7nv8GetCnpuHzkawBA\nR5n9L+ZEJJFjCpPTCdtvf/tbNDQ04PHHH8f69evthj7Xrl2L//iP/8DLL7+MdevWYePGjS4Ploho\nOMp79K4lT1mIGhXXXfWk1aVbjzvKmbARKYnTn1Y7duxAZmYmNmzY4HCeWmBgINavX4/MzEzs2LHD\npUESEblCz/lrKVOvlzESZbJJ2CpLIXIDdCLFcDphq6iowOzZs6Hq5zdStVqNWbNm2a1+JCKSm8Vs\nsqkfmjL1BhmjUaaAsHAERMUAAESjEZ3V/CwnUgqnEzatVouGhoYB72toaIBWy2XyRKQstQVHYGi9\nDAAIjdUhKoX7rzkSnMJhUSIlcjphy8rKwp49e3DmzJk+7zl37hzy8/MxZcoUlwRHROQqZd99YT1O\nmXqDXa1kkmh1GdZjLjwgUg6nE7Z/+7d/g8FgwPXXX48333wTBoPB+prBYMBbb72F6667DgaDAY88\n8ohbgiUiGqqSI59Zj1OmcTi0L1pdmvWYPWxEyuF0wvbggw9i6dKlqKqqwiOPPILQ0FCkpaUhPT0d\noaGhePjhh1FZWYmlS5fiwQcfdGfMRESD0qlvRPXZ/dKJICB1+k3yBqRg2pQM63FHeTFEUZQvGCKy\ncjphEwQB//u//4uNGzciMzMTZrMZZWVlKC0thdlsxsiRI7Fx40a899577oyXiGjQyr7bCdFiAQAk\njLkawZHxMkekXIExcVAFSyWpzG2tMDbWyxwREQGDrHQgCAJWrlyJlStXoqyszLpTf0pKCjfKJSLF\nKjnyqfU4dcYiGSNRPkEQoNWlo+2CNF+5o6wIQTFxMkdFRE73sEVHR2P+/PnW85SUFMyePRuzZ89m\nskZEiiWKIkqPds9fS2PCNiCuFCVSHqd72AwGA9LS0ga+kZzWe786OUpdEPm6huKTaK2X/q1pwqKR\nMHamzBEpn80GulwpSmRHr9dDr9d79JlO97CNHj0adXV17ozF7+h0OpuvvLw8uUMi8jk9h0NTpt0I\nlXpQM0H8Us+FB+1lRbLFQaRUeXl5dj/D3c3pT65ly5bh17/+NQoLCzFy5Eh3xuQ3uuYAdmHvGpHr\nlRzuTtjSZtwsYyTeQ5OYDCEwEKLRCFNTA0zNl+UOiUhRcnJykJ2dbXPN3Umb0wnbL3/5S3z11Ve4\n/vrrsW7dOtx1113QaDTujM3nJScnyx0CkU8ztOlRdXqv9ZwLDpwjqNXQ6jLQXlQAAGgvLQQQIm9Q\nRAoixxQmpxO20aNHQxRFlJSU4IEHHoAgCEhISEBwcLDD+wsLC10WJBHRUJQf3w2LyQgAiM3MQmjM\nCJkj8h7BaZndCVvJJQAT5Q2IyM85nbAVF9tOPBVFEdXV1S4PiIjIVUqPcDh0qILTuqe+tJdeAkYw\nYSOSk9MJ26VLlwCAu14TkSK9vHE92ow9Vm2JIsL3vQ/1ldOvCiuxe0OuzXsOHT6AuYtZBN6R4NRM\n63FHSSGQxM9+IjkNmLA1Njbis88+Q0lJCTQaDaZOnYoFCxZ4IjYiIqe1GfU2yVdndQUu7GoCAKg0\nWsz80fVQBdh+5H39Tb5HYxwOUQSaDUGobgtFVVsoatpCccfIAgSpLW55XlDCCKg0Wlg6O2DSX4bQ\n6dktDIjIVr8J29/+9jf89Kc/RXNzs/WaIAiYOnUqPvzwQ6Smpro9QCKiodCf+tZ6HDp2ol2y5k12\nFGWisDkK7SbbP0Ntewh0YS1ueaagUkGbkoG2i2cBAAHNFQO8g4jcqc992I4dO4Zly5ahubkZISEh\nmDp1qnU7j2+//RZ33323x4IkIhos/cmj1uPwSdNljGRgBrMKpfpwtBodJ5Ud5gC7ZA0AqttC3RpX\nz3ls6uZKtz6LiPrX56+cL774IkwmE370ox/htddeQ1hYGADgu+++w913340jR45gz549uPbaaz0V\nKxGRU0yterQVnpdOBAHhE6fKG1AvjR0alLZEoLI1FJVtYahvD4YI4Oa0Sw7vTwppxcXLUdCqzUgM\nabV+Oepdq2kLhkUUkBTaNuw4g9O657Gp2cNGJKs+E7Yvv/wSSUlJ+POf/wytVmu9PnXqVLz00ku4\n88478dVXXzFhIyLFaTl9TJr0BSA4YzQCwiNljsjW8foEHKpOsrte2Rbm8P7JcbWYEFOPyKBOCELf\n7da1B+PvF8bDIgr4wahzSA5rHVac2h4LD9T6SoiiCKG/AIjIbfocEq2qqsKsWbNskrUuXUXge9fC\nJCJSArmGQy0iUN0WgqM1Cfj40iiHSRkAjAix7RkTAMQFtyM80ODw/rBAI6I0/Sdrogj889IotJsC\n0GlWY8uF8SjTD29jz6C4RKiCpQ1zVcZ26KuLhtUeEQ1dnz1snZ2diImJcfhadHS09R4iIiWxmIxo\nOXPceu6JhK2qNQRfVaSiojUMRkv378FtxkCH948IbcHYqEYkhbRiRGgLEkNaras99zp8x8AEAbg1\n4yK2XBiPNlMADBYVtlwci7tGFiA9onngBhy2KSA4dSRaz58EANQUHEJEUuYA7yIid/DeZVM+oHcP\npRylLoh8TVvBGVg6OwAAQXEJ0CS6pgScKAImlePKLmqViGJ9hN31ytYwWKw7wXULDzLijpEXXBJX\nTwkh7bh/zBl8cGE8Wo2BMFlU2FY4Bg9PPI6wQOOQ2gxOy7QmbNVnD2D0/PtcGTKRV9Lr9dDrPbvV\nTb8JW1VVFb788ku7612b5/b1OgBcc801LgjPt/UuFJubm4s1a9bIEwyRj2juNRw61DlXogg0dGpR\npg9HWUs4SlsicD5JuDKPy/beOG07NGozOs1qRAQZkBzaguRQPXRhLXgX5uH8cQYtNrgD9485i78X\njIPeGISFupIhJ2sAEJI5xnpcffaAK0Ik8np5eXlYu3atR5/Zb8L26aef4tNPP3X6dUEQrJNSzWbP\nfkh5o/Lycptz9q4RDY8oimg52b3/2lCHQ00WAW+emgK9Mcj2ujoUlw3SfLKeBAG4c2QBojQdCA+y\nTY7kmKIfo+3A/WPPolQfjslxdcNqKzhjtPW49sJRmI2dUAdqhhsikVfLyclBdna2zbXenTCu1mfC\nlpaWNuRGuYrIOcnJrhmqISJJR3kJjE31AAB1SChCRo7t815RBNoD42GyCAhQ2ZZdClCJCAk02SVs\nKosBTZ1au4QNAFLDlVUJIErT6TDOwQoIi0BQXCIMddWwmAyovXAUSRO+74IIibyXHFOY+kzYioqK\nPBgGEdHw9VwdGjYhC4K6+yNOFIGmTg2K9ZEo0UegRB+BgqQwlLWokOFgUn5KWDMud2qgC9MjNawZ\nKWF6bPrHH5AR8YhH/izuZBaCBr6ph+CM0TDUVQOQhkWZsBF5HhcdEJHPsNnOY7LtcOjnJRk4UR9v\n955SfYTDhG3uiHIs0JVC1WPAQID3F0CvaQvBueR/w8n6aEyKdW64NCRjNC4f3geA89iI5NLnPmxy\nMJlMyM3NRVZWFhYuXIgZM2bg2WefHdR8uMG20dnZid27d+O2227Dc88959bYiMh9hPYmdJRKlQIE\ntRph46fYvB4fbL/zf4C5HSrBcRIWpLbYJGu+QNpYdxxMqmB8WpyJY3X2CawjwT0WHlSd3e+u8Iio\nH4rqYVu5ciV27tyJgwcPIi4uDnV1dZg9ezYKCgrw7rvvurSNmpoaPPjggwgNDUVSUhJ27NiB2bNn\nuzU2InItUQSKm4FTdUBZdSe66hmEjp0I9ZUNX7ukRzQjSGVBangz0sObkRbejLf+8RrmJmfbN+yj\nQgKNNpvzflGSAYsoYFp8Tb/v045IhagOhGA2orWuDC11ZQiLS3F3uETUg2J62Pbt24c33ngDzzzz\nDOLi4gAAcXFxWLVqFTZv3oy9ewfeTnIwbSQkJODzzz/Htm3b8MMf/tDtsRGRaxVdBp7eDazbD2wv\nAOJquofqwrNm2d0fo+nAY1lHcdeoAkxPqEZccLssKzjlFBJgwn1jziLEUGW9tqs0HYerE/t9n6BW\nwxTRvUiKw6JEnqeYhO2dd94BACxZssTm+h133GHzujva6NpXzp2xEdHQ9PXPMyEEaL2yg0ZgSzkS\nm6XqBqKgRuAE+4RNEAB1H8Of/kQbYEZmzRYkh0rlsYQr1wZijuzuUavmsCiRxykmYcvPz0dsbCwS\nEhJsricmJiI6OtqpXixXtOHJdonIsVYD8E0F8OYx4Jl8wOAgnwgJBEZGAeFBQFbdNuv1sDHjER4V\nYv8GslKLBvxg9DmkhulxY1qRU4sPTD0Stqoz7GEj8jRFzGEzmUy4dOkSRo8e7fD1uLg4FBcXu70N\nT7ZLRPbyS4BDlcDFJqmQepfzDcAkB/PjH50KhAUB2z/fiq5CbxEOhkPJnkZtwb1jzjq9sMIc2b0p\naO2FwzB1tiNA47hUFxG5niJ62JqammA2mxEc7Pgfv1arhcFgQFub/SovV7bhyXaJyN6ZeqCg0TZZ\nA6SEzZFwDdDeVI2Kk1dK5AkCIqZc7d4gfchgVsGKQaGITp0AALCYjJzHRuRhikjYOjqkQs0BAY47\n/FQqKczLly+7tQ1PtkvkjzpNwLfVwMVGx69nXZl1IAjAqGjgzjHAr+cAd/VdsACX9m+zTnQLGTUO\nARGRfd9MTqlsDcVX5Sl28wdHTJpvPa445biONBG5hyKGRKOiovp9vaVFmhyr1Wrd2oYn2wWAioqK\nAe+Ro/wFkSu1GoBjNcDRaqkHzWQBrk6SErLepsQDP54ETI4HIpwsV1mQ/771mMOhw1fVGoItF8ah\n06yG0aLCwpQSa7H75EkLcHrHnwAAFSeYsJF/0Ov10OvlLz2niIQtLCwMwcHBsFgsDl9vbW2FWq1G\nRESEW9vwZLuAc4Vic3NzsWbNmkG3TaQE5xuADYfshzhP1kmJW0CvPv7QIGDuILb3aqkrQ+WprwAA\nIgRETu17L0VyzrG6BHSa1QCAo7WJsEDA9SnSPN2ePWzVZ/fDbDRAHTi4MldE3iYvLw9r166VOwxl\nJGwAkJmZicZG+3ESi8WCpqYmZGZmQq1Wu70NT7ZbXl4+4D3sXSNvlh4BqFWApccqz5RwaejTUcI2\nWBe+/Jt1ONQUk8nhUBe4Ia0YBosa5xpjAADf1SZAFAUEi+cQFpeCiKSRaK4qhNnQgdqCw0i6ao7M\nERO5V05ODrKzB95g25lOmOFQTMJ2yy234MUXX0RLSwvCwsKs1wsKCtDR0YH58+f3827XteHJdpOT\nkwe+iUjB6tulOWnHaoCfTwc0vT5RNAHApDigqROYkQhMSwTiXLjjRsGev1qPjUkTXdewH1MLIm7L\nuAgVRJxpjAUAHK+Lx1hIY9jJk69Bc1UhAKDiZD4TNvJ5SpmapIhFB4C0Ka0oiti2bZvN9S1btgAA\nli1bZnN9165d2L59+7DacFdsRL6suRPYXQz87hvgV/nA389KQ58n+9jK65EsYNX3gBszXZusNZad\nQ91Fqdi7KiAIxvjxrmvcz6kE4JaMQkyIqYcA6ThGkEYZRky8xnpfxcmvZIqQyP8oJmGbN28ebr31\nVqxevRqVlZUAgJKSErzyyitYtmwZFixYYL23qakJixYtwp133omzZ88OqY2euoYmu94znNiIfN37\nZ6Sv3is9j1Y5vl/tpk+ZC/ndvWvpM2+DGDj4hT/UN5UA3JJeiPvHnMVVMfXW68mTuz/vqk7vhcVs\nkiM8Ir+jmCFRANi6dStWr16Nm266CVFRUairq8OKFSvsJvtFRERgzpw5qK+vtxszdrYNAJg5cybq\n6upQXFwMQRDw+uuvY9u2bdDpdHjjjTcwbdq0IbVL5MuuTgKOXEnOVAIwIRaYkdS9JYcniKJoszp0\nzIIf4tvDJz0XgJ9QCUBKuLQ67sCB/Vi3IRcQRURoIqDqbIaxvQXrn/0ZzBH20ztCAsPxxM+f8nTI\nRD5LUQmbRqPBCy+8gBdeeKHf+1QqFfLz84fVBgAcOnTI5bEReTOLCJytBw5USD+sfzLZ/p7J8VLV\ngawEYFqCtHmtp1Wf+waXy88DAAKDw5A+63aACZtbWQQD5i4eBwAoa5qEy0e+BgCMTmpF3PXj7O7f\n9/E5j8ZH5OsUlbARkTwqW4D95cA3lUCTtFc0AtXADycA2l6fEoFq4PEZno+xp3M737Eej5p3L0sk\neZghbTpwJWFrOXsScdffLnNERL5PMXPYiEgenSbg+f3AZ5e6kzUAMJqB0wPXBPc4U2e7tJ3HFeNu\n+Il8wfihpk4Nvgi423quv3gexk6jjBER+QcmbER+ThMgbbfRJTwIuD4d+K85tteV4tKBj2BolUrB\nRSSNxIiJ82SOyL9EBnVidHogWiJHAgBUZgP2fN0Mk2UQhUmJaNA4JErkByr0wN4yYGIcMDHe/vW5\nOmkj2+8lS/e4a2WnK5zb+a71eNwND0EQmCh4kiAA16UU4/CoacBRaT+2joJj+CT9ESzOvAh+O4jc\ngwkbkY/qNAGHq4B95d1bcNS0OU7YxsVKX0rXUleOsu++sJ6Pu/7HMkbjvwQBGDc9HaXSNniIq/ga\nsdE/YLJG5EZM2Ih8UNFlqYZnR68tsk7VAY0dQLSXbll2bte7EK/U9dVlXYfwhHSZI/JfoWMmACo1\nYDEjovEsRqqLALA0GJG7MGGTUUVFhc25UspfkPfThQHqHr0dahUwNQGYlwJEybANhytYzGac+ewN\n6/l4LjaQlVobjJDM0Wi7KG3f0XL+JKKunitzVESeodfrodfrPfpMBc9U8X06nc7mKy8vT+6QyMuU\nNEurOXsLVAOzk4GkUOCeccALC4DsqcBVcfDaYavSbz+HvroIAKAJj8HIeffIGxAhdNwk63HrOe6D\nR/4jLy/P7me4u7GHTUZdJbG6sHeNnGE0S5UG9pQCl5qkzW2/7+Cz4q6xwH3jvTdB6+30jj9Zj8ff\n8BACgrx0XNeHhI2bjNpPtgIAWs6egGixQFBJ/QB1YixePQo8nAUEqeWMksj1cnJykJ2dbXPN3Ukb\nEzYZJSfbl3Mh6ktjB7CnRFrt2WLovr6nxHHC5ks/JFvqylB88GPr+YRF2f3cTZ4SnDYS6pAwmNta\nYGpuQkdZEYLTRqJMH46vzaPQUgNsPAI8Nl3aPobIV8gxhYlDokReorQZ+LTQNlkLUAGJoY6HRX3J\nmc/esC42SJ6yENEp9qWQyPMElQphE6daz/UnpWWjlW2hMEP6jeFcA7DxqLRqmYiGjgkbkZeYFA/E\nhUjHMcHSkOdvFwArpkhz1nyV2WTEmc/etJ5PvPWnMkZDvYVPmm497krYZiZWYaLqjPX6+QbglSP2\nq5aJyHnspCZSkIZ2IL8UuDkTCAm0fU0lAD8YK634nBwvnfuDwn1b0VovzfcMjkpA5vfulDki6ils\n/GQI6gCIZhM6yktgaKhDUEwcxqou4OpxwJYrNeALL0uLZMbGyBsvkbdiwkakAIVNwK4i4Gg1YBGB\nsEDgxkz7+6YneTw0Wby8cT3ajHpAFBF26C3rB1Vj9Hj8buNzDt9z6PABzF3MoVJPU2uDETpmAlrO\nngAA6E99i9j5NwKQ/h8WBOAf54GfTmWyRjQcTNiIZHSxUeqBKGyyvf5/JcD1Gf7Ti9Zbm1GPuYvH\noe1SAS7tkvYrFNQByFpxPwIiHG/O+vU3+Z4MkXoInzS9O2E7edSasAHADRnSHoBdw/lENDScw0Yk\ns97J2vhYYOkEwE9zNRv1e3ZYjyOvntNnskby6jmPra3gNMwdbTavM1kjGj72sBHJaGQUkBklze2Z\nNQK4IR1IiZA7KmUwNNSh+dgh63nsgptljIb6ExgdC21KOjrKiiGazWg5cxxA9IDvK2gAksOA0CD3\nx0jk7ZiwEblZfTvwxSVg0Uggqtder4IAPHgVEK4BIr20ZJS7NOR/CogiACB0zFXQ6lg3VMnCJ81A\nR1kxAKD522+A+EX93n+mDvjDt8CIUOAXVzNpIxoIh0SJ3KRcD7x1HPj1l8DuEmBXseP7UiKYrPUm\nGNrQ8PVu63nswltkjIacETlttvVYf/o7wNTZ573NncCr30r7B5Y0AxsOA62GPm8nIrCHTVYs/u6b\nKluAreeAE7W2178sBW4dCQQHOn4fddOUfAPRIP3A1+rSEHbV1AHeQXLTJOmg1aWho7wEotGIwNpz\nfd4boZHmaW46JXWill5J2n5xNRDGnjbyAiz+7mdY/N13nayzPZ8QCzw6FdDyV6QBdbZehqase+5a\n3I13QPCVgqg+LmLa96zHQVWn+r13Tgrw0KTuWrelzVJFhCuj4ESKxuLvfobF333TiDBpG4PvaoBp\nidImuBlc3Oi0U/96FcKV4bSghCREZM2SOSJyVuT076Hmnx8AAAIaCtHRXA9tRGyf93fVwH33JKAW\ngNtHdSdwRErG4u9+hsXfvZcoSkOeI8KAeAdbFtw1VvpKDPV8bN7M0KbHsW0brOdx1y+GoOJAgLcI\nik1AcMZotBddgCBaUPj1P3DVokf6fc/3ddIWNmFBUvk1Im/A4u9ECieKwLEa4Pn9wB+OAv+66Pi+\nxFAma0NxYvvL6GiWxpMDo2MRNXOuzBHRYEX2GBYtyH/fqfd8T8dkjWggTNiInCCKwLfVwHP7gVeP\nSivbAOCbCqCmVd7YfEVHcz2+27reeh6/6G4Iag4CeJuIabOt45oVx3ejuerSsNqzcE4bEQAmbERO\naeoE/nxMmhjdJVANLEwDgplTuMS3W16AoU36CzaHxCJq5jyZI6KhCIyMRtj4KdbzM5+/OeS2TtQC\n6/ZL24AQ+TsmbEROiNYC81Ok4yA1cGMG8Pw1wH0TpE1vaXha6ytw4uON1vOOUddCUKtljIiGI/r7\n11qPz+18BxazadBtnKwF/vjtlX3aDjFpI2LCRtSL2eL4+q2jgJsypUTtnvHSXlLeQBSBThPQ1AFU\ntWAZlTsAACAASURBVDi+54tLjrdTePMY8Nq3wP87DJgc/L387hvH1397APiffcCzX0vP7u2VI7bX\nD27+b5gNHQAAtW46jsbdDYPZ/uOpoCkKJov9MkKDWQWOnClH+KRpsARJkzhb6ytQfOiTQbfRbuoe\nDq1oAV5k0kZ+jgkb0RUVeuD176QvRyI1wA/GydujZrJIiVdZs/1rFlFKsBwlXk/sAv5zD5C71/Gc\noI8uOE68vq0BvqsGTtU5TmRLmx1fL9dLX6UO4gSA8w3dxzUFh3F25zvdr139PC6IYxwmYJ8Vj4TR\nYv+x9aeTU3Ei9Um8/N0MtJvse+a+LE9Bp9n+ekdADPSGQBgtKu7/5UKCOgCG5O7Njs989sag25g5\nAvi3KYDqSn5e2QLkHQQuM2kjP8WEjfxefTvw9nHgf74GjlZJq0ALm+SLRxSlqgi9EwiLCDz+hZR4\n/eZrqaxPTypB2vvN0Ou6IADaHrlKh4MerwABMDpIvAJ7fEI4SvRUguPrYq97HL2uEgBRFLH3j09Y\n/7DNmbdDn3YTAEAt2DYsikCnWY1AlX2ghitJnNGicvj60dpECA5SwIuJD+D1k1Px8ncz0OEgodtf\nmeywp89RLx/Z6pmwlRz+BC11ZYNu4+oRwMNZ3f8P1XdwkQ/5L06XJr/28QXgs0v2yc/ZemBklPue\n+8UloLZdShZ/Ng0I6JETCAKw7TwwI9G2ILZKAMKDunsYWoxAdK8cIywI0BsATa9/2ZEaae6dNsBx\nYnZ9huPE6seTpP8GqqT395Yzy/5ZAPBf35d63kTY/tm6PDFDul6w5y+oPrtf+vMFBOLq5XmYFQcY\nT52CWrCt4SUCGB9djwCVbeJlsgjW5E4liHaJnskiwCIKdomcRQTMKukvWACgVdv+TyCKwP6qZMxM\nrLS7vvHYDKhVFoQGGvHguFMIUtu2XdkaisSQVod/p/7CEhIDXdb1KD+2C6LFglP/eg2zH3pu0O3M\nSJL+u+mkVC1kTIyLAyXyEkzYyK+ZLbbJ2qR4YMkYIC3CNe1vPgncO96+JNWuYqBRmrKFhnYgodee\nbVEaaWVqaK+6ijHBUuISHmSfZALAg1c5rsW4dn7/cS4e7fj6tMT+39fX39OIsP7fNyZGKkF14O3/\ntF6bsuQX+P6MMQCAA6pCCMI4m/eoBOC2zEK7tgJUIp6YegS/2/In/PzhRx3ulH9DarHddaNFDa2x\nHqGBRgD2O+x3mNUIUlnsEkSDRQWTKMBkVsPsoEfPLAr46/kJ+MXUwzbXRRH4vCQDYYFGhAUZMDm2\n1ucTukm3/Qzlx3YBAE598kdMv+8ZBAYP8D+HAzOSgPEx9v8eiPwJEzbyazdnAl+VSdUKfjB28L+9\n7y8HLl2W5tf8ZDIQG2z7enEzUN0KpPcqTRUX3J2w1TtI2Oam2A5HdvnP2f2X7pnoRZuPHnhnFVrr\nKwAAIdFJmPHDXw+rPQGw6+kCpIRuSlyt3XWN2oyxVe/iZ5MdT0pUCcC8ZPthvA5TAARIiXNYkMHu\n+9FmDEBIgMkuGWs3B+BEvfQNClJZMCXWNiaTRcAnRSPtBm67hsa9sWRTxveWIDJ5NC5XXEBnSyPO\nfP4mpix5YkhtMVkjf8eETUYVFRU253KUuvAXxZel3qDeP/SCA4FV35MSqP5+IB6rATIj7VeGflUG\nXGyUjqta7BO2hBCgps0+YbsmFZieJN2f6qCX6oYMx3F44w9tRypOfonTn7xuPZ/705cQFKKs//c1\najOmxtfYXY/UGPDktEPoMKvRabb/CDVa1EgPv2x3vcXQPcQbEdRp971sMQahui0Uvb/FraZA/Plk\nFsKDDIjVtuOuUQU2r4siFLtCVqVWY8qdv8RXrz4GADj+4UuYdPtjULlwQ+STtUBKOBCldVmTRAPS\n6/XQ6/UefSYTNhn1LhSbm5uLNWvWyBOMj6puBf5+VtqA899nOO6B6qoFarJI2wdEa+xXgn5dLr3e\nNZ+mS3JYd8JW0wZM7NX2zZmOhyhn+XEZWZOhA3v+X3fR5IzZd2DUvHtljGjwBAEIDjAjOMB+XDpG\n24FbMux39w8LNOLG1CK0GIMQpLZ/X7MhCBFBBvRe76I3BMEsCmjq1CBIZf++pk4NCpJ+bHfdZBFw\nuVODSE2n3bCuJxw4sB/rNuQCZiMiAkOgMrZBX1OMF391P4xJkxy+JyQwHE/8/Cmnn/FdNfCnY0Cs\nFnhylrRfIpEn5OXlYe3atR59JhM2GZWXl9ucs3fNddqMUp3P3SXd205sPQ9MiHM8uX7beWBnkZSU\nPTgRmJ9q+7ouTErmZvR634xEID4Y0IU7ns/Vu2fNX728cT3ajNJvo9rzX0Bbfh4AIKo1OBaYie9e\nWmNz/6HDBzB38bjezXi1kEATsuLth2a7xGnbcY2uFP/b67re2J3xR2rs97RoMmgRYK4EYJutVLeF\n4q/nJwAAMiIu457R521eN1kEmCyq/9/encc3Vaz/A/9M0mzd0iVdaIW2srQVlKWyU20Vyr4jUJDF\nBfCLcFHxIl+9LihXQEHBHyKCXwVZhCvKRQTByyog+2XfkbaspfveJk0yvz+mSZsm6YJtk8bn/Xr1\n1XbO5JxJzjnJkzlznoHSRtBZF4xMZ96Hacq+SP/lBwCAf/ZJPPzCUDCJ9TX/Q1uv1Hj9+Vrg63Pi\n/E4rEik/ZlLQRhrIzJkzMXnyZIuyyp0wdY0CNgcKCfkLd7PUo+RckZi1QFdexhgQ5g2cTBVTSVWe\naNrdrTwPWUoeUHmMfmsNkFViva1ojfghVSsqzUf3gZEouHwOKbuOmMtDho1Bmx4drer/fnR/QzbP\nKbjL9HCXWedcaeWTjb+1PYl8ndzmJfE8nRxyfS4AywGYubrybmJbPXO3Crxx4n4wnmlpGSQV6d2Q\np5XDV1kChY0xgQ/Cr0dPZOz+GVynRcmdm8g7fRTqDl3/1Dq9FCJP25enRdCWXha0vdZR3JxDSH1y\nxBAmysNGXE4TD8BoFL1sANDSF3izKzDhUUBrAI7fs36MqSdM4w54yKyXN/cViTzJg9MX5OHOuuXm\n/z2j28K3+1MObFHjIZca4a8qgZ/S+lvDY/7pCMneY1XOOeCj0IJBjLurLLtEAR+F9fqSctVYe6U1\n/t+ZGOxIibBarjVIbOamq4qbpxf8n0gw/5+27XsY9bWfrqqytoEi1Ye0rDnpRcDS/9pOHk1IY0c9\nbMSlXMsC1l4AkvNEwPbhk0CHoPLB+g+rgR3WmSHQwhf45Cm6E63ecI4761dCnycG40s9vRE6ZjKY\nq9xF4UCMARJY96C19s9Ea/9MGDmgtzE7hM4ohUZVbFWeoy2/pujuVmq1/EKmBpkl7ujVLNmiPF8n\ng94ogVqhtTnsQPP0AGT/vgeGokLoMtKQc3gv/GJ71eAZVu2xsqDty9MicEuMdp2bcwipiAI20ihl\nFwMH74jxY10qDBvwVgCpheJGAqVU5BGr+ObdxBMY1EJ8A69Y7iYB3ChYqzeKpAMouHHK/H/os1Pg\n5k0D/BqChNlOd9Il2EZXMwC51ACNshg5WiV8bfTA5WiVNnvmzmUG4Pd7oZAwjlgb6VCYygOangNx\n/6cNAID0nf+GulMspIo/P+jssUDgpfaAQkqJdYnrooCNNAqcA7fyxS38FzKASxnA8VSgV7iYvsaU\nTT/QXWT1LywVlzkLdJapOBj7a9+h6QhJR36C6kb5mDT/uL7wim7rwBaRqnQMSkXHoFQYOWDk1l1V\nei6Bv9K6Zy6rRAwcM3IGpdT6cue+O83gE/UsPPbvhD43G/r8XGT8ugU+/cZAJjH86STCjzaiHISE\nPAgK2IjTKtQBFzOBS5nAM5HAx0fL58mUScW36dRCkbLDlJGfMeCVx0UPm8zGVEqkYWXdvIjdC8eZ\n//do+QiCBo12YItITUmYmOqrsoRKl0JNFFIDPGWlKCiV2Rxrl12iRFhAHvz6jcDd71YCADL2bMeZ\nJiNxXtoRfooSqHlmnT4HE73R9hRphDQmdAgTp8E5cDcf0JZ9OV9wFPjqDHDotrhzM7LCpQ7GgHZB\nQPdQkQutohAvCtacQUHGbWx7py9Ki0U6D5lfAB6aOB1MSjvHFfVqloyXHj2N6W1PIsjdeob2XJ0C\nvooS+HSKhXtEK1FoNED960cwGjkySlSQwPrS7apzYmxqZTW9seDEPeC9g0BGUW2eDSHOh3rYiEMZ\nOXDwFnAjVySgTSsCprQTswA84i8S3wLiMujjwYC7DGijAaL9rZPbEudRkp+Fn9/ug4L0WwAALpWh\n6QuvwM2Tcg26OnupQCZGnwMDwJgETUa/gBsfvQluMMDz/jk0u/IdbkaNhRcKrB73R7ZIQF3ZJ8fF\n0IcgDzGtnMbdus7JVOD/zor3mUXHgZkdbdcjpDGggI04zKHbwL+viWzlUonIkwYAp9NEwNYmALiZ\nL3KgtQsUyWm71G9eQlIHdEV52P7eQGTfvAgAkEjdkPfYM1A9FObglhFHqjhGTRkcCk3PQUjfuRkA\n0ObUAnTrqkHybcv0I3ojkK0tn43EhHPgVh5QrAfu5AOjoqy3t+qc+NInlQBGA5BVLIK21zpar4+Q\nxoAuiZIGoTcCZ9NEcGaidAPytGI+zczi8jJ52RWzNgHArM5A/+YiWCPOT1uQg63/6I37lw+by+Jf\nWwW9f3MHtoo4I02vgZAHiTuAuE6Lkg0fgRkt04hIGfBBrPX4swKdCNYA8Z6hrtTbbjACJ1LF2NaX\n25cPkcgsAkZtAVacBrZeL0+WTUhjQD1spN4YOXAlEzibDhy5K/KihXiKsWeA6Dlzk4iJmzXuwKTH\ngEc0NP6ssSrJy8TPb/dB+vWT5rIeU5agVdwY4NS7DmwZcUYSmRxNJ0zDjU/fBS8thTb1NlTsFwAf\nmuswZnuqKS8F8OnTYghFntY671pGMeCjEO8l0RoRtH1+StzIVKwXl0oVbsCACt8j7hcCm64ASTnA\nsFZAsCcQ7CGGYRDiDChgc6C7d+9a/O+IqS7qmtEI/JEjvt2eTAXydeJbssndAnFjQYiX+Gb8j25i\nDMqfvaWfOFbOnavY/t4A5N69bi6L/Z+laDNgqgNbRZydMrQZmgwfj7sb/g8AoLh3Bud//hxtBrxc\n7WPdZUC4nVR+agXwYoXMMdEaYFoHYMERMTUdAAS5WwZ6t/OBo3eAcxnifcukfRAwvg2w4ZJ4r3rI\nS8ywQP7a8vPzkZ+f36DbpIDNgSpPFPvuu+/ivffec0xj6oBODzy9EWjpY9lLZuCARgWAiRsHVBW+\nsTbxtFoNcXIVJ3IHAGl2CjzOfg9JqbiuzQEURw/A1mv3sfVT0bPmipO5k7rh0yUOhdcvI/fEIQDA\ngeV/g8onCM17jHjgdSrdrIO5KH9g8dPA9RxxJ3rly6yphaL3zb3Sp6IpGffRsu/XTb1FwPbfVOCn\n6yKIU8vFY+PDqFfur2LRokWYM2dOg26TAjYHunPnjsX/jb13Te4mbhzIKC4PxNQKEaQ93gSIUNOU\nMa7ANJE7NxqRsWcb0vZ8L7pWATCZHE3H/Q+821pO6P5XnMyd1AxjDCEjn4MuPRXFKX8AnGPXx89C\n4eWHh9rW7VyzaiUQE2x7WacmgBTiCoFMKi6R3i8SAVhqhZtXg8puWLhTANwr+8kqETc/HLsHPBUG\njIoWddIKgf/eF0FdgEq8L0pp5LhLmDlzJiZPnmxRVrkTpq5RwOZAISGNL+W+3igG617KBHqGWc8a\nMLQVsOwU8GQzEai18KXLna5In5eLO+tXoODSGXOZm7cazV58DaowusGA1I5EoUSzKa/j4tx/QFqU\nCaNeh1/mDESv2RsR3mlAg7QhwB3oU+nQ5VxcIcguAca1EYFbs7K72SsGccWlFS61epSX38gBNl8V\nf5veB/1V5QGcwg14yBPo2Pg+Cv7yHDGEiQI2UiOZxSINx9oLYmYBTdlcnZUDtsEtgYHNRW8bcT2c\nc8junsH1eZ/AUFSeHFUV3hJNJ06DzNffga0jjZmbhxcKOoxFyKUfUJh5B3ptMXZ8MBRxf1uJqF4T\nHdImxgA3JoK5yqlAxrUBEiJET9zRu6KXTcIsE3mnFlquy2AE0ovEDyB65WKCrQO25Fzg4G3Aoyzv\n5MM+1DNHKGAj1cgsBr67CJzPEN823WXijSerWJTllAA+Fe7icpOAksW4qMzkc/j9q9fhcfE/MFQo\n9396AIL6jwCT0tsJ+XO4Uo3B8/di6z96I/9+ErjRgL2Ln0dm8ll0mTgfUpnc0U00U7qJ+YrD1Pbn\nJ27pC2jDRFB3Jx/I0VouL9aLoSKVnUkDvjwtZmdo5i0CNlPPXP/mgEwibuYKadyjaEgt0TusA5ju\nLMnPz3facWvFpcCnJ4C/xQDXssungVFIxRvMI/7iLiwfG7fcE2v5+flYtGgRZs6c6bT73J78tJs4\nuWEuLv/na3BjeeIqmV8AQkY9D8+oRx3YOudWVFCMK+eTUVRQDHdPlaOb0yioQ1pg2MJD+PmdvshM\nEpfcz/57MVIvHkLPWeuhbuLcl9wrnuutA7zQusKk9DqD6F1LKxLj2/bdAtrbGFOXVijegwFxqdXI\ny3vm+j4srnYEelgGbJsuixRKBqMI8toGAa18xXs0DUupfw3xue5UfSF6vR7vvvsu2rZti/j4eMTE\nxGDu3LkwGAzVP/gB1lFfdatTccc6C84t5+ZTycQlz6tZYjAuIHKkTWkH/DQc+PgpIJKuftVYfn4+\n5syZ41T7vDo5d65i75IXsX5SS1za+ZU5WONg8HsiAc1nz6NgrRpFhSW4diEFRYXWk6ET+9z9gjF4\nwT6EVRi/lnb1ODZOfRTH18+BXlvswNZVrapzXS4VScDbBwG9HwbmPWk7RcijAUCXEBFwVb6TPtBd\nBHyVL9GeTQf23QR+vAosPgHMPwz8734xI4TJkTvAzbL/UwtEDruazslKqtYQn+tO1cM2depU7Nq1\nC8eOHYNGo0FGRgY6d+6Ma9euYfXq1XW+jvqq25gU6IBvzwPXs8WYjPZB5ctim4p8asMjxVgNms7F\n9RlKtUg5tg0Xti/H7dO7rJY37dAbF+ThaDM81gGtI38lCg81+r6zBWf/vRhHVs2GUV8Kg64EJ9bN\nwZVdqxEz6i20emqcU10mrStdQi2n4dMZxOXRtCLASw5E+AChFQI5zsXwlRJ9eZmy7NNdU6Fj98hd\noGe4+HvJSTG0RSYFbueJdDwB7sDszkALv/p6ZuTPcJqA7dChQ/jqq6/w5ZdfQqPRAAA0Gg1mz56N\nKVOmYNKkSejRo0edraO+6jYWmcXA12dFMsiiUnGimr75mXQIEv9XzldEXMuSJfOhu38G8rRLkKVd\nATNorerofZqiJCIW5/ya4/iJI+gKCthI/WOMoe3QVxHS5gnsX/qSeRaN/PvJ2PfZJJz47n20GfAy\nIp8aD3c/O/k6XIBcKi5/mi6BDmxhuZwDmB4D/HZLzNRwt0CMezNwy5xwGcUigNMbxZ2vAFBqEClK\nCnTiioqhk/X2P/+vCOpCvQA/FeCrEJdaC0uBKD8xG4VpfDOpP04TsK1atQoAMHjwYIvyQYMGYcqU\nKVi1alW1QVFt1lFfdRuDSxnAZydFNu+isnESGcXAlSzRRe5dNi8f3ZXkmrjRiMyks7h9ZjfunNkL\n2aldkBt01hUZg1frdvCP7w+PFuWza1NONVJfjhw5jHmf2pnGLKwP5G5BUP6x15ykuSD9Fo58MxtH\nV7+FZjF9ENF1CMI69nfp4M0WCROJgaOqGaaSECFuXigqFT102SUi6NKWjeyRSS3TkpjczAPu5Ys7\nYSs6eV98sWcA3ulePucz58DGS8CtfPGlv4mHyMmpVohpxciDcZqAbf/+/fD390dgoOUF/aCgIPj6\n+uLgwYN1uo76qussKg589fT0wrVscccSY0BLP9GtbuTiW5KUiXQcLz5WHqzVdhv1NcjSVbbREGw9\nD21+NnLvXUf2rUtI/+O/yLh+Chk3TqG0uDyJVOUvxTL/QKhjusK3azzkfhqLZQ0xiL6hBuq7yg0B\nrrJPigqKcenCVfzP/46qYhvRMJQMQdbB3cjc+wsMBWJAFjcakHJ8G1KObwMA+IW1QXB0VwRFd0NQ\nVBeom7SARCp16XO9Jp5oKn7LpMDb3cXfWj1wMRO4mSu+uJs+A0zbeO21mbhf6AWFnWjB9P7hU+Gz\no0AH7L0pLsFeyBA3qwEiTcknTwNzfxc3R3jJgcTm+Vi2ZBFaD52JID8veMrFpdpIP9GbV5vPJHtc\nZb87RcCm1+uRlJSEFi1a2Fyu0WiQkpJSZ+uor7rOxDTw9fkXJ8PD0wvfngcmPioS2bpJgKfDgMtZ\nwIQ24pb0B7nsadrG5MmT6zWYcoVt1CVuNKK0pBC6ojzoCnNQlHMfRdmpSPnjCubMeR9R+rOQFd5F\n7r3r0OZn1WidMv8AeLfrDHX7zlA+FA5m59pGxUH09fbB3QDbaMjt1DdX2Sc13YZU6Y6AngPh/0QC\n8k4fRcq2HXDLuWlRJyvlPLJSzuPijpUAAImbHD6hrWDwDsOcBT+jS2AxQh96CDJ3b8gr/Jj+lyk9\nIJUpIXGT2T0XHKku37MUbqIXrOJwmIrbmDRpMj59ygt5OtHDll32k1UMFJSKHrkCneWl15yymxn0\nRkBe4bPFUy7K7xWIZQCgbZKPuR/MwdjIyfDwF8/l9zviZrcAd2B+XPnj5x8RefEYE8GeWiHuonWX\niSnF7hUAQyOt74rNzmlc7/H2OEXAlpOTA4PBAJXK9kmqVCqh0+lQVFQEd3fbI99rs46ioqJ6qWuv\nbfXt3oWDSE26hMNlc91JwGEszgEA7N6yBp0e9sHjWcCvlwBtU3FLUCgHHmIAv89x+UyFlVndMsQr\nLLJclpYhtnFp59fI9FeDo9Jjuf3HVrWdivXTsnIBAOe3fYE0P3VZzWrWxW2vy9520rPEt/SzWz7D\nPd/KJ3PNn0NV7UrPFncOnfphIW77egGcgxsNMOh1MOp14nepTgysNpWVit8iOMuFrigPpUV50BXn\n27y1K6dElCUd3gwfZdUfMka5J/S+YdD7heO/t3Mw+e2XnPKDiRB7JHIFfDo9gf/bcgPdug2ELP0q\n3DKuwi3nJlil88Oo1yEr5TxySs4BAE798BGSqjlHAACMwU2uhFSuEr9lSkjLfotyJaQyBZjEDRKp\n+MkqEGNAD654DQG+nuZyJnWDRCI112USKZhUCgYRgYjzz/Jv8znJysrLlqdni/esCztWIsPfx2KZ\nqF5pXQ9wbqdlivf3q3vXINDfBwAgBxBU9gMA3dwAlHXWX9xR/tjiUqBXDhBWCATeFvnmivWApww4\nkwuoL4t6UgYklX2O+F5eAy+1DzgHonOAwCwGfxVwseyGYCOAvAvib50ByJBYPi3OxSXYyK6W6S84\ngM8Oim1M/XgtYsJ8IJOKwM9HCXQNBQ7cKu99BMRl4gsZQEqeaKObRIwJ9JCV580zcjGNWUtf8dyu\n3Mmp9WtcW04RsJWUiAvjbm62myORiJc/NzfXblBUm3WYUnHUdd3aBmxHjhwx38Rgj4eHBzw8PNC8\neXPIZLZnFL66dy0u/rLC3DXNAeSWfXin/jgbv5W9MTEAv9WqhVUzBQjH1r5dbYDwZ7dxcsPcet/G\nqU0L6n0bZ//9ab1twxYmk0OuCYRcEwRlaDOomkZA+VA43NS+5g+Dff9YQcEaabSMTIeuo7oC6AoA\nMGhLUHLzBoqSrqEo6RpKbidDn/eAH6acQ68thl5bDOtbcWwznet/HNiIzHp+Pzmx7r16f8868s3s\nB96GHwA9AFnZDwAcBlAhNsKRsu2E/F6+nWYVllccMVvxcbY0A3DgpHV5eNk2Op99Az5Xy59LKco/\nE22NzDUNgirRc/xRdgfu2Up1Lpb9zqvpAfInOEXA5uPjU+XyggIRwiuV9rO01mYd9gKfP1u3toYP\nH15tnYkTJ+K5555DdnY2zp07Z7OO8dKlWm+bNHJSOeCmBGQqQOENpvAG0ysAHEJxqwRIA5rAqPIF\nV3iVfw3VA0gCkJQOIN28KgXzwqGtV2q02bxc0VN4/D9/wFtd80sLzraNB90ObcO5tmF/O1IAUUBI\nFBACQF8CaWEmiu7fAvb8Cm3TjtAqAKbXirui9Trz3+J3KWDUg3GjjS2Sv5pdN4Dt1x3dCoBxq+s8\njuHh4YHo6GicOHHCallISAgyMjJQXFwMqVRaJ+uor7o1kZ+fD29v7xrVJYQQQkjjkJeXV2/j5Jyi\nhw0AIiIikJ2dbVVuNBqRk5ODiIiIagOi2qyjvurWhJeXl/V4KEIIIYQQO5wm01bfvn2RnJxsvsRo\ncu3aNZSUlCA2tvpEnbVZR33VJYQQQgipa04TsA0ePBicc2zevNmifNOmTQCAcePGWZTv3r0bP/30\n0wOvo77qEkIIIYTUNacZwwYAAwYMwIULF/D777+jSZMmuHnzJjp16oTevXtbzNeZk5ODgIAAGAwG\nXLx4EVFRUbVeR33WJYQQQgipS04VsGm1WrzzzjvYvn07fHx8kJGRgaFDh2LOnDkWd2sajUbEx8cj\nMzMThw8fthjgV9N11GddQgghhJC65FQBGyGEEEIIseY0Y9gIIYQQQohtFLARQgghhDg5CtgIIYQQ\nQpwcBWyEEEIIIU6OArYGpNfr8e6776Jt27aIj49HTEwM5s6da55gnjRuvXr1gkKhgJeXF/z9/aFW\nq+Hh4YF58+ZZ1aVjoXHSarXYu3cv+vfvj3/+859269Vm/9Kx4Nxqus/p/Hcd9+/fx+TJk9GrVy+0\nbdsWMTExWLp0KYxG67llG/Rc56TBTJo0iUdERPD09HTOOefp6en84Ycf5uPHj3dwy0hdiIuL45GR\nkVypVPLAwEA+dOhQfvDgQZt16VhoXO7fv8979erFhwwZwl966SXOGONz5syxW782+5eOBedU231O\n579rSEtL4127duWnT582l61atYpLJBLer18/bjAYLOo35LlOAVsDOXjwIGeM8RUrVliUr1ix0yXe\nIwAAFbZJREFUgjPG+IEDBxzUMlJX4uLialSPjoXGbd++fVV+eNdm/9Kx0DhUt885p/PfVcyYMYNv\n2rTJqnz06NGcMcaXLVtmLmvoc50uiTaQVatWARDTXFU0aNAgi+XE9dGx0LjxalJX1mb/0rHQOFS3\nz2uD9rlz2717N5577jns3r3boty0f/71r3+Zyxr6XKeArYHs378f/v7+CAwMtCgPCgqCr68vDh48\n6KCWkYZGx4Jrq83+pWPhr4f2uXOLiopCYWEhsrOzLcr9/f0BiPFtJg19rlPA1gD0ej2SkpKg0Whs\nLtdoNEhJSWngVpH6kJycjMGDByM+Ph7t2rXDBx98YDGglI4F11ab/UvHguuh87/x27hxI+7evYsR\nI0ZYlJv2S4sWLQA45lx3q/GzIA8sJycHBoMBKpXK5nKlUgmdToeioiK4u7s3cOtIXeGcY/r06Vix\nYgWaNGmC1NRUdOzYEZcuXcL69esB0LHg6mqzf4uKiuhYcCF0/rsGiUSCoKAgq/LvvvsOAPDiiy8C\ncMy5Tj1sDaCkpAQA4OZmOz6WSMRuyM3NbbA2kbqn0WiwbNkyNGnSBAAQHByMV199FRs2bMDOnTsB\n0LHg6mqzf+lYcC10/ruuQ4cOYd++fRg5cqR5zJkjznUK2BqAj49PlcsLCgoAiCibNF6bNm1C06ZN\nLcpat24NAPj2228B0LHg6mqzf+lYcC10/rumwsJCPPfcc+jdu7d5PwKOOdcpYGsAnp6eUKlUNpPu\nAeKAkEql8Pb2buCWkbpSWlqKtLQ0q3KFQgEAOH/+PAA6FlxdbfYvHQuug85/18Q5x4QJE9C+fXts\n3boVcrncvMwR5zoFbA0kIiLC6q4TADAajcjJyUFERASkUqkDWkbqwsCBAxEaGoojR45YlJu+Oclk\nMnMZHQuurTb7l44F10Dnv2v6+9//joCAAGzcuNF8ObO4uNi8vKHPdQrYGkjfvn2RnJxsPoFNrl27\nhpKSEsTGxjqoZaQupKWlwcfHB2q12qL8zp07AICYmBhzGR0Lrq02+5eOBddA57/r+fzzz6HX6/HF\nF19YlD///PPmvxv6XKeArYEMHjwYnHNs3rzZonzTpk0AgHHjxjmiWaSO9OrVC+vWrUN0dLRF+c6d\nOyGTyTBt2jRzGR0Lrq02+5eOBddA579r2bp1K27evInFixdblKenp5s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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181495990>"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{8}(x)$ compared with the histogram of the 8th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(7)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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HG264AZs2bRp1IG+88QYAYOXKlQ7nb775Zofrnqpjx44dWL16NXbs2OHy3vfe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\nPF8CLF4uc0RE46fX66HX60e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RRGYVpc3TD9ZKX9Y/me18z+wEaW20/ERgXqK0eK2/aK04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\nDkZmZmYjl4o0hIyMDIwYMQIpKSno0qUL3n33XbsOpXQtNG+unF+6Fpo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FARshpFpDhw5F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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa1818df850>"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{9}(x)$ compared with the histogram of the 9th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(8)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Ny56DYJ30R2hHQyXaaopkiYPI0/Lz850+w73N7YQtMTER99xzD44cOeLNeAJKdXW1w8t+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\n9Mp53PnuK5RdvWhX7nNfF+zJUKJ7IwZrZSXluJCWjrKScqh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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181c7df50>"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{10}(x)$ compared with the histogram of the 10th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(9)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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1a7Bo0SKsW7eOtTUtlJ+fb7TP3jUichSiKCLrSGPC1hDSr5WrHYtnr75SwgZp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\nIV7u/wE7cwvDwxwyLwAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa1819c8510>"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "## NOTE: From now on, *the data does not need to be sorted*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Probability Calculus: Are You $r$th of $n$? ##\n",
+ "\n",
+ "### $\\subNsubR{n}{f}{r}(x)$ is the PDF of the $r$th of $n$ position:\n",
+ "\n",
+ "$$ {\\Large P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n, f) \\equiv \\subNsubR{n}{f}{r}(x) dx } $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Use Bayes' Theorem:\n",
+ "\n",
+ "$$ {\\large P(B\\ |\\ A) = \\frac{P(A\\ |\\ B)\\ P(B)}{P(A)} } $$\n",
+ "$$ {\\large \\Rightarrow P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f) = \\frac{\\subNsubR{n}{f}{r}(x) dx\\ \\frac{1}{n}}{f(x) dx} } $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ {\\Large = \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r}} $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "${\\Large ({\\rm HW}-2) }$\n",
+ "$${\\large {\\rm Prove}: \\qquad \\Sum{r=1}{n} \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} = 1, \\quad \\forall x. }$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Proof (special thanks to Ola Liab\u00f8tr\u00f8, who solved this *in his head* during my talk):\n",
"\n",
- "%matplotlib inline\n",
- "from matplotlib import pyplot as plt\n",
+ "$$\\frac{\\subNsubR{n}{K}{r}}{n} = \\frac{(n-1)!}{(n-r)!(r-1)!} = \\frac{(n-1)!}{(n-1-[r-1])!(r-1)!} = \\subNsubR{n-1}{C}{r-1}$$\n",
"\n",
- "import operator as op\n",
- "def get_nKrArray(n):\n",
- " # nKr has a symmetry: nKr = nK(n-r+1)... Only need to calculate ~half the values.\n",
- " if n // 2 * 2 == n:\n",
- " one_or_two = 1\n",
- " else:\n",
- " one_or_two = 2\n",
- " return np.concatenate(( [n], [reduce(op.mul, xrange(n, n-r, -1)) / reduce(op.mul, xrange(1, r))\n",
- " for r in xrange(2, n // 2 + one_or_two)] ))\n",
+ "Thus,\n",
"\n",
- "def quickData():\n",
- " # This returns data from the easyEndpoint function evaluated at 384 x values in [8.5,200]\n",
- " # if funcs.settings['simpleSortedOutput'] = True, returns only the data\n",
- " # else, returns x, f, F, data\n",
- " return funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n",
+ "$$ \\Sum{r=1}{n} \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} = \\Sum{r=1}{n} \\subNsubR{n-1}{C}{r-1} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} $$\n",
"\n",
+ "$$ = \\Sum{r'=0}{n-1} \\subNsubR{n-1}{C}{r'} F^{r'}(x) \\left(1 - F(x)\\right)^{n-1-r'} = (F(x) + 1 - F(x))^{n-1} = 1. \\quad {}_\\blacksquare $$\n",
"\n",
- "def quickBG():\n",
- " # This returns data from the easyEndpoint function evaluated at 320 x values in [8.5,200]\n",
- " # if funcs.settings['simpleSortedOutput'] = True, returns only the data\n",
- " # else, returns x, f, F, data\n",
- " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n",
- "\n",
- "\n",
- "class HistoContainer:\n",
- " def __init__(self, binEdges, data=None, normed=False):\n",
- " \"\"\" A histogram as a container, not as a plot. More data values may be added later with addValue(value). \"\"\"\n",
- " self.binEdges = binEdges\n",
- " self.binContents = np.zeros(len(binEdges)-1)\n",
- " self.area = None\n",
- " if data != None:\n",
- " for value in data:\n",
- " self.addValue(value)\n",
- " def __len__(self):\n",
- " return len(self.binContents)\n",
- " def __call__(self, value):\n",
- " self.addValue(value)\n",
- " def integral(self):\n",
- " \"\"\" Returns the total integration over the entire histogram. \"\"\"\n",
- " if self.area == None:\n",
- " self.area = funcs.A(self.binContents, np.diff(self.binEdges))[-1]\n",
- " return self.area\n",
- " def normalize(self):\n",
- " \"\"\" Normalize the histogram contents. \"\"\"\n",
- " self.binContents /= self.integral()\n",
- " def plot(self, **kwargs):\n",
- " \"\"\" Plots the result, filling under the 'histogram'. \n",
- " Passes **kwargs on to the matplotlib.pyplot.fill_between function.\n",
- " Returns a proxy matplotlib.patches.Rectangle for legend control. \"\"\"\n",
- " if normed:\n",
- " self.normalize()\n",
- " x = np.sort(np.concatenate((self.binEdges, self.binEdges)))\n",
- " y = np.array([[value, value] for value in self.binContents / self.integral()])\n",
- " y = np.concatenate(([1e-6], y.flatten(), [1e-6]))\n",
- " plt.fill_between(x, y, 1e-6, **kwargs)\n",
- " return Rectangle((0, 0), 1, 1, fill=True, **kwargs)\n",
- " def addValue(self, value):\n",
- " \"\"\" Insert a value to the histogram. \"\"\"\n",
- " # demand that integral() must recalculate\n",
- " self.area = None\n",
- " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
- " index = bisect.bisect_left(self.binEdges, value) - 1\n",
- " if index == -1:\n",
- " raise ValueError('HistoContainer warning: Underflow')\n",
- " elif index >= len(self.binContents):\n",
- " raise ValueError('HistoContainer warning: Overflow')\n",
- " else:\n",
- " self.binContents[index] += 1\n",
- " \n",
- " \n",
- "def verticalColorBand(histo, x, dx, colors=None):\n",
- " \"\"\" Add to an existing plot a histogram, painted as a vertical band of color.\n",
- " The band is a rectangle of width [x-0.5dx, x+0.5dx]. \"\"\"\n",
- " if colors == None:\n",
- " colors = np.array([(1.,1.,0.), (1.,0.,0.), (1.,1.,1.), (0.,0.,1.)])\n",
- " \n",
- " # Special normalization to show FWHM transition.\n",
- " histo.binContents /= (max(histo.binContents) / 2)\n",
- " \n",
- " # Horizontal width of the band.\n",
- " base = np.array([x-dx/2, x+dx/2])\n",
- " \n",
- " for bindex in xrange(len(histo)):\n",
- " upper = np.array([histo.binEdges[bindex+1], histo.binEdges[bindex+1]])\n",
- " lower = np.array([histo.binEdges[bindex], histo.binEdges[bindex]])\n",
- " value = histo.binContents[bindex]\n",
- " if value >= 1.:\n",
- " color = tuple((value - 1.) * colors[0] + (2. - value) * colors[1])\n",
- " alp = 1.\n",
- " else:\n",
- " color = tuple((value) * colors[2] + (1. - value) * colors[3])\n",
- " alp = 0.35\n",
- " if value > 0.1:\n",
- " plt.fill_between(base, upper, lower,\n",
- " edgecolor='none', facecolor=color, alpha=alp, zorder=2)"
- ],
- "language": "python",
+ "Note: I proved this also. The hard way. Term-by-term. I could not see the relation to $\\subNsubR{n-1}{C}{r-1}$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "slide"
}
},
- "outputs": [],
- "prompt_number": 2
+ "source": [
+ "# The debinning Calculation:\n",
+ "\n",
+ "## \"Whoa, I can calculate something else!\""
+ ]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# nPulls is used in many functions below to set the number of data points to pull\n",
- "# from our \"true\" PDF, $f(x)$.\n",
- "nPulls = 10\n",
- "\n",
- "\"\"\" Set up the demonstration of the ithPDF equations working correctly. \"\"\"\n",
- "pullData = {index:[] for index in xrange(nPulls)}\n",
- "funcs.settings['simpleSortedOutput'] = True\n",
- "for iteration in xrange(2000):\n",
- " for i,v in enumerate(quickData()):\n",
- " pullData[i].append(v)\n",
- " \n",
- "funcs.settings['simpleSortedOutput'] = False\n",
- "x, f, F, data = quickData()\n",
- "f = f / F[-1]\n",
- "F = F / F[-1]\n",
- "\n",
- "ithPDF = {}\n",
- "for i in xrange(1, nPulls+1):\n",
- " ithPDF[i-1] = np.array([f[j] * F[j]**(i-1) * (1 - F[j])**(nPulls-i)\n",
- " * funcs.nKr(nPulls, i) for j in xrange(len(x))])\n",
- " "
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "slide"
}
},
- "outputs": [],
- "prompt_number": 3
+ "source": [
+ "## The debinning Algorithm"
+ ]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "histogramRange = np.arange(0, 201, 5)\n",
- "majorTicksRange = np.arange(0, 201, 50)\n",
- "minorTicksRange = np.arange(0, 201, 10)\n",
- "\n",
- "def makeHist(i=0):\n",
- " fig, axes = plt.subplots(figsize=(9,5), facecolor='#ffffff')\n",
- " plt.hist(pullData[i], bins=histogramRange, alpha=0.4, color='#66a61e', normed=True)\n",
- " plt.plot(x, ithPDF[i], '#964a01')\n",
- " \n",
- " axes.set_xticks(majorTicksRange)\n",
- " axes.set_xticks(minorTicksRange, minor=True)\n",
- " axes.set_xticklabels([r'$%i$' % int(num) for num in majorTicksRange], fontsize=20)\n",
- " \n",
- " axes.set_ylim(bottom=-0.0001, top=0.0401)\n",
- " axes.set_yticks(np.arange(0, 0.04, 0.01))\n",
- " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.04, 0.01)], fontsize=20)\n",
- " axes.set_yticks(np.arange(0, 0.04, 0.01/5), minor=True)\n",
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "![nfr Smoothing](nfrSmoothing.png \"nfr Smoothing\")\n",
"\n",
- " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
- " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
+ "### Thought experiment: The Flat PDF\n",
"\n",
- " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
- " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
- " axes.minorticks_on()"
- ],
- "language": "python",
+ "$$ f_{\\rm \\color{gray}{flat}}(x) = \\left\\{ \\begin{array}{rcl} 1 & {\\rm if} & x \\in [0, 1] \\\\ 0 & & {\\rm otherwise} \\end{array} \\right. $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "fragment"
}
},
- "outputs": [],
- "prompt_number": 4
+ "source": [
+ "### Select a point, $x_j$, from the sample $\\{x_1, x_2, x_3\\}$"
+ ]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{1}(x)$ compared with the histogram of the 1st point of 2000 samples:"
+ "### Randomly choose an appropriate $r$ value using\n",
+ "$${\\large P(x_j\\ {\\rm is\\ } r{\\rm th\\ of\\ } 3\\ |\\ x_j, f_{\\rm \\color{Gray}{flat}})\n",
+ " = \\frac{\\subNsubR{3}{K}{r}}{3} F_{\\rm \\color{Gray}{flat}}^{r-1}(x_j) \\left(1 - F_{\\rm \\color{Gray}{flat}}(x_j)\\right)^{3-r} }$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Generate a random point from\n",
+ "$${\\large \\subNsubR{3}{f}{{\\rm(\\color{Gray}{flat})}r}(x) = \\subNsubR{3}{K}{r} f_{\\rm \\color{Gray}{flat}}(x)\n",
+ " F_{\\rm \\color{Gray}{flat}}^{r-1}(x) \\left(1 - F_{\\rm \\color{Gray}{flat}}(x)\\right)^{3-r} = \\mathcal{O}(x^2) }$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## The debinning Algorithm... Expectation"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(0)"
+ "from IPython.display import HTML\n",
+ "HTML('<iframe src=http://upliftingplay.com/wp-upliftingplay/wp-content/themes/UpliftingPlay-1.0/sketchpad/tablet-horizontal.html width=800 height=700></iframe>')"
],
"language": "python",
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "metadata": {},
"outputs": [
{
+ "html": [
+ "<iframe src=http://upliftingplay.com/wp-upliftingplay/wp-content/themes/UpliftingPlay-1.0/sketchpad/tablet-horizontal.html width=800 height=700></iframe>"
+ ],
"metadata": {},
- "output_type": "display_data",
- "png": 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MUadHyqd/Q9uo/zNBQiIiIuPUWbBxhIys3bHP34BfaDg6jXzeZH16P9Qf5TmZSNv4MdB2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\n1EGekuSDWwAAAABJRU5ErkJggg==\n",
+ "output_type": "pyout",
+ "prompt_number": 18,
"text": [
- "<matplotlib.figure.Figure at 0x7f6f84c6e990>"
+ "<IPython.core.display.HTML at 0x7fa18154bc50>"
]
}
],
- "prompt_number": 5
+ "prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The Experiment Inspired debinning Algorithm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
+ "### Suppose our data comes from\n",
+ "$${\\huge f(x) = w\\ f_{\\rm \\sky{sig}}(x) + (1 - w)\\ f_{\\rm \\rust{bg}}(x)}$$\n",
"\n",
- "Here's $\\subNsubR{10}{f}{2}(x)$ compared with the histogram of the 2nd point of 2000 samples:"
+ "![BG nfr Smoothing](nfbgrSmoothing.png \"BG nfr Smoothing\")"
]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "makeHist(1)"
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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JsrOzjZ5zdE1ZSk4chUd4Jzh5cr8AgG//YTi37C/AgP6ioxARCRUTE4Po6Gij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\ngykAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x7f6f6b000750>"
- ]
+ "source": [
+ "### Select a point from our data..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
}
- ],
- "prompt_number": 6
+ },
+ "source": [
+ "### Randomly choose an appropriate $r$ value using\n",
+ "$${\\large P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f_{\\rm \\rust{bg}}) \\cdots}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Generate a random point from $\\subNsubR{n}{f}{{\\rm(\\rust{bg})}r}(x)$... need *3 random numbers* just to get one back!!"
+ ]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
+ "## The debinning Algorithm... Calculation ## \n",
"\n",
- "Here's $\\subNsubR{10}{f}{3}(x)$ compared with the histogram of the 3rd point of 2000 samples:"
+ "### \"Det er dumt!\" Let's just calculate it!"
]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "makeHist(2)"
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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ddBwiImi1Wmi1Wpvu0+xz2G4pLy/Hhg0bMGvWLIwbNw7jxo1DTEwMNmzYYDLt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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x7f6f6a6f2790>"
- ]
+ "source": [
+ "$$ f_{\\rm debin}(x) dx = P_{\\rm debin}\\left(\\tilde{x} \\in [x, x + dx] | \\{x_i\\}_{i=1}^{n}, f_{\\rm\\rust{bg}} \\right) $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
}
- ],
- "prompt_number": 7
+ },
+ "source": [
+ "$$ = \\sum\\limits_{j=1}^{n} P( x_j | \\{x_i\\}_{i=1}^{n} ) \\sum\\limits_{r=1}^{N} P(r{\\rm th}\\ {\\rm of}\\ N | x_j, f_{\\rm\\rust{bg}}) P(\\tilde{x} \\in [x, x + dx] | r{\\rm th}\\ {\\rm of}\\ N, f_{\\rm\\rust{bg}}) $$"
+ ]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ = \\sum\\limits_{j=1}^{n} \\frac{1}{n} \\sum\\limits_{r=1}^{N} \\left(\\frac{{}_NK_r}{N} F_{\\rm\\rust{bg}}(x_j)^{(r-1)}(1 - F_{\\rm\\rust{bg}}(x_j))^{(N-r)} \\right) $$\n",
+ "$$ \\quad\\times \\left( {}_NK_r f_{\\rm\\rust{bg}}(x) F_{\\rm\\rust{bg}}(x)^{(r-1)}(1 - F_{\\rm\\rust{bg}}(x))^{(N-r)} dx \\right) $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
+ "$$ {\\Large \\Rightarrow f_{\\rm debinnning}(x) = \\frac{f_{\\rm\\rust{bg}}(x)}{n N} \\displaystyle \\vec{G} \\cdot \\sum\\limits_{j=1}^{n} \\vec{G}_j } $$\n",
+ "\n",
+ "${\\large \\left[\\vec{G}_{(j)} \\equiv {}_N K_r F^{r-1}_{\\rm\\rust{bg}}(x_{(j)}) \\left( 1 - F_{\\rm\\rust{bg}}(x_{(j)}) \\right)^{N-r} \\right] }$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "settings['simpleSortedOutput'] = False\n",
+ "nPulls = 96\n",
+ "nFictitious=96\n",
+ "\n",
+ "x, f, F, data = quickData()\n",
+ "x, bgf, bgF, bgData = quickBG()\n",
+ "f /= F[-1]\n",
+ "F /= F[-1]\n",
+ "bgf /= bgF[-1]\n",
+ "bgF /= bgF[-1]\n",
+ "\n",
+ " \n",
+ "def mapDataToX(dindex):\n",
+ " # maps elements of data to elements of x\n",
+ " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
+ " xindex = bisect.bisect_left(x, data[dindex])\n",
+ " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
+ " return xindex - 1\n",
+ " return xindex\n",
+ "dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
+ "\n",
+ "\n",
+ "def vecG_rth(rindex, xindex):\n",
+ " r = rindex+1\n",
+ " return pc.nKr(nFictitious, r) * bgF[xindex]**(r-1) * (1 - bgF[xindex])**(nFictitious - r)\n",
+ "\n",
+ "\n",
+ "vecG_rx = np.array([[vecG_rth(rindex, xindex) for xindex in xrange(len(x))]\n",
+ " for rindex in xrange(nFictitious)])\n",
+ "sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
+ "debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
+ "\n",
+ "# One more pull for plotting purposes\n",
+ "x, f, F, data = quickData()\n",
+ "x, bgf, bgF, bgData = quickBG()\n",
+ "f /= F[-1]\n",
+ "bgf /= F[-1]\n",
+ "bgF /= F[-1]\n",
+ "F /= F[-1]\n",
+ "\n",
+ "def makeDebinningPlot():\n",
+ " fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ " plt.plot(x, f, '--', color='#0088ff', alpha=0.6, linewidth=3)\n",
+ " plt.plot(x, bgf, '-.', color='#0088ff', alpha=0.6, linewidth=3)\n",
+ " plt.hist(data, bins=np.arange(0, 201, 5), alpha=0.4, color='#66a61e', normed=True)\n",
+ " plt.plot(x, debinningData, '#964a01', linewidth=3)\n",
+ " \n",
+ " axes.set_xticks(np.arange(0, 201, 50))\n",
+ " axes.set_xticks(np.arange(0, 201, 10), minor=True)\n",
+ " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n",
+ " \n",
+ " axes.set_ylim(bottom=-0.0001, top=0.0201)\n",
+ " axes.set_yticks(np.arange(0, 0.02, 0.005))\n",
+ " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.02, 0.005)], fontsize=20)\n",
+ " axes.set_yticks(np.arange(0, 0.02, 0.005/5), minor=True)\n",
"\n",
- "Here's $\\subNsubR{10}{f}{4}(x)$ compared with the histogram of the 4th point of 2000 samples:"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "makeHist(3)"
+ " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
+ " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
+ "\n",
+ " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ " axes.minorticks_on()"
],
"language": "python",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "skip"
}
},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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vR05ODrp164aZM2c2OJwTESmDLMtwvHkRXlMnNNy4BQiLnIjkY9+gfb+xoqMQ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\nHfuPJq9VVVU4cuQIVCoVioqK7MYuXboUXl5eqK2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- "text": [
- "<matplotlib.figure.Figure at 0x7f6f6a26c990>"
- ]
- }
- ],
- "prompt_number": 8
+ "outputs": [],
+ "prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{5}(x)$ compared with the histogram of the 5th point of 2000 samples:"
+ "## debinning Demonstration ##"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(4)"
+ "makeDebinningPlot()"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
- "png": 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w3HnnnfD19cX//u//Ij8/H926dcOGDRtQWFiIefPm2TMzETmRjANbUdd1fNsN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\nTk7UYRMEQRAEQejkRMImCIIgCILQyYmETRAEQRAEoZMTCZs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Hpy9Sfepkg9eJSe5L8uDxRCZfxJIT3akjFEtdBVdEH8WZu5X8PWtx1FZ7nRPdPY1J818m\nfdQMMz40EenA2nXYPqOmpobHHnuM//t//69nX2RkJHfddRf//d//TXJy8oXeotNR2Jb27IUXn6Gy\nrvXL2UaGWHnowYf9WJFvAln3hdx78zcb+I8n7mrVudBxwvb2AvjT6WfsByVAwfpXibZnYxhgqSoh\nLHsjoXnfYTjrvM5zGQb2bn2p7TEEe7cMXOExnq/Ve3vgyCn3A5Uje7hnLamrKufQmg/Y9vGzFGfv\n9LrWyB88wpg7nsQSFNRGH7WItHdmZ7ILmmfb4XCwaNEiXnrpJVasWAFAfHw8V1xxBcuWLePPf/4z\n7777LkuXLmXMmDF+KVhEzFdZZ7vgntZACGTdF3LvdRtXtfq+7dGpGogNq79/WHeY2ts9hV+fWHh6\nTTaXjgylcPnnlH230b2KzTlC4hLoNmkGcZeNJzgm1uu9M1+rmwdCkOG90E1IRDQXT7+bgdPuZP/K\nt1n3ysOeXvKt7/+O0pz9XPXwWwSHRSAiYrZWhe3jx4/z8ssv89e//pW8vDwAhg4dyoMPPsicOXOI\niIjg5MmTPPXUU7zwwgv853/+J6tWda4fJiIi4u1gCXx2ELJOwVOTvGcRAXcg/uEgcLlcHP3mC6K+\nfYvDy7LqXSc8NZ2EqdcSO3IsRlDTP6bOf7DS634WCwOnziF91EyWPzOHY1u+BODIuo/4fGEx1zz+\nGSHhkS39MEVEWqRFYXvFihW89NJLfPLJJ9jtdoKCgpg9ezbz589n8uTJXsd2796d5557ju3bt7Np\n0yZ/1iwiIu3IgWL4/BDsKTq7b8VRuLaf93H2mir2r/g72z95gZKjuzkvixM1YCiJ064lauBQDD+u\nyR4R251rn/gX6/72MNsXPQ9A3o6VLP3NbGY99gnBoeF+u5eIyPl8DtuDBw9m7969AHTr1o17772X\nn/3sZ6SlpTV5XkZGhmeIiYiIdC6L9sOSw977LAaUn7OqY0XxcXZ9/hK7/vUXqssKzzvYQuyIsSRM\nu5aIXn1Mq9OwWBj/k2eJiE1i4xu/AiBn61eseP7HXPWff/druBcROZfPYXvv3r0MHz6c+fPnc9tt\ntxEe7ltPwNy5c5k4cWKrCxQRkfbrkqSzYdtiuBejmdUXEkJrObz2M/Yue52j3yzB5XR4nRcSEU15\n4mCG3nMroQnd/VZPtd09f/e4VPfqk+e79AeP4HTUsfnvCwE4uOpd4lIvYvTtj/utBhGRc/kctlev\nXs2ECRNafINx48Yxbty4Fp8nIiLtX984d+CODoGrU8qp3PsFO/78CVmbPqO2orTe8dHd0xl2w3wG\nzbiXZ19+1q9Be3kWfHoQquzu9tRG1lob9aP/oqIol91LXgbgm3f+D0kDxtB79DV+q0VE5Ayfw/ah\nQ4ewWCzNBuf169dz4MAB7rzzzgsuTkREAi+/HP512D3zx5lZRlxOJ7aCbIqydnDpnnUc37maxQe+\nwemwN3iNnkOvZNh1PyNj3GwszTz02FrBlrNBe3k2TE5397afzzAMJtz3R07lHSJ323L38Zl38v0/\nbMGalG5KbSLSdfn8L94999zD3Xff3WzY/tvf/sZrr72msC0inZ7DXoftRBan8g4QmruFk1/tw1FR\njrOmCpfd7n45Tr+cjc/helnlUbL/8kwj7zY/92vUiQo+X/htvf2GJYigkLDTr9BztsOwnP5vcGi4\nVzsoJIyg4DAMi4WSsgq2HC3nSGEFllobHwSdINWZS3lhDqU5e6mrKm+yruju6QycNoeBV91NbM9+\nTR7rD1ekwuKD7vHihZWw9QSMamSZh6DgEKb/8h3+Of9SKopyqbEV8+9n7+aGp5ZhWJqY4kREpIX8\n3r3gcrm0WIuPzkybeIbVasVqtQaoGhFpTmVxPrk7VnJ852rydn1N6bG9nrHIkUDBntZdNwko313c\n6rpCgKNFB1t9fnNST/+3FjjSzLHd+gwj4/IbyLhiNon9Rrbpg4ehQTApzT0zCsBXWXBpD+85uM8V\nEdud6b98l08emYzL6SRvx0p2fPYil9zwv9qsZhFpWzabDZut9YuftYbfw3ZOTo4Co49SU1O92gsX\nLuTxxx8PTDEi0iB7bTVZGz5h71evcWzrV/UWXunKwmMS6NZ7GIn9RpAy9EqSB08gIjYxoDVNTocv\njoDdCUdK4WgZ9I5t/PieQyYw4pZfsPX93wGw4bVH6DP6OmJ69m2jikWkLWVmZvLEE2274m6TYfuN\nN97wWsLy4MGDvPnmmw0ea7fb2b17N8uXL2f06NH+r7QTys3N9WrrlxSR9qOm4hQ7Fv+B7Z+8QI2t\n8V7nqIRUYlMu4khhCSmDUgmKjCYoIhIjOAQjOBgjKNj9X6PxoQkf/X0p37tjZuPFNNM5vHtTLj+4\n8fZ6+50OOw57DY4698tZd3a73qu2Gkddrad9rMxJkT2K6OhIMrpH0z0uivCYRKK7pxGd0IuY5L5E\nxPdod1PmxYS5Z0Sx1bqXcE+Paf6c0bct5Ojmf1F0ZDuO2mpW//lBrn3i83b3sYnIhVuwYAHz5s3z\n2nd+56e/NRm277nnHq/2mjVrWLNmTZMXtFgsPPzwwxdeWReQkpIS6BJE5Dwup5O9y15nw+uPepb4\nPlfykAmkXjKFlGGT6DFwLCHhUQA8/dxCklu5XHtB8GasQ0e2umb74Uh6j7m2xec5XVDraHiKvKIq\nOF4OQxIbH4bRXt0+pOEHIxsTFBLGpPkv89GCK8Dl4ti3Szm05p/0n/gD84oUkYAIxJDdJsP2uQ85\nvvnmm/Tr14/x48c3eGxoaCi9evXixhtvZPjw4f6tUkSkDRjVp/j0v64md9u/vfZbe/Th4qvuZuBV\nd2FNamQ+uQ7E5YJdhfDRfuhlhbmX1D8mIcL96ohaErTP6DFwDEOvvZ+dn70EwIZXf0mfsTdodUkR\nuWBNhu3XX3/ds/3mm28yYcIEXnvtNbNrEhFpc+V7tmPd8DK59mrPvujuaYy+4/8wYMrtpk1X19ay\nT7lD9t7TS6vn2tzDLdJ8GG7R2Y2587ccXP0+1WWF2Aqy2fnpi4y4WX+pFZEL4/NPj8OHD2tMsYh0\nSkWrviD/479jOf18imGxMHz2Ai677THPMJGOzuWCN3bCeu9HRQgNgrxyhW2AsKhYLrv1v1nzl4cA\n+Pa9p7j46rmEW7sFuDIR6ch8nky0T58+JCQkmFmLiEibcrlcnPj8n+R/9JZnlpGohFRu/N1Krpj7\n+04TtME97jrynO4ViwFXpsFvroSxnfzxkdJq+Owg1DmaP3bwrJ8Sm9IfgNqKUra891uTqxORzq7R\nnu2jR48C7of4goODPW1fpadrFS4Rab9cLhcFn71P4bJPPfvssanc8vxmIrs1shJKB3dNP1iXCwMT\nYPZFkBwd6IrM9/F+93zbDifEh8P4Xk0fHxQSyti7n+bLp74PwI5P/8TQ6x4kJjnD/GJFpFNqNGz3\n6dMHwzDYs2cPAwYM8LSb43K5MAwDh8OHLgQRkQApXPapV9COHjycnB6zOkXQPlbW8LCQ6FD4PxPd\n0+N1FVEh7qANsCwLxqU2P7tK33HfI3nQOPL3rMNpr2XTW49x1X++ZXqtItI5NRq209PTMQyDkJAQ\nT9tXmptURNqz0m/WUfDZ+5529JCRpM19iJwlhwJY1YU7Xg4f7IOdJ+HhMXBRA0ONu1LQBpjYy72i\nZLXdPTZ9VyEM7d70OYZhcMXc/+Hj/5wAwMHV7zL69oWe4SUiIi3RaNjOyspqsi0i0hFVZh0k752X\nPe2oiwaTds98LMEdd7aRWlcI7+2BlUfdc2cDvL8XfnVFx5sj298iQmBCL3evNriHlDQXtgGSB4+j\n18jp5Gz9CpfTydYPfs/k//VXM0sVkU7K5wckRUQ6Ont5Gcde+wMuhx2AsB4ppM19CEtIaIAra73c\n8mi+ckzl39lng7ZhuFdOrNVoPgCm9j479/beIjhZ6dt5o374K8/2vuVvUn7ymAnViUhnp7AtIl2C\ny+Ui960/Yy91L71uiYgkfd7DBEV27BlHEiMqseDytAd2g19fAXOGQljH7az3q4QI9xLuE9Pg8QnQ\nPdK383oOvZLkwe6F3Jz2Or776BkTqxSRzkphW0S6hJJ1/6Z87w5Pu9ec+wlNTApgRf4RFuRkkGUv\n3SPh/pHw89GaM7shdw6FO4ZAzxbMwGIYBpf+4FFPe88Xr1BZWmBCdSLSmTXa75GRkXFBDzoePny4\n1eeKiPhTbVEBJxa942knTLkG65CRAayo5exOg4q6EGLDauu9l24c45cTIFjdJ41q7Y+z9Mtmkdhv\nJIWHtmKvqWL7oue4/O6n/VuciHRqjYbt7OzstqxDRMQULqeTvHdfwVlbA0BojxSSrrklwFW1TFZZ\nDMuP9SbI4uLOi3d6xh+fYTFcCtomOdO7/eXTPwBg17/+wqgf/VenWvBIRMzVaNhWz7SIdAbFa5ZR\ncWC3u2EYpN42D0tox3gg8lRNKKty09lfGu/Z993JHlyadCKAVXU9GVfMJqZnP8qOH6K2opQDK95m\n8Kx5gS5LRDqIJhe1ERHpyOpOlXjNp5047Toi+3SMuZK3FCSxOi8Nu/Nsl3VYkIMgizOAVXUeuTZY\nmwO3XEy9vxSczxIUxNDrfsa6v/5vALZ/+kcGzfyJ1pQQEZ/oWfUAysvL82pbrVasVmuAqhHpfAo+\n/yfOmmrAPc1f91nfC3BFvgsNcnoF7SHdCrky9RhRIfYAVtU5vLodNp7+5zcjDkb3bP6ci6ffw6a3\n/ht7dQUl2bvI3b6CXsOnmluoiPidzWbDZrO16T01yi+AUlNTvV6ZmZmBLkmk06g6doTSTV972snf\nm4MlOCSAFbXMkG6FpEXbSIqo5NYBe5jV54iCtp+cO/XfsixwuRo91CMsKpaLr7rL096x+I/+L0xE\nTJeZmVkvf5mt0Z7te+65B8MwePrpp+nRo4en7atXX33VLwV2Zrm5uV5t9WqL+IfL5SL/o7c8KSp6\nyEiiLx4W4Koa5nJBQ1nPMOD6jIOEB9ubHeYgLTM5Db44AnUOyDoFB0saXtr+fEOve5Cdn70EQNbG\nxZTlHyEmOcPkakXEnxYsWMC8ed7PXJgduBsN22+88QYAjzzyCD169PC0faWw3byUlJRAlyDSKZV9\nt5HKw/sBMIKCSL7ptgBX1LDi6nC+OtqHougRDb4fqZ5sU1jD3IvcfH16QcivsnwL2/FpF5N26QyO\nbfkCXC52fvYnxt2rhW5EOpJADNltNGy/+uqrGIZBcnKyp+0rPTQiIoHitNs5sfg9T7vbxKsJS/Jh\nUG4bsjsNNuansOlETxwug/zYCdhqXVhD6wJdWpdxVe+zYXt3Edhq3CG8OcNumO8O28Der15jzJ2/\nITg03MRKRaSjazRs33333U22RUTao9KNq6grPglAUFQ03WfcFOCKvOWWR/PF0QyKq88GNJcRQk55\nOIO6FQWwsq4lORrGpUJ8OExO9y1oA6SPmom1Rwa2E0eoKS/h8LqPGDC5ff7lRETaBz0gKSKdh9NO\n4ZeLPc3Eq64nKLL9LD7icsHK3HSvoN0zqoL+J/6uoB0Adw2DGy6CGB+DNoBhsTDo6rme9p6lr5hQ\nmYh0Jq0O23l5eWzevJnNmzfXm8JORCQQQvO2UVfqDq1B0TF0Gz8twBV5MwyYnnYEi+Ei1OJkWlo2\ntw7YTUTdyUCXJi0w8Kq7MSzuH595O1ZSmnsgwBWJSHvWorDtcrn485//zIABA0hLS+Pyyy/n8ssv\nJy0tjQEDBvCnP/3JrDpFRJrkqKsh/MgaTztx2nVYwtrfWNqkyCpm9T7MPYO3M7J7gWYa6YCiE1NJ\nv+xaT3vvl38LYDUi0t75HLYdDgc333wzP/vZzzh48CAAPXv2pGdP94NHBw8eZP78+dx00004HA5z\nqhURacSeL1/FUlMGnO7VnhDYXu39pfFU2ht+LGZQt2I9DNnBDZ55r2d777I3cNj19RSRhvkctl94\n4QUWLVpEamoqr776KlVVVeTk5JCTk0NVVRWvvfYavXr1YvHixTz//PNm1iwi4sVRV8uW95/2tBOv\nug5LaAsG4vpRRV0wiw/3Z/Hh/qzISQ9IDdJyLhfsLYJ3dvu2yE36ZbOISnBP31pVeoLsTZ+ZXKGI\ndFQ+h+1KUiiRAAAgAElEQVRXX32V8PBwVqxYwd13301oaKjnvdDQUO666y5WrFhBWFiY5tgWkTZ1\ncPU/qCjMASDYGhuQsdouF+wp7sZruy9hf2k8AHuKEzh8KrbNa5GWcbkgcxM8txlWHYXdhc2fYwkK\nZuBVd3vae77Qg5Ii0rBGp/4738GDB5k2bRr9+/dv9Jh+/foxZcoUVqxY0api7HY7Tz75JIsWLaJb\nt26UlZUxe/ZsHn30UYKCgky5Rk1NDevWreOZZ55h3Lhx/PrXvzatNumYXnjxGSrrbK06NzLEykMP\nPuznitq/DRvW8/RzC1t1bks/Zy6Xi+8+yvS0u02a0ea92k4XfOMchT2rn9f+YQknSYkqb9Na2tKF\n/L8BsPmbDYy/fmCrzr2Q77FvN21h1JhLvfZtdwzhkKsvAL/ceZLxQRsaPf/M9+igq3/MlveeAuDY\nli+oKMrz9HaLiJzhc9iOjY0lJiam2eOsVqtPxzXkgQceYNmyZWzatInExEQKCwsZO3YsBw4c8HkF\nS1+vUVBQwB133EFUVBTJycksWbKEsWPHmlqbdEyVdbZWB4K1n+7zczUdg9OobbPPWc53yyjO2gGA\nKygkIL3aFgNCqeHMeo8xobVcnX6EPjFlbV5LW7qQ/zcA1m1c1epzL+R7bN3GVfXOHVITxN92xeIe\nQRLLwEHVJEZUNXj+me/RmOQMUi6ZQt72FbicTg6sfIcRN3e9X65FpGk+DyOZPn06a9asoba2ttFj\namtrWbduHVOnTm1xIWvXruWVV17h0UcfJTExEYDExEQeeeQR3nrrLdasWdPMFVp2jaSkJL788ks+\n/vhjfvSjH5lem4iYY9s5vdq1KSMDNq/2EMse4sNquCTxJHcN2tHpg3ZnExdWw0VxxZ72NwXJPp03\ncOocz/a+5W/i8mXAt4h0KT6H7SeffJLKykruuOMOCgvrD2grKirizjvvpKqqiqeeeqrFhbz++usA\n3HjjjV77b7jhBq/3zbhGc/84+qM2EfG/oiPbObblS8C92EhN+piA1RJsOLjj4p1cnZ5FWJAzYHVI\n612WlO/ZPlIWi93Z/LyMfcffTHBYBADF2TspOrzNtPpEpGNqdBjJE088gWF4/0Nz/fXX8+abb7Jk\nyRKmT59ORkYGAEeOHOHLL7+ksrKSOXPm8NZbb/HYY4+1qJBVq1aRkJBAUlKS1/4ePXoQHx/vU++x\nP67RltcVkQuz7ePnPNt9x93Mt+Hxpt6vxg4f74cxKdA3rv77CtkdW0p0BYPii+gZVc7QhEKCLc33\nUodGWsm4YjYHVr4DwL5/v0livxFmlyoiHUiTYbsxFRUVLFq0qMH33nrrLQzDaFHYttvtHDlypNGH\nLxMTE8nOzjb9Gm15XRG5MJXF+RxY9Y6nPXz2/+bbJf8y7X6HS+HV7XCyEnYXwX+Ng1A9G93pXJtx\nuMXnDJg6xxO2D6x8lyvm/g+WIJ8fiRKRTq7Rfw1a2jN9rvN7xJtTWlqKw+EgIiKiwffDw8Opra2l\nsrKSyMhI067RltcVkQuze+nLOE8vJJI8aBw9Lh4LJoRtpwuWHIbPDrq3AU5UwKbjMKGX328nHVCv\nEdOI7NaTyuLjVJWe4NjWr+h92axAlyUi7USjYfvxxx9vsyKqq6sBCA5uuByLxT20/NSpU40GWn9c\noy2vC5CXl9fsMVarFavV2qLrinR2Dnsdu5e+7GkPvf5B0+710hbYcfJsOyIYfjgILtcMb3KaJSiY\niybf5nlYd//ytxS2RdoBm82Gzdb66Un9pV38nSsuroHBj+coL3fPUxseHm7qNdryugCpqanNHrNw\n4cI2/cVHpCPI2riYiiL3L6sRcT3oO+57pt1rbMrZsN0/HuZeAgkN/6FLurCB0+70hO0jGxZRW1lG\naGTrpsEVEf/IzMxsclh0W2kXYTs6OpqIiAiczoYfLqqoqCAoKKjJ+bv9cY22vC5Abm5us8eoV1uk\nvp2fveTZHjzzXoJCQps4+sKM7gl7iiAxAmb2dc+pLV2Dw2Wwv6QbxyuimJp2tMljE/oMIyHjEoqO\nbMdRW03WhsUMmHpHG1UqIg1ZsGAB8+bNa/Y4Xzo/L0SLw3ZVVRUrVqzgwIEDlJWVNTptXkvHfGdk\nZFBSUlJvv9PppLS0lIyMjGZXavTHNdryuikp+ju0SEuVHN1D3nb3KrWGJYjBs35q+j3nDIEWPooi\nHZzdafDa7mGcqnWvRjo04SRJkQ0vcnNG/yt/RNGR7QAcXP2ewrZIgLWXobgtCtsffPAB9913H8XF\nxU0e19LZSABmzZrFs88+S3l5OdHR0Z79Bw4coLq6mokTJ7bJNdryuiLScjs/P9ur3WfsDUQnXvhT\nik4XrD+eyiFnTYPvK2h3PcEWF8lRFZ6wveVkMjN7H2nynP5X/pCNb/wKcC/fXm0rJtzazfRaRaR9\n83lRm40bN3Lrrbdis9m49dZbGTZsGACPPvoot9xyC7GxsQDMnTu3VTOZ3HjjjbhcLj7++GOv/R98\n8AEAc+bM8dq/fPlyFi9efEHXMKs2ETFHXVU5+5a/6WkPve6BC76mrTaE9/YPYn1+Crucg8kN/LM0\n0k6cu8jN7uIEyutCmjw+JjmDpIFjAXA67Bxe95Gp9YlIx+Bz2H7mmWdwOBx8+OGHvP3224wcORLD\nMPjtb3/L+++/z/79+7n22mtZsmQJ9913X4sLmTBhAtdccw2PPfYYx48fB+Do0aP88Y9/ZM6cOUya\nNMlzbGlpKTNnzuSmm25i7969rbrGuc6MnT5zzoXUJiLmOfj1+9RVudNwXK+BpA6fekHXO3Qqljf2\nDCO3wv0XKwdBrGh6aK50IT2jKkiJcj8E73QZfHcyqZkz3L3bZxxc9Z5ptYlIx+Fz2F67di1Dhw7l\nuuuu8+w7d7x29+7deeedd6iurm71HN0ffvghP/jBD7j66quZOHEiM2bMYO7cubzyyitex8XExDBu\n3DgGDx5cb1C7r9cAGD16NBkZGcyZMwfDMPjLX/5CcnIyo0aNYuvWra2+roiYY+9Xr3m2B824t8Vz\n+p9rS0ESHx8aQLXD/byFAQy27OG2wRdapXQm5y/h3shjSh79JnzfM+4ob8cKKovzmz5BRDo9n8ds\nFxYWMmHChLMnnp53uqqqyrPgi9Vq5corr2Tp0qWtKiYsLIzf//73/P73v2/yOIvFwqpVqy7oGgCb\nN2/2e20iYo6SnH3k714LuOc1HjDlwh4+6xNTRqjFSa3TgjWklmszDpGde1CzjYiX/nElDIgr5uL4\nYvrHlTQ7fj86MZWUoVeSt2MVLqeTQ2v+ybAb5rdNsSLSLvncsx0fH09NzdmHh87MP52Tk+N1nGEY\nFBQU+Kk8ERG3fcte92ynj76WyPgeF3S9buHVTE/Pom/MKeYM2kWv6PILrFA6I4sBN/Q9xID4Ep9/\nEfMaSrJaQ0lEujqfw3ZaWhpHj54dzDh06FAAPv30U8++iooK1q5da/p8hSLStTgddq8HIy+efo9f\nrjuoWxGz++0nMtjul+uJAPQdfwuGxT08KX/POmwF2QGuSEQCyeewPWXKFHbu3MnJk+6l1K677joi\nIiL41a9+xS9+8Qv+8Ic/MGnSJE6ePMlVV11lWsEi0vUc2/IllcXuh5Mj4pJIb8FS2KU1YazNS210\nrK2m9RN/i4hNpNfI6Z72wa/fD2A1IhJoPoftW265hUmTJrFlyxYAEhMTefbZZ6mtreWZZ57hP/7j\nP9iyZQtpaWk8+eSTphUsIl3PuQ9GDpg6h6DgpqdgO+PQqTje2juE9fkpbC/sblZ5IvVoVhIROcPn\nByTHjh3LsmXLvPb99Kc/5dJLL+XDDz+kuLiYQYMGcc8993jGc4uIXKiqU4VkbTw7p74vQ0jOLFKz\nPv/sKq2r89IYGF9MeLDDlDqla6hxWDjo7MvH+2H2gMaPy7jiJlb98ac47bUUHtpCae5+4lKbOEFE\nOq0WL9d+vtGjRzN69Gh/1CIiUs+BlW/jtNcBkDRwLN3Sm56br9oexGdZ/cgqi/Xsiwmt5fqMgwra\nckFstSG8vmcY2c5ywrJgSjrEhTd8bFhULL1HX8OR9YsAOLjqH1x2W+umxRWRjs3nYSQiIm3N5XJ5\nz63tQ6+2xXBRXhfqafe2lnHHxbvoGVVhSo3SdVhD60gMrwLA4aTZBZDOHUpyaO2HZpYmIu1Yi3u2\na2pq+PDDD1m1apVn2r/U1FQmT57MzTffTFhYmN+LFJGuqfDQVoqObAcgOCyCfueEl8aEBjm5IeMg\nb+8bzIjEAsan5GjubPGbUT3y+Xa3e/z/6mNwTV8Ia+Qnae/R1xIUGo6jtprirB2U5OwjvtfANqxW\nRNqDFoXttWvXctttt3Hs2LF6773yyis88sgjvP3220ycONFvBYpI17X3q1c9233H3UxYVGwTR5/V\nLbyaHw/eTmSIpvQT/+ofW0IUkQBU1sH6PJic3vCxIRHRpI+a6RlKcnjth4z64a/aqlQRaSd8Hkay\na9cuZsyYwbFjx+jbty+//vWvefnll3n55Zf51a9+Rd++fcnJyWHWrFns2rXLzJpFpAuw11ZzYOW7\nnvbA6XfXO6aoCmoaydMK2mIGiwH9LIc97QPFTR/fd/zNnu3Daz8yqywRacd87tl+7LHHqKys5JFH\nHuE3v/kNFot3Tn/iiSdYuHAhTz31FI899hgffqjxaSLSelkbPqGmvAQAa48+pA6b7PX+viJ4eRsM\nToC5l2i+bGk7vY1jpPSEK9Ogf3wzx465DktwqGdWkrLjh4np2bdtChWRdsHnnu2VK1cyYMAAnnrq\nqXpBGyAoKIgnn3ySAQMGsGrVKr8W2Vnl5eV5vWw2W6BLEmk3zn0w8uKr7sY4/e+OywUrsuH5b6C8\nFjYdh5XNPKgm4k/BhoMfD4eLujX/S15YVCxpl17taR9ap44okUCy2Wz18pfZfA7bVVVVjBo1qslj\nDMPg0ksvpaqq6oIL6wpSU1O9XpmZmYEuSaRdKD95jGNbv3I3DIOBV90FgN0Jf98F/9jjnksbIDYM\n0mMCVKiID7yGkqxR2BYJpMzMzHr5y2w+DyMZOHAgx48fb/a4/Px8LrroogsqqqvIzc31alut1gBV\nItK+7Fv+BmfWV+81fBrWpN4AfHEE1uScPa5PLNw3EuIbmetYpD3IGHsDq4KCcTrsFOzfhK0g2/M9\nLSJta8GCBcybN89rn9mB2+ee7fvvv5/Vq1ezZs2aRo9Zu3Ytq1ev5qc//alfiuvsUlJSvF4K2yKA\ny8Xer173NM99MPKq3pB2uhd7bAo8PEZBW9q/MGs8qSOu8rT1oKRI4Fit1nr5y2w+h+158+Yxf/58\nZs6cyS9+8Qu2b9+OzWbDZrOxfft2fvnLXzJz5kweeugh7r//fjNrFpFOLKj0KGX57tkeQqNi6XvF\nbM97YcHwwEj44SC4ZxiEBAWqSpGzSqrh4/3wr0ONH9PPa1YSDSUR6UoaHUZisVgwznvyw3X6z7rP\nPPNMvfHFZ9577rnneP7553E4tCyyiLRcWN53nu2LJt1KcFiE1/vdImCq/gIv7cTRMvjdBveKkhHB\nMK13w4vc9Ln8RowX78PldJC/Zx3lhblEJ5o/VlREAq/Jnm2Xy+X1asl7IiIt5aiuJOTEHk+779Tm\nl2cXCaQ0KyScHspUZYd1uQ0fFxGbSOolUzztI+s0lESkq2g0bDudzgt6iYi0VNnWjRjOOgCqEoby\nWfVl6Hd3ac8MA67qc7a9PPvsTDnn6zv+e57tQxpKItJl+DxmW0TEbAXrzj6AXTzobraeMNhbFMCC\nRHxweQpEhbi3T1bCtoKGj8u4YrZnYu7ju76msji/jSoUkUBS2BaRdmHfgXLsR/cB4LIEc2rQHdw1\nFAYlBrgwkWaEBbtXkzwj+1TDx0XG9yBl6JXuhsvF4fUfm1+ciAScz/Nsn1FbW8sHH3zAqlWrPPNE\np6amMnnyZG655RZCQkL8XqSIdH5FG9YQe3q7IuM6HpyYxMCEgJYk4rPJ6VBR535AMjm68eP6jr+Z\nvB3uVZYPr/2Qoddq9i6Rzq5FYfubb77h+9//PtnZ2fXe++tf/8qvf/1r/vnPfza70qSIyLlcDgfd\n9n3GmTmMpt98j4K2dChx4XD7kOaP6zvue6z5f/8LgLwdK6k6dZKI2O4mVycigeRz2M7JyWHmzJkU\nFxeTnp7O7bffTkZGBgCHDx/m7bffJisrixkzZrBt27Y2Wf5SRDqH8j3bcdhKAXCERnPJhFkBrkjE\nHFEJKSQPHk/+7rW4nE6ObPiEwTPuDXRZImIin8ds/+53v6O4uJj58+dz4MABfvvb33Lvvfdy7733\n8tRTT3Hw4EEeeughiouLefrpp82sWUQ6mZKNqz3bdT2HYQlq8Qg3kQ6j77kL3Kz5IICViEhb8Pkn\n2pIlS8jIyOC5557DYqmf0UNCQnjmmWdYvHgxS5Ys8WuRIh3Vhg3refq5ha0+PzLEykMPPuzHigKv\noDKSr/N6cV3GQcKCnNjLy7Dt3OJ5f/NJWv052/zNBsZfP9BfpXYYF/J91hm/x9qzF158hipbjuf5\nhKNbl/G7//kFrpCIJs87Q18vkY7H57Cdl5fH7NmzGwzaZwQFBTFmzBgWLVrkl+JEOjqnUXtB4W/t\np/v8WE3gZZXFsPjwRdQ6LXx6+CJu6refU9+sA6d7tHZEn/7YikJa/Tlbt3GVP8vtMC7k+6yzfY+1\nFzll7jm3+8TCpPSz+yvrbIz//hgOH+tHVfYhDJeTQallxI8d4dN19fUS6Xh8HkYSHh5OcXFxs8cV\nFxcTHh5+QUWJSOezsyiRjw4NoNbp/mcnvzKKkuowSjacDchxYycFqjwRv9lWAE+uc68m+WVWw4vc\nxAwf7dku27a57YoTkTbnc9gePnw4K1euZM+ePY0es2/fPlatWsUll1zil+JEpONzuWD98RSWZmfg\ndLkX9IgJreVHA/YQXbibmuPHADBCQom9dGwgSxXxi0EJZxe5KayE707UPyZm+BjPdsXeHTiqK9uo\nOhFpaz6H7R//+MfU1tYybdo0/va3v1FbW+t5r7a2lldffZWpU6dSW1vLT37yE1OKFZGO6VRtmGe7\ne0QVtw7YTWJElVevdsyIMQSFRwaiPBG/Cg3yHjqyrP5suYQmJhHeqzcALocd287v2qg6EWlrPo/Z\nvuOOO1i6dCnvvvsuP/nJT7jvvvvo2bMnhmGQl5eHw+Eec3nrrbdyxx13mFZwZ5KXl+fVtlqtWK3W\nAFUjYg7DgOnpWVTUheB0GdzQ9wBhQU6cNdWc+nad57j4sVcGsEoR/5qcDl8cAYcTDpXA4VLoG+d9\nTMzwMVTnuJN42bZNxF02LgCVinQtNpsNm83Wpvf0uWfbMAz+/ve/8+KLL5KRkYHD4SAnJ4djx47h\ncDjo27cvL774Im+//baZ9XYqqampXq/MzMxAlyRiiiDDxfUZB5ndbz9hQU7AHS6c1VUAhCb2ILL/\noECWKOJXsWEwpqd7O9gCOQ38bD933Hb5nm04aqrbqDqRriszM7Ne/jJbiyazNQyDBx54gAceeICc\nnBzPcu29evXSIjatcObzd4Z6taUzCz0dss8oWb/Ssx13xWQMw2jjikTMNb0PJETApDSICav/fliP\nFMJ69qLmeA6uujrKd28jdqSeWxAx04IFC5g3b57XPrMzrM9hOz4+nqFDh/L1118D7oDdq1cv0wrr\nClJSUgJdgohfFVeHszInHbul6RmJak7kUXl4v7thCSJuzMQ2qE6kbaVa3a+mxAwfzcnjOYD7rz0K\n2yLmCsSQXZ+HkdTW1pKent78gSLSJeVXRPLu/kEcLoslK/Emah2N//Nybq+2dehIQmLiGj1WpDM7\nd1aS8l3f4Txn8gER6Rx8Dtv9+/ensLDQzFpEpIPKLovh/QODqLK7/1hWHdKdouqGV8Rz2u2Ubvra\n046/Ykqb1CjSHoX17EVokntwt7O2hvK92wNckYj4m89he86cOaxatYrDhw+bWY+IdDD7S+K9FqsJ\nD3LQ9+Q/6RlV0eDxtp1bcFS4nxYLjutG9MXD2qxWkfbGMAzvBW6+2xTAakTEDD6H7Z///OfMmDGD\nadOm8Y9//IOamhoz6xKRDiKn3Irj9GI11pBabh2wm8ja/EaPL1m/wrMdP3YShsXnf4ZEOiyXC/YU\nwjrHWA6Ueg+bihlxdiiJbddWnPa6ti5PREzk8wOS/fv3x+VycfToUW677TYMwyApKYmIiIb/VKwe\ncJGuYUqvo1TYQzhZFckt/fcRE9r4mNPaopNU7NvpbhgGcZdreXbpGpZnwz/3wglXEt8WWLgortTz\nXnhqb0ISulNXdBJndRUV+3ZiHTIygNWKiD/5HLazs72XwHK5XJw40cAatCLSpRgGzOp9mDqnhYhg\nR5PHlm5c7e7iA6IHDiW0W2JblCgScJclw0enJ+DJKbeSXxFJcpR7iXb3UJIxFP37cwDKtm1W2Bbp\nRHwO20eOHAHcIVtE5FzBFhfBlqaDtsvppGTj2eXZ4/RgpHQhceHuwP3NNnf725PJXBt19i/AMSPO\nhm3bjm9xOewYQS1aCkNE2qlm/08uKSnhiy++4OjRo4SFhTFixAgmTdKffkW6GqcLNuanMDyxgMgQ\ne4vPt+3air20GICg6BisQy/1d4ki7dq03vD/Tm/vK+nGlSnHsIa6x2dHpPclJC6ButIiHJUVVBzY\no4eHRTqJJsP2e++9x09/+lPKyso8+wzDYMSIESxatIi0tDTTCxSRwHO6YEl2X/YUJ3CgNJ4fXLSX\n8GaGjJyveM0yz3b85ZOwBKvXTrqW3rGQYBQDsYRanBRWR2INPQW4f7Zah4+meNVSwL3AjcK2SOfQ\n6DQA27ZtY86cOZSVlREZGcmIESPo27cvAFu3buV73/temxUpIoFjdxp8eqQ/e4oTACioiuS7kz1a\ndI2aguNU7N3hbhgG8eOm+rtMkQ7hYss+rkrLZt7Q78iIOeX1ntcUgNu/xeV0tnV5ImKCRsP2s88+\ni91u5/bbbyc/P58tW7Zw8OBBvv32W/r06cO3337LypUr27BUEWlrdU4Lnxy+iAOl8Z59wxMLGJuc\n16LrFK9Z7tm2DhlBaEJ3v9Uo0pEkGYWM6F5AaFD9IB2ZcRHBp1dTdZSXUXlob1uXJyImaDRsr169\nmuTkZP76178SHR3t2T9ixAief/55AL7++uvGTheRTmBHYXeOlMV62pcl5XNVWjaG4fs1nDXVlG5a\n7Wl3mzDdnyWKdBqGxeLdu71tcwCrERF/aTRs5+fnM2bMGMLDw+u9N3HiRADy8lrWuyUiHcvI7ie4\nJPEkAFck5zEp9ViLgjbAqS3rcVa5pzgLTexB1MCh/i5TpNM4P2xrKIlIx9foE0o1NTV069atwffi\n4+M9x4hI52UYMD0ti/6xJfSNPdX8CedxuVwUf33Og5ETpmnFSJEmRPYdSFB0DI7yMuxlpVRlHSSy\n74BAlyUiF0A/9USkSYZBq4I2QOXh/VTnuhfEMkJCiR+raUNFzrA7DXYXJ/DW3sEUVLpXYzaCgogZ\nNspzTNm2TYEqT0T8pMm5t/Lz81m9enW9/WcWtmnsfYArr7zSD+WJSFuprAO7E2LC/HfNopVLPdux\nl40jKDLKfxcX6eCWH+vNjiL3w8JbTiYzs7d78biYEWMoWb8CgLLvNtPjptsxWjp+S0TajSbD9tKl\nS1m6dKnP7xuGgcvlwjAMHI6WzcHbFZ0/5t1qtWK1WgNUjXRllXXwwjdQ64D/Pbr5431RW3gC245v\nPO2ESTP9c2GRTmJoQqEnbO8pTmBiyjGiQuxEXTSIoMgoHJUV1JUWUXX0MJG9+wW4WpHOwWazYbPZ\n2vSejYbt9PT0Vl9Uv4H7JjU11au9cOFCHn/88cAUI11WZR08/w1knx4p8tw3YHFd+AizolVfwOm/\ngkUPuoTwnr0u+JoinUlKVDk9oyo4XhGFw2Xw3ckejE/JxQgKxjr0Uko3uWf8Ktu2WWFbxE8yMzN5\n4okn2vSejYbtrKysNiyja8rNzfVqq1db2lpFrTtoHz27SCxT0mHNpgubASHYZad0wypPO2HyrAu6\nnkhnZBgwKimfz464g/S2wiTGJucRbHERM2LM2bD93SZ6XP9DdWSJ+MGCBQuYN2+e177zOz/9Tesl\nB1BKSkqgS5AurMZeP2jPGQoTesGaC7x2Wt1xnLXu2YrCevbSdH8ijRgQV0xMaBpltaGEWBycqgkj\nIaKaqIFDsYRH4Kyuoq6ogOpjR4hI7xvockU6vEAM2VXYFumiQoOgb5w7bBsGzBkC4/0w0sPlsNOn\n9uxfbRImz1KPnEgjLAZMSj2KYUD/2BIsp/9XsQSHEHPJZZ7e7VNbNihsi3RQmvpPpIsyDPjRIJje\nB+7wU9CG06HAVQtAsDWW2MvG+efCIp3UwPgSBsSdDdpnxFx6uWf71NYNWuBGpINSz7ZIF2YYcMvF\n/ruey+mk8KvFnna3idOxBIf47wYiXUj0gCEERUXjqCjHXlpM5ZEDgS5JRFpBPdsi4je27d9Qc8I9\npaUlLJxuE6cHuCKRjssICvZevn3rhgBWIyKtpbAt0gXYnfDeHjhVY949XC4XJ8/r1dYiNiKtc3rW\nTGIvvcKz79TWjaChJCIdjsK2SCdnd8LL38G/syFzE5RWm3Of8r3bqc7JAsCBhYTJWsRGpKVqHEFs\nPpHM63uGUWUPIrLfxQTHxALgKC8juDQ7wBWKSEspbIt0Yk4X/G07bCtwt09UwDf55tyr8MtPPNvH\nQpIJtsaacyORTmzRoYtYlZtGUXU42wqTMCwWYkaM9bwfkr8rgNWJSGsobIt0Ui4XvLkTtpwTrmdk\nwLTe/r9XxcE9VB7e725YgjgcqtUiRVpjaMJJz/bWkz2wOw2voSQhBXtw1NUGojQRaSWFbZFO6tt8\nWH/OIqXTesPsAe4ZSPzJ5XJR8Pk/Pe240ROotoT79yYiXcTA+GKiQuoAqKgLYV9JNyL69CckPgEA\nixkjHdMAACAASURBVL2anO+WBbJEEWkhhW2RTmpUMlyd4d6e0Au+f7H/gzZAxd4dnl5tIyiI7jNu\n9P9NRLqIYIuLkYkFnvaWk8mAQczIs3NuH1z9XgAqE5HWUtgW6aQMA743AO4bCbcPMSdou1wuTpzb\nq335ZEITkvx/I5Eu5JLuBQQb7ulIDFxUO4KIPWeBmyPrF2GvqQpUeSLSQlrURqSTeuHFZ6isswGw\ntIXnbv5mA+OvH9jscbYd31J97AgARkgI3a9Wr3ZHs2HDep5+bmGrzvX1+0RaJjLYztS0bBLCq0iJ\nKscwwNWrD6Hdk6k9mU9dlY3nF95FXY9BLbtuiJWHHnzYpKpFpDEK2yKdhNOF13LPlXW2VgehdRtX\nNXuMy+mk4F8feNrdxl9FSFy3Vt1PAsdp1Jr6fSKtc0niSa+2YRjEXno5J79YBECykU369Te16Jpr\nP93nt/pExHcaRiLSCew8Cb9ZByUmzaHdkFNb1lNzPAcAS2gYiVdd13Y3F+mCYkeN82yX79qKvaI8\ngNWIiK8UtkU6uP3F8P++g1wb/M9GKKgw/57O2loKPn3f0+42aYbm1RYxWViPFEotVgBcDjtlWzcG\nuCIR8YWGkQRQXl6eV9tqtWK1WgNUjXREx8rgT1ugzuFuWwwIDTL/vkWrllJXWgRAUHSMerVF2oDL\nBbkhScTVuJ/FKP1mDd0mTAtwVSIdi81mw2aztek91bMdQKmpqV6vzMzMQJckHUhhJfzhW6i2u9ux\nYfAfl0GcyVNc222nKPxqsaedNOt7BIVHmntTkS7MVhvCqtw03tw7lLzgJLC4f6OuOnKAmpMmLQkr\n0kllZmbWy19mU892AOXm5nq11astLbHpOJTVuLf/P3v3HR7ldSZ+//tMn9GMNNKoF0ASooOoLhRj\ncHeMjR332HHixPb+EjvZLNlsspvEdpzdbDZL8u4m2SSOE/cSxx133LDBYIoxXUiAEKjXkUbTy/P+\n8cAIMaJLGkncn+vShc5T7xHSzD1nzjm31QDfnQ1Zg5DzNr/1ErGgNjjcnJNP+vmLBv6mQpylYio8\ntXsy3rARgI6UKTiKA3i2bwagc+Masq/4cjJDFGJYWbZsGXfffXevbQOdcEuynUT5+fnJDkEMY1eU\naP++uQ++PRMKBuG9WqCxjo61H8bbOdfciqIfhHErQpyldApMc7WwtlF7vWhNnUXabEs82XZvWEPW\n5dehDMRC+kKMQMkYsivDSIQYphQFriyFn82HskFYcU9VVRpfeBxiMQBSxk3BPql84G8sxFluelYT\n+kNFbnymXLrHzEdn1T7GCrc146+uSmZ4QogTkGRbiGEuwzo49+n64jO8VTu1hk5H7tJbpTdNiEGQ\nYowwMaMt3t7UMYq06efG2+4Nq5MRlhDiJEmyLcQwoKo9EyGTIRoM0PjKM/F2xvyLsRSMSl5AQpxl\nZmb1TISMqQqps+fF252b1xELh5IRlhDiJEiyLcQw8G61VrSmxZec+7e++yoRdzugLfUnE7KEGFzZ\nNj+LCw8wvuFRlpbuIaVkHEZXFgAxv4/uHV8kOUIhxLFIsi3EELe2Dl6q1BLt//oMmgahaM2Rgk31\ntH34Zryde83N6G0pgxuEEIKZ2U2YIx0AKDodziN6t2UoiRBDlyTbQgxhzWomT+7oaeelQMYAr6N9\nJDUWo/5vf0WNalVzrMVlpM2eP3gBCCGO6ci/Rc/OLUS6u5IYjRDiWCTZFmKIavZZ+Sw6h6i2+AeF\nDvh/M8A4iCvtdXz6Ib69FVpDpyPv+q+h6ORpQ4ihwJydi3VMmdaIRXFvWJPcgIQQfZJXTSGGqH1d\nTiKHlsJPt8B9s8BqHLz7hzvaaHrt2Xg7c/GXsBaOHrwAhBAn5Dz3gvj37nUfoapqEqMRQvRlSCXb\nkUiE+++/n/LychYtWsSsWbP4+c9/TvTQR9j9fY1TOfaSSy7BbDbjcDhwuVykpaWRkpLCL37xizN6\nzEIcy3m5DUzTbcNm1BLtgS7D3ouqUv/8o/FKkabsPLIuv3YQAxBCHE+zz8Zb+4v5MO12dCYzAMHG\nOvz79yQ5MiHE0YZUBclvfetbvPfee6xfv57MzExaW1s599xzqaqq4vHHH+/3a5zKsZFIhOLiYmpq\narDZbCxcuJBly5Yxb948hBgopbr9fGcBpJgG9775kRa6dx4aPqIoFNxyFzrjIAchhOiTL2Lgqd2T\niKnaOvfl0+YT3Pg+AB1rP8JWXJbM8IQQRxkyPdtr1qzhkUce4Uc/+hGZmZkAZGZm8sMf/pAnn3yS\n1atPPNP6VK5xOverqKjA7/fT1NTESy+9JIm2GBSDnWhHPJ1MCvb0jmXMvxhbybjBDUIIcUw2Q4Tx\nzvZ4e//Ym+Lfd25eRzSQpDVChRB9GjLJ9mOPPQbANddc02v71Vdf3Wt/f12jP+4nRH8Kx4bGn2PD\nS09iUrUKOsZ0F9lX3ZjkiIQQR5uV3VPkZqt5AcacQgDUUJDOzz9LVlhCiD4MjVd3YNWqVbhcLrKz\ns3ttz8nJIT09/aR6tk/lGv1xPyH6y852F4/unEqrf5Bqrx9D17ZNdH2+Lt7Ov+kb6C3JjUkIkSg3\nxUeh3QNADB3uyT0dR+51HyUpKiFEX4ZEsh2JRKiuro4P5zhaZmYmNTU1/XaN073f/v37ueaaa1i0\naBHTp0/noYceOqXJm0L05aDHwds1xXSFTDxbOZEGb3IKxkT9Phr+/li87TxnAfaJ05ISixDixGZm\nNwFgUFQCky5F0WvTsPw1ewnUHf81UwgxeIbEBEm32000GsVq7bsHzWKxEAqF8Pl82Gy2M76Gz+c7\n5fupqsp9993Hww8/TF5eHo2NjcyZM4ddu3bxzDPPnMajFgI6AmZe3VcWn+jkMIXIsASSEkvTa88S\n6dSq0wUVIzlLv5KUOIQQJ2dsWgcLCw4yOaMVmzHCwWmz6dqsfTLVvvp98m+6M8kRCiFgiCTbgYCW\nXBgMfYejO1REo7Oz85jJ9qlc43Bv9KncLzMzk9/85jfk5eUBkJuby/e+9z2+//3vc8cdd3DZZZcd\n/0H2ob6+/oTHOBwOHA7HKV9bDH2BiJ6X9o4jENWq1KQYw1xXWolZP/iflnirdtLx6Yfx9g7zWGam\n2Ac9DiHEydMpMCenZ+x2xvyL48l258Y15Fx9M3pr36+ZQpwNPB4PHo8n2WEMjWTb6XQed393dzeg\n9Tj3xzWMxuNXBunrfi+88ELCcZMnTwbgiSeeOK1ku6Cg4ITH3H///TzwwAOnfG0x9O3pTKcjqP2O\nGRSVpSVVpJpCgx5HLBSk7tlH4m3HtNk07pNx2kIMN7bS8ZhzCwk21hILBXFvWI3rgkuTHZYQSbN8\n+XIefPDBZIcxNJJtu92O1WolFov1ud/r9aLX60lNTe2Xa+j1+lO6XzgcpqOjI2EypdmsFRLYvn37\nCR9jX+rq6k54jPRqj1xTXK0oqKw8UMwVY/aSl+JNShzNb75IuK0ZAJ3VRt71d8Cv/p6UWIQQp09R\nFDIWXByfe9G++j0yFlyCoijJDUyIJFm2bBl33333CY87mc7PMzEkkm2A4uJiOjo6ErbHYjHcbjfF\nxcXo9fp+u8apHLtkyRLef/99PvnkE84777z4sYd7wE/UU34s+fn5p3WeGDkmu9oY5ejCYQon5f6+\nmr20ffRWvJ279CsY09KTEsvJ8oSMNPjshKJ67MYQY1K7eu2v706hzuvo9fE6QK3HwQe1owAotHtY\nXHSg1/4GbwrbYpMS7tfQDR8dAKsBclPgvKOek8NR8Cbnv0+IBGmz59H02nPEggFCTfV4q3ZiHzc5\n2WEJkRRDZSjukFiNBOCKK65g//798QT2sKqqKgKBAAsWLOjXa5zKsc3NzTidTtLS0node7hnetas\nWSf3IIXoQ7IS7VgkQv2zfwZVBSBl3BSc514wqDEEozpa/Fba/IlDxPZ2Ovmotihhe4PXzmv7xvJ2\nTTFbWrMT9vsiRmq7E59cgzE9zX4bzX4b7mDi/XwRAx418bw2v5Zsv7UPPmtIfAzVnfDnLYnbW/1W\n3qgu4YPaUWxv63vlIyH6i6pCdVcaL9eW0znhyvj2jtXvJTEqIQQMoWT7mmuuQVVVXn755V7bD4+V\nvv3223ttf//993nttddO+xqncuwll1zC008/zcSJE3sd+84772A0Grn33ntP+nGKs9ehnHbIaF35\nGsGGWgAUk5n8m+8ckI+bAxE97YHE5HZ3Rzq/3TKLx3dNYU1DYcJ+naLS6k+c3GU6YgJpIJL44ZxB\nFyN6GgWCoqoOHYlDy8JHbLL08VlgdwgcfVT5dAfN7Opw8XlzDhUdGQn7a7vtvF1T3Mf9dPgihiH3\n+yKGtkZfCi/uGcf+rjS2jvl6fHvXtk2E3W1JjEwIMWSS7fnz53PllVfy05/+lIYGrfvowIED/Pa3\nv+X2229n4cKF8WPdbjeXX345S5cupaKi4rSucSrH/vCHP+TBBx/sVehm9erVvPXWW/z6179m6tSp\nA/NDESOGN2zg2cqJNHqHxsoAgfqDtK58Nd7O+dINmFyJvcQnK6ZCm9/S5xrhdV4HHx4avnEku7Gn\nR78zZE7Yn2II440kDtFyGEOUprmZlNFGSZo7YX+21cd5uYkr/RTaPXx1wg6+OmEHi4sS1yAuTPEw\nSbcrYXuRA26aCNeUwezchN0A5PSxNLr/iDcCRz7WwzqDZqKxxDc3NV2p/N/WGfx2yyxWHhidsD+m\nDr03biL5cm3e+LyPLuc4IkXl2o5YjPZPpHdbiGQaMmO2AV588UV++tOfcumll+J0OmltbeXOO+9M\nmEmamprK3LlzaWtrSxjUfrLXOJVj09PTefHFF/nBD37AT37yExRFwWg08sYbb7B48eL+/0GIESUS\nU3h1Xxn1XjvPVU3kyjH7GOdMnC8wWNRYjPrnHkE9tASmdUwZGWewYkF9dwrP75lAJKYjx+bl9gk7\ne+3PMPv77NlONQUxKCoOUxCnOXFt8QyLn2tKqhK2u6wBri1N3H6YzRjBZkxc6smsj5Jt8x33vFSl\nO2F7pg0WJ+a8cTNzta9fvNF7e5HDwxWj9+GLGHFZ/AnndYdN2PsYQnT4jUfoGL3zuzsy2Nfl5Etj\n9vXaHokp6BQVncyFOyspCszMauQNbykAFePuZMrB7wLQvuZ9Mi+95ninCyEG0JBKts1mM7/85S/5\n5S9/edzjdDodq1atOqNrnOqxubm5PPHEEyc8TogjqcB7B8dQ79XWrI7GdBiUvlfBGSxtq97BX7MX\nAEVvIP+Wb6LoTvwhV0fAzCf1hVxdsrfX9jRzkMihxLA9YE3odU0zB0k1hYip9EoE7cYw352+kWON\nXDHoVJzm4Mk/sCHGaQ4eN/7yzOZ4MaMjRWI6TLoYoZiuz/PbA1acpsTtW1uz+biuiAyLn/LMZsqz\nWs7sAYhhZ1x6Bx/XhfCETRzMv4TJ6XkoHQ3E/D7c6z8BEj9hEkIMvCEzjESIkajNPqPX5LgLCw9Q\nktaZtHhCbc00v9mzZnzWZUux5PZ8OhSJKdR222mzlyecazeF2deZTuSooQ8pxgh2Y5gUY5hCuyeh\nR1anwE3jKhJ6XBWFYybaZwOLIYrNGEnYfm5uA/eVb+JbUzcz1ZWYMLtD5j6rjLYFLERUhWa/jWA0\nsR+l0p3Ovs60hO1i5NAraryEu8UIsXOui+9r/+gtUJP7Rl+Is9WQ6tkWYiRxB800OBeSdag9xdXK\nzKympMWjqir1zz+KGtJ6Rc15Rbguuiq+PxJT+P3WmYRjOurSwRsOkHJEMmjUxci0+mjx2xLWBP/6\npK2Y9fJC3l8UhT4TcYArR++jryHbviPGt2f1MVymqiOd0UctkwjQbR5FldtJrs2btJVxRP+Z6mrB\npIsyydWGbsIMKj+2EfP7CLU2Y2ypTHZ4QpyVJNkWYoA4zUGK2j7CoJtIltXPxUX7k9qT27lxDd6K\nbQCoig7XjXejM/Q8BRh0KllWX3zIS73XTpmz9wTEq4r3ktLHZD9JtAePokBfv0bXlOzBH9HT6reR\nbUsskNTitzH7qLXHAVocs3h1XxkAS4r3MD49efMJxJmzGKI9Q4jMFjLmXUTreyu05oHPkhiZEGcv\nGUYixABy+iu5ddxOri6uwqBL3hISEU8njS89FW93lN9IS/rMhONGO7pINwdI9+7ocwUNpzmIUSeJ\n9VBlNUQpcnj6fPNzXl59wkRNVQW/uWeJlWxrYo/4ewdH0+K39n+wYlBkLLgEdFqBNoP7AE271yc5\nIiHOPpJsCzHAsm3+Qf94vjMI+2OjeHlvGZUd6TS+/DRR36GKpxmZWC++lRpPasJ5c/Pq+MbkbRS1\nv5O08vFiYExIb094wxdVFZzenRTZPTiMoYQJmTEVdrZl9vlpxq52Fz5jDjFZhnBIMzozSJt1frz9\n+fO/SGI0QpydJNkWYgRadQA2x8rZ2+nk4ObddG76NL4v78avMzY7SKE9cXm8s3nC4tnIoFPJd6/i\npnEV3D1lS8L/f6vfht0UwmboPX48FNXx5v4S9uR+hd9tmUX4NIoIicHjWtwzN2P/uldpq96axGiE\nOPvIM6QQ/WRvp5O6bvug3tMThMr2xO0zc7R/9WEvzvd+Fd+eNmsujonlOM1BJmb0caI4a/X1Rivd\nEuCa4sQ1zRu89vgkzdQ+hhaFojo2NuUMQJTiVERiCjvaXPy98zLC4xfEt0vvthCDS5JtIfpBi9/K\n69WlPF81gW2tmSc+oZ94QvDotsSKggUOGKUcZHHVQ1i8WoVUfYqd3OtuG7TYxPBn1MVwWROXGTTp\no0xMb8MY8VCQkvgJSb3Xzp7O9ITtUVWRYSeDqMqdwVs1JTT7bWybeF98+55PnqejdncSIxPi7CKr\nkYizwv/87r/xhROTgpOxYeM65i0Zf8z9gYieV/eVxT9K/6wpnwkZ7f0ykXDdurX84jf3E1V1tKiZ\n5CjNvXogVRXWRxfxg02byVB6rxxi3/AOBu+GeDv32tsw2BPHaYseh3/ep+NEvycjSV6Kly8V72Nn\nw59ZVHhPwv4DnlSK+himVOVO570DYxjl6GRSRttghDoghsvvSZmznRRjEd6wkaa0cupMoykI1YCq\n8sQDN+GbfPJVJW1GB9+99/sDGK0QI5ck2+Ks4At7TvsF7tPP+q5WClqy++b+UtxBrcS2SRdjaUlV\nv63YEVNCRGdexNbWbAJRPXPH70yYuOhqD+I0l/TarkYj6D7YEe/ytk+YStrsef0S00gWU0ID8nsy\nkvW1yk6h3UOqKZSw/aDHQSCqp9Kd0WdhHlUdHvMGhsvviUG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DKA0RojdvCB7eAk9uhzoP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l+ipwOLbSJqdqZOnWpQxJWVlWHs2LFYs2YNxo8fj+joaLi7u+u3i0hTDLNaf/jDH3DmzBnY2Ng0\n9VAs8ttvvyE8PBxFRUUYOnQoFi1aBE9PT/32e/fuYfr06UhPT0d0dDT27NmDV155xaif5viZEBE1\nBf4NioiaPXt7eyxevBiOjo4oLi7Gtm3bmnpINbK2tka7du2a7DGSukpJSUFRURESEhKwbt06g0Ib\nABwdHfHPf/4T7777LioqKpCUlIQHDx400WiJiJo/FttE9FRwdnZGu3btAAAXLlww2ebHH3/EgAED\n4OHhAXt7e3Tq1AnLly83ate2bVtoNBocOnTI7PEGDx4MjUaDJUuW6GOFhYWYNm0a2rdvD0dHRzg4\nOKB169aIiIjA3LlzDfav6Xnc0tJSLFiwAN27d4ebmxscHR3Rpk0bDB06FN9++61B21OnTmHGjBno\n0aMHfH19YWtri5YtW6Jfv371+sVj9+7dOHjwIGxtbZGRkVFt29mzZ8PT0xN5eXlYu3atyTYigt27\nd6N3795wd3eHs7MzwsPDsWnTJpPtLbm+OhcvXkRaWhqCgoLg4OAAV1dX9OrVCytWrDDZ/tHnyb/7\n7jv069cPnp6esLKyQk5ODl599VVoNBps3LjR7Lm///770Gg0mDx5sj5WUFCA9PR09OnTB4GBgbC3\nt4ebmxu6d++OjIwMVFVVme0PALRaLebOnYuQkBDY29vD29sbo0ePxsWLF6vdz5QHDx5gyZIlCA8P\nh7u7OxwcHNCuXTv89a9/RUFBgcX9EdETEiKiZsLf31+UUrJnzx6T29u0aSNKKVm4cKE+9tprr4lS\nSqZMmSK2trby8ssvS3JysvTq1UuUUqKUkk8++cSgn4ULF4pSSkaOHGnyOJcuXRJra2txdXWVu3fv\niohIaWmpvPjii6KUEh8fH4mPj5fk5GSJjIwULy8vcXBwMOjj/PnzopSSwMBAo/7z8vIkKChIlFLS\nokUL6du3ryQlJUnPnj3F2dlZIiMjDdq/9dZbopSS9u3bS9++fWX48OHStWtX/fl9+umnRsfYvXu3\nKKWM+qrOu+++K0opiYuLq1X7SZMmiVJKBg0aZBDXfSZpaWliZWUlHTt2lBEjRhh8Jo+P2dLrKyKy\na9cucXV1FaWUtGvXTgYNGiTR0dHi4uJi9vPVje2dd94RKysrfb5ER0fLli1bZMmSJaKUkoEDB5o8\n58rKSvHx8RGNRiMnT57Ux1etWiVKKXn++eflz3/+s37s9vb2opSShIQEo750ORIQECCDBg0SOzs7\n6dOnjyQlJcnzzz8vSinx9vaWn3/+2WhfpZRoNBqjeFFRkf46u7u7S+/evSUxMVECAwNFKSX+/v6S\nl5dn8tyIqGGw2CaiZqO6YvvIkSOi0WhEo9FIbm6uPq4rnpRS8sUXXxjss3r1alFKiaurq9y7d08f\nLyoqEicnJ3F0dJRbt24ZHevDDz8UpZSkpqbqYytWrBCllPTv31+0Wq1Be61WK7t37zaImSu2tVqt\nhIaG6gu6wsJCg+0lJSWya9cug9iePXskPz/faJyHDh0SV1dXsbW1lUuXLhlsq0uxHR4eLkop+fjj\nj2vVXndNAgICDOKPfiaPf9HZtGmT2NjYiLW1tRw7dsyor9pe3ytXroi7u7vY2NjIypUrDbZdvHhR\nf40zMzPNjm3ZsmVG51RYWCj29vZiZ2cnBQUFRts3b94sSinp2rWrQfz06dNy+PBho/ZXr17Vj2X9\n+vUG23Q5ovuCcfr0af22iooKSUlJEaWUdOvWzahfc8X2sGHDRCklQ4cONcgtrVYrU6ZMEaWURERE\nGO1HRA2HxTYRNRu6YvvRYvr27duSk5OjvzPXuXNng310xdOQIUNM9hkSEiJKKfnuu+8M4hMnThSl\nlMyfP98gXlFRob9z+WjxM3/+fFFKSXp6eq3OxVyxnZ2dLUopeeGFF6SsrKxWfVVn2rRpopSSzz77\nzCBel2I7ODhYlFKydOnSWrX/9ttvRSklTk5OBnHdZ2KqSBQRGTVqlCilZOzYsfqYpdd38uTJopSS\nqVOnmtz+v//9T5RSEhYWZnJsMTExZvtOSkoSpZT861//Mto2ZMgQk9e7Otu3bzeZo48W26b6Kyws\n1N+5379/v8E2U8X2yZMn9TlnKreqqqrk5ZdfFqWUHD9+vNbjJ6Inw9VIiKjZMbc2dFhYGDZs2GBy\nW1xcnMl4cHAwzpw5g6tXrxrEJ02ahMWLF+Pzzz/H+++/r19GbcOGDbh+/ToiIyMRHBysb9+tWzcA\nwNy5c+Hh4YF+/frBzc3N4nPbunUrAGDEiBGws7Or9X4lJSXYvHkzjh49itu3b6OiogIAcPbsWYP/\nbU5GjBhhMp6SkoKVK1carMNt6fXdsmULACAxMdHk9s6dO8PJyQk//fQTKioqYGtra7B90KBBZvse\nPXo01q1bh8zMTKSmpurjd+7cwcaNG2FnZ4fk5GSj/SorK7Fr1y4cOHAA165dQ1lZGUQEJSUlAMx/\nRkopvPHGG0ZxV1dX9O/fH2vWrEFubi569OhhdswA9M/6x8XFmcwtpRR69eqF48eP48CBA+jQoUO1\n/RFR/WCxTUTNzqPrbNvZ2cHX1xfh4eGIiIgwu8/zzz9vMt6iRQsAD5cPfFRISAh69+6NHTt2YOvW\nrYiNjQUA/Q8D33nnHYP2r732GiZPnowFCxYgJSUFSikEBQUhPDwcgwcPRnR0dK3OLT8/HwAMCvma\n5OTk4M0338SdO3cM4kop/RJ7xcXFte7PHE9PT/z888+4fv16rdrr2rVs2dLkdnM/DvX39wcAXLp0\nSR+z9PqeO3cOANC1a9dqx6iUwq1bt9CqVSuTYzAlKioKfn5+OHLkCE6cOKEvStevX4+KigokJiYa\nfRH45ZdfkJCQgDNnzpjt19xn5Obmps/Tx+nGefnyZbP96uiuyaJFi7Bo0aJq2/KHkkSNh8U2ETU7\nj6+zXRt1eZteamoqduzYgYyMDMTGxuLEiRPYu3cv/Pz8kJCQYNR+7ty5mDBhAnJycrB//37s27cP\ny5Ytw7JlyxAdHY3NmzfDysqq2mNa+iKSS5cuISkpCeXl5Zg2bRqSkpIQEBAAJycnAMCyZcswfvz4\nelnXukuXLti/fz8OHjxYq/aHDx8G8PAvDvXBkuur1WoBAMOHD4e9vX21/T5+VxsAHBwczLZXSmHk\nyJGYM2cOMjMzsWDBAgDQr3AyevRoo30SExNx5swZxMfHY/LkyQgJCYGrqyuUUjh79iyCgoIafO1x\n3TXp0qVLjXet27dv36BjIaL/j8U2ET2z4uLiEBgYiK1btyI/P19/V3vcuHFmi/eAgACkpaUhLS0N\nALB//34kJSVh+/btWL58OcaOHVvtMXV3Kqu7A/qob775BmVlZUhMTMSsWbOMttfn4yMDBgxAeno6\nduzYgatXrxrdDX7U/fv38dVXXwEA+vfvb7LN+fPnTcbz8vIAAH5+fkbbant9W7dujXPnzuHDDz9E\nSEhIrc+xtkaPHo05c+Zg7dq1mDdvHn799VccOnQIrVq1Qp8+fQzanjlzBidOnIC3tzc2bNhg9IWq\nps+osLAQxcXFJu9uV3etHqf7605kZCTmzZtXY3siahxcZ5uInllKKUycOBFarRb/+Mc/sHr1atja\n2mLcuHG17qNnz54YNWoUAODYsWM1to+JiQEArF69GuXl5TW2v337NoCHxeXjysvL8Z///KfWY61J\nZGQkunXrhoqKCkycOLHaO7HTpk3DrVu34O/vb/bZ7DVr1lQbr+6xIB1z17dv374QEX3BX9/atm2L\nHj164Nq1a9i6dav+rvaIESOMvojpPiNfX1+Tf7kwdx10RMRkm6KiInzzzTdQStXqWukehcrOztbf\n5Saipsdim4iaFUsfs3hSb731FhwdHZGRkYG7d+8iISEB3t7eRu2ys7Oxd+9eowL0/v372LFjB4Dq\nnwPWiY+PR6dOnZCXl4cRI0YYPcdbUlKCnTt36v9dd9c2KysLN27c0McrKiqQmppq9u5xXa1evRqu\nrq7IyclBUlKS0bO9paWleO+995Ceng5bW1usXbsW1tam/0j6ww8/YOHChQaxLVu2YPXq1bC2tsak\nSZP0cUuv7wcffIAWLVpg9uzZyMjIMFlcnjx5EtnZ2ZZdgEfoHhdZvnw5Vq1aBaWUyUdI2rVrB41G\ng+PHj2Pv3r0G27744gusW7euxmN99NFHBn/tePDgAdLS0lBcXIywsLAafxwJAKGhoUhISMCvv/6K\noUOHmnzO+86dO/j8889ZjBM1piZbB4WI6DE1vdTGFN1Sbub20S0zt2LFCrN9jB8/Xr+U2uNLBOqk\npaWJUkq8vLwkOjpaRowYIXFxcfLcc8+JUkpefPFFKS4u1rev7qU258+fl7Zt2+pfahMbGyvDhw+X\nnj17ipOTk8FyfZWVldK5c2d92/79+8uQIUPE19dXXFxc9OMaM2aMwTHqsvSfzrFjx/RLLdrZ2UlE\nRIQkJydLTEyMODs766/D42tf65h6qY3upT2667xgwYInur66c/Tw8BCllPj6+krv3r0lOTlZ+vbt\nK61btxallCQlJZkcW21yrLi4WBwdHfXL8z2+tvajUlNTRSklVlZWEhkZKUlJSdKhQwdRSsn06dNN\n5oIuR/z9/fUvtYmNjZVhw4bpx+/l5WWwBKWOuXW2i4uLJSIiQpRS4uDgIK+88ooMGzZMBg8eLKGh\noWJlZSUajUbKy8trPH8iqh8stomo2QgICBCNRmNRsR0REVHtPqNHjxaNRlNtsf3111+LUkpeeukl\ns22OHj0qU6dOlfDwcPHz8xM7Ozvx8fGRV199VdLT0/VvmtSprtgWefjymtmzZ0tYWJi4uLiIk5OT\ntGnTRpKSkmT79u1GbadMmSJBQUHi4OAgvr6+kpycLL/88otkZmaaLLZzc3PrXGyLiJSXl0tGRob0\n7t1bvL29xc7OTjw9PaVXr14yb948KSkpMbvvo5/Jjh075PXXXxdXV1dxdnaWXr16SU5OjtE+ll5f\nnWvXrsn06dOlU6dO4uLiIg4ODhIYGCiRkZEyb948OXfunNmx1cYbb7yhL2yrW1u7qqpKli1bJp07\ndxYXFxd57rnnJCoqSrZt2yZ5eXnVFtuBgYGi1Wpl1qxZEhQUJPb29uLt7S0jR440+TIjEfPFtsjD\nF9isWrVKYmJipGXLlmJrayve3t4SGhoqkyZNkv/+97+1Onciqh9KpIF/Hk1E1MwNHjwY2dnZWLx4\nMcaPH9/UwyEiot8RFttE9Ew7cuQIunTpAg8PD+Tn51e7JBwREZGluPQfET2T3n77bZSWlurfuvfR\nRx+x0CYionrHO9tE9EzSaDSwsrKCv78/Jk6ciL/85S9NPSQiIvodYrFNRERERNRAuM42EREREVED\nYbFNRERERNRAWGwTERERETUQFttERERERA2ExTYRERERUQP5v0sbZdfQJF5yAAAAAElFTkSuQmCC\n",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f6a079890>"
+ "<matplotlib.figure.Figure at 0x7fa181544b50>"
]
}
],
- "prompt_number": 9
+ "prompt_number": 20
},
{
- "cell_type": "markdown",
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "fwhmValues=None"
+ ],
+ "language": "python",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "skip"
}
},
- "source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{6}(x)$ compared with the histogram of the 6th point of 2000 samples:"
- ]
+ "outputs": [],
+ "prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(5)"
+ "# Let's try some GPU programming:\n",
+ "import pycuda.driver as cuda\n",
+ "import pycuda.autoinit\n",
+ "from pycuda.compiler import SourceModule\n",
+ "from string import Template\n",
+ "\n",
+ "settings['simpleSortedOutput'] = False\n",
+ "nPulls = 96\n",
+ "nFictitious = 96 # Multiple of 32 for GPU programming ease.\n",
+ "lenXdomain = len(np.arange(8.5, 200.2, 0.5))\n",
+ "\n",
+ "mod_template = Template(\"\"\"\n",
+ " __global__ void vecG(double *vecG_rx, double *bgF, double *nKr) {\n",
+ " const int idr = threadIdx.y + blockDim.y * blockIdx.y;\n",
+ " const int idx = threadIdx.x + blockDim.x * blockIdx.x;\n",
+ " const int idrx = idx + idr*${lenX};\n",
+ " const int r = (idr + 1) < (${nFic} - idr) ? (idr + 1) : ${nFic} - idr;\n",
+ " vecG_rx[idrx] = nKr[r-1] * pow(bgF[idx], idr) * pow(1 - bgF[idx], ${nFic} - idr - 1);\n",
+ " }\n",
+ " \"\"\")\n",
+ "\n",
+ "mod = SourceModule(mod_template.substitute(nFic=nFictitious, lenX=lenXdomain))\n",
+ "\n",
+ "timer = time()\n",
+ "\n",
+ "# initialize the loop\n",
+ "nKr = pc.get_nKrArray(nFictitious)\n",
+ "chisq = []\n",
+ "bgchisq = []\n",
+ "ks = []\n",
+ "bgks = []\n",
+ "\n",
+ "for trial in xrange(100000):\n",
+ "\n",
+ " x, f, F, data = quickData()\n",
+ " x, bgf, bgF, bgData = quickBG()\n",
+ " f /= F[-1]\n",
+ " F /= F[-1]\n",
+ " bgf /= bgF[-1]\n",
+ " bgF /= bgF[-1]\n",
+ "\n",
+ " def mapDataToX(dindex):\n",
+ " # maps elements of data to elements of x\n",
+ " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
+ " xindex = bisect.bisect_left(x, data[dindex])\n",
+ " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
+ " return xindex - 1\n",
+ " return xindex\n",
+ " dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
+ "\n",
+ " # Use the GPU for the most expensive / paralellizable part of the calculation:\n",
+ " # =====\n",
+ " \n",
+ " # Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n",
+ " vecG_rx = np.empty([nFictitious, len(x)])\n",
+ " \n",
+ " # Allocate memory on the GPU for vecG calculation\n",
+ " vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n",
+ " bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n",
+ " nKr_gpu = cuda.mem_alloc(nKr.nbytes)\n",
+ " \n",
+ " # Transfer data to the GPU\n",
+ " cuda.memcpy_htod(bgF_gpu, bgF)\n",
+ " cuda.memcpy_htod(nKr_gpu, nKr)\n",
+ " \n",
+ " # Get a reference to the GPU module function and do the calculation\n",
+ " # NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n",
+ " vecG_func = mod.get_function('vecG')\n",
+ " vecG_func(vecG_rx_gpu, bgF_gpu, nKr_gpu, block=(16, 4, 1), grid=(24, 24))\n",
+ "\n",
+ " # Get the result back from the GPU and use it!\n",
+ " cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n",
+ " sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
+ " debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
+ " \n",
+ " # Chisq test....\n",
+ " if type(fwhmValues) == np.ndarray:\n",
+ " chisq.append(sum(4.*(debinningData - f)**2 / fwhmValues**2) / len(fwhmValues))\n",
+ " bgchisq.append(sum(4.*(debinningData - bgf)**2 / fwhmValues**2) / len(fwhmValues))\n",
+ " \n",
+ " # KS test...\n",
+ " debinningCDF = pc.A(debinningData, 0.5)\n",
+ " ks.append(max(abs(debinningCDF - F)))\n",
+ " bgks.append(max(abs(debinningCDF - bgF)))\n",
+ " \n",
+ " if trial == 0:\n",
+ " # Infinity sigma upper and lower bands...\n",
+ " debinningUpper = debinningData.copy()\n",
+ " debinningLower = debinningData.copy()\n",
+ " # Uncertainty PDFs for each x value...\n",
+ " uncertaintyHistos = [debinPlot.HistoContainer(np.arange(0., 0.024, 0.0002), debinningData[i])\n",
+ " for i in xrange(len(x))]\n",
+ " else:\n",
+ " debinningUpper = np.clip(debinningData, debinningUpper, 20.)\n",
+ " debinningLower = np.clip(debinningData, -1., debinningLower)\n",
+ " for i in xrange(len(x)):\n",
+ " try:\n",
+ " uncertaintyHistos[i].addValue(debinningData[i])\n",
+ " except ValueError as e:\n",
+ " print e.message\n",
+ " print 'xindex = ' + str(i) + ', debinningData[xindex] = ' + str(debinningData[i])\n",
+ "\n",
+ "if not type(fwhmValues) == np.ndarray:\n",
+ " fwhmValues = np.array([np.diff(uncertaintyHistos[i].fwhm()) for i in xrange(len(x))]).flatten()\n",
+ " print \"Run this again for the Chisq test data...\"\n",
+ "print time() - timer"
],
"language": "python",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "skip"
}
},
"outputs": [
{
- "metadata": {},
- "output_type": "display_data",
- "png": 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xnI4kSQjqdwc8r18QHYWIFMimmQ527tyJ9957D1999RWMRiPUajWmT5+O+fPnY8yYMRZt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\nSUVORK5CYII=\n",
+ "output_type": "stream",
+ "stream": "stdout",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f6afdb450>"
+ "254.671765804\n"
]
}
],
- "prompt_number": 10
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "subslide"
- }
- },
- "source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{7}(x)$ compared with the histogram of the 7th point of 2000 samples:"
- ]
+ "prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(6)"
+ "# Try with a HUGE data set:\n",
+ "nPulls = 10000\n",
+ "\n",
+ "timer = time()\n",
+ "x, f, F, data = quickData()\n",
+ "x, bgf, bgF, bgData = quickBG()\n",
+ "f /= F[-1]\n",
+ "F /= F[-1]\n",
+ "bgf /= bgF[-1]\n",
+ "bgF /= bgF[-1]\n",
+ "\n",
+ "def mapDataToX(dindex):\n",
+ " # maps elements of data to elements of x\n",
+ " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
+ " xindex = bisect.bisect_left(x, data[dindex])\n",
+ " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
+ " return xindex - 1\n",
+ " return xindex\n",
+ "dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
+ "\n",
+ "# Use the GPU for the most expensive / paralellizable part of the calculation:\n",
+ "# =====\n",
+ "\n",
+ "# Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n",
+ "vecG_rx = np.empty([nFictitious, len(x)])\n",
+ "\n",
+ "# Allocate memory on the GPU for vecG calculation\n",
+ "vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n",
+ "bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n",
+ "nKr_gpu = cuda.mem_alloc(nKr.nbytes)\n",
+ "\n",
+ "# Transfer data to the GPU\n",
+ "cuda.memcpy_htod(bgF_gpu, bgF)\n",
+ "cuda.memcpy_htod(nKr_gpu, nKr)\n",
+ "\n",
+ "# Get a reference to the GPU module function and do the calculation\n",
+ "# NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n",
+ "vecG_func = mod.get_function('vecG')\n",
+ "vecG_func(vecG_rx_gpu, bgF_gpu, nKr_gpu, block=(16, 4, 1), grid=(24, 24))\n",
+ "\n",
+ "# Get the result back from the GPU and use it!\n",
+ "cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n",
+ "sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
+ "BIGdebinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
+ "print time() - timer"
],
"language": "python",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "skip"
}
},
"outputs": [
{
- "metadata": {},
- "output_type": "display_data",
- "png": 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rq/UQY4v09HTU19djypQpNunjjTfegMFgMCvWWn4Pa2YjIuVrKMx1iflrLYKj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\n58KFC3IZFYVCQYGBgRQTE0Njxowhe3t7eR2erY2mY6xwrq4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+ "output_type": "stream",
+ "stream": "stdout",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f6afe2390>"
+ "0.05406498909\n"
]
}
],
- "prompt_number": 11
+ "prompt_number": 24
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "slide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{8}(x)$ compared with the histogram of the 8th point of 2000 samples:"
+ "## debinning Performace: Uncertainty"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(7)"
+ "# One more pull for plotting purposes\n",
+ "x, f, F, data = quickData()\n",
+ "x, bgf, bgF, bgData = quickBG()\n",
+ "f /= F[-1]\n",
+ "bgf /= F[-1]\n",
+ "bgF /= F[-1]\n",
+ "F /= F[-1]\n",
+ "\n",
+ "# Pretty plot\n",
+ "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ "plt.fill_between(x, debinningUpper, debinningLower, color='#0088ff', alpha=0.3, zorder=1)\n",
+ "plt.plot(x, f, color='#0088ff', linewidth=3, zorder=3)\n",
+ "plt.plot(x, bgf, color='#0088ff', linestyle='-.', linewidth=3, zorder=3)\n",
+ "plt.plot(x, BIGdebinningData, color='black', linestyle='--', linewidth=3, zorder=4)\n",
+ "colors = np.array([(0.8,1.,0.4), (0.8,0.3,0.), (1.,1.,1.), (0.,0.,1.)])\n",
+ "for i, v in enumerate(x):\n",
+ " debinPlot.verticalColorBand(uncertaintyHistos[i], v, 0.5, colors)\n",
+ "\n",
+ "axes.set_xticks(np.arange(0, 201, 50))\n",
+ "axes.set_xticks(np.arange(0, 201, 10), minor=True)\n",
+ "axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n",
+ "\n",
+ "axes.set_ylim(bottom=-0.0001, top=0.0201)\n",
+ "axes.set_yticks(np.arange(0, 0.02, 0.005))\n",
+ "axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.02, 0.005)], fontsize=20)\n",
+ "axes.set_yticks(np.arange(0, 0.02, 0.005/5), minor=True)\n",
+ "\n",
+ "axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
+ "axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
+ "\n",
+ "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ "axes.minorticks_on()\n",
+ "\n",
+ "print"
],
"language": "python",
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "metadata": {},
"outputs": [
{
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ },
+ {
"metadata": {},
"output_type": "display_data",
- "png": 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LeOIBkZKwYCMiUhAvQ6mwEw7aaaLj0FxWDIupVWgOIvp/LNiIiBSisbYSkqkJPqFhQnOo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\nNKtk3nKPAgMDba6g2hsHC2a2Wae6uhqfffYZiKhZY2X5WL+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AG+UiSSE84UVkVy6QFKKERJPwVhO80gDVQa97I0Rp8lvq4uSI1NsWoiQYtm3L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\n5c/8b0n9MsvWRK4Pfi2XP9g0Gs3usd3BdiKR2K1/Gk1DicSFRjBLD7b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rNO2APgfkccBg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dKqL2nhV2Xla66NilEVCOmIXV9RS+yvol5Nox6Pp5btFNBxxcEsKf8wlJTrhuJSaMjb7Ort94SZ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"text": [
- "<matplotlib.figure.Figure at 0x7f6f6a3361d0>"
+ "<matplotlib.figure.Figure at 0x7fa181a46f10>"
]
}
],
- "prompt_number": 12
+ "prompt_number": 25
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{9}(x)$ compared with the histogram of the 9th point of 2000 samples:"
+ "## debinning Performace: Discrimination"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(8)"
+ "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ "plt.hist(chisq, bins=np.arange(0, 7.01, .05), color='#0088ff', edgecolor='#555555')\n",
+ "plt.hist(bgchisq, bins=np.arange(0, 7.01, .05), color='#66a61e', edgecolor='#555555', alpha=0.5)\n",
+ "\n",
+ "axes.set_xticks(np.arange(0, 7.01, 1))\n",
+ "axes.set_xticks(np.arange(0, 7.01, .25), minor=True)\n",
+ "axes.set_xticklabels([r'$%1.1f$' % num for num in np.arange(0, 7.01, 1)], fontsize=20)\n",
+ "\n",
+ "axes.set_ylim(bottom=-0.0001, top=6000)\n",
+ "axes.set_yticks(np.arange(0, 6001, 1000))\n",
+ "axes.set_yticks(np.arange(0, 6001, 250), minor=True)\n",
+ "axes.set_yticklabels([r'$%i$' % int(num) for num in np.arange(0, 6001, 1000)], fontsize=20)\n",
+ "\n",
+ "axes.set_xlabel(r'$\\chi^2$ per d.o.f.', labelpad=5, fontsize=22)\n",
+ "axes.set_ylabel('Number of Counts', labelpad=5, fontsize=22)\n",
+ "\n",
+ "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ "axes.minorticks_on()\n",
+ "print"
],
"language": "python",
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "metadata": {},
"outputs": [
{
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ },
+ {
"metadata": {},
"output_type": "display_data",
- "png": 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29PR0jBgxAvPn/9+snWvHrwUGBuLDDz9EQ0NDr3rYJk2ahHnz5mHNmjUoLCwE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\nIptvh4aFhUFRFBw7dgz79u3T1L377rtYv359o+eaO3euZtX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AAHQp4WyrbTVMS9L111+v66+/XpIUFxenSZMmuVf3AAAAALo6v1fzmDZtmkaN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\nvL29cerUKdSpU0fv8czXsKSkJHTu3Bnt2rUzaR2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o0CGr1CKEwPr167F582aUlJTg2LFj\nKC4uxvDhw3HlyhX07dtXY42bmxuuXr2KLVu2wNfXF7du3cKRI0dw5coV2NvbIyoqCkeOHLF4rSEh\nIbh8+TKGDBmCwsJCHD9+HGVlZdi6dSvWrVun8/npepNhr169kJGRgcjISFRVVeHo0aNIT09Hnz59\nsG/fPtWtwU3ZU9+cMfNE9O/G24kTERlhyZIlGDZsGLp37w4A8PDwQGVlJR4+fAiF4t2dl6i5xbex\nt98mIqLaxTPTREQGrFu3Dv7+/qpGGnhzw5GCggIkJSVZsTIiIrI2NtNERHrExcXBwcEBgwYNUhuP\njIyEjY0N1q5dCwD4448/cPz4cWuUSEREVsRmmohIh+vXr+Pu3bta3yjn7u6OhIQE/PXXXxg6dCi2\nbNmC0NBQK1RJRETWxGumiYiIiIjMxDPTRERERERmYjNNRERERGQmNtNERERERGZiM01EREREZCY2\n00REREREZmIzTURERERkJjbTRERERERmYjNNRERERGSm/wJyXa/mBeKXzAAAAABJRU5ErkJggg==\n",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f6af83450>"
+ "<matplotlib.figure.Figure at 0x7fa181590ad0>"
]
}
],
- "prompt_number": 13
+ "prompt_number": 26
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{10}(x)$ compared with the histogram of the 10th point of 2000 samples:"
+ "## debinning Performace: Discrimination"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(9)"
+ "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ "plt.hist(ks, bins=np.arange(0, 0.3, .002), color='#0088ff', edgecolor='#555555')\n",
+ "plt.hist(bgks, bins=np.arange(0, 0.3, .002), color='#66a61e', edgecolor='#555555', alpha=0.5)\n",
+ "\n",
+ "axes.set_xticks(np.arange(0, 0.26, .05))\n",
+ "axes.set_xticks(np.arange(0, 0.26, .01), minor=True)\n",
+ "axes.set_xticklabels([r'$%0.2f$' % num for num in np.arange(0, 0.26, .05)], fontsize=20)\n",
+ "\n",
+ "axes.set_ylim(bottom=-0.0001, top=5000)\n",
+ "axes.set_yticks(np.arange(0, 5001, 1000))\n",
+ "axes.set_yticks(np.arange(0, 5001, 250), minor=True)\n",
+ "axes.set_yticklabels([r'$%i$' % int(num) for num in np.arange(0, 5001, 1000)], fontsize=20)\n",
+ "\n",
+ "axes.set_xlabel('KS test value', labelpad=5, fontsize=22)\n",
+ "axes.set_ylabel('Number of Counts', labelpad=5, fontsize=22)\n",
+ "\n",
+ "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ "axes.minorticks_on()\n",
+ "print"
],
"language": "python",
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "metadata": {},
"outputs": [
{
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ },
+ {
"metadata": {},
"output_type": "display_data",
- "png": 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O0mQe7TuyYCOnYXbB9txzz2HPnj1ISUmpd5vU1FTs2bMHzzzzjFXCERGRNDIP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\nRyNqsTzbR6Hdc68hYvoLKM/OgG/qCqT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WLUpNTe3gW4gtGRkZkS4BAADAUYKdomo5EP/ud7/T7t27dcstt+ipp55SWlpa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\n",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f69e63350>"
+ "<matplotlib.figure.Figure at 0x7fa16bd9ef90>"
]
}
],
- "prompt_number": 14
+ "prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
- "## Samples - V: To be $r$th out of $n$ (cont'd)... ## \n",
+ "# The Future, and Shameless Advertising:\n",
"\n",
- "As stated above, $\\subNsubR{n}{f}{r}(x)$ is the PDF of the $r$th data point within a sample of $n$ data points. We can write that as a conditional probability:\n",
- "\n",
- "$$ {\\Large P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n, f) \\equiv \\subNsubR{n}{f}{r}(x) dx } $$"
+ "## \"Yikes.... There is so much more!\""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "subslide"
}
},
"source": [
- "We can \"invert\" that using Bayes' Theorem: \n",
- "\n",
- "\\begin{align}\n",
- " P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f)\n",
- " &= \\frac{P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n, f)\\ \n",
- " P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n)}{P(\\tilde{x} \\in [x, x + dx])} \\\\\n",
- " &= \\frac{\\subNsubR{n}{f}{r}(x) dx\\ \\frac{1}{n}}{f(x) dx}\n",
- "\\end{align}"
+ "## Probability Calculus: Future"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ {\\large \\therefore P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f)\n",
- " = \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} .} $$"
+ "### Two-point correlation distribution, $\\subNsubR{n}{f}{r,s}(x_r, x_s)$...\n",
+ "### $\\qquad$ Form is known already, but use...?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "This proof is so very fun, I will leave it as an exercise:\n",
- "\n",
- "$$ {\\large \\Sum{r=1}{n} \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} = 1, \\quad \\forall x.} $$"
+ "### Re-derive or Re-interpret current statistical methods?\n",
+ "### $\\qquad$ Poisson and Multinomial changes?\n",
+ "### $\\qquad$ Likelihoods... Unbinned likelihoods... Re-derive?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "subslide"
}
},
"source": [
- "## The Debinning Algorithm ##\n",
- "\n",
- "Imagine the following scenario:\n",
- "\n",
- " - An experiment measures a sample, $\\{x_i\\}_{i=1}^n$, which follow some PDF $f(x)$.\n",
- " - The background PDF, $f_{\\rm bg}(x)$, is known.\n",
- " - Based upon the sample probabilities, here is a data smoothing algorithm:"
+ "## debinning: Statistical impact"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- " - Choose a size for the number of points in some fictitious data set, $N_{\\rm fic}$.\n",
- " - To generate some huge number of smoothed points, $\\aleph$.\n",
- " 1. Randomly choose a point, $x_j$, from the sample.\n",
- " 1. Based upon $P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } N_{\\rm fic}\\ |\\ \\tilde{x} \\in [x_j, x_j + dx_j], f_{\\rm bg})$, randomly choose which $r$ this $x_j$ might be.\n",
- " 1. Return a random pull from $\\subNsubR{N_{\\rm fic}}{f}{r}(x) \\equiv P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } N_{\\rm fic}, f_{\\rm bg})$."
+ "### Full comparison: debinning vs histograms\n",
+ "### $\\qquad$ Discovery signifigance?\n",
+ "### $\\qquad$ Parameter estimation performance?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "This algorithm needs to generate $3\\aleph$ random numbers. Very slow..."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "## The Debinning Algorithm... Calculation ## \n",
- "\n",
- "So, let's just calculate the PDF which results from that algorithm:"
+ "### Full comparison: debinning vs unbinned maximum likelihood\n",
+ "### $\\qquad$ Discovery signifigance?\n",
+ "### $\\qquad$ Parameter estimation performance?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "subslide"
}
},
"source": [
- "$$ f_{\\rm debinnning}(x) dx = P_{\\rm binfull}\\left(\\tilde{x} \\in [x, x + dx] | \\{x_i\\}_{i=1}^{n}, f_{\\rm bg} \\right) $$"
+ "## debinning: Generalize / Specialize"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ = \\sum\\limits_{j=1}^{n} P( x_j | \\{x_i\\}_{i=1}^{n} ) \\sum\\limits_{r=1}^{N} P(r{\\rm th}\\ {\\rm of}\\ N | x_j, f_{\\rm bg}) P(\\tilde{x} \\in [x, x + dx] | r{\\rm th}\\ {\\rm of}\\ N, f_{\\rm bg}) $$"
+ "### $\\qquad$ data-driven backgrounds?\n",
+ "### $\\qquad$ detector resolution \"unfolding\"?\n",
+ "### $\\qquad$ \"Max Gap Method\"?\n",
+ "### $\\qquad$ 2-debinning? N-debinning?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "slide"
}
},
"source": [
- "$$ = \\sum\\limits_{j=1}^{n} \\frac{1}{n} \\sum\\limits_{r=1}^{N} \\left(\\frac{{}_NK_r}{N} F_{\\rm bg}(x_j)^{(r-1)}(1 - F_{\\rm bg}(x_j))^{(N-r)} \\right) \\left( {}_NK_r f_{\\rm bg}(x) F_{\\rm bg}(x)^{(r-1)}(1 - F_{\\rm bg}(x))^{(N-r)} dx \\right) $$"
+ "## Searching for \"New Stuff\" with Statistics"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ \\Rightarrow f_{\\rm debinnning}(x) = \\frac{f_{\\rm bg}(x)}{n N} \\displaystyle \\vec{G} \\cdot \\sum\\limits_{j=1}^{n} \\vec{G}_j $$\n",
- "\n",
- "where $\\vec{G}_{(j)} \\equiv {}_N K_r F^{r-1}_{\\rm bg}(x_{(j)}) \\left( 1 - F_{\\rm bg}(x_{(j)}) \\right)^{N-r}$."
+ "### New global-fitting tool for any \"New Stuff\": Gambit\n",
+ "### The Global And Modular BSM Inference Tool"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "funcs.settings['simpleSortedOutput'] = False\n",
- "nPulls = 96\n",
- "nFictitious=96\n",
- "\n",
- "x, f, F, data = quickData()\n",
- "x, bgf, bgF, bgData = quickBG()\n",
- "f = f / F[-1]\n",
- "F = F / F[-1]\n",
- "bgf = bgf / bgF[-1]\n",
- "bgF = bgF / bgF[-1]\n",
- "\n",
- " \n",
- "def mapDataToX(dindex):\n",
- " # maps elements of data to elements of x\n",
- " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
- " xindex = bisect.bisect_left(x, data[dindex])\n",
- " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
- " return xindex - 1\n",
- " return xindex\n",
- "dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
- "\n",
- "\n",
- "def vecG_rth(rindex, xindex):\n",
- " r = rindex+1\n",
- " return funcs.nKr(nFictitious, r) * bgF[xindex]**(r-1) * (1 - bgF[xindex])**(nFictitious - r)\n",
- "\n",
- "\n",
- "vecG_rx = np.array([[vecG_rth(rindex, xindex) for xindex in xrange(len(x))]\n",
- " for rindex in xrange(nFictitious)])\n",
- "sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
- "debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
- "\n",
- "# Discard trivial data\n",
- "x = x.compress(bgf > 0)\n",
- "debinningData = debinningData.compress(bgf > 0)\n",
- "f = f.compress(bgf > 0)\n",
- "\n",
- "def makeDebinningPlot():\n",
- " fig, axes = plt.subplots(figsize=(9,5), facecolor='#ffffff')\n",
- " plt.hist(data, bins=histogramRange, alpha=0.4, color='#66a61e', normed=True)\n",
- " plt.plot(x, debinningData, '#964a01')\n",
- " plt.plot(x, f, '--')\n",
- " \n",
- " axes.set_xticks(majorTicksRange)\n",
- " axes.set_xticks(minorTicksRange, minor=True)\n",
- " axes.set_xticklabels([r'$%i$' % int(num) for num in majorTicksRange], fontsize=20)\n",
- " \n",
- " axes.set_ylim(bottom=-0.0001, top=0.0201)\n",
- " axes.set_yticks(np.arange(0, 0.02, 0.005))\n",
- " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.02, 0.005)], fontsize=20)\n",
- " axes.set_yticks(np.arange(0, 0.02, 0.005/5), minor=True)\n",
- "\n",
- " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
- " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
- "\n",
- " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
- " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
- " axes.minorticks_on()"
+ "from IPython.display import HTML\n",
+ "HTML('<iframe src=http://gambit.hepforge.org/ width=1000 height=350></iframe>')"
],
"language": "python",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "fragment"
}
},
- "outputs": [],
- "prompt_number": 15
+ "outputs": [
+ {
+ "html": [
+ "<iframe src=http://gambit.hepforge.org/ width=1000 height=350></iframe>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 28,
+ "text": [
+ "<IPython.core.display.HTML at 0x7fa181b92510>"
+ ]
+ }
+ ],
+ "prompt_number": 28
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "subslide"
}
},
"source": [
- "## The Debinning Demonstration ## \n",
- "\n",
- "Here's what it looks like:"
+ "## Shameless Gambit Advertising:"
]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "makeDebinningPlot()"
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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p6fPHmtIksSMiqo7UauDsCVf8vK05HGtnw7f3TUOHRETVQKkJW3R0dJmPiYjof7Kz5Di8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\nAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x7f6f69ebb4d0>"
- ]
- }
- ],
- "prompt_number": 16
+ "source": [
+ "### Our flagship scan: Supersymmetry!\n",
+ "### $\\qquad$ Our PMSSM-25 scan: Scanning 25 parameters!"
+ ]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### About us:\n",
+ "GAMBIT is a global fitting code for generic Beyond the Standard Model theories, designed to allow fast and easy definition of new models, observables, likelihoods, scanners and backend physics codes.\n",
+ "\n",
+ "GAMBIT is developed by a group of nearly 30 theorists and experimentalists. The Collaboration includes members of the AMS-02, ATLAS, CDMS, CTA, DARWIN, DM-ICE, Fermi-LAT, HESS, IceCube, LHCb and XENON experiments, as well as developers of the public theory codes DarkSUSY, FlexibleSUSY, IsaJet, SoftSUSY and SuperIso.\n",
+ "\n",
+ "We are currently finalising the code in preparation for first public release in Summer 2015 \u2014 stay tuned!"
+ ]
}
],
"metadata": {}
}
]
}
\ No newline at end of file
diff --git a/slides/GaussianSmoothing.png b/slides/GaussianSmoothing.png
new file mode 100644
index 0000000..1a2a403
Binary files /dev/null and b/slides/GaussianSmoothing.png differ
diff --git a/slides/GaussianSmoothing.xcf b/slides/GaussianSmoothing.xcf
new file mode 100644
index 0000000..72659b5
Binary files /dev/null and b/slides/GaussianSmoothing.xcf differ
diff --git a/slides/NewStatistics.ipynb b/slides/NewStatistics.ipynb
index aa9a5fd..65fbaff 100644
--- a/slides/NewStatistics.ipynb
+++ b/slides/NewStatistics.ipynb
@@ -1,1328 +1,2490 @@
{
"metadata": {
"celltoolbar": "Slideshow",
"name": "",
- "signature": "sha256:2bce91243675c2ebc3aedc4b2f7015599bac408ed281212c97958575a1a2ccbf"
+ "signature": "sha256:c94e26b181dc86a4f55663831151d0f22921545ad617cd94c6a17b51f70ae569"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
- "cell_type": "heading",
- "level": 1,
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import sys\n",
+ "sys.path[0] = '..'\n",
+ "from __future__ import division\n",
+ "import numpy as np\n",
+ "from time import time\n",
+ "import bisect\n",
+ "import operator as op\n",
+ "\n",
+ "from utilities import settings\n",
+ "import utilities.sampleFunctions as funcs\n",
+ "import utilities.probCalc as pc\n",
+ "import utilities.plotting as debinPlot\n",
+ "import utilities.minimizers as miniz\n",
+ "reload(funcs)\n",
+ "reload(pc)\n",
+ "reload(debinPlot)\n",
+ "reload(miniz)\n",
+ "\n",
+ "%matplotlib inline\n",
+ "from matplotlib import pyplot as plt\n",
+ "from IPython.display import HTML"
+ ],
+ "language": "python",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
}
},
- "source": [
- "<center> Data Smoothing with a New Probability Calculus </center>"
- ]
+ "outputs": [],
+ "prompt_number": 1
},
{
- "cell_type": "heading",
- "level": 3,
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "slide"
}
},
"source": [
- "<center> Abram Krislock$^{[1]}$ and Nathan Krislock$^{[2]}$ </center>"
+ "# <center> debinning: Data Smoothing with a New Probability Calculus </center>"
]
},
{
- "cell_type": "heading",
- "level": 4,
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "cell_type": "markdown",
+ "metadata": {},
"source": [
- "<center> $^{[1]}$ Fysisk institutt, Universitetet i Oslo. </center> \n",
- "\n",
- "<center> [a.m.b.krislock@fys.uio.no](mailto:a.m.b.krislock@fys.uio.no \"Email Abram\") </center>"
+ "## <center> Abram Krislock </center>"
]
},
{
- "cell_type": "heading",
- "level": 4,
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "cell_type": "markdown",
+ "metadata": {},
"source": [
- "<center> $^{[2]}$ Department of Mathematical Sciences, Northern Illinois University. </center> \n",
+ "### <center> Fysisk institutt, Universitetet i Oslo. </center> \n",
"\n",
- "<center> [krislock@math.niu.edu](mailto:krislock@math.niu.edu \"Email Nathan\") </center>"
+ "### <center> [a.m.b.krislock@fys.uio.no](mailto:a.m.b.krislock@fys.uio.no \"Email Abram\") </center>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"Set some useful LaTeX commands for later in the document:\n",
"$ \\newcommand{\\Int}[2] {\\displaystyle \\int\\limits_{#1}^{#2}} $\n",
"$ \\newcommand{\\Prod}[2] {\\displaystyle \\prod\\limits_{#1}^{#2}} $\n",
"$ \\newcommand{\\Sum}[2] {\\displaystyle \\sum\\limits_{#1}^{#2}} $ \n",
"\n",
"### \\Int{lower}{upper} : $ \\Int{lower}{upper},\\qquad $ \\Prod{lower}{upper} : $ \\Prod{lower}{upper},\\qquad $ \\Sum{lower}{upper} : $ \\Sum{lower}{upper} $ ###\n",
"\n",
- "$ \\newcommand{subNsubR}[3] {{}_{#1} {#2}_{#3}} $\n",
+ "$ \\newcommand{subNsubR}[3] {{}_{#1} #2_{#3}} $\n",
+ "$ \\newcommand{rust}[1] {{\\require{color}\\color{Bittersweet}#1}} $\n",
+ "$ \\newcommand{sky}[1] {{\\require{color}\\color{SkyBlue}#1}} $\n",
"\n",
- "### \\subNsubR{n}{K}{r} : $ \\subNsubR{n}{K}{r} $"
+ "### \\subNsubR{n}{K}{r} : $ \\subNsubR{n}{K}{r},\\qquad $ \\rust{q} : $ \\rust{q},\\qquad $ \\sky{q} : $ \\sky{q} $"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
- "Motivation"
+ "Once Upon A Time..."
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "subslide"
}
},
"source": [
- "## Histogram Bin Dilemmas ##\n",
- "\n",
- "Suppose we draw some (experimental or simulated) data for some physical observable, $x$. \n",
- "\n",
- "This data will follow some probability distribution function (PDF), which we will call $f(x)$."
+ "We knew all the stuff!"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "-"
}
},
"source": [
- "The easiest way to empirically determine the shape of $f(x)$ is to repeatedly measure $x$, and throw the results into a histogram."
+ "### \"At the end of the 19th century... it was generally accepted that all the important laws of physics had been discovered...\" ([Source](http://en.wikipedia.org/wiki/History_of_physics \"http://en.wikipedia.org/wiki/History_of_physics\"))"
]
},
{
- "cell_type": "heading",
- "level": 2,
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "Probability of Datum and Data Samples"
+ "### Then this stuff happened:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "## Basic Datum Probability ##\n",
+ "$${\\huge{\\rm He}^{++},~{\\rm e}^-,~\\gamma \\qquad\\qquad \\hbar \\qquad\\qquad g^{\\mu\\nu}}$$\n",
"\n",
- "Suppose we draw some data (experimental or simulated) for some physical observable, $x$. \n",
- "\n",
- "This data will follow some probability distribution function (PDF)."
+ "$${\\huge E^2 = (mc^2)^2 + (pc)^2}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "The PDF, which we will call $f(x)$, gives the probability for a datum to lie between $x$ and $x + dx$. Thus,\n",
- "\n",
- "$$ P(\\tilde{x}\\in[x,x+dx]) = f(x) dx \\qquad {\\rm and} \\qquad \\Int{-\\infty}{\\infty} f(x) dx = 1~. $$"
+ "$${\\Large \\cdots {\\rm SU}(3)_C \\times {\\rm SU}(2)_L \\times {\\rm U}(1)_Y}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "--- \n",
- "\n",
- "The cumulative distribution function (CDF) is the anti-derivative of the PDF: \n",
- "\n",
- "$$ \\Int{-\\infty}{x} f(\\tilde{x}) d\\tilde{x} \\equiv F(x)~. $$\n",
- "\n",
- "It represents the probability to draw some value less than or equal to $x$."
+ "### Okay... But after that... Surely, we knew all the stuff!"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Well, actually...."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "notes"
+ "slide_type": "-"
}
},
"source": [
- "$$ \\Int{x}{\\infty} f(\\tilde{x}) d\\tilde{x} \\equiv 1 - F(x)~. $$"
+ "### Then this stuff happened:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "-"
}
},
"source": [
- "## Samples - I: Probability Density ## \n",
- "\n",
- "Let us define a sample of data as $\\{x_1, x_2, x_3 \\cdots\\}$, or just $\\{x_i\\}_{i=1}^n$ for a general sample with n data points."
+ "![We know almost nothing.](stuffWeKnow.png \"We know almost nothing.\")"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Let's face it."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "-"
}
},
"source": [
- "WLOG, let us take $x_i > x_j$ for any $i > j$."
+ "### Large Hadron Collider: A \"New Stuff\" Experiment"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "-"
}
},
"source": [
- "\\begin{align} \n",
- " P(\\{x_1\\}\\ d\\{x_1\\} &= f(x_1) dx_1 \\\\\n",
- " P(\\{x_1, x_2\\})\\ d\\{x_1, x_2\\} &= 2 \\times f(x_1) dx_1 f(x_2) dx_2 \\\\\n",
- " P(\\{x_1, x_2, x_3\\})\\ d\\{x_1, x_2, x_3\\} &= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3\n",
- "\\end{align}"
+ "![New stuff experiment!](epicLHCHighFive.png \"New stuff experiment!\")"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Dark Matter @ Large Hadron Collider\n",
+ "\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"\\begin{align}\n",
- " &{\\phantom=}\\mkern-17mu\\vdots \\\\\n",
- " P(\\{x_i\\}_{i=1}^n) d\\{x_i\\}_{i=1}^n &= n! \\Prod{i = 1}{n} f(x_i) dx_i \\\\\n",
- " \\phantom{d^3P(\\{x_1, x_2, x_3\\} \\equiv \\{x_1, x_3, x_2\\}\\cdots)} &\\phantom{= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}\n",
+ " {\\Huge \\widetilde{q_L}} & {\\Huge\\rightarrow} & {\\Huge \\rust{q}} \\\\\n",
+ " & {\\Huge\\searrow} \\\\\n",
+ " & & {\\Huge\\widetilde{\\chi}^0_2} & {\\Huge\\rightarrow} & {\\Huge h^0} & {\\Huge\\rightarrow} & {\\Huge \\rust{b}}\\\\\n",
+ " & & & {\\Huge\\searrow} & & {\\Huge \\hookrightarrow} & {\\Huge \\rust{b}} \\\\\n",
+ " & & & & {\\Huge \\color{Gray}{\\widetilde{\\chi}^0_1}}\n",
"\\end{align}"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "## Samples - II: Integration ## \n",
+ "### Calculate as one particle, the mass:\n",
"\n",
- "Since the sorted data is the most general, we must have care with integration limits:"
+ "$${\\huge m_{\\rust{q h^0}} \\qquad {\\rm using} \\qquad E^2 = (mc^2)^2 + (pc)^2}$$"
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "subslide"
}
},
"source": [
- "$$ \\Int{\\{x_1\\}_1}{} dP(\\{x_1\\}_1) = \\Int{-\\infty}{\\infty} f(x_1) dx_1 = 1 $$"
+ "The $m_{\\rust{qh^0}}$ Maximum Measurement"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ \\Int{\\{x_2\\}_2}{} dP(\\{x_1, x_2\\}_2) = 2 \\times \\Int{-\\infty}{\\infty} f(x_2) \\left[ \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right] dx_2, $$"
+ "![You want me to try.... What?!](tryChangingTheBins.png \"You want me to try.... What?!\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ \\Int{\\{x_3\\}_3}{} dP(\\{x_1, x_2, x_3\\}_3) = 3! \\times \\Int{-\\infty}{\\infty} f(x_3) \\left[ \\Int{-\\infty}{x_3} f(x_2) \\left( \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right) dx_2 \\right] dx_3 $$\n",
- "$$ \\vdots $$"
+ "### Change the... bins? Seriously?!"
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "subslide"
}
},
"source": [
- "## Samples - III: To be $r$th out of $n$... ## \n",
- "\n",
- "Let us define a new notation:"
+ "Change the bins! How bad could it be?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ {\\Large \\subNsubR{n}{f}{r} \\left[g\\left(\\{x_i\\}_n\\right)\\right] dx_r \\equiv \\Int{\\{x_{i \\neq r}\\}_n}{} g\\left(\\{x_i\\}_n\\right) dP(\\{x_i\\}_n) } $$ \n",
- "\n",
- "Interpretation: The expectation value of the function $g(\\{x_i\\}_n)$ as a function of the $r$th point of the sorted sample."
+ "![It could be very bad...](binningDilemma_final_orig.png \"It could be very bad...\")"
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "subslide"
}
},
"source": [
- "Then, $\\subNsubR{n}{f}{r} \\left[1\\right]$ is just the PDF of the $r$th data point for any sample of $n$ data points. Let us call it $\\subNsubR{n}{f}{r}(x_r)$.\n",
+ "Okay, that's bad, but how often...?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "funcs.randomGenerator.setSeed('seedOne')\n",
+ "funcs.settings['simpleSortedOutput'] = True\n",
"\n",
- "Theorem:\n",
+ "nPulls = 400\n",
+ "basePars = (0.00006, 10., 200., 110., 1.5, 50., 140.)\n",
+ "baseGuess = (140., -2., -0.1, 10.)\n",
"\n",
- "$$ {\\Large \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r}\\ f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. $$"
+ "def fitTwoHistograms(percentile):\n",
+ " data = funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, (0,200), basePars)\n",
+ " percentieth = data[data > np.percentile(data, percentile)]\n",
+ "\n",
+ " # The histograms are filled with the same data, only different binning.\n",
+ " binContentsOne, binEdgesOne = np.histogram(percentieth, np.arange(3., 204., 10.))\n",
+ " binContentsTwo, binEdgesTwo = np.histogram(percentieth, np.arange(0., 201., 5.))\n",
+ " \n",
+ " # The fit ranges are defined to be from the value of the 70th percentile data point\n",
+ " # to \"the last non-zero bin\", blindly.\n",
+ " fitBinsOne = np.flatnonzero(binContentsOne[binContentsOne.argmax():]) + binContentsOne.argmax()\n",
+ " fitBinsTwo = np.flatnonzero(binContentsTwo[binContentsTwo.argmax():]) + binContentsTwo.argmax()\n",
+ " \n",
+ " ### FITTING METHOD: Binned Maximum Likelihood ###\n",
+ " fitGuessOne = np.array([value * funcs.randomGenerator.normal(1., 0.1) for value in baseGuess])\n",
+ " fitGuessTwo = fitGuessOne.copy()\n",
+ "\n",
+ " def chiSqOne(pars):\n",
+ "# return funcs.chiSqSimple(binContentsOne, binEdgesOne, fitBinsOne, funcs.theKink, pars)\n",
+ " return -2. * funcs.theKink_BinnedLikelihood(binContentsOne, binEdgesOne, fitBinsOne, pars)\n",
+ " def chiSqTwo(pars):\n",
+ "# return funcs.chiSqSimple(binContentsTwo, binEdgesTwo, fitBinsTwo, funcs.theKink, pars)\n",
+ " return -2. * funcs.theKink_BinnedLikelihood(binContentsTwo, binEdgesTwo, fitBinsTwo, pars)\n",
+ "\n",
+ " fitOne = miniz.nelderMead(chiSqOne, fitGuessOne, xtol=0.01, ftol=0.05, disp=0)\n",
+ " fitTwo = miniz.nelderMead(chiSqTwo, fitGuessTwo, xtol=0.01, ftol=0.05, disp=0)\n",
+ " return (data, fitOne, fitTwo)\n",
+ "\n",
+ "xKinkOne = []\n",
+ "xKinkTwo = []\n",
+ "xKinkDiff = []\n",
+ "percentile = 60\n",
+ "nTrials = 1000\n",
+ "\n",
+ "for i in xrange(nTrials):\n",
+ " data, fitOne, fitTwo = fitTwoHistograms(percentile)\n",
+ " xKinkOne.append(fitOne[0])\n",
+ " xKinkTwo.append(fitTwo[0])\n",
+ " xKinkDiff.append(baseGuess[0] + fitTwo[0] - fitOne[0])"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def plotHistoFitCompare():\n",
+ " fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ " plt.hist(xKinkOne, range=(80,180), color='#66a61e', bins=np.arange(80, 181, 2), alpha=0.6, zorder=2)\n",
+ " plt.hist(xKinkTwo, range=(80,180), color='#0088ff', bins=np.arange(80, 181, 2), alpha=0.6, zorder=2)\n",
+ " plt.hist(xKinkDiff, range=(80,180), color='#000000', bins=np.arange(80, 181, 2), alpha=0.8, zorder=1)\n",
+ "\n",
+ " axes.set_xticks(np.arange(80, 181, 10))\n",
+ " axes.set_xticks(np.arange(80, 181, 2), minor=True)\n",
+ " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(80., 181., 10.)], fontsize=20)\n",
+ "\n",
+ " axes.set_yticks(np.arange(0, 250, 50))\n",
+ " axes.set_yticks(np.arange(0, 250, 10), minor=True)\n",
+ " axes.set_yticklabels([r'$%i$' % num for num in np.arange(0, 250, 50)], fontsize=20)\n",
+ "\n",
+ " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ " axes.minorticks_on() \n",
+ " axes.set_xlabel('Kink Fit Result', labelpad=5, fontsize=22)\n",
+ " axes.set_ylabel('Number of Counts (400 total)', labelpad=5, fontsize=22)\n",
+ "\n",
+ " print"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "plotHistoFitCompare()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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79+7V0aNHzUkcYDTKABAcaJQBmN2XGZ564XK5dO7cuYrjoqIi7du3T3379q1o\nkiWpdevWOnXqlG9TAgAAAH5muFHu2LGjdu3aVXG8Zs0auVwu9e3b16MuPz+/1o0+AAAAgGBnuFG+\n8847dejQIU2dOlUffPCBnnvuOUnSyJEjPep2796thIQE36YEAAAA/Mxwo/z888+rXbt2mj9/vsaO\nHatvvvlG9913X8W20ZL09ddfKycnR7fccospYQEAAAB/MbzhSHx8vHbu3KmFCxfq+PHj6tWrV6U1\niPfs2aPRo0fr7rvv9nlQAAAAwJ8Mr3qBC1j1AgCCA6teAAiaVS8mTZqkP/7xj7XWpaena/LkyfUK\nBQAAAASa4UY5IyOj0vbVVdm8ebMyMjLqFQoAAAAINMNzlI06f/68x7rKjZHD4fA4tlqtslqtAUoD\nADBLydlz+ukDI2sv/P9ahFq1+J1ltRcC8JrT6ZTT6d+pUD5vlPfv36/Y2Fhf3zao2Gw2j+OUlBSl\npqYGJgwAwDShERbd9Xg3w/WrXt1jYhqgabPb7UpLS/Prd9bYKE+aNMljkvTmzZurnX9cVlam/fv3\na+fOnRoxYoTvkwaRnJwcj2NGkwEAAMyVnJyspKQkj3OXDl76Wo2N8qVzjQ8ePKiDBw/WeMP27dvr\npZdeqn+yIBYfHx/oCAAAAE1KIKa61tgo/3CVi8mTJ6tv37566KGHqlyGIywsTB07dlTv3r0VFhbm\n+6QAAACAH9XYKD/44IMVv05NTVXv3r01ceJEszMBAAAAAWf4Zb5Dhw6ZGAMAAO8UFJ9WWZ53b8Bb\nDC+KCgAmrHoBAIA/NI+Qev3Mu5351i1mlz0AxnndKG/dulVr167VsWPHVFJSUm2dkV38AAAAgGBl\nuFE+d+6cxo0bpw8//NBQPY0yAAAAGjLDjXJqaqo+/PBDRUVFafz48br22msVHR1dZW1j35kPAAAA\njZ/hRvm9995TixYttGPHDl133XVmZgIAAAACznCj7HA4NGTIEJpkAIApunbtqqKiIsP152p4TwYA\nfMFwo9ymTZtqp1oAAFBfRUVFatPG+CoWpw87TEwDAJLhFSVHjBihrVu3qqyszMw8AAAAQFAwPKL8\nq1/9Sv/4xz/02GOP6dVXX1V4eLiZuQAACLjC4pZ6OWW74fq8rFwT0wDwN8ON8vz583XnnXdq4cKF\n+uSTTzRkyBB16tRJzZpVPSg9c+ZMn4UMNg6H53/us1qtslqtAUoDADCLO+wyxd03x3D98dmPmZgG\naNqcTqc4MKkTAAAgAElEQVScTv9uGmS4UU5LS6v49ZEjR5Senl5trcViadSNss1m8zhOSUlRampq\nYMIAAAA0AXa73aMf9QfDjbI3jW9jX0c5JyfH45jRZAAAAHMlJycrKSnJ49ylg5e+5tWGI7ggPj4+\n0BEAAACalEBMdTW86gUAAADQlNAoAwAAAFXw6mU+b+YeN+aX+QAAAND41WnVi9o09lUvAAAA0PjV\ne9WL8vJyHT58WBs2bNDRo0c1adIkderUyWcBAQAAgEDw2aoXZ8+e1aOPPqpPPvlEO3furG8uAAAA\nIKB89jJfZGSk3nrrLZWVlemFF17w1W0BAACAgPDpqheRkZHq0aOHVq9e7cvbAgAAAH7n8+XhysrK\ndOrUKV/fFgAAAPArw3OUjfjmm2+0efNmdq4DAASlorNR2vJpiOF6l8t4LYDGx3CjnJGRUe06yoWF\nhTpw4ICWLFmi4uJi3XvvvT4LCACAz4RfphZ3GV++1P1GqnlZAAQ9w43ypEmTDNWNHDlSKSkpdQ7U\nEDgcDo/jQOw9DgAA0JQ4nU45nU6/fqfhRnnChAnVfhYWFqaOHTvq1ltvVd++fX0SLJjZbDaP45SU\nlFqXzwMAAEDd2e12rzbA8wXDjXJ6erqJMRqWnJwcj2NGkwEAAMyVnJyspKQkj3OXDl76mk9f5msq\neFkRAADAvwIx1bXOjbLD4aiYq2uz2dShQwefhQIAAAACzet1lN9++21dc801uvzyy9WrVy/16tVL\nHTt21LXXXquFCxeakREAAADwO69GlCdOnKglS5ZUHF+cguBwOJSZmakpU6Zoy5YtzGcGAJiupNS7\nNZElqczFjEMAxhn+E2PZsmVasmSJ2rZtq7S0ND344IMKDw+XJJWUlCgjI0MpKSlasmSJhg4dqv/+\n7/82LTQAAG4v10SWJLEuMgAvGJ56sXDhQoWGhmrt2rWaMmVKRZMsSREREZoyZYrWrVunkJAQvf32\n26aEBQAAAPzFcKO8a9cuDRo0SNdff321NV27dtXgwYO1e/dun4QDAAAAAsVwo1xUVKTWrVvXWteq\nVSsVFxfXKxQAAAAQaIYbZZvNph07dsjtdldb43a79eWXX7LOMAAAABo8w43ynXfeqaysLD399NNy\nuVyVPne5XHruuef07bff6s477/RpSAAAAMDfDK968dxzz2nZsmX67W9/q1WrVum+++5TYmKiLBaL\nvv32Wy1btkzZ2dmKiYnR9OnTzcwMAAAAmM5wo5yQkKDVq1dr3Lhxys7O1ksvvVSp5vLLL9df/vIX\nderUyachAQAAAH/zauX13r1765tvvtH777+vjRs3KicnR9KF+cuDBg3Sz372M49l4wAAAICGyust\niiIiIjR+/HiNHz/ejDwNgsPh8Di2Wq2yWq0BSgMAAND4OZ1OOZ1Ov36n4Zf58H9sNpvHj91uD3Qk\nAACARs1ut1fqwcxWY6M8btw4de/eXVu2bKn1Rps2bdKPf/xj3X///T4LF6xycnI8fpKTkwMdCQAA\noFFLTk6u1IOZrdqpF2vXrtXy5cs1btw49e3bt9YbDRgwQJ07d9ayZcv0yCOPqH///j4NGkxYJxoA\nAMC/AjHVtdoR5WXLlkmSUlJSDN8sNTVVkvSnP/2pfqkAAACAAKu2Ud62bZuuueYadenSxfDNunbt\nqmuuuUZbt271STgAAAAgUKqdenH06FHddtttXt+wS5cuWrt2bb1CAQCanlOF55Wvc4brXW6vF24C\nAK9U+6fMuXPnFBkZ6fUNIyMjde6c8T/oAACQpPIwq8KGphm/4IPnzQsDAKph6kWrVq0qrRdshMPh\nUGxsbJ0DnTt3TuvXr9eIESOq3P3vorKyMqWkpOiGG27Q4MGD1b17d7344otyuVz1qgUAAACkGkaU\nr7/+em3btk1FRUVq2bKloZsVFhZqx44d6tOnj9dBTpw4oQceeEAtW7ZU+/bttXr1avXq1ava+qlT\np2rNmjXasWOH4uLidOrUKfXq1UuZmZnKyMiocy0AAAAg1dAoDxs2TOvWrdOvf/3rGkd2f2j27Nkq\nKSnRsGHDvA7Stm1bffrpp5KkjRs3asGCBdXWbtmyRYsWLdKCBQsUFxcnSYqLi9P06dM1ZcoUPfzw\nw+rXr5/XtQAA1IezwKmfPjDScH2LUKsWv7PMxEQA6qPaRjkpKUmzZ8/W3Llz1bZtWz3xxBM13uj3\nv/+95syZo9jYWD388MP1CuV2u2v8PD09XZI0ZswYj/OjR4/WlClTlJ6eXtH8elMLAEC9WNy66/Fu\nhstXvbrHxDAA6qvaRtlqtWrx4sUaNWqUnnzySWVkZGjChAnq2bOn2rZtK0k6fvy4vvjiCy1evFi7\nd++WxWJRenq6oqOjTQ29ceNGtW7duiLHRe3atVNsbKw2b95cp1oAAADgohrX1hk+fLhWrlypCRMm\naNeuXdq1a5csFotHzcXR3+joaKWnp2vUqFHmpdWFF/Oys7PVuXPnKj+Pi4vT4cOHva4FAAAAfqja\nVS8uGj16tL799lvNnDlTN9xwg6QLzfHFBvnGG2/UzJkzdfDgQd11113mppWUn58vl8tV7dJ1ERER\nKi0tVXFxsVe1AAAAwA8ZWq29devWSk1NVWpqqsrKyvT9999XnG/e3L8LvpeUlEhStd/brNmF3v/M\nmTMVy78ZqW3RooWvowIAAKAB87rLbd68udq1a2dGFkNiYmJq/LywsFDShdHi0NBQw7XeMLK+tNVq\nldVq9eq+AAAAkJxOp5xOZ6BjeN8oB1pUVJQiIyNVXl5e5edFRUUKCQlRdHS0QkJCDNd6w2az1VqT\nkpKi1NRUr+4LAE1ZmatMxaUFgY4BIAjY7XalpXmxU6dJGlyjLEmJiYnKy8urdL68vFz5+flKTExU\nSEiI17VG5eTk1FrDaDIAeMcSIrW90vh/4TtkXhQAAZacnKykpKRa64wMXtZHg2yUhw0bpnnz5qmw\nsFBRUVEV5zMzM1VSUqL+/fvXqdao+Pj4+j0AAAAAqhUsU1hrXfUiGI0ZM0Zut1srV670OL98+XJJ\n0vjx4+tUCwAAAFwUlI3yxakNx44dq/Lzfv36afjw4Zo5c2ZFzZEjR/Taa69p/PjxGjhwYJ1qAQAA\ngIuqbZQLCgp09uxZf2ZRz549lZiYqPHjx8tisWjBggVq3769unfvrq+//tqjdsWKFRo3bpzuuOMO\n9e/fX0OHDtXkyZO1aNGiSvf1phYAAACQapijHBMTowcffFB//OMfJUlpaWm66aabNHr0aNPCfPHF\nF4Zrw8PDNXfuXM2dO9entQAAAIDkxdSLtLQ0rVq1yswsAAAAQNCotlGOjIzU6dOn/ZkFAAAACBrV\nTr247rrr9Nlnn+kPf/iDOnfuLEnKzc3Vpk2bDN14wIABvkkIAAAABEC1jfKjjz6qpKQkPfzwwxXn\nPv74Y3388ce13tRiscjlcvkmIQAAABAA1TbKDz30kNq3b6/3339fR48e1YYNG9SuXTtde+21td7U\nYrH4NCQAAADgbzXuzDdy5EiNHDlSktSsWTMNGzasYhUMAADg6VxRsV5O2W64Pi8r18Q0AOrL8BbW\nEyZMUN++fc3MAgBAwxZuVdx9cwyXH5/9mIlhANSX4UY5PT3dxBgNi8Ph8DgOlv3IAQAAGiun0ymn\n0+nX7zTcKP/Q1q1btWHDhoqG0WazadCgQbrlllt8Gi5Y2Ww2j+OUlBSlpqYGJgwAAEATYLfblZaW\n5tfv9KpRzs7O1v3336/t2yvPv7JYLOrdu7eWLl2qK664wlf5glJOTo7HMaPJAAAA5kpOTlZSUpLH\nuUsHL33NcKN8+vRpDRkyRIcPH1ZUVJRGjRqlxMRESVJWVpY+/PBDbdu2TYMHD9bOnTsVGxtrWuhA\ni4+PD3QEAACAJiUQU10NN8q/+c1vdPjwYd19992aP3++Wrdu7fH5999/r0cffVTLly/Xyy+/rNmz\nZ/s8LAAAAOAv1W5hfakPPvhA7du315IlSyo1yZLUunVrLV68WO3bt9cHH3zg05AAAACAvxlulA8d\nOqQBAwYoIiKi2pqIiAj1799fhw4d8kU2AAAAIGAMN8rNmzdXcXFxrXVnz55V8+Z1WkwDAAAACBqG\nG+UuXbpo/fr1OnbsWLU1ubm5Wr9+vbp06eKTcAAAAECgGG6Ux48fr6KiIt12221au3Ztpc/XrVun\n22+/XUVFRRo/frxPQwIAAAD+ZniOxJQpU7RixQpt3LhRd9xxh+Lj45WYmCiLxaLs7Gx99913kqRB\ngwbpkUceMS0wAAAA4A+GR5RDQ0O1evVqPf3002rRooVycnK0efNmff755/ruu+8UFRWlp59+WqtX\nr2aOMgAAABo8rzraiIgIvfzyy0pLS9NXX31VsUNdx44d1b179xpXxAAAAAAakjoN/UZGRqpfv36+\nzgIAAAAEDcNTLwAAAICmhEYZAAAAqAJv3dWBw+HwOLZarbJarQFKAwAA0Pg5nU45nU6/ficjynVg\ns9k8fux2e6AjAQAANGp2u71SD2Y2RpTr4OJqHxcxmgwAAGCu5ORkJSUleZwzu1mmUa6D+Pj4QEcA\nAABoUgIx1dXw1IsPPvhAq1evNjMLAAAAEDQMN8o/+clP9Lvf/c7MLAAAAEDQMNwox8bGKi4uzsws\nAAAAQNAw3Cj36tVLe/fuNTMLAAAAEDQMN8rPPfec9u3bp0WLFpmZBwAAAAgKhle9cLvdeuSRR5SU\nlKTly5frJz/5iRISEhQZGVll/YABA3wWEgCAQDmYedBwbXm528QkAPzNcKM8ePDgil9/+umn+vTT\nT6uttVgscrlc9UsGAEAQCGkeEugIAALEcKPszQixxWKpUxgAAAAgWBhulDds2GBiDAAAACC4GH6Z\nDwAAAGhK6twol5aW6tixY/r+++99mQcAAAAICl43yhkZGerRo4datmypjh076plnnqn4bOXKlbrv\nvvuUnZ3t05DBxuFwePw4nc5ARwIAAGjUnE5npR7MbF41yhMnTtSkSZO0c+dORUREyO32XAbnmmuu\n0Xvvvaf333/fpyGDjc1m8/ix2+2BjgQAANCo2e32Sj2Y2Qw3yhkZGVqyZIluvPFGffHFFyooKKhU\nc/3116tjx476+OOPfRoy2OTk5Hj8JCcnBzoSAABAo5acnFypBzOb4VUvFi5cqKioKP3tb39Tx44d\nq63r1q2bDhw44JNwwSo+Pj7QEQAAAJoUq9Uqq9Xq1+80PKK8Z88e3XLLLTU2yZIUExOj3NzcegcD\nAAAAAslwo1xaWqqoqKha606cOKHmzQ0PVAMAAABByXBH26lTJ+3du7fGGpfLpf379+uqq66qdzAA\nQMPWtWtXFRUVGa4vd7GrK4DgYnhE+c4771RmZqaWLFlSbc2CBQt07NgxjRgxwifhAAANV1FRkdq0\naWP4BwCCjeFG+emnn1Z0dLT+53/+RzNmzNBXX30lSSopKdGBAweUlpamJ598Uq1atdK0adNMCwwA\nAAD4g+FG+fLLL9fKlSsVFRWluXPnqmfPnpKk9957T//1X/+ltLQ0RUZGavny5WrXrp1pgQEAAAB/\n8GrDkcGDB2vfvn165plndP311ysyMlJhYWG68sorNW3aNO3du1eDBg0yKSoAAADgP14vT9GhQwfN\nnTtXc+fONSMPAAAAEBS8GlEGAAAAmoo6LXj83XffadOmTRVbB9psNg0YMKDWzUgAAACAhsKrRvnE\niROaNm2a/vrXv8rlcnl81qxZM40dO1ZvvPGG2rZt69OQAAAAgL8ZbpRPnz6t/v37KzMzU82aNVOf\nPn10xRVXSJIOHTqk7du3a8WKFdq9e7e2b9+uVq1amZUZANAAnCo8r3ydM1zvcje9XV2dBU799IGR\nXl3TItSqxe8sMykRgB8y/KdSamqqMjMzdeutt2r+/PmVdt/79ttvNXXqVH322WdKTU3Vq6++6vOw\nwcLhcHgcW61WWa3WAKUBgOBUHmZV2NA04xd88Lx5YYKVxa27Hu/m1SWrXt1jUhgguDmdTjmdTr9+\np+GX+VauXKm4uDitXLmyyi2qr7rqKq1YsUJxcXFatWqVT0MGG5vN5vFjt9sDHQkAAKBRs9vtlXow\nsxkeUT5x4oTGjBmjqKioamuioqI0cOBA/f3vf/dJuGB18SXGixhNBgAAMFdycrKSkpI8zpndLBtu\nlG02m0pLS2utO3/+vDp06FCvUMEuPj4+0BEAAACalEBMdTXcKI8bN05vvPGGjh07Vm0jnJubq3Xr\n1mnKlCk+CwgAAP7P11/t8uoFQF7+A+rOcKM8c+ZMbdiwQUOGDJHdbtfw4cM9Pl+9erWSk5PVtWtX\n/epXv/J5UAAAIFlCXV69AMjLf0DdVdsoDx48WBaLxeNcSEiI/vOf/2jUqFGKiYnxWB4uLy9PknTL\nLbdoxIgRWrdunXmpAQB+d++DU5RfYry+1OU2LwwA+EG1jfLGjRurvcjtdisvL6+iOf6hbdu2+SYZ\nACCo5JdICQ8uMH7B+q7mhQEAP6i2Ua7PiPClI9FmuP3227Vp0yaFhYUpLCxMZWVlKisr0y9/+UvN\nmDHDo7asrEyzZs3SqlWr1KpVKxUUFGjs2LGaMWOGQkJCTM8KAACAhqfaRnnQoEF+jOG9srIyJSYm\n6vDhw2rRooUGDhyo5ORk9e3bt1Lt1KlTtWbNGu3YsUNxcXE6deqUevXqpczMTGVkZAQgPQAAAIJd\ng94v9N///netNVu2bNGiRYu0YMECxcXFSZLi4uI0ffp0TZkyRQ8//LD69etndlQAAAA0MIZ35muo\n0tPTJUljxozxOD969GiPzwEAAIAf8mpE+fTp03rzzTe1YcMGORwOlZRU//pzVlZWvcP5wsaNG9W6\ndWu1bdvW43y7du0UGxurzZs3BygZAAAAgpnhRvngwYMaMGCAcnNzzczjlUOHDumJJ55QQUGB8vLy\ndPfdd+v555+veEGvrKxM2dnZ6ty5c5XXx8XF6fDhw/6MDAAAgAbCcKOcnJys3Nxc9e/fX08++aQ6\nd+6sqKgoM7PVyO12a9q0aXr77bfVoUMH5ebmqmfPnjpw4IDeffddSVJ+fr5cLpciIyOrvEdERIRK\nS0tVXFysFi1a+DM+AAAAgpzhRnn9+vVKSEjQp59+qvDwcDMzGRIXF6ff/va3Fdtpt2/fXk8++aSe\nfvppTZw4UUOHDq2YGtK8edWP2azZhSnaZ86coVEGAACAB8ONssViUa9evYKiSZak5cuXVzp3/fXX\nS5IWL16soUOHKiYmpsZ7FBYWSrowsuwNh8NRa43VapXVavXqvgAAAJCcTqecTmegYxhvlH/0ox8F\nzfzk8+fPKy8vr9ILeheb+L1790qSoqKiFBkZqfLy8irvU1RUpJCQEEVHR3v1/TabrdaalJQUpaam\nenVfAAAASHa7XWlpaYGOYbxRfvrpp3X33Xdry5YtVW7q4U+jRo3S2rVr9fnnn6t3794V5y+OEIeG\nhlacS0xMrHKr7fLycuXn5ysxMdHr3flycnJqrWE0GQAAoG6Sk5OVlJRUa52Rwcv6MNwojxkzRnPn\nztXw4cM1bdo03XnnnerYsWPFPN9LderUyWchL3XixAnFxMTosssu8zh/sYHt3r17xblhw4Zp3rx5\nKiws9Hj5MDMzUyUlJerfv7/X3x8fH1/H5AAAAKhNsExh9Wod5R49eiguLk6//vWvNXv27Cpr3G63\nLBaLXC6XTwJW5fbbb9ett96qLl26eJz/5JNPFBoaqp///OcV58aMGSO73a6VK1dq/PjxFecvznH+\n4TkAgO+Uy63i0oJAxwCAOjPcKK9du1bDhg1TWVmZJCk2Nrba5eEsFotv0lVj+vTpGjlypFq0aFGx\n/fTmzZu1evVqzZs3T926dauo7devn4YPH66ZM2fqtttuU4cOHXTkyBG99tprGj9+vAYOHGhqVgBo\nqiyS2l5p/GXpQ6YlAYC6Mdwoz5w5U2VlZXr22Wc1ffr0WleUMFNsbKxWrFihZ599Vv/7v/8ri8Wi\n0NBQ/eMf/9CQIUMq1a9YsUIzZ87UHXfcoZiYGJ06dUqTJ08OikniAAAACE6GG+Xdu3ere/fumjNn\njpl5DGvfvr0WL15sqDY8PFxz587V3LlzTU4FAACAxqLqN/GqEBERoauvvtrMLAAAAEDQMNwoDxw4\nUPv27TMzCwAAABA0DE+9+NWvfqVevXrpd7/7nX7xi1+YmQkA4KV7H5yi/BLj9TER0nvpC7z6js2b\nN2tL2FLD9W65vbo/AAQbw43yl19+qUmTJumpp57S8uXLa11HecKECT4LCQCoWX6JlPCg8cb3cPoU\nr7/D5SpTVESk4fpCr78BAIKL4UZ50qRJFb/eunWrtm7dWm2txWKhUQYAoAGaMOm/VXze6dU1LUKt\nWvzOMpMSAYFjuFH2pvE1ex1lAABgjuLzTt31eLfaC39g1at7TEoDBJbhRjk9Pd3EGAAAAEBw8WoL\na1zgcDg8joNlP3IAAC719Ve79NMHRhqu37Nnt+6SdyPKgD84nU45nd5NC6ovGuU6sNlsHscpKSlK\nTU0NTBgAqIPNmzcrISHBq2tKzlkUZVIemMcS6vJqKsWuh74yMQ1Qd3a73e+7KhtulDMyMryae9yY\nX+bLycnxOGY0GUBD43KVqU37Nl5dc8R5yqQ0AFC75ORkJSUleZy7dPDS1+q06kVtGvuqF/Hx8YGO\nAAAA0KQEYqprvVe9KC8v1+HDh7Vz504VFRXprrvu0mWXXeazgAAANFbnior1csp2r67JPcFGLoC/\n+GzVi+PHj2vixIk6ePBgjWssAwCA/y/cqrj75nh1ycG9400KA+BSVW+rVwft2rXTu+++q5ycHKWk\npPjqtgAAAEBA+KxRlqRWrVqpR48e+utf/+rL2wIAAAB+59NGWZLCwsJ07NgxX98WAAAA8CufNsq5\nubnaunWr2rTxbskhAAAAINgYfplv48aN1a6jXFhYqAMHDuiNN95QXl6e7r33Xp8FBAAAAALBcKM8\nePBgWSwWud01L0tz00036cUXX6x3MABAcLE0k4pLCwIdI+gdzDxouLa8nKXegGBmuFEeMGBAtZ+F\nhYXJZrPptttu07hx4xQaGuqTcACA4NGsmdT2ygjD9YfMixLUQpqHBDoCAB8x3Chv2LDBxBgAAABA\ncDHcKAMAgtfmzZu1JWyp4fqSc+ck+XcrWABoaGiUAaARcLnKFBURabi+0MQsANBYVNso17TKhRE1\nzWlu6BwOh8ex1WqV1crIDAAAgFmcTqecTqdfv7PaRtnoKhdVsVgscrlc9QoWzGw2m8dxSkqKUlNT\nAxMGAACgCbDb7UpLS/Prd1bbKHft2tWrG1ksFmVnZ6u4uLjeoYJdTk6OxzGjyQAAAOZKTk5WUlKS\nx7lLBy99rdpGee/evYZvsm/fPj3//PPat2+fJPNDB1p8fHygIwAAADQpgZjqWq+X+Y4cOaKZM2dq\n6dKlcrlcio2N1YwZMzRt2jRf5QOABu/eB6cov8S7a2IipPfSF5gTCABgSJ0a5VOnTumll17S/Pnz\nde7cObVo0UJPPPGEnn32WV122WW+zggADVp+iZTwoHdN7+H0KSalAQAY5VWjXFRUJLvdLrvdLqfT\nqebNm+uRRx7RzJkz1b59e7MyAgAAAH5nqFE+f/685s+fr5deekknTpyQxWLRPffcoxdffFFXXXWV\n2RkBoMnZvfML3Xmv8VHlUpf3KxQBAGpWY6Psdru1dOlSpaSkKDs7W5J0xx13aPbs2brpppv8EhAA\nmqLzIS28m66x3ruVigAAtau2Uf7HP/6h559/Xnv27JEk3XzzzZo9e7YGDx7st3AAEIy8fTlv9559\nSjAvTt2UlSrz5DmvLnG52cwVQNNS7Z96o0aNkiS1aNFCjz/+uO6++25ZLBbt3LnT0I1//OMf+yYh\nAASZv6/ZLMuQ5w3XF3+/2cQ0dRQerbChXi7c/4HxZwaAxqDW4YHi4mLNmTNHc+fOlXRhOkZNW1tf\n/Lwx78wHoGlzucoUFRFpuL64DjucAgACr9pGuVOnTvXawhoAAABoyKptlA8dOuTHGAAAAEBwaRbo\nAAAAAEAw4hVmAAhCeXl5evfdpYbry8vLvfsCi1RcWuBlKgBoWmiU68DhcHgcW61WWa3WAKUB0Ci5\n3Yrw4oXBQm/vb5HaXhnh1SWHvP0OAPAhp9Mpp9Pp1++kUa4Dm83mcZySkqLU1NTAhAFQSdeuXVVU\nVGS4Pjc3V+3btzdcX3LOoqi6BAN84FxRsV5O2W64PvcEq66gcbDb7UpL83JZy3qiUa6DnJwcj2NG\nk4HgUlRUpDZt2hiuz8nJ8ar+iPNUXWIBvhFuVdx9cwyX7/vn3TTWaBSSk5OVlJTkce7SwUtfo1Gu\ng/j4+EBHAADAGC8b64N7x5sYBqi7QEx1pVEG0OicKjyvfBnfntkVyn8VAgBURqMMoNEpD7N6tz3z\n8qfMC6MLK1J4s4LFxWsAAIFFowwAfuDNChZSHVaxAAD4HBuOAAAAAFVgRBkAANTL11/t0k8fGGm4\nvkWoVYvfWWZiIsA3aJQBAEC9WEJduuvxbobrV726x8Q0gO/QKAOoF28392jZsqX2799v2v0lNgQB\nAPgGjTKAevF2c4+TJ096df/Dx/PVPKq1d6EsZ72rbwwsUnFpQaBTAECjQqMMIKh5vdSbJK183pww\nwcwitb0ywnD5IfOSAECjwaoXAAAAQBVolAEAAIAqMPWiDhwOh8dxIPYeBwA0DgczD3pVX17uNikJ\nENycTqecTqdfv5NGuQ5sNpvHcUpKilJTUwMTBkD9lZUq8+Q54/UW/uiE74Q0Dwl0BKBBsNvtSkvz\n8p2VeuJP+zrIycnxOGY0GWjgwqO9e2GwKb4sCAABlpycrKSkJI9zlw5e+hqNch3Ex8cHOgLQYB09\nWaDIDtcari8pdbEmMgAgIFNdaZQB+JU74jJFjZptuL6E0Vsg6OWecOvllO2G6/Oyck1MA/gOjTIA\nAFZ1/MsAAB9wSURBVKiX8tBoxd03x3D98dmPmZgG8B0aZaABMXu7aAAA8H9olL1wcUkSp9PZpF7g\nczqdstvtSk5ObjLP7a9n9rbxdTgcuuGGGwzX7969WwkJCYZqy8vL5XA4FB8fr2bNjC+x7nA4vNrC\nOtiUl56Vik6pvPSsmoVFBjqOX5SfOysVnlL5ubNqFt40nllqms9ddrZI5c6TKjtbpOaRLQMdxy+c\nTqf69b9FV1zbUaGhxtucFqFWLX5nmYnJzNVU/1l98a9mPXOTaJTLyso0a9YsrVq1Sq1atVJBQYHG\njh2rGTNmKCTE+LI8TblRTktLU1JSUpN5bn89c1FRkVdN5qUrrtTG7XYbvn9paam+++47xcbGKiws\nzLRMwcZ9/qx09vsLf21KjXLx902qYZSa5nO7Soqlou/lKiluUo3yv3bv00MvDVJsG+N/fq96dY+J\nqczXVP9ZffGvNMr1MHXqVK1Zs0Y7duxQXFycTp06pV69eikzM1MZGRmBjocg1rNnTzVvbuz/Jo1l\nmkP296Vq1tz4hgau8FjWIAb8zOgmJS5nnslJgMat0f8Ta8uWLVq0aJEWLFiguLg4SVJcXJymT5+u\nKVOm6OGHH1a/fv0CnBLBqnXr1oZHV0+ePGlyGv8IHfS0Qlq2Mn7ByudZgxjwM6OblLhDjE+jAlBZ\no2+U09PTJUljxozxOD969GhNmTJF6enpNMoAAPiRs8Cpnz4w0nD9v77eqx/d9F+Gas8Wl9Q1FlBJ\no2+UN27cqNatW6tt27Ye59u1a6fY2Fj9v/buPCyK844D+HdWObxAEUVAUYwiqAUFBC/kUFS8UBut\nRzwATUi1NVpppK1GaiyNUaNPveKRYAwGT0wTD1QCCkbEI6ZqbTRWUYMiCMu9sLu8/YPuhHUHdwdh\n2Z38Ps/D88g778y839l197fDO7OZmZlNun+xk+tNrX9DGGNMppZbrVZDLpeLmidVWloKuVwOOzs7\ng+bKq9Vq1NTUQK1WG9xfjZa4k1cBTqa/f41KadC4tdYReSFcU/dv6DpimGKGmuqmv0hN7IVwpta/\nIUwxQ1PnVlWWo7LgKeL/nIkWBk47U6tUqCwsMPiCQVVlOZQlBRgTNR6t2ljp7V9ZXoVvZqRjTJSb\nQf2L8ktxIjnVoLHX3UfqqfMI/81Ygy4AVCpVePDDY2RmXKT36mbeR1OTdKGsUqlw//599OrVS3C5\nvb09cnJymnQMYifXm1r/hjDGmEwtt1qtRklJiehCuaSkRFThyxgT1R/qKrQcscygqRTq8kJg/0KD\nxq4h9kK4pu7f0HXEMMUMTNn0F6mJvRDO1Po3hClmaOrcakUFoChF+4nvwqqDYRcCVxXlA2cnGnzB\noFpRAVVpIRQV1QYVvoqKahQ9Kze4f0MoKqohf16KUXN7GXQBYFF+KX4/IcXg13xTe88y1phMMbdY\nki6U5XI51Go1WrUSfjGxtrZGdXU1Kioq0Lp1ayOPrnmJuUhNpVKJWkfT3xjEjqnngABwLfT3Z2rj\nZTD04jnNGV+x/UnTqFSWQlat/7lUoyw1wmgIkb5t66/Bwlp/oaxUiLi4mBA9JF0oKxS185TqK6Q0\n94otLi42+0J51tt/hLUBn+QVlbX37BVzkVp1dTVyc3MNXkfT3xiFtdgxtQ6NNfjsatX+haKLUkMf\nB+Dnx8LQi+c0Z3zF9idNw97FCi1trPX2U5VY4TEML6yBn4trKsZJY3lw/wFaFBTr7fcqd8kQu4/k\n5GRYt9X//FaU1b5H2E35k0FnuauK8oH0iXr7NYaFi+eiVWv9rwM0b9p8SbpQbt++/UuXl5WVAag9\nsyzG4MGD9RaAMpkMMpkMnp6eorbdUF2nr0Objk56+5U/zwX+mWiEEYkvYk2R2KLU0McBMO5jQZqf\noYU18HNxLbYYJ6Q+shYyg+6U8Sp3yRC7Dysra1hbG/AXPqXx/sIn1tgod4OnaoidN/1LV1payt8n\nuT5Pnz5t8nFwjDHDb5hqhtq0aQMPDw9cuXJFZ5mTkxMKCgpQWVlp0JzP0tJS2NjYNMUwCSGEEEJI\nA5SUlNAXjjSUq6sriop0/5RUU1MDuVwOV1dXg7+dr127dvwFW4b0NZWJ6IQQQggh5sSQM8pA09db\nki+Uw8LCsHHjRpSVlaFt27Z8+927d6FQKBAQECBqe1QAE0IIIYQ0LVOptyT/lT3h4eFgjCE5OVmr\n/fDhwwCAOXPmNMewCCGEEEKIiZP8HGUAmDBhAm7duoVvv/0Wjo6OePjwIfz8/DBmzBjs3bu3uYdH\nCCGEEEJM0C+iUK6qqsKqVatw4sQJtG/fHgUFBZgyZQri4uJgYWHR3MMjhBBCCCEm6BdRKBNCCCGE\nECKW5OcoE0IIIYQQ0hBUKBNCCCGEECKACmVCCCGEEEIEUKFMCCGEEEKIACqUX6BQKLBq1SoEBwcj\nODgYfn5+WLlyJcrLy3X6qlQqvPfee/Dy8kJwcDB8fHzw/vvvQ61WN8PIG666uhpr166Fv78/QkJC\nMGTIEGzbtk2wr7lmrqqqQlpaGsaPH4+1a9fW209MPlM/FoZmFtPX1DMDhmfJy8vDm2++idDQUHh5\necHHxwdbtmxBTU2NTl9Tz21o5pycHCxYsACjRo1CYGAgfH19sXbtWrN9fRPzHK+rpKQEPXv2RG5u\nrs4yU89taObQ0FBYWVmhXbt26NixI2xtbdGmTRvEx8fr9JVKZqD2/ezvf/87/Pz8EBwcjEmTJuHD\nDz/U6WfqmQHDcj979gyWlpbo0aMHevfujT59+sDd3V3rJzo6mu9v6rkNfayNWqsxwquurmajR49m\nycnJfFtVVRVbsmQJ8/f3Z0qlUqv/woULmaurK8vPz2eMMZafn8969uzJ5s6da9Rxv4qqqio2YsQI\nNmTIEFZaWsoYY0wul7PevXuzv/71rzr9zS1zXl4eCw0NZZMnT2bR0dGM4zgWFxdXb38x+Uz1WIjJ\n3JTHx9jEZHn27BkbMmQIu379Ot+WkJDAZDIZGzduHFOr1Vr9TTW32Md6yJAh7O7du3xbZmYmk8lk\nzMfHh1VUVGj1N9XMjIl/3r4oMjKScRzHcnJydJaZam6xmYOCglifPn2YtbU169y5M5syZQrLzMwU\n7CuVzAqFggUHB7OwsDBWWFjIGGNsz549rGXLluzgwYNafU01M2Picp89e5ZxHMdkMpnOD8dxzMLC\ngmVlZfH9TTW3mMzGrtWoUK4jISGBvf3224LL+vfvz5KSkvjfMzMzGcdxbOfOnVr9du7cyTiOYxkZ\nGU061sYSFxfHOI5jJ06c0Gpft24ds7KyYg8fPuTbzD1zenr6S//ziclnLsdCX2Yxfc0lM2P6syxZ\nsoQdPnxYp33GjBmM4zi2bds2vs1ccuvLvHnzZsZxHJs4caJW+4ABAxjHcVpvOuaSmTFxz3HGGDtx\n4gTr1q0bk8lkOoWyueQ2JHNQUJBB25JS5sjISObh4cEqKyv5tvj4eCaTydjevXv5NnPJzJj+3Js2\nbWKHDx9mVVVVrKamRmvZgQMH2OrVq/nfzSW3vszGrtVo6kUd2dnZgqftAcDDwwOPHz/mf09ISABQ\n+xXZdU2aNElruan7+OOPwXEcBg8erNU+dOhQVFdXIykpiW8z98xMzy3DxeQzl2OhL7OYvuaSGdCf\nJTU1FREREUhNTdVq12Q5ePAg32YuufVl9vLyQvv27dGtWzet9oqKCgBAu3bt+DZzyQyIe47L5XIk\nJCQgIiJCcD1zyS0msz5Syfz9998jISEBf/jDH2Btbc23r1ixAo8fP8bcuXP5NnPJDOjP/Z///Afj\nxo2DpaUlOI7j23NycrBnzx6sXLmSbzOX3PoyG7tWo0K5DicnJyQmJmLz5s1a7QqFApcuXcKoUaP4\ntnPnzqFjx47o3LmzVl8HBwd06NABmZmZRhnzqygsLMSTJ08AALa2tlrLunTpAgA4f/483yaFzC8j\nJp/Uj4UQKWV2d3dHeXk5ioqKtNo7duwIoHb+soZUcgcGBqKwsBBbt27l2woKCnDv3j24ubkhKCiI\nb5dK5hetWLECf/vb37QKirqkmvtlpJJ5+/btYIxh9OjROsscHR21fpdKZgD4y1/+glatWmm11dTU\nIDo6Glu3boVM9nOZJ5Xcxq7VqFCuIyIiAjY2Nli6dCmGDRuGmzdvoqqqClFRUVi6dCm8vLwA1E4M\nv3//Puzt7QW3Y29vj5ycHGMOvUHqvlm8+MbRokULAMCPP/4IQDqZ6yMmn9SPhRCpZT5w4AByc3Px\n+uuva7VrMvTq1QuA9HLXpVQq8fvf/x7u7u44fvw4/39eqpmPHTsGT09PvPbaa4LLpZj7wYMHCA8P\nR3BwMAYMGIA1a9ZoXcAkpcwnT54Ex3Gws7PD4sWLERISAi8vL/z5z3+GQqHg+0kpMwA4OzvrtG3f\nvh0jRozgX8cAaeU2dq3WslFHb+acnJxw/PhxTJs2DRcvXsTAgQPx2muvYcuWLVqfUORyOdRqtc6n\nOA1ra2tUV1ejoqICrVu3NtbwRevQoQO6deuGx48fo6SkROus8qNHjwAAz58/ByCdzPURk6+iokLS\nx0KI1B5/mUwGBwcHnfYvvvgCALBgwQIA0ssN1P6J+p133sFPP/2ENm3a4MiRI1rFoxQzFxQU4ODB\ng9i/f3+9faSWmzGG3/3ud9i5cyccHR3x9OlTDBo0CLdv3+aPg1QyKxQK/j1r48aNiI2NhbOzM4qL\nixEYGIisrCycOXMGMplMMpnr8+zZM2zevBnXr1/XapdSbmPXanRG+QW+vr6YP38+vL29UVNTgzt3\n7uDNN99EVlYW30fz6bRlS+HPGZo/dRQXFzf9gF/RW2+9BcYYrl27ptWekpICoPY2SoC0MgsRk0/q\nx0LILyHzhQsXkJ6ejunTp/Pz16SY28vLC2lpabhz5w6WLVsGT09PbNiwgV8uxcwrVqzABx988NI+\nUsttb2+Pbdu28dMOunTpgqVLlyIpKYl/fZdK5sLCQv7fLi4u/FlWW1tbLF++HGlpadi1axcA6WSu\nz4YNGzBixAidwk9quY1Zq1GhXEdJSQlCQ0PRqVMnXLlyBRkZGejbty8ePHiAkJAQ/Otf/wIAtG/f\n/qXbKSsrAwCtCwpMVUxMDIKDgxEbG8ufPU5NTYVKpQLw85xNKWUWIiaf1I+FEKlnLi8vR0REBMaM\nGYPPPvuMb5d67jlz5iAwMBAxMTH8BYxSy3zgwAEMGTJE5yLGF0kt9+HDh3Uy9+vXDwD457hUMmsu\nROU4TuuMIgD07dsXwM8XbUkls5Dy8nLs3r1b63oDDSnlNnatRoVyHcuWLUPXrl2xZMkSALV3fvju\nu+8QGxsLhUKB2NhYAEDbtm3RqlUrwS8mAGqfrC1atICNjY3Rxt5QFhYWOHnyJKZPn46pU6di5MiR\nuHLlCn+Dcjc3NwDSyixETD6pHwshUs7MGMO8efMwcOBAfPXVV7C0tOSXSTm3RkhICADwX0Qhpcx5\neXk4fvw4oqKiBJfXvbpeSrmVSiWePXum025lZQUAuHnzJgDpZG7Xrh1/1tDJyUlrmWbsUsssJDk5\nGUVFRfyHg7qklNvYtRrNUf4/pVKJffv24dy5c1rtFhYWWLt2LQoLC5GYmMi3u7q66lwxD9RebSqX\ny+Hq6spfHGPqLC0tsWzZMixbtoxvu3DhAoDab3fSkFJmIWLySf1YCJFq5piYGHTq1Anbt2/n2yor\nK/l5bVLJHR0djdzcXOzfvx9t27bl2+3s7AAAd+7c4dukkvnUqVP44YcfEBwcrNWuuUh5xowZsLa2\nxocffghfX1/J5J44cSJSU1ORkZGhdetPzRk0CwsLvk0qmd3c3HD79m1UVVVpnSHU/HldiplfdPr0\naQAQvP4CkEbu5qjV6Izy/5WUlECpVNb7yWLChAlaby5hYWF48OAB/8KjcffuXSgUCgQEBDTpeBtT\n3VthaZw/fx6WlpaYN28e3yalzELE5JP6sRAixcxbt26FSqXSKpIBIDIykv+3FHLn5+dj586d+Prr\nr3XuHa15E3FxceHbpJAZAObNm4dLly4hLS1N62fkyJEAaqdlpKWlwdfXF4B0cj979gzt27fXue3n\nTz/9BADw8fHh26SSOTQ0FIwx/panGnK5HAD4OyEA0sn8onPnzoHjuHqnHEghd3PUalQo/1/Hjh3h\n4eGB5ORkweW3bt3C1KlT+d/Dw8PBGNPpf/jwYQC1c//MQVxcHBwdHXHo0CG+raKiAjt27MCiRYu0\nbj0jlcz1EZNP6sdCiNQyf/XVV3j48CE2bdqk1Z6fn8//iRqQRu5OnTrBwcEBLi4u8PPz01qmuY9o\nREQE3yaFzA0hldyhoaFITEyEh4eHVntKSgosLCywePFivk0qmaOioiCTyZCdna3VfuXKFQDAwoUL\n+TapZK6rpqaG/yBU310epJC7WWo1vd/d9wty4cIFZmdnxxISEvg2lUrFEhISmJ+fH5PL5Vr9x48f\nz3r06MFyc3MZY4zl5OQwBweHZv/OdDE++ugjZm1tzVJSUhhjjMnlchYeHs5GjhzJVCqVTn9zzvz5\n558zjuNYdHR0vX3E5DOHY2FIZjF9zSEzY/qzXL58mbVt25a5u7uzPn36aP106dKFxcfHa/U3h9z6\nMh85coQtWrSIFRUV8W2XL19mlpaWbMyYMTr/380hM2PinuMaYWFhjOM4lp2drbPMHHLry1xYWMiG\nDh2q9fW8GRkZzNramm3ZskWnvxQyM8bY8uXLWb9+/VhhYSFjjLHnz5+zvn37smnTpun0NYfMjBn+\n/M7Ly2McxzGZTPbSfuaQW19mY9dqVCi/4N69eywyMpINGjSIjRgxgg0ZMoT96U9/YuXl5Tp9FQoF\n++Mf/8j69+/Phg8fztzd3VlsbCyrrq5uhpE3jFqtZu+//z6bOnUqCwoKYgMGDGCrVq1iVVVVgv3N\nMbOvry/r0aMH/yLCcRxzcHBg3t7e7Nq1a1p9xeQz5WMhJnNTHZ/mYGiW/v37M5lMVu/P0aNHtbZr\nyrnFPH5Xr15ls2fPZqGhoSwoKIj5+PiwzZs3s5qaGp3tmnJmxsTl1pg3bx5zcHDg17GysmJubm7s\nypUrfB9Tzi0m85MnT9icOXNYUFAQCw4OZqNHj2apqamC25VKZsYY27hxIxs0aBALCgpi/v7+bOPG\njb+I53dVVRXr168fCw0Nfel2TTm3mMzGrNU4xhrxS+MJIYQQQgiRCJqjTAghhBBCiAAqlAkhhBBC\nCBFAhTIhhBBCCCECqFAmhBBCCCFEABXKhBBCCCGECKBCmRBCCCGEEAFUKBNCCCGEECKACmVCCCGE\nEEIEUKFMCJGMHj16QCaT4dy5c4LLb9y4AUdHR8hkMkyfPh1KpRIAsHr1ashkMsTFxTXKOBISEiCT\nyRAREdEo29OM72U/U6ZM0erbWFk05s+fr7NPS0tLODg4YOzYsUhKSmrU/RlDYz9OhBDpadncAyCE\nkMbEcRw4jtNpv3TpEsLCwiCXyxEZGYldu3bx/TTrCK33qmNpTL169cLw4cMFl3l7e/P7FMqSnp6O\nkJAQBAYGIi0trcFjGDBgAAYMGAAAqKysxL///W+cPn0ap0+fxsmTJ7F3794Gb7u5vHisHjx4gJ49\ne6J79+64f/9+M42KEGIKqFAmhEgKY0yn7ZtvvkF4eDgqKiqwdOlSbNiwQWv54sWLMXPmTNjb2xtr\nmA0yfPhwfPLJJy/tU1+Wuh8KXsXkyZOxatUqrbbPP/8cc+fOxb59+zBz5kyMHTv2lfbR3BrrWBFC\nzB9NvSCESNo///lPjBs3DhUVFXjvvfd0imQA6NixI9zc3GBnZ9cMI2xc9WUR+gDRWN544w2MGjUK\nAJCcnNxk+zGWpjxWhBDzQoUyIUSyEhMT8etf/xoqlQqbNm3SOROqUd+83rpzWMvKyhATEwNXV1dY\nWVnB2dkZv/3tb1FUVCRqTLdu3YKLiwtkMhni4+MbnK0+QlmCgoIQEhICoHYKRt15xsHBwY2yX09P\nTwDAo0ePBJdfunQJM2bMQNeuXWFpaYnOnTsjPDwcFy5cEOz/ww8/YN68eejevTssLS1hY2MDV1dX\nTJ06FUePHtXqq5k/Xd+0DzHztufPn4+ePXsCqJ2CUfdYubq66l2fECItNPWCECIpHMeBMYbt27dj\n0aJFaNmyJfbs2YO5c+catK6Q4uJiDB06FLm5uQgMDISnpycyMjKwY8cOZGdnIysrCy1b6n85TUtL\nw5QpU6BQKLBv3z7Mnj1bdD5D1c0SFhaGVq1aISUlBQ4ODggLC+OXubu7N8r+iouLAQDt2rXTWbZh\nwwbExMRAJpPB29sbw4YNw6NHj3D8+HEcP34cO3bswIIFC/j+N27cwLBhw1BWVgYPDw+Eh4eD4zg8\nfvwYKSkpUCgUmDp16kszCzFkKkVAQADKy8tx5MgRtGnTBtOmTeOXmfrUHEJI46NCmRAiKYwxbNq0\nCV9++SWsrKzwxRdfYPLkya+0zWPHjmH8+PHIyspC69atAQBPnjzB4MGDce3aNRw8eBCzZs166TYS\nExMRGRmJ1q1b4+TJkw06k9vQKQHvvvsuBg8ejJSUFHh4eOid5yyWQqHA2bNnAQA+Pj5ay06ePImY\nmBg4Ozvj6NGjGDRoEL/s22+/xbhx47Bo0SIEBgaid+/eAICPPvoIZWVliI+Px7vvvqu1vfLycty8\nebNRx19XVFQURo0ahSNHjqBTp06NfqwIIeaFpl4QQiTnyy+/BAC88847r1wkA7VnSffs2cMXyQDg\n6OiIxYsXA6i9WPBl4uPjMWfOHDg4OCAzM7PB0x327t1b7+3h9Gmsebd1t1NZWYmrV69iypQpyMnJ\ngbOzMxYuXKjVf/Xq1QCA3bt3axXJADB06FCsXLkSSqUSH3/8Md+el5cHAIIXBbZp0wb+/v6NkqU+\nNEeZEKJBZ5QJIZITFBSE9PR0rF+/Ht7e3lp/Pm8IHx8fdO7cWae9T58+AIDc3FzB9VQqFaKjo7Fz\n5054enrixIkTcHJyavA4XnZ7OGOJi4sTnOs7ZswY/OMf/0CHDh34toKCAly+fBm2trYIDQ0V3N6I\nESMAAFlZWXybv78/Tp48iejoaKxZswYBAQGwsrJq5CSEEKIfFcqEEEnhOA6rV6/G119/jfXr1/Pz\ngF+lWHZxcRFst7GxAVA79UBIUlISVCoVnJyckJGRITh/VwxDbg/X1OreR7moqAhZWVnIy8vD8+fP\ntc64A+DvQVxcXKx3Dnd+fj7/75iYGGRkZCA1NRWjR4+GlZUVvLy8EBQUhDfeeAP9+/dv5FSEECKM\nCmVCiKRo/my+bt06AGiUYtmQqQ1CAgICcP/+fTx48ACxsbHYsmVLg7ZjSl68j3J1dTWioqKQmJiI\niRMnIisrCxYWFgAAtVoNALC1teW/ObA+dS+Ua9WqFc6cOYPs7GycOnUKFy5cwMWLF5GdnY1169Yh\nLi4OK1euNHjMNTU1YiISQgiPCmVCiGS9WCxzHIfXX3/daPvv3r07PvvsM4wcORLbtm1DZWUldu/e\nLakvsrC0tMTu3buRnZ2N7777Dhs3buQvwNOcibe0tGzQmXA/Pz/4+fkBAJRKJfbv34+FCxdi9erV\n+M1vfgM3Nzd++wBQVlYmuJ2cnBzR+yaEEIAu5iOESNy6deuwfPlyqFQqzJo1C4cPHzbq/p2dnXH+\n/Hn0798fn376KWbPns2faTUmTTGpUqkafdtWVlb8h5L4+Hg8f/4cAODk5IRf/epXyM/Px7lz515p\nHxYWFpg3bx78/f3BGMONGzf4ZV27dgUA3L59W2e9yspKpKeni9pXUx4rQoh5oUKZECIpQmdrXyyW\njxw5YtQxde7cGenp6fDx8UFSUhKmTZsGpVJp1DFoiskff/yxSQr18PBwDB48GCUlJVi7di3fvmbN\nGgC139535swZnfXUajW++eYbXLp0iW/btm0b7ty5o9P3v//9L27dugWO49C9e3e+feTIkQCAffv2\naa1XWVmJt99+u94vQalPp06dYGFhgby8PMjlclHrEkKkhQplQoik1Hdrr7rF8syZM41eLNvZ2SE1\nNRVDhw7FsWPHMHnyZFRVVRlt/y4uLhg4cCCePn0KT09PzJkzBwsWLMD69esbbR8ffPABAGD79u18\ncTpp0iRs2LABT58+xZgxY+Du7o5JkyZh1qxZCAkJgb29PUaNGoXvv/+e387OnTvh7u6OXr16ITw8\nHLNnz8bIkSPh4eEBuVyOGTNmwNfXl+8/bNgwTJgwASUlJfD29sbYsWMxYcIEuLq64uzZs4iIiBCV\nw8LCAhMmTIBSqcTAgQMxe/ZsLFiwALGxsY1wlAgh5oQKZUKIZHAc99L5vy+eWdZ8FXJ96zX0m97q\na7exscHp06cREhKCU6dOYfz48aioqHjpPl42PrF9jx49iunTp6OoqAhJSUn49NNPceLEiVferkZA\nQADGjRuH6upq/v7JALB06VJcvXoVUVFRUKvVSE1NxfHjx5Gbm4ugoCDs3r1b60LLtWvX4q233oKt\nrS0uXryIo0eP4t69ewgODsahQ4eQmJios+9Dhw5hxYoV/Nn769evY+LEibh27RpcXFxEP767du1C\nVFQUampqcOjQIXzyySc4cOCAAUeKECIlHKM7qxNCCCGEEKKDzigTQgghhBAigAplQgghhBBCBFCh\nTAghhBBCiAAqlAkhhBBCCBFAhTIhhBBCCCECqFAmhBBCCCFEABXKhBBCCCGECKBCmRBCCCGEEAFU\nKBNCCCGEECKACmVCCCGEEEIE/A+gOP4Tl4r+OwAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa19505f290>"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "The debinning Project: Data Smoothing without Bins"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "## Samples - IV: To be $r$th out of $n$ (cont'd)... ## \n",
+ "### Histograms \"smooth\" the data in this way:\n",
"\n",
- "Suppose $n$ identical siblings have a race. Suppose we only care about who came in $r$th place.\n",
- "If we sorted them all: $n!$ But then we've overcounted, since we don't care who is 1st through $(r-1)$th, or who is $(r+1)$th through Nth.\n",
+ "![Let's try to find other shapes!](notTheOnlyShape.png \"Let's try to find other shapes!\")\n",
"\n",
- "$$ {}_nK_r \\equiv \\frac{n!}{(n-r)!(r-1)!} $$"
+ "### Is there a more appropriate smoothing shape?"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Gaussian Smoothing: binfull Histogram"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "Our sample is just like this, except that there is a certain probability to get $x_r$, as well as the probability to get $r-1$ points less than $x_r$ and $n-r$ points greater than $x_r$ in the sample. \n",
+ "### aka \"Kernel Density Estimation\":\n",
"\n",
- "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. $$"
+ "![Gaussian Smoothing](GaussianSmoothing.png \"Gaussian Smoothing\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "notes"
+ "slide_type": "fragment"
}
},
"source": [
- "If that was too much magic for anyone, the proof is down on sub-slides."
+ "### Select a point from our data..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
}
},
"source": [
- "Proof:\n",
- "\n",
- "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_2} f(x_1) \\Prod{i=1}{r-1} dx_i $$\n",
- "\n",
- "$$ \\times f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-1}}{\\infty} f(x_n) \\Prod{j=r+1}{n} dx_j $$"
+ "### Add a random deviate from a Gaussian distribution..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
"source": [
- "$\\phantom{Integration by parts:}$\n",
- "\n",
- "$$ \\phantom{\\Int{-\\infty}{x} f(\\widetilde{x}) F^{a-1}(\\widetilde{x}) d\\widetilde{x} = \\frac{1}{a} F^a(x) \\qquad {\\rm and} \\qquad \n",
- "\\Int{x}{\\infty} f(\\widetilde{x}) \\left(1 - F(\\widetilde{x})\\right)^{a-1} d\\widetilde{x} = \\frac{1}{a} \\left(1 - F(\\widetilde{x})\\right)^a } $$"
+ "### And repeat ad nauseam.\n",
+ "### Put all results into a binfull Histogram (\"full\" of arbitrarily small bins)."
]
},
{
- "cell_type": "markdown",
+ "cell_type": "heading",
+ "level": 2,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Proof:\n",
- "\n",
- "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_3} f(x_2) F(x_2) \\Prod{i=2}{r-1} dx_i $$\n",
- "\n",
- "$$ \\times f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-2}}{\\infty} f(x_{n-1}) \\left(1 - F(x_{n-1})\\right) \\Prod{j=r+1}{n-1} dx_j $$"
+ "binfull Histogram Demo"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
"source": [
- "Integration by parts:\n",
+ "![Linearly Increasing Gaussian Smoothing](easyEndpoint_binfullLinearExpanding_final.png \"Linearly Increasing Gaussian Smoothing\")\n",
"\n",
- "$$ \\Int{-\\infty}{x} f(\\widetilde{x}) F^{a-1}(\\widetilde{x}) d\\widetilde{x} = \\frac{1}{a} F^a(x) \\qquad {\\rm and} \\qquad \n",
- "\\Int{x}{\\infty} f(\\widetilde{x}) \\left(1 - F(\\widetilde{x})\\right)^{a-1} d\\widetilde{x} = \\frac{1}{a} \\left(1 - F(\\widetilde{x})\\right)^a $$"
+ "### Algorithm issues: Speed, choosing $\\sigma$, over/underflow, \"LinearExpanding\" - Kernel depends on \"time\"..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "slide"
}
},
"source": [
- "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\frac{1}{2} \\Int{-\\infty}{x_4} f(x_3) F^2 (x_3) \\Prod{i=3}{r-1} dx_i $$\n",
+ "## 1) New Probability Calculus:\n",
"\n",
- "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\frac{1}{2} \\Int{x_{n-2}}{\\infty} f(x_{n-2}) \\left(1 - F(x_{n-2})\\right)^2 \\Prod{j=r+1}{n-2} dx_j $$"
+ "### $\\qquad$ \"Can't I just calculate that thing?\""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ \\vdots $$\n",
+ "## 2) The debinning Calculation:\n",
"\n",
- "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = n! \\left(\\frac{1}{(r-1)!} F^{r-1}(x_r)\\right) f(x_r) dx_r \\left(\\frac{1}{(n-r)!} \\left(1 - F(x_r)\\right)^{n-r}\\right) $$"
+ "### $\\qquad$ \"Whoa, I can calculate something else!\""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. \\quad {}_\\blacksquare$$"
+ "## 3) The Future, and Shameless Advertising:\n",
+ "\n",
+ "### $\\qquad$ \"Yikes.... There is so much more!\""
]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import sys\n",
- "sys.path[0] = '..'"
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "slide"
}
},
- "outputs": [],
- "prompt_number": 1
+ "source": [
+ "# New Probability Calculus:\n",
+ "\n",
+ "## \"Can't I just calculate that thing?\""
+ ]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\" Presumably, skip slides are for non-output code blocks. \n",
- " Here, just import and define a few functions. \"\"\"\n",
- "from os import listdir as ls\n",
- "from __future__ import division\n",
- "import numpy as np\n",
- "import bisect\n",
- "import utilities.sampleFunctions as funcs\n",
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Datum Probability"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "### What's the probability to get some datum, $x$?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ {\\large P(\\widetilde{x}\\in[x,x+dx]) = f(x) dx \\quad {\\rm and} \\quad \\Int{-\\infty}{\\infty} f(x) dx = 1~.} $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "#### $f(x)$ is the Probability Distribution Function (PDF). \n",
+ "#### Its anti-derivative is the Cumulative Distribution Function (CDF):\n",
+ "\n",
+ "$$ F(x) = \\Int{-\\infty}{x} f(x') dx' = P(\\tilde{x} \\le x)$$\n",
+ "$$ 1 - F(x) = \\Int{x}{\\infty} f(x') dx' = P(\\tilde{x} > x) $$"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Sample Probability"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "### Probability to get a sample of data points, $\\{x_i\\}_{i=1}^n$?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\\begin{align} \n",
+ " dP(\\{x_1\\}) &= \\phantom{3!} \\phantom{\\times!!} f(x_1) dx_1 \\\\\n",
+ " dP(\\{x_1, x_2\\}) &= \\rust{2}\\phantom{!} \\rust{\\times} f(x_1) dx_1 f(x_2) dx_2 \\\\\n",
+ " dP(\\{x_1, x_2, x_3\\}) &= \\rust{3!} \\rust{\\times} f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Order doesn't matter... WLOG, sort:\n",
+ "\\begin{align}\n",
+ " \\{x_1, x_2\\} &\\equiv \\{x_2, x_1\\} \\\\\n",
+ " \\{x_1, x_2, x_3\\} &\\equiv \\{x_2, x_3, x_1\\} \\equiv \\cdots \\\\\n",
+ " \\phantom{dP(\\{x_1, x_2, x_3\\})} &\\phantom{= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}\n",
+ "\\end{align}\n",
+ "\n",
+ "$$ \\Rightarrow\\ {\\rm WLOG}\\ x_j < x_k\\ {\\rm for}\\ j < k\\ {\\rm for\\ all}\\ x_j, x_k \\in \\{x_i\\}_{i=1}^n$$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\\begin{align}\n",
+ " \\therefore dP(\\{x_i\\}_{i=1}^n) &= \\rust{n!} \\Prod{i = 1}{n} f(x_i) dx_i \\\\\n",
+ " \\phantom{dP(\\{x_1, x_2, x_3\\})} &\\phantom{= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Probability Calculus: Integration"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "### The data is all sorted... Careful with those integration limits!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ \\Int{\\{x_1, x_2\\}}{} dP(\\{x_1, x_2\\}) = 2 \\Int{-\\infty}{\\infty} f(x_2) \\left[ \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right] dx_2, $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$\\Int{\\{x_1, x_2, x_3\\}}{} dP(\\{x_1, x_2, x_3\\}) = 3!\\Int{-\\infty}{\\infty} f(x_3) \\left[ \\Int{-\\infty}{x_3} f(x_2) \\left( \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right) dx_2 \\right] dx_3$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$\\vdots$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Limits of inner integrals are *also* integration variables...\n",
+ "### Thus, integrals are \"chained\" together... Chain Integrals."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Probability Calculus: Being $r$th of $n$ ##"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "\\begin{align}\n",
+ " \\subNsubR{n}{f}{r} (x_r)\\ dx_r &\\equiv\\ \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_{i=1}^n) \\\\\n",
+ " \\quad = n!\\ f(x_r)\\ dx_r\n",
+ " &\\phantom\\times\\ \\Int{-\\infty}{\\infty} f(x_n) \\Int{-\\infty}{x_n} f(x_{n-1}) \\cdots \\Int{-\\infty}{x_{r+2}} f(x_{r+1}) \\Prod{i=r+1}{n} dx_i \\\\\n",
+ " &\\times\\ \\Int{-\\infty}{\\infty} f(x_1) \\Int{x_1}{\\infty} f(x_2) \\cdots \\Int{x_{r-2}}{\\infty} f(x_{r-1}) \\Prod{i'=1}{r-1} dx_{i'}\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### $\\subNsubR{n}{f}{r}$ Theorem:\n",
+ "\n",
+ "$$ {\\Large \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r}\\ f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## Probability Calculus: Being $r$th of $n$ ##"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### $n$ identical siblings: Race! $\\quad$ ... Outcomes? $n!$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Only care about $r$th place. $\\quad$ ... $n!$ is overcounting.\n",
+ "### $\\quad$ ... $(r-1)$ faster... who cares what order...\n",
+ "### $\\quad$ ... $(n-r)$ slower... who cares what order...\n",
+ "\n",
+ "### $$ \\Rightarrow \\subNsubR{n}{K}{r} \\equiv \\frac{n!}{(n-r)!(r-1)!} $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r}\\ f(x_r)\\ F^{r-1}(x_r)\\ \\left(1 - F(x_r)\\right)^{n-r} } $$\n",
+ "\n",
+ "$ {\\Large ({\\rm HW}-1)}$\n",
+ "$${\\large {\\rm Prove\\ the}\\ \\subNsubR{n}{f}{r}\\ {\\rm Theorem\\ by\\ computing\\ the\\ chain\\ integral.} }$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Proof:\n",
+ "\n",
+ "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_2} f(x_1) \\Prod{i=1}{r-1} dx_i $$\n",
+ "\n",
+ "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-1}}{\\infty} f(x_n) \\Prod{j=r+1}{n} dx_j $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_3} f(x_2) F(x_2) \\Prod{i=2}{r-1} dx_i $$\n",
+ "\n",
+ "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-2}}{\\infty} f(x_{n-1}) \\left(1 - F(x_{n-1})\\right) \\Prod{j=r+1}{n-1} dx_j $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Integration by parts:\n",
+ "\n",
+ "$$ \\Int{-\\infty}{x} f(\\widetilde{x}) F^{a-1}(\\widetilde{x}) d\\widetilde{x} = \\frac{1}{a} F^a(x) \\qquad {\\rm and} \\qquad \n",
+ "\\Int{x}{\\infty} f(\\widetilde{x}) \\left(1 - F(\\widetilde{x})\\right)^{a-1} d\\widetilde{x} = \\frac{1}{a} \\left(1 - F(x)\\right)^a $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\frac{1}{2} \\Int{-\\infty}{x_4} f(x_3) F^2 (x_3) \\Prod{i=3}{r-1} dx_i $$\n",
+ "\n",
+ "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\frac{1}{2} \\Int{x_{n-2}}{\\infty} f(x_{n-2}) \\left(1 - F(x_{n-2})\\right)^2 \\Prod{j=r+1}{n-2} dx_j $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ \\cdots\\ = n! \\left(\\frac{1}{(r-1)!} F^{r-1}(x_r)\\right) f(x_r) dx_r \\left(\\frac{1}{(n-r)!} \\left(1 - F(x_r)\\right)^{n-r}\\right) $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. \\quad {}_\\blacksquare$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
"reload(funcs)\n",
+ "def quickData():\n",
+ " ''' Shorthand for getting easyEndpoint data (384 x values in [8.5,200])\n",
+ " - set nPulls before calling\n",
+ " - see utilities.sampleFunctions.functionToData for more details\n",
+ " '''\n",
+ " return funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n",
+ "\n",
+ "\n",
+ "def quickBG():\n",
+ " ''' Shorthand for getting endpointBG data (384 x values in [8.5,200])\n",
+ " - set nPulls before calling\n",
+ " - see utilities.sampleFunctions.functionToData for more details\n",
+ " '''\n",
+ " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "nPulls = 10\n",
+ "pullData = {index:[] for index in xrange(nPulls)}\n",
+ "settings['simpleSortedOutput'] = True\n",
+ "for iteration in xrange(2000):\n",
+ " for i,v in enumerate(quickData()):\n",
+ " pullData[i].append(v)\n",
+ "\n",
+ "settings['simpleSortedOutput'] = False\n",
+ "x, f, F, data = quickData()\n",
+ "bgx, bgf, bgF, bgdata = quickBG()\n",
+ "f /= F[-1]\n",
+ "bgf /= F[-1]\n",
+ "bgF /= bgF[-1]\n",
+ "F /= F[-1]\n",
+ "\n",
+ "ithPDF = {}\n",
+ "for i in xrange(1, nPulls+1):\n",
+ " ithPDF[i-1] = np.array([f[j] * F[j]**(i-1) * (1 - F[j])**(nPulls-i) * pc.nKr(nPulls, i) for j in xrange(len(x))])"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def makeHist(i=0):\n",
+ " fig, axes = plt.subplots(figsize=(9,5), facecolor='#ffffff')\n",
+ " plt.plot(x, f, '--', color='#0088ff', alpha=0.6, linewidth=3)\n",
+ " plt.plot(x, bgf, '-.', color='#0088ff', alpha=0.6, linewidth=3)\n",
+ " plt.hist(pullData[i], bins=np.arange(0, 201, 5), alpha=0.4, color='#66a61e', normed=True)\n",
+ " plt.plot(x, ithPDF[i], '#964a01', linewidth=3)\n",
+ " \n",
+ " axes.set_xticks(np.arange(0, 201, 50))\n",
+ " axes.set_xticks(np.arange(0, 201, 10), minor=True)\n",
+ " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n",
+ " \n",
+ " axes.set_ylim(bottom=-0.0001, top=0.0401)\n",
+ " axes.set_yticks(np.arange(0, 0.04, 0.01))\n",
+ " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.04, 0.01)], fontsize=20)\n",
+ " axes.set_yticks(np.arange(0, 0.04, 0.01/5), minor=True)\n",
+ "\n",
+ " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
+ " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
+ "\n",
+ " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ " axes.minorticks_on()"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{1}(x)$ compared with the histogram of the 1st smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(0)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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48cUX3RYwtU17Vsy37rkW0isVob1SJY5IWjGjJ1nfl+3aBNOlovdERESOON3F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\n+qJr164AgGvXrjnNc+zYMTz66KMIDAyEQqFAz5498emnnzrk69KlC0Q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DBw/mwcHBXCaT\n8dDQUN6rVy8+Z84c/tNPPzXqsxPSkhjnzfxYDiGkzRs7diw2bdqEDz74ALNmzWrt6hBCyB2HAjZC\nSL2OHz+O++67D4GBgcjMzKx3uAdCCCHNg4b1IIQ49cwzz6C8vNw2Ovzrr79OwRohhLQSamEjhDgl\nEokgFosRFRWF2bNn469//WtrV4kQQu5YFLARQgghhHg4GoeNEEIIIcTDUcBGCCGEEOLhKGAjhBBC\nCPFwFLARQgghhHg4CtgIIYQQQjwcBWyEEEIIIR7u/wEDekbHW2M/kQAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181c0eed0>"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{2}(x)$ compared with the histogram of the 2nd smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(1)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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KSkoAALfffju8vLzw8ssv489//jPee+89TJkyBSUlJbjlllscFjCRM+Uc+A/0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\nRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181be8ad0>"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{3}(x)$ compared with the histogram of the 3rd smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(2)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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JrKXw6FbINPplZeSBwfCIiZM4IvtRDxgFxfldAIALhzajsaYMnv6hXdxFRNR/\nWZywBQQEoKXl8liStuUuCgsLkZiYaDguCALKysp6FIy7uzteeeUVvPLKK51eJ5PJkJZmfnC1pXWc\nOHHCJrERWUvOrm8M731Hj3eq5S10noEIHzYJF09nQKfVIHvnlxh1yx+lDouISDIWd4lGR0ejoKDA\nUB4xYgQA/TiwNg0NDcjIyLD51Fai/k7b2oLzey/v1+s3epyE0UhjcLsFgrN2/E/CSIiIpGdxwjZj\nxgycPHkS5eXlAICbbroJHh4e+Otf/4q//OUvePPNNzFt2jSUl5fjuuuus1nARM6g8MhWqBtqAQDy\nwBAonKg7tE3cpNshc5UDAMrO7UNtSY7EERERScfihO2OO+7AtGnTcPjwYQD6Tc9fffVVqNVqrFq1\nCn/6059w+PBhREdH4/nnn7dZwETOIDu9XXfoVc7VHdpG4RuE6DGzDeXsNLayEZHzsngM2/jx47F1\n61ajY4888gjGjBmD9evXo6qqCkOHDsWiRYu63M6JiDqmbW1B3h7n7g5tkzh9AfL364ddZG5fizF3\n/c0pk1ciol7vJTp27FiMHTvWGrEQEYALR36FulG/WK7Wwx+K6FiJI5LOoPE3w1XhBU1zA2oKz6Iy\n9xiC40dLHRYRkd05xObvzqq4uNio7CjbX5C02s8ObQ0d5tQtSnKFF2Kv+R2ydnwBAMhKW8uEjYgk\np1KpoFKp7PrMbi+b3tLSgrVr1+KRRx7B3LlzMXfuXCxZsgRr1641WvaDuhYZGWn0UiqVUodEEtOo\nm5G39ztDuTVsmITROIbE6QsM77PSvoSo00kYDRERoFQqTT7Dba1bLWwZGRm45557cOHCBZNzH330\nEZYtW4YvvviCe2taqKioyKjM1jW6cPgXQ3eob3gcanzCJY5IelFXXQ+FbxCa6yrRUFGIktPpiBgx\nVeqwiMiJpaamYsmSJUbHbJ20WZywnTp1CrNmzUJjYyPi4uKwYMECDBw4EACQl5eHL7/8Erm5ubjx\nxhuxb98+DB/e/zep7q2IiAipQyAHk5u+zvA+fsqdKKh23u7QNi6ucsRPvhOnfnoPAJC1Yy0TNiKS\nlBRDmCzuEn3uuefQ2NiIZcuWITMzE88//zwWL16MxYsX44UXXsC5c+fw17/+FY2NjT3aS5TI2WnU\nzTjfrjs0fsp8CaNxLInT7zG8z0lfB22rWsJoiIjsz+KEbceOHUhKSsJLL70Emcz0NhcXFzz//PNI\nSkrqcNsB/1GQAAAgAElEQVQoIurYhUM/o7VJP4jVd0A8guM4uL5N+NCJ8A6JAQC0qKpw4cgvEkdE\nRGRfFidsTU1NSElJ6fQaQRAwZswYNDU19TowImeT026x3Pgpdzr17NArCTIZEqfdbShzqyoicjYW\nJ2yDBw9GSUlJl9ddvHjRaDN4IuqapqUJefs2GcoJk9kdeqX23aJ5e79Da1O9hNEQEdmXxQnbH/7w\nB+zcuRPp6ekdXpORkYGdO3fikUcesUpwRM7iwuGfDQmIX0QiguKSJY7I8QQOGomAgfrJTJqWRqPx\nfkRE/Z3FCduSJUvwxBNPYPbs2fjLX/6C48ePGxaOO378OP7f//t/mD17Np588kn84Q9/sGXMRP1O\ndrvFcuMn38HuUDMEQUDitMtrsmWnfSlhNERE9tXhsh4ymczkQ0MURQDAqlWrTBZ5bTv32muv4fXX\nX4dWq7V2rET9kqalybBfJsDZoZ1JnHo39n/+dwD6VsnmukoofIMkjoqIyPY6bWETRdHo1Z1zRGSZ\ngkNbLneHRiYhKHaUxBE5Lt8BcQgdPB4AoNNqkJuxXuKIiIjso8MWNh23fyGyixx2h5rYu3cPXn5t\nudlzbqIfPC+93/rFy/jurH7HEE+5D558/Gk7RUhEZF/c/J1IQpqWJuS16w5NYHcoAEAnqDHp5sFm\nz7XWhiJz+a+AKEJeU4BxU0Ig9w9Exvfn7BwlEZH9MGGTUHFxsVFZiq0uSFoFBzdD09wAAPCPGozA\nQSMljsjxyf0C4JUwFA1ZpwFRRO2RfQiecaPUYRGRE2mbdGlP3U7Y1Go11q1bh7S0NMPm5ZGRkZg+\nfTruuOMOyOVyqwfZX125Uezy5cuxYsUKaYIhSRgtlsvuUIv5pUzQJ2wA6g7vYcJGRHalVCqxcuVK\nuz6zWwnbwYMHceeddyI/P9/k3Icffoi//e1v+Oabb7rcEYH02hLeNmxdcy6tzY3I28fZoT3hmzwO\nJd+shqjVoqkgFy3lF6UOiYicSGpqKpYsWWJ07MpGGGuzOGErLCzE7NmzUVVVhZiYGNx7772IjY0F\nAOTm5uKLL75AXl4eZs2ahWPHjtk88P4gIiJC6hBIQgWHNkPT0ggA8I8agsCBIySOqO9w8fSC99BR\nUJ08AgCoO7wXwFBpgyIipyHFECaLF8795z//iaqqKjzxxBPIysrCiy++iMWLF2Px4sV46aWXkJ2d\njSeffBJVVVV4+eWXbRkzUb9gNDuUe4d2m9+YCYb3tYf3AFxOiIj6MYsTts2bNyM2Nhavvfaa2XFq\ncrkcq1atQmxsLDZv3mzVIIn6m9bmBuTv/8FQjp98p4TR9E0+I8ZAcHMHALRcLIKsvkziiIiIbMfi\nhK24uBjjx4+HTNbxLS4uLhg3bpzJ7EciMlZw4CdDd2hA9FAEXtojkywnc1fAZ8RVhrJb6UkJoyEi\nsi2LEzaFQoGqqqour6uqqoJCoehVUET9XU76OsN7dof2XPtuUfnF09xlhYj6LYsTtuTkZOzYsQNn\nzpzp8Jpz584hLS0No0Zxax2ijrQ2NyD/ALtDrcF76CjIPPT7Hrg016D07F6JIyIisg2LE7aHHnoI\narUa1157LT7++GOo1WrDObVajU8++QQzZ86EWq3Gww8/bJNgifqD/AM/QtPSBAAIiBnG7tBekLnK\n4Zs81lDOTvufhNEQEdmOxQnbfffdhwULFuDixYt4+OGH4eXlhZiYGAwcOBBeXl5YvHgxSkpKsGDB\nAtx33322jJmoT8vZZdwdSr3Tvls0e9c30Gk1EkZDRGQbFq/DJggC/vvf/2LSpElQKpU4f/48CgsL\nDefj4uLw1FNPYenSpTYJlKive+PtVWhsqoTfno1oG7H2W04ptnawyTkAHDi4t8M9NUnPK3EYXH39\noKmrRVNNKYqP70DUVddJHRYRkVV1a6cDQRCwdOlSLF26FIWFhYaV+qOiorhQLlEXGltVGDGwAYU6\nfQuQe3gUJiyY3Ok9u/el2SO0Pk2QyeA7ejyqdv4CAMhK+x8TNiLqdyzuEg0ICMCUKVMM5aioKIwf\nPx7jx49nskZkodoj+wzvfa8aL2Ek/YtfykTD+9zd30Lb2iJhNERE1mdxC5tarUZMTIwtY3E6V65X\nJ8VWF2RHGjXqzxw1FP1Gj5MwmP7FY2A8tB7+cGmqgbqhFgUHtyB2wjypwyKifkqlUkGlUtn1mRa3\nsCUkJKCiosKWsTidyMhIo5dSqZQ6JLIheUUmxNZWAID7gCi4h7Nl2loEQUBr2OXZttk7v5QwGiLq\n75RKpclnuK1Z3MK2cOFC/P3vf0dubi7i4uJsGZPTaBsD2Iata/2bvPS04T27Q61PHT4cirwMAEDe\nvk1obaqH3MNb4qiIqD9KTU3FkiVLjI7ZOmmzuIXtz3/+M2bNmoVrr70WX375JVpaOEaktyIiIoxe\nTNj6L3WjCvLKHEPZbzQTNmvTeYch4NKadpqWJuTt+17iiIiov/Lx8TH5DLc1i1vYEhISIIoiCgoK\ncM8990AQBISGhsLDw8Ps9bm5uVYLkqivy9//A4S22aERMXAPs/0vtzNKnHoX9q95DgCQlfYlEqcv\nkDgiIiLrsDhhy8/PNyqLoojS0lKrB0TUH+Wkf2N4z8kGtpMw9W5Dwnbh8BY0q6qg8AmUOCoiot6z\nOGE7f/48AHBzZaJuUjfWoeDgZkPZlwmbzfhFJCA0aSzKMg9Ap2lF7u5vMWzWYqnDIiLqtS4Tturq\navz8888oKCiAu7s7Ro8ejWnTptkjNqJ+IW/f94Z1wRSR7A61tYSpd6Ms8wAAIDvty36TsIkiUNUM\n5NcC+XVAQR3w6GjAvVvLnxNRX9Xpr/pXX32FRx55BHV1dYZjgiBg9OjR2LhxI6Kjo20eIFFfl73z\na8N7X042sLmEqXdh98dPA6KIouPb0VBVAq/AAVKH1SurTwAnyoF6tfHxQhUQHyBNTERkXx3OEj12\n7BgWLlyIuro6eHp6YvTo0YblPI4cOYLbbrvNbkES9VUtqmpcOLzFUPYbc42E0TgHr6AIRIy41Asg\nisjZ9XXnNziAFg2QWQXUdTD5vrHVNFkD9C1tROQcOkzYXn31VWg0Gtx77724ePEiDh8+jOzsbBw6\ndAiDBg3CoUOHsGPHDjuGStT3nN+7ETqNfrFcje8AuAWHSRyRc0icdrfhfVaa4y2iW9YApBcCa04C\n/8gA/rQNUO7Xt6KZM9BP/19POTA0CJgVCywZDaSEm15bWKfvNiWi/qXDhG3nzp0IDw/Hhx9+CG/v\ny4tPjh49Gq+//joAYNeuXbaPkKgPa98d2n4lfrKtuEm3Q+aiH/FRdm4f6koca5mhXZeStfRCoEgF\n6C7N5TrfQaI1OQp4YSrw6kzgT2OB2wbrkzU/d+PrilXAaweB1w4AuTW2/RqIyL46TNguXryIcePG\nQaFQmJxr2wT+yr0wieiyptpyFB7daiirw4ZJGI1zUfgGIXrMLEM5y05bVelE/WSA7fnAh0eBX8+b\nvy7Wz7gsE4BIHyDA9M8tAH1iFuIJCELHzxZF4MNj+q7TJg3wxkEgq6pnXwcROZ4OJx20tLQgMND8\n+kUBAQGGa4jIvNzd30LUaQEA4UMnokbh18UdZE0J0+5G/oEfAehni6bc9VebPSu/FtiQCeTW6sej\ntalTA9fHml4f5w+MCQcG+QKx/sBA397P9hQE4KFRwOsHAZUaaNYAbx4CHhsDDAnqXd1EJD1OCJfQ\nlS2UPj4+3J6qH8lO+8rwPn7qfJzNqZQwmv5v7949ePm15ZcPaNTwk7lC0GlQlX8Srzz/B+i8Q43u\n8ZT74MnHn7aoflEEGloBbzfTc64y4IyZH+/5WkCj059vz18BPDLaosd2S5QvkDpO3yVa2wKotcA7\nh/XdqVd2nxJRz6lUKqhUKrs+s9OE7eLFi9i5c6fJ8bbFczs6DwBTp061Qnj925UbxS5fvhwrVqyQ\nJhiyqoaqEhSfTNMXBAHxk+8Ect6TNqh+TieoMenmwUbHLtSmoO7IPgBAnE8Jwm6aYnQ+4/tzHdYn\nikBpA5BZre9azKzWH3tlumnXZIQ34OGq74oM9ADi/S+9AgCXTroxbWGA9+WkrboZuHMIkzUia1Mq\nlVi5cqVdn9lpwrZlyxZs2bLF4vOCIEAURQiCAK1Wa70o+6mioiKjMlvX+o+c9G/0n+4AIkZM6/Pr\ngPVVfmMmGBK22sN7EDr3TgidDQS7RKMD/r5Tn/BcqbIJCPY0PiYIwNIx+nFmHY1Ds6cwL33SllkF\nTIqSOhqi/ic1NRVLliwxOnZlI4y1dZiwxcTE9LhSS/4gEhARwRXv+6ucdrNDE6bdJWEkzs17WDJk\nHp7QNTWitbIcTeez4BmXBECfT9eKvmjVAnIX4/tcZYCPm2nCpnAFyhtNEzYASHKwLUtDPPUvIrI+\nKYYwdZiw5eXl2TEMov5DVVaAi2d2AwAEmQviJt4ucUTOS+Yqh99V41G9ezsAoHRPBmp9JqNA5YsC\nlS/ytPV4oBoYGmx6b1IgUNEEJAbo3ycGANG++hmdfV1TK+AhlzoKIuoOTjogsrL2K+tHjb4OHn5m\nsgGyG/+xUwwJW+2R/fgtMQw618v9lueqzCdstyQAtw/uHwlaexfq9DNJ7xgMTLBtDw4RWVGH67BJ\nQaPRYPny5UhOTsaMGTOQkpKCF154oVvj4bpbR0tLC7Zv3465c+fixRdftGls5Byy2yVsCVPnSxiJ\n81FrZVCpjZuOPGIT4Rasnx0qb1UhtPA3wzl3tMClg7+C7q79L1krVumTtXq1fn/SXRekjoiILOVQ\nLWxLly7F1q1bsX//fgQHB6OiogLjx49HVlYWPvvsM6vWUVZWhvvuuw9eXl4IDw/H5s2bMX58xxtz\nWyM26v9qi7NRnnUQgL47LnbCrRJH1L+JInCx0Qt5dX7ICb0Lbx8fg8EBVZg76PLOBoIgwG/sFJRv\nXg8ASMz/BsMmj0CMTx3OFh7FzQmTpArf7nzd9ZMi2vYl/e8pQCsC03s+ZJmI7MRhWtgyMjLw0Ucf\n4dlnn0VwsL5/Ijg4GMuWLcOaNWuQnp5u1TpCQ0Pxyy+/YMOGDbj77rs7qtJqsZFzyG63on70mNlw\n9/aXMJr+raTBC++euApfnBuGjJJINLhHQicKKFD5tk3QNfAfezkp8y7Yi5GKcwj2aOp054D+yNsN\neGosMKjdGs7/Ow1szZMsJCKykMO0sK1evRoAMG/ePKPjt9xyCx555BGsXr0akydPtkkd4pV/3W0Q\nG/U/b7y9Co2t7RZOFEX47PkP2iYcnm50xbF2C7keOLjXZJ0w6poomt+SKcC9GU0a0z9hHq4aNGlc\n4Sm/vOWAW1AoPOOHoDHnLKDTofbQbgTPmGPLsB2Wpxz409XAW4eBnGr999aLExCIHJ7DJGxpaWkI\nCgpCaKjxSuRhYWEICAiwqBXLGnXYs17q2xpbVUYJWFN+DnK36TdvlLkrcPUDN0HmdnnF0t370uwe\nY1+lkSlwuioI52v9UFjvgweHn4BcpjO6RuGqRYRXPapbFBjkW4uqyp/wh5HN8GqXqLXnP3ayPmED\nUHsg3WkTNkA/Q/SPKfpdEMZHcPIBUV/gEAmbRqPB+fPnkZCQYPZ8cHAw8vPzbV6HPeul/qfmYIbh\nvW/yWKNkjSxztDwUZ6sDcSbiD5DnxRmOX1D5IM6v1uT6eXFZ8HDVQBCAU41n4SXveIcV36vGoWT9\nZxBbW9FcVIDmIuf+vVW4An8e2/8mVhD1Vw4xhq2mpgZarRYeHh5mzysUCqjVajQ2Ntq0DnvWS/2L\nqNWg9vBeQ9nvaucZyG5N+SpfFNb7QLyiD7Sw3vwClZ5yjcXj0FwUnvAdebWhXLOfLeNM1oj6DodI\n2Jqb9cuJu7qab/CTyfRh1taa/gvbmnXYs17qX+rPnoC2vg4A4OoXAK/EYRJH5JjUWhkyawJQVO9t\n9ny8X43hfYRXPSZHFOL+IacwJaLQKs/3G3d5rGnNwQxAx2V5zMmrBTZmwmTyBhFJxyG6RP39O59J\nV19fD0DfmmXLOuxZLwAUFxd3eY0U219Q97XvDvVLmQhB5hD/FnIITRoXVHkNx7fZSchX+UIrChgc\nUIVI73qTa+P9qjErBlBvfA/3DL7P6rF4Dx4JV78AaGqroa2vg7wi0+rP6Ovya4HXD+g3sm/RAvOH\nmJ/0QeQsVCoVVCpV1xfamEMkbN7e3vDw8IBOpzN7vqGhAS4uLvD19bVpHfasF7Bso9jly5djxYoV\n3a6b7Efb3AjViUOGsj+7Qw0uqHzwddYQFAZ6IKju8loS52v9odEJcJUZN+F4uGoxMrgCW3S2GWIg\nyGTwHz8VFb98BwBwKzpqk+f0ZTsv6JM1APgtH9CJwN1DmbSR81IqlVi5cqXUYThGwgYAsbGxqK6u\nNjmu0+lQU1OD2NhYuLi4mLnTunXYs96ioqIur2HrmuOrO3YQYmsrAMB9QDQUkVyFtE2YZwNcBOOk\nLMSjCQl+1dCKAlxh/z63gGumGRI218oc1JdfgHdItN3jcFT3DAOaNcDBi/ryjgJ90nbPMCZt5JxS\nU1OxZMmSLq+zpBGmNxwmYbvxxhvx6quvor6+Ht7el8e3ZGVlobm5GVOmTLFLHfasNyIiokf3kWOp\nbdcd2n6BVmdQ2+KGrJoA5NQG4Nb4TLi5GLdEu7noEOtXgzPqi5gW6Y1E/2r4u7dIFO2lmIJC4ZU0\nAg2ZJyFAxNmtq3H1gv+TNCZH4iIDHkrWT0jYX6I/ll6oX/ojjutAkxNylKFJDjPQZt68eRBFERs2\nbDA6vm7dOgDAwoULjY5v27YNmzZt6lUdtoqNnEdrTSUask7rC4IAv5QJ0gZkB60yTxwuC8Xac0Px\n4alk7CiKwYV6H5xv1+XZ3k2xOUgoXYuxYRclT9baBEyYbnh/9pdPIHYw5MFZyQRg0Sj9Gm2CAPx+\nJJM1Iqk5TMI2efJkzJkzB8899xxKSvT/rCsoKMBbb72FhQsXYtq0aYZra2pqMHv2bPzud7/D2bNn\ne1RHe21dk2339CY2ci41+9MNU+m8EodB7h8kcUS2VxwwE78VDkRxg/FMz8yaQLPXX9kl6gh8RqXA\nxVMfv6osH4XHtkkckeORXUrUUsfqEzcikpbDJGwAsH79esyfPx833HADpkyZglmzZuHBBx/ERx99\nZHSdr68vJk6ciGHDhpn0GVtaBwCMHTsWsbGxWLhwIQRBwPvvv4/w8HCkpKTgyJEjPa6XnIQoonrv\n5d0L/Mc7R+Lu33jO8F4AMMi3FrNizuPa6L6zEK3MVQ6/dt3XZ3/5RMJoHJdMABLN5+FEZGcOM4YN\nANzd3fHKK6/glVde6fQ6mUyGtDTz2/xYWgcAHDhwwOqxkfNwrc5Ha2UZAEDm4QnfUVd3cYfj04lA\ngcoXp6qCIYOIGwedN7nGpykXsb61SPCrRqJ/tdGenX1JwDXTUZX2MwAgd/cGNNVWwMMvWOKo+o5i\nFRDuzcV3iezFoRI2or7ErfjykhB+KRMhc3OTMJreqWxS4FRVME5XBaO+Vb8TuKsgYmZ0PtyvmEgg\ngxa3J/T99csUEdHQ+EbCta4IOo0amb+tQfKtf5Y6rD4hpxp48xAwIvjyBAUisi2H6hIl6ita6msg\nLztjKAdc03e7Q7WCHGvODcf+0gGGZA0ANKKA/A4mEvQX6sirDO9P/fQeJx9YoLxRn6y1Lf3x0TFA\ny28bkc0xYSPqgeydX0LQ6bsCFZED4REdK3FEPecitiLR//I6g56uGowJLcXCIaeMjvdH6vDhcPPS\nJ6W1xVkoPLpV4ogcX7AHMKHdJIRDF4GPjgMaJm1ENsUuUaIeONNukLp/H2hdq2jywPHKEMT61iLW\n13Tf25FB5dDqBAwPqsQg31qHnNlpEy5uGHzdAzjx3ZsAgJM//AfRY26QOCjHJgjAXUP13aDbLs0z\nOXxRPwHl4WQurktkK0zYiLqp8vxxlGcdBAAIrnL4pUyUOCLz1FoZzlUH4kRliGEJjppmhdmELcZH\nhRgf6ffKk8KIuUsNCVv+gR+gKsuHT+hAiaNybIIA3DlEn7T9mqf/79XhTNaIbIldokTddObXy61r\nPqNS4Orl3cnV0ihp8MJ7J67CzwWxRuulna/zg0ot7+RO5+MfmYSoq64HAIg6HU799J7EEfUNggDc\nPhiYHQc8NAoYEy51RET9G1vYJFRcXGxUdpTtL6hjmpYmZP72X0M54Jrp0gXTiRCPRsjadWvKBBEJ\nftUYFVwOb3mrhJE5phFzl6LwyK8AgDM/f4yr71kOVzeFxFE5PkEAbk2SOgoi+1OpVFCp7NsrwRY2\nCUVGRhq9lEql1CFRF7J3fokWVRUAQOvhD6/EYZLGU9roCY3OtB/KVSZiWGAFAhXNmBZ5AY+OOIpb\n4nIwyLeO3VZmDBx3E7xDYgAAzXUVyEn/RuKIiMiRKZVKk89wW2MLm4TatsRqw9Y1xyaKIk7+8B9D\nWR2ZAkFm/3/zaHQCzlUH4mhFGEoavDB74HmMCKowuW5KZCFmCAVM0Cwgc3HB8DmPYN9nfwMAnPz+\nHQyeyT2CeyOzCtiaByxOBtxcpI6GyLpSU1OxZMkSo2O2TtqYsEkoIoIb9PUlZef2ozz7EADAxU0B\ndcRouz5fpZbjSHkYTlSGoElz+Vf3aHmo2YRNLuM6C13Zu3cPXn5tOQBAUDfAV3CBIGpRlrkf/1rx\nMLR+xr+jnnIfPPn401KE2qdkVQFvHQLUWuDtQ8BjYwB3ftpQPyLFECb+ChFZ6OQP7xjeJ067G3tF\nT7s+v6zJC/tLBxgdcxFEBCiaodEJcJU5yVIcVqQT1Jh082BDubBpAmoPpAMAIjWnEH3zDKPrM74/\nB+ra+Vp9sgYA56qAtw8DjzNpI+oVjmEjskBjTRmyd31tKI+Y+5jdY4j1rYGfWwsAwNdNjSkRhXhk\nxFHMHZTLZM1KgqbfaHhfd3Qf1Jf2iqXuuSHWeDJC5qUWt+a+ue0skUNgwkZkgbO/fAydRg0ACBty\nDUISU2zynDq1G3YWRaFZYzroRyYA0yIv4HdxWVg8/BjGh5f02Y3XHZVH1EB4JY3QF0QRlTu2SBtQ\nHzY7DrjjcuMlcmuBgjrp4iHq69hATdQFnVZjtDbXiLlLrf6M4novHCoPR2Z1IEQAHq4ajA27aHJd\nUkD/3irKEQTPnIOGzJMAgOq9aQiZfZtDrrXXF1wfq1/649tM4JHRQFKg1BER9V1M2Ii6kL//B9SX\nXwAAKPxCED/lTqvVXVTvjbSiaKPFbQHgSHkYUkJNEzayPa8hI+E+IBotJRcgqltQnbENITfMkzqs\nPuu6QcDoUCDYvkM+ifoddokSdeH4prcM74fNWgwXubtV678yWYvxqcO10fngahzSEAQBwTPnGMpV\nO3+BrlUtYUR9H5M1ot5jwkbUifKsQyg+vh0AIMhcMHzOo1atP8KrHgO8GiATRAwPrMD9Q05ifuI5\nxPvVcP00CfmOmQBXvwAAgEZVi9qDuyWOqH/KqgIamAsTWYRdokSdOPrtKsP7hKl3wzskutt11La4\n4WDZALS6mI6DEgTg+ujz8JRruGWUA5G5uiJo2iyUbvoSAFCx/Sf4j58qcVT9y5kK4J0jwAAv4E9X\nA15uUkdE5NjYwkbUgbrSPKMtikbfltqt+8ubPPBjXhw+OpWMI+WhqPAeY/a6UM8mJmsOKGDiTMjc\n9fuJqkuLUXf8oMQR9R91LcB/jgCtWv3M0dcOsqWNqCtsYZMQN393bMc3vgZRp98tIGr0dQiOt2xn\ng8omBdKKYpBb52d83HsUWrRauLtorR4rWZ+LhycCp1yPiq3fAwDKt2wAhj0gcVT9g687sGAo8Pkp\nQBSBC5eStj9dDXizpY36AG7+7mS4+bvjalZV4cwvnxjKyd1sXTt/RbI20KcOAys2wU3GZK0vCZox\nBzI3/SSTlpILkJdzpwNrmRgFPDAChrGaF+r0OyKIXAOa+gBu/u5kuPm74zq+8XVomhsAAIGDRiJ6\nzA0W3xvk0YwE/2pk1wQg0b8aY8NKMMCrAXkt3Ii9r3H19kHA5OtQ+duPAAD33J0QRRECf5BWMeHS\nZ9xnJwEXAbgpHvwdoT6Bm787GW7+7pha6mtwYtObhvKY+c+afECLIlCiC0NNizv83VtM6pgSUYgp\nEYUIVDTbPF6yreCZc1CVvhWiugWu9aXI27sJsRO4Lpu1TIgEBOi7QkeESB0NkWWkGMLELlGiK5zY\n9CbUjfo9dPyjBiN+8uWFckUROFYGvLQH2Ksbhz0l5pPuQEUzk7V+wtXHD4GTrjWU96/5P+i07Nq2\npmsimawRdYUJG1E76sY6HNv4uqGcctffIHNxgSgCR0qBF/cA/zl8eU/E01XBqG627kK65HiCr51r\nGMtWlX8SWWlrJY7Ieeg4po0IABM2IiMnNr0FdUMNAMAvIgEJ0+4GANS0AB8e0w+MbuMCLa4KLeWs\nTyfg6uOHoBmXdz848N/l0LaadoWTdZ0oB17eo18GhMjZMWEjuqRZVWW0UO6Y+X+FzEU/zDNAAUyJ\n0h93cwGuHwTc4LINM6MK4CnXSBAt2VvQzBuhk+v3WFKV5uHU5vcljqh/O1kOvHfk0jptB5i0ETFh\nI7rkyDf/hLqhFgDgF5GIxBn3Gp2fEw/cEAu8NBW4YwigEPrGJ4goAmqtDCq1HJXNCrPXHCgNN7uc\nwo/n47AxJwHrspOg0ZlO31t7bqjZ41+cG4bVZ0bg8zPDodaa/plZn51k9vhvhTHYemEgiv2nmT2f\nVeNv9nlqrQy27jlzUXiiJXayoXzoyxfRcun/F7K+Js3l7tDieuBVJm3k5JiwEQGoryjE8U1vG8rj\n738BLq5yo2v83IHbBwM+Eg5Z0+gEqNRylDV6mJzTiUBB4Byziddbx1Lw/snR+PT0SLNjgjKKo6AV\nTROhrJpAZNcGIK/ODzoz58uaPM0eL2/yQEWTB8qazO/6faHe/OyqkxUhOFoeigqfFLMJ2M/5cWjV\nmeg6m0MAACAASURBVP7Z+uDkaJyIfgpvHE1Bk8bF5PzOoii0aE2PN7sGQqWWo1Uns2j9r5aoFHiH\nxOjvrS3HoS9f6Pom6pGxA4CHRgGyS/97ldQDyv1ALZM2clJM2MjpVTYBa99aAV2rflZnY+jVwIg7\nJItHFIFj5SEmCYROBN44ejXePzkan58dYdLSJBOAOs8Ek4RGEAC3duPs1GYSFxeZDhoziZCrTHc5\nLpgmZrIOjqNdEicTzGRComD2uKbdfS5XnBdFoEXrAnm7mNqoL8XeqpOZPX+4PAyCmRQwJ+wevH9y\nNN44moJmM9+XPSURxi19Mldcs+ifhuKJTW+ipijT9Osjq7h6ALA4+XLSVtkMlDVIGxORVJiwkVP7\nPht4aeNJaA6tNhwrnvgyzlXZdvXOA6Xh+LVgINab6WoUBGBXcbRJAiETAM92e442aUyXUXTRNqFR\nIzc57iVvhZe8FQHuzdCIpr/2Y0JKIZhJoG4YeB63xGXjtvhMo+StzV1JZyA3s3vDwiEncf+Qk7h/\nyCmTxAsA7kg4Z/b4ddH5mBmVjwE1aaYJG4AhAZVwlRkf1+gEw7UyQTS5T6MToBMFk0ROJwJamX4f\nJAGA4orJI6II7LkYYZJYxk+5Cw0Rk/R1aFqR/uHTJl9HXi1nN1pLSrg+aVO4Ao9dBSQGSh0RkTS4\ncC45NY1WRNiOP0EQ9R/muvjr8eRd1yLG1zr1/5w/CNOjCuDuYpwsHC4Lg6pVnyyo1G4IUBj383jL\n1ahvNd1U0ddNDYiAh1xjtkUsqvpXeLjONjn+4LATncY5KaLI7PEk/+pO7wvzbDR7PMij8zXoonzM\n78E3KrgcALBNdQiCkGJ0TiYAc2NzTe5xlYl4cvQh/GvdB3h88aNmV8q/Ljrf5HirzgWK1kp4XUqC\nrzzfrHWBm0xnkiCqdQIKp7yOpK/GQYCICwd+QMHBLYi5Wv991+qAf+0D3r7euD5RBP57St+1HqAA\nJkVdbjmizqWEA0MCAS/uM0pOjAkbObUhF7/FxcLfAACiIEN9SBy++Hi5RfceOLgXfhMnoaTBC1XN\nHpg9MBd+7mqja0obvVDdrEC4l3Fi4+feYkjYatXuJgnbiKByuAqmLVr3JJ3udOsen+Y8k+TQWQgA\n3Mx87a4y0ZAItufuokXSxc/wh5HmByXKBGByRKHJ8YZWoCUsBVXDFiHotH6/2V3vPo757xyHXOGJ\nOjXg42aajDW0AumXqlO4ApOjjM9rdMAnx4GHk42Tx7aucWffsonJGjk7JmwSKi4uNipLsdWFs8iv\nBWJ8jT/0WpsbcfDTy5u6B025DiNun2L2/uwafwzwqodXuyU8du9Lw/GKEBQ3eAMAqlo8TBI2f/dm\nVLeYJmzJweVI8q+Gr1sLQs20Ul0dVmo2Dmf/0LYndxctRoeUmRwP8gD+cwNQedVL2Pj4t2htqEHd\nxVwc+vJ5XPP7l6HWAkODTOuradfoGKgw/VlWNwP5dabH69TAX9P0rXIR3sDSMcbnnT2hO1kORPkA\n/uYnQBPZhEqlgkplvqfAVpiwSejKjWKXL1+OFStWSBNMP1XaAHxzVr8A5x9TgOHttr85su4V1JcX\nAAB0ck8EzroDpY2e8JGrTdZWO1kZDK0oYHCAcRdhsEeTIWGrbnZH7BVdqePCSuDharpO29DASit8\ndWRve/fuwcuvXW6BdYuZDM8zPwAADq/7F9IKqqHzCQMAvLxVf42n3AdPPv40/NyBe4frEzcPM395\nq5r0iZy54xodUN6ob5m7Unkj8N5R4LlJxsdbtUBFExDsAchN51P0C0dLgQ+OAUEK4Klx+qSWyB6U\nSiVWrlxp12cyYZNQUZHxuCG2rllPYyvwYw6wvUA/pggA1mcCQ4P1XVWVeSdx5JvLs/1y4xZga9ZU\n/P/27js+qir9H/jnzCSZSU9ImZAASURIaEIIoJSsidJ7EwhIsQD+EL64ouDiqsuKIq4o7CIoWEIV\nVlYElAWlCkhAXelVJKGEJKT3TGbm+f1xMpNMZlIGUybheb9eeUHOPXPvnVsyz5zyXD0J9GuVgM4V\nutD8nAuRVuhiEbC19cqAl1MxfJ0LoHGxnL5WsWWNNW4GoUXvYWGm34naIuFfv6Hg2iUIImiS9yN0\n/OsQyrII6diuywBkOpg/tax83YFuMm1MRVnlest9LbO54G4B4GGlu/BGjhxLBwAdfIH/62a+vEQP\nlBgAF8s5Ko1CbjHw2Vl5f6cWyJQf8zhoY/Vk3rx5mDFjhllZxUaY2sYBWwMKDLT+4HD2xyRkA//6\nBcgr1zspBBDsAfySDKgVelxZ8SwMOjnYXBP+CE42723KQ5ZS4ArAPGAL8chGjtbyUzHEIwchHjkW\n5ez+IIRA4PincW3pQpBeh8LEa0jb/w38+o+weV3uKus5/iI0wD/7AhlF1icpZBQBvlbS3aUVlv3f\nWsvclQzg+wTghe7m5XlamepG42r9dfbCXSXztH18SgZtd0uDthe7A82sBLaM1aaGGMLEaT1Yk9Pc\nFTAYZCsbALTxBhb2BKZ2Aor1QPy2FUi9chIAoHBwQvTcT+ClkGMRPJ2KoVZadmEGueWhXbOMensP\nrPFQaQLhN3CU6ffU/36FwpvXa3cbDkBzNxlEVdSnBTChnWU5EeDnIoM8HysBTGoB4G9lfefuAm8f\nB+buA9ZZmVxcpAOK7eRpbJ39gee6AMrST7K7BcDK/6FGSZAZa2zs+PsTY7a7miFTJyTkyIDt7UeB\nrpqyAdl++Zdx+rvXTN9UusX+Fc1atYcPvsTAh/4HZwd+kDuzne/jQ5F7/hQKE64CBj1ubViN1i8t\nhsKp7qc2CgE4WGl5eyRI/hhIdn9WVKST3bAVpZbrxfew0uJ3/LZ8VNSkDublWUWAVi9b++ozXclD\npUHbx6dk4Bbb7v6dgMGaNm5hY41SZqFMehtfIX2YhwpIzpctC2HNZHeS8Y+3vqQYZz6cCIVO9hX5\nhD6ELmMXAACUwsDBGrtnQqlE0JMzoXCSEY42JQnJ2zc28F5JCiFb6Coa1BqIbmVZ7uwgAzlHJeBv\npas1tcB6+dFbwGtHgNnfA99ZaWCsy0TCD/kDz0UAs7tyYl3WdHELG2sUiICbubK75nwacDEN+CkZ\n6BciH1/jUPrVw99FJibNLwGCPeV4HGMrQXzcX5B27VcAsiv0sRfXWTwvlLF7pfILgGbUk7iz9VMA\nQOaPB+AS2gaAf8PumI36hcofA1kPskoMsnu2ouTSOTd6A+Bq5bbadkm2vj0WbF5eWCIDyj/aKtfJ\nr/o6jDVmHLAxu5WvBS6kAxfTgSfCgH+ckF0ugPz2r1LKD4mzd2VLGiBb09zOroaHLhVaYcCHx2S5\nQ9pVuJ3aYlp33gMxWLvjKwBfAZBJcMvP/mPsXnj3jEb+lfPI+TUeAJD078+hiJzWsDt1jxTCehD1\nZAfLMkC2zHmpZddogJWxcSkFQLiV/HRfXAR+TgY0LsC4cDmTu7bpDGVf6hhrrDhgY3aDCLiTJwdI\nqxyApSdkHjUA6NFcdnGeLZ28KQTQRQNE+FuOw3HUJ6P38LLgqzg1Gb+/vxPGHPhuHSLQfvqTEOUG\nuvx44nAdvjN2vxBCIDD2WRQl3YA2JQlUooXr6W0oynkLag8r0UoTMqkDMAlybJy14CitwPqkieR8\n2SqXlGf9dXFngd5Bll2dRDUbq/bzHeDrq8AL3azPpmWsseCAjTUoAwFHbwK/ZwPXMuX4mJldgK4B\nQHufsoDtfBrQLUDmjOroKzPJW0uBUJG+sAA3PnkfhkI5ktrB0xtBE6ebBWuM1SalSo2WT8/F9WWv\nw6AthrIwA3sWj8awt76D0rEGF20jV1kqkDf6yMeHVVR+xqm1lrlrmcCAUMvy93+SQx80rsCYttaD\nsV+SgU/PyL8zy34C5nXnoI01XhywsQZz7Jb85nsqRc7uCi59SsCpVBmwdfQDbuTKpJ9d/IEgdznr\nrabIYMCt9augTZGPABOOjmj1zAtwcKulJ7szVgl1QBCCJs3Ezc//CQC4c/4IDi5/Bo+/tOG+/bJQ\n2Ri1RVGyVS4lH3CrMKlWZwAyi+UkovKIgJs5QKEOuJ0LjA+3XG/cWfmlT6kADHr5xIhlP8k8bRXX\nx1hjwL36rF7oDMCZVBmcGakdgJxi2QWaXlhW5lSaJL6jHzD/YWBIaxms2YKIkLT1U+RdOGUqC5ww\nHc7Brf/gO2GsZjy69IBm+ATT71cPbcbxT18GcZIwC2oHOUmoYiyrFMCbUZZdpXlaGawZX+tZoeFS\nb5Dj4iI0wPMRZY/mSi8Axu8A1pySs8x1BjDWaHALG6szBgIupwNn7gLxSTIvWqCbHHsGyJYzB4V8\ncLOvCzD9IaC9by0895AIKTu/QFZ82bg038eHwqtbrz+4YsZs4/PYEPy0+wha6WT+mdPb38eJX0+i\n6MGYSl9jfPYokwGctUdNuauADx6XQyhyii0DvbRCwEsl/5a085VB24e/yolMhTrZVapyAIaW+/6W\nkg9suwxczwJGtwUC3GQXbWN9dBdrejhga0BJSUlmvzfEoy5qm8EAXMuS325/SQZytfJbslFSHpCU\nCwS6y2/Gf+0lx6DUVqJNIoLq+hGk/14WrHn1iIL/0HG1swHGbCCEwHn1A+gQGoDcs78AANQJR9Ey\n3B9+A0dZ7R41PnuUVc3FEQjxtL7MUwU827ns93a+Mkfb0ng5mxWQs1LLH/5bucCJ28DZNPl3yyhC\nA0zpCGy5KP9WtXCXT1hg97fc3Fzk5ubW6zY5YGtAFR8U+8Ybb+Bvf/tbw+xMLdDqgMe3Am28zFvJ\n9FT60GohJw44l/vGai2f070iIhz/9CU4lwvW3DtFInDCsxAK7v1nDYOEQItps3Hz0+XIu3AaAHB3\nz1fQF+YjYOQkvjbrgNrBMpgL9wGWPw78liUnOlTsZk3Ol61vLhU+FY3JuE+Ufr9u6SEDtv8lAzt/\nk0Gcp5N8bUwwt8rdL5YtW4ZFixbV6zY5YGtAt2+bp+lv7K1rTg5y4kBaYVkg5qmSQVq35kColTEq\ntUWvK8EPK5/Dpe8/N5W5hndCi6nPQyj/aB8rY3+MwsERLZ+eixuffID8S/IBnRmH90KXm42gSTOh\n4ATO9cJTDUQGWF/WozmghOwhcFTKLtKUAhmAJeeV1dOUTli4nSfTEN3JAzKK5OSHk3dkYuDxpc92\nTc0H/pcigzo/Z/l3UcnxeZMwb948zJgxw6ysYiNMbeOArQEFBgY29C7YTGeQg3UvpgN9g4EeFd7C\nqLbAql+BR1vJQO1B77p/rmBBViq+WzIOd879YCpzf6g7WkydxR+EzG4oHJ3Q6tk/4/bGj5Bz6iQA\nIOd/8SjJSEfLp+bA0YufqdSQ/FyAgRXmJBHJHoLMImByRxm4tSqdZF4+iCssKdfVWi41ye9ZwPYr\n8v/Gv4M+zmUBnMoBaOEGdG98HwX3vYYYwsQBG6uR9EKZhmPjeZm81tcFUCstA7YRbYBhrWVrW31I\nvngc3y+dgLy7N01lxc07o/202dyyxuyOwtEJLabORrL7BmQc+R4AUJhwFdf+8Ve0nDYbrm3aN/Ae\nsvKEAByEDOYqpgKZ3BHoHypb4k4kyVY2hTBP5G18XJdxXXoDcLdA/gCyVS4ywDJgS8iWz2Z1Lc07\n+YAXt8wxDthYNdILgS8uAOfS5LdNF0f5hyejUJZlFcnH0Rg5KFAvyWLyM+7g501/w4W9n8gdAwAh\n8PCUxdh7q5CDNWa3hEKBgDFT4Ojjh5SdWwCDAfq8HCR8uAQ+MYMA6lz9SliDM6YiCfa0/OJq1MYb\nKA6WQd3tXCCr2Hx5oU4OFanodCrw8Sn5dIhWHjJgM7bMDWkNOCrkZK7Axj2KhtmIA7YGYJxZkpub\na7fj1gpLgA9+Bv4vEriaWRYTqZTyD0x7HzkLy8vKlPu6VJSTjtNff4AzXy+HrrjAVO7k4oG+L29C\ncI8h2PvBG/W7UzVQkFeIy+cSUJBXCBc354beHVZPKjvvQgj4xgyGc4sQ3IxbCX1eDkCE9AO74e5y\nAknnBiCw458acM/ZvcrNzcWyZcswb948dPBzR4dyD6XX6mXrWmqBHN926CYQYWVMXWq+/BsMyK5W\nA5W1zA16QPZ2+LuaB2zbLskUSnqDDPI6a4C23vJvdF0PS2H187luVwGbTqfDm2++ia+//hrNmjVD\nTk4ORo0ahb/85S9Q1rDFxJZ11FXd6thjwFaukQqAnMmpVgJXMuRg3B9uyhxpUS3kDKn6bp7PTU3E\n6e3v4+LeT80CNQBo1W0QomZ9CA9NSP3ulA0K8otw9XwiCvKLOGC7j1R33l3btEfrlxfj9uY1yL98\nDgCgLEjHjgXRaN3nCTzy9FK7vq6ZpdzcXCxatAgzZsyw+PvupJRJwI2JwAc8YH0dnfyARwLl0xya\nu8mAzcjfRQZ85QNBQAZrh26UdbeGNZMtcgt7ylZAAIi/LYO8Vh5yDJ6LI+DuVHeTwe4n913ANmvW\nLOzbtw8nT56Er68v0tLS8PDDD+Pq1atYt25dra+jruo2JnlaYP054LdMOSYjQlO2LKqlzKc2JkyO\n1ajvx7mQwYDbZw/h63+9BEXyaYgKGeL1bhoUPvgYzni2xpnNZbNDf/o5Hr2HhVVcHWN2ydGrGYL/\n3wJk/ngAKV9vhkEr+82uHf0S1+O/RtjjU9D1ib/Ao3kln+6syXkkyPwxfFq97B5NLZABVqgXEFRu\nrByRHL5SVO65rMZnuvqW+54QnwT0DZH/X/GLHNriqARu5QAE+Tf+lYeBB3n+i12ym4Dt2LFj+OST\nT/Dxxx/D19cXAODr64tXXnkFM2fOxPTp09GnT59aW0dd1W0s0guBz87IZJAFJfJGDXI3D9i6auTv\nFfMV1bWs21dx9fBmXN63DrkpCajYfqkKbAW/vkPhEfGI1RxWP544bFHGmD0TQqBZ78fh3r4Lzq1e\nA6eU8wAAg64EF/d+ikvff46Qh4ej/aCZaBnRj3O33WeclLJlzNgFOuxB8+UEYE6k7Am5niUTlD/g\nJWe4ls8Jl1YoAzidQc58BYASvUxRkqeVPSr6Hpbb//B/MqgLcgeaOQPeKtnVml8ChDeTT6Mwjm9m\ndcduAra4uDgAwIgRI8zKhw8fjpkzZyIuLq7aoMiWddRV3cbgYhrwz19kNu+C0nESaYXA5Qz5mBeP\n0ufy1Ve3p15XgtQrJ5EQvxMJJ3Yh69Ylq/VcHmwH375D4Rb+0H37AG3WtDl6+6Cg02iMe+kjxMf9\nBcnnjwKQrc3Xj3+N68e/hptfSzzQewxa93kC/m17QMETbO57CiETA4f7VF2vf6icvFBQIlvoMotk\n0FWsl8sdleZpSYxu5AB3cuVM2PJ+SZFf7AWA13uXdfUSAVsvAjdz5Zf+5q4yJ6enSj5WjN0buwnY\nDh8+DB8fH/j7mz/zQ6PRwNvbG0ePHq3VddRVXXtRfuCrm5s7rmbKGUtCAG2ayWZ1A8lvSUoh03E8\n+1BZsGbrNmraZ7/iX/9AYX4ylHkpcMi6BWXWDThk34YwlFitXwAVtl9zwrz3X4BP27rp5mwqEwLq\n4300lW3U53buRfP2vTHq3R+QdPYwftnyFm6d2mdalnf3Js58vRxnvl4OJ1cveIdHYd9vOiz469/Q\nMqxrnQRw93Kv36/bqA/3+j7+1FL+66gEXust/1+sAy6kAzey5Rd342eAcRsvvjgPKfnuUFUSLRi/\nOnuV++zI0wIHb8gu2PNpcrIaINOUvP84sPhHOTnC3QmIbZ2LVSuWocOoedA0c4ebk+yqDWsmW/Ns\n+UyqTFM573YRsOl0Oly/fh0PPvig1eW+vr5ITEystXXUVV17Yhz4+vSzM+Dq5o7154BpnWQiWwcF\n8HgwcCkDmNpRTkm/l27PygbX6ku0KMpJQ0HGHeSkJiA3+TpyUxOQefMSHC7Ew7OkoIq1AsLRCW5h\nHeHZrReK/UNxLPpFvOhZdw/vayoTAurjfTSVbdTndv6IwE6PIrDTo8i8eQkX9qzB5f3rUZybYVqu\nzc/C5WM7sfoA0DJlNzxdHKF300DvroHB1RcGtQcMai8Y1B4gR2dAyBvd1gfMVzWQvrY0lW3Uh9p8\nHyoH2QpWfjhM+W1Mnz4DHzzmjhytbGHLLP3JKATySmSLXJ7WvOs1q1i2sukMgFO5zxY3J1l+J08u\nA4Di5rlY/OYiTAqbAVcf+V5+vC0nu/m5AO9El73+nXiZF08IGex5quQsWhdH+UixO3nAqDDLWbGZ\nWU3jvNtFwJaVlQW9Xg9nZ+t/NNVqNbRaLQoKCuDiYn3kuy3rKCgoqJO6le1bXbtz/iiSr1/E8dsE\ngKAAwZAv/6jv++pzdA/xQNcMwndnCflBBBBBQwQNCEgknCUDQAQi+XoiKp02WvZ/gvxXr9NCV1wA\nXVE+klPTAQDfvzsR7kotCrPvoij7LrQFOZXua2VxoWMzX7i27QCPTpFwbdsRCicnAEBaSmbtHSjG\nGoH4+ONYYjU1jTvQ/Tk4ZCbAMeUCHNN+g0KbZ1ZDGHRwyLkNh5zbVl4PKJxdoHRxRaFWiZ1Je+Gg\ncoHSUQUHJzWUTiooHVVQOqqhdFRB4egEIRQQQoG0LLmdc9+sQqqPlxxDJxQQCgUERNnvf2CoQmp6\nFgDg8v71yPTxKn1DtTv04W56NgDgyoGNyDJu44+wsn/G93Hl4Kba2YYV9bmNq4c2wb90GyoAAaU/\nANDbEUBpcuCLe8teW6gD+mUCrQoAzW35e6EOcHMEzuQCHhdkPQcFkFC6Ha9Lm+Du6QUCEJ4J+GfK\n7tsLpd2wREC2HNoJrV6O66voRg4Q3tP8tBAB/zwqtzHrH5sQGeIFR4Xctpca6BkIHLlV1voIAPla\n4Hw6kJgte6AcFHJMoKujnPAByB6qa5myx6pIB1y+nWXzMbaVXQRsRUXyjDg4WN8dRekA2+zs7EqD\nIlvWodfr66SurQFbfHy8aRJDZVxdXeHq6orWrVvD0dH6Y5Yu71+Pi3s/MTVNE4DsIjmjMmXHX3FU\nLZcIAD/atIdVyyrdRtLZw/BS1/wPq3BSQd28BdQtQuDaOgwuD4TB0buawReM3ScMQlvNLOf2AAaD\niFCckoSbJ04CB7bBwd0TKKn8yxIAGAoLYCgsgAOA26eTa7xPxnv9l61v2XSv28K4jfi4v9T5No5/\nvqDut/HZ/Pt+Gz4AdAAcS38A+RnUqlyd46XbCfqxbDvB5ZaXn0JW/nXWtALwwy+W5SGl23j4zHx4\nXSl7LyUAjA80tDZVzdivU6QjXCudgXumQp3S2BM5FZIi1wW7CNi8vKr+hpCXJ7/dqdWVZ2m1ZR2V\nBT5/tK6txowZU22dadOm4amnnkJmZibOnj1rtY7h8mWbt123BODkBqjcARcfCJdmgIsvhKsfErIL\n4NGiVdlXoCQASWkA0qyuKSdb5rb56ftr8PCsWVO2Srjj2K6aH5N72Yat2+Ft2Nc27nU7drmNXNk0\nkNHlaejVAsq8FChzU6AoyoKiKAeKwiyI4lwodEXVrIkxZs2+34HdvzX0XgCCqEJyqwbi6uqKdu3a\n4eeff7ZYFhgYiLS0NBQWFlaZpNaWddRV3ZrIzc2Fh4dHjeoyxhhjrHHIyclp+olzQ0NDkZlpOV7J\nYDAgKysLoaGh1QZEtqyjrurWhLu7O+wkTmaMMcZYI2A32RcHDRqEhIQEUxej0dWrV1FUVISoqKha\nXUdd1WWMMcYYq212E7CNGDECRITt27eblW/btg0AMHnyZLPy/fv3Y+fOnfe8jrqqyxhjjDFW2+xm\nDBsADB06FOfPn8ePP/6I5s2b48aNG+jRowcGDBhg9rzOrKws+Pn5Qa/X48KFCwgPD7d5HXVZlzHG\nGGOsNtlVwFZcXIzXX38du3fvhpeXF9LS0jBq1CgsWrTIbLamwWBATEwM0tPTcfz4cbMBfjVdR13W\nZYwxxhirTXYVsDHGGGOMMUt2M4aNMcYYY4xZxwEbY4wxxpid44CNMcYYY8zOccDGGGOMMWbnOGCr\nRzqdDm+88QY6d+6MmJgYREZGYvHixaYHzLPGrV+/flCpVHB3d4ePjw88PT3h6uqKJUuWWNTla6Fx\nKi4uxsGDBzFkyBC89dZbldaz5fzytWDfanrO+f5vOlJSUjBjxgz069cPnTt3RmRkJFauXAmDwWBR\nt17vdWL1Zvr06RQaGkp3794lIqK7d+/SAw88QFOmTGngPWO1ITo6msLCwkitVpO/vz+NGjWKjh49\narUuXwuNS0pKCvXr149GjhxJzz33HAkhaNGiRZXWt+X88rVgn2w953z/Nw2pqanUs2dPOnXqlKks\nLi6OFAoFDR48mPR6vVn9+rzXOWCrJ0ePHiUhBK1Zs8asfM2aNSSEoCNHjjTQnrHaEh0dXaN6fC00\nbocOHaryw9uW88vXQuNQ3Tkn4vu/qZg7dy5t27bNonzChAkkhKBVq1aZyur7Xucu0XoSFxcHQD7m\nqrzhw4ebLWdNH18LjRtVk7rSlvPL10LjUN05twWfc/u2f/9+PPXUU9i/f79ZufH8/Pvf/zaV1fe9\nzgFbPTl8+DB8fHzg7+9vVq7RaODt7Y2jR4820J6x+sbXQtNmy/nla+H+w+fcvoWHhyM/Px+ZmZlm\n5T4+PgDk+Daj+r7XOWCrBzqdDtevX4evr6/V5b6+vkhMTKznvWJ1ISEhASNGjEBMTAy6dOmCN998\n02xAKV8LTZst55evhaaH7//Gb+vWrUhKSsLYsWPNyo3n5cEHHwTQMPe6Q43fBbtnWVlZ0Ov1cHZ2\ntrpcrVZDq9WioKAALi4u9bx3rLYQEebMmYM1a9agefPmSE5ORvfu3XHx4kVs3rwZAF8LTZ0t57eg\noICvhSaE7/+mQaFQQKPRWJR/8cUXAIBnn30WQMPc69zCVg+KiooAAA4O1uNjhUKehuzs7HrbJ1b7\nfH19sWrVKjRv3hwAEBAQgD//+c/YsmUL9u7dC4CvhabOlvPL10LTwvd/03Xs2DEcOnQI48aNrz03\nEgAAE89JREFUM405a4h7nQO2euDl5VXl8ry8PAAyymaN17Zt29CyZUuzsg4dOgAA1q9fD4CvhabO\nlvPL10LTwvd/05Sfn4+nnnoKAwYMMJ1HoGHudQ7Y6oGbmxucnZ2tJt0D5AWhVCrh4eFRz3vGaktJ\nSQlSU1MtylUqFQDg3LlzAPhaaOpsOb98LTQdfP83TUSEqVOnIiIiArt27YKTk5NpWUPc6xyw1ZPQ\n0FCLWScAYDAYkJWVhdDQUCiVygbYM1Ybhg0bhqCgIMTHx5uVG785OTo6msr4WmjabDm/fC00DXz/\nN00vv/wy/Pz8sHXrVlN3ZmFhoWl5fd/rHLDVk0GDBiEhIcF0AxtdvXoVRUVFiIqKaqA9Y7UhNTUV\nXl5e8PT0NCu/ffs2ACAyMtJUxtdC02bL+eVroWng+7/p+fDDD6HT6bB69Wqz8qefftr0//q+1zlg\nqycjRowAEWH79u1m5du2bQMATJ48uSF2i9WSfv36YdOmTWjXrp1Z+d69e+Ho6IjZs2ebyvhaaNps\nOb98LTQNfP83Lbt27cKNGzewfPlys/K7d++aurmBBrjXa/KoBlY7hgwZQiEhIZSUlERERImJiaTR\naPj5cU1ARkYG9erVy+zxIkeOHCG1Wk0rV660qM/XQuO1ceNGEkLQc889V2kdW84vXwv2r7pzzvd/\n0/HTTz+Rm5sbhYeHU1hYmNlPQEAALVmyxKx+fd7rgqgWn7nBqlRcXIzXX38du3fvhpeXF9LS0jBq\n1CgsWrTIbIwDa5ySk5Mxf/583Lx5E0IIODo6YsGCBXjssccs6vK10Ph0794daWlpSExMhBACRAR/\nf38EBQXhk08+QUREhKmuLeeXrwX7Zcs55/u/aejUqRMuXLhQ6fJt27Zh1KhRpt/r817ngI0xxhhj\nzM7xGDbGGGOMMTvHARtjjDHGmJ3jgI0xxhhjzM5xwMYYY4wxZuc4YGOMMcYYs3McsDHGGGOM2TkO\n2BhjjDHG7BwHbIwxxhhjdo4DNsYakZCQECgUCrMfZ2dnhIaGYurUqTh9+rTFa6Kjo6FQKHD48OEG\n2OPKJSQkQKFQIDQ0tEG2f+jQISgUCsTExNzT67VaLT766CP0798fAQEBUKlU8Pf3R58+ffDuu+9a\nPOS5PHs9J/bmj1wjxvuDsabCoaF3gDFmu4EDByIgIAAAkJGRgZMnT2LDhg344osvsGHDBowfP96s\nvhACQoiG2NVqNfR+3cv2z507hxEjRuD69etQqVTo2bMnAgMDkZ6ejqNHj+LHH3/EsmXL8OWXX+JP\nf/pTpdtt6PfeWNzrceLjy5oSDtgYa4ReeeUVs0CgqKgI06dPx6ZNmzBz5kz0798f3t7epuX2+AS6\nFi1a4NKlS43u2YnXrl1DVFQUsrOzMW7cOKxcuRK+vr6m5QUFBXj11VexYsUK9O/fH4cPH8bDDz9s\nsR57PCeMMfvF7cWMNQFqtRqrV6+Gi4sLcnJysHfv3obepWo5ODigbdu2DdYleq8mT56M7OxsjBw5\nElu2bDEL1gDAxcUFH3zwAV544QVotVrExsaipKSkgfaWMdZUcMDGWBPh5uaGtm3bAgBu3Lhhtc4v\nv/yC4cOHw8fHB2q1Gl26dMFnn31mUa9NmzZQKBQ4ceJEpdsbM2YMFAoFPvroI1NZVlYWFi5ciA4d\nOsDFxQXOzs5o2bIloqOj8c4775i9vrrxSfn5+XjvvffQs2dPeHl5wcXFBa1bt8a4cePw3//+16zu\nhQsX8Prrr6NXr14IDAyEk5MT/Pz8MGTIkFoNXg8ePIj4+Hg4OTlh1apVVdZ9++234evri4SEBGze\nvNlqHSLCwYMH0bdvX3h7e8PNzQ1RUVHYtWuX1fq2HF+jmzdvYu7cuQgLC4OzszM8PT3Rp08frFu3\nzmr98uPrfvjhBwwZMgS+vr5QKpXYsWMHHnnkESgUCuzcubPS9/7SSy9BoVBg/vz5prK0tDSsWLEC\nAwcORGhoKNRqNby8vNCzZ0+sWrUKBoOh0vUBgF6vxzvvvIN27dpBrVZDo9Fg2rRpuHnzZpWvs6ak\npAQfffQRoqKi4O3tDWdnZ7Rt2xbz5s1DWlqazetjrF4QY6zRCA4OJiEEHT582Ory1q1bkxCCli9f\nbip79NFHSQhBCxYsICcnJ3rooYdo4sSJ1KdPHxJCkBCCli1bZrae5cuXkxCCpkyZYnU7t27dIgcH\nB/L09KS8vDwiIsrPz6f27duTEIICAgJoxIgRNHHiRIqJiSF/f39ydnY2W8f169dJCEGhoaEW609I\nSKCwsDASQpCHhwcNHjyYYmNjqXfv3uTm5kYxMTFm9Z955hkSQlCHDh1o8ODBNGHCBOrevbvp/b3/\n/vsW2zh48CAJISzWVZUXXniBhBA0dOjQGtWfPXs2CSFo9OjRZuXGczJ37lxSKpXUuXNnmjRpktk5\nqbjPth5fIqIDBw6Qp6cnCSGobdu2NHr0aOrfvz+5u7tXen6N+/b888+TUqk0XS/9+/en3bt300cf\nfURCCBo1apTV96zT6SggIIAUCgWdP3/eVL5hwwYSQlCrVq3o8ccfN+27Wq0mIQSNHDnSYl3GayQk\nJIRGjx5NKpWKBg4cSLGxsdSqVSsSQpBGo6HLly9bvFYIQQqFwqI8OzvbdJy9vb2pb9++NHbsWAoN\nDSUhBAUHB1NCQoLV98ZYQ+KAjbFGpKqA7ddffyWFQkEKhYIOHTpkKjd+AAsh6PPPPzd7zcaNG0kI\nQZ6enlRQUGAqz87OJldXV3JxcaH09HSLbb322mskhKA5c+aYytatW0dCCBo2bBjp9Xqz+nq9ng4e\nPGhWVlnAptfrKSIiwhQUZGVlmS3Pzc2lAwcOmJUdPnyYEhMTLfbzxIkT5OnpSU5OTnTr1i2zZfcS\nsEVFRZEQgt58880a1Tcek5CQELPy8uekYrC8a9cucnR0JAcHBzpz5ozFump6fJOSksjb25scHR1p\n/fr1Zstu3rxpOsZxcXGV7tvatWst3lNWVhap1WpSqVSUlpZmsfzbb78lIQR1797drPzixYt08uRJ\ni/p37twx7cvWrVvNlhmvEWOQevHiRdMyrVZLkydPJiEE9ejRw2K9lQVs48ePJyEEjRs3zuza0uv1\ntGDBAhJCUHR0tMXrGGtoHLAx1ogYA7byAVlGRgbt2LHD1ELQtWtXs9cYP4CfeOIJq+ts164dCSHo\nhx9+MCufNWsWCSHo3XffNSvXarWmFpTyH6DvvvsuCSFoxYoVNXovlQVs27dvJyEEPfDAA1RUVFSj\ndVVl4cKFJISgDz/80Kz8XgK28PBwEkLQmjVralT/v//9LwkhyNXV1azceE6sBRpERFOnTiUhBE2f\nPt1UZuvxnT9/Pgkh6JVXXrG6/OeffyYhBEVGRlrdtwEDBlS67tjYWBJC0D//+U+LZU888YTV412V\n7777zuo1Wj5gs7a+rKwsUwvisWPHzJZZC9jOnz9vuuasXVsGg4EeeughEkLQ2bNna7z/jNUHniXK\nWCNUWe6wyMhIfPXVV1aXDR061Gp5eHg4Ll26hDt37piVz549G6tXr8bHH3+Ml156yZQi4auvvkJK\nSgpiYmIQHh5uqt+jRw8AwDvvvAMfHx8MGTIEXl5eNr+3PXv2AAAmTZoElUpV49fl5ubi22+/xalT\np5CRkQGtVgsAuHr1qtm/9mTSpElWyydPnoz169eb5Wmz9fju3r0bADB27Firy7t27QpXV1ecPn0a\nWq0WTk5OZstHjx5d6bqnTZuGLVu2IC4uDnPmzDGVZ2ZmYufOnVCpVJg4caLF63Q6HQ4cOIDjx48j\nOTkZRUVFICLk5uYCqPwcCSHw5JNPWpR7enpi2LBh2LRpEw4dOoRevXpVus8ATGMfhw4davXaEkKg\nT58+OHv2LI4fP46OHTtWuT7G6hMHbIw1QuXzsKlUKgQGBiIqKgrR0dGVvqZVq1ZWyz08PADI1CDl\ntWvXDn379sW+ffuwZ88eDBo0CABMg+2ff/55s/qPPvoo5s+fj/feew+TJ0+GEAJhYWGIiorCmDFj\n0L9//xq9t8TERAAwCwars2PHDjz99NPIzMw0KxdCmNJn5OTk1Hh9lfH19cXly5eRkpJSo/rGen5+\nflaXVzbhIjg4GABw69YtU5mtx/f3338HAHTv3r3KfRRCID09Hc2bN7e6D9b069cPQUFB+PXXX3Hu\n3DlTYLN161ZotVqMHTvWIpi8cuUKRo4ciUuXLlW63srOkZeXl+k6rci4n7dv3650vUbGY7Jy5Uqs\nXLmyyro8+YDZGw7YGGuEKuZhq4l7yfo+Z84c7Nu3D6tWrcKgQYNw7tw5HDlyBEFBQRg5cqRF/Xfe\neQfPPfccduzYgWPHjuHo0aNYu3Yt1q5di/79++Pbb7+FUqmscpu2Jju9desWYmNjUVxcjIULFyI2\nNhYhISFwdXUFAKxduxYzZ86slbxn3bp1w7FjxxAfH1+j+idPngQgWz5rgy3HV6/XAwAmTJgAtVpd\n5Xortq4BgLOzc6X1hRCYMmUKlixZgri4OLz33nsAYJp5Om3aNIvXjB07FpcuXcKIESMwf/58tGvX\nDp6enhBC4OrVqwgLC6vz3HTGY9KtW7dqW886dOhQp/vCmK04YGOMVWro0KEIDQ3Fnj17kJiYaGpd\nmzFjRqUBYEhICObOnYu5c+cCAI4dO4bY2Fh89913+OyzzzB9+vQqt2lsMamqJaa8b775BkVFRRg7\ndiwWL15ssbw2u0KHDx+OFStWYN++fbhz545Fq1R5hYWF+Pe//w0AGDZsmNU6169ft1qekJAAAAgK\nCrJYVtPj27JlS/z+++947bXX0K5duxq/x5qaNm0alixZgs2bN2Pp0qX47bffcOLECTRv3hwDBw40\nq3vp0iWcO3cOGo0GX331lUVQXt05ysrKQk5OjtVWtqqOVUXGVuaYmBgsXbq02vqM2RPOw8YYq5QQ\nArNmzYJer8c//vEPbNy4EU5OTpgxY0aN19G7d29MnToVAHDmzJlq6w8YMAAAsHHjRhQXF1dbPyMj\nA4AMUCoqLi7Gf/7znxrva3ViYmLQo0cPaLVazJo1q8oWoYULFyI9PR3BwcGVjlXbtGlTleVVdXEb\nVXZ8Bw8eDCIyBY21rU2bNujVqxeSk5OxZ88eU+vapEmTLIJ54zkKDAy02oJa2XEwIiKrdbKzs/HN\nN99ACFGjY2Xs1t++fbuptY2xxoIDNsYamfp+PuIzzzwDFxcXrFq1Cnl5eRg5ciQ0Go1Fve3bt+PI\nkSMWQUxhYSH27dsHoOpxUUYjRoxAly5dkJCQgEmTJlmMa8rNzcX+/ftNvxtbj7Zt24bU1FRTuVar\nxZw5cyptxbpXGzduhKenJ3bs2IHY2FiLsU75+fn485//jBUrVsDJyQmbN2+Gg4P1zoyffvoJy5cv\nNyvbvXs3Nm7cCAcHB8yePdtUbuvxffnll+Hh4YG3334bq1atshqgnD9/Htu3b7ftAJRj7Pr87LPP\nsGHDBgghrHaHtm3bFgqFAmfPnsWRI0fMln3++efYsmVLtdv6+9//btbqWlJSgrlz5yInJweRkZHV\nTjgAgIiICIwcORK//fYbxo0bZ3XcW2ZmJj7++GMO6Jj9abD5qYwxm1WXONcaY5qGyl5jTCGxbt26\nStcxc+ZMU5qEiuk/jObOnUtCCPL396f+/fvTpEmTaOjQodSsWTMSQlD79u0pJyfHVL+qxLnXr1+n\nNm3amBLnDho0iCZMmEC9e/cmV1dXs1QcOp2Ounbtaqo7bNgweuKJJygwMJDc3d1N+/XUU0+ZbeNe\n0noYnTlzxpRGRaVSUXR0NE2cOJEGDBhAbm5upuNQMTeakbXEucbEwMbj/N577/2h42t8jz4+PiSE\noMDAQOrbty9NnDiRBg8eTC1btiQhBMXGxlrdt5pcYzk5OeTi4mJKvVEx91p5c+bMISEEKZVKiomJ\nodjYWOrYsSMJIejVV1+1ei0Yr5Hg4GBT4txBgwbR+PHjTfvv7+9vll7GqLI8bDk5ORQdHU1CCHJ2\ndqaHH36Yxo8fT2PGjKGIiAhSKpWkUCiouLi42vfPWH3igI2xRiQkJIQUCoVNAVt0dHSVr5k2bRop\nFIoqA7Yvv/yShBDUqVOnSuucOnWKXnnlFYqKiqKgoCBSqVQUEBBAjzzyCK1YscL0RASjqgI2Ipkg\n9+2336bIyEhyd3cnV1dXat26NcXGxtJ3331nUXfBggUUFhZGzs7OFBgYSBMnTqQrV65QXFyc1YDt\n0KFD9xywEREVFxfTqlWrqG/fvqTRaEilUpGvry/16dOHli5dSrm5uZW+tvw52bdvHz322GPk6elJ\nbm5u1KdPH9qxY4fFa2w9vkbJycn06quvUpcuXcjd3Z2cnZ0pNDSUYmJiaOnSpfT7779Xum818eST\nT5qCo6pyrxkMBlq7di117dqV3N3dqVmzZtSvXz/au3cvJSQkVBmwhYaGkl6vp8WLF1NYWBip1WrS\naDQ0ZcoUqwmTiSoP2IhkktwNGzbQgAEDyM/Pj5ycnEij0VBERATNnj2bvv/++xq9d8bqkyCq42k5\njLFGb8yYMdi+fTtWr16NmTNnNvTuMMbYfYcDNsZYlX799Vd069YNPj4+SExMrDLdA2OMsbrBaT0Y\nY1Y9++yzyM/PN2WH//vf/87BGmOMNRBuYWOMWaVQKKBUKhEcHIxZs2bhxRdfbOhdYoyx+xYHbIwx\nxhhjdo7zsDHGGGOM2TkO2BhjjDHG7BwHbIwxxhhjdo4DNsYYY4wxO8cBG2OMMcaYneOAjTHGGGPM\nzv1/9nTkgTneT+QAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa18192fe50>"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{4}(x)$ compared with the histogram of the 4th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(3)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
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Ehx56CBs2bED//v1tHkOGDEH//v3b1S5Rl2M2QX/ixnBowLDuvTq0qfhbZ1uf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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181785550>"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{5}(x)$ compared with the histogram of the 5th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(4)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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1+PTTTzF27FgIgoBXXnkFX3zxBXJycnDnnXdi48aNePrpp7sdyJw5cyCKItat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\nIAiCIAgrhwQbQRAEQRCElUOCjSAIgiAIwsohwUYQBEEQBGHlkGAjCII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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa18148c810>"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{6}(x)$ compared with the histogram of the 6th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(5)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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zCGZpWEdgQl8Ep/aXLZa2rWyq8u9ki4OIvFeP1mEbMGAAVq5cCa1Wi5/97GcAgCtXruCn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\nJgwdOtT4vTbvdRJsBEEQBEEQdg7ZsBEEQRAEQdg5JNgIgiAIgiDsHBJ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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa1811e53d0>"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{7}(x)$ compared with the histogram of the 7th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(6)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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BRK7FhI2IaJhaGypRf+k4AEAVEIjkyfLtzRgUlwhBLQ2emC43wtzWKlssROQ6HBKVUUVF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\nOyGTyTBt2jRzGR0Lrq02+5eOBddA579r2bp1K27evInFixdblKenp5s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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181495990>"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{8}(x)$ compared with the histogram of the 8th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(7)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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HG264AZs2bRp1IG+88QYAYOXKlQ7nb775Zofrnqpjx44dWL16NXbs2OHy3vfe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\nPF8CLF4uc0RE46fX66HX60e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RRGYVpc3TD9ZKX9Y/me18z+wEaW20/ERgXqK0eK2/aK04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\nDkZmZmYjl4o0hIyMDIwYMQIpKSno0qUL3n33XbsOpXQtNG+unF+6Fpo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FARshpFpDhw5F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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa1818df850>"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{9}(x)$ compared with the histogram of the 9th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(8)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Ny56DYJ30R2hHQyXaaopkiYPI0/Lz850+w73N7YQtMTER99xzD44cOeLNeAJKdXW1w8t+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\n9Mp53PnuK5RdvWhX7nNfF+zJUKJ7IwZrZSXluJCWjrKScqh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+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa181c7df50>"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n",
+ "\n",
+ "### Here's $\\subNsubR{10}{f}{10}(x)$ compared with the histogram of the 10th smallest point of 2000 samples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "makeHist(9)"
+ ],
+ "language": "python",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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1a7Bo0SKsW7eOtTUtlJ+fb7TP3jUichSiKCLrSGPC1hDSr5WrHYtnr75SwgZp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\nIV7u/wE7cwvDwxwyLwAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7fa1819c8510>"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "## NOTE: From now on, *the data does not need to be sorted*."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Probability Calculus: Are You $r$th of $n$? ##\n",
+ "\n",
+ "### $\\subNsubR{n}{f}{r}(x)$ is the PDF of the $r$th of $n$ position:\n",
+ "\n",
+ "$$ {\\Large P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n, f) \\equiv \\subNsubR{n}{f}{r}(x) dx } $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Use Bayes' Theorem:\n",
+ "\n",
+ "$$ {\\large P(B\\ |\\ A) = \\frac{P(A\\ |\\ B)\\ P(B)}{P(A)} } $$\n",
+ "$$ {\\large \\Rightarrow P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f) = \\frac{\\subNsubR{n}{f}{r}(x) dx\\ \\frac{1}{n}}{f(x) dx} } $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ {\\Large = \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r}} $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "${\\Large ({\\rm HW}-2) }$\n",
+ "$${\\large {\\rm Prove}: \\qquad \\Sum{r=1}{n} \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} = 1, \\quad \\forall x. }$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Proof (special thanks to Ola Liab\u00f8tr\u00f8, who solved this *in his head* during my talk):\n",
"\n",
- "%matplotlib inline\n",
- "from matplotlib import pyplot as plt\n",
+ "$$\\frac{\\subNsubR{n}{K}{r}}{n} = \\frac{(n-1)!}{(n-r)!(r-1)!} = \\frac{(n-1)!}{(n-1-[r-1])!(r-1)!} = \\subNsubR{n-1}{C}{r-1}$$\n",
"\n",
- "import operator as op\n",
- "def get_nKrArray(n):\n",
- " # nKr has a symmetry: nKr = nK(n-r+1)... Only need to calculate ~half the values.\n",
- " if n // 2 * 2 == n:\n",
- " one_or_two = 1\n",
- " else:\n",
- " one_or_two = 2\n",
- " return np.concatenate(( [n], [reduce(op.mul, xrange(n, n-r, -1)) / reduce(op.mul, xrange(1, r))\n",
- " for r in xrange(2, n // 2 + one_or_two)] ))\n",
+ "Thus,\n",
"\n",
- "def quickData():\n",
- " # This returns data from the easyEndpoint function evaluated at 384 x values in [8.5,200]\n",
- " # if funcs.settings['simpleSortedOutput'] = True, returns only the data\n",
- " # else, returns x, f, F, data\n",
- " return funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n",
+ "$$ \\Sum{r=1}{n} \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} = \\Sum{r=1}{n} \\subNsubR{n-1}{C}{r-1} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} $$\n",
"\n",
+ "$$ = \\Sum{r'=0}{n-1} \\subNsubR{n-1}{C}{r'} F^{r'}(x) \\left(1 - F(x)\\right)^{n-1-r'} = (F(x) + 1 - F(x))^{n-1} = 1. \\quad {}_\\blacksquare $$\n",
"\n",
- "def quickBG():\n",
- " # This returns data from the easyEndpoint function evaluated at 320 x values in [8.5,200]\n",
- " # if funcs.settings['simpleSortedOutput'] = True, returns only the data\n",
- " # else, returns x, f, F, data\n",
- " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n",
- "\n",
- "\n",
- "class HistoContainer:\n",
- " def __init__(self, binEdges, data=None, normed=False):\n",
- " \"\"\" A histogram as a container, not as a plot. More data values may be added later with addValue(value). \"\"\"\n",
- " self.binEdges = binEdges\n",
- " self.binContents = np.zeros(len(binEdges)-1)\n",
- " self.area = None\n",
- " if data != None:\n",
- " for value in data:\n",
- " self.addValue(value)\n",
- " def __len__(self):\n",
- " return len(self.binContents)\n",
- " def __call__(self, value):\n",
- " self.addValue(value)\n",
- " def integral(self):\n",
- " \"\"\" Returns the total integration over the entire histogram. \"\"\"\n",
- " if self.area == None:\n",
- " self.area = funcs.A(self.binContents, np.diff(self.binEdges))[-1]\n",
- " return self.area\n",
- " def normalize(self):\n",
- " \"\"\" Normalize the histogram contents. \"\"\"\n",
- " self.binContents /= self.integral()\n",
- " def plot(self, **kwargs):\n",
- " \"\"\" Plots the result, filling under the 'histogram'. \n",
- " Passes **kwargs on to the matplotlib.pyplot.fill_between function.\n",
- " Returns a proxy matplotlib.patches.Rectangle for legend control. \"\"\"\n",
- " if normed:\n",
- " self.normalize()\n",
- " x = np.sort(np.concatenate((self.binEdges, self.binEdges)))\n",
- " y = np.array([[value, value] for value in self.binContents / self.integral()])\n",
- " y = np.concatenate(([1e-6], y.flatten(), [1e-6]))\n",
- " plt.fill_between(x, y, 1e-6, **kwargs)\n",
- " return Rectangle((0, 0), 1, 1, fill=True, **kwargs)\n",
- " def addValue(self, value):\n",
- " \"\"\" Insert a value to the histogram. \"\"\"\n",
- " # demand that integral() must recalculate\n",
- " self.area = None\n",
- " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
- " index = bisect.bisect_left(self.binEdges, value) - 1\n",
- " if index == -1:\n",
- " raise ValueError('HistoContainer warning: Underflow')\n",
- " elif index >= len(self.binContents):\n",
- " raise ValueError('HistoContainer warning: Overflow')\n",
- " else:\n",
- " self.binContents[index] += 1\n",
- " \n",
- " \n",
- "def verticalColorBand(histo, x, dx, colors=None):\n",
- " \"\"\" Add to an existing plot a histogram, painted as a vertical band of color.\n",
- " The band is a rectangle of width [x-0.5dx, x+0.5dx]. \"\"\"\n",
- " if colors == None:\n",
- " colors = np.array([(1.,1.,0.), (1.,0.,0.), (1.,1.,1.), (0.,0.,1.)])\n",
- " \n",
- " # Special normalization to show FWHM transition.\n",
- " histo.binContents /= (max(histo.binContents) / 2)\n",
- " \n",
- " # Horizontal width of the band.\n",
- " base = np.array([x-dx/2, x+dx/2])\n",
- " \n",
- " for bindex in xrange(len(histo)):\n",
- " upper = np.array([histo.binEdges[bindex+1], histo.binEdges[bindex+1]])\n",
- " lower = np.array([histo.binEdges[bindex], histo.binEdges[bindex]])\n",
- " value = histo.binContents[bindex]\n",
- " if value >= 1.:\n",
- " color = tuple((value - 1.) * colors[0] + (2. - value) * colors[1])\n",
- " alp = 1.\n",
- " else:\n",
- " color = tuple((value) * colors[2] + (1. - value) * colors[3])\n",
- " alp = 0.35\n",
- " if value > 0.1:\n",
- " plt.fill_between(base, upper, lower,\n",
- " edgecolor='none', facecolor=color, alpha=alp, zorder=2)"
- ],
- "language": "python",
+ "Note: I proved this also. The hard way. Term-by-term. I could not see the relation to $\\subNsubR{n-1}{C}{r-1}$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "slide"
}
},
- "outputs": [],
- "prompt_number": 2
+ "source": [
+ "# The debinning Calculation:\n",
+ "\n",
+ "## \"Whoa, I can calculate something else!\""
+ ]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# nPulls is used in many functions below to set the number of data points to pull\n",
- "# from our \"true\" PDF, $f(x)$.\n",
- "nPulls = 10\n",
- "\n",
- "\"\"\" Set up the demonstration of the ithPDF equations working correctly. \"\"\"\n",
- "pullData = {index:[] for index in xrange(nPulls)}\n",
- "funcs.settings['simpleSortedOutput'] = True\n",
- "for iteration in xrange(2000):\n",
- " for i,v in enumerate(quickData()):\n",
- " pullData[i].append(v)\n",
- " \n",
- "funcs.settings['simpleSortedOutput'] = False\n",
- "x, f, F, data = quickData()\n",
- "f = f / F[-1]\n",
- "F = F / F[-1]\n",
- "\n",
- "ithPDF = {}\n",
- "for i in xrange(1, nPulls+1):\n",
- " ithPDF[i-1] = np.array([f[j] * F[j]**(i-1) * (1 - F[j])**(nPulls-i)\n",
- " * funcs.nKr(nPulls, i) for j in xrange(len(x))])\n",
- " "
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "slide"
}
},
- "outputs": [],
- "prompt_number": 3
+ "source": [
+ "## The debinning Algorithm"
+ ]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "histogramRange = np.arange(0, 201, 5)\n",
- "majorTicksRange = np.arange(0, 201, 50)\n",
- "minorTicksRange = np.arange(0, 201, 10)\n",
- "\n",
- "def makeHist(i=0):\n",
- " fig, axes = plt.subplots(figsize=(9,5), facecolor='#ffffff')\n",
- " plt.hist(pullData[i], bins=histogramRange, alpha=0.4, color='#66a61e', normed=True)\n",
- " plt.plot(x, ithPDF[i], '#964a01')\n",
- " \n",
- " axes.set_xticks(majorTicksRange)\n",
- " axes.set_xticks(minorTicksRange, minor=True)\n",
- " axes.set_xticklabels([r'$%i$' % int(num) for num in majorTicksRange], fontsize=20)\n",
- " \n",
- " axes.set_ylim(bottom=-0.0001, top=0.0401)\n",
- " axes.set_yticks(np.arange(0, 0.04, 0.01))\n",
- " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.04, 0.01)], fontsize=20)\n",
- " axes.set_yticks(np.arange(0, 0.04, 0.01/5), minor=True)\n",
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "![nfr Smoothing](nfrSmoothing.png \"nfr Smoothing\")\n",
"\n",
- " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
- " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
+ "### Thought experiment: The Flat PDF\n",
"\n",
- " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
- " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
- " axes.minorticks_on()"
- ],
- "language": "python",
+ "$$ f_{\\rm \\color{gray}{flat}}(x) = \\left\\{ \\begin{array}{rcl} 1 & {\\rm if} & x \\in [0, 1] \\\\ 0 & & {\\rm otherwise} \\end{array} \\right. $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "fragment"
}
},
- "outputs": [],
- "prompt_number": 4
+ "source": [
+ "### Select a point, $x_j$, from the sample $\\{x_1, x_2, x_3\\}$"
+ ]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "fragment"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{1}(x)$ compared with the histogram of the 1st point of 2000 samples:"
+ "### Randomly choose an appropriate $r$ value using\n",
+ "$${\\large P(x_j\\ {\\rm is\\ } r{\\rm th\\ of\\ } 3\\ |\\ x_j, f_{\\rm \\color{Gray}{flat}})\n",
+ " = \\frac{\\subNsubR{3}{K}{r}}{3} F_{\\rm \\color{Gray}{flat}}^{r-1}(x_j) \\left(1 - F_{\\rm \\color{Gray}{flat}}(x_j)\\right)^{3-r} }$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Generate a random point from\n",
+ "$${\\large \\subNsubR{3}{f}{{\\rm(\\color{Gray}{flat})}r}(x) = \\subNsubR{3}{K}{r} f_{\\rm \\color{Gray}{flat}}(x)\n",
+ " F_{\\rm \\color{Gray}{flat}}^{r-1}(x) \\left(1 - F_{\\rm \\color{Gray}{flat}}(x)\\right)^{3-r} = \\mathcal{O}(x^2) }$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "## The debinning Algorithm... Expectation"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(0)"
+ "from IPython.display import HTML\n",
+ "HTML('<iframe src=http://upliftingplay.com/wp-upliftingplay/wp-content/themes/UpliftingPlay-1.0/sketchpad/tablet-horizontal.html width=800 height=700></iframe>')"
],
"language": "python",
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "metadata": {},
"outputs": [
{
+ "html": [
+ "<iframe src=http://upliftingplay.com/wp-upliftingplay/wp-content/themes/UpliftingPlay-1.0/sketchpad/tablet-horizontal.html width=800 height=700></iframe>"
+ ],
"metadata": {},
- "output_type": "display_data",
- "png": 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MUadHyqd/Q9uo/zNBQiIiIuPUWbBxhIys3bHP34BfaDg6jXzeZH16P9Qf5TmZSNv4MdB2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\n1EGekuSDWwAAAABJRU5ErkJggg==\n",
+ "output_type": "pyout",
+ "prompt_number": 18,
"text": [
- "<matplotlib.figure.Figure at 0x7f6f84c6e990>"
+ "<IPython.core.display.HTML at 0x7fa18154bc50>"
]
}
],
- "prompt_number": 5
+ "prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## The Experiment Inspired debinning Algorithm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
+ "### Suppose our data comes from\n",
+ "$${\\huge f(x) = w\\ f_{\\rm \\sky{sig}}(x) + (1 - w)\\ f_{\\rm \\rust{bg}}(x)}$$\n",
"\n",
- "Here's $\\subNsubR{10}{f}{2}(x)$ compared with the histogram of the 2nd point of 2000 samples:"
+ "![BG nfr Smoothing](nfbgrSmoothing.png \"BG nfr Smoothing\")"
]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "makeHist(1)"
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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JsrOzjZ5zdE1ZSk4chUd4Jzh5cr8AgG//YTi37C/AgP6ioxARCRUTE4Po6Gij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\ngykAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x7f6f6b000750>"
- ]
+ "source": [
+ "### Select a point from our data..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
}
- ],
- "prompt_number": 6
+ },
+ "source": [
+ "### Randomly choose an appropriate $r$ value using\n",
+ "$${\\large P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f_{\\rm \\rust{bg}}) \\cdots}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### Generate a random point from $\\subNsubR{n}{f}{{\\rm(\\rust{bg})}r}(x)$... need *3 random numbers* just to get one back!!"
+ ]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
+ "## The debinning Algorithm... Calculation ## \n",
"\n",
- "Here's $\\subNsubR{10}{f}{3}(x)$ compared with the histogram of the 3rd point of 2000 samples:"
+ "### \"Det er dumt!\" Let's just calculate it!"
]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "makeHist(2)"
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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ddBwiImi1Wmi1Wpvu0+xz2G4pLy/Hhg0bMGvWLIwbNw7jxo1DTEwMNmzYYDLt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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x7f6f6a6f2790>"
- ]
+ "source": [
+ "$$ f_{\\rm debin}(x) dx = P_{\\rm debin}\\left(\\tilde{x} \\in [x, x + dx] | \\{x_i\\}_{i=1}^{n}, f_{\\rm\\rust{bg}} \\right) $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
}
- ],
- "prompt_number": 7
+ },
+ "source": [
+ "$$ = \\sum\\limits_{j=1}^{n} P( x_j | \\{x_i\\}_{i=1}^{n} ) \\sum\\limits_{r=1}^{N} P(r{\\rm th}\\ {\\rm of}\\ N | x_j, f_{\\rm\\rust{bg}}) P(\\tilde{x} \\in [x, x + dx] | r{\\rm th}\\ {\\rm of}\\ N, f_{\\rm\\rust{bg}}) $$"
+ ]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "$$ = \\sum\\limits_{j=1}^{n} \\frac{1}{n} \\sum\\limits_{r=1}^{N} \\left(\\frac{{}_NK_r}{N} F_{\\rm\\rust{bg}}(x_j)^{(r-1)}(1 - F_{\\rm\\rust{bg}}(x_j))^{(N-r)} \\right) $$\n",
+ "$$ \\quad\\times \\left( {}_NK_r f_{\\rm\\rust{bg}}(x) F_{\\rm\\rust{bg}}(x)^{(r-1)}(1 - F_{\\rm\\rust{bg}}(x))^{(N-r)} dx \\right) $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
+ "$$ {\\Large \\Rightarrow f_{\\rm debinnning}(x) = \\frac{f_{\\rm\\rust{bg}}(x)}{n N} \\displaystyle \\vec{G} \\cdot \\sum\\limits_{j=1}^{n} \\vec{G}_j } $$\n",
+ "\n",
+ "${\\large \\left[\\vec{G}_{(j)} \\equiv {}_N K_r F^{r-1}_{\\rm\\rust{bg}}(x_{(j)}) \\left( 1 - F_{\\rm\\rust{bg}}(x_{(j)}) \\right)^{N-r} \\right] }$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "settings['simpleSortedOutput'] = False\n",
+ "nPulls = 96\n",
+ "nFictitious=96\n",
+ "\n",
+ "x, f, F, data = quickData()\n",
+ "x, bgf, bgF, bgData = quickBG()\n",
+ "f /= F[-1]\n",
+ "F /= F[-1]\n",
+ "bgf /= bgF[-1]\n",
+ "bgF /= bgF[-1]\n",
+ "\n",
+ " \n",
+ "def mapDataToX(dindex):\n",
+ " # maps elements of data to elements of x\n",
+ " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
+ " xindex = bisect.bisect_left(x, data[dindex])\n",
+ " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
+ " return xindex - 1\n",
+ " return xindex\n",
+ "dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
+ "\n",
+ "\n",
+ "def vecG_rth(rindex, xindex):\n",
+ " r = rindex+1\n",
+ " return pc.nKr(nFictitious, r) * bgF[xindex]**(r-1) * (1 - bgF[xindex])**(nFictitious - r)\n",
+ "\n",
+ "\n",
+ "vecG_rx = np.array([[vecG_rth(rindex, xindex) for xindex in xrange(len(x))]\n",
+ " for rindex in xrange(nFictitious)])\n",
+ "sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
+ "debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
+ "\n",
+ "# One more pull for plotting purposes\n",
+ "x, f, F, data = quickData()\n",
+ "x, bgf, bgF, bgData = quickBG()\n",
+ "f /= F[-1]\n",
+ "bgf /= F[-1]\n",
+ "bgF /= F[-1]\n",
+ "F /= F[-1]\n",
+ "\n",
+ "def makeDebinningPlot():\n",
+ " fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ " plt.plot(x, f, '--', color='#0088ff', alpha=0.6, linewidth=3)\n",
+ " plt.plot(x, bgf, '-.', color='#0088ff', alpha=0.6, linewidth=3)\n",
+ " plt.hist(data, bins=np.arange(0, 201, 5), alpha=0.4, color='#66a61e', normed=True)\n",
+ " plt.plot(x, debinningData, '#964a01', linewidth=3)\n",
+ " \n",
+ " axes.set_xticks(np.arange(0, 201, 50))\n",
+ " axes.set_xticks(np.arange(0, 201, 10), minor=True)\n",
+ " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n",
+ " \n",
+ " axes.set_ylim(bottom=-0.0001, top=0.0201)\n",
+ " axes.set_yticks(np.arange(0, 0.02, 0.005))\n",
+ " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.02, 0.005)], fontsize=20)\n",
+ " axes.set_yticks(np.arange(0, 0.02, 0.005/5), minor=True)\n",
"\n",
- "Here's $\\subNsubR{10}{f}{4}(x)$ compared with the histogram of the 4th point of 2000 samples:"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "makeHist(3)"
+ " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
+ " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
+ "\n",
+ " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ " axes.minorticks_on()"
],
"language": "python",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "skip"
}
},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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vR05ODrp164aZM2c2OJwTESmDLMtwvHkRXlMnNNy4BQiLnIjkY9+gfb+xoqMQ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\nHfuPJq9VVVU4cuQIVCoVioqK7MYuXboUXl5eqK2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- "text": [
- "<matplotlib.figure.Figure at 0x7f6f6a26c990>"
- ]
- }
- ],
- "prompt_number": 8
+ "outputs": [],
+ "prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{5}(x)$ compared with the histogram of the 5th point of 2000 samples:"
+ "## debinning Demonstration ##"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(4)"
+ "makeDebinningPlot()"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
- "png": 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w3HnnnfD19cX//u//Ij8/H926dcOGDRtQWFiIefPm2TMzETmRjANbUdd1fNsN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\nTk7UYRMEQRAEQejkRMImCIIgCILQyYmETRAEQRAEoZMTCZs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Hpy9Sfepkg9eJSe5L8uDxRCZfxJIT3akjFEtdBVdEH8WZu5X8PWtx1FZ7nRPdPY1J818m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\nkvW1yk6h3UOqKZSw/aDHQSCqp9Kd0WdhHlUdHvMGhsvviUG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DKA0RojdvCB7eAk9uhzoP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l+ipwOLbSJqdqZOnWpQxJWVlWHs2LFYs2YNxo8fj+joaLi7u+u3i0hTDLNaf/jDH3DmzBnY2Ng0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\n",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f6a079890>"
+ "<matplotlib.figure.Figure at 0x7fa181544b50>"
]
}
],
- "prompt_number": 9
+ "prompt_number": 20
},
{
- "cell_type": "markdown",
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "fwhmValues=None"
+ ],
+ "language": "python",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "skip"
}
},
- "source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{6}(x)$ compared with the histogram of the 6th point of 2000 samples:"
- ]
+ "outputs": [],
+ "prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(5)"
+ "# Let's try some GPU programming:\n",
+ "import pycuda.driver as cuda\n",
+ "import pycuda.autoinit\n",
+ "from pycuda.compiler import SourceModule\n",
+ "from string import Template\n",
+ "\n",
+ "settings['simpleSortedOutput'] = False\n",
+ "nPulls = 96\n",
+ "nFictitious = 96 # Multiple of 32 for GPU programming ease.\n",
+ "lenXdomain = len(np.arange(8.5, 200.2, 0.5))\n",
+ "\n",
+ "mod_template = Template(\"\"\"\n",
+ " __global__ void vecG(double *vecG_rx, double *bgF, double *nKr) {\n",
+ " const int idr = threadIdx.y + blockDim.y * blockIdx.y;\n",
+ " const int idx = threadIdx.x + blockDim.x * blockIdx.x;\n",
+ " const int idrx = idx + idr*${lenX};\n",
+ " const int r = (idr + 1) < (${nFic} - idr) ? (idr + 1) : ${nFic} - idr;\n",
+ " vecG_rx[idrx] = nKr[r-1] * pow(bgF[idx], idr) * pow(1 - bgF[idx], ${nFic} - idr - 1);\n",
+ " }\n",
+ " \"\"\")\n",
+ "\n",
+ "mod = SourceModule(mod_template.substitute(nFic=nFictitious, lenX=lenXdomain))\n",
+ "\n",
+ "timer = time()\n",
+ "\n",
+ "# initialize the loop\n",
+ "nKr = pc.get_nKrArray(nFictitious)\n",
+ "chisq = []\n",
+ "bgchisq = []\n",
+ "ks = []\n",
+ "bgks = []\n",
+ "\n",
+ "for trial in xrange(100000):\n",
+ "\n",
+ " x, f, F, data = quickData()\n",
+ " x, bgf, bgF, bgData = quickBG()\n",
+ " f /= F[-1]\n",
+ " F /= F[-1]\n",
+ " bgf /= bgF[-1]\n",
+ " bgF /= bgF[-1]\n",
+ "\n",
+ " def mapDataToX(dindex):\n",
+ " # maps elements of data to elements of x\n",
+ " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
+ " xindex = bisect.bisect_left(x, data[dindex])\n",
+ " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
+ " return xindex - 1\n",
+ " return xindex\n",
+ " dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
+ "\n",
+ " # Use the GPU for the most expensive / paralellizable part of the calculation:\n",
+ " # =====\n",
+ " \n",
+ " # Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n",
+ " vecG_rx = np.empty([nFictitious, len(x)])\n",
+ " \n",
+ " # Allocate memory on the GPU for vecG calculation\n",
+ " vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n",
+ " bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n",
+ " nKr_gpu = cuda.mem_alloc(nKr.nbytes)\n",
+ " \n",
+ " # Transfer data to the GPU\n",
+ " cuda.memcpy_htod(bgF_gpu, bgF)\n",
+ " cuda.memcpy_htod(nKr_gpu, nKr)\n",
+ " \n",
+ " # Get a reference to the GPU module function and do the calculation\n",
+ " # NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n",
+ " vecG_func = mod.get_function('vecG')\n",
+ " vecG_func(vecG_rx_gpu, bgF_gpu, nKr_gpu, block=(16, 4, 1), grid=(24, 24))\n",
+ "\n",
+ " # Get the result back from the GPU and use it!\n",
+ " cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n",
+ " sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
+ " debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
+ " \n",
+ " # Chisq test....\n",
+ " if type(fwhmValues) == np.ndarray:\n",
+ " chisq.append(sum(4.*(debinningData - f)**2 / fwhmValues**2) / len(fwhmValues))\n",
+ " bgchisq.append(sum(4.*(debinningData - bgf)**2 / fwhmValues**2) / len(fwhmValues))\n",
+ " \n",
+ " # KS test...\n",
+ " debinningCDF = pc.A(debinningData, 0.5)\n",
+ " ks.append(max(abs(debinningCDF - F)))\n",
+ " bgks.append(max(abs(debinningCDF - bgF)))\n",
+ " \n",
+ " if trial == 0:\n",
+ " # Infinity sigma upper and lower bands...\n",
+ " debinningUpper = debinningData.copy()\n",
+ " debinningLower = debinningData.copy()\n",
+ " # Uncertainty PDFs for each x value...\n",
+ " uncertaintyHistos = [debinPlot.HistoContainer(np.arange(0., 0.024, 0.0002), debinningData[i])\n",
+ " for i in xrange(len(x))]\n",
+ " else:\n",
+ " debinningUpper = np.clip(debinningData, debinningUpper, 20.)\n",
+ " debinningLower = np.clip(debinningData, -1., debinningLower)\n",
+ " for i in xrange(len(x)):\n",
+ " try:\n",
+ " uncertaintyHistos[i].addValue(debinningData[i])\n",
+ " except ValueError as e:\n",
+ " print e.message\n",
+ " print 'xindex = ' + str(i) + ', debinningData[xindex] = ' + str(debinningData[i])\n",
+ "\n",
+ "if not type(fwhmValues) == np.ndarray:\n",
+ " fwhmValues = np.array([np.diff(uncertaintyHistos[i].fwhm()) for i in xrange(len(x))]).flatten()\n",
+ " print \"Run this again for the Chisq test data...\"\n",
+ "print time() - timer"
],
"language": "python",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "skip"
}
},
"outputs": [
{
- "metadata": {},
- "output_type": "display_data",
- "png": 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xnI4kSQjqdwc8r18QHYWIFMimmQ527tyJ9957D1999RWMRiPUajWmT5+O+fPnY8yYMRZt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\nSUVORK5CYII=\n",
+ "output_type": "stream",
+ "stream": "stdout",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f6afdb450>"
+ "254.671765804\n"
]
}
],
- "prompt_number": 10
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "subslide"
- }
- },
- "source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{7}(x)$ compared with the histogram of the 7th point of 2000 samples:"
- ]
+ "prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(6)"
+ "# Try with a HUGE data set:\n",
+ "nPulls = 10000\n",
+ "\n",
+ "timer = time()\n",
+ "x, f, F, data = quickData()\n",
+ "x, bgf, bgF, bgData = quickBG()\n",
+ "f /= F[-1]\n",
+ "F /= F[-1]\n",
+ "bgf /= bgF[-1]\n",
+ "bgF /= bgF[-1]\n",
+ "\n",
+ "def mapDataToX(dindex):\n",
+ " # maps elements of data to elements of x\n",
+ " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
+ " xindex = bisect.bisect_left(x, data[dindex])\n",
+ " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
+ " return xindex - 1\n",
+ " return xindex\n",
+ "dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
+ "\n",
+ "# Use the GPU for the most expensive / paralellizable part of the calculation:\n",
+ "# =====\n",
+ "\n",
+ "# Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n",
+ "vecG_rx = np.empty([nFictitious, len(x)])\n",
+ "\n",
+ "# Allocate memory on the GPU for vecG calculation\n",
+ "vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n",
+ "bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n",
+ "nKr_gpu = cuda.mem_alloc(nKr.nbytes)\n",
+ "\n",
+ "# Transfer data to the GPU\n",
+ "cuda.memcpy_htod(bgF_gpu, bgF)\n",
+ "cuda.memcpy_htod(nKr_gpu, nKr)\n",
+ "\n",
+ "# Get a reference to the GPU module function and do the calculation\n",
+ "# NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n",
+ "vecG_func = mod.get_function('vecG')\n",
+ "vecG_func(vecG_rx_gpu, bgF_gpu, nKr_gpu, block=(16, 4, 1), grid=(24, 24))\n",
+ "\n",
+ "# Get the result back from the GPU and use it!\n",
+ "cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n",
+ "sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
+ "BIGdebinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
+ "print time() - timer"
],
"language": "python",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "skip"
}
},
"outputs": [
{
- "metadata": {},
- "output_type": "display_data",
- "png": 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rq/UQY4v09HTU19djypQpNunjjTfegMFgMCvWWn4Pa2YjIuVrKMx1iflrLYKj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\n58KFC3IZFYVCQYGBgRQTE0Njxowhe3t7eR2erY2mY6xwrq4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+ "output_type": "stream",
+ "stream": "stdout",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f6afe2390>"
+ "0.05406498909\n"
]
}
],
- "prompt_number": 11
+ "prompt_number": 24
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "subslide"
+ "slide_type": "slide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{8}(x)$ compared with the histogram of the 8th point of 2000 samples:"
+ "## debinning Performace: Uncertainty"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(7)"
+ "# One more pull for plotting purposes\n",
+ "x, f, F, data = quickData()\n",
+ "x, bgf, bgF, bgData = quickBG()\n",
+ "f /= F[-1]\n",
+ "bgf /= F[-1]\n",
+ "bgF /= F[-1]\n",
+ "F /= F[-1]\n",
+ "\n",
+ "# Pretty plot\n",
+ "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ "plt.fill_between(x, debinningUpper, debinningLower, color='#0088ff', alpha=0.3, zorder=1)\n",
+ "plt.plot(x, f, color='#0088ff', linewidth=3, zorder=3)\n",
+ "plt.plot(x, bgf, color='#0088ff', linestyle='-.', linewidth=3, zorder=3)\n",
+ "plt.plot(x, BIGdebinningData, color='black', linestyle='--', linewidth=3, zorder=4)\n",
+ "colors = np.array([(0.8,1.,0.4), (0.8,0.3,0.), (1.,1.,1.), (0.,0.,1.)])\n",
+ "for i, v in enumerate(x):\n",
+ " debinPlot.verticalColorBand(uncertaintyHistos[i], v, 0.5, colors)\n",
+ "\n",
+ "axes.set_xticks(np.arange(0, 201, 50))\n",
+ "axes.set_xticks(np.arange(0, 201, 10), minor=True)\n",
+ "axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n",
+ "\n",
+ "axes.set_ylim(bottom=-0.0001, top=0.0201)\n",
+ "axes.set_yticks(np.arange(0, 0.02, 0.005))\n",
+ "axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.02, 0.005)], fontsize=20)\n",
+ "axes.set_yticks(np.arange(0, 0.02, 0.005/5), minor=True)\n",
+ "\n",
+ "axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
+ "axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
+ "\n",
+ "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ "axes.minorticks_on()\n",
+ "\n",
+ "print"
],
"language": "python",
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "metadata": {},
"outputs": [
{
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ },
+ {
"metadata": {},
"output_type": "display_data",
- "png": 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LeOIBkZKwYCMiUhAvQ6mwEw7aaaLj0FxWDIupVWgOIvp/LNiIiBSisbYSkqkJPqFhQnOo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\nNKtk3nKPAgMDba6g2hsHC2a2Wae6uhqfffYZiKhZY2X5WL+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AG+UiSSE84UVkVy6QFKKERJPwVhO80gDVQa97I0Rp8lvq4uSI1NsWoiQYtm3L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\n5c/8b0n9MsvWRK4Pfi2XP9g0Gs3usd3BdiKR2K1/Gk1DicSFRjBLD7b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rNO2APgfkccBg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dKqL2nhV2Xla66NilEVCOmIXV9RS+yvol5Nox6Pp5btFNBxxcEsKf8wlJTrhuJSaMjb7Ort94SZ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"text": [
- "<matplotlib.figure.Figure at 0x7f6f6a3361d0>"
+ "<matplotlib.figure.Figure at 0x7fa181a46f10>"
]
}
],
- "prompt_number": 12
+ "prompt_number": 25
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{9}(x)$ compared with the histogram of the 9th point of 2000 samples:"
+ "## debinning Performace: Discrimination"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(8)"
+ "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ "plt.hist(chisq, bins=np.arange(0, 7.01, .05), color='#0088ff', edgecolor='#555555')\n",
+ "plt.hist(bgchisq, bins=np.arange(0, 7.01, .05), color='#66a61e', edgecolor='#555555', alpha=0.5)\n",
+ "\n",
+ "axes.set_xticks(np.arange(0, 7.01, 1))\n",
+ "axes.set_xticks(np.arange(0, 7.01, .25), minor=True)\n",
+ "axes.set_xticklabels([r'$%1.1f$' % num for num in np.arange(0, 7.01, 1)], fontsize=20)\n",
+ "\n",
+ "axes.set_ylim(bottom=-0.0001, top=6000)\n",
+ "axes.set_yticks(np.arange(0, 6001, 1000))\n",
+ "axes.set_yticks(np.arange(0, 6001, 250), minor=True)\n",
+ "axes.set_yticklabels([r'$%i$' % int(num) for num in np.arange(0, 6001, 1000)], fontsize=20)\n",
+ "\n",
+ "axes.set_xlabel(r'$\\chi^2$ per d.o.f.', labelpad=5, fontsize=22)\n",
+ "axes.set_ylabel('Number of Counts', labelpad=5, fontsize=22)\n",
+ "\n",
+ "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ "axes.minorticks_on()\n",
+ "print"
],
"language": "python",
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "metadata": {},
"outputs": [
{
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ },
+ {
"metadata": {},
"output_type": "display_data",
- "png": 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29PR0jBgxAvPn/9+snWvHrwUGBuLDDz9EQ0NDr3rYJk2ahHnz5mHNmjUoLCwE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\nIptvh4aFhUFRFBw7dgz79u3T1L377rtYv359o+eaO3euZtX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AAHQp4WyrbTVMS9L111+v66+/XpIUFxenSZMmuVf3AAAAALo6v1fzmDZtmkaN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\nvL29cerUKdSpU0fv8czXsKSkJHTu3Bnt2rUzaR2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o0CGr1CKEwPr167F582aUlJTg2LFj\nKC4uxvDhw3HlyhX07dtXY42bmxuuXr2KLVu2wNfXF7du3cKRI0dw5coV2NvbIyoqCkeOHLF4rSEh\nIbh8+TKGDBmCwsJCHD9+HGVlZdi6dSvWrVun8/npepNhr169kJGRgcjISFRVVeHo0aNIT09Hnz59\nsG/fPtWtwU3ZU9+cMfNE9O/G24kTERlhyZIlGDZsGLp37w4A8PDwQGVlJR4+fAiF4t2dl6i5xbex\nt98mIqLaxTPTREQGrFu3Dv7+/qpGGnhzw5GCggIkJSVZsTIiIrI2NtNERHrExcXBwcEBgwYNUhuP\njIyEjY0N1q5dCwD4448/cPz4cWuUSEREVsRmmohIh+vXr+Pu3bta3yjn7u6OhIQE/PXXXxg6dCi2\nbNmC0NBQK1RJRETWxGumiYiIiIjMxDPTRERERERmYjNNRERERGQmNtNERERERGZiM01EREREZCY2\n00REREREZmIzTURERERkJjbTRERERERmYjNNRERERGSm/wJyXa/mBeKXzAAAAABJRU5ErkJggg==\n",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f6af83450>"
+ "<matplotlib.figure.Figure at 0x7fa181590ad0>"
]
}
],
- "prompt_number": 13
+ "prompt_number": 26
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
- "Let's try it! We will pull 2000 samples of 10 data points each.\n",
- "\n",
- "Here's $\\subNsubR{10}{f}{10}(x)$ compared with the histogram of the 10th point of 2000 samples:"
+ "## debinning Performace: Discrimination"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "makeHist(9)"
+ "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n",
+ "plt.hist(ks, bins=np.arange(0, 0.3, .002), color='#0088ff', edgecolor='#555555')\n",
+ "plt.hist(bgks, bins=np.arange(0, 0.3, .002), color='#66a61e', edgecolor='#555555', alpha=0.5)\n",
+ "\n",
+ "axes.set_xticks(np.arange(0, 0.26, .05))\n",
+ "axes.set_xticks(np.arange(0, 0.26, .01), minor=True)\n",
+ "axes.set_xticklabels([r'$%0.2f$' % num for num in np.arange(0, 0.26, .05)], fontsize=20)\n",
+ "\n",
+ "axes.set_ylim(bottom=-0.0001, top=5000)\n",
+ "axes.set_yticks(np.arange(0, 5001, 1000))\n",
+ "axes.set_yticks(np.arange(0, 5001, 250), minor=True)\n",
+ "axes.set_yticklabels([r'$%i$' % int(num) for num in np.arange(0, 5001, 1000)], fontsize=20)\n",
+ "\n",
+ "axes.set_xlabel('KS test value', labelpad=5, fontsize=22)\n",
+ "axes.set_ylabel('Number of Counts', labelpad=5, fontsize=22)\n",
+ "\n",
+ "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
+ "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
+ "axes.minorticks_on()\n",
+ "print"
],
"language": "python",
- "metadata": {
- "slideshow": {
- "slide_type": "-"
- }
- },
+ "metadata": {},
"outputs": [
{
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ },
+ {
"metadata": {},
"output_type": "display_data",
- "png": 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O0mQe7TuyYCOnYXbB9txzz2HPnj1ISUmpd5vU1FTs2bMHzzzzjFXCERGRNDIP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\nRyNqsTzbR6Hdc68hYvoLKM/OgG/qCqT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WLUpNTe3gW4gtGRkZkS4BAADAUYKdomo5EP/ud7/T7t27dcstt+ipp55SWlpa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\n",
"text": [
- "<matplotlib.figure.Figure at 0x7f6f69e63350>"
+ "<matplotlib.figure.Figure at 0x7fa16bd9ef90>"
]
}
],
- "prompt_number": 14
+ "prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
- "## Samples - V: To be $r$th out of $n$ (cont'd)... ## \n",
+ "# The Future, and Shameless Advertising:\n",
"\n",
- "As stated above, $\\subNsubR{n}{f}{r}(x)$ is the PDF of the $r$th data point within a sample of $n$ data points. We can write that as a conditional probability:\n",
- "\n",
- "$$ {\\Large P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n, f) \\equiv \\subNsubR{n}{f}{r}(x) dx } $$"
+ "## \"Yikes.... There is so much more!\""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "subslide"
}
},
"source": [
- "We can \"invert\" that using Bayes' Theorem: \n",
- "\n",
- "\\begin{align}\n",
- " P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f)\n",
- " &= \\frac{P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n, f)\\ \n",
- " P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n)}{P(\\tilde{x} \\in [x, x + dx])} \\\\\n",
- " &= \\frac{\\subNsubR{n}{f}{r}(x) dx\\ \\frac{1}{n}}{f(x) dx}\n",
- "\\end{align}"
+ "## Probability Calculus: Future"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ {\\large \\therefore P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f)\n",
- " = \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} .} $$"
+ "### Two-point correlation distribution, $\\subNsubR{n}{f}{r,s}(x_r, x_s)$...\n",
+ "### $\\qquad$ Form is known already, but use...?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "This proof is so very fun, I will leave it as an exercise:\n",
- "\n",
- "$$ {\\large \\Sum{r=1}{n} \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} = 1, \\quad \\forall x.} $$"
+ "### Re-derive or Re-interpret current statistical methods?\n",
+ "### $\\qquad$ Poisson and Multinomial changes?\n",
+ "### $\\qquad$ Likelihoods... Unbinned likelihoods... Re-derive?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "subslide"
}
},
"source": [
- "## The Debinning Algorithm ##\n",
- "\n",
- "Imagine the following scenario:\n",
- "\n",
- " - An experiment measures a sample, $\\{x_i\\}_{i=1}^n$, which follow some PDF $f(x)$.\n",
- " - The background PDF, $f_{\\rm bg}(x)$, is known.\n",
- " - Based upon the sample probabilities, here is a data smoothing algorithm:"
+ "## debinning: Statistical impact"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- " - Choose a size for the number of points in some fictitious data set, $N_{\\rm fic}$.\n",
- " - To generate some huge number of smoothed points, $\\aleph$.\n",
- " 1. Randomly choose a point, $x_j$, from the sample.\n",
- " 1. Based upon $P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } N_{\\rm fic}\\ |\\ \\tilde{x} \\in [x_j, x_j + dx_j], f_{\\rm bg})$, randomly choose which $r$ this $x_j$ might be.\n",
- " 1. Return a random pull from $\\subNsubR{N_{\\rm fic}}{f}{r}(x) \\equiv P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } N_{\\rm fic}, f_{\\rm bg})$."
+ "### Full comparison: debinning vs histograms\n",
+ "### $\\qquad$ Discovery signifigance?\n",
+ "### $\\qquad$ Parameter estimation performance?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "This algorithm needs to generate $3\\aleph$ random numbers. Very slow..."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "## The Debinning Algorithm... Calculation ## \n",
- "\n",
- "So, let's just calculate the PDF which results from that algorithm:"
+ "### Full comparison: debinning vs unbinned maximum likelihood\n",
+ "### $\\qquad$ Discovery signifigance?\n",
+ "### $\\qquad$ Parameter estimation performance?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "fragment"
+ "slide_type": "subslide"
}
},
"source": [
- "$$ f_{\\rm debinnning}(x) dx = P_{\\rm binfull}\\left(\\tilde{x} \\in [x, x + dx] | \\{x_i\\}_{i=1}^{n}, f_{\\rm bg} \\right) $$"
+ "## debinning: Generalize / Specialize"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ = \\sum\\limits_{j=1}^{n} P( x_j | \\{x_i\\}_{i=1}^{n} ) \\sum\\limits_{r=1}^{N} P(r{\\rm th}\\ {\\rm of}\\ N | x_j, f_{\\rm bg}) P(\\tilde{x} \\in [x, x + dx] | r{\\rm th}\\ {\\rm of}\\ N, f_{\\rm bg}) $$"
+ "### $\\qquad$ data-driven backgrounds?\n",
+ "### $\\qquad$ detector resolution \"unfolding\"?\n",
+ "### $\\qquad$ \"Max Gap Method\"?\n",
+ "### $\\qquad$ 2-debinning? N-debinning?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "slide"
}
},
"source": [
- "$$ = \\sum\\limits_{j=1}^{n} \\frac{1}{n} \\sum\\limits_{r=1}^{N} \\left(\\frac{{}_NK_r}{N} F_{\\rm bg}(x_j)^{(r-1)}(1 - F_{\\rm bg}(x_j))^{(N-r)} \\right) \\left( {}_NK_r f_{\\rm bg}(x) F_{\\rm bg}(x)^{(r-1)}(1 - F_{\\rm bg}(x))^{(N-r)} dx \\right) $$"
+ "## Searching for \"New Stuff\" with Statistics"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
- "$$ \\Rightarrow f_{\\rm debinnning}(x) = \\frac{f_{\\rm bg}(x)}{n N} \\displaystyle \\vec{G} \\cdot \\sum\\limits_{j=1}^{n} \\vec{G}_j $$\n",
- "\n",
- "where $\\vec{G}_{(j)} \\equiv {}_N K_r F^{r-1}_{\\rm bg}(x_{(j)}) \\left( 1 - F_{\\rm bg}(x_{(j)}) \\right)^{N-r}$."
+ "### New global-fitting tool for any \"New Stuff\": Gambit\n",
+ "### The Global And Modular BSM Inference Tool"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "funcs.settings['simpleSortedOutput'] = False\n",
- "nPulls = 96\n",
- "nFictitious=96\n",
- "\n",
- "x, f, F, data = quickData()\n",
- "x, bgf, bgF, bgData = quickBG()\n",
- "f = f / F[-1]\n",
- "F = F / F[-1]\n",
- "bgf = bgf / bgF[-1]\n",
- "bgF = bgF / bgF[-1]\n",
- "\n",
- " \n",
- "def mapDataToX(dindex):\n",
- " # maps elements of data to elements of x\n",
- " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n",
- " xindex = bisect.bisect_left(x, data[dindex])\n",
- " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n",
- " return xindex - 1\n",
- " return xindex\n",
- "dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n",
- "\n",
- "\n",
- "def vecG_rth(rindex, xindex):\n",
- " r = rindex+1\n",
- " return funcs.nKr(nFictitious, r) * bgF[xindex]**(r-1) * (1 - bgF[xindex])**(nFictitious - r)\n",
- "\n",
- "\n",
- "vecG_rx = np.array([[vecG_rth(rindex, xindex) for xindex in xrange(len(x))]\n",
- " for rindex in xrange(nFictitious)])\n",
- "sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n",
- "debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n",
- "\n",
- "# Discard trivial data\n",
- "x = x.compress(bgf > 0)\n",
- "debinningData = debinningData.compress(bgf > 0)\n",
- "f = f.compress(bgf > 0)\n",
- "\n",
- "def makeDebinningPlot():\n",
- " fig, axes = plt.subplots(figsize=(9,5), facecolor='#ffffff')\n",
- " plt.hist(data, bins=histogramRange, alpha=0.4, color='#66a61e', normed=True)\n",
- " plt.plot(x, debinningData, '#964a01')\n",
- " plt.plot(x, f, '--')\n",
- " \n",
- " axes.set_xticks(majorTicksRange)\n",
- " axes.set_xticks(minorTicksRange, minor=True)\n",
- " axes.set_xticklabels([r'$%i$' % int(num) for num in majorTicksRange], fontsize=20)\n",
- " \n",
- " axes.set_ylim(bottom=-0.0001, top=0.0201)\n",
- " axes.set_yticks(np.arange(0, 0.02, 0.005))\n",
- " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.02, 0.005)], fontsize=20)\n",
- " axes.set_yticks(np.arange(0, 0.02, 0.005/5), minor=True)\n",
- "\n",
- " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n",
- " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n",
- "\n",
- " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n",
- " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n",
- " axes.minorticks_on()"
+ "from IPython.display import HTML\n",
+ "HTML('<iframe src=http://gambit.hepforge.org/ width=1000 height=350></iframe>')"
],
"language": "python",
"metadata": {
"slideshow": {
- "slide_type": "skip"
+ "slide_type": "fragment"
}
},
- "outputs": [],
- "prompt_number": 15
+ "outputs": [
+ {
+ "html": [
+ "<iframe src=http://gambit.hepforge.org/ width=1000 height=350></iframe>"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 28,
+ "text": [
+ "<IPython.core.display.HTML at 0x7fa181b92510>"
+ ]
+ }
+ ],
+ "prompt_number": 28
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "subslide"
}
},
"source": [
- "## The Debinning Demonstration ## \n",
- "\n",
- "Here's what it looks like:"
+ "## Shameless Gambit Advertising:"
]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "makeDebinningPlot()"
- ],
- "language": "python",
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "fragment"
}
},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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p6fPHmtIksSMiqo7UauDsCVf8vK05HGtnw7f3TUOHRETVQKkJW3R0dJmPiYjof7Kz5Di8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\nGUqlEpcuXYK/v7/OZdRnXsYYY4yxumRUAVtRURE+/vhj7Nu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- "text": [
- "<matplotlib.figure.Figure at 0x7f6f69ebb4d0>"
- ]
- }
- ],
- "prompt_number": 16
+ "source": [
+ "### Our flagship scan: Supersymmetry!\n",
+ "### $\\qquad$ Our PMSSM-25 scan: Scanning 25 parameters!"
+ ]
},
{
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "source": [
+ "### About us:\n",
+ "GAMBIT is a global fitting code for generic Beyond the Standard Model theories, designed to allow fast and easy definition of new models, observables, likelihoods, scanners and backend physics codes.\n",
+ "\n",
+ "GAMBIT is developed by a group of nearly 30 theorists and experimentalists. The Collaboration includes members of the AMS-02, ATLAS, CDMS, CTA, DARWIN, DM-ICE, Fermi-LAT, HESS, IceCube, LHCb and XENON experiments, as well as developers of the public theory codes DarkSUSY, FlexibleSUSY, IsaJet, SoftSUSY and SuperIso.\n",
+ "\n",
+ "We are currently finalising the code in preparation for first public release in Summer 2015 \u2014 stay tuned!"
+ ]
}
],
"metadata": {}
}
]
}
\ No newline at end of file
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p{margin:0 0 10px}
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small{font-size:85%}
strong{font-weight:bold}
em{font-style:italic}
cite{font-style:normal}
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a.muted:hover,a.muted:focus{color:#808080}
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a.text-warning:hover,a.text-warning:focus{color:#a47e3c}
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a.text-error:hover,a.text-error:focus{color:#953b39}
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a.text-info:hover,a.text-info:focus{color:#2d6987}
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a.text-success:hover,a.text-success:focus{color:#356635}
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h4 small{font-size:13px}
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dl{margin-bottom:20px}
dt,dd{line-height:20px}
dt{font-weight:bold}
dd{margin-left:10px}
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abbr.initialism{font-size:90%;text-transform:uppercase}
blockquote{padding:0 0 0 15px;margin:0 0 20px;border-left:5px solid #eee}blockquote p{margin-bottom:0;font-size:16.25px;font-weight:300;line-height:1.25}
blockquote small{display:block;line-height:20px;color:#999}blockquote small:before{content:'\2014 \00A0'}
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blockquote.pull-right small:before{content:''}
blockquote.pull-right small:after{content:'\00A0 \2014'}
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label{display:block;margin-bottom:5px}
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input,textarea,.uneditable-input{width:206px}
textarea{height:auto}
textarea,input[type="text"],input[type="password"],input[type="datetime"],input[type="datetime-local"],input[type="date"],input[type="month"],input[type="time"],input[type="week"],input[type="number"],input[type="email"],input[type="url"],input[type="search"],input[type="tel"],input[type="color"],.uneditable-input{background-color:#fff;border:1px solid #ccc;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-webkit-transition:border linear .2s, box-shadow linear .2s;-moz-transition:border linear .2s, box-shadow linear .2s;-o-transition:border linear .2s, box-shadow linear .2s;transition:border linear .2s, box-shadow linear .2s}textarea:focus,input[type="text"]:focus,input[type="password"]:focus,input[type="datetime"]:focus,input[type="datetime-local"]:focus,input[type="date"]:focus,input[type="month"]:focus,input[type="time"]:focus,input[type="week"]:focus,input[type="number"]:focus,input[type="email"]:focus,input[type="url"]:focus,input[type="search"]:focus,input[type="tel"]:focus,input[type="color"]:focus,.uneditable-input:focus{border-color:rgba(82,168,236,0.8);outline:0;outline:thin dotted \9;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(82,168,236,.6);-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(82,168,236,.6);box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(82,168,236,.6)}
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input::-webkit-input-placeholder,textarea::-webkit-input-placeholder{color:#999}
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input,textarea,.uneditable-input{margin-left:0}
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input.span12,textarea.span12,.uneditable-input.span12{width:926px}
input.span11,textarea.span11,.uneditable-input.span11{width:846px}
input.span10,textarea.span10,.uneditable-input.span10{width:766px}
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input.span8,textarea.span8,.uneditable-input.span8{width:606px}
input.span7,textarea.span7,.uneditable-input.span7{width:526px}
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.input-append .add-on,.input-prepend .add-on{display:inline-block;width:auto;height:20px;min-width:16px;padding:4px 5px;font-size:13px;font-weight:normal;line-height:20px;text-align:center;text-shadow:0 1px 0 #fff;background-color:#eee;border:1px solid #ccc}
.input-append .add-on,.input-prepend .add-on,.input-append .btn,.input-prepend .btn,.input-append .btn-group>.dropdown-toggle,.input-prepend .btn-group>.dropdown-toggle{vertical-align:top;border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.input-append .active,.input-prepend .active{background-color:#a9dba9;border-color:#46a546}
.input-prepend .add-on,.input-prepend .btn{margin-right:-1px}
.input-prepend .add-on:first-child,.input-prepend .btn:first-child{border-radius:4px 0 0 4px;-webkit-border-radius:4px 0 0 4px;-moz-border-radius:4px 0 0 4px;border-radius:4px 0 0 4px}
.input-append input,.input-append select,.input-append .uneditable-input{border-radius:4px 0 0 4px;-webkit-border-radius:4px 0 0 4px;-moz-border-radius:4px 0 0 4px;border-radius:4px 0 0 4px}.input-append input+.btn-group .btn:last-child,.input-append select+.btn-group .btn:last-child,.input-append .uneditable-input+.btn-group .btn:last-child{border-radius:0 4px 4px 0;-webkit-border-radius:0 4px 4px 0;-moz-border-radius:0 4px 4px 0;border-radius:0 4px 4px 0}
.input-append .add-on,.input-append .btn,.input-append .btn-group{margin-left:-1px}
.input-append .add-on:last-child,.input-append .btn:last-child,.input-append .btn-group:last-child>.dropdown-toggle{border-radius:0 4px 4px 0;-webkit-border-radius:0 4px 4px 0;-moz-border-radius:0 4px 4px 0;border-radius:0 4px 4px 0}
.input-prepend.input-append input,.input-prepend.input-append select,.input-prepend.input-append .uneditable-input{border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}.input-prepend.input-append input+.btn-group .btn,.input-prepend.input-append select+.btn-group .btn,.input-prepend.input-append .uneditable-input+.btn-group .btn{border-radius:0 4px 4px 0;-webkit-border-radius:0 4px 4px 0;-moz-border-radius:0 4px 4px 0;border-radius:0 4px 4px 0}
.input-prepend.input-append .add-on:first-child,.input-prepend.input-append .btn:first-child{margin-right:-1px;border-radius:4px 0 0 4px;-webkit-border-radius:4px 0 0 4px;-moz-border-radius:4px 0 0 4px;border-radius:4px 0 0 4px}
.input-prepend.input-append .add-on:last-child,.input-prepend.input-append .btn:last-child{margin-left:-1px;border-radius:0 4px 4px 0;-webkit-border-radius:0 4px 4px 0;-moz-border-radius:0 4px 4px 0;border-radius:0 4px 4px 0}
.input-prepend.input-append .btn-group:first-child{margin-left:0}
input.search-query{padding-right:14px;padding-right:4px \9;padding-left:14px;padding-left:4px \9;margin-bottom:0;border-radius:15px;-webkit-border-radius:15px;-moz-border-radius:15px;border-radius:15px}
.form-search .input-append .search-query,.form-search .input-prepend .search-query{border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.form-search .input-append .search-query{border-radius:14px 0 0 14px;-webkit-border-radius:14px 0 0 14px;-moz-border-radius:14px 0 0 14px;border-radius:14px 0 0 14px}
.form-search .input-append .btn{border-radius:0 14px 14px 0;-webkit-border-radius:0 14px 14px 0;-moz-border-radius:0 14px 14px 0;border-radius:0 14px 14px 0}
.form-search .input-prepend .search-query{border-radius:0 14px 14px 0;-webkit-border-radius:0 14px 14px 0;-moz-border-radius:0 14px 14px 0;border-radius:0 14px 14px 0}
.form-search .input-prepend .btn{border-radius:14px 0 0 14px;-webkit-border-radius:14px 0 0 14px;-moz-border-radius:14px 0 0 14px;border-radius:14px 0 0 14px}
.form-search input,.form-inline input,.form-horizontal input,.form-search textarea,.form-inline textarea,.form-horizontal textarea,.form-search select,.form-inline select,.form-horizontal select,.form-search .help-inline,.form-inline .help-inline,.form-horizontal .help-inline,.form-search .uneditable-input,.form-inline .uneditable-input,.form-horizontal .uneditable-input,.form-search .input-prepend,.form-inline .input-prepend,.form-horizontal .input-prepend,.form-search .input-append,.form-inline .input-append,.form-horizontal .input-append{display:inline-block;*display:inline;*zoom:1;margin-bottom:0;vertical-align:middle}
.form-search .hide,.form-inline .hide,.form-horizontal .hide{display:none}
.form-search label,.form-inline label,.form-search .btn-group,.form-inline .btn-group{display:inline-block}
.form-search .input-append,.form-inline .input-append,.form-search .input-prepend,.form-inline .input-prepend{margin-bottom:0}
.form-search .radio,.form-search .checkbox,.form-inline .radio,.form-inline .checkbox{padding-left:0;margin-bottom:0;vertical-align:middle}
.form-search .radio input[type="radio"],.form-search .checkbox input[type="checkbox"],.form-inline .radio input[type="radio"],.form-inline .checkbox input[type="checkbox"]{float:left;margin-right:3px;margin-left:0}
.control-group{margin-bottom:10px}
legend+.control-group{margin-top:20px;-webkit-margin-top-collapse:separate}
.form-horizontal .control-group{margin-bottom:20px;*zoom:1}.form-horizontal .control-group:before,.form-horizontal .control-group:after{display:table;content:"";line-height:0}
.form-horizontal .control-group:after{clear:both}
.form-horizontal .control-label{float:left;width:160px;padding-top:5px;text-align:right}
.form-horizontal .controls{*display:inline-block;*padding-left:20px;margin-left:180px;*margin-left:0}.form-horizontal .controls:first-child{*padding-left:180px}
.form-horizontal .help-block{margin-bottom:0}
.form-horizontal input+.help-block,.form-horizontal select+.help-block,.form-horizontal textarea+.help-block,.form-horizontal .uneditable-input+.help-block,.form-horizontal .input-prepend+.help-block,.form-horizontal .input-append+.help-block{margin-top:10px}
.form-horizontal .form-actions{padding-left:180px}
table{max-width:100%;background-color:transparent;border-collapse:collapse;border-spacing:0}
.table{width:100%;margin-bottom:20px}.table th,.table td{padding:8px;line-height:20px;text-align:left;vertical-align:top;border-top:1px solid #ddd}
.table th{font-weight:bold}
.table thead th{vertical-align:bottom}
.table caption+thead tr:first-child th,.table caption+thead tr:first-child td,.table colgroup+thead tr:first-child th,.table colgroup+thead tr:first-child td,.table thead:first-child tr:first-child th,.table thead:first-child tr:first-child td{border-top:0}
.table tbody+tbody{border-top:2px solid #ddd}
.table .table{background-color:#fff}
.table-condensed th,.table-condensed td{padding:4px 5px}
.table-bordered{border:1px solid #ddd;border-collapse:separate;*border-collapse:collapse;border-left:0;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}.table-bordered th,.table-bordered td{border-left:1px solid #ddd}
.table-bordered caption+thead tr:first-child th,.table-bordered caption+tbody tr:first-child th,.table-bordered caption+tbody tr:first-child td,.table-bordered colgroup+thead tr:first-child th,.table-bordered colgroup+tbody tr:first-child th,.table-bordered colgroup+tbody tr:first-child td,.table-bordered thead:first-child tr:first-child th,.table-bordered tbody:first-child tr:first-child th,.table-bordered tbody:first-child tr:first-child td{border-top:0}
.table-bordered thead:first-child tr:first-child>th:first-child,.table-bordered tbody:first-child tr:first-child>td:first-child,.table-bordered tbody:first-child tr:first-child>th:first-child{-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px}
.table-bordered thead:first-child tr:first-child>th:last-child,.table-bordered tbody:first-child tr:first-child>td:last-child,.table-bordered tbody:first-child tr:first-child>th:last-child{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px}
.table-bordered thead:last-child tr:last-child>th:first-child,.table-bordered tbody:last-child tr:last-child>td:first-child,.table-bordered tbody:last-child tr:last-child>th:first-child,.table-bordered tfoot:last-child tr:last-child>td:first-child,.table-bordered tfoot:last-child tr:last-child>th:first-child{-webkit-border-bottom-left-radius:4px;-moz-border-radius-bottomleft:4px;border-bottom-left-radius:4px}
.table-bordered thead:last-child tr:last-child>th:last-child,.table-bordered tbody:last-child tr:last-child>td:last-child,.table-bordered tbody:last-child tr:last-child>th:last-child,.table-bordered tfoot:last-child tr:last-child>td:last-child,.table-bordered tfoot:last-child tr:last-child>th:last-child{-webkit-border-bottom-right-radius:4px;-moz-border-radius-bottomright:4px;border-bottom-right-radius:4px}
.table-bordered tfoot+tbody:last-child tr:last-child td:first-child{-webkit-border-bottom-left-radius:0;-moz-border-radius-bottomleft:0;border-bottom-left-radius:0}
.table-bordered tfoot+tbody:last-child tr:last-child td:last-child{-webkit-border-bottom-right-radius:0;-moz-border-radius-bottomright:0;border-bottom-right-radius:0}
.table-bordered caption+thead tr:first-child th:first-child,.table-bordered caption+tbody tr:first-child td:first-child,.table-bordered colgroup+thead tr:first-child th:first-child,.table-bordered colgroup+tbody tr:first-child td:first-child{-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px}
.table-bordered caption+thead tr:first-child th:last-child,.table-bordered caption+tbody tr:first-child td:last-child,.table-bordered colgroup+thead tr:first-child th:last-child,.table-bordered colgroup+tbody tr:first-child td:last-child{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px}
.table-striped tbody>tr:nth-child(odd)>td,.table-striped tbody>tr:nth-child(odd)>th{background-color:#f9f9f9}
.table-hover tbody tr:hover>td,.table-hover tbody tr:hover>th{background-color:#f5f5f5}
table td[class*="span"],table th[class*="span"],.row-fluid table td[class*="span"],.row-fluid table th[class*="span"]{display:table-cell;float:none;margin-left:0}
.table td.span1,.table th.span1{float:none;width:44px;margin-left:0}
.table td.span2,.table th.span2{float:none;width:124px;margin-left:0}
.table td.span3,.table th.span3{float:none;width:204px;margin-left:0}
.table td.span4,.table th.span4{float:none;width:284px;margin-left:0}
.table td.span5,.table th.span5{float:none;width:364px;margin-left:0}
.table td.span6,.table th.span6{float:none;width:444px;margin-left:0}
.table td.span7,.table th.span7{float:none;width:524px;margin-left:0}
.table td.span8,.table th.span8{float:none;width:604px;margin-left:0}
.table td.span9,.table th.span9{float:none;width:684px;margin-left:0}
.table td.span10,.table th.span10{float:none;width:764px;margin-left:0}
.table td.span11,.table th.span11{float:none;width:844px;margin-left:0}
.table td.span12,.table th.span12{float:none;width:924px;margin-left:0}
.table tbody tr.success>td{background-color:#dff0d8}
.table tbody tr.error>td{background-color:#f2dede}
.table tbody tr.warning>td{background-color:#fcf8e3}
.table tbody tr.info>td{background-color:#d9edf7}
.table-hover tbody tr.success:hover>td{background-color:#d0e9c6}
.table-hover tbody tr.error:hover>td{background-color:#ebcccc}
.table-hover tbody tr.warning:hover>td{background-color:#faf2cc}
.table-hover tbody tr.info:hover>td{background-color:#c4e3f3}
[class^="icon-"],[class*=" icon-"]{display:inline-block;width:14px;height:14px;*margin-right:.3em;line-height:14px;vertical-align:text-top;background-image:url("../img/glyphicons-halflings.png");background-position:14px 14px;background-repeat:no-repeat;margin-top:1px}
.icon-white,.nav-pills>.active>a>[class^="icon-"],.nav-pills>.active>a>[class*=" icon-"],.nav-list>.active>a>[class^="icon-"],.nav-list>.active>a>[class*=" icon-"],.navbar-inverse .nav>.active>a>[class^="icon-"],.navbar-inverse .nav>.active>a>[class*=" icon-"],.dropdown-menu>li>a:hover>[class^="icon-"],.dropdown-menu>li>a:focus>[class^="icon-"],.dropdown-menu>li>a:hover>[class*=" icon-"],.dropdown-menu>li>a:focus>[class*=" icon-"],.dropdown-menu>.active>a>[class^="icon-"],.dropdown-menu>.active>a>[class*=" icon-"],.dropdown-submenu:hover>a>[class^="icon-"],.dropdown-submenu:focus>a>[class^="icon-"],.dropdown-submenu:hover>a>[class*=" icon-"],.dropdown-submenu:focus>a>[class*=" icon-"]{background-image:url("../img/glyphicons-halflings-white.png")}
.icon-glass{background-position:0 0}
.icon-music{background-position:-24px 0}
.icon-search{background-position:-48px 0}
.icon-envelope{background-position:-72px 0}
.icon-heart{background-position:-96px 0}
.icon-star{background-position:-120px 0}
.icon-star-empty{background-position:-144px 0}
.icon-user{background-position:-168px 0}
.icon-film{background-position:-192px 0}
.icon-th-large{background-position:-216px 0}
.icon-th{background-position:-240px 0}
.icon-th-list{background-position:-264px 0}
.icon-ok{background-position:-288px 0}
.icon-remove{background-position:-312px 0}
.icon-zoom-in{background-position:-336px 0}
.icon-zoom-out{background-position:-360px 0}
.icon-off{background-position:-384px 0}
.icon-signal{background-position:-408px 0}
.icon-cog{background-position:-432px 0}
.icon-trash{background-position:-456px 0}
.icon-home{background-position:0 -24px}
.icon-file{background-position:-24px -24px}
.icon-time{background-position:-48px -24px}
.icon-road{background-position:-72px -24px}
.icon-download-alt{background-position:-96px -24px}
.icon-download{background-position:-120px -24px}
.icon-upload{background-position:-144px -24px}
.icon-inbox{background-position:-168px -24px}
.icon-play-circle{background-position:-192px -24px}
.icon-repeat{background-position:-216px -24px}
.icon-refresh{background-position:-240px -24px}
.icon-list-alt{background-position:-264px -24px}
.icon-lock{background-position:-287px -24px}
.icon-flag{background-position:-312px -24px}
.icon-headphones{background-position:-336px -24px}
.icon-volume-off{background-position:-360px -24px}
.icon-volume-down{background-position:-384px -24px}
.icon-volume-up{background-position:-408px -24px}
.icon-qrcode{background-position:-432px -24px}
.icon-barcode{background-position:-456px -24px}
.icon-tag{background-position:0 -48px}
.icon-tags{background-position:-25px -48px}
.icon-book{background-position:-48px -48px}
.icon-bookmark{background-position:-72px -48px}
.icon-print{background-position:-96px -48px}
.icon-camera{background-position:-120px -48px}
.icon-font{background-position:-144px -48px}
.icon-bold{background-position:-167px -48px}
.icon-italic{background-position:-192px -48px}
.icon-text-height{background-position:-216px -48px}
.icon-text-width{background-position:-240px -48px}
.icon-align-left{background-position:-264px -48px}
.icon-align-center{background-position:-288px -48px}
.icon-align-right{background-position:-312px -48px}
.icon-align-justify{background-position:-336px -48px}
.icon-list{background-position:-360px -48px}
.icon-indent-left{background-position:-384px -48px}
.icon-indent-right{background-position:-408px -48px}
.icon-facetime-video{background-position:-432px -48px}
.icon-picture{background-position:-456px -48px}
.icon-pencil{background-position:0 -72px}
.icon-map-marker{background-position:-24px -72px}
.icon-adjust{background-position:-48px -72px}
.icon-tint{background-position:-72px -72px}
.icon-edit{background-position:-96px -72px}
.icon-share{background-position:-120px -72px}
.icon-check{background-position:-144px -72px}
.icon-move{background-position:-168px -72px}
.icon-step-backward{background-position:-192px -72px}
.icon-fast-backward{background-position:-216px -72px}
.icon-backward{background-position:-240px -72px}
.icon-play{background-position:-264px -72px}
.icon-pause{background-position:-288px -72px}
.icon-stop{background-position:-312px -72px}
.icon-forward{background-position:-336px -72px}
.icon-fast-forward{background-position:-360px -72px}
.icon-step-forward{background-position:-384px -72px}
.icon-eject{background-position:-408px -72px}
.icon-chevron-left{background-position:-432px -72px}
.icon-chevron-right{background-position:-456px -72px}
.icon-plus-sign{background-position:0 -96px}
.icon-minus-sign{background-position:-24px -96px}
.icon-remove-sign{background-position:-48px -96px}
.icon-ok-sign{background-position:-72px -96px}
.icon-question-sign{background-position:-96px -96px}
.icon-info-sign{background-position:-120px -96px}
.icon-screenshot{background-position:-144px -96px}
.icon-remove-circle{background-position:-168px -96px}
.icon-ok-circle{background-position:-192px -96px}
.icon-ban-circle{background-position:-216px -96px}
.icon-arrow-left{background-position:-240px -96px}
.icon-arrow-right{background-position:-264px -96px}
.icon-arrow-up{background-position:-289px -96px}
.icon-arrow-down{background-position:-312px -96px}
.icon-share-alt{background-position:-336px -96px}
.icon-resize-full{background-position:-360px -96px}
.icon-resize-small{background-position:-384px -96px}
.icon-plus{background-position:-408px -96px}
.icon-minus{background-position:-433px -96px}
.icon-asterisk{background-position:-456px -96px}
.icon-exclamation-sign{background-position:0 -120px}
.icon-gift{background-position:-24px -120px}
.icon-leaf{background-position:-48px -120px}
.icon-fire{background-position:-72px -120px}
.icon-eye-open{background-position:-96px -120px}
.icon-eye-close{background-position:-120px -120px}
.icon-warning-sign{background-position:-144px -120px}
.icon-plane{background-position:-168px -120px}
.icon-calendar{background-position:-192px -120px}
.icon-random{background-position:-216px -120px;width:16px}
.icon-comment{background-position:-240px -120px}
.icon-magnet{background-position:-264px -120px}
.icon-chevron-up{background-position:-288px -120px}
.icon-chevron-down{background-position:-313px -119px}
.icon-retweet{background-position:-336px -120px}
.icon-shopping-cart{background-position:-360px -120px}
.icon-folder-close{background-position:-384px -120px;width:16px}
.icon-folder-open{background-position:-408px -120px;width:16px}
.icon-resize-vertical{background-position:-432px -119px}
.icon-resize-horizontal{background-position:-456px -118px}
.icon-hdd{background-position:0 -144px}
.icon-bullhorn{background-position:-24px -144px}
.icon-bell{background-position:-48px -144px}
.icon-certificate{background-position:-72px -144px}
.icon-thumbs-up{background-position:-96px -144px}
.icon-thumbs-down{background-position:-120px -144px}
.icon-hand-right{background-position:-144px -144px}
.icon-hand-left{background-position:-168px -144px}
.icon-hand-up{background-position:-192px -144px}
.icon-hand-down{background-position:-216px -144px}
.icon-circle-arrow-right{background-position:-240px -144px}
.icon-circle-arrow-left{background-position:-264px -144px}
.icon-circle-arrow-up{background-position:-288px -144px}
.icon-circle-arrow-down{background-position:-312px -144px}
.icon-globe{background-position:-336px -144px}
.icon-wrench{background-position:-360px -144px}
.icon-tasks{background-position:-384px -144px}
.icon-filter{background-position:-408px -144px}
.icon-briefcase{background-position:-432px -144px}
.icon-fullscreen{background-position:-456px -144px}
.dropup,.dropdown{position:relative}
.dropdown-toggle{*margin-bottom:-3px}
.dropdown-toggle:active,.open .dropdown-toggle{outline:0}
.caret{display:inline-block;width:0;height:0;vertical-align:top;border-top:4px solid #000;border-right:4px solid transparent;border-left:4px solid transparent;content:""}
.dropdown .caret{margin-top:8px;margin-left:2px}
.dropdown-menu{position:absolute;top:100%;left:0;z-index:1000;display:none;float:left;min-width:160px;padding:5px 0;margin:2px 0 0;list-style:none;background-color:#fff;border:1px solid #ccc;border:1px solid rgba(0,0,0,0.2);*border-right-width:2px;*border-bottom-width:2px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;-webkit-box-shadow:0 5px 10px rgba(0,0,0,0.2);-moz-box-shadow:0 5px 10px rgba(0,0,0,0.2);box-shadow:0 5px 10px rgba(0,0,0,0.2);-webkit-background-clip:padding-box;-moz-background-clip:padding;background-clip:padding-box}.dropdown-menu.pull-right{right:0;left:auto}
.dropdown-menu .divider{*width:100%;height:1px;margin:9px 1px;*margin:-5px 0 5px;overflow:hidden;background-color:#e5e5e5;border-bottom:1px solid #fff}
.dropdown-menu>li>a{display:block;padding:3px 20px;clear:both;font-weight:normal;line-height:20px;color:#333;white-space:nowrap}
.dropdown-menu>li>a:hover,.dropdown-menu>li>a:focus,.dropdown-submenu:hover>a,.dropdown-submenu:focus>a{text-decoration:none;color:#fff;background-color:#0081c2;background-image:-moz-linear-gradient(top, #08c, #0077b3);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#08c), to(#0077b3));background-image:-webkit-linear-gradient(top, #08c, #0077b3);background-image:-o-linear-gradient(top, #08c, #0077b3);background-image:linear-gradient(to bottom, #08c, #0077b3);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff0088cc', endColorstr='#ff0077b3', GradientType=0)}
.dropdown-menu>.active>a,.dropdown-menu>.active>a:hover,.dropdown-menu>.active>a:focus{color:#fff;text-decoration:none;outline:0;background-color:#0081c2;background-image:-moz-linear-gradient(top, #08c, #0077b3);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#08c), to(#0077b3));background-image:-webkit-linear-gradient(top, #08c, #0077b3);background-image:-o-linear-gradient(top, #08c, #0077b3);background-image:linear-gradient(to bottom, #08c, #0077b3);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff0088cc', endColorstr='#ff0077b3', GradientType=0)}
.dropdown-menu>.disabled>a,.dropdown-menu>.disabled>a:hover,.dropdown-menu>.disabled>a:focus{color:#999}
.dropdown-menu>.disabled>a:hover,.dropdown-menu>.disabled>a:focus{text-decoration:none;background-color:transparent;background-image:none;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);cursor:default}
.open{*z-index:1000}.open>.dropdown-menu{display:block}
.dropdown-backdrop{position:fixed;left:0;right:0;bottom:0;top:0;z-index:990}
.pull-right>.dropdown-menu{right:0;left:auto}
.dropup .caret,.navbar-fixed-bottom .dropdown .caret{border-top:0;border-bottom:4px solid #000;content:""}
.dropup .dropdown-menu,.navbar-fixed-bottom .dropdown .dropdown-menu{top:auto;bottom:100%;margin-bottom:1px}
.dropdown-submenu{position:relative}
.dropdown-submenu>.dropdown-menu{top:0;left:100%;margin-top:-6px;margin-left:-1px;border-radius:0 6px 6px 6px;-webkit-border-radius:0 6px 6px 6px;-moz-border-radius:0 6px 6px 6px;border-radius:0 6px 6px 6px}
.dropdown-submenu:hover>.dropdown-menu{display:block}
.dropup .dropdown-submenu>.dropdown-menu{top:auto;bottom:0;margin-top:0;margin-bottom:-2px;border-radius:5px 5px 5px 0;-webkit-border-radius:5px 5px 5px 0;-moz-border-radius:5px 5px 5px 0;border-radius:5px 5px 5px 0}
.dropdown-submenu>a:after{display:block;content:" ";float:right;width:0;height:0;border-color:transparent;border-style:solid;border-width:5px 0 5px 5px;border-left-color:#ccc;margin-top:5px;margin-right:-10px}
.dropdown-submenu:hover>a:after{border-left-color:#fff}
.dropdown-submenu.pull-left{float:none}.dropdown-submenu.pull-left>.dropdown-menu{left:-100%;margin-left:10px;border-radius:6px 0 6px 6px;-webkit-border-radius:6px 0 6px 6px;-moz-border-radius:6px 0 6px 6px;border-radius:6px 0 6px 6px}
.dropdown .dropdown-menu .nav-header{padding-left:20px;padding-right:20px}
.typeahead{z-index:1051;margin-top:2px;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.well{min-height:20px;padding:19px;margin-bottom:20px;background-color:#f5f5f5;border:1px solid #e3e3e3;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.05);-moz-box-shadow:inset 0 1px 1px rgba(0,0,0,0.05);box-shadow:inset 0 1px 1px rgba(0,0,0,0.05)}.well blockquote{border-color:#ddd;border-color:rgba(0,0,0,0.15)}
.well-large{padding:24px;border-radius:6px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px}
.well-small{padding:9px;border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
.fade{opacity:0;-webkit-transition:opacity .15s linear;-moz-transition:opacity .15s linear;-o-transition:opacity .15s linear;transition:opacity .15s linear}.fade.in{opacity:1}
.collapse{position:relative;height:0;overflow:hidden;-webkit-transition:height .35s ease;-moz-transition:height .35s ease;-o-transition:height .35s ease;transition:height .35s ease}.collapse.in{height:auto}
.close{float:right;font-size:20px;font-weight:bold;line-height:20px;color:#000;text-shadow:0 1px 0 #fff;opacity:.2;filter:alpha(opacity=20)}.close:hover,.close:focus{color:#000;text-decoration:none;cursor:pointer;opacity:.4;filter:alpha(opacity=40)}
button.close{padding:0;cursor:pointer;background:transparent;border:0;-webkit-appearance:none}
.btn{display:inline-block;*display:inline;*zoom:1;padding:4px 12px;margin-bottom:0;font-size:13px;line-height:20px;text-align:center;vertical-align:middle;cursor:pointer;color:#333;text-shadow:0 1px 1px rgba(255,255,255,0.75);background-color:#f5f5f5;background-image:-moz-linear-gradient(top, #fff, #e6e6e6);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fff), to(#e6e6e6));background-image:-webkit-linear-gradient(top, #fff, #e6e6e6);background-image:-o-linear-gradient(top, #fff, #e6e6e6);background-image:linear-gradient(to bottom, #fff, #e6e6e6);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffffffff', endColorstr='#ffe6e6e6', GradientType=0);border-color:#e6e6e6 #e6e6e6 #bfbfbf;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#e6e6e6;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);border:1px solid #ccc;*border:0;border-bottom-color:#b3b3b3;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;*margin-left:.3em;-webkit-box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05)}.btn:hover,.btn:focus,.btn:active,.btn.active,.btn.disabled,.btn[disabled]{color:#333;background-color:#e6e6e6;*background-color:#d9d9d9}
.btn:active,.btn.active{background-color:#ccc \9}
.btn:first-child{*margin-left:0}
.btn:hover,.btn:focus{color:#333;text-decoration:none;background-position:0 -15px;-webkit-transition:background-position .1s linear;-moz-transition:background-position .1s linear;-o-transition:background-position .1s linear;transition:background-position .1s linear}
.btn:focus{outline:thin dotted #333;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}
.btn.active,.btn:active{background-image:none;outline:0;-webkit-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05)}
.btn.disabled,.btn[disabled]{cursor:default;background-image:none;opacity:.65;filter:alpha(opacity=65);-webkit-box-shadow:none;-moz-box-shadow:none;box-shadow:none}
.btn-large{padding:11px 19px;font-size:16.25px;border-radius:6px;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px}
.btn-large [class^="icon-"],.btn-large [class*=" icon-"]{margin-top:4px}
.btn-small{padding:2px 10px;font-size:11.049999999999999px;border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
.btn-small [class^="icon-"],.btn-small [class*=" icon-"]{margin-top:0}
.btn-mini [class^="icon-"],.btn-mini [class*=" icon-"]{margin-top:-1px}
.btn-mini{padding:0 6px;font-size:9.75px;border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
.btn-block{display:block;width:100%;padding-left:0;padding-right:0;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}
.btn-block+.btn-block{margin-top:5px}
input[type="submit"].btn-block,input[type="reset"].btn-block,input[type="button"].btn-block{width:100%}
.btn-primary.active,.btn-warning.active,.btn-danger.active,.btn-success.active,.btn-info.active,.btn-inverse.active{color:rgba(255,255,255,0.75)}
.btn-primary{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#006dcc;background-image:-moz-linear-gradient(top, #08c, #04c);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#08c), to(#04c));background-image:-webkit-linear-gradient(top, #08c, #04c);background-image:-o-linear-gradient(top, #08c, #04c);background-image:linear-gradient(to bottom, #08c, #04c);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff0088cc', endColorstr='#ff0044cc', GradientType=0);border-color:#04c #04c #002a80;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#04c;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-primary:hover,.btn-primary:focus,.btn-primary:active,.btn-primary.active,.btn-primary.disabled,.btn-primary[disabled]{color:#fff;background-color:#04c;*background-color:#003bb3}
.btn-primary:active,.btn-primary.active{background-color:#039 \9}
.btn-warning{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#faa732;background-image:-moz-linear-gradient(top, #fbb450, #f89406);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fbb450), to(#f89406));background-image:-webkit-linear-gradient(top, #fbb450, #f89406);background-image:-o-linear-gradient(top, #fbb450, #f89406);background-image:linear-gradient(to bottom, #fbb450, #f89406);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fffbb450', endColorstr='#fff89406', GradientType=0);border-color:#f89406 #f89406 #ad6704;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#f89406;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-warning:hover,.btn-warning:focus,.btn-warning:active,.btn-warning.active,.btn-warning.disabled,.btn-warning[disabled]{color:#fff;background-color:#f89406;*background-color:#df8505}
.btn-warning:active,.btn-warning.active{background-color:#c67605 \9}
.btn-danger{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#da4f49;background-image:-moz-linear-gradient(top, #ee5f5b, #bd362f);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#ee5f5b), to(#bd362f));background-image:-webkit-linear-gradient(top, #ee5f5b, #bd362f);background-image:-o-linear-gradient(top, #ee5f5b, #bd362f);background-image:linear-gradient(to bottom, #ee5f5b, #bd362f);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffee5f5b', endColorstr='#ffbd362f', GradientType=0);border-color:#bd362f #bd362f #802420;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#bd362f;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-danger:hover,.btn-danger:focus,.btn-danger:active,.btn-danger.active,.btn-danger.disabled,.btn-danger[disabled]{color:#fff;background-color:#bd362f;*background-color:#a9302a}
.btn-danger:active,.btn-danger.active{background-color:#942a25 \9}
.btn-success{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#5bb75b;background-image:-moz-linear-gradient(top, #62c462, #51a351);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#62c462), to(#51a351));background-image:-webkit-linear-gradient(top, #62c462, #51a351);background-image:-o-linear-gradient(top, #62c462, #51a351);background-image:linear-gradient(to bottom, #62c462, #51a351);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff62c462', endColorstr='#ff51a351', GradientType=0);border-color:#51a351 #51a351 #387038;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#51a351;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-success:hover,.btn-success:focus,.btn-success:active,.btn-success.active,.btn-success.disabled,.btn-success[disabled]{color:#fff;background-color:#51a351;*background-color:#499249}
.btn-success:active,.btn-success.active{background-color:#408140 \9}
.btn-info{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#49afcd;background-image:-moz-linear-gradient(top, #5bc0de, #2f96b4);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#5bc0de), to(#2f96b4));background-image:-webkit-linear-gradient(top, #5bc0de, #2f96b4);background-image:-o-linear-gradient(top, #5bc0de, #2f96b4);background-image:linear-gradient(to bottom, #5bc0de, #2f96b4);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff5bc0de', endColorstr='#ff2f96b4', GradientType=0);border-color:#2f96b4 #2f96b4 #1f6377;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#2f96b4;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-info:hover,.btn-info:focus,.btn-info:active,.btn-info.active,.btn-info.disabled,.btn-info[disabled]{color:#fff;background-color:#2f96b4;*background-color:#2a85a0}
.btn-info:active,.btn-info.active{background-color:#24748c \9}
.btn-inverse{color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#363636;background-image:-moz-linear-gradient(top, #444, #222);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#444), to(#222));background-image:-webkit-linear-gradient(top, #444, #222);background-image:-o-linear-gradient(top, #444, #222);background-image:linear-gradient(to bottom, #444, #222);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff444444', endColorstr='#ff222222', GradientType=0);border-color:#222 #222 #000;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#222;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false)}.btn-inverse:hover,.btn-inverse:focus,.btn-inverse:active,.btn-inverse.active,.btn-inverse.disabled,.btn-inverse[disabled]{color:#fff;background-color:#222;*background-color:#151515}
.btn-inverse:active,.btn-inverse.active{background-color:#080808 \9}
button.btn,input[type="submit"].btn{*padding-top:3px;*padding-bottom:3px}button.btn::-moz-focus-inner,input[type="submit"].btn::-moz-focus-inner{padding:0;border:0}
button.btn.btn-large,input[type="submit"].btn.btn-large{*padding-top:7px;*padding-bottom:7px}
button.btn.btn-small,input[type="submit"].btn.btn-small{*padding-top:3px;*padding-bottom:3px}
button.btn.btn-mini,input[type="submit"].btn.btn-mini{*padding-top:1px;*padding-bottom:1px}
.btn-link,.btn-link:active,.btn-link[disabled]{background-color:transparent;background-image:none;-webkit-box-shadow:none;-moz-box-shadow:none;box-shadow:none}
.btn-link{border-color:transparent;cursor:pointer;color:#08c;border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.btn-link:hover,.btn-link:focus{color:#005580;text-decoration:underline;background-color:transparent}
.btn-link[disabled]:hover,.btn-link[disabled]:focus{color:#333;text-decoration:none}
.btn-group{position:relative;display:inline-block;*display:inline;*zoom:1;font-size:0;vertical-align:middle;white-space:nowrap;*margin-left:.3em}.btn-group:first-child{*margin-left:0}
.btn-group+.btn-group{margin-left:5px}
.btn-toolbar{font-size:0;margin-top:10px;margin-bottom:10px}.btn-toolbar>.btn+.btn,.btn-toolbar>.btn-group+.btn,.btn-toolbar>.btn+.btn-group{margin-left:5px}
.btn-group>.btn{position:relative;border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.btn-group>.btn+.btn{margin-left:-1px}
.btn-group>.btn,.btn-group>.dropdown-menu,.btn-group>.popover{font-size:13px}
.btn-group>.btn-mini{font-size:9.75px}
.btn-group>.btn-small{font-size:11.049999999999999px}
.btn-group>.btn-large{font-size:16.25px}
.btn-group>.btn:first-child{margin-left:0;-webkit-border-top-left-radius:4px;-moz-border-radius-topleft:4px;border-top-left-radius:4px;-webkit-border-bottom-left-radius:4px;-moz-border-radius-bottomleft:4px;border-bottom-left-radius:4px}
.btn-group>.btn:last-child,.btn-group>.dropdown-toggle{-webkit-border-top-right-radius:4px;-moz-border-radius-topright:4px;border-top-right-radius:4px;-webkit-border-bottom-right-radius:4px;-moz-border-radius-bottomright:4px;border-bottom-right-radius:4px}
.btn-group>.btn.large:first-child{margin-left:0;-webkit-border-top-left-radius:6px;-moz-border-radius-topleft:6px;border-top-left-radius:6px;-webkit-border-bottom-left-radius:6px;-moz-border-radius-bottomleft:6px;border-bottom-left-radius:6px}
.btn-group>.btn.large:last-child,.btn-group>.large.dropdown-toggle{-webkit-border-top-right-radius:6px;-moz-border-radius-topright:6px;border-top-right-radius:6px;-webkit-border-bottom-right-radius:6px;-moz-border-radius-bottomright:6px;border-bottom-right-radius:6px}
.btn-group>.btn:hover,.btn-group>.btn:focus,.btn-group>.btn:active,.btn-group>.btn.active{z-index:2}
.btn-group .dropdown-toggle:active,.btn-group.open .dropdown-toggle{outline:0}
.btn-group>.btn+.dropdown-toggle{padding-left:8px;padding-right:8px;-webkit-box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 1px 0 0 rgba(255,255,255,.125), inset 0 1px 0 rgba(255,255,255,.2), 0 1px 2px rgba(0,0,0,.05);*padding-top:5px;*padding-bottom:5px}
.btn-group>.btn-mini+.dropdown-toggle{padding-left:5px;padding-right:5px;*padding-top:2px;*padding-bottom:2px}
.btn-group>.btn-small+.dropdown-toggle{*padding-top:5px;*padding-bottom:4px}
.btn-group>.btn-large+.dropdown-toggle{padding-left:12px;padding-right:12px;*padding-top:7px;*padding-bottom:7px}
.btn-group.open .dropdown-toggle{background-image:none;-webkit-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);-moz-box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05);box-shadow:inset 0 2px 4px rgba(0,0,0,.15), 0 1px 2px rgba(0,0,0,.05)}
.btn-group.open .btn.dropdown-toggle{background-color:#e6e6e6}
.btn-group.open .btn-primary.dropdown-toggle{background-color:#04c}
.btn-group.open .btn-warning.dropdown-toggle{background-color:#f89406}
.btn-group.open .btn-danger.dropdown-toggle{background-color:#bd362f}
.btn-group.open .btn-success.dropdown-toggle{background-color:#51a351}
.btn-group.open .btn-info.dropdown-toggle{background-color:#2f96b4}
.btn-group.open .btn-inverse.dropdown-toggle{background-color:#222}
.btn .caret{margin-top:8px;margin-left:0}
.btn-large .caret{margin-top:6px}
.btn-large .caret{border-left-width:5px;border-right-width:5px;border-top-width:5px}
.btn-mini .caret,.btn-small .caret{margin-top:8px}
.dropup .btn-large .caret{border-bottom-width:5px}
.btn-primary .caret,.btn-warning .caret,.btn-danger .caret,.btn-info .caret,.btn-success .caret,.btn-inverse .caret{border-top-color:#fff;border-bottom-color:#fff}
.btn-group-vertical{display:inline-block;*display:inline;*zoom:1}
.btn-group-vertical>.btn{display:block;float:none;max-width:100%;border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.btn-group-vertical>.btn+.btn{margin-left:0;margin-top:-1px}
.btn-group-vertical>.btn:first-child{border-radius:4px 4px 0 0;-webkit-border-radius:4px 4px 0 0;-moz-border-radius:4px 4px 0 0;border-radius:4px 4px 0 0}
.btn-group-vertical>.btn:last-child{border-radius:0 0 4px 4px;-webkit-border-radius:0 0 4px 4px;-moz-border-radius:0 0 4px 4px;border-radius:0 0 4px 4px}
.btn-group-vertical>.btn-large:first-child{border-radius:6px 6px 0 0;-webkit-border-radius:6px 6px 0 0;-moz-border-radius:6px 6px 0 0;border-radius:6px 6px 0 0}
.btn-group-vertical>.btn-large:last-child{border-radius:0 0 6px 6px;-webkit-border-radius:0 0 6px 6px;-moz-border-radius:0 0 6px 6px;border-radius:0 0 6px 6px}
.alert{padding:8px 35px 8px 14px;margin-bottom:20px;text-shadow:0 1px 0 rgba(255,255,255,0.5);background-color:#fcf8e3;border:1px solid #fbeed5;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.alert,.alert h4{color:#c09853}
.alert h4{margin:0}
.alert .close{position:relative;top:-2px;right:-21px;line-height:20px}
.alert-success{background-color:#dff0d8;border-color:#d6e9c6;color:#468847}
.alert-success h4{color:#468847}
.alert-danger,.alert-error{background-color:#f2dede;border-color:#eed3d7;color:#b94a48}
.alert-danger h4,.alert-error h4{color:#b94a48}
.alert-info{background-color:#d9edf7;border-color:#bce8f1;color:#3a87ad}
.alert-info h4{color:#3a87ad}
.alert-block{padding-top:14px;padding-bottom:14px}
.alert-block>p,.alert-block>ul{margin-bottom:0}
.alert-block p+p{margin-top:5px}
.nav{margin-left:0;margin-bottom:20px;list-style:none}
.nav>li>a{display:block}
.nav>li>a:hover,.nav>li>a:focus{text-decoration:none;background-color:#eee}
.nav>li>a>img{max-width:none}
.nav>.pull-right{float:right}
.nav-header{display:block;padding:3px 15px;font-size:11px;font-weight:bold;line-height:20px;color:#999;text-shadow:0 1px 0 rgba(255,255,255,0.5);text-transform:uppercase}
.nav li+.nav-header{margin-top:9px}
.nav-list{padding-left:15px;padding-right:15px;margin-bottom:0}
.nav-list>li>a,.nav-list .nav-header{margin-left:-15px;margin-right:-15px;text-shadow:0 1px 0 rgba(255,255,255,0.5)}
.nav-list>li>a{padding:3px 15px}
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.nav-list [class^="icon-"],.nav-list [class*=" icon-"]{margin-right:2px}
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.nav-tabs{border-bottom:1px solid #ddd}
.nav-tabs>li{margin-bottom:-1px}
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.nav-stacked>li{float:none}
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.tabs-below>.nav-tabs>li>a{border-radius:0 0 4px 4px;-webkit-border-radius:0 0 4px 4px;-moz-border-radius:0 0 4px 4px;border-radius:0 0 4px 4px}.tabs-below>.nav-tabs>li>a:hover,.tabs-below>.nav-tabs>li>a:focus{border-bottom-color:transparent;border-top-color:#ddd}
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.tabs-left>.nav-tabs>li>a{margin-right:-1px;border-radius:4px 0 0 4px;-webkit-border-radius:4px 0 0 4px;-moz-border-radius:4px 0 0 4px;border-radius:4px 0 0 4px}
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.nav>.disabled>a{color:#999}
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.navbar-inner{min-height:36px;padding-left:20px;padding-right:20px;background-color:#fafafa;background-image:-moz-linear-gradient(top, #fff, #f2f2f2);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fff), to(#f2f2f2));background-image:-webkit-linear-gradient(top, #fff, #f2f2f2);background-image:-o-linear-gradient(top, #fff, #f2f2f2);background-image:linear-gradient(to bottom, #fff, #f2f2f2);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffffffff', endColorstr='#fff2f2f2', GradientType=0);border:1px solid #d4d4d4;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:0 1px 4px rgba(0,0,0,0.065);-moz-box-shadow:0 1px 4px rgba(0,0,0,0.065);box-shadow:0 1px 4px rgba(0,0,0,0.065);*zoom:1}.navbar-inner:before,.navbar-inner:after{display:table;content:"";line-height:0}
.navbar-inner:after{clear:both}
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.navbar .brand{float:left;display:block;padding:8px 20px 8px;margin-left:-20px;font-size:20px;font-weight:200;color:#777;text-shadow:0 1px 0 #fff}.navbar .brand:hover,.navbar .brand:focus{text-decoration:none}
.navbar-text{margin-bottom:0;line-height:36px;color:#777}
.navbar-link{color:#777}.navbar-link:hover,.navbar-link:focus{color:#333}
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.navbar .btn,.navbar .btn-group{margin-top:3px}
.navbar .btn-group .btn,.navbar .input-prepend .btn,.navbar .input-append .btn,.navbar .input-prepend .btn-group,.navbar .input-append .btn-group{margin-top:0}
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.navbar-form:after{clear:both}
.navbar-form input,.navbar-form select,.navbar-form .radio,.navbar-form .checkbox{margin-top:3px}
.navbar-form input,.navbar-form select,.navbar-form .btn{display:inline-block;margin-bottom:0}
.navbar-form input[type="image"],.navbar-form input[type="checkbox"],.navbar-form input[type="radio"]{margin-top:3px}
.navbar-form .input-append,.navbar-form .input-prepend{margin-top:5px;white-space:nowrap}.navbar-form .input-append input,.navbar-form .input-prepend input{margin-top:0}
.navbar-search{position:relative;float:left;margin-top:3px;margin-bottom:0}.navbar-search .search-query{margin-bottom:0;padding:4px 14px;font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;font-weight:normal;line-height:1;border-radius:15px;-webkit-border-radius:15px;-moz-border-radius:15px;border-radius:15px}
.navbar-static-top{position:static;margin-bottom:0}.navbar-static-top .navbar-inner{border-radius:0;-webkit-border-radius:0;-moz-border-radius:0;border-radius:0}
.navbar-fixed-top,.navbar-fixed-bottom{position:fixed;right:0;left:0;z-index:1030;margin-bottom:0}
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.navbar-fixed-top{top:0}
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.navbar .nav .dropdown-toggle .caret{margin-top:8px}
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.navbar .nav>.active>a,.navbar .nav>.active>a:hover,.navbar .nav>.active>a:focus{color:#555;text-decoration:none;background-color:#e5e5e5;-webkit-box-shadow:inset 0 3px 8px rgba(0,0,0,0.125);-moz-box-shadow:inset 0 3px 8px rgba(0,0,0,0.125);box-shadow:inset 0 3px 8px rgba(0,0,0,0.125)}
.navbar .btn-navbar{display:none;float:right;padding:7px 10px;margin-left:5px;margin-right:5px;color:#fff;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#ededed;background-image:-moz-linear-gradient(top, #f2f2f2, #e5e5e5);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#f2f2f2), to(#e5e5e5));background-image:-webkit-linear-gradient(top, #f2f2f2, #e5e5e5);background-image:-o-linear-gradient(top, #f2f2f2, #e5e5e5);background-image:linear-gradient(to bottom, #f2f2f2, #e5e5e5);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fff2f2f2', endColorstr='#ffe5e5e5', GradientType=0);border-color:#e5e5e5 #e5e5e5 #bfbfbf;border-color:rgba(0,0,0,0.1) rgba(0,0,0,0.1) rgba(0,0,0,0.25);*background-color:#e5e5e5;filter:progid:DXImageTransform.Microsoft.gradient(enabled = false);-webkit-box-shadow:inset 0 1px 0 rgba(255,255,255,.1), 0 1px 0 rgba(255,255,255,.075);-moz-box-shadow:inset 0 1px 0 rgba(255,255,255,.1), 0 1px 0 rgba(255,255,255,.075);box-shadow:inset 0 1px 0 rgba(255,255,255,.1), 0 1px 0 rgba(255,255,255,.075)}.navbar .btn-navbar:hover,.navbar .btn-navbar:focus,.navbar .btn-navbar:active,.navbar .btn-navbar.active,.navbar .btn-navbar.disabled,.navbar .btn-navbar[disabled]{color:#fff;background-color:#e5e5e5;*background-color:#d9d9d9}
.navbar .btn-navbar:active,.navbar .btn-navbar.active{background-color:#ccc \9}
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.btn-navbar .icon-bar+.icon-bar{margin-top:3px}
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.navbar-inverse .brand{color:#999}
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.navbar-inverse .navbar-link{color:#999}.navbar-inverse .navbar-link:hover,.navbar-inverse .navbar-link:focus{color:#fff}
.navbar-inverse .divider-vertical{border-left-color:#111;border-right-color:#222}
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.navbar-inverse .nav li.dropdown>.dropdown-toggle .caret{border-top-color:#999;border-bottom-color:#999}
.navbar-inverse .nav li.dropdown.open>.dropdown-toggle .caret,.navbar-inverse .nav li.dropdown.active>.dropdown-toggle .caret,.navbar-inverse .nav li.dropdown.open.active>.dropdown-toggle .caret{border-top-color:#fff;border-bottom-color:#fff}
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.navbar-inverse .btn-navbar:active,.navbar-inverse .btn-navbar.active{background-color:#000 \9}
.breadcrumb{padding:8px 15px;margin:0 0 20px;list-style:none;background-color:#f5f5f5;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}.breadcrumb>li{display:inline-block;*display:inline;*zoom:1;text-shadow:0 1px 0 #fff}.breadcrumb>li>.divider{padding:0 5px;color:#ccc}
.breadcrumb>.active{color:#999}
.pagination{margin:20px 0}
.pagination ul{display:inline-block;*display:inline;*zoom:1;margin-left:0;margin-bottom:0;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:0 1px 2px rgba(0,0,0,0.05);-moz-box-shadow:0 1px 2px rgba(0,0,0,0.05);box-shadow:0 1px 2px rgba(0,0,0,0.05)}
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.pagination ul>li>a,.pagination ul>li>span{float:left;padding:4px 12px;line-height:20px;text-decoration:none;background-color:#fff;border:1px solid #ddd;border-left-width:0}
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.pagination ul>.active>a,.pagination ul>.active>span{color:#999;cursor:default}
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.pagination-centered{text-align:center}
.pagination-right{text-align:right}
.pagination-large ul>li>a,.pagination-large ul>li>span{padding:11px 19px;font-size:16.25px}
.pagination-large ul>li:first-child>a,.pagination-large ul>li:first-child>span{-webkit-border-top-left-radius:6px;-moz-border-radius-topleft:6px;border-top-left-radius:6px;-webkit-border-bottom-left-radius:6px;-moz-border-radius-bottomleft:6px;border-bottom-left-radius:6px}
.pagination-large ul>li:last-child>a,.pagination-large ul>li:last-child>span{-webkit-border-top-right-radius:6px;-moz-border-radius-topright:6px;border-top-right-radius:6px;-webkit-border-bottom-right-radius:6px;-moz-border-radius-bottomright:6px;border-bottom-right-radius:6px}
.pagination-mini ul>li:first-child>a,.pagination-small ul>li:first-child>a,.pagination-mini ul>li:first-child>span,.pagination-small ul>li:first-child>span{-webkit-border-top-left-radius:3px;-moz-border-radius-topleft:3px;border-top-left-radius:3px;-webkit-border-bottom-left-radius:3px;-moz-border-radius-bottomleft:3px;border-bottom-left-radius:3px}
.pagination-mini ul>li:last-child>a,.pagination-small ul>li:last-child>a,.pagination-mini ul>li:last-child>span,.pagination-small ul>li:last-child>span{-webkit-border-top-right-radius:3px;-moz-border-radius-topright:3px;border-top-right-radius:3px;-webkit-border-bottom-right-radius:3px;-moz-border-radius-bottomright:3px;border-bottom-right-radius:3px}
.pagination-small ul>li>a,.pagination-small ul>li>span{padding:2px 10px;font-size:11.049999999999999px}
.pagination-mini ul>li>a,.pagination-mini ul>li>span{padding:0 6px;font-size:9.75px}
.pager{margin:20px 0;list-style:none;text-align:center;*zoom:1}.pager:before,.pager:after{display:table;content:"";line-height:0}
.pager:after{clear:both}
.pager li{display:inline}
.pager li>a,.pager li>span{display:inline-block;padding:5px 14px;background-color:#fff;border:1px solid #ddd;border-radius:15px;-webkit-border-radius:15px;-moz-border-radius:15px;border-radius:15px}
.pager li>a:hover,.pager li>a:focus{text-decoration:none;background-color:#f5f5f5}
.pager .next>a,.pager .next>span{float:right}
.pager .previous>a,.pager .previous>span{float:left}
.pager .disabled>a,.pager .disabled>a:hover,.pager .disabled>a:focus,.pager .disabled>span{color:#999;background-color:#fff;cursor:default}
.modal-backdrop{position:fixed;top:0;right:0;bottom:0;left:0;z-index:1040;background-color:#000}.modal-backdrop.fade{opacity:0}
.modal-backdrop,.modal-backdrop.fade.in{opacity:.8;filter:alpha(opacity=80)}
.modal{position:fixed;top:10%;left:50%;z-index:1050;width:560px;margin-left:-280px;background-color:#fff;border:1px solid #999;border:1px solid rgba(0,0,0,0.3);*border:1px solid #999;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;-webkit-box-shadow:0 3px 7px rgba(0,0,0,0.3);-moz-box-shadow:0 3px 7px rgba(0,0,0,0.3);box-shadow:0 3px 7px rgba(0,0,0,0.3);-webkit-background-clip:padding-box;-moz-background-clip:padding-box;background-clip:padding-box;outline:none}.modal.fade{-webkit-transition:opacity .3s linear, top .3s ease-out;-moz-transition:opacity .3s linear, top .3s ease-out;-o-transition:opacity .3s linear, top .3s ease-out;transition:opacity .3s linear, top .3s ease-out;top:-25%}
.modal.fade.in{top:10%}
.modal-header{padding:9px 15px;border-bottom:1px solid #eee}.modal-header .close{margin-top:2px}
.modal-header h3{margin:0;line-height:30px}
.modal-body{position:relative;overflow-y:auto;max-height:400px;padding:15px}
.modal-form{margin-bottom:0}
.modal-footer{padding:14px 15px 15px;margin-bottom:0;text-align:right;background-color:#f5f5f5;border-top:1px solid #ddd;-webkit-border-radius:0 0 6px 6px;-moz-border-radius:0 0 6px 6px;border-radius:0 0 6px 6px;-webkit-box-shadow:inset 0 1px 0 #fff;-moz-box-shadow:inset 0 1px 0 #fff;box-shadow:inset 0 1px 0 #fff;*zoom:1}.modal-footer:before,.modal-footer:after{display:table;content:"";line-height:0}
.modal-footer:after{clear:both}
.modal-footer .btn+.btn{margin-left:5px;margin-bottom:0}
.modal-footer .btn-group .btn+.btn{margin-left:-1px}
.modal-footer .btn-block+.btn-block{margin-left:0}
.tooltip{position:absolute;z-index:1030;display:block;visibility:visible;font-size:11px;line-height:1.4;opacity:0;filter:alpha(opacity=0)}.tooltip.in{opacity:.8;filter:alpha(opacity=80)}
.tooltip.top{margin-top:-3px;padding:5px 0}
.tooltip.right{margin-left:3px;padding:0 5px}
.tooltip.bottom{margin-top:3px;padding:5px 0}
.tooltip.left{margin-left:-3px;padding:0 5px}
.tooltip-inner{max-width:200px;padding:8px;color:#fff;text-align:center;text-decoration:none;background-color:#000;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.tooltip-arrow{position:absolute;width:0;height:0;border-color:transparent;border-style:solid}
.tooltip.top .tooltip-arrow{bottom:0;left:50%;margin-left:-5px;border-width:5px 5px 0;border-top-color:#000}
.tooltip.right .tooltip-arrow{top:50%;left:0;margin-top:-5px;border-width:5px 5px 5px 0;border-right-color:#000}
.tooltip.left .tooltip-arrow{top:50%;right:0;margin-top:-5px;border-width:5px 0 5px 5px;border-left-color:#000}
.tooltip.bottom .tooltip-arrow{top:0;left:50%;margin-left:-5px;border-width:0 5px 5px;border-bottom-color:#000}
.popover{position:absolute;top:0;left:0;z-index:1010;display:none;max-width:276px;padding:1px;text-align:left;background-color:#fff;-webkit-background-clip:padding-box;-moz-background-clip:padding;background-clip:padding-box;border:1px solid #ccc;border:1px solid rgba(0,0,0,0.2);-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px;-webkit-box-shadow:0 5px 10px rgba(0,0,0,0.2);-moz-box-shadow:0 5px 10px rgba(0,0,0,0.2);box-shadow:0 5px 10px rgba(0,0,0,0.2);white-space:normal}.popover.top{margin-top:-10px}
.popover.right{margin-left:10px}
.popover.bottom{margin-top:10px}
.popover.left{margin-left:-10px}
.popover-title{margin:0;padding:8px 14px;font-size:14px;font-weight:normal;line-height:18px;background-color:#f7f7f7;border-bottom:1px solid #ebebeb;border-radius:5px 5px 0 0;-webkit-border-radius:5px 5px 0 0;-moz-border-radius:5px 5px 0 0;border-radius:5px 5px 0 0}.popover-title:empty{display:none}
.popover-content{padding:9px 14px}
.popover .arrow,.popover .arrow:after{position:absolute;display:block;width:0;height:0;border-color:transparent;border-style:solid}
.popover .arrow{border-width:11px}
.popover .arrow:after{border-width:10px;content:""}
.popover.top .arrow{left:50%;margin-left:-11px;border-bottom-width:0;border-top-color:#999;border-top-color:rgba(0,0,0,0.25);bottom:-11px}.popover.top .arrow:after{bottom:1px;margin-left:-10px;border-bottom-width:0;border-top-color:#fff}
.popover.right .arrow{top:50%;left:-11px;margin-top:-11px;border-left-width:0;border-right-color:#999;border-right-color:rgba(0,0,0,0.25)}.popover.right .arrow:after{left:1px;bottom:-10px;border-left-width:0;border-right-color:#fff}
.popover.bottom .arrow{left:50%;margin-left:-11px;border-top-width:0;border-bottom-color:#999;border-bottom-color:rgba(0,0,0,0.25);top:-11px}.popover.bottom .arrow:after{top:1px;margin-left:-10px;border-top-width:0;border-bottom-color:#fff}
.popover.left .arrow{top:50%;right:-11px;margin-top:-11px;border-right-width:0;border-left-color:#999;border-left-color:rgba(0,0,0,0.25)}.popover.left .arrow:after{right:1px;border-right-width:0;border-left-color:#fff;bottom:-10px}
.thumbnails{margin-left:-20px;list-style:none;*zoom:1}.thumbnails:before,.thumbnails:after{display:table;content:"";line-height:0}
.thumbnails:after{clear:both}
.row-fluid .thumbnails{margin-left:0}
.thumbnails>li{float:left;margin-bottom:20px;margin-left:20px}
.thumbnail{display:block;padding:4px;line-height:20px;border:1px solid #ddd;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px;-webkit-box-shadow:0 1px 3px rgba(0,0,0,0.055);-moz-box-shadow:0 1px 3px rgba(0,0,0,0.055);box-shadow:0 1px 3px rgba(0,0,0,0.055);-webkit-transition:all .2s ease-in-out;-moz-transition:all .2s ease-in-out;-o-transition:all .2s ease-in-out;transition:all .2s ease-in-out}
a.thumbnail:hover,a.thumbnail:focus{border-color:#08c;-webkit-box-shadow:0 1px 4px rgba(0,105,214,0.25);-moz-box-shadow:0 1px 4px rgba(0,105,214,0.25);box-shadow:0 1px 4px rgba(0,105,214,0.25)}
.thumbnail>img{display:block;max-width:100%;margin-left:auto;margin-right:auto}
.thumbnail .caption{padding:9px;color:#555}
.media,.media-body{overflow:hidden;*overflow:visible;zoom:1}
.media,.media .media{margin-top:15px}
.media:first-child{margin-top:0}
.media-object{display:block}
.media-heading{margin:0 0 5px}
.media>.pull-left{margin-right:10px}
.media>.pull-right{margin-left:10px}
.media-list{margin-left:0;list-style:none}
.label,.badge{display:inline-block;padding:2px 4px;font-size:10.998px;font-weight:bold;line-height:14px;color:#fff;vertical-align:baseline;white-space:nowrap;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#999}
.label{border-radius:3px;-webkit-border-radius:3px;-moz-border-radius:3px;border-radius:3px}
.badge{padding-left:9px;padding-right:9px;border-radius:9px;-webkit-border-radius:9px;-moz-border-radius:9px;border-radius:9px}
.label:empty,.badge:empty{display:none}
a.label:hover,a.label:focus,a.badge:hover,a.badge:focus{color:#fff;text-decoration:none;cursor:pointer}
.label-important,.badge-important{background-color:#b94a48}
.label-important[href],.badge-important[href]{background-color:#953b39}
.label-warning,.badge-warning{background-color:#f89406}
.label-warning[href],.badge-warning[href]{background-color:#c67605}
.label-success,.badge-success{background-color:#468847}
.label-success[href],.badge-success[href]{background-color:#356635}
.label-info,.badge-info{background-color:#3a87ad}
.label-info[href],.badge-info[href]{background-color:#2d6987}
.label-inverse,.badge-inverse{background-color:#333}
.label-inverse[href],.badge-inverse[href]{background-color:#1a1a1a}
.btn .label,.btn .badge{position:relative;top:-1px}
.btn-mini .label,.btn-mini .badge{top:0}
@-webkit-keyframes progress-bar-stripes{from{background-position:40px 0} to{background-position:0 0}}@-moz-keyframes progress-bar-stripes{from{background-position:40px 0} to{background-position:0 0}}@-ms-keyframes progress-bar-stripes{from{background-position:40px 0} to{background-position:0 0}}@-o-keyframes progress-bar-stripes{from{background-position:0 0} to{background-position:40px 0}}@keyframes progress-bar-stripes{from{background-position:40px 0} to{background-position:0 0}}.progress{overflow:hidden;height:20px;margin-bottom:20px;background-color:#f7f7f7;background-image:-moz-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#f5f5f5), to(#f9f9f9));background-image:-webkit-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:-o-linear-gradient(top, #f5f5f5, #f9f9f9);background-image:linear-gradient(to bottom, #f5f5f5, #f9f9f9);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fff5f5f5', endColorstr='#fff9f9f9', GradientType=0);-webkit-box-shadow:inset 0 1px 2px rgba(0,0,0,0.1);-moz-box-shadow:inset 0 1px 2px rgba(0,0,0,0.1);box-shadow:inset 0 1px 2px rgba(0,0,0,0.1);border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.progress .bar{width:0;height:100%;color:#fff;float:left;font-size:12px;text-align:center;text-shadow:0 -1px 0 rgba(0,0,0,0.25);background-color:#0e90d2;background-image:-moz-linear-gradient(top, #149bdf, #0480be);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#149bdf), to(#0480be));background-image:-webkit-linear-gradient(top, #149bdf, #0480be);background-image:-o-linear-gradient(top, #149bdf, #0480be);background-image:linear-gradient(to bottom, #149bdf, #0480be);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff149bdf', endColorstr='#ff0480be', GradientType=0);-webkit-box-shadow:inset 0 -1px 0 rgba(0,0,0,0.15);-moz-box-shadow:inset 0 -1px 0 rgba(0,0,0,0.15);box-shadow:inset 0 -1px 0 rgba(0,0,0,0.15);-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box;-webkit-transition:width .6s ease;-moz-transition:width .6s ease;-o-transition:width .6s ease;transition:width .6s ease}
.progress .bar+.bar{-webkit-box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15);-moz-box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15);box-shadow:inset 1px 0 0 rgba(0,0,0,.15), inset 0 -1px 0 rgba(0,0,0,.15)}
.progress-striped .bar{background-color:#149bdf;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);-webkit-background-size:40px 40px;-moz-background-size:40px 40px;-o-background-size:40px 40px;background-size:40px 40px}
.progress.active .bar{-webkit-animation:progress-bar-stripes 2s linear infinite;-moz-animation:progress-bar-stripes 2s linear infinite;-ms-animation:progress-bar-stripes 2s linear infinite;-o-animation:progress-bar-stripes 2s linear infinite;animation:progress-bar-stripes 2s linear infinite}
.progress-danger .bar,.progress .bar-danger{background-color:#dd514c;background-image:-moz-linear-gradient(top, #ee5f5b, #c43c35);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#ee5f5b), to(#c43c35));background-image:-webkit-linear-gradient(top, #ee5f5b, #c43c35);background-image:-o-linear-gradient(top, #ee5f5b, #c43c35);background-image:linear-gradient(to bottom, #ee5f5b, #c43c35);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffee5f5b', endColorstr='#ffc43c35', GradientType=0)}
.progress-danger.progress-striped .bar,.progress-striped .bar-danger{background-color:#ee5f5b;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}
.progress-success .bar,.progress .bar-success{background-color:#5eb95e;background-image:-moz-linear-gradient(top, #62c462, #57a957);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#62c462), to(#57a957));background-image:-webkit-linear-gradient(top, #62c462, #57a957);background-image:-o-linear-gradient(top, #62c462, #57a957);background-image:linear-gradient(to bottom, #62c462, #57a957);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff62c462', endColorstr='#ff57a957', GradientType=0)}
.progress-success.progress-striped .bar,.progress-striped .bar-success{background-color:#62c462;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}
.progress-info .bar,.progress .bar-info{background-color:#4bb1cf;background-image:-moz-linear-gradient(top, #5bc0de, #339bb9);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#5bc0de), to(#339bb9));background-image:-webkit-linear-gradient(top, #5bc0de, #339bb9);background-image:-o-linear-gradient(top, #5bc0de, #339bb9);background-image:linear-gradient(to bottom, #5bc0de, #339bb9);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff5bc0de', endColorstr='#ff339bb9', GradientType=0)}
.progress-info.progress-striped .bar,.progress-striped .bar-info{background-color:#5bc0de;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}
.progress-warning .bar,.progress .bar-warning{background-color:#faa732;background-image:-moz-linear-gradient(top, #fbb450, #f89406);background-image:-webkit-gradient(linear, 0 0, 0 100%, from(#fbb450), to(#f89406));background-image:-webkit-linear-gradient(top, #fbb450, #f89406);background-image:-o-linear-gradient(top, #fbb450, #f89406);background-image:linear-gradient(to bottom, #fbb450, #f89406);background-repeat:repeat-x;filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#fffbb450', endColorstr='#fff89406', GradientType=0)}
.progress-warning.progress-striped .bar,.progress-striped .bar-warning{background-color:#fbb450;background-image:-webkit-gradient(linear, 0 100%, 100% 0, color-stop(.25, rgba(255,255,255,0.15)), color-stop(.25, transparent), color-stop(.5, transparent), color-stop(.5, rgba(255,255,255,0.15)), color-stop(.75, rgba(255,255,255,0.15)), color-stop(.75, transparent), to(transparent));background-image:-webkit-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-moz-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:-o-linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent)}
.accordion{margin-bottom:20px}
.accordion-group{margin-bottom:2px;border:1px solid #e5e5e5;border-radius:4px;-webkit-border-radius:4px;-moz-border-radius:4px;border-radius:4px}
.accordion-heading{border-bottom:0}
.accordion-heading .accordion-toggle{display:block;padding:8px 15px}
.accordion-toggle{cursor:pointer}
.accordion-inner{padding:9px 15px;border-top:1px solid #e5e5e5}
.carousel{position:relative;margin-bottom:20px;line-height:1}
.carousel-inner{overflow:hidden;width:100%;position:relative}
.carousel-inner>.item{display:none;position:relative;-webkit-transition:.6s ease-in-out left;-moz-transition:.6s ease-in-out left;-o-transition:.6s ease-in-out left;transition:.6s ease-in-out left}.carousel-inner>.item>img,.carousel-inner>.item>a>img{display:block;line-height:1}
.carousel-inner>.active,.carousel-inner>.next,.carousel-inner>.prev{display:block}
.carousel-inner>.active{left:0}
.carousel-inner>.next,.carousel-inner>.prev{position:absolute;top:0;width:100%}
.carousel-inner>.next{left:100%}
.carousel-inner>.prev{left:-100%}
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[class^="icon-"].pull-left,[class*=" icon-"].pull-left{margin-right:.3em}
[class^="icon-"].pull-right,[class*=" icon-"].pull-right{margin-left:.3em}
[class^="icon-"],[class*=" icon-"]{display:inline;width:auto;height:auto;line-height:normal;vertical-align:baseline;background-image:none;background-position:0 0;background-repeat:repeat;margin-top:0}
.icon-white,.nav-pills>.active>a>[class^="icon-"],.nav-pills>.active>a>[class*=" icon-"],.nav-list>.active>a>[class^="icon-"],.nav-list>.active>a>[class*=" icon-"],.navbar-inverse .nav>.active>a>[class^="icon-"],.navbar-inverse .nav>.active>a>[class*=" icon-"],.dropdown-menu>li>a:hover>[class^="icon-"],.dropdown-menu>li>a:hover>[class*=" icon-"],.dropdown-menu>.active>a>[class^="icon-"],.dropdown-menu>.active>a>[class*=" icon-"],.dropdown-submenu:hover>a>[class^="icon-"],.dropdown-submenu:hover>a>[class*=" icon-"]{background-image:none}
.btn [class^="icon-"].icon-large,.nav [class^="icon-"].icon-large,.btn [class*=" icon-"].icon-large,.nav [class*=" icon-"].icon-large{line-height:.9em}
.btn [class^="icon-"].icon-spin,.nav [class^="icon-"].icon-spin,.btn [class*=" icon-"].icon-spin,.nav [class*=" icon-"].icon-spin{display:inline-block}
.nav-tabs [class^="icon-"],.nav-pills [class^="icon-"],.nav-tabs [class*=" icon-"],.nav-pills [class*=" icon-"],.nav-tabs [class^="icon-"].icon-large,.nav-pills [class^="icon-"].icon-large,.nav-tabs [class*=" icon-"].icon-large,.nav-pills [class*=" icon-"].icon-large{line-height:.9em}
.btn [class^="icon-"].pull-left.icon-2x,.btn [class*=" icon-"].pull-left.icon-2x,.btn [class^="icon-"].pull-right.icon-2x,.btn [class*=" icon-"].pull-right.icon-2x{margin-top:.18em}
.btn [class^="icon-"].icon-spin.icon-large,.btn [class*=" icon-"].icon-spin.icon-large{line-height:.8em}
.btn.btn-small [class^="icon-"].pull-left.icon-2x,.btn.btn-small [class*=" icon-"].pull-left.icon-2x,.btn.btn-small [class^="icon-"].pull-right.icon-2x,.btn.btn-small [class*=" icon-"].pull-right.icon-2x{margin-top:.25em}
.btn.btn-large [class^="icon-"],.btn.btn-large [class*=" icon-"]{margin-top:0}.btn.btn-large [class^="icon-"].pull-left.icon-2x,.btn.btn-large [class*=" icon-"].pull-left.icon-2x,.btn.btn-large [class^="icon-"].pull-right.icon-2x,.btn.btn-large [class*=" icon-"].pull-right.icon-2x{margin-top:.05em}
.btn.btn-large [class^="icon-"].pull-left.icon-2x,.btn.btn-large [class*=" icon-"].pull-left.icon-2x{margin-right:.2em}
.btn.btn-large [class^="icon-"].pull-right.icon-2x,.btn.btn-large [class*=" icon-"].pull-right.icon-2x{margin-left:.2em}
.nav-list [class^="icon-"],.nav-list [class*=" icon-"]{line-height:inherit}
.icon-stack{position:relative;display:inline-block;width:2em;height:2em;line-height:2em;vertical-align:-35%}.icon-stack [class^="icon-"],.icon-stack [class*=" icon-"]{display:block;text-align:center;position:absolute;width:100%;height:100%;font-size:1em;line-height:inherit;*line-height:2em}
.icon-stack .icon-stack-base{font-size:2em;*line-height:1em}
.icon-spin{display:inline-block;-moz-animation:spin 2s infinite linear;-o-animation:spin 2s infinite linear;-webkit-animation:spin 2s infinite linear;animation:spin 2s infinite linear}
a .icon-stack,a .icon-spin{display:inline-block;text-decoration:none}
@-moz-keyframes spin{0%{-moz-transform:rotate(0deg)} 100%{-moz-transform:rotate(359deg)}}@-webkit-keyframes spin{0%{-webkit-transform:rotate(0deg)} 100%{-webkit-transform:rotate(359deg)}}@-o-keyframes spin{0%{-o-transform:rotate(0deg)} 100%{-o-transform:rotate(359deg)}}@-ms-keyframes spin{0%{-ms-transform:rotate(0deg)} 100%{-ms-transform:rotate(359deg)}}@keyframes spin{0%{transform:rotate(0deg)} 100%{transform:rotate(359deg)}}.icon-rotate-90:before{-webkit-transform:rotate(90deg);-moz-transform:rotate(90deg);-ms-transform:rotate(90deg);-o-transform:rotate(90deg);transform:rotate(90deg);filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=1)}
.icon-rotate-180:before{-webkit-transform:rotate(180deg);-moz-transform:rotate(180deg);-ms-transform:rotate(180deg);-o-transform:rotate(180deg);transform:rotate(180deg);filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=2)}
.icon-rotate-270:before{-webkit-transform:rotate(270deg);-moz-transform:rotate(270deg);-ms-transform:rotate(270deg);-o-transform:rotate(270deg);transform:rotate(270deg);filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=3)}
.icon-flip-horizontal:before{-webkit-transform:scale(-1, 1);-moz-transform:scale(-1, 1);-ms-transform:scale(-1, 1);-o-transform:scale(-1, 1);transform:scale(-1, 1)}
.icon-flip-vertical:before{-webkit-transform:scale(1, -1);-moz-transform:scale(1, -1);-ms-transform:scale(1, -1);-o-transform:scale(1, -1);transform:scale(1, -1)}
a .icon-rotate-90:before,a .icon-rotate-180:before,a .icon-rotate-270:before,a .icon-flip-horizontal:before,a .icon-flip-vertical:before{display:inline-block}
.icon-glass:before{content:"\f000"}
.icon-music:before{content:"\f001"}
.icon-search:before{content:"\f002"}
.icon-envelope-alt:before{content:"\f003"}
.icon-heart:before{content:"\f004"}
.icon-star:before{content:"\f005"}
.icon-star-empty:before{content:"\f006"}
.icon-user:before{content:"\f007"}
.icon-film:before{content:"\f008"}
.icon-th-large:before{content:"\f009"}
.icon-th:before{content:"\f00a"}
.icon-th-list:before{content:"\f00b"}
.icon-ok:before{content:"\f00c"}
.icon-remove:before{content:"\f00d"}
.icon-zoom-in:before{content:"\f00e"}
.icon-zoom-out:before{content:"\f010"}
.icon-power-off:before,.icon-off:before{content:"\f011"}
.icon-signal:before{content:"\f012"}
.icon-gear:before,.icon-cog:before{content:"\f013"}
.icon-trash:before{content:"\f014"}
.icon-home:before{content:"\f015"}
.icon-file-alt:before{content:"\f016"}
.icon-time:before{content:"\f017"}
.icon-road:before{content:"\f018"}
.icon-download-alt:before{content:"\f019"}
.icon-download:before{content:"\f01a"}
.icon-upload:before{content:"\f01b"}
.icon-inbox:before{content:"\f01c"}
.icon-play-circle:before{content:"\f01d"}
.icon-rotate-right:before,.icon-repeat:before{content:"\f01e"}
.icon-refresh:before{content:"\f021"}
.icon-list-alt:before{content:"\f022"}
.icon-lock:before{content:"\f023"}
.icon-flag:before{content:"\f024"}
.icon-headphones:before{content:"\f025"}
.icon-volume-off:before{content:"\f026"}
.icon-volume-down:before{content:"\f027"}
.icon-volume-up:before{content:"\f028"}
.icon-qrcode:before{content:"\f029"}
.icon-barcode:before{content:"\f02a"}
.icon-tag:before{content:"\f02b"}
.icon-tags:before{content:"\f02c"}
.icon-book:before{content:"\f02d"}
.icon-bookmark:before{content:"\f02e"}
.icon-print:before{content:"\f02f"}
.icon-camera:before{content:"\f030"}
.icon-font:before{content:"\f031"}
.icon-bold:before{content:"\f032"}
.icon-italic:before{content:"\f033"}
.icon-text-height:before{content:"\f034"}
.icon-text-width:before{content:"\f035"}
.icon-align-left:before{content:"\f036"}
.icon-align-center:before{content:"\f037"}
.icon-align-right:before{content:"\f038"}
.icon-align-justify:before{content:"\f039"}
.icon-list:before{content:"\f03a"}
.icon-indent-left:before{content:"\f03b"}
.icon-indent-right:before{content:"\f03c"}
.icon-facetime-video:before{content:"\f03d"}
.icon-picture:before{content:"\f03e"}
.icon-pencil:before{content:"\f040"}
.icon-map-marker:before{content:"\f041"}
.icon-adjust:before{content:"\f042"}
.icon-tint:before{content:"\f043"}
.icon-edit:before{content:"\f044"}
.icon-share:before{content:"\f045"}
.icon-check:before{content:"\f046"}
.icon-move:before{content:"\f047"}
.icon-step-backward:before{content:"\f048"}
.icon-fast-backward:before{content:"\f049"}
.icon-backward:before{content:"\f04a"}
.icon-play:before{content:"\f04b"}
.icon-pause:before{content:"\f04c"}
.icon-stop:before{content:"\f04d"}
.icon-forward:before{content:"\f04e"}
.icon-fast-forward:before{content:"\f050"}
.icon-step-forward:before{content:"\f051"}
.icon-eject:before{content:"\f052"}
.icon-chevron-left:before{content:"\f053"}
.icon-chevron-right:before{content:"\f054"}
.icon-plus-sign:before{content:"\f055"}
.icon-minus-sign:before{content:"\f056"}
.icon-remove-sign:before{content:"\f057"}
.icon-ok-sign:before{content:"\f058"}
.icon-question-sign:before{content:"\f059"}
.icon-info-sign:before{content:"\f05a"}
.icon-screenshot:before{content:"\f05b"}
.icon-remove-circle:before{content:"\f05c"}
.icon-ok-circle:before{content:"\f05d"}
.icon-ban-circle:before{content:"\f05e"}
.icon-arrow-left:before{content:"\f060"}
.icon-arrow-right:before{content:"\f061"}
.icon-arrow-up:before{content:"\f062"}
.icon-arrow-down:before{content:"\f063"}
.icon-mail-forward:before,.icon-share-alt:before{content:"\f064"}
.icon-resize-full:before{content:"\f065"}
.icon-resize-small:before{content:"\f066"}
.icon-plus:before{content:"\f067"}
.icon-minus:before{content:"\f068"}
.icon-asterisk:before{content:"\f069"}
.icon-exclamation-sign:before{content:"\f06a"}
.icon-gift:before{content:"\f06b"}
.icon-leaf:before{content:"\f06c"}
.icon-fire:before{content:"\f06d"}
.icon-eye-open:before{content:"\f06e"}
.icon-eye-close:before{content:"\f070"}
.icon-warning-sign:before{content:"\f071"}
.icon-plane:before{content:"\f072"}
.icon-calendar:before{content:"\f073"}
.icon-random:before{content:"\f074"}
.icon-comment:before{content:"\f075"}
.icon-magnet:before{content:"\f076"}
.icon-chevron-up:before{content:"\f077"}
.icon-chevron-down:before{content:"\f078"}
.icon-retweet:before{content:"\f079"}
.icon-shopping-cart:before{content:"\f07a"}
.icon-folder-close:before{content:"\f07b"}
.icon-folder-open:before{content:"\f07c"}
.icon-resize-vertical:before{content:"\f07d"}
.icon-resize-horizontal:before{content:"\f07e"}
.icon-bar-chart:before{content:"\f080"}
.icon-twitter-sign:before{content:"\f081"}
.icon-facebook-sign:before{content:"\f082"}
.icon-camera-retro:before{content:"\f083"}
.icon-key:before{content:"\f084"}
.icon-gears:before,.icon-cogs:before{content:"\f085"}
.icon-comments:before{content:"\f086"}
.icon-thumbs-up-alt:before{content:"\f087"}
.icon-thumbs-down-alt:before{content:"\f088"}
.icon-star-half:before{content:"\f089"}
.icon-heart-empty:before{content:"\f08a"}
.icon-signout:before{content:"\f08b"}
.icon-linkedin-sign:before{content:"\f08c"}
.icon-pushpin:before{content:"\f08d"}
.icon-external-link:before{content:"\f08e"}
.icon-signin:before{content:"\f090"}
.icon-trophy:before{content:"\f091"}
.icon-github-sign:before{content:"\f092"}
.icon-upload-alt:before{content:"\f093"}
.icon-lemon:before{content:"\f094"}
.icon-phone:before{content:"\f095"}
.icon-unchecked:before,.icon-check-empty:before{content:"\f096"}
.icon-bookmark-empty:before{content:"\f097"}
.icon-phone-sign:before{content:"\f098"}
.icon-twitter:before{content:"\f099"}
.icon-facebook:before{content:"\f09a"}
.icon-github:before{content:"\f09b"}
.icon-unlock:before{content:"\f09c"}
.icon-credit-card:before{content:"\f09d"}
.icon-rss:before{content:"\f09e"}
.icon-hdd:before{content:"\f0a0"}
.icon-bullhorn:before{content:"\f0a1"}
.icon-bell:before{content:"\f0a2"}
.icon-certificate:before{content:"\f0a3"}
.icon-hand-right:before{content:"\f0a4"}
.icon-hand-left:before{content:"\f0a5"}
.icon-hand-up:before{content:"\f0a6"}
.icon-hand-down:before{content:"\f0a7"}
.icon-circle-arrow-left:before{content:"\f0a8"}
.icon-circle-arrow-right:before{content:"\f0a9"}
.icon-circle-arrow-up:before{content:"\f0aa"}
.icon-circle-arrow-down:before{content:"\f0ab"}
.icon-globe:before{content:"\f0ac"}
.icon-wrench:before{content:"\f0ad"}
.icon-tasks:before{content:"\f0ae"}
.icon-filter:before{content:"\f0b0"}
.icon-briefcase:before{content:"\f0b1"}
.icon-fullscreen:before{content:"\f0b2"}
.icon-group:before{content:"\f0c0"}
.icon-link:before{content:"\f0c1"}
.icon-cloud:before{content:"\f0c2"}
.icon-beaker:before{content:"\f0c3"}
.icon-cut:before{content:"\f0c4"}
.icon-copy:before{content:"\f0c5"}
.icon-paperclip:before,.icon-paper-clip:before{content:"\f0c6"}
.icon-save:before{content:"\f0c7"}
.icon-sign-blank:before{content:"\f0c8"}
.icon-reorder:before{content:"\f0c9"}
.icon-list-ul:before{content:"\f0ca"}
.icon-list-ol:before{content:"\f0cb"}
.icon-strikethrough:before{content:"\f0cc"}
.icon-underline:before{content:"\f0cd"}
.icon-table:before{content:"\f0ce"}
.icon-magic:before{content:"\f0d0"}
.icon-truck:before{content:"\f0d1"}
.icon-pinterest:before{content:"\f0d2"}
.icon-pinterest-sign:before{content:"\f0d3"}
.icon-google-plus-sign:before{content:"\f0d4"}
.icon-google-plus:before{content:"\f0d5"}
.icon-money:before{content:"\f0d6"}
.icon-caret-down:before{content:"\f0d7"}
.icon-caret-up:before{content:"\f0d8"}
.icon-caret-left:before{content:"\f0d9"}
.icon-caret-right:before{content:"\f0da"}
.icon-columns:before{content:"\f0db"}
.icon-sort:before{content:"\f0dc"}
.icon-sort-down:before{content:"\f0dd"}
.icon-sort-up:before{content:"\f0de"}
.icon-envelope:before{content:"\f0e0"}
.icon-linkedin:before{content:"\f0e1"}
.icon-rotate-left:before,.icon-undo:before{content:"\f0e2"}
.icon-legal:before{content:"\f0e3"}
.icon-dashboard:before{content:"\f0e4"}
.icon-comment-alt:before{content:"\f0e5"}
.icon-comments-alt:before{content:"\f0e6"}
.icon-bolt:before{content:"\f0e7"}
.icon-sitemap:before{content:"\f0e8"}
.icon-umbrella:before{content:"\f0e9"}
.icon-paste:before{content:"\f0ea"}
.icon-lightbulb:before{content:"\f0eb"}
.icon-exchange:before{content:"\f0ec"}
.icon-cloud-download:before{content:"\f0ed"}
.icon-cloud-upload:before{content:"\f0ee"}
.icon-user-md:before{content:"\f0f0"}
.icon-stethoscope:before{content:"\f0f1"}
.icon-suitcase:before{content:"\f0f2"}
.icon-bell-alt:before{content:"\f0f3"}
.icon-coffee:before{content:"\f0f4"}
.icon-food:before{content:"\f0f5"}
.icon-file-text-alt:before{content:"\f0f6"}
.icon-building:before{content:"\f0f7"}
.icon-hospital:before{content:"\f0f8"}
.icon-ambulance:before{content:"\f0f9"}
.icon-medkit:before{content:"\f0fa"}
.icon-fighter-jet:before{content:"\f0fb"}
.icon-beer:before{content:"\f0fc"}
.icon-h-sign:before{content:"\f0fd"}
.icon-plus-sign-alt:before{content:"\f0fe"}
.icon-double-angle-left:before{content:"\f100"}
.icon-double-angle-right:before{content:"\f101"}
.icon-double-angle-up:before{content:"\f102"}
.icon-double-angle-down:before{content:"\f103"}
.icon-angle-left:before{content:"\f104"}
.icon-angle-right:before{content:"\f105"}
.icon-angle-up:before{content:"\f106"}
.icon-angle-down:before{content:"\f107"}
.icon-desktop:before{content:"\f108"}
.icon-laptop:before{content:"\f109"}
.icon-tablet:before{content:"\f10a"}
.icon-mobile-phone:before{content:"\f10b"}
.icon-circle-blank:before{content:"\f10c"}
.icon-quote-left:before{content:"\f10d"}
.icon-quote-right:before{content:"\f10e"}
.icon-spinner:before{content:"\f110"}
.icon-circle:before{content:"\f111"}
.icon-mail-reply:before,.icon-reply:before{content:"\f112"}
.icon-github-alt:before{content:"\f113"}
.icon-folder-close-alt:before{content:"\f114"}
.icon-folder-open-alt:before{content:"\f115"}
.icon-expand-alt:before{content:"\f116"}
.icon-collapse-alt:before{content:"\f117"}
.icon-smile:before{content:"\f118"}
.icon-frown:before{content:"\f119"}
.icon-meh:before{content:"\f11a"}
.icon-gamepad:before{content:"\f11b"}
.icon-keyboard:before{content:"\f11c"}
.icon-flag-alt:before{content:"\f11d"}
.icon-flag-checkered:before{content:"\f11e"}
.icon-terminal:before{content:"\f120"}
.icon-code:before{content:"\f121"}
.icon-reply-all:before{content:"\f122"}
.icon-mail-reply-all:before{content:"\f122"}
.icon-star-half-full:before,.icon-star-half-empty:before{content:"\f123"}
.icon-location-arrow:before{content:"\f124"}
.icon-crop:before{content:"\f125"}
.icon-code-fork:before{content:"\f126"}
.icon-unlink:before{content:"\f127"}
.icon-question:before{content:"\f128"}
.icon-info:before{content:"\f129"}
.icon-exclamation:before{content:"\f12a"}
.icon-superscript:before{content:"\f12b"}
.icon-subscript:before{content:"\f12c"}
.icon-eraser:before{content:"\f12d"}
.icon-puzzle-piece:before{content:"\f12e"}
.icon-microphone:before{content:"\f130"}
.icon-microphone-off:before{content:"\f131"}
.icon-shield:before{content:"\f132"}
.icon-calendar-empty:before{content:"\f133"}
.icon-fire-extinguisher:before{content:"\f134"}
.icon-rocket:before{content:"\f135"}
.icon-maxcdn:before{content:"\f136"}
.icon-chevron-sign-left:before{content:"\f137"}
.icon-chevron-sign-right:before{content:"\f138"}
.icon-chevron-sign-up:before{content:"\f139"}
.icon-chevron-sign-down:before{content:"\f13a"}
.icon-html5:before{content:"\f13b"}
.icon-css3:before{content:"\f13c"}
.icon-anchor:before{content:"\f13d"}
.icon-unlock-alt:before{content:"\f13e"}
.icon-bullseye:before{content:"\f140"}
.icon-ellipsis-horizontal:before{content:"\f141"}
.icon-ellipsis-vertical:before{content:"\f142"}
.icon-rss-sign:before{content:"\f143"}
.icon-play-sign:before{content:"\f144"}
.icon-ticket:before{content:"\f145"}
.icon-minus-sign-alt:before{content:"\f146"}
.icon-check-minus:before{content:"\f147"}
.icon-level-up:before{content:"\f148"}
.icon-level-down:before{content:"\f149"}
.icon-check-sign:before{content:"\f14a"}
.icon-edit-sign:before{content:"\f14b"}
.icon-external-link-sign:before{content:"\f14c"}
.icon-share-sign:before{content:"\f14d"}
.icon-compass:before{content:"\f14e"}
.icon-collapse:before{content:"\f150"}
.icon-collapse-top:before{content:"\f151"}
.icon-expand:before{content:"\f152"}
.icon-euro:before,.icon-eur:before{content:"\f153"}
.icon-gbp:before{content:"\f154"}
.icon-dollar:before,.icon-usd:before{content:"\f155"}
.icon-rupee:before,.icon-inr:before{content:"\f156"}
.icon-yen:before,.icon-jpy:before{content:"\f157"}
.icon-renminbi:before,.icon-cny:before{content:"\f158"}
.icon-won:before,.icon-krw:before{content:"\f159"}
.icon-bitcoin:before,.icon-btc:before{content:"\f15a"}
.icon-file:before{content:"\f15b"}
.icon-file-text:before{content:"\f15c"}
.icon-sort-by-alphabet:before{content:"\f15d"}
.icon-sort-by-alphabet-alt:before{content:"\f15e"}
.icon-sort-by-attributes:before{content:"\f160"}
.icon-sort-by-attributes-alt:before{content:"\f161"}
.icon-sort-by-order:before{content:"\f162"}
.icon-sort-by-order-alt:before{content:"\f163"}
.icon-thumbs-up:before{content:"\f164"}
.icon-thumbs-down:before{content:"\f165"}
.icon-youtube-sign:before{content:"\f166"}
.icon-youtube:before{content:"\f167"}
.icon-xing:before{content:"\f168"}
.icon-xing-sign:before{content:"\f169"}
.icon-youtube-play:before{content:"\f16a"}
.icon-dropbox:before{content:"\f16b"}
.icon-stackexchange:before{content:"\f16c"}
.icon-instagram:before{content:"\f16d"}
.icon-flickr:before{content:"\f16e"}
.icon-adn:before{content:"\f170"}
.icon-bitbucket:before{content:"\f171"}
.icon-bitbucket-sign:before{content:"\f172"}
.icon-tumblr:before{content:"\f173"}
.icon-tumblr-sign:before{content:"\f174"}
.icon-long-arrow-down:before{content:"\f175"}
.icon-long-arrow-up:before{content:"\f176"}
.icon-long-arrow-left:before{content:"\f177"}
.icon-long-arrow-right:before{content:"\f178"}
.icon-apple:before{content:"\f179"}
.icon-windows:before{content:"\f17a"}
.icon-android:before{content:"\f17b"}
.icon-linux:before{content:"\f17c"}
.icon-dribbble:before{content:"\f17d"}
.icon-skype:before{content:"\f17e"}
.icon-foursquare:before{content:"\f180"}
.icon-trello:before{content:"\f181"}
.icon-female:before{content:"\f182"}
.icon-male:before{content:"\f183"}
.icon-gittip:before{content:"\f184"}
.icon-sun:before{content:"\f185"}
.icon-moon:before{content:"\f186"}
.icon-archive:before{content:"\f187"}
.icon-bug:before{content:"\f188"}
.icon-vk:before{content:"\f189"}
.icon-weibo:before{content:"\f18a"}
.icon-renren:before{content:"\f18b"}
code{color:#000}
pre{font-size:inherit;line-height:inherit}
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<body>
<div class="reveal">
<div class="slides">
-<section>
- <section>
+<div style=display:none>
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+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
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+In&nbsp;[1]:
</div>
<div class="inner_cell">
-<div class="text_cell_render border-box-sizing rendered_html">
-<h1 id="-A-New-Probability-Calculus-"><center> A New Probability Calculus </center><a class="anchor-link" href="#-A-New-Probability-Calculus-">&#182;</a></h1>
+ <div class="input_area">
+<div class="highlight"><pre><span class="kn">import</span> <span class="nn">sys</span>
+<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="s">&#39;..&#39;</span>
+<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">time</span>
+<span class="kn">import</span> <span class="nn">bisect</span>
+<span class="kn">import</span> <span class="nn">operator</span> <span class="kn">as</span> <span class="nn">op</span>
+
+<span class="kn">from</span> <span class="nn">utilities</span> <span class="kn">import</span> <span class="n">settings</span>
+<span class="kn">import</span> <span class="nn">utilities.sampleFunctions</span> <span class="kn">as</span> <span class="nn">funcs</span>
+<span class="kn">import</span> <span class="nn">utilities.probCalc</span> <span class="kn">as</span> <span class="nn">pc</span>
+<span class="kn">import</span> <span class="nn">utilities.plotting</span> <span class="kn">as</span> <span class="nn">debinPlot</span>
+<span class="kn">import</span> <span class="nn">utilities.minimizers</span> <span class="kn">as</span> <span class="nn">miniz</span>
+<span class="nb">reload</span><span class="p">(</span><span class="n">funcs</span><span class="p">)</span>
+<span class="nb">reload</span><span class="p">(</span><span class="n">pc</span><span class="p">)</span>
+<span class="nb">reload</span><span class="p">(</span><span class="n">debinPlot</span><span class="p">)</span>
+<span class="nb">reload</span><span class="p">(</span><span class="n">miniz</span><span class="p">)</span>
+
+<span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
+<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
+<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">HTML</span>
+</pre></div>
+
+</div>
</div>
</div>
+
</div>
+</div>
+ </div></section>
+ </section><section>
+ <section>
+
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<h3 id="-Abram-Krislock$^{[1]}$-and-Nathan-Krislock$^{[2]}$-"><center> Abram Krislock$^{[1]}$ and Nathan Krislock$^{[2]}$ </center><a class="anchor-link" href="#-Abram-Krislock$^{[1]}$-and-Nathan-Krislock$^{[2]}$-">&#182;</a></h3>
+<h1 id="-center-debinning-data-smoothing-with-a-new-probability-calculus-center-"><center> debinning: Data Smoothing with a New Probability Calculus </center></h1>
</div>
</div>
</div>
-
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<h4 id="-$^{[1]}$-Fysisk-institutt,-Universitetet-i-Oslo.------a.m.b.krislock@fys.uio.no-"><center> $^{[1]}$ Fysisk institutt, Universitetet i Oslo. </center> <center> <a href="mailto:a.m.b.krislock@fys.uio.no" title="Email Abram">a.m.b.krislock@fys.uio.no</a> </center><a class="anchor-link" href="#-$^{[1]}$-Fysisk-institutt,-Universitetet-i-Oslo.------a.m.b.krislock@fys.uio.no-">&#182;</a></h4>
+<h2 id="-center-abram-krislock-center-"><center> Abram Krislock </center></h2>
</div>
</div>
</div>
-
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<h4 id="-$^{[2]}$-Department-of-Mathematical-Sciences,-Northern-Illinois-University.------krislock@math.niu.edu-"><center> $^{[2]}$ Department of Mathematical Sciences, Northern Illinois University. </center> <center> <a href="mailto:krislock@math.niu.edu" title="Email Nathan">krislock@math.niu.edu</a> </center><a class="anchor-link" href="#-$^{[2]}$-Department-of-Mathematical-Sciences,-Northern-Illinois-University.------krislock@math.niu.edu-">&#182;</a></h4>
+<h3 id="-center-fysisk-institutt-universitetet-i-oslo-center-"><center> Fysisk institutt, Universitetet i Oslo. </center></h3>
+<h3 id="-center-a-m-b-krislock-fys-uio-no-mailto-a-m-b-krislock-fys-uio-no-email-abram-center-"><center> <a href="mailto:a.m.b.krislock@fys.uio.no" title="Email Abram">a.m.b.krislock@fys.uio.no</a> </center></h3>
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<p>Set some useful LaTeX commands for later in the document:
$ \newcommand{\Int}[2] {\displaystyle \int\limits_{#1}^{#2}} $
$ \newcommand{\Prod}[2] {\displaystyle \prod\limits_{#1}^{#2}} $
$ \newcommand{\Sum}[2] {\displaystyle \sum\limits_{#1}^{#2}} $ </p>
<h3 id="-int-lower-upper-3-prod-lower-upper-4-sum-lower-upper-5-">\Int{lower}{upper} : $ \Int{lower}{upper},\qquad $ \Prod{lower}{upper} : $ \Prod{lower}{upper},\qquad $ \Sum{lower}{upper} : $ \Sum{lower}{upper} $</h3>
-<p>$ \newcommand{subNsubR}[3] {{}_{#1} {#2}_{#3}} $</p>
-<h3 id="-subnsubr-n-k-r-7-">\subNsubR{n}{K}{r} : $ \subNsubR{n}{K}{r} $</h3>
+<p>$ \newcommand{subNsubR}[3] {{}_{#1} #2_{#3}} $
+$ \newcommand{rust}[1] {{\require{color}\color{Bittersweet}#1}} $
+$ \newcommand{sky}[1] {{\require{color}\color{SkyBlue}#1}} $</p>
+<h3 id="-subnsubr-n-k-r-9-rust-q-10-sky-q-11-">\subNsubR{n}{K}{r} : $ \subNsubR{n}{K}{r},\qquad $ \rust{q} : $ \rust{q},\qquad $ \sky{q} : $ \sky{q} $</h3>
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-<h2 id="Motivation">Motivation<a class="anchor-link" href="#Motivation">&#182;</a></h2>
+<h2 id="Once-Upon-A-Time...">Once Upon A Time...<a class="anchor-link" href="#Once-Upon-A-Time...">&#182;</a></h2>
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-<h2 id="Probability-of-Datum-and-Data-Samples">Probability of Datum and Data Samples<a class="anchor-link" href="#Probability-of-Datum-and-Data-Samples">&#182;</a></h2>
+<h2 id="We-knew-all-the-stuff!">We knew all the stuff!<a class="anchor-link" href="#We-knew-all-the-stuff!">&#182;</a></h2>
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-<h2 id="basic-datum-probability">Basic Datum Probability</h2>
-<p>Suppose we draw some data (experimental or simulated) for some physical observable, $x$. </p>
-<p>This data will follow some probability distribution function (PDF).</p>
+<h3 id="-at-the-end-of-the-19th-century-it-was-generally-accepted-that-all-the-important-laws-of-physics-had-been-discovered-source-http-en-wikipedia-org-wiki-history_of_physics-http-en-wikipedia-org-wiki-history_of_physics-">&quot;At the end of the 19th century... it was generally accepted that all the important laws of physics had been discovered...&quot; (<a href="http://en.wikipedia.org/wiki/History_of_physics" title="http://en.wikipedia.org/wiki/History_of_physics">Source</a>)</h3>
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-<p>The PDF, which we will call $f(x)$, gives the probability for a datum to lie between $x$ and $x + dx$. Thus,</p>
-<p>$$ P(\tilde{x}\in[x,x+dx]) = f(x) dx \qquad {\rm and} \qquad \Int{-\infty}{\infty} f(x) dx = 1~. $$</p>
+<h3 id="then-this-stuff-happened-">Then this stuff happened:</h3>
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-<hr>
-<p>The cumulative distribution function (CDF) is the anti-derivative of the PDF: </p>
-<p>$$ \Int{-\infty}{x} f(\tilde{x}) d\tilde{x} \equiv F(x)~. $$</p>
-<p>It represents the probability to draw some value less than or equal to $x$.</p>
+<p>$${\huge{\rm He}^{++},~{\rm e}^-,~\gamma \qquad\qquad \hbar \qquad\qquad g^{\mu\nu}}$$</p>
+<p>$${\huge E^2 = (mc^2)^2 + (pc)^2}$$</p>
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-<p>$$ \Int{x}{\infty} f(\tilde{x}) d\tilde{x} \equiv 1 - F(x)~. $$</p>
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+<p>$${\Large \cdots {\rm SU}(3)_C \times {\rm SU}(2)_L \times {\rm U}(1)_Y}$$</p>
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-<h2 id="samples-i-probability-density">Samples - I: Probability Density</h2>
-<p>Let us define a sample of data as $\{x_1, x_2, x_3 \cdots\}$, or just $\{x_i\}_{i=1}^n$ for a general sample with n data points.</p>
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-<p>WLOG, let us take $x_i &gt; x_j$ for any $i &gt; j$.</p>
+<h3 id="okay-but-after-that-surely-we-knew-all-the-stuff-">Okay... But after that... Surely, we knew all the stuff!</h3>
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-<p>\begin{align}
- P(\{x_1\}\ d\{x_1\} &amp;= f(x_1) dx_1 \\
- P(\{x_1, x_2\})\ d\{x_1, x_2\} &amp;= 2 \times f(x_1) dx_1 f(x_2) dx_2 \\
- P(\{x_1, x_2, x_3\})\ d\{x_1, x_2, x_3\} &amp;= 3! \times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3
-\end{align}</p>
+<h2 id="Well,-actually....">Well, actually....<a class="anchor-link" href="#Well,-actually....">&#182;</a></h2>
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-<p>\begin{align}
- &amp;{\phantom=}\mkern-17mu\vdots \\
- P(\{x_i\}_{i=1}^n) d\{x_i\}_{i=1}^n &amp;= n! \Prod{i = 1}{n} f(x_i) dx_i \\
- \phantom{d^3P(\{x_1, x_2, x_3\} \equiv \{x_1, x_3, x_2\}\cdots)} &amp;\phantom{= 3! \times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}
-\end{align}</p>
+<h3 id="then-this-stuff-happened-">Then this stuff happened:</h3>
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-<h2 id="samples-ii-integration">Samples - II: Integration</h2>
-<p>Since the sorted data is the most general, we must have care with integration limits:</p>
+<p><img src="stuffWeKnow.png" alt="We know almost nothing." title="We know almost nothing."></p>
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-<p>$$ \Int{\{x_1\}_1}{} dP(\{x_1\}_1) = \Int{-\infty}{\infty} f(x_1) dx_1 = 1 $$</p>
+<h2 id="Let's-face-it.">Let's face it.<a class="anchor-link" href="#Let's-face-it.">&#182;</a></h2>
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-<p>$$ \Int{\{x_2\}_2}{} dP(\{x_1, x_2\}_2) = 2 \times \Int{-\infty}{\infty} f(x_2) \left[ \Int{-\infty}{x_2} f(x_1) dx_1 \right] dx_2, $$</p>
+<h3 id="large-hadron-collider-a-new-stuff-experiment">Large Hadron Collider: A &quot;New Stuff&quot; Experiment</h3>
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-<p>$$ \Int{\{x_3\}_3}{} dP(\{x_1, x_2, x_3\}_3) = 3! \times \Int{-\infty}{\infty} f(x_3) \left[ \Int{-\infty}{x_3} f(x_2) \left( \Int{-\infty}{x_2} f(x_1) dx_1 \right) dx_2 \right] dx_3 $$
-$$ \vdots $$</p>
+<p><img src="epicLHCHighFive.png" alt="New stuff experiment!" title="New stuff experiment!"></p>
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-<h2 id="samples-iii-to-be-0-th-out-of-1-">Samples - III: To be $r$th out of $n$...</h2>
-<p>Let us define a new notation:</p>
+<h2 id="Dark-Matter-@-Large-Hadron-Collider">Dark Matter @ Large Hadron Collider<a class="anchor-link" href="#Dark-Matter-@-Large-Hadron-Collider">&#182;</a></h2>
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+</div>
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-<p>$$ {\Large \subNsubR{n}{f}{r} \left[g\left(\{x_i\}_n\right)\right] dx_r \equiv \Int{\{x_{i \neq r}\}_n}{} g\left(\{x_i\}_n\right) dP(\{x_i\}_n) } $$ </p>
-<p>Interpretation: The expectation value of the function $g(\{x_i\}_n)$ as a function of the $r$th point of the sorted sample.</p>
+<p>\begin{align}
+ {\Huge \widetilde{q_L}} &amp; {\Huge\rightarrow} &amp; {\Huge \rust{q}} \\
+ &amp; {\Huge\searrow} \\
+ &amp; &amp; {\Huge\widetilde{\chi}^0_2} &amp; {\Huge\rightarrow} &amp; {\Huge h^0} &amp; {\Huge\rightarrow} &amp; {\Huge \rust{b}}\\
+ &amp; &amp; &amp; {\Huge\searrow} &amp; &amp; {\Huge \hookrightarrow} &amp; {\Huge \rust{b}} \\
+ &amp; &amp; &amp; &amp; {\Huge \color{Gray}{\widetilde{\chi}^0_1}}
+\end{align}</p>
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-<p>Then, $\subNsubR{n}{f}{r} \left[1\right]$ is just the PDF of the $r$th data point for any sample of $n$ data points. Let us call it $\subNsubR{n}{f}{r}(x_r)$.</p>
-<p>Theorem:</p>
-<p>$$ {\Large \subNsubR{n}{f}{r}(x_r) = \subNsubR{n}{K}{r}\ f(x_r) F^{r-1}(x_r) \left(1 - F(x_r)\right)^{n-r} }. $$</p>
+<h3 id="calculate-as-one-particle-the-mass-">Calculate as one particle, the mass:</h3>
+<p>$${\huge m_{\rust{q h^0}} \qquad {\rm using} \qquad E^2 = (mc^2)^2 + (pc)^2}$$</p>
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-<h2 id="samples-iv-to-be-0-th-out-of-1-cont-d-">Samples - IV: To be $r$th out of $n$ (cont&#39;d)...</h2>
-<p>Suppose $n$ identical siblings have a race. Suppose we only care about who came in $r$th place.
-If we sorted them all: $n!$ But then we&#39;ve overcounted, since we don&#39;t care who is 1st through $(r-1)$th, or who is $(r+1)$th through Nth.</p>
-<p>$$ {}_nK_r \equiv \frac{n!}{(n-r)!(r-1)!} $$</p>
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-<p>Our sample is just like this, except that there is a certain probability to get $x_r$, as well as the probability to get $r-1$ points less than $x_r$ and $n-r$ points greater than $x_r$ in the sample. </p>
-<p>$$ {\Large \therefore \quad \subNsubR{n}{f}{r}(x_r) = \subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \left(1 - F(x_r)\right)^{n-r} }. $$</p>
+<h2 id="The-$m_{\rust{qh^0}}$-Maximum-Measurement">The $m_{\rust{qh^0}}$ Maximum Measurement<a class="anchor-link" href="#The-$m_{\rust{qh^0}}$-Maximum-Measurement">&#182;</a></h2>
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-<p>If that was too much magic for anyone, the proof is down on sub-slides.</p>
+<p><img src="tryChangingTheBins.png" alt="You want me to try.... What?!" title="You want me to try.... What?!"></p>
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-<p>Proof:</p>
-<p>$$ \subNsubR{n}{f}{r}(x_r) dx_r = \Int{\{x_{i \neq r}\}_n}{} dP(\{x_i\}_n) = n! \Int{-\infty}{x_r} f(x_{r-1}) \Int{-\infty}{x_{r-1}} f(x_{r-2}) \cdots \Int{-\infty}{x_2} f(x_1) \Prod{i=1}{r-1} dx_i $$</p>
-<p>$$ \times f(x_r) dx_r \Int{x_r}{\infty} f(x_{r+1}) \Int{x_{r+1}}{\infty} f(x_{r+2}) \cdots \Int{x_{n-1}}{\infty} f(x_n) \Prod{j=r+1}{n} dx_j $$</p>
-</div>
+<h3 id="change-the-bins-seriously-">Change the... bins? Seriously?!</h3>
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-<p>$\phantom{Integration by parts:}$</p>
-<p>$$ \phantom{\Int{-\infty}{x} f(\widetilde{x}) F^{a-1}(\widetilde{x}) d\widetilde{x} = \frac{1}{a} F^a(x) \qquad {\rm and} \qquad
-\Int{x}{\infty} f(\widetilde{x}) \left(1 - F(\widetilde{x})\right)^{a-1} d\widetilde{x} = \frac{1}{a} \left(1 - F(\widetilde{x})\right)^a } $$</p>
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-<p>Proof:</p>
-<p>$$ \subNsubR{n}{f}{r}(x_r) dx_r = \Int{\{x_{i \neq r}\}_n}{} dP(\{x_i\}_n) = n! \Int{-\infty}{x_r} f(x_{r-1}) \Int{-\infty}{x_{r-1}} f(x_{r-2}) \cdots \Int{-\infty}{x_3} f(x_2) F(x_2) \Prod{i=2}{r-1} dx_i $$</p>
-<p>$$ \times f(x_r) dx_r \Int{x_r}{\infty} f(x_{r+1}) \Int{x_{r+1}}{\infty} f(x_{r+2}) \cdots \Int{x_{n-2}}{\infty} f(x_{n-1}) \left(1 - F(x_{n-1})\right) \Prod{j=r+1}{n-1} dx_j $$</p>
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-<p>Integration by parts:</p>
-<p>$$ \Int{-\infty}{x} f(\widetilde{x}) F^{a-1}(\widetilde{x}) d\widetilde{x} = \frac{1}{a} F^a(x) \qquad {\rm and} \qquad
-\Int{x}{\infty} f(\widetilde{x}) \left(1 - F(\widetilde{x})\right)^{a-1} d\widetilde{x} = \frac{1}{a} \left(1 - F(\widetilde{x})\right)^a $$</p>
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+<h2 id="Change-the-bins!-How-bad-could-it-be?">Change the bins! How bad could it be?<a class="anchor-link" href="#Change-the-bins!-How-bad-could-it-be?">&#182;</a></h2>
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-<p>$$ \subNsubR{n}{f}{r}(x_r) dx_r = \Int{\{x_{i \neq r}\}_n}{} dP(\{x_i\}_n) = n! \Int{-\infty}{x_r} f(x_{r-1}) \Int{-\infty}{x_{r-1}} f(x_{r-2}) \cdots \frac{1}{2} \Int{-\infty}{x_4} f(x_3) F^2 (x_3) \Prod{i=3}{r-1} dx_i $$</p>
-<p>$$ \times\ f(x_r) dx_r \Int{x_r}{\infty} f(x_{r+1}) \Int{x_{r+1}}{\infty} f(x_{r+2}) \cdots \frac{1}{2} \Int{x_{n-2}}{\infty} f(x_{n-2}) \left(1 - F(x_{n-2})\right)^2 \Prod{j=r+1}{n-2} dx_j $$</p>
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-<p>$$ \vdots $$</p>
-<p>$$ \subNsubR{n}{f}{r}(x_r) dx_r = n! \left(\frac{1}{(r-1)!} F^{r-1}(x_r)\right) f(x_r) dx_r \left(\frac{1}{(n-r)!} \left(1 - F(x_r)\right)^{n-r}\right) $$</p>
+<p><img src="binningDilemma_final_orig.png" alt="It could be very bad..." title="It could be very bad..."></p>
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-<p>$$ {\Large \therefore \quad \subNsubR{n}{f}{r}(x_r) = \subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \left(1 - F(x_r)\right)^{n-r} }. \quad {}_\blacksquare$$</p>
+<h2 id="Okay,-that's-bad,-but-how-often...?">Okay, that's bad, but how often...?<a class="anchor-link" href="#Okay,-that's-bad,-but-how-often...?">&#182;</a></h2>
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+In&nbsp;[2]:
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-<div class="highlight"><pre><span class="kn">import</span> <span class="nn">sys</span>
-<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="s">&#39;..&#39;</span>
+<div class="highlight"><pre><span class="n">funcs</span><span class="o">.</span><span class="n">randomGenerator</span><span class="o">.</span><span class="n">setSeed</span><span class="p">(</span><span class="s">&#39;seedOne&#39;</span><span class="p">)</span>
+<span class="n">funcs</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s">&#39;simpleSortedOutput&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">True</span>
+
+<span class="n">nPulls</span> <span class="o">=</span> <span class="mi">400</span>
+<span class="n">basePars</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.00006</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">200.</span><span class="p">,</span> <span class="mf">110.</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mf">50.</span><span class="p">,</span> <span class="mf">140.</span><span class="p">)</span>
+<span class="n">baseGuess</span> <span class="o">=</span> <span class="p">(</span><span class="mf">140.</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">10.</span><span class="p">)</span>
+
+<span class="k">def</span> <span class="nf">fitTwoHistograms</span><span class="p">(</span><span class="n">percentile</span><span class="p">):</span>
+ <span class="n">data</span> <span class="o">=</span> <span class="n">funcs</span><span class="o">.</span><span class="n">functionToData</span><span class="p">(</span><span class="n">funcs</span><span class="o">.</span><span class="n">easyEndpoint</span><span class="p">,</span> <span class="n">nPulls</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">200</span><span class="p">),</span> <span class="n">basePars</span><span class="p">)</span>
+ <span class="n">percentieth</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">data</span> <span class="o">&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">percentile</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">percentile</span><span class="p">)]</span>
+
+ <span class="c"># The histograms are filled with the same data, only different binning.</span>
+ <span class="n">binContentsOne</span><span class="p">,</span> <span class="n">binEdgesOne</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">percentieth</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">3.</span><span class="p">,</span> <span class="mf">204.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">))</span>
+ <span class="n">binContentsTwo</span><span class="p">,</span> <span class="n">binEdgesTwo</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">percentieth</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">201.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">))</span>
+
+ <span class="c"># The fit ranges are defined to be from the value of the 70th percentile data point</span>
+ <span class="c"># to &quot;the last non-zero bin&quot;, blindly.</span>
+ <span class="n">fitBinsOne</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">flatnonzero</span><span class="p">(</span><span class="n">binContentsOne</span><span class="p">[</span><span class="n">binContentsOne</span><span class="o">.</span><span class="n">argmax</span><span class="p">():])</span> <span class="o">+</span> <span class="n">binContentsOne</span><span class="o">.</span><span class="n">argmax</span><span class="p">()</span>
+ <span class="n">fitBinsTwo</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">flatnonzero</span><span class="p">(</span><span class="n">binContentsTwo</span><span class="p">[</span><span class="n">binContentsTwo</span><span class="o">.</span><span class="n">argmax</span><span class="p">():])</span> <span class="o">+</span> <span class="n">binContentsTwo</span><span class="o">.</span><span class="n">argmax</span><span class="p">()</span>
+
+ <span class="c">### FITTING METHOD: Binned Maximum Likelihood ###</span>
+ <span class="n">fitGuessOne</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">value</span> <span class="o">*</span> <span class="n">funcs</span><span class="o">.</span><span class="n">randomGenerator</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span> <span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">baseGuess</span><span class="p">])</span>
+ <span class="n">fitGuessTwo</span> <span class="o">=</span> <span class="n">fitGuessOne</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
+
+ <span class="k">def</span> <span class="nf">chiSqOne</span><span class="p">(</span><span class="n">pars</span><span class="p">):</span>
+<span class="c"># return funcs.chiSqSimple(binContentsOne, binEdgesOne, fitBinsOne, funcs.theKink, pars)</span>
+ <span class="k">return</span> <span class="o">-</span><span class="mf">2.</span> <span class="o">*</span> <span class="n">funcs</span><span class="o">.</span><span class="n">theKink_BinnedLikelihood</span><span class="p">(</span><span class="n">binContentsOne</span><span class="p">,</span> <span class="n">binEdgesOne</span><span class="p">,</span> <span class="n">fitBinsOne</span><span class="p">,</span> <span class="n">pars</span><span class="p">)</span>
+ <span class="k">def</span> <span class="nf">chiSqTwo</span><span class="p">(</span><span class="n">pars</span><span class="p">):</span>
+<span class="c"># return funcs.chiSqSimple(binContentsTwo, binEdgesTwo, fitBinsTwo, funcs.theKink, pars)</span>
+ <span class="k">return</span> <span class="o">-</span><span class="mf">2.</span> <span class="o">*</span> <span class="n">funcs</span><span class="o">.</span><span class="n">theKink_BinnedLikelihood</span><span class="p">(</span><span class="n">binContentsTwo</span><span class="p">,</span> <span class="n">binEdgesTwo</span><span class="p">,</span> <span class="n">fitBinsTwo</span><span class="p">,</span> <span class="n">pars</span><span class="p">)</span>
+
+ <span class="n">fitOne</span> <span class="o">=</span> <span class="n">miniz</span><span class="o">.</span><span class="n">nelderMead</span><span class="p">(</span><span class="n">chiSqOne</span><span class="p">,</span> <span class="n">fitGuessOne</span><span class="p">,</span> <span class="n">xtol</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">ftol</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">disp</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+ <span class="n">fitTwo</span> <span class="o">=</span> <span class="n">miniz</span><span class="o">.</span><span class="n">nelderMead</span><span class="p">(</span><span class="n">chiSqTwo</span><span class="p">,</span> <span class="n">fitGuessTwo</span><span class="p">,</span> <span class="n">xtol</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">ftol</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">disp</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+ <span class="k">return</span> <span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">fitOne</span><span class="p">,</span> <span class="n">fitTwo</span><span class="p">)</span>
+
+<span class="n">xKinkOne</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">xKinkTwo</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">xKinkDiff</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">percentile</span> <span class="o">=</span> <span class="mi">60</span>
+<span class="n">nTrials</span> <span class="o">=</span> <span class="mi">1000</span>
+
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">nTrials</span><span class="p">):</span>
+ <span class="n">data</span><span class="p">,</span> <span class="n">fitOne</span><span class="p">,</span> <span class="n">fitTwo</span> <span class="o">=</span> <span class="n">fitTwoHistograms</span><span class="p">(</span><span class="n">percentile</span><span class="p">)</span>
+ <span class="n">xKinkOne</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fitOne</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+ <span class="n">xKinkTwo</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">fitTwo</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+ <span class="n">xKinkDiff</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">baseGuess</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">fitTwo</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">fitOne</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
</pre></div>
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-In&nbsp;[2]:
+In&nbsp;[3]:
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-<div class="highlight"><pre><span class="sd">&quot;&quot;&quot; Presumably, skip slides are for non-output code blocks. </span>
-<span class="sd"> Here, just import and define a few functions. &quot;&quot;&quot;</span>
-<span class="kn">from</span> <span class="nn">os</span> <span class="kn">import</span> <span class="n">listdir</span> <span class="k">as</span> <span class="n">ls</span>
-<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
-<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">bisect</span>
-<span class="kn">import</span> <span class="nn">utilities.sampleFunctions</span> <span class="kn">as</span> <span class="nn">funcs</span>
-<span class="nb">reload</span><span class="p">(</span><span class="n">funcs</span><span class="p">)</span>
-
-<span class="o">%</span><span class="k">matplotlib</span> <span class="n">inline</span>
-<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
-
-<span class="kn">import</span> <span class="nn">operator</span> <span class="kn">as</span> <span class="nn">op</span>
-<span class="k">def</span> <span class="nf">get_nKrArray</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
- <span class="c"># nKr has a symmetry: nKr = nK(n-r+1)... Only need to calculate ~half the values.</span>
- <span class="k">if</span> <span class="n">n</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">==</span> <span class="n">n</span><span class="p">:</span>
- <span class="n">one_or_two</span> <span class="o">=</span> <span class="mi">1</span>
- <span class="k">else</span><span class="p">:</span>
- <span class="n">one_or_two</span> <span class="o">=</span> <span class="mi">2</span>
- <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span> <span class="p">[</span><span class="n">n</span><span class="p">],</span> <span class="p">[</span><span class="nb">reduce</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">mul</span><span class="p">,</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="o">-</span><span class="n">r</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span> <span class="o">/</span> <span class="nb">reduce</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">mul</span><span class="p">,</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">))</span>
- <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">n</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">one_or_two</span><span class="p">)]</span> <span class="p">))</span>
-
-<span class="k">def</span> <span class="nf">quickData</span><span class="p">():</span>
- <span class="c"># This returns data from the easyEndpoint function evaluated at 384 x values in [8.5,200]</span>
- <span class="c"># if funcs.settings[&#39;simpleSortedOutput&#39;] = True, returns only the data</span>
- <span class="c"># else, returns x, f, F, data</span>
- <span class="k">return</span> <span class="n">funcs</span><span class="o">.</span><span class="n">functionToData</span><span class="p">(</span><span class="n">funcs</span><span class="o">.</span><span class="n">easyEndpoint</span><span class="p">,</span> <span class="n">nPulls</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">8.5</span><span class="p">,</span> <span class="mf">200.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">))</span>
+<div class="highlight"><pre><span class="k">def</span> <span class="nf">plotHistoFitCompare</span><span class="p">():</span>
+ <span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">11</span><span class="p">,</span><span class="mi">7</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">&#39;#ffffff&#39;</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">xKinkOne</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">80</span><span class="p">,</span><span class="mi">180</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#66a61e&#39;</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">80</span><span class="p">,</span> <span class="mi">181</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">xKinkTwo</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">80</span><span class="p">,</span><span class="mi">180</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">80</span><span class="p">,</span> <span class="mi">181</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">xKinkDiff</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">80</span><span class="p">,</span><span class="mi">180</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#000000&#39;</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">80</span><span class="p">,</span> <span class="mi">181</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">80</span><span class="p">,</span> <span class="mi">181</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">80</span><span class="p">,</span> <span class="mi">181</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span><span class="p">)</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">80.</span><span class="p">,</span> <span class="mf">181.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
-<span class="k">def</span> <span class="nf">quickBG</span><span class="p">():</span>
- <span class="c"># This returns data from the easyEndpoint function evaluated at 320 x values in [8.5,200]</span>
- <span class="c"># if funcs.settings[&#39;simpleSortedOutput&#39;] = True, returns only the data</span>
- <span class="c"># else, returns x, f, F, data</span>
- <span class="k">return</span> <span class="n">funcs</span><span class="o">.</span><span class="n">functionToData</span><span class="p">(</span><span class="n">funcs</span><span class="o">.</span><span class="n">endpointBG</span><span class="p">,</span> <span class="n">nPulls</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">8.5</span><span class="p">,</span> <span class="mf">200.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">))</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">250</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">250</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="n">num</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">250</span><span class="p">,</span> <span class="mi">50</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">length</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">which</span><span class="o">=</span><span class="s">&#39;minor&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">minorticks_on</span><span class="p">()</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">&#39;Kink Fit Result&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">&#39;Number of Counts (400 total)&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
-<span class="k">class</span> <span class="nc">HistoContainer</span><span class="p">:</span>
- <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">binEdges</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">normed</span><span class="o">=</span><span class="bp">False</span><span class="p">):</span>
- <span class="sd">&quot;&quot;&quot; A histogram as a container, not as a plot. More data values may be added later with addValue(value). &quot;&quot;&quot;</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">binEdges</span> <span class="o">=</span> <span class="n">binEdges</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">binContents</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">binEdges</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">area</span> <span class="o">=</span> <span class="bp">None</span>
- <span class="k">if</span> <span class="n">data</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span>
- <span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">data</span><span class="p">:</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">addValue</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
- <span class="k">def</span> <span class="nf">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
- <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">binContents</span><span class="p">)</span>
- <span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">addValue</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
- <span class="k">def</span> <span class="nf">integral</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
- <span class="sd">&quot;&quot;&quot; Returns the total integration over the entire histogram. &quot;&quot;&quot;</span>
- <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">area</span> <span class="o">==</span> <span class="bp">None</span><span class="p">:</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">area</span> <span class="o">=</span> <span class="n">funcs</span><span class="o">.</span><span class="n">A</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">binContents</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">binEdges</span><span class="p">))[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
- <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">area</span>
- <span class="k">def</span> <span class="nf">normalize</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
- <span class="sd">&quot;&quot;&quot; Normalize the histogram contents. &quot;&quot;&quot;</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">binContents</span> <span class="o">/=</span> <span class="bp">self</span><span class="o">.</span><span class="n">integral</span><span class="p">()</span>
- <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
- <span class="sd">&quot;&quot;&quot; Plots the result, filling under the &#39;histogram&#39;. </span>
-<span class="sd"> Passes **kwargs on to the matplotlib.pyplot.fill_between function.</span>
-<span class="sd"> Returns a proxy matplotlib.patches.Rectangle for legend control. &quot;&quot;&quot;</span>
- <span class="k">if</span> <span class="n">normed</span><span class="p">:</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">normalize</span><span class="p">()</span>
- <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">binEdges</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">binEdges</span><span class="p">)))</span>
- <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">value</span><span class="p">,</span> <span class="n">value</span><span class="p">]</span> <span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">binContents</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">integral</span><span class="p">()])</span>
- <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(([</span><span class="mf">1e-6</span><span class="p">],</span> <span class="n">y</span><span class="o">.</span><span class="n">flatten</span><span class="p">(),</span> <span class="p">[</span><span class="mf">1e-6</span><span class="p">]))</span>
- <span class="n">plt</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="mf">1e-6</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
- <span class="k">return</span> <span class="n">Rectangle</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">fill</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
- <span class="k">def</span> <span class="nf">addValue</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
- <span class="sd">&quot;&quot;&quot; Insert a value to the histogram. &quot;&quot;&quot;</span>
- <span class="c"># demand that integral() must recalculate</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">area</span> <span class="o">=</span> <span class="bp">None</span>
- <span class="c"># bisect_left(x, datum) locates the left-most entry in x which is &gt;= datum</span>
- <span class="n">index</span> <span class="o">=</span> <span class="n">bisect</span><span class="o">.</span><span class="n">bisect_left</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">binEdges</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
- <span class="k">if</span> <span class="n">index</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
- <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">&#39;HistoContainer warning: Underflow&#39;</span><span class="p">)</span>
- <span class="k">elif</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">binContents</span><span class="p">):</span>
- <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">&#39;HistoContainer warning: Overflow&#39;</span><span class="p">)</span>
- <span class="k">else</span><span class="p">:</span>
- <span class="bp">self</span><span class="o">.</span><span class="n">binContents</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
-
-
-<span class="k">def</span> <span class="nf">verticalColorBand</span><span class="p">(</span><span class="n">histo</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
- <span class="sd">&quot;&quot;&quot; Add to an existing plot a histogram, painted as a vertical band of color.</span>
-<span class="sd"> The band is a rectangle of width [x-0.5dx, x+0.5dx]. &quot;&quot;&quot;</span>
- <span class="k">if</span> <span class="n">colors</span> <span class="o">==</span> <span class="bp">None</span><span class="p">:</span>
- <span class="n">colors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([(</span><span class="mf">1.</span><span class="p">,</span><span class="mf">1.</span><span class="p">,</span><span class="mf">0.</span><span class="p">),</span> <span class="p">(</span><span class="mf">1.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">),</span> <span class="p">(</span><span class="mf">1.</span><span class="p">,</span><span class="mf">1.</span><span class="p">,</span><span class="mf">1.</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">1.</span><span class="p">)])</span>
-
- <span class="c"># Special normalization to show FWHM transition.</span>
- <span class="n">histo</span><span class="o">.</span><span class="n">binContents</span> <span class="o">/=</span> <span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">histo</span><span class="o">.</span><span class="n">binContents</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
-
- <span class="c"># Horizontal width of the band.</span>
- <span class="n">base</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">x</span><span class="o">-</span><span class="n">dx</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">x</span><span class="o">+</span><span class="n">dx</span><span class="o">/</span><span class="mi">2</span><span class="p">])</span>
-
- <span class="k">for</span> <span class="n">bindex</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">histo</span><span class="p">)):</span>
- <span class="n">upper</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">histo</span><span class="o">.</span><span class="n">binEdges</span><span class="p">[</span><span class="n">bindex</span><span class="o">+</span><span class="mi">1</span><span class="p">],</span> <span class="n">histo</span><span class="o">.</span><span class="n">binEdges</span><span class="p">[</span><span class="n">bindex</span><span class="o">+</span><span class="mi">1</span><span class="p">]])</span>
- <span class="n">lower</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">histo</span><span class="o">.</span><span class="n">binEdges</span><span class="p">[</span><span class="n">bindex</span><span class="p">],</span> <span class="n">histo</span><span class="o">.</span><span class="n">binEdges</span><span class="p">[</span><span class="n">bindex</span><span class="p">]])</span>
- <span class="n">value</span> <span class="o">=</span> <span class="n">histo</span><span class="o">.</span><span class="n">binContents</span><span class="p">[</span><span class="n">bindex</span><span class="p">]</span>
- <span class="k">if</span> <span class="n">value</span> <span class="o">&gt;=</span> <span class="mf">1.</span><span class="p">:</span>
- <span class="n">color</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">((</span><span class="n">value</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">*</span> <span class="n">colors</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span><span class="mf">2.</span> <span class="o">-</span> <span class="n">value</span><span class="p">)</span> <span class="o">*</span> <span class="n">colors</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
- <span class="n">alp</span> <span class="o">=</span> <span class="mf">1.</span>
- <span class="k">else</span><span class="p">:</span>
- <span class="n">color</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">((</span><span class="n">value</span><span class="p">)</span> <span class="o">*</span> <span class="n">colors</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span><span class="mf">1.</span> <span class="o">-</span> <span class="n">value</span><span class="p">)</span> <span class="o">*</span> <span class="n">colors</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
- <span class="n">alp</span> <span class="o">=</span> <span class="mf">0.35</span>
- <span class="k">if</span> <span class="n">value</span> <span class="o">&gt;</span> <span class="mf">0.1</span><span class="p">:</span>
- <span class="n">plt</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">upper</span><span class="p">,</span> <span class="n">lower</span><span class="p">,</span>
- <span class="n">edgecolor</span><span class="o">=</span><span class="s">&#39;none&#39;</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="n">alp</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+ <span class="k">print</span>
</pre></div>
</div>
</div>
</div>
</div>
</div>
- </div><div style=display:none>
-
+ </div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input_hidden">
<div class="input">
<div class="prompt input_prompt">
-In&nbsp;[3]:
+In&nbsp;[4]:
</div>
<div class="inner_cell">
<div class="input_area">
-<div class="highlight"><pre><span class="c"># nPulls is used in many functions below to set the number of data points to pull</span>
-<span class="c"># from our &quot;true&quot; PDF, $f(x)$.</span>
-<span class="n">nPulls</span> <span class="o">=</span> <span class="mi">10</span>
-
-<span class="sd">&quot;&quot;&quot; Set up the demonstration of the ithPDF equations working correctly. &quot;&quot;&quot;</span>
-<span class="n">pullData</span> <span class="o">=</span> <span class="p">{</span><span class="n">index</span><span class="p">:[]</span> <span class="k">for</span> <span class="n">index</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">nPulls</span><span class="p">)}</span>
-<span class="n">funcs</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s">&#39;simpleSortedOutput&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">True</span>
-<span class="k">for</span> <span class="n">iteration</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">2000</span><span class="p">):</span>
- <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">v</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">quickData</span><span class="p">()):</span>
- <span class="n">pullData</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
-
-<span class="n">funcs</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s">&#39;simpleSortedOutput&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
-<span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">data</span> <span class="o">=</span> <span class="n">quickData</span><span class="p">()</span>
-<span class="n">f</span> <span class="o">=</span> <span class="n">f</span> <span class="o">/</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-<span class="n">F</span> <span class="o">=</span> <span class="n">F</span> <span class="o">/</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-
-<span class="n">ithPDF</span> <span class="o">=</span> <span class="p">{}</span>
-<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">nPulls</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
- <span class="n">ithPDF</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">f</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">*</span> <span class="n">F</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">**</span><span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">F</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="o">**</span><span class="p">(</span><span class="n">nPulls</span><span class="o">-</span><span class="n">i</span><span class="p">)</span>
- <span class="o">*</span> <span class="n">funcs</span><span class="o">.</span><span class="n">nKr</span><span class="p">(</span><span class="n">nPulls</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))])</span>
-
+<div class="highlight"><pre><span class="n">plotHistoFitCompare</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
</div>
-</div>
- </div><div style=display:none>
-
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input_hidden">
-<div class="input">
-<div class="prompt input_prompt">
-In&nbsp;[4]:
-</div>
-<div class="inner_cell">
- <div class="input_area">
-<div class="highlight"><pre><span class="n">histogramRange</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
-<span class="n">majorTicksRange</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">50</span><span class="p">)</span>
-<span class="n">minorTicksRange</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
+<div class="output_wrapper">
+<div class="output">
-<span class="k">def</span> <span class="nf">makeHist</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
- <span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">9</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">&#39;#ffffff&#39;</span><span class="p">)</span>
- <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">pullData</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="n">histogramRange</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#66a61e&#39;</span><span class="p">,</span> <span class="n">normed</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
- <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">ithPDF</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="s">&#39;#964a01&#39;</span><span class="p">)</span>
-
- <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">majorTicksRange</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">minorTicksRange</span><span class="p">,</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span><span class="p">)</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">majorTicksRange</span><span class="p">],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
-
- <span class="n">axes</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">bottom</span><span class="o">=-</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.0401</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">))</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%0.3f</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="n">num</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.01</span><span class="o">/</span><span class="mi">5</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">&#39;Physical Observable&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">&#39;Probability&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+<div class="output_area"><div class="prompt"></div>
+<div class="output_subarea output_stream output_stdout output_text">
+<pre>
- <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">length</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">which</span><span class="o">=</span><span class="s">&#39;minor&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">minorticks_on</span><span class="p">()</span>
-</pre></div>
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+>
</div>
</div>
</div>
- </div></section>
+</div>
+
+</div></section>
</section><section>
<section>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{1}(x)$ compared with the histogram of the 1st point of 2000 samples:</p>
+<h2 id="The-debinning-Project:-Data-Smoothing-without-Bins">The debinning Project: Data Smoothing without Bins<a class="anchor-link" href="#The-debinning-Project:-Data-Smoothing-without-Bins">&#182;</a></h2>
</div>
</div>
</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input_hidden">
-<div class="input">
+<div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
-In&nbsp;[5]:
</div>
<div class="inner_cell">
- <div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-</pre></div>
-
-</div>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="histograms-smooth-the-data-in-this-way-">Histograms &quot;smooth&quot; the data in this way:</h3>
+<p><img src="notTheOnlyShape.png" alt="Let&#39;s try to find other shapes!" title="Let&#39;s try to find other shapes!"></p>
+<h3 id="is-there-a-more-appropriate-smoothing-shape-">Is there a more appropriate smoothing shape?</h3>
</div>
</div>
-
</div>
-
-<div class="output_wrapper">
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-
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-"
->
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
</div>
-
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="Gaussian-Smoothing:-binfull-Histogram">Gaussian Smoothing: binfull Histogram<a class="anchor-link" href="#Gaussian-Smoothing:-binfull-Histogram">&#182;</a></h2>
</div>
-
</div>
</div>
-
-</div></section><section>
+<div class="fragment">
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{2}(x)$ compared with the histogram of the 2nd point of 2000 samples:</p>
+<h3 id="aka-kernel-density-estimation-">aka &quot;Kernel Density Estimation&quot;:</h3>
+<p><img src="GaussianSmoothing.png" alt="Gaussian Smoothing" title="Gaussian Smoothing"></p>
</div>
</div>
</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input_hidden">
-<div class="input">
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
-In&nbsp;[6]:
</div>
<div class="inner_cell">
- <div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-</pre></div>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="select-a-point-from-our-data-">Select a point from our data...</h3>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="add-a-random-deviate-from-a-gaussian-distribution-">Add a random deviate from a Gaussian distribution...</h3>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="and-repeat-ad-nauseam-">And repeat ad nauseam.</h3>
+<h3 id="put-all-results-into-a-binfull-histogram-full-of-arbitrarily-small-bins-">Put all results into a binfull Histogram (&quot;full&quot; of arbitrarily small bins).</h3>
+</div>
+</div>
+</div>
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="binfull-Histogram-Demo">binfull Histogram Demo<a class="anchor-link" href="#binfull-Histogram-Demo">&#182;</a></h2>
+</div>
+</div>
+</div>
+<div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p><img src="easyEndpoint_binfullLinearExpanding_final.png" alt="Linearly Increasing Gaussian Smoothing" title="Linearly Increasing Gaussian Smoothing"></p>
+<h3 id="algorithm-issues-speed-choosing-0-over-underflow-linearexpanding-kernel-depends-on-time-">Algorithm issues: Speed, choosing $\sigma$, over/underflow, &quot;LinearExpanding&quot; - Kernel depends on &quot;time&quot;...</h3>
+</div>
+</div>
+</div>
+ </div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="1-new-probability-calculus-">1) New Probability Calculus:</h2>
+<h3 id="-0-can-t-i-just-calculate-that-thing-">$\qquad$ &quot;Can&#39;t I just calculate that thing?&quot;</h3>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="2-the-debinning-calculation-">2) The debinning Calculation:</h2>
+<h3 id="-0-whoa-i-can-calculate-something-else-">$\qquad$ &quot;Whoa, I can calculate something else!&quot;</h3>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="3-the-future-and-shameless-advertising-">3) The Future, and Shameless Advertising:</h2>
+<h3 id="-0-yikes-there-is-so-much-more-">$\qquad$ &quot;Yikes.... There is so much more!&quot;</h3>
+</div>
+</div>
+</div>
+ </div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="new-probability-calculus-">New Probability Calculus:</h1>
+<h2 id="-can-t-i-just-calculate-that-thing-">&quot;Can&#39;t I just calculate that thing?&quot;</h2>
+</div>
+</div>
+</div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="Datum-Probability">Datum Probability<a class="anchor-link" href="#Datum-Probability">&#182;</a></h2>
+</div>
+</div>
+</div>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="what-s-the-probability-to-get-some-datum-0-">What&#39;s the probability to get some datum, $x$?</h3>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ {\large P(\widetilde{x}\in[x,x+dx]) = f(x) dx \quad {\rm and} \quad \Int{-\infty}{\infty} f(x) dx = 1~.} $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h4 id="-0-is-the-probability-distribution-function-pdf-">$f(x)$ is the Probability Distribution Function (PDF).</h4>
+<h4 id="its-anti-derivative-is-the-cumulative-distribution-function-cdf-">Its anti-derivative is the Cumulative Distribution Function (CDF):</h4>
+<p>$$ F(x) = \Int{-\infty}{x} f(x') dx' = P(\tilde{x} \le x)$$
+$$ 1 - F(x) = \Int{x}{\infty} f(x') dx' = P(\tilde{x} &gt; x) $$</p>
+</div>
+</div>
+</div>
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="Sample-Probability">Sample Probability<a class="anchor-link" href="#Sample-Probability">&#182;</a></h2>
+</div>
+</div>
+</div>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="probability-to-get-a-sample-of-data-points-0-">Probability to get a sample of data points, $\{x_i\}_{i=1}^n$?</h3>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>\begin{align}
+ dP(\{x_1\}) &amp;= \phantom{3!} \phantom{\times!!} f(x_1) dx_1 \\
+ dP(\{x_1, x_2\}) &amp;= \rust{2}\phantom{!} \rust{\times} f(x_1) dx_1 f(x_2) dx_2 \\
+ dP(\{x_1, x_2, x_3\}) &amp;= \rust{3!} \rust{\times} f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3
+\end{align}</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="order-doesn-t-matter-wlog-sort-">Order doesn&#39;t matter... WLOG, sort:</h3>
+<p>\begin{align}
+ \{x_1, x_2\} &amp;\equiv \{x_2, x_1\} \\
+ \{x_1, x_2, x_3\} &amp;\equiv \{x_2, x_3, x_1\} \equiv \cdots \\
+ \phantom{dP(\{x_1, x_2, x_3\})} &amp;\phantom{= 3! \times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}
+\end{align}</p>
+<p>$$ \Rightarrow\ {\rm WLOG}\ x_j &lt; x_k\ {\rm for}\ j &lt; k\ {\rm for\ all}\ x_j, x_k \in \{x_i\}_{i=1}^n$$ </p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>\begin{align}
+ \therefore dP(\{x_i\}_{i=1}^n) &amp;= \rust{n!} \Prod{i = 1}{n} f(x_i) dx_i \\
+ \phantom{dP(\{x_1, x_2, x_3\})} &amp;\phantom{= 3! \times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}
+\end{align}</p>
+</div>
+</div>
+</div>
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="Probability-Calculus:-Integration">Probability Calculus: Integration<a class="anchor-link" href="#Probability-Calculus:-Integration">&#182;</a></h2>
+</div>
+</div>
+</div>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="the-data-is-all-sorted-careful-with-those-integration-limits-">The data is all sorted... Careful with those integration limits!</h3>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ \Int{\{x_1, x_2\}}{} dP(\{x_1, x_2\}) = 2 \Int{-\infty}{\infty} f(x_2) \left[ \Int{-\infty}{x_2} f(x_1) dx_1 \right] dx_2, $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$\Int{\{x_1, x_2, x_3\}}{} dP(\{x_1, x_2, x_3\}) = 3!\Int{-\infty}{\infty} f(x_3) \left[ \Int{-\infty}{x_3} f(x_2) \left( \Int{-\infty}{x_2} f(x_1) dx_1 \right) dx_2 \right] dx_3$$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$\vdots$$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="limits-of-inner-integrals-are-also-integration-variables-">Limits of inner integrals are <em>also</em> integration variables...</h3>
+<h3 id="thus-integrals-are-chained-together-chain-integrals-">Thus, integrals are &quot;chained&quot; together... Chain Integrals.</h3>
+</div>
+</div>
+</div>
+ </div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="probability-calculus-being-0-th-of-1-">Probability Calculus: Being $r$th of $n$</h2>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>\begin{align}
+ \subNsubR{n}{f}{r} (x_r)\ dx_r &amp;\equiv\ \Int{\{x_{i \neq r}\}_n}{} dP(\{x_i\}_{i=1}^n) \\
+ \quad = n!\ f(x_r)\ dx_r
+ &amp;\phantom\times\ \Int{-\infty}{\infty} f(x_n) \Int{-\infty}{x_n} f(x_{n-1}) \cdots \Int{-\infty}{x_{r+2}} f(x_{r+1}) \Prod{i=r+1}{n} dx_i \\
+ &amp;\times\ \Int{-\infty}{\infty} f(x_1) \Int{x_1}{\infty} f(x_2) \cdots \Int{x_{r-2}}{\infty} f(x_{r-1}) \Prod{i'=1}{r-1} dx_{i'}
+\end{align}</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="-0-theorem-">$\subNsubR{n}{f}{r}$ Theorem:</h3>
+<p>$$ {\Large \subNsubR{n}{f}{r}(x_r) = \subNsubR{n}{K}{r}\ f(x_r) F^{r-1}(x_r) \left(1 - F(x_r)\right)^{n-r} }. $$</p>
+</div>
+</div>
+</div>
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="probability-calculus-being-0-th-of-1-">Probability Calculus: Being $r$th of $n$</h2>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="-0-identical-siblings-race-1-outcomes-2-">$n$ identical siblings: Race! $\quad$ ... Outcomes? $n!$</h3>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="only-care-about-0-th-place-1-2-is-overcounting-">Only care about $r$th place. $\quad$ ... $n!$ is overcounting.</h3>
+<h3 id="-3-4-faster-who-cares-what-order-">$\quad$ ... $(r-1)$ faster... who cares what order...</h3>
+<h3 id="-5-6-slower-who-cares-what-order-">$\quad$ ... $(n-r)$ slower... who cares what order...</h3>
+<h3 id="-7-">$$ \Rightarrow \subNsubR{n}{K}{r} \equiv \frac{n!}{(n-r)!(r-1)!} $$</h3>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ {\Large \therefore \quad \subNsubR{n}{f}{r}(x_r) = \subNsubR{n}{K}{r}\ f(x_r)\ F^{r-1}(x_r)\ \left(1 - F(x_r)\right)^{n-r} } $$</p>
+<p>$ {\Large ({\rm HW}-1)}$
+$${\large {\rm Prove\ the}\ \subNsubR{n}{f}{r}\ {\rm Theorem\ by\ computing\ the\ chain\ integral.} }$$</p>
+</div>
+</div>
+</div>
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>Proof:</p>
+<p>$$ \subNsubR{n}{f}{r}(x_r) dx_r = \Int{\{x_{i \neq r}\}_n}{} dP(\{x_i\}_n) = n! \Int{-\infty}{x_r} f(x_{r-1}) \Int{-\infty}{x_{r-1}} f(x_{r-2}) \cdots \Int{-\infty}{x_2} f(x_1) \Prod{i=1}{r-1} dx_i $$</p>
+<p>$$ \times\ f(x_r) dx_r \Int{x_r}{\infty} f(x_{r+1}) \Int{x_{r+1}}{\infty} f(x_{r+2}) \cdots \Int{x_{n-1}}{\infty} f(x_n) \Prod{j=r+1}{n} dx_j $$</p>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ = n! \Int{-\infty}{x_r} f(x_{r-1}) \Int{-\infty}{x_{r-1}} f(x_{r-2}) \cdots \Int{-\infty}{x_3} f(x_2) F(x_2) \Prod{i=2}{r-1} dx_i $$</p>
+<p>$$ \times\ f(x_r) dx_r \Int{x_r}{\infty} f(x_{r+1}) \Int{x_{r+1}}{\infty} f(x_{r+2}) \cdots \Int{x_{n-2}}{\infty} f(x_{n-1}) \left(1 - F(x_{n-1})\right) \Prod{j=r+1}{n-1} dx_j $$</p>
+</div>
+</div>
+</div>
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>Integration by parts:</p>
+<p>$$ \Int{-\infty}{x} f(\widetilde{x}) F^{a-1}(\widetilde{x}) d\widetilde{x} = \frac{1}{a} F^a(x) \qquad {\rm and} \qquad
+\Int{x}{\infty} f(\widetilde{x}) \left(1 - F(\widetilde{x})\right)^{a-1} d\widetilde{x} = \frac{1}{a} \left(1 - F(x)\right)^a $$</p>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ \subNsubR{n}{f}{r}(x_r) dx_r = n! \Int{-\infty}{x_r} f(x_{r-1}) \Int{-\infty}{x_{r-1}} f(x_{r-2}) \cdots \frac{1}{2} \Int{-\infty}{x_4} f(x_3) F^2 (x_3) \Prod{i=3}{r-1} dx_i $$</p>
+<p>$$ \times\ f(x_r) dx_r \Int{x_r}{\infty} f(x_{r+1}) \Int{x_{r+1}}{\infty} f(x_{r+2}) \cdots \frac{1}{2} \Int{x_{n-2}}{\infty} f(x_{n-2}) \left(1 - F(x_{n-2})\right)^2 \Prod{j=r+1}{n-2} dx_j $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ \cdots\ = n! \left(\frac{1}{(r-1)!} F^{r-1}(x_r)\right) f(x_r) dx_r \left(\frac{1}{(n-r)!} \left(1 - F(x_r)\right)^{n-r}\right) $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ {\Large \therefore \quad \subNsubR{n}{f}{r}(x_r) = \subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \left(1 - F(x_r)\right)^{n-r} }. \quad {}_\blacksquare$$</p>
+</div>
+</div>
+</div>
+ </div><div style=display:none>
+
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[5]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="nb">reload</span><span class="p">(</span><span class="n">funcs</span><span class="p">)</span>
+<span class="k">def</span> <span class="nf">quickData</span><span class="p">():</span>
+ <span class="sd">&#39;&#39;&#39; Shorthand for getting easyEndpoint data (384 x values in [8.5,200])</span>
+<span class="sd"> - set nPulls before calling</span>
+<span class="sd"> - see utilities.sampleFunctions.functionToData for more details</span>
+<span class="sd"> &#39;&#39;&#39;</span>
+ <span class="k">return</span> <span class="n">funcs</span><span class="o">.</span><span class="n">functionToData</span><span class="p">(</span><span class="n">funcs</span><span class="o">.</span><span class="n">easyEndpoint</span><span class="p">,</span> <span class="n">nPulls</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">8.5</span><span class="p">,</span> <span class="mf">200.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">))</span>
+
+
+<span class="k">def</span> <span class="nf">quickBG</span><span class="p">():</span>
+ <span class="sd">&#39;&#39;&#39; Shorthand for getting endpointBG data (384 x values in [8.5,200])</span>
+<span class="sd"> - set nPulls before calling</span>
+<span class="sd"> - see utilities.sampleFunctions.functionToData for more details</span>
+<span class="sd"> &#39;&#39;&#39;</span>
+ <span class="k">return</span> <span class="n">funcs</span><span class="o">.</span><span class="n">functionToData</span><span class="p">(</span><span class="n">funcs</span><span class="o">.</span><span class="n">endpointBG</span><span class="p">,</span> <span class="n">nPulls</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">8.5</span><span class="p">,</span> <span class="mf">200.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">))</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+</div>
+ </div><div style=display:none>
+
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[6]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">nPulls</span> <span class="o">=</span> <span class="mi">10</span>
+<span class="n">pullData</span> <span class="o">=</span> <span class="p">{</span><span class="n">index</span><span class="p">:[]</span> <span class="k">for</span> <span class="n">index</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">nPulls</span><span class="p">)}</span>
+<span class="n">settings</span><span class="p">[</span><span class="s">&#39;simpleSortedOutput&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">True</span>
+<span class="k">for</span> <span class="n">iteration</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">2000</span><span class="p">):</span>
+ <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">v</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">quickData</span><span class="p">()):</span>
+ <span class="n">pullData</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+
+<span class="n">settings</span><span class="p">[</span><span class="s">&#39;simpleSortedOutput&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">data</span> <span class="o">=</span> <span class="n">quickData</span><span class="p">()</span>
+<span class="n">bgx</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="n">bgF</span><span class="p">,</span> <span class="n">bgdata</span> <span class="o">=</span> <span class="n">quickBG</span><span class="p">()</span>
+<span class="n">f</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgf</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgF</span> <span class="o">/=</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">F</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+
+<span class="n">ithPDF</span> <span class="o">=</span> <span class="p">{}</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">nPulls</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
+ <span class="n">ithPDF</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">f</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">*</span> <span class="n">F</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">**</span><span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">F</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="o">**</span><span class="p">(</span><span class="n">nPulls</span><span class="o">-</span><span class="n">i</span><span class="p">)</span> <span class="o">*</span> <span class="n">pc</span><span class="o">.</span><span class="n">nKr</span><span class="p">(</span><span class="n">nPulls</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))])</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+</div>
+ </div><div style=display:none>
+
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[7]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="k">def</span> <span class="nf">makeHist</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+ <span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">9</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">&#39;#ffffff&#39;</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="s">&#39;--&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="s">&#39;-.&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">pullData</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#66a61e&#39;</span><span class="p">,</span> <span class="n">normed</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">ithPDF</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="s">&#39;#964a01&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span><span class="p">)</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">50</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">bottom</span><span class="o">=-</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.0401</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">))</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%0.3f</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="n">num</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.01</span><span class="o">/</span><span class="mi">5</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">&#39;Physical Observable&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">&#39;Probability&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+
+ <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">length</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">which</span><span class="o">=</span><span class="s">&#39;minor&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">minorticks_on</span><span class="p">()</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+</div>
+ </div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-1st-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{1}(x)$ compared with the histogram of the 1st smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[8]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+<div class="output_wrapper">
+<div class="output">
+
+
+<div class="output_area"><div class="prompt"></div>
+
+
+<div class="output_png output_subarea ">
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+"
+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-2nd-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{2}(x)$ compared with the histogram of the 2nd smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[9]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
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+
+
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+
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+"
+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-3rd-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{3}(x)$ compared with the histogram of the 3rd smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[10]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+<div class="output_wrapper">
+<div class="output">
+
+
+<div class="output_area"><div class="prompt"></div>
+
+
+<div class="output_png output_subarea ">
+<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmwAAAFcCAYAAAB1B+IVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz
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+"
+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-4th-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{4}(x)$ compared with the histogram of the 4th smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[11]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+<div class="output_wrapper">
+<div class="output">
+
+
+<div class="output_area"><div class="prompt"></div>
+
+
+<div class="output_png output_subarea ">
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+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-5th-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{5}(x)$ compared with the histogram of the 5th smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[12]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+<div class="output_wrapper">
+<div class="output">
+
+
+<div class="output_area"><div class="prompt"></div>
+
+
+<div class="output_png output_subarea ">
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+"
+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-6th-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{6}(x)$ compared with the histogram of the 6th smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[13]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+<div class="output_wrapper">
+<div class="output">
+
+
+<div class="output_area"><div class="prompt"></div>
+
+
+<div class="output_png output_subarea ">
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+"
+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-7th-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{7}(x)$ compared with the histogram of the 7th smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[14]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+<div class="output_wrapper">
+<div class="output">
+
+
+<div class="output_area"><div class="prompt"></div>
+
+
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+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-8th-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{8}(x)$ compared with the histogram of the 8th smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[15]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
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+
+
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+
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+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-9th-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{9}(x)$ compared with the histogram of the 9th smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[16]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">8</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+</div>
+
+</div>
+
+<div class="output_wrapper">
+<div class="output">
+
+
+<div class="output_area"><div class="prompt"></div>
+
+
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+"
+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="let-s-measure-10-0-values-for-some-1-and-repeat-that-2000-times-">Let&#39;s &quot;measure&quot; 10 $x$ values for some $f(x)$, and repeat that 2000 times.</h3>
+<h3 id="here-s-2-compared-with-the-histogram-of-the-10th-smallest-point-of-2000-samples-">Here&#39;s $\subNsubR{10}{f}{10}(x)$ compared with the histogram of the 10th smallest point of 2000 samples:</h3>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
+<div class="prompt input_prompt">
+In&nbsp;[17]:
+</div>
+<div class="inner_cell">
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">9</span><span class="p">)</span>
+</pre></div>
</div>
</div>
</div>
-
+
+</div>
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+"
+>
+</div>
+
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="note-from-now-on-the-data-does-not-need-to-be-sorted-">NOTE: From now on, <em>the data does not need to be sorted</em>.</h2>
+</div>
+</div>
+</div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="probability-calculus-are-you-0-th-of-1-">Probability Calculus: Are You $r$th of $n$?</h2>
+<h3 id="-2-is-the-pdf-of-the-3-th-of-4-position-">$\subNsubR{n}{f}{r}(x)$ is the PDF of the $r$th of $n$ position:</h3>
+<p>$$ {\Large P(\tilde{x} \in [x, x + dx]\ |\ \tilde{x}\ {\rm is\ } r{\rm th\ of\ } n, f) \equiv \subNsubR{n}{f}{r}(x) dx } $$</p>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="use-bayes-theorem-">Use Bayes&#39; Theorem:</h3>
+<p>$$ {\large P(B\ |\ A) = \frac{P(A\ |\ B)\ P(B)}{P(A)} } $$
+$$ {\large \Rightarrow P(\tilde{x}\ {\rm is\ } r{\rm th\ of\ } n\ |\ \tilde{x} \in [x, x + dx], f) = \frac{\subNsubR{n}{f}{r}(x) dx\ \frac{1}{n}}{f(x) dx} } $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ {\Large = \frac{\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \left(1 - F(x)\right)^{n-r}} $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>${\Large ({\rm HW}-2) }$
+$${\large {\rm Prove}: \qquad \Sum{r=1}{n} \frac{\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \left(1 - F(x)\right)^{n-r} = 1, \quad \forall x. }$$</p>
+</div>
+</div>
</div>
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-"
->
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
</div>
-
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>Proof (special thanks to Ola Liabøtrø, who solved this <em>in his head</em> during my talk):</p>
+<p>$$\frac{\subNsubR{n}{K}{r}}{n} = \frac{(n-1)!}{(n-r)!(r-1)!} = \frac{(n-1)!}{(n-1-[r-1])!(r-1)!} = \subNsubR{n-1}{C}{r-1}$$</p>
+<p>Thus,</p>
+<p>$$ \Sum{r=1}{n} \frac{\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \left(1 - F(x)\right)^{n-r} = \Sum{r=1}{n} \subNsubR{n-1}{C}{r-1} F^{r-1}(x) \left(1 - F(x)\right)^{n-r} $$</p>
+<p>$$ = \Sum{r'=0}{n-1} \subNsubR{n-1}{C}{r'} F^{r'}(x) \left(1 - F(x)\right)^{n-1-r'} = (F(x) + 1 - F(x))^{n-1} = 1. \quad {}_\blacksquare $$</p>
+<p>Note: I proved this also. The hard way. Term-by-term. I could not see the relation to $\subNsubR{n-1}{C}{r-1}$.</p>
</div>
-
</div>
+</div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="the-debinning-calculation-">The debinning Calculation:</h1>
+<h2 id="-whoa-i-can-calculate-something-else-">&quot;Whoa, I can calculate something else!&quot;</h2>
</div>
-
-</div></section><section>
+</div>
+</div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="the-debinning-algorithm">The debinning Algorithm</h2>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p><img src="nfrSmoothing.png" alt="nfr Smoothing" title="nfr Smoothing"></p>
+<h3 id="thought-experiment-the-flat-pdf">Thought experiment: The Flat PDF</h3>
+<p>$$ f_{\rm \color{gray}{flat}}(x) = \left\{ \begin{array}{rcl} 1 &amp; {\rm if} &amp; x \in [0, 1] \\ 0 &amp; &amp; {\rm otherwise} \end{array} \right. $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="select-a-point-0-from-the-sample-1-">Select a point, $x_j$, from the sample $\{x_1, x_2, x_3\}$</h3>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="randomly-choose-an-appropriate-0-value-using">Randomly choose an appropriate $r$ value using</h3>
+<p>$${\large P(x_j\ {\rm is\ } r{\rm th\ of\ } 3\ |\ x_j, f_{\rm \color{Gray}{flat}})
+ = \frac{\subNsubR{3}{K}{r}}{3} F_{\rm \color{Gray}{flat}}^{r-1}(x_j) \left(1 - F_{\rm \color{Gray}{flat}}(x_j)\right)^{3-r} }$$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{3}(x)$ compared with the histogram of the 3rd point of 2000 samples:</p>
+<h3 id="generate-a-random-point-from">Generate a random point from</h3>
+<p>$${\large \subNsubR{3}{f}{{\rm(\color{Gray}{flat})}r}(x) = \subNsubR{3}{K}{r} f_{\rm \color{Gray}{flat}}(x)
+ F_{\rm \color{Gray}{flat}}^{r-1}(x) \left(1 - F_{\rm \color{Gray}{flat}}(x)\right)^{3-r} = \mathcal{O}(x^2) }$$</p>
+</div>
+</div>
+</div>
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="the-debinning-algorithm-expectation">The debinning Algorithm... Expectation</h2>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input_hidden">
<div class="input">
<div class="prompt input_prompt">
-In&nbsp;[7]:
+In&nbsp;[18]:
</div>
<div class="inner_cell">
<div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<div class="highlight"><pre><span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">HTML</span>
+<span class="n">HTML</span><span class="p">(</span><span class="s">&#39;&lt;iframe src=http://upliftingplay.com/wp-upliftingplay/wp-content/themes/UpliftingPlay-1.0/sketchpad/tablet-horizontal.html width=800 height=700&gt;&lt;/iframe&gt;&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
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+<div class="output_area"><div class="prompt output_prompt">
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-"
->
+<div class="output_html rendered_html output_subarea output_pyout">
+<iframe src=http://upliftingplay.com/wp-upliftingplay/wp-content/themes/UpliftingPlay-1.0/sketchpad/tablet-horizontal.html width=800 height=700></iframe>
</div>
</div>
</div>
</div>
-</div></section><section>
+</div></section>
+ </section><section>
+ <section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="the-experiment-inspired-debinning-algorithm">The Experiment Inspired debinning Algorithm</h2>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="suppose-our-data-comes-from">Suppose our data comes from</h3>
+<p>$${\huge f(x) = w\ f_{\rm \sky{sig}}(x) + (1 - w)\ f_{\rm \rust{bg}}(x)}$$</p>
+<p><img src="nfbgrSmoothing.png" alt="BG nfr Smoothing" title="BG nfr Smoothing"></p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="select-a-point-from-our-data-">Select a point from our data...</h3>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="randomly-choose-an-appropriate-0-value-using">Randomly choose an appropriate $r$ value using</h3>
+<p>$${\large P(\tilde{x}\ {\rm is\ } r{\rm th\ of\ } n\ |\ \tilde{x} \in [x, x + dx], f_{\rm \rust{bg}}) \cdots}$$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="generate-a-random-point-from-0-need-3-random-numbers-just-to-get-one-back-">Generate a random point from $\subNsubR{n}{f}{{\rm(\rust{bg})}r}(x)$... need <em>3 random numbers</em> just to get one back!!</h3>
+</div>
+</div>
+</div>
+ </div></section><section>
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="the-debinning-algorithm-calculation">The debinning Algorithm... Calculation</h2>
+<h3 id="-det-er-dumt-let-s-just-calculate-it-">&quot;Det er dumt!&quot; Let&#39;s just calculate it!</h3>
+</div>
+</div>
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ f_{\rm debin}(x) dx = P_{\rm debin}\left(\tilde{x} \in [x, x + dx] | \{x_i\}_{i=1}^{n}, f_{\rm\rust{bg}} \right) $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ = \sum\limits_{j=1}^{n} P( x_j | \{x_i\}_{i=1}^{n} ) \sum\limits_{r=1}^{N} P(r{\rm th}\ {\rm of}\ N | x_j, f_{\rm\rust{bg}}) P(\tilde{x} \in [x, x + dx] | r{\rm th}\ {\rm of}\ N, f_{\rm\rust{bg}}) $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>$$ = \sum\limits_{j=1}^{n} \frac{1}{n} \sum\limits_{r=1}^{N} \left(\frac{{}_NK_r}{N} F_{\rm\rust{bg}}(x_j)^{(r-1)}(1 - F_{\rm\rust{bg}}(x_j))^{(N-r)} \right) $$
+$$ \quad\times \left( {}_NK_r f_{\rm\rust{bg}}(x) F_{\rm\rust{bg}}(x)^{(r-1)}(1 - F_{\rm\rust{bg}}(x))^{(N-r)} dx \right) $$</p>
+</div>
+</div>
+</div>
+ </div><div class="fragment">
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{4}(x)$ compared with the histogram of the 4th point of 2000 samples:</p>
+<p>$$ {\Large \Rightarrow f_{\rm debinnning}(x) = \frac{f_{\rm\rust{bg}}(x)}{n N} \displaystyle \vec{G} \cdot \sum\limits_{j=1}^{n} \vec{G}_j } $$</p>
+<p>${\large \left[\vec{G}_{(j)} \equiv {}_N K_r F^{r-1}_{\rm\rust{bg}}(x_{(j)}) \left( 1 - F_{\rm\rust{bg}}(x_{(j)}) \right)^{N-r} \right] }$.</p>
</div>
</div>
</div>
+ </div><div style=display:none>
+
<div class="cell border-box-sizing code_cell rendered">
<div class="input_hidden">
<div class="input">
<div class="prompt input_prompt">
-In&nbsp;[8]:
+In&nbsp;[19]:
</div>
<div class="inner_cell">
<div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
-</pre></div>
+<div class="highlight"><pre><span class="n">settings</span><span class="p">[</span><span class="s">&#39;simpleSortedOutput&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
+<span class="n">nPulls</span> <span class="o">=</span> <span class="mi">96</span>
+<span class="n">nFictitious</span><span class="o">=</span><span class="mi">96</span>
-</div>
-</div>
-</div>
+<span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">data</span> <span class="o">=</span> <span class="n">quickData</span><span class="p">()</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="n">bgF</span><span class="p">,</span> <span class="n">bgData</span> <span class="o">=</span> <span class="n">quickBG</span><span class="p">()</span>
+<span class="n">f</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">F</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgf</span> <span class="o">/=</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgF</span> <span class="o">/=</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-</div>
+
+<span class="k">def</span> <span class="nf">mapDataToX</span><span class="p">(</span><span class="n">dindex</span><span class="p">):</span>
+ <span class="c"># maps elements of data to elements of x</span>
+ <span class="c"># bisect_left(x, datum) locates the left-most entry in x which is &gt;= datum</span>
+ <span class="n">xindex</span> <span class="o">=</span> <span class="n">bisect</span><span class="o">.</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">])</span>
+ <span class="k">if</span> <span class="n">xindex</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">x</span><span class="p">[</span><span class="n">xindex</span><span class="p">]</span> <span class="o">-</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">]</span> <span class="o">-</span> <span class="n">x</span><span class="p">[</span><span class="n">xindex</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="n">xindex</span> <span class="o">-</span> <span class="mi">1</span>
+ <span class="k">return</span> <span class="n">xindex</span>
+<span class="n">dataToX</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">mapDataToX</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">))])</span>
-<div class="output_wrapper">
-<div class="output">
+<span class="k">def</span> <span class="nf">vecG_rth</span><span class="p">(</span><span class="n">rindex</span><span class="p">,</span> <span class="n">xindex</span><span class="p">):</span>
+ <span class="n">r</span> <span class="o">=</span> <span class="n">rindex</span><span class="o">+</span><span class="mi">1</span>
+ <span class="k">return</span> <span class="n">pc</span><span class="o">.</span><span class="n">nKr</span><span class="p">(</span><span class="n">nFictitious</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="o">*</span> <span class="n">bgF</span><span class="p">[</span><span class="n">xindex</span><span class="p">]</span><span class="o">**</span><span class="p">(</span><span class="n">r</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">bgF</span><span class="p">[</span><span class="n">xindex</span><span class="p">])</span><span class="o">**</span><span class="p">(</span><span class="n">nFictitious</span> <span class="o">-</span> <span class="n">r</span><span class="p">)</span>
-<div class="output_area"><div class="prompt"></div>
+<span class="n">vecG_rx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">vecG_rth</span><span class="p">(</span><span class="n">rindex</span><span class="p">,</span> <span class="n">xindex</span><span class="p">)</span> <span class="k">for</span> <span class="n">xindex</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))]</span>
+ <span class="k">for</span> <span class="n">rindex</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">nFictitious</span><span class="p">)])</span>
+<span class="n">sumG_j</span> <span class="o">=</span> <span class="n">vecG_rx</span><span class="o">.</span><span class="n">take</span><span class="p">(</span><span class="n">dataToX</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">debinningData</span> <span class="o">=</span> <span class="n">bgf</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">sumG_j</span><span class="p">,</span> <span class="n">vecG_rx</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">nFictitious</span><span class="o">*</span><span class="n">nPulls</span><span class="p">)</span>
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-"
->
-</div>
+<span class="c"># One more pull for plotting purposes</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">data</span> <span class="o">=</span> <span class="n">quickData</span><span class="p">()</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="n">bgF</span><span class="p">,</span> <span class="n">bgData</span> <span class="o">=</span> <span class="n">quickBG</span><span class="p">()</span>
+<span class="n">f</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgf</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgF</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">F</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-</div>
+<span class="k">def</span> <span class="nf">makeDebinningPlot</span><span class="p">():</span>
+ <span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">11</span><span class="p">,</span><span class="mi">7</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">&#39;#ffffff&#39;</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="s">&#39;--&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="s">&#39;-.&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#66a61e&#39;</span><span class="p">,</span> <span class="n">normed</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">debinningData</span><span class="p">,</span> <span class="s">&#39;#964a01&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span><span class="p">)</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">50</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">bottom</span><span class="o">=-</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.0201</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">))</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%0.3f</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="n">num</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="o">/</span><span class="mi">5</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">&#39;Physical Observable&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">&#39;Probability&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+
+ <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">length</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">which</span><span class="o">=</span><span class="s">&#39;minor&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
+ <span class="n">axes</span><span class="o">.</span><span class="n">minorticks_on</span><span class="p">()</span>
+</pre></div>
</div>
</div>
+</div>
-</div></section><section>
+</div>
+
+</div>
+ </div></section><section>
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<div class="prompt input_prompt">
</div>
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<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{5}(x)$ compared with the histogram of the 5th point of 2000 samples:</p>
+<h2 id="debinning-demonstration">debinning Demonstration</h2>
</div>
</div>
</div>
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<div class="input_hidden">
<div class="input">
<div class="prompt input_prompt">
-In&nbsp;[9]:
+In&nbsp;[20]:
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<div class="inner_cell">
<div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<div class="highlight"><pre><span class="n">makeDebinningPlot</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
</div>
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"
>
</div>
</div>
</div>
</div>
-</div></section><section>
+</div><div style=display:none>
-<div class="cell border-box-sizing text_cell rendered">
+<div class="cell border-box-sizing code_cell rendered">
+<div class="input_hidden">
+<div class="input">
<div class="prompt input_prompt">
+In&nbsp;[21]:
</div>
<div class="inner_cell">
-<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{6}(x)$ compared with the histogram of the 6th point of 2000 samples:</p>
+ <div class="input_area">
+<div class="highlight"><pre><span class="n">fwhmValues</span><span class="o">=</span><span class="bp">None</span>
+</pre></div>
+
+</div>
</div>
</div>
+
+</div>
+
</div>
+ </div><div style=display:none>
+
<div class="cell border-box-sizing code_cell rendered">
<div class="input_hidden">
<div class="input">
<div class="prompt input_prompt">
-In&nbsp;[10]:
+In&nbsp;[23]:
</div>
<div class="inner_cell">
<div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<div class="highlight"><pre><span class="c"># Let&#39;s try some GPU programming:</span>
+<span class="kn">import</span> <span class="nn">pycuda.driver</span> <span class="kn">as</span> <span class="nn">cuda</span>
+<span class="kn">import</span> <span class="nn">pycuda.autoinit</span>
+<span class="kn">from</span> <span class="nn">pycuda.compiler</span> <span class="kn">import</span> <span class="n">SourceModule</span>
+<span class="kn">from</span> <span class="nn">string</span> <span class="kn">import</span> <span class="n">Template</span>
+
+<span class="n">settings</span><span class="p">[</span><span class="s">&#39;simpleSortedOutput&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
+<span class="n">nPulls</span> <span class="o">=</span> <span class="mi">96</span>
+<span class="n">nFictitious</span> <span class="o">=</span> <span class="mi">96</span> <span class="c"># Multiple of 32 for GPU programming ease.</span>
+<span class="n">lenXdomain</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">8.5</span><span class="p">,</span> <span class="mf">200.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">))</span>
+
+<span class="n">mod_template</span> <span class="o">=</span> <span class="n">Template</span><span class="p">(</span><span class="s">&quot;&quot;&quot;</span>
+<span class="s"> __global__ void vecG(double *vecG_rx, double *bgF, double *nKr) {</span>
+<span class="s"> const int idr = threadIdx.y + blockDim.y * blockIdx.y;</span>
+<span class="s"> const int idx = threadIdx.x + blockDim.x * blockIdx.x;</span>
+<span class="s"> const int idrx = idx + idr*${lenX};</span>
+<span class="s"> const int r = (idr + 1) &lt; (${nFic} - idr) ? (idr + 1) : ${nFic} - idr;</span>
+<span class="s"> vecG_rx[idrx] = nKr[r-1] * pow(bgF[idx], idr) * pow(1 - bgF[idx], ${nFic} - idr - 1);</span>
+<span class="s"> }</span>
+<span class="s"> &quot;&quot;&quot;</span><span class="p">)</span>
+
+<span class="n">mod</span> <span class="o">=</span> <span class="n">SourceModule</span><span class="p">(</span><span class="n">mod_template</span><span class="o">.</span><span class="n">substitute</span><span class="p">(</span><span class="n">nFic</span><span class="o">=</span><span class="n">nFictitious</span><span class="p">,</span> <span class="n">lenX</span><span class="o">=</span><span class="n">lenXdomain</span><span class="p">))</span>
+
+<span class="n">timer</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
+
+<span class="c"># initialize the loop</span>
+<span class="n">nKr</span> <span class="o">=</span> <span class="n">pc</span><span class="o">.</span><span class="n">get_nKrArray</span><span class="p">(</span><span class="n">nFictitious</span><span class="p">)</span>
+<span class="n">chisq</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">bgchisq</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">ks</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">bgks</span> <span class="o">=</span> <span class="p">[]</span>
+
+<span class="k">for</span> <span class="n">trial</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">100000</span><span class="p">):</span>
+
+ <span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">data</span> <span class="o">=</span> <span class="n">quickData</span><span class="p">()</span>
+ <span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="n">bgF</span><span class="p">,</span> <span class="n">bgData</span> <span class="o">=</span> <span class="n">quickBG</span><span class="p">()</span>
+ <span class="n">f</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+ <span class="n">F</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+ <span class="n">bgf</span> <span class="o">/=</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+ <span class="n">bgF</span> <span class="o">/=</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+
+ <span class="k">def</span> <span class="nf">mapDataToX</span><span class="p">(</span><span class="n">dindex</span><span class="p">):</span>
+ <span class="c"># maps elements of data to elements of x</span>
+ <span class="c"># bisect_left(x, datum) locates the left-most entry in x which is &gt;= datum</span>
+ <span class="n">xindex</span> <span class="o">=</span> <span class="n">bisect</span><span class="o">.</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">])</span>
+ <span class="k">if</span> <span class="n">xindex</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">x</span><span class="p">[</span><span class="n">xindex</span><span class="p">]</span> <span class="o">-</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">]</span> <span class="o">-</span> <span class="n">x</span><span class="p">[</span><span class="n">xindex</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="n">xindex</span> <span class="o">-</span> <span class="mi">1</span>
+ <span class="k">return</span> <span class="n">xindex</span>
+ <span class="n">dataToX</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">mapDataToX</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">))])</span>
+
+ <span class="c"># Use the GPU for the most expensive / paralellizable part of the calculation:</span>
+ <span class="c"># =====</span>
+
+ <span class="c"># Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))</span>
+ <span class="n">vecG_rx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">([</span><span class="n">nFictitious</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)])</span>
+
+ <span class="c"># Allocate memory on the GPU for vecG calculation</span>
+ <span class="n">vecG_rx_gpu</span> <span class="o">=</span> <span class="n">cuda</span><span class="o">.</span><span class="n">mem_alloc</span><span class="p">(</span><span class="n">vecG_rx</span><span class="o">.</span><span class="n">nbytes</span><span class="p">)</span>
+ <span class="n">bgF_gpu</span> <span class="o">=</span> <span class="n">cuda</span><span class="o">.</span><span class="n">mem_alloc</span><span class="p">(</span><span class="n">bgF</span><span class="o">.</span><span class="n">nbytes</span><span class="p">)</span>
+ <span class="n">nKr_gpu</span> <span class="o">=</span> <span class="n">cuda</span><span class="o">.</span><span class="n">mem_alloc</span><span class="p">(</span><span class="n">nKr</span><span class="o">.</span><span class="n">nbytes</span><span class="p">)</span>
+
+ <span class="c"># Transfer data to the GPU</span>
+ <span class="n">cuda</span><span class="o">.</span><span class="n">memcpy_htod</span><span class="p">(</span><span class="n">bgF_gpu</span><span class="p">,</span> <span class="n">bgF</span><span class="p">)</span>
+ <span class="n">cuda</span><span class="o">.</span><span class="n">memcpy_htod</span><span class="p">(</span><span class="n">nKr_gpu</span><span class="p">,</span> <span class="n">nKr</span><span class="p">)</span>
+
+ <span class="c"># Get a reference to the GPU module function and do the calculation</span>
+ <span class="c"># NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious</span>
+ <span class="n">vecG_func</span> <span class="o">=</span> <span class="n">mod</span><span class="o">.</span><span class="n">get_function</span><span class="p">(</span><span class="s">&#39;vecG&#39;</span><span class="p">)</span>
+ <span class="n">vecG_func</span><span class="p">(</span><span class="n">vecG_rx_gpu</span><span class="p">,</span> <span class="n">bgF_gpu</span><span class="p">,</span> <span class="n">nKr_gpu</span><span class="p">,</span> <span class="n">block</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">grid</span><span class="o">=</span><span class="p">(</span><span class="mi">24</span><span class="p">,</span> <span class="mi">24</span><span class="p">))</span>
+
+ <span class="c"># Get the result back from the GPU and use it!</span>
+ <span class="n">cuda</span><span class="o">.</span><span class="n">memcpy_dtoh</span><span class="p">(</span><span class="n">vecG_rx</span><span class="p">,</span> <span class="n">vecG_rx_gpu</span><span class="p">)</span>
+ <span class="n">sumG_j</span> <span class="o">=</span> <span class="n">vecG_rx</span><span class="o">.</span><span class="n">take</span><span class="p">(</span><span class="n">dataToX</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+ <span class="n">debinningData</span> <span class="o">=</span> <span class="n">bgf</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">sumG_j</span><span class="p">,</span> <span class="n">vecG_rx</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">nFictitious</span><span class="o">*</span><span class="n">nPulls</span><span class="p">)</span>
+
+ <span class="c"># Chisq test....</span>
+ <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">fwhmValues</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+ <span class="n">chisq</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="mf">4.</span><span class="o">*</span><span class="p">(</span><span class="n">debinningData</span> <span class="o">-</span> <span class="n">f</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="n">fwhmValues</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">fwhmValues</span><span class="p">))</span>
+ <span class="n">bgchisq</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="mf">4.</span><span class="o">*</span><span class="p">(</span><span class="n">debinningData</span> <span class="o">-</span> <span class="n">bgf</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="n">fwhmValues</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">fwhmValues</span><span class="p">))</span>
+
+ <span class="c"># KS test...</span>
+ <span class="n">debinningCDF</span> <span class="o">=</span> <span class="n">pc</span><span class="o">.</span><span class="n">A</span><span class="p">(</span><span class="n">debinningData</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)</span>
+ <span class="n">ks</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">debinningCDF</span> <span class="o">-</span> <span class="n">F</span><span class="p">)))</span>
+ <span class="n">bgks</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">debinningCDF</span> <span class="o">-</span> <span class="n">bgF</span><span class="p">)))</span>
+
+ <span class="k">if</span> <span class="n">trial</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+ <span class="c"># Infinity sigma upper and lower bands...</span>
+ <span class="n">debinningUpper</span> <span class="o">=</span> <span class="n">debinningData</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
+ <span class="n">debinningLower</span> <span class="o">=</span> <span class="n">debinningData</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
+ <span class="c"># Uncertainty PDFs for each x value...</span>
+ <span class="n">uncertaintyHistos</span> <span class="o">=</span> <span class="p">[</span><span class="n">debinPlot</span><span class="o">.</span><span class="n">HistoContainer</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.024</span><span class="p">,</span> <span class="mf">0.0002</span><span class="p">),</span> <span class="n">debinningData</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))]</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">debinningUpper</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="n">debinningData</span><span class="p">,</span> <span class="n">debinningUpper</span><span class="p">,</span> <span class="mf">20.</span><span class="p">)</span>
+ <span class="n">debinningLower</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="n">debinningData</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">,</span> <span class="n">debinningLower</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)):</span>
+ <span class="k">try</span><span class="p">:</span>
+ <span class="n">uncertaintyHistos</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">addValue</span><span class="p">(</span><span class="n">debinningData</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+ <span class="k">except</span> <span class="ne">ValueError</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
+ <span class="k">print</span> <span class="n">e</span><span class="o">.</span><span class="n">message</span>
+ <span class="k">print</span> <span class="s">&#39;xindex = &#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">+</span> <span class="s">&#39;, debinningData[xindex] = &#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">debinningData</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+
+<span class="k">if</span> <span class="ow">not</span> <span class="nb">type</span><span class="p">(</span><span class="n">fwhmValues</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">:</span>
+ <span class="n">fwhmValues</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">uncertaintyHistos</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">fwhm</span><span class="p">())</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))])</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
+ <span class="k">print</span> <span class="s">&quot;Run this again for the Chisq test data...&quot;</span>
+<span class="k">print</span> <span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">timer</span>
</pre></div>
</div>
</div>
</div>
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+<div class="output_subarea output_stream output_stdout output_text">
+<pre>
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-SUVORK5CYII=
-"
->
+</pre>
</div>
-
</div>
</div>
</div>
-</div></section><section>
-
-<div class="cell border-box-sizing text_cell rendered">
-<div class="prompt input_prompt">
-</div>
-<div class="inner_cell">
-<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{7}(x)$ compared with the histogram of the 7th point of 2000 samples:</p>
-</div>
-</div>
</div>
+ </div><div style=display:none>
+
<div class="cell border-box-sizing code_cell rendered">
<div class="input_hidden">
<div class="input">
<div class="prompt input_prompt">
-In&nbsp;[11]:
+In&nbsp;[24]:
</div>
<div class="inner_cell">
<div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span>
+<div class="highlight"><pre><span class="c"># Try with a HUGE data set:</span>
+<span class="n">nPulls</span> <span class="o">=</span> <span class="mi">10000</span>
+
+<span class="n">timer</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">data</span> <span class="o">=</span> <span class="n">quickData</span><span class="p">()</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="n">bgF</span><span class="p">,</span> <span class="n">bgData</span> <span class="o">=</span> <span class="n">quickBG</span><span class="p">()</span>
+<span class="n">f</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">F</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgf</span> <span class="o">/=</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgF</span> <span class="o">/=</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+
+<span class="k">def</span> <span class="nf">mapDataToX</span><span class="p">(</span><span class="n">dindex</span><span class="p">):</span>
+ <span class="c"># maps elements of data to elements of x</span>
+ <span class="c"># bisect_left(x, datum) locates the left-most entry in x which is &gt;= datum</span>
+ <span class="n">xindex</span> <span class="o">=</span> <span class="n">bisect</span><span class="o">.</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">])</span>
+ <span class="k">if</span> <span class="n">xindex</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">x</span><span class="p">[</span><span class="n">xindex</span><span class="p">]</span> <span class="o">-</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">]</span> <span class="o">-</span> <span class="n">x</span><span class="p">[</span><span class="n">xindex</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="n">xindex</span> <span class="o">-</span> <span class="mi">1</span>
+ <span class="k">return</span> <span class="n">xindex</span>
+<span class="n">dataToX</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">mapDataToX</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">))])</span>
+
+<span class="c"># Use the GPU for the most expensive / paralellizable part of the calculation:</span>
+<span class="c"># =====</span>
+
+<span class="c"># Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))</span>
+<span class="n">vecG_rx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">([</span><span class="n">nFictitious</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)])</span>
+
+<span class="c"># Allocate memory on the GPU for vecG calculation</span>
+<span class="n">vecG_rx_gpu</span> <span class="o">=</span> <span class="n">cuda</span><span class="o">.</span><span class="n">mem_alloc</span><span class="p">(</span><span class="n">vecG_rx</span><span class="o">.</span><span class="n">nbytes</span><span class="p">)</span>
+<span class="n">bgF_gpu</span> <span class="o">=</span> <span class="n">cuda</span><span class="o">.</span><span class="n">mem_alloc</span><span class="p">(</span><span class="n">bgF</span><span class="o">.</span><span class="n">nbytes</span><span class="p">)</span>
+<span class="n">nKr_gpu</span> <span class="o">=</span> <span class="n">cuda</span><span class="o">.</span><span class="n">mem_alloc</span><span class="p">(</span><span class="n">nKr</span><span class="o">.</span><span class="n">nbytes</span><span class="p">)</span>
+
+<span class="c"># Transfer data to the GPU</span>
+<span class="n">cuda</span><span class="o">.</span><span class="n">memcpy_htod</span><span class="p">(</span><span class="n">bgF_gpu</span><span class="p">,</span> <span class="n">bgF</span><span class="p">)</span>
+<span class="n">cuda</span><span class="o">.</span><span class="n">memcpy_htod</span><span class="p">(</span><span class="n">nKr_gpu</span><span class="p">,</span> <span class="n">nKr</span><span class="p">)</span>
+
+<span class="c"># Get a reference to the GPU module function and do the calculation</span>
+<span class="c"># NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious</span>
+<span class="n">vecG_func</span> <span class="o">=</span> <span class="n">mod</span><span class="o">.</span><span class="n">get_function</span><span class="p">(</span><span class="s">&#39;vecG&#39;</span><span class="p">)</span>
+<span class="n">vecG_func</span><span class="p">(</span><span class="n">vecG_rx_gpu</span><span class="p">,</span> <span class="n">bgF_gpu</span><span class="p">,</span> <span class="n">nKr_gpu</span><span class="p">,</span> <span class="n">block</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">grid</span><span class="o">=</span><span class="p">(</span><span class="mi">24</span><span class="p">,</span> <span class="mi">24</span><span class="p">))</span>
+
+<span class="c"># Get the result back from the GPU and use it!</span>
+<span class="n">cuda</span><span class="o">.</span><span class="n">memcpy_dtoh</span><span class="p">(</span><span class="n">vecG_rx</span><span class="p">,</span> <span class="n">vecG_rx_gpu</span><span class="p">)</span>
+<span class="n">sumG_j</span> <span class="o">=</span> <span class="n">vecG_rx</span><span class="o">.</span><span class="n">take</span><span class="p">(</span><span class="n">dataToX</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">BIGdebinningData</span> <span class="o">=</span> <span class="n">bgf</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">sumG_j</span><span class="p">,</span> <span class="n">vecG_rx</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">nFictitious</span><span class="o">*</span><span class="n">nPulls</span><span class="p">)</span>
+<span class="k">print</span> <span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">timer</span>
</pre></div>
</div>
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</div>
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<div class="output_area"><div class="prompt"></div>
+<div class="output_subarea output_stream output_stdout output_text">
+<pre>
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-"
->
+</pre>
</div>
-
</div>
</div>
</div>
-</div></section><section>
+</div>
+ </div></section>
+ </section><section>
+ <section>
<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{8}(x)$ compared with the histogram of the 8th point of 2000 samples:</p>
+<h2 id="debinning-performace-uncertainty">debinning Performace: Uncertainty</h2>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input_hidden">
<div class="input">
<div class="prompt input_prompt">
-In&nbsp;[12]:
+In&nbsp;[25]:
</div>
<div class="inner_cell">
<div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>
+<div class="highlight"><pre><span class="c"># One more pull for plotting purposes</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">data</span> <span class="o">=</span> <span class="n">quickData</span><span class="p">()</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="n">bgF</span><span class="p">,</span> <span class="n">bgData</span> <span class="o">=</span> <span class="n">quickBG</span><span class="p">()</span>
+<span class="n">f</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgf</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">bgF</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">F</span> <span class="o">/=</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+
+<span class="c"># Pretty plot</span>
+<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">11</span><span class="p">,</span><span class="mi">7</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">&#39;#ffffff&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">debinningUpper</span><span class="p">,</span> <span class="n">debinningLower</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s">&#39;-.&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">BIGdebinningData</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;black&#39;</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s">&#39;--&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
+<span class="n">colors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([(</span><span class="mf">0.8</span><span class="p">,</span><span class="mf">1.</span><span class="p">,</span><span class="mf">0.4</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.8</span><span class="p">,</span><span class="mf">0.3</span><span class="p">,</span><span class="mf">0.</span><span class="p">),</span> <span class="p">(</span><span class="mf">1.</span><span class="p">,</span><span class="mf">1.</span><span class="p">,</span><span class="mf">1.</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">1.</span><span class="p">)])</span>
+<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+ <span class="n">debinPlot</span><span class="o">.</span><span class="n">verticalColorBand</span><span class="p">(</span><span class="n">uncertaintyHistos</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">v</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">colors</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span><span class="p">)</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">201</span><span class="p">,</span> <span class="mi">50</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">bottom</span><span class="o">=-</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.0201</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">))</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%0.3f</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="n">num</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="o">/</span><span class="mi">5</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">&#39;Physical Observable&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">&#39;Probability&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">length</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">which</span><span class="o">=</span><span class="s">&#39;minor&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">minorticks_on</span><span class="p">()</span>
+
+<span class="k">print</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area"><div class="prompt"></div>
+<div class="output_subarea output_stream output_stdout output_text">
+<pre>
+
+
+</pre>
+</div>
+</div>
+
+<div class="output_area"><div class="prompt"></div>
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"
>
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</div>
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</div></section><section>
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-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{9}(x)$ compared with the histogram of the 9th point of 2000 samples:</p>
+<h2 id="debinning-performace-discrimination">debinning Performace: Discrimination</h2>
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-In&nbsp;[13]:
+In&nbsp;[26]:
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<div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">8</span><span class="p">)</span>
+<div class="highlight"><pre><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">11</span><span class="p">,</span><span class="mi">7</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">&#39;#ffffff&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">chisq</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">7.01</span><span class="p">,</span> <span class="o">.</span><span class="mo">05</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s">&#39;#555555&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">bgchisq</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">7.01</span><span class="p">,</span> <span class="o">.</span><span class="mo">05</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#66a61e&#39;</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s">&#39;#555555&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">7.01</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">7.01</span><span class="p">,</span> <span class="o">.</span><span class="mi">25</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%1.1f</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="n">num</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">7.01</span><span class="p">,</span> <span class="mi">1</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">bottom</span><span class="o">=-</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mi">6000</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">6001</span><span class="p">,</span> <span class="mi">1000</span><span class="p">))</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">6001</span><span class="p">,</span> <span class="mi">250</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span><span class="p">)</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">6001</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">r&#39;$\chi^2$ per d.o.f.&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">&#39;Number of Counts&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">length</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">which</span><span class="o">=</span><span class="s">&#39;minor&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">minorticks_on</span><span class="p">()</span>
+<span class="k">print</span>
</pre></div>
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+<div class="output_subarea output_stream output_stdout output_text">
+<pre>
+
+
+</pre>
+</div>
+</div>
+
+<div class="output_area"><div class="prompt"></div>
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"
>
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</div>
</div></section><section>
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<div class="text_cell_render border-box-sizing rendered_html">
-<p>Let&#39;s try it! We will pull 2000 samples of 10 data points each.</p>
-<p>Here&#39;s $\subNsubR{10}{f}{10}(x)$ compared with the histogram of the 10th point of 2000 samples:</p>
+<h2 id="debinning-performace-discrimination">debinning Performace: Discrimination</h2>
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</div>
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-In&nbsp;[14]:
+In&nbsp;[27]:
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<div class="input_area">
-<div class="highlight"><pre><span class="n">makeHist</span><span class="p">(</span><span class="mi">9</span><span class="p">)</span>
+<div class="highlight"><pre><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">11</span><span class="p">,</span><span class="mi">7</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">&#39;#ffffff&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">ks</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="o">.</span><span class="mo">002</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#0088ff&#39;</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s">&#39;#555555&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">bgks</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="o">.</span><span class="mo">002</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#66a61e&#39;</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s">&#39;#555555&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.26</span><span class="p">,</span> <span class="o">.</span><span class="mo">05</span><span class="p">))</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.26</span><span class="p">,</span> <span class="o">.</span><span class="mo">01</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%0.2f</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="n">num</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.26</span><span class="p">,</span> <span class="o">.</span><span class="mo">05</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">bottom</span><span class="o">=-</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mi">5000</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5001</span><span class="p">,</span> <span class="mi">1000</span><span class="p">))</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5001</span><span class="p">,</span> <span class="mi">250</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span><span class="p">)</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5001</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">&#39;KS test value&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">&#39;Number of Counts&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
+
+<span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">length</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">which</span><span class="o">=</span><span class="s">&#39;minor&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
+<span class="n">axes</span><span class="o">.</span><span class="n">minorticks_on</span><span class="p">()</span>
+<span class="k">print</span>
</pre></div>
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+<div class="output_subarea output_stream output_stdout output_text">
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+</div>
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+SaPR0Mcff0z9/f3SZzT8+YGBgSN+dq2trbRmzRpSq9Ukl8vJw8ODkpKS6MaNGxQbG0symczkYI5B
+R48epaioKHJzcyOFQkEODg7k7e1NUVFRpNVqqaOjY0zvgTE2MfEKMWOMMcYYm9S4h5gxxhhjjE1q
+XBAzxhhjjLFJjQtixhhjjDE2qXFBzBhjjDHGJjUuiBljjDHG2KTGBTFjjDHGGJvUuCBmjDHGGGOT
+GhfEjDHGGGNsUuOCmDHGGGOMTWpcEDPGGGOMsUntPzpBzASQHa3CAAAAAElFTkSuQmCC
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-<h2 id="samples-v-to-be-0-th-out-of-1-cont-d-">Samples - V: To be $r$th out of $n$ (cont&#39;d)...</h2>
-<p>As stated above, $\subNsubR{n}{f}{r}(x)$ is the PDF of the $r$th data point within a sample of $n$ data points. We can write that as a conditional probability:</p>
-<p>$$ {\Large P(\tilde{x} \in [x, x + dx]\ |\ \tilde{x}\ {\rm is\ } r{\rm th\ of\ } n, f) \equiv \subNsubR{n}{f}{r}(x) dx } $$</p>
+<h1 id="the-future-and-shameless-advertising-">The Future, and Shameless Advertising:</h1>
+<h2 id="-yikes-there-is-so-much-more-">&quot;Yikes.... There is so much more!&quot;</h2>
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+</div></section><section>
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-<p>We can &quot;invert&quot; that using Bayes&#39; Theorem: </p>
-<p>\begin{align}
- P(\tilde{x}\ {\rm is\ } r{\rm th\ of\ } n\ |\ \tilde{x} \in [x, x + dx], f)
- &amp;= \frac{P(\tilde{x} \in [x, x + dx]\ |\ \tilde{x}\ {\rm is\ } r{\rm th\ of\ } n, f)\
- P(\tilde{x}\ {\rm is\ } r{\rm th\ of\ } n)}{P(\tilde{x} \in [x, x + dx])} \\
- &amp;= \frac{\subNsubR{n}{f}{r}(x) dx\ \frac{1}{n}}{f(x) dx}
-\end{align}</p>
+<h2 id="probability-calculus-future">Probability Calculus: Future</h2>
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+</div><div class="fragment">
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-<p>$$ {\large \therefore P(\tilde{x}\ {\rm is\ } r{\rm th\ of\ } n\ |\ \tilde{x} \in [x, x + dx], f)
- = \frac{\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \left(1 - F(x)\right)^{n-r} .} $$</p>
+<h3 id="two-point-correlation-distribution-0-">Two-point correlation distribution, $\subNsubR{n}{f}{r,s}(x_r, x_s)$...</h3>
+<h3 id="-1-form-is-known-already-but-use-">$\qquad$ Form is known already, but use...?</h3>
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-<p>This proof is so very fun, I will leave it as an exercise:</p>
-<p>$$ {\large \Sum{r=1}{n} \frac{\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \left(1 - F(x)\right)^{n-r} = 1, \quad \forall x.} $$</p>
+<h3 id="re-derive-or-re-interpret-current-statistical-methods-">Re-derive or Re-interpret current statistical methods?</h3>
+<h3 id="-0-poisson-and-multinomial-changes-">$\qquad$ Poisson and Multinomial changes?</h3>
+<h3 id="-1-likelihoods-unbinned-likelihoods-re-derive-">$\qquad$ Likelihoods... Unbinned likelihoods... Re-derive?</h3>
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- </section><section>
- <section>
+ </div></section><section>
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-<h2 id="the-debinning-algorithm">The Debinning Algorithm</h2>
-<p>Imagine the following scenario:</p>
-<ul>
-<li>An experiment measures a sample, $\{x_i\}_{i=1}^n$, which follow some PDF $f(x)$.</li>
-<li>The background PDF, $f_{\rm bg}(x)$, is known.</li>
-<li>Based upon the sample probabilities, here is a data smoothing algorithm:</li>
-</ul>
+<h2 id="debinning-statistical-impact">debinning: Statistical impact</h2>
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-<ul>
-<li>Choose a size for the number of points in some fictitious data set, $N_{\rm fic}$.</li>
-<li>To generate some huge number of smoothed points, $\aleph$.<ol>
-<li>Randomly choose a point, $x_j$, from the sample.</li>
-<li>Based upon $P(\tilde{x}\ {\rm is\ } r{\rm th\ of\ } N_{\rm fic}\ |\ \tilde{x} \in [x_j, x_j + dx_j], f_{\rm bg})$, randomly choose which $r$ this $x_j$ might be.</li>
-<li>Return a random pull from $\subNsubR{N_{\rm fic}}{f}{r}(x) \equiv P(\tilde{x} \in [x, x + dx]\ |\ \tilde{x}\ {\rm is\ } r{\rm th\ of\ } N_{\rm fic}, f_{\rm bg})$.</li>
-</ol>
-</li>
-</ul>
+<h3 id="full-comparison-debinning-vs-histograms">Full comparison: debinning vs histograms</h3>
+<h3 id="-0-discovery-signifigance-">$\qquad$ Discovery signifigance?</h3>
+<h3 id="-1-parameter-estimation-performance-">$\qquad$ Parameter estimation performance?</h3>
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-<p>This algorithm needs to generate $3\aleph$ random numbers. Very slow...</p>
+<h3 id="full-comparison-debinning-vs-unbinned-maximum-likelihood">Full comparison: debinning vs unbinned maximum likelihood</h3>
+<h3 id="-0-discovery-signifigance-">$\qquad$ Discovery signifigance?</h3>
+<h3 id="-1-parameter-estimation-performance-">$\qquad$ Parameter estimation performance?</h3>
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- </section><section>
- <section>
+ </div></section><section>
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-<h2 id="the-debinning-algorithm-calculation">The Debinning Algorithm... Calculation</h2>
-<p>So, let&#39;s just calculate the PDF which results from that algorithm:</p>
+<h2 id="debinning-generalize-specialize">debinning: Generalize / Specialize</h2>
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-<p>$$ f_{\rm debinnning}(x) dx = P_{\rm binfull}\left(\tilde{x} \in [x, x + dx] | \{x_i\}_{i=1}^{n}, f_{\rm bg} \right) $$</p>
+<h3 id="-0-data-driven-backgrounds-">$\qquad$ data-driven backgrounds?</h3>
+<h3 id="-1-detector-resolution-unfolding-">$\qquad$ detector resolution &quot;unfolding&quot;?</h3>
+<h3 id="-2-max-gap-method-">$\qquad$ &quot;Max Gap Method&quot;?</h3>
+<h3 id="-3-2-debinning-n-debinning-">$\qquad$ 2-debinning? N-debinning?</h3>
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- </div><div class="fragment">
+ </div></section>
+ </section><section>
+ <section>
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-<p>$$ = \sum\limits_{j=1}^{n} P( x_j | \{x_i\}_{i=1}^{n} ) \sum\limits_{r=1}^{N} P(r{\rm th}\ {\rm of}\ N | x_j, f_{\rm bg}) P(\tilde{x} \in [x, x + dx] | r{\rm th}\ {\rm of}\ N, f_{\rm bg}) $$</p>
-</div>
+<h2 id="searching-for-new-stuff-with-statistics">Searching for &quot;New Stuff&quot; with Statistics</h2>
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-<p>$$ = \sum\limits_{j=1}^{n} \frac{1}{n} \sum\limits_{r=1}^{N} \left(\frac{{}_NK_r}{N} F_{\rm bg}(x_j)^{(r-1)}(1 - F_{\rm bg}(x_j))^{(N-r)} \right) \left( {}_NK_r f_{\rm bg}(x) F_{\rm bg}(x)^{(r-1)}(1 - F_{\rm bg}(x))^{(N-r)} dx \right) $$</p>
+<h3 id="new-global-fitting-tool-for-any-new-stuff-gambit">New global-fitting tool for any &quot;New Stuff&quot;: Gambit</h3>
+<h3 id="the-global-and-modular-bsm-inference-tool">The Global And Modular BSM Inference Tool</h3>
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-<p>$$ \Rightarrow f_{\rm debinnning}(x) = \frac{f_{\rm bg}(x)}{n N} \displaystyle \vec{G} \cdot \sum\limits_{j=1}^{n} \vec{G}_j $$</p>
-<p>where $\vec{G}_{(j)} \equiv {}_N K_r F^{r-1}_{\rm bg}(x_{(j)}) \left( 1 - F_{\rm bg}(x_{(j)}) \right)^{N-r}$.</p>
-</div>
-</div>
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-In&nbsp;[15]:
+In&nbsp;[28]:
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-<div class="highlight"><pre><span class="n">funcs</span><span class="o">.</span><span class="n">settings</span><span class="p">[</span><span class="s">&#39;simpleSortedOutput&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
-<span class="n">nPulls</span> <span class="o">=</span> <span class="mi">96</span>
-<span class="n">nFictitious</span><span class="o">=</span><span class="mi">96</span>
-
-<span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">data</span> <span class="o">=</span> <span class="n">quickData</span><span class="p">()</span>
-<span class="n">x</span><span class="p">,</span> <span class="n">bgf</span><span class="p">,</span> <span class="n">bgF</span><span class="p">,</span> <span class="n">bgData</span> <span class="o">=</span> <span class="n">quickBG</span><span class="p">()</span>
-<span class="n">f</span> <span class="o">=</span> <span class="n">f</span> <span class="o">/</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-<span class="n">F</span> <span class="o">=</span> <span class="n">F</span> <span class="o">/</span> <span class="n">F</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-<span class="n">bgf</span> <span class="o">=</span> <span class="n">bgf</span> <span class="o">/</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-<span class="n">bgF</span> <span class="o">=</span> <span class="n">bgF</span> <span class="o">/</span> <span class="n">bgF</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-
-
-<span class="k">def</span> <span class="nf">mapDataToX</span><span class="p">(</span><span class="n">dindex</span><span class="p">):</span>
- <span class="c"># maps elements of data to elements of x</span>
- <span class="c"># bisect_left(x, datum) locates the left-most entry in x which is &gt;= datum</span>
- <span class="n">xindex</span> <span class="o">=</span> <span class="n">bisect</span><span class="o">.</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">])</span>
- <span class="k">if</span> <span class="n">xindex</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">x</span><span class="p">[</span><span class="n">xindex</span><span class="p">]</span> <span class="o">-</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">data</span><span class="p">[</span><span class="n">dindex</span><span class="p">]</span> <span class="o">-</span> <span class="n">x</span><span class="p">[</span><span class="n">xindex</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
- <span class="k">return</span> <span class="n">xindex</span> <span class="o">-</span> <span class="mi">1</span>
- <span class="k">return</span> <span class="n">xindex</span>
-<span class="n">dataToX</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">mapDataToX</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">))])</span>
-
-
-<span class="k">def</span> <span class="nf">vecG_rth</span><span class="p">(</span><span class="n">rindex</span><span class="p">,</span> <span class="n">xindex</span><span class="p">):</span>
- <span class="n">r</span> <span class="o">=</span> <span class="n">rindex</span><span class="o">+</span><span class="mi">1</span>
- <span class="k">return</span> <span class="n">funcs</span><span class="o">.</span><span class="n">nKr</span><span class="p">(</span><span class="n">nFictitious</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="o">*</span> <span class="n">bgF</span><span class="p">[</span><span class="n">xindex</span><span class="p">]</span><span class="o">**</span><span class="p">(</span><span class="n">r</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">bgF</span><span class="p">[</span><span class="n">xindex</span><span class="p">])</span><span class="o">**</span><span class="p">(</span><span class="n">nFictitious</span> <span class="o">-</span> <span class="n">r</span><span class="p">)</span>
-
+<div class="highlight"><pre><span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">HTML</span>
+<span class="n">HTML</span><span class="p">(</span><span class="s">&#39;&lt;iframe src=http://gambit.hepforge.org/ width=1000 height=350&gt;&lt;/iframe&gt;&#39;</span><span class="p">)</span>
+</pre></div>
-<span class="n">vecG_rx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">vecG_rth</span><span class="p">(</span><span class="n">rindex</span><span class="p">,</span> <span class="n">xindex</span><span class="p">)</span> <span class="k">for</span> <span class="n">xindex</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))]</span>
- <span class="k">for</span> <span class="n">rindex</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">nFictitious</span><span class="p">)])</span>
-<span class="n">sumG_j</span> <span class="o">=</span> <span class="n">vecG_rx</span><span class="o">.</span><span class="n">take</span><span class="p">(</span><span class="n">dataToX</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
-<span class="n">debinningData</span> <span class="o">=</span> <span class="n">bgf</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">sumG_j</span><span class="p">,</span> <span class="n">vecG_rx</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">nFictitious</span><span class="o">*</span><span class="n">nPulls</span><span class="p">)</span>
+</div>
+</div>
+</div>
-<span class="c"># Discard trivial data</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">compress</span><span class="p">(</span><span class="n">bgf</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span>
-<span class="n">debinningData</span> <span class="o">=</span> <span class="n">debinningData</span><span class="o">.</span><span class="n">compress</span><span class="p">(</span><span class="n">bgf</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span>
-<span class="n">f</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="n">compress</span><span class="p">(</span><span class="n">bgf</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span>
+</div>
-<span class="k">def</span> <span class="nf">makeDebinningPlot</span><span class="p">():</span>
- <span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">9</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span> <span class="n">facecolor</span><span class="o">=</span><span class="s">&#39;#ffffff&#39;</span><span class="p">)</span>
- <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">histogramRange</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">&#39;#66a61e&#39;</span><span class="p">,</span> <span class="n">normed</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
- <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">debinningData</span><span class="p">,</span> <span class="s">&#39;#964a01&#39;</span><span class="p">)</span>
- <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="s">&#39;--&#39;</span><span class="p">)</span>
-
- <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">majorTicksRange</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">minorTicksRange</span><span class="p">,</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%i</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span><span class="p">)</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">majorTicksRange</span><span class="p">],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
-
- <span class="n">axes</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">bottom</span><span class="o">=-</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.0201</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">))</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">([</span><span class="s">r&#39;$</span><span class="si">%0.3f</span><span class="s">$&#39;</span> <span class="o">%</span> <span class="n">num</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">)],</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.005</span><span class="o">/</span><span class="mi">5</span><span class="p">),</span> <span class="n">minor</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
+<div class="output_wrapper">
+<div class="output">
- <span class="n">axes</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">&#39;Physical Observable&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">&#39;Probability&#39;</span><span class="p">,</span> <span class="n">labelpad</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">22</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">length</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="mi">22</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">pad</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">which</span><span class="o">=</span><span class="s">&#39;minor&#39;</span><span class="p">,</span> <span class="n">length</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="mf">1.2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">)</span>
- <span class="n">axes</span><span class="o">.</span><span class="n">minorticks_on</span><span class="p">()</span>
-</pre></div>
+<div class="output_area"><div class="prompt output_prompt">
+ Out[28]:</div>
+<div class="output_html rendered_html output_subarea output_pyout">
+<iframe src=http://gambit.hepforge.org/ width=1000 height=350></iframe>
</div>
-</div>
+
</div>
</div>
+</div>
</div>
- </div></section>
- </section><section>
- <section>
+ </div></section><section>
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<div class="prompt input_prompt">
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<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<h2 id="the-debinning-demonstration">The Debinning Demonstration</h2>
-<p>Here&#39;s what it looks like:</p>
+<h2 id="shameless-gambit-advertising-">Shameless Gambit Advertising:</h2>
</div>
</div>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input_hidden">
-<div class="input">
+</div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
-In&nbsp;[16]:
</div>
<div class="inner_cell">
- <div class="input_area">
-<div class="highlight"><pre><span class="n">makeDebinningPlot</span><span class="p">()</span>
-</pre></div>
-
-</div>
-</div>
-</div>
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-</div>
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-"
->
-</div>
-
-</div>
-
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="our-flagship-scan-supersymmetry-">Our flagship scan: Supersymmetry!</h3>
+<h3 id="-0-our-pmssm-25-scan-scanning-25-parameters-">$\qquad$ Our PMSSM-25 scan: Scanning 25 parameters!</h3>
</div>
</div>
-
</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input_hidden">
-<div class="input">
+ </div><div class="fragment">
+
+<div class="cell border-box-sizing text_cell rendered">
<div class="prompt input_prompt">
-In&nbsp;[]:
</div>
<div class="inner_cell">
- <div class="input_area">
-<div class="highlight"><pre>
-</pre></div>
-
-</div>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="about-us-">About us:</h3>
+<p>GAMBIT is a global fitting code for generic Beyond the Standard Model theories, designed to allow fast and easy definition of new models, observables, likelihoods, scanners and backend physics codes.</p>
+<p>GAMBIT is developed by a group of nearly 30 theorists and experimentalists. The Collaboration includes members of the AMS-02, ATLAS, CDMS, CTA, DARWIN, DM-ICE, Fermi-LAT, HESS, IceCube, LHCb and XENON experiments, as well as developers of the public theory codes DarkSUSY, FlexibleSUSY, IsaJet, SoftSUSY and SuperIso.</p>
+<p>We are currently finalising the code in preparation for first public release in Summer 2015 — stay tuned!</p>
</div>
</div>
-
</div>
-
-</div></section>
- </section>
+ </div>
</div>
</div>
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</body>
+<!-- Loading mathjax macro -->
+<!-- Load mathjax -->
+ <script src="/home/krill/.ipython/nbextensions/mathjax/MathJax.js?config=TeX-AMS_HTML"></script>
+ <!-- MathJax configuration -->
+ <script type="text/x-mathjax-config">
+ MathJax.Hub.Config({
+ tex2jax: {
+ inlineMath: [ ['$','$'], ["\\(","\\)"] ],
+ displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
+ processEscapes: true,
+ processEnvironments: true
+ },
+ // Center justify equations in code and markdown cells. Elsewhere
+ // we use CSS to left justify single line equations in code cells.
+ displayAlign: 'center',
+ "HTML-CSS": {
+ styles: {'.MathJax_Display': {"margin": 0}},
+ linebreaks: { automatic: true }
+ }
+ });
+ </script>
+ <!-- End of mathjax configuration -->
<script>
Reveal.initialize({
// Control settings
// ----------------
//controls: true,
//keyboard: true,
//mouseWheel: false,
//touch: true,
//autoSlide: 0, // in milliseconds
//overview: true, // enable overview mode with Esc
//loop: false,
// Appearance settings
// -------------------
//progress: true, // progress bar
//center: true,
//rtl: false, // right to left. Torture your audience!!
// Transition settings
// -------------------
transition: 'none', // default/cube/page/concave/zoom/linear/fade/none
//transitionSpeed: 'default', // default/fast/slow
//backgroundTransition: 'default', // default/linear/none
theme: 'castiron' // available themes are in /css/theme
// Other settings
// --------------
// Push each slide change to the browser history
//history: false,
});
</script>
</html>
diff --git a/slides/binningDilemma_final_orig.png b/slides/binningDilemma_final_orig.png
new file mode 100644
index 0000000..c91772c
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diff --git a/slides/easyEndpoint_binfullLinearExpanding_final.png b/slides/easyEndpoint_binfullLinearExpanding_final.png
new file mode 100644
index 0000000..3e0d85b
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diff --git a/slides/epicLHCHighFive.png b/slides/epicLHCHighFive.png
new file mode 100644
index 0000000..e5e5703
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diff --git a/slides/epicLHCHighFive.xcf b/slides/epicLHCHighFive.xcf
new file mode 100644
index 0000000..9fa238c
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diff --git a/slides/localDefaults.tpl b/slides/localDefaults.tpl
index 6bb291f..0778007 100644
--- a/slides/localDefaults.tpl
+++ b/slides/localDefaults.tpl
@@ -1,81 +1,106 @@
{%- extends 'slides_reveal.tpl' -%}
+{%- macro myMathjax() -%}
+ <!-- Load mathjax -->
+ <script src="/home/krill/.ipython/nbextensions/mathjax/MathJax.js?config=TeX-AMS_HTML"></script>
+ <!-- MathJax configuration -->
+ <script type="text/x-mathjax-config">
+ MathJax.Hub.Config({
+ tex2jax: {
+ inlineMath: [ ['$','$'], ["\\(","\\)"] ],
+ displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
+ processEscapes: true,
+ processEnvironments: true
+ },
+ // Center justify equations in code and markdown cells. Elsewhere
+ // we use CSS to left justify single line equations in code cells.
+ displayAlign: 'center',
+ "HTML-CSS": {
+ styles: {'.MathJax_Display': {"margin": 0}},
+ linebreaks: { automatic: true }
+ }
+ });
+ </script>
+ <!-- End of mathjax configuration -->
+{%- endmacro %}
{% block input_group -%}
<div class="input_hidden">
{{ super() }}
</div>
{% endblock input_group %}
{%- block header -%}
{{ super() }}
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<style type="text/css">
//div.output_wrapper {
// margin-top: 0px;
//}
.input_hidden {
display: none;
// margin-top: 5px;
}
</style>
<script>
$(document).ready(function(){
$(".output_wrapper").click(function(){
$(this).prev('.input_hidden').slideToggle();
});
})
</script>
{%- endblock header -%}
{% block body %}
{{ super() }}
+<!-- Loading mathjax macro -->
+{{ myMathjax() }}
<script>
Reveal.initialize({
// Control settings
// ----------------
//controls: true,
//keyboard: true,
//mouseWheel: false,
//touch: true,
//autoSlide: 0, // in milliseconds
//overview: true, // enable overview mode with Esc
//loop: false,
// Appearance settings
// -------------------
//progress: true, // progress bar
//center: true,
//rtl: false, // right to left. Torture your audience!!
// Transition settings
// -------------------
transition: 'none', // default/cube/page/concave/zoom/linear/fade/none
//transitionSpeed: 'default', // default/fast/slow
//backgroundTransition: 'default', // default/linear/none
theme: 'castiron' // available themes are in /css/theme
// Other settings
// --------------
// Push each slide change to the browser history
//history: false,
});
</script>
{% endblock body %}
diff --git a/slides/nfbgrSmoothing.png b/slides/nfbgrSmoothing.png
new file mode 100644
index 0000000..7f81510
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diff --git a/slides/nfbgrSmoothing.xcf b/slides/nfbgrSmoothing.xcf
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index 0000000..08bc5bc
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diff --git a/slides/nfrSmoothing.png b/slides/nfrSmoothing.png
new file mode 100644
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diff --git a/slides/notTheOnlyShape.png b/slides/notTheOnlyShape.png
new file mode 100644
index 0000000..e5c76b7
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diff --git a/slides/notTheOnlyShape.xcf b/slides/notTheOnlyShape.xcf
new file mode 100644
index 0000000..8ac032d
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diff --git a/slides/stuffWeKnow.png b/slides/stuffWeKnow.png
new file mode 100644
index 0000000..c7a0d62
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diff --git a/slides/stuffWeKnow.xcf b/slides/stuffWeKnow.xcf
new file mode 100644
index 0000000..a15e0aa
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diff --git a/slides/tryChangingTheBins.png b/slides/tryChangingTheBins.png
new file mode 100644
index 0000000..4e606a9
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diff --git a/slides/tryChangingTheBins.xcf b/slides/tryChangingTheBins.xcf
new file mode 100644
index 0000000..ad87d48
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diff --git a/utilities/__init__.py b/utilities/__init__.py
index e69de29..6f48325 100644
--- a/utilities/__init__.py
+++ b/utilities/__init__.py
@@ -0,0 +1,21 @@
+'''
+__init__.py
+Global settings for debinning utilities.
+Copyright (C) 2014, 2015 Abram Krislock
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the, 110., 1.5, 50., 140.
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see http://www.gnu.org/licenses/gpl-3.0.txt.
+'''
+settings = {}
+settings['simpleSortedOutput'] = False
+settings['debug'] = False
diff --git a/utilities/plotting.py b/utilities/plotting.py
index fbe0b3d..00a4b45 100644
--- a/utilities/plotting.py
+++ b/utilities/plotting.py
@@ -1,103 +1,148 @@
'''
plotting.py
Handy utilities for debinning plots with matplotlib.
Copyright (C) 2015 Abram Krislock
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see http://www.gnu.org/licenses/gpl-3.0.txt.
'''
import numpy as np
import bisect
from matplotlib import pyplot as plt
+from utilities import settings
class HistoContainer(object):
+
def __init__(self, binEdges, data=None, normed=False):
- ''' A histogram as a container. Data values may be added with addValue(value). '''
- self.binEdges = binEdges
- self.binContents = np.zeros(len(binEdges)-1)
- self.area = None
- if type(data) in [list, tuple, np.ndarray]:
- for value in data:
- self.addValue(value)
+ ''' A histogram as a container. Data values may be added with addValue(value). '''
+ self.binEdges = binEdges
+ self.binContents = np.zeros(len(binEdges)-1)
+ self.area = None
+ self.maxi = None
+ if type(data) in [list, tuple, np.ndarray]:
+ for value in data:
+ self.addValue(value)
+
def __len__(self):
- return len(self.binContents)
+ return len(self.binContents)
+
def __call__(self, value):
- self.addValue(value)
+ self.addValue(value)
+
def integral(self):
- ''' Returns the total integration over the entire histogram. '''
- if self.area == None:
- self.area = funcs.A(self.binContents, np.diff(self.binEdges))[-1]
- return self.area
- def normalize(self):
- ''' Normalize the histogram contents. '''
+ ''' Returns the total integration over the entire histogram. '''
+ if self.area == None:
+ self.area = funcs.A(self.binContents, np.diff(self.binEdges))[-1]
+ return self.area
+
+ def maximum(self):
+ ''' Returns the content of the histogram bin with maximum content. '''
+ if self.maxi == None:
+ self.maxi = max(self.binContents)
+ if self.maxi > 0:
+ return self.maxi
+ else:
+ return np.infty
+
+ def normalize(self, norm=np.infty):
+ ''' Normalize the histogram contents. '''
+ if norm == 'fwhm':
+ self.binContents /= (self.maximum() / 2)
+ elif norm < np.infty:
+ self.binContents /= norm
+ else:
self.binContents /= self.integral()
+ # demand that integral() and maximum() must recalculate
+ self.maxi = None
+ self.area = None
+
+ def fwhm(self):
+ ''' Obtain the Full Width at Half Maximum for this histogram. '''
+ self.normalize('fwhm')
+ if self.maximum() == np.infty:
+ return (-np.infty, np.infty)
+ lower = np.infty
+ upper = -np.infty
+ for bindex in xrange(len(self)):
+ if self.binContents[bindex] >= 1.:
+ if self.binEdges[bindex+1] > upper:
+ upper = self.binEdges[bindex+1]
+ if self.binEdges[bindex] < lower:
+ lower = self.binEdges[bindex]
+ return (lower, upper)
+
def plot(self, **kwargs):
- ''' Plots the result, filling under the 'histogram'.
- Passes **kwargs on to the matplotlib.pyplot.fill_between function.
- Returns a proxy matplotlib.patches.Rectangle for legend control.
- '''
- if normed:
- self.normalize()
- x = np.sort(np.concatenate((self.binEdges, self.binEdges)))
- y = np.array([[value, value] for value in self.binContents / self.integral()])
- y = np.concatenate(([1e-6], y.flatten(), [1e-6]))
- plt.fill_between(x, y, 1e-6, **kwargs)
- return Rectangle((0, 0), 1, 1, fill=True, **kwargs)
+ ''' Plots the result, filling under the 'histogram'.
+ Passes **kwargs on to the matplotlib.pyplot.fill_between function.
+ Returns a proxy matplotlib.patches.Rectangle for legend control.
+ '''
+ if normed:
+ self.normalize()
+ x = np.sort(np.concatenate((self.binEdges, self.binEdges)))
+ y = np.array([[value, value] for value in self.binContents / self.integral()])
+ y = np.concatenate(([1e-6], y.flatten(), [1e-6]))
+ plt.fill_between(x, y, 1e-6, **kwargs)
+ return Rectangle((0, 0), 1, 1, fill=True, **kwargs)
+
def addValue(self, value):
- ''' Insert a value, or set of values, into the histogram. '''
- if type(value) in [list, tuple, np.ndarray]:
- for v in value:
- self.addValue(v)
+ ''' Insert a value, or set of values, into the histogram. '''
+ if type(value) in [list, tuple, np.ndarray]:
+ for v in value:
+ self.addValue(v)
+ else:
+ # demand that integral() and maximum() must recalculate
+ self.area = None
+ self.maxi = None
+ # bisect_left(x, datum) locates the left-most entry in x which is >= datum
+ index = bisect.bisect_left(self.binEdges, value) - 1
+ if index == -1:
+ if settings['debug']:
+ raise ValueError('HistoContainer warning: Underflow')
+ elif index >= len(self.binContents):
+ if settings['debug']:
+ raise ValueError('HistoContainer warning: Overflow')
else:
- # demand that integral() must recalculate
- self.area = None
- # bisect_left(x, datum) locates the left-most entry in x which is >= datum
- index = bisect.bisect_left(self.binEdges, value) - 1
- if index == -1:
- raise ValueError('HistoContainer warning: Underflow')
- elif index >= len(self.binContents):
- raise ValueError('HistoContainer warning: Overflow')
- else:
- self.binContents[index] += 1
+ self.binContents[index] += 1
+
def verticalColorBand(histo, x, dx, colors=None):
''' Plot the result of a debinning Monte Carlo as colored uncertainty bands:
This function adds one histogram, painted as a vertical band of color.
The band is a rectangle of width [x-0.5dx, x+0.5dx].
'''
if not type(histo) == HistoContainer:
raise TypeError('Please provide a HistoContainer instance for "histo"')
if colors == None:
- colors = np.array([(1.,1.,0.), (1.,0.,0.), (1.,1.,1.), (0.,0.,1.)])
+ colors = np.array([(1.,1.,0.), (1.,0.,0.), (1.,1.,1.), (0.,0.,1.)])
# Special normalization to show FWHM transition.
- histo.binContents /= (max(histo.binContents) / 2)
+ histo.normalize('fwhm')
# Horizontal width of the band.
base = np.array([x-dx/2, x+dx/2])
for bindex in xrange(len(histo)):
- upper = np.array([histo.binEdges[bindex+1], histo.binEdges[bindex+1]])
- lower = np.array([histo.binEdges[bindex], histo.binEdges[bindex]])
- value = histo.binContents[bindex]
- if value >= 1.:
- color = tuple((value - 1.) * colors[0] + (2. - value) * colors[1])
- alp = 1.
- else:
- color = tuple((value) * colors[2] + (1. - value) * colors[3])
- alp = 0.35
- if value > 0.1:
- plt.fill_between(base, upper, lower,
- edgecolor='none', facecolor=color, alpha=alp, zorder=2)
+ upper = np.array([histo.binEdges[bindex+1], histo.binEdges[bindex+1]])
+ lower = np.array([histo.binEdges[bindex], histo.binEdges[bindex]])
+ value = histo.binContents[bindex]
+ if value >= 1.:
+ color = tuple((value - 1.) * colors[0] + (2. - value) * colors[1])
+ alp = 1.
+ else:
+ color = tuple((value) * colors[2] + (1. - value) * colors[3])
+ alp = 0.35
+ if value > 0.1:
+ plt.fill_between(base, upper, lower,
+ edgecolor='none', facecolor=color, alpha=alp, zorder=2)
diff --git a/utilities/sampleFunctions.py b/utilities/sampleFunctions.py
index e4af338..552949f 100644
--- a/utilities/sampleFunctions.py
+++ b/utilities/sampleFunctions.py
@@ -1,221 +1,217 @@
'''
sampleFunctions.py
Functions to generate fake test data, inspired by high energy phenomenology.
Copyright (C) 2014, 2015 Abram Krislock
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the, 110., 1.5, 50., 140.
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see http://www.gnu.org/licenses/gpl-3.0.txt.
'''
import operator as op
import numpy as np
import bisect
import utilities.probCalc as pCalc
+from utilities import settings
-settings = {}
-settings['simpleSortedOutput'] = False
-settings['debug'] = False
-
-
###### UTILITIES TO GENERATE FAKE DATA GIVEN A PDF ######
class MyRandom(np.random.RandomState):
def __init__(self, seedIn=None):
np.random.RandomState.__init__(self)
self.seedSet = False
self.setSeed(seedIn)
def setSeed(self, seedIn=None):
if seedIn == None:
return self.seedSet
try:
self.seed(seedIn)
except:
self.seed(abs(hash(str(seedIn))) % (2**32 - 1))
self.seedSet = True
randomGenerator = MyRandom('default')
### Fake data generation
def functionToData(func, npoints=100, step=0.01, domain=(0,200), par=None):
''' functionToData(func, npoints=100, step=0.01, domain=(0,200), par=None):
Uses func(x, par) to generate four numpy.ndarrays:
x - x values, from within domain with step inbetween
y - y values, evaluating func for each x value
cdf - values from the cumulative distribution of func.
data - randomly sampled values from the probability distribution of func.
npoints may be an integer, or a list of length two. If the latter,
the second element of npoints will be used to determine a scale factor.
Also, boring x values and y values are discarded (ex, any x with y=0).
returns (x, y, cdf, data)
'''
# determine precision via step
decimals = 0
while step - np.around(step, decimals) > .09 * step:
decimals += 1
# set initial x values
if type(domain) == np.ndarray:
x = np.around(domain, decimals)
elif type(domain) in (tuple, list):
if len(domain) == 2:
x = np.around(np.arange(domain[0], domain[1], step), decimals)
elif len(domain) > 2:
x = np.around(np.array(domain), decimals)
else:
raise ValueError('domain should be at least indicate (x_min, xmax)')
else:
raise TypeError('domain should be something to indicate the range of x values')
# set initial y values
y = func(x, par)
# calculate the cumulative distribution function; use it to generate data
cdf = pCalc.A(y, step)
if type(npoints) == list and len(npoints) == 2:
npoints[0] = int(round(npoints[0] * cdf[-1] / npoints[1]))
elif type(npoints) == int:
npoints = [npoints]
else:
raise TypeError('functionToData cannot handle npoints of type '
+ str(type(npoints)))
# bisect_left(cdf, p) locates the left-most entry in cdf which is >= p
data = np.array([x[bisect.bisect_left(cdf, p)]
for p in (randomGenerator.rand(npoints[0]) * cdf[-1])])
if settings['simpleSortedOutput']:
data.sort()
return data
return (x, y, cdf, data)
###### PDF FUNCTIONS ######
def easyEndpoint(x, par):
if type(x) != np.ndarray:
raise TypeError("It would be so much better to use a numpy.ndarray as input!!")
# par = (BG scale, BG zero1, BG zero2, SG intersect, SG scale, SG zero1, SG zero2)
if par == None:
par = (0.00006, 10., 200., 110., 1.5, 50., 140.)
cubicPart = par[0] * (x - par[1]) * (x - par[2])**2
# make all entries of cubicPart non-negative
np.clip(cubicPart, 0., np.inf, cubicPart)
linearPart = np.concatenate(( par[4] * x[x < par[3]] - par[5],
-(par[4]*par[3] - par[5])/(par[6] - par[3])*(x[x >= par[3]] - par[6]) ))
# make all entries of linearPart non-negative
np.clip(linearPart, 0., np.inf, linearPart)
return cubicPart + linearPart
def hardEndpoint(x, par):
if type(x) != np.ndarray:
raise TypeError("It would be so much better to use a numpy.ndarray as input!!")
# par = (BG scale, BG zero1, BG zero2, SG intersect, SG scale, SG zero1, SG zero2)
if par == None:
par = (0.00006, 10., 200., 120., 0.55, 60., 140.)
return easyEndpoint(x, par)
def endpointBG(x, par):
if type(x) != np.ndarray:
raise TypeError("It would be so much better to use a numpy.ndarray as input!!")
# par = (BG scale, BG zero1, BG zero2)
if par == None:
par = (0.00006, 10., 200.)
cubicPart = par[0] * (x - par[1]) * (x - par[2])**2
# make all entries of cubicPart non-negative
np.clip(cubicPart, 0., np.inf, cubicPart)
return cubicPart
def theLine(x, par):
if type(x) != np.ndarray:
raise TypeError("It would be so much better to use a numpy.ndarray as input!!")
# par = (BG scale, BG slope, SG scale, SG mean, SG sigma)
if par == None:
par = (1000., -0.02, 60., 130., 4.)
return (par[0] * np.exp(par[1] * x)
+ par[2] * np.exp(-(x - par[3])**2 / (2 * par[4]**2)))
def twoLines(x, par):
if type(x) != np.ndarray:
raise TypeError("It would be so much better to use a numpy.ndarray as input!!")
# par = (BG scale, BG slope, SG scale, SG mean, SG sigma, SG scale2, SG mean2, SG sigma2)
if par == None:
par = (1000., -0.02, 40., 130., 4., 40., 122., 3.)
return (par[0] * np.exp(par[1] * x)
+ par[2] * np.exp(-(x - par[3])**2 / (2 * par[4]**2))
+ par[5] * np.exp(-(x - par[6])**2 / (2 * par[7]**2)))
def broadExcess(x, par):
if type(x) != np.ndarray:
raise TypeError("It would be so much better to use a numpy.ndarray as input!!")
# par = (BG scale, BG slope, SG scale, SG mean, SG sigma)
if par == None:
par = (1000., -0.02, 130., 90., 30.)
return (par[0] * np.exp(par[1] * x)
+ par[2] * np.exp(-(x - par[3])**2 / (2 * par[4]**2)))
def exponentialBG(x, par):
if type(x) != np.ndarray:
raise TypeError("It would be so much better to use a numpy.ndarray as input!!")
# par = (BG scale, BG slope)
if par == None:
par = (1000., -0.02)
return (par[0] * np.exp(par[1] * x))
###### CONVENIENT FUNCTION LISTS AND NAMES ######
allFunctions = (easyEndpoint, hardEndpoint, theLine, twoLines, broadExcess)
bgMap = {easyEndpoint: endpointBG, hardEndpoint: endpointBG,
theLine: exponentialBG, twoLines: exponentialBG,
broadExcess: exponentialBG}
nameMap = {easyEndpoint: "easyEndpoint", hardEndpoint: "hardEndpoint",
theLine: "theLine", twoLines: "twoLines",
broadExcess: "broadExcess"}
###### FITTING FUNCTIONS ######
# This function is used primarily in binDilemmaDemo.py
def theKink(x, par):
# par = (kink location, slope before kink, slope after kink, kink intersect)
if par == None:
par = (140., -2., -0.1, 10.)
if type(x) == np.ndarray:
return np.concatenate(( par[1] * (x[x < par[0]] - par[0]) + par[3],
par[2] * (x[x >= par[0]] - par[0]) + par[3] ))
else:
return (par[1] * (x - par[0]) + par[3] if x < par[0] else
par[2] * (x - par[0]) + par[3])
def theKink_BinnedLikelihood(binContents, binEdges, fitBins, fitPars):
# Bob Cousins says, "How did you do the fit? Integral of the bins? Proper likelihood?"
# Alex Read says, "Integrating the bin shouldn't matter. You're fitting with straight lines."
#### Right, but the bin containing the kink is special.
x = 0.5*np.array([binEdges[i] + binEdges[i+1] for i in fitBins])
ikink = 0
xL = 0
xR = 0
if not fitPars[0] in binEdges:
ikink = bisect.bisect_left(binEdges, fitPars[0]) - 1
if ikink in fitBins:
xR = binEdges[ikink+1]
xL = binEdges[ikink]
ikink = np.abs(x - fitPars[0]).argmin()
assert 0.5*(xL + xR) - x[ikink] < 10**(-8)
y = theKink(x, fitPars)
if ikink * xR * xL != 0:
# Correction for the bin which contains xkink:
y[ikink] = (fitPars[3] + 0.5 * ((xR - fitPars[0])**2 * fitPars[2]
- (fitPars[0] - xL)**2 * fitPars[1]) / (xR - xL))
y = y.clip(10**(-10), y.max())
logy = np.log(y)
return sum(binContents[fitBins] * logy) - sum(y)

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