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June 29, 2015 14:08
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Replicating the Grey's Anatomy Hookup ERGM with PyMC
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Grey's Anatomy ERGM in Python\n", | |
"\n", | |
"### [David Masad](https://twitter.com/badnetworker)\n", | |
"\n", | |
"This is really a mashup of two tutorials: Benjamin Lind's [ERGM tutorial using the Grey's Anatomy hookup network](http://badhessian.org/2012/09/lessons-on-exponential-random-graph-modeling-from-greys-anatomy-hook-ups/), and this [tutorial on ERGMs using PyMC](http://socialabstractions.tumblr.com/post/53391947460/exponential-random-graph-models-in-python) (which I don't know the author of). Mostly, I wanted to work through the latter tutorial with a different dataset, to make sure I understood what was going on. I'm sharing this in case anyone else finds it useful.\n", | |
"\n", | |
"For a more detailed explanation of ERGMs, check out both of the tutorials linked above, or my own [tutorial on implementing ERGMs from scratch in Python](http://davidmasad.com/blog/ergms-from-scratch/) (the end of that has a good roundup of papers for further reading).\n", | |
"\n", | |
"For more information on [PyMC](https://github.com/pymc-devs/pymc), you might also want to check out the excellent free handbook [Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers) by [Cam Davidson-Pilon](http://www.camdp.com/)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"from scipy.misc import comb\n", | |
"from itertools import product\n", | |
"import pymc\n", | |
"import networkx as nx\n", | |
"\n", | |
"import matplotlib.pyplot as plt\n", | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Loading the data\n", | |
"\n", | |
"Unfortunately, the data from the original Grey's Anatomy tutorial seems to be offline. Fortunately, it was [preserved on GitHub](https://github.com/alexleavitt/SNAinRworkshop) by Alex Leavitt and Joshua Clark.\n", | |
"\n", | |
"The data comes in two tables: the adjacency table gives us the graph itself, and a node attribute table gives us node-level information on each character. Below, I'm going to load both into NetworkX." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Loading the adjacency table\n", | |
"\n", | |
"NetworkX doesn't have a native loader for an adjacency matrix with row and column headers, so here's some code to load it manually.\n", | |
"\n", | |
"First, we get the top row; this tell us how many nodes there are, and will be useful for labeling them." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"with open(\"grey_adjacency.tsv\") as f:\n", | |
" first_line = f.readline()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"\taddison\tadele\taltman\tamelia\tarizona\tava\tavery\tbailey\tben\tburton\tcatherine\tchief\tcolin\tdenny\tderek\tellis grey\tfinn\tgrey\thahn\thank\tizzie\tkarev\tkepner\tlexi\tlloyd\tlucy\tmegan\tmostow\tmrs. seabury\tnancy\tolivia\to'malley\towen\tperkins\tpierce\tpreston\treed\tsloan\tsteve\tsusan grey\tthatch grey\ttorres\ttucker\tyang\n", | |
"\n" | |
] | |
} | |
], | |
"source": [ | |
"print(first_line)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"45" | |
] | |
}, | |
"execution_count": 4, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"len(first_line.split(\"\\t\"))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"There are 45 tab-delimited entries in the top row, including the first one which is just empty (the row labels begin below it). That means there are 44 actual characters in the matrix.\n", | |
"\n", | |
"Now that we know how many rows there are, we can load the matrix into NumPy, skipping the top row and the first column:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"adj = np.loadtxt(\"grey_adjacency.tsv\", delimiter=\"\\t\",skiprows=1, usecols=list(range(1,45)))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(44, 44)" | |
] | |
}, | |
"execution_count": 6, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"# Make sure the matrix is the size we expect\n", | |
"adj.shape" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Next, we want to turn the adjacency matrix into a nice network. We convert it into a NetworkX network object, and then rename the nodes based on their column headers." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"G = nx.from_numpy_matrix(adj)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"names = [name.strip() for name in first_line.split(\"\\t\")[1:]]" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"G = nx.relabel_nodes(G, {i: names[i] for i in range(44)})" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Loading attributes\n", | |
"\n", | |
"The attribute data is in a nice, conventional table: each row is a character, and each column is a character attribute. (See the [original tutorial](http://badhessian.org/2012/09/lessons-on-exponential-random-graph-modeling-from-greys-anatomy-hook-ups/) for more information on where this data comes from).\n", | |
"\n", | |
"Using Python's built-in *csv* module, we can read in all the rows as dictionaries, which makes it easy to assign the attributes to the network." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import csv" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"node_attributes = []\n", | |
"with open(\"grey_nodes.tsv\") as f:\n", | |
" reader = csv.DictReader(f, dialect=csv.excel_tab)\n", | |
" for row in reader:\n", | |
" node_attributes.append(row)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Spot-check the dictionary keys:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"{'birthyear': '1967',\n", | |
" 'name': 'addison',\n", | |
" 'position': 'Attending',\n", | |
" 'race': 'White',\n", | |
" 'season': '1',\n", | |
" 'sex': 'F',\n", | |
" 'sign': 'Libra'}" | |
] | |
}, | |
"execution_count": 12, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"node_attributes[0]" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Assign the attributes to each node, which are now keyed on the character names:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"for node in node_attributes:\n", | |
" name = node[\"name\"]\n", | |
" for key, val in node.items():\n", | |
" if key == \"name\":\n", | |
" continue\n", | |
" G.node[name][key] = val" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Drawing the hookup graph\n", | |
"\n", | |
"Now that we have the data loaded in, we can draw the hookup graph. I color the male characters in blue and the female characters in pink (because gender norms)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 14, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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E6D7gDXefDyTCr+Xlqeq//OGdh1IT572z3uOrkjX88o1xlY6vCc+XJqjNvNLM\nisxsGHAmqinKWUqK5EvcPeXuE4EngdFmdnDYb97cVGwtIi3hLmB7wq4zdy8Hvg88BLxYnar7BEjP\nLl9C/ZQ1ZsY7y2ay7+OXVy6uWvUkweKx9S4B2hM82N0F3E/Q8i05SPMUyQaZWQlwHFAMPOLuK5vx\nWtsAu7j7vc11DRERM+sLfAJ0d/eK9e0Ti0THlMQKf1eaKOw8sKw7iypXRZdUr65MefpPtenkde6e\nWd9x4fn/BHRz93Oa6RakGSkpkq8VFj8PB0YCzwHvNcdM2GbWATjP3a9t6nOLiACEy3RcB5S6+/nf\nsK8BOwPbADsBP1vfrPtmtjVB0fUHBDWZTxF8lj3ZxOFLC8jm3DSSA8IE6A0zm00wE/YQM5tQPxlk\nE1oDxM2spDXMsi0i+SVs+V4CzCIYjv+1ws++d8JJHfsBG2odKiPoMusVnv8aJUS5S0mRbBR3X2Jm\n/wIOISjCftTd5zbh+d3M6outta6QiDSp8GGrdDOOqzEzB4qAqvW8Pw3YassjlNZAhday0cJZsp8G\nniEYtr9/E68arWJrEWmNVhFMcit5TkmRbDJ3/xS4hWA+jnPMrKk+LDQsX0Rao1VoHrU2QUmRbJZw\nGOs9wMfABWa2QxOcVi1FItIarUYtRW2CkiLZbOFM2FMJ5vsYaWbHh7PDbq7lQLstPIeISFNT91kb\noaRItpi7LwL+STDd/YVm1mczz5MhmDa/exOGJyKypdR91kYoKZIm4e517j4eeB44zcz23cwibHWh\niUhro+6zNkJJkTQpd/+IoNVoMDDWzNpv4ilUbC0irc1qgq59/c7Mc/oLlibn7muAccDnwLfNbNtN\nOFwtRSLSqrh7imCOorJsxyLNS0mRNAt3z7j7ZILVqA82s1FmltiIQ5cAXVpoEVoRkY2lLrQ2QEmR\nNCt3X0Awp1EE+I6ZfW3XmLsnCT58urZAeCIiG0sj0NoAJUXS7Ny91t0fB14GxpjZiHCxxQ1ZjLrQ\nRKR10Qi0NkBJkbQYd/8Q+BcwDDjTzDbUP69iaxFpbdR91gYoKZIW5e6rgTuBuQTdaVuvZ7elwF5m\ndpCZDW3J+ERENkDdZ22AuXu2Y5A2ysz6AaOBGcBzgCcisctikehPuhV1KOlcWFbz+ZpFCWDG6rrK\ny9x9YlYDFpE2y8zaARe4+7XZjkWaj5IiySozKwSOBnqUxYuO27HzwL3+uvcFxbt12wqAVCbNE7Ne\n54JJN1SxBORsAAAgAElEQVSVJ6svSaZTd2Q1YBFpk8I6yF8CfwoHhEgeUveZtBgz28XM3jWztWb2\nkJk9SPAhsxy4ul2ieP/P1ywqvuGD8bg7f3znYYbdfyHf+c9N7Nlt6+KYRW8ys75m9pSZXdLo3O+b\n2bFZuTERyXsetCCsQcXWeU1JkbSIcI6ix4DbCfrl7weOAzz8KhvZc/vo3DPv4JaRl3D9B0/y5Ow3\n+M9xf2TR2HH0K+tK75LOicJo/CKCmqQxDc79LaAX8FQL35aItC0agZbnlBRJS9kTiLr7De6edvfH\ngDfD97oC3H7AD4hHYxTGEtzy0bP8bviZ9CrpTDwa49e7nc6c8qXRwmjieGA8MNTMBofHnwk8EM46\nKyLSXDQCLc/Fsh2AtBm9gAWNts0DDEhEMC+IJdbNXTS7fCnHT/w9Eb6YzigWiZDxTIm715jZQwTD\n+n8DnAqc0Py3ICJtnEag5TklRdJSFgG9G23rB8wEVmRwllStontx8HnTr7QrdxzwA/bqsc26nW/9\naCKXvnb7x+G3dxGsr/YqUOXubzT3DYhIm7cK6JPtIKT5qPtMWspUIG1ml5hZLCyK3j18rxao/sf0\nZ9L1O1+47RH84o1xzC1fCsDiypVc8dY91avrKq8DcPfXCGqRriFIjkREmpu6z/KcWoqkRbh70sxG\nA7cCfwCeASYAdQTJzZq//PeR0p26DCw7buBe/GDHUTjOoROuYGHlCgBqUnW1wKQGpx0H/BbQqDMR\naQmrgI5mZq75bPKSWoqkxbj72+6+s7uXufvJBM3Q89x9krv3qkrVHnjGC9esGPHoT8vHffoSW7Xv\nxdlbH5QpiRdWGkxJevrbwNkNlgeZA0xx99nZuicRaVNqCB7iCrMdiDQPTd4oLcbM9gM+I5iX6Azg\n78Agd1/SYJ8CYHTHgtIxEbPO1am6aFWq9hK+GKm2N7Ab8CjwEHCju9/TkvchIm2XmV0IPOnuC7Md\nizQ9dZ9JS9qaIJEpAT4HTmyYEAG4ey3BHEb3hzPIXg582KCpeoqZbU+wNMjLwH0tFbyICF+MQFNS\nlIfUUiStmpmdDUx2988bbR9MsG7a0+4+PRuxiUjbY2aHApXu/mq2Y5Gmp5oiae0WAT0bbwyTpLuB\nw8xszxaPSkTaKo1Ay2NKiqS1W29SBODuiwmWDdnVzA4Lu9tERJqTJnDMY0qKpLXbYFIE4O6rCRKj\nXsCJZqY6ORFpTqvR+md5S0mRtHYrgFIz2+AQWHevJuhKM2CMmRW1VHAi0uasBtqbmX5/5iH9pUqr\n5u4ZYAnQ4xv2SwEPA4uBc8ysfQuEJyJtjLsngWqg7Jv2ldyjpEhywdd2odXzwLPAu8B5Zta92SMT\nkbZIXWh5SkmR5IKFbERSVC9cF+05YKyZDWy2qESkrVKxdZ5SUiS5YKNaihpy9w8JutNONLMdmiUq\nEWmrlBTlKSVFkguWAx3MLLEpB4Vrot0FHGxme2vIvog0EXWf5SklRdLquXsaWApsco2Quy8FbgN2\nBI7QiBERaQJqKcpT+gUhuWIRwVxEm8zd1wJ3AF2Bk8ws3pSBiUibo6QoTykpklyxyXVFDbl7DXAv\nkCIowC5uqsBEpM0pB4o1WWz+UVIkuWKLkiJYN5fRo8Bc4Fwz05OeiGyycP60NaiuKO8oKZJcsRTo\ntKVPZuFcRs8DbxEkRluUaIlIm6UutDykpEhyQtjKs4LNKLbewPneAJ4BzjSzIU1xThFpUzQCLQ8p\nKZJcssVdaA25+0fAA8BxZrZTU51XRNoEtRTlISVFkkuaNCkCcPe5wJ3A/ma2n+YyEpFvYmbDYrGi\niwoLOtxYXNh5UiQS+4mZdcp2XLLlzN2zHYPIRjGzvsAR7v7PZjh3GXA6wZIiT4WFlCIi65hZLBEv\nvdUscvIu254T79dzRCyVrmH6zEerZsx51tLpuvPcM/dnO07ZfEqKJGeEM1pfCvwxnNCxqc9fAJwM\npIF/u3tdU19DRHJXQaL0lm6dthtz6lEPFxckyr703tKVH3H340dV19StOcHdn8lSiLKF1H0mOSNM\nUlYTTMLYHOevBe4DqoGzzKykOa4jIq2PmW1jZq+Y2Soz+9DMjjGzgWa2Ony/bzJVc97KNZ+vS4ie\nePFC3nz/ZgDalfShZ7edi8DGm9l8M7uqfgZ9MzvbzKaY2V/MbKWZ/c/MDs/WvcqGKSmSXNPkdUUN\nhS1QjwOfA+epTmDjmdkZZjbxa97f3sxOCH/Z6OcqrUY4y/144FmCh67vEUz2GgfWmNnO0UjivES8\nJFKQaMfyVZ8BMHfRVPr32geA8S9fTId2Aygu7FwDjAUOBc5vcJnhwCdAZ+DPBMsPSSujpEhyTbMm\nRbBuLqOXgKkEcxn1bs7r5Qt3v9fdD2u83cxGdiwofb9zQdkbh/TZ+fZ9emx7d2E0saB9ovh+M+uc\njVhFGtkTKHH3P7p7yt1fBiYApwGTgP2jsYJdY9FCGzZoFHMXTWX12jnU1ZXTvcv2VFQt5fN5L3Do\niKvp2W2nNEHi81fg1AbXmOPut3lQszIO6Glm3Vr4PuUbaIpyyTWLgG1b4kLuPs3MyoEzzOxxd/+s\nJa6bi8wsur46LzM7qixe9NAtIy8pHj1oBLFIFIBl1Wv4zbT7R9/5yQt7mdmu7r6ixYMW+UIvYF6j\nbXOA3gRJ0ah0qq6sa8dh9Os1gg8/e4hYtIC+vUYAsKZ8HplMkr+N24baZEU7grUW0wSz59dbXP/C\n3avCga6lBBPTSiuhliLJNYuB7i212r27f0pQZzTKzHZtiWu2Jmb2MzObaWZrzWy6mR0Xbj/bzF41\ns+vMbDlwZbhtcvj+ZWFCOSHtmeIzXryGC165AYCFlSs47+W/cf+MSYloJNIvEYmNb3C9K83sITO7\nK7zmhw1/7huKR2QLLQT6NpqSoz8wnyAp2jedqa0qr1xY3bfHnsxb/AZzFr5K/55BUtSutDfRaAHf\nPmUq0UisBujj7u3dfYcWvxPZIkqKJKeEC7tWEDRPt9Q15xM8+e1tZge0sbmMZgL7uHs74DfAPWbW\nI3xvOEHtVTfg9w0Pcvc/Az84sPeOFZ+edgvditpz6pB9ATj1+T/Tr6wri84ax2OH/cLqMqm9zOzo\nBocfA9wPtAeeBG7cyHhENtfrQBVwmZnFzWx/4GjgAXefCdQAe1dVr6icvWAyJUVd+XTWePr12huA\nspIeDOqzP/eNH502iz0KrDWzwWa2X5buRzaTkiLJRc1eV9RY2L1zO7AVQatRtCWvny3u/m93Xxy+\nfgiYQZAMASx095vcPRMmq1/SsaD0mJMH71t67DNX8cMdjuWwfrsyr2IZUxd/zJ/2PIdENM6BfXai\nR3HHWoLC1nqT3f3ZsPbiHuBbGxmPyGZx9yRBMn4EsIwgET+zQZf5K8DyVLrmqMdfvKAiHivBHXp0\nCf5prlo7m0gkUbtyzeflyVTlSGAl8DBQn7B7+PWlyzbrTclmUU2R5KL6pOj9lryou1eY2Z3AScBp\nZvZQvs9lZGZjgR8BA8JNpUAXgnqJxjUYXz4WKxj36Uts07Evl+58AgALK1fSqaCMknjhuv1KY4UZ\ngtameksavK4CCs0s4u6ZDcSjYm3ZYuGyP/tv4L3T61+b2Z5LVrz/l0wmeci/Ht63Kp2uZW3FgqhZ\n5PaMp37p7uXrOf4u4K5G29rEg1WuUVIkuWgRsG82LuzudWZ2P0HT+jlmdq+7V2QjluZmZv2BfwIH\nAq+5u5vZu0B99+HXPumurqsonLFmgb907NXruht7lXRiZW05FclqSuNF1KaTzK1YFifoFtvSeESa\nnbtPN7PzgbHLVn40BUgB77l7dZZDkyag7jPJRYsIhrNm5ZdhuATIeII5R84zsy7ZiKMFlBAkPsuB\niJmdA2wfvve1P3szOyLjvm15sqa2MvlFz1rf0q6M6LENP3/9LmrTSf787r9JZlIO/GML4xFpSYMI\nEqEp7v66EqL8oaRIco67VxEUPmZthepwLqNJwH+As8N12fJK2J1wLfAawai/7YEpfFEfsb4aifpt\nJwMda9J10a53nE7pv07kov/8HYD7D76U2eVL6HrH6fz6rfvc4ZpwXqjG52h43q+LR6SlDSYYZCB5\nRmufSU4ys1OBD9x9eiuIZSvgeOBJd/8k2/G0JmYWKYkVXpPxzEWnbjUyul/P7WLVqTrGffZi+XvL\nZ6Wr03Wjw4nyRHJCOPv1pcC14dJAkkeUFElOCoe6Jtz9hWzHAmBmvQhmv/2Pu7+V7XhaGzPbOWaR\nq8oSxXUZ95o1dZVPAo/me6G65B8zGwyMdPfbsx2LND0VWkuuWkQwNX+r4O4Lzex2YIyZtQdedD1x\nNFSW8swNK2vKN7g2mkiOGAT8L9tBSPNQTZHkqqwWW6+Pu68iWOSxP3B8W5nLaCMNYSNGmInkANUT\n5TElRZKTwmHwaaBdtmNpKCwCHwckCNZMK8hySFlnZoVAd4K1pERylpmVAB0IlgWRPKSkSHLZIoKF\nHFsFM7vTzK4KZ8d9CFgBnGtmZY32629me5vZjhuzhpuZvWJm5zVT2C1hEDDP3VPZDkRkCw0kWO3+\nK4sfS35QUiS5rMWX+/gG64aTh3MZPQ18QDCXUVczO7CwoMMbiXjpx107DnuqtLjHq4l4yYJoNP6j\nb0iO1jdMPZeo60zyxWBUT5TXVGgtuWwR0NpWrl9X4xQWWk8JVou3vxUkyo4/fN+/FG4zaBTRaKLI\n3Zm/+I3S56f+4ncrVs/cx8xOCpOpvBHWfA0BpmY7FpEtEf5bHgS8mu1YpPmopUhyWVZbisxsZzN7\nx8zWmtkDQGGD9442s/+a2Srg1mgkMfqs454p3H6rE/nH/bvz2rvXc+vD+3LfhNGcOWpCcUlRtyOA\nz8xsVXjcyA1cs6eZvW9mP2mh29xSXYEMQVeiSC7rRPDQo3/LeUxJkeSytQTLPZR9455NzMwSwOME\nizx2JFgR+wTAzWxnglFoFwCdzKILo9FYolP7IeuOn/75o5xy5EP85NxZVNeuprJ6WVEsVlRM8MH7\nU+ARM+vc6JoDCVbrvt7dr23+u2wSg4GZmp5A8sAg4H/6t5zflBRJzgo/nLLVWrQnEHP3v7l72t0f\nAd4ieJK8ALjF3d9ydy9IlA0rLOhoC5ZOC440Y/ftv0270l7EogV8OONhhg44gohFOgK9wgkppwFH\nNbjedsBLwBXufmsL3ueWUj2R5AvVE7UBSook12UrKeoFLGi0rX7IeX/gJ2FX2Kqa2tVbVVWvoKJy\n0bod25X2Xvd6Tfk8Pvnfk9QlqwqBj8Iut72BHuEuBpwBzAceaZa7aQZha1pfYFa2YxHZEuFAiAEo\nKcp7Sook12UrKVoE9G60rX/45zzg9+7e0d07Fibav3zEftew7ZDR63ZsOOdk+7I+DAuKr2sIWoo6\nunuZu/853MWBXxPUMty3McP4W4n+wEKtDyV5oBewJpwfTfJYrny4imxItpKiqUDKzL5vZnEzGw3s\nTpDA/Au40MyGm5nV1K35xytvXl1dW7d2vSfafquT+HT2U/XnrDGzQjPb38waJl1J4CSgBBjXmmby\n/hrqOpN8oaU92gglRZLrVgEFZlbckhcNJ2gcDZxN0IJzMmHXlru/TVBXdCOwEri+ompx7QuvXVG3\nvhH3S1d8RCaTqkqna0uBpcBc4Cc0GN7f6JrdgdtyIDFSUiT5Qkt7tBGmQnrJdWZ2NjDZ3Vvth5aZ\ndUrEyyYWFrQftseOF5V07TTMqmpW8M70O2oWLn0nlUrXHOLur2c7zqZiZp2Ac4FrNVpHcllYG/dT\n4Bp3r8t2PNK8NHmj5IP6LrRWmxS5+0ozG16XLN/vP9P+eHEkEhvk7mtralc9TDAMf3q2Y2xiGoov\n+aK+Nk4JURuQF0mRmc0GznP3F79hPwNGFiTa/QjsW2aWTKfrnk2mqq539xmN9h1A0Iccy7dZhvPQ\nImDrbAfxTcIEYVL4tY6ZHQqMBCZkI65mMoRgiRORXKd6ojYkX2qKvnFtKDMrTMRLn25X0nv8yN1/\nfsyYUU/2P/XIh4bsut25347HSt6LxQovb6FYpem1tjXQNtVkYFsz65LtQJqCmUVpgeHLZjbbzA7a\nyH0LzWxMp8Kyp2KR6OpENDbJzHZqzvgkb6ieqA3Ji5aijVEQL7urb68RI0889K6iaDSxbnvv7rsl\ndt/hO9z52KFXRKPxhel08u4shimbZwVQamaF7l6T7WA2lbtXm9mrwIHAQ9mOpwn0A5a5e1UzX2ej\nFso1sxFF0cSEXbsOiZ2/zWFl17z3KIPa9dhn6uKPX21fUDJpbV3ViS0Qq+QgMysFyggevKQNyJeW\nIoCdzew9M1ttZg+YWYGZdTSzCWa2ojZZfrJn0kWV1cvXHXD3E8cw6a2reeyF86mpXV3s7v/a0NO6\nmZ1gZrPMbNsWuyPZKGH35hK+mOwwF70J9DGzPtkOpAkMoZU8WZvZdsWxgomPHPaLjpOP/3PZWcMO\nokthO44dsEdkwdi7ig/ps/MB7eLFT+TASD7JjkHAbJVQtB35khQZwRwuhwEDgR0JhkobcFvE4v/c\nZZtz6hLxEiZO+XIv2fQZj3LMATfxo7NmEonEYsD/NT63mZ0D/BE4yN0/auZ7kc2T011o4XD7l4FD\n8uAXdEsOxf+6h6GlwLv9y7qW7th5wJcOml2+lAOf/CXPzXunsDadPIDgswMzG2BmGTMba2ZzzGyZ\nmf2ihe5FWh8t7dHG5EtS5ASLZC5291XAeGAnd1/p7o/F48WDenbbKTFilx8zd9Gr6w4yM7417HQ6\ntR9EPF5Ep/aDk8AOjc79I4LhmCPdXf85Wq+cTopC7wHFwFbZDmRzhYvztuOrS6A0y+X4moch4FsF\nkVhm6/Z9uGTKzesOcpz7ZkzizgN/yNKz76VPaedoPBJt/DC0NzAUOAi4wsyGNf/tSGsSPpwMopW0\nekrLyJekCGBxg9fVBDUmRWZ2S23dmiOfnXIZ9zx5NLV1a2k4SrikuNu618lUlQPxRuf9CXCTuy9s\nxthly+V8UhQ20b8AHJxDS3k0NoRgJfGW6G742ochoEevks61v979dCYt/HDdQYZx7rBDGNK+F4Wx\nBMcN3At3Gndb/sbda939fYJk9VstcD/SunQB0gQTxEobkasfvN+kPuv5KcHT3tiy4h4VY44ZHyZE\nX63NXFuxgLXl86PA6kZvHQr8KlzGQVqvZUCHcKK1XPYZUEPQ6pGLWnoW6w0+DAETZpcvaTfyiZ+x\npq7qSw9DPYo7rHvt7jjeuMuy4XmrCJZXkbZlEEGCr7m22pB8TYrqP+BKCT4on66sXrZ8/CuXfHVP\ndzKZNM9OviyJ8SlfzZimA4cDN5nZMc0Ys2yZDEG3zffMbEzDguUGdSKR8PtXzOy8bAX6dcIP4OeB\nA8yscatlqxb+fAeRvaU9Gj8M7VocK1z2930vqk981nvQ1MUf16U9s6ylgpScoXqiNihfk6L65qC/\nAkXA8mSqKrN81acVAGvK563bafXaOdz/1AnVcxZOfjeTSb0M9DSzvg3OQ9iEfjTwLzM7rGVvpe0w\nszvN7KzNOO7oRLxsVruS3t/fdvDoq4b0P+zvsVjRjMKC9s+Y2fq61DZqKHe2uPs8gu7A3bMdyybq\nBax19/IsXb/xw9CqmlTdv3/w6i1f+buu3/D+illMWzYTgtGLG3NuaQPCubb6o6SozcmLeYrcfWCj\n73/T4NsD6l+YWe94rORXtzy459hEvCyTztRFFy97d00qVXtdxlPXu3utmf0DOAWYBsTrayPCRT5z\nech3LtjkRMUsckphov0dxx9yW9HAPgdQP3Crtq6cqe/+9eC3PrjlnWSqalSTR9r8XgDOMbN33b06\n28FspGwvANvwYeh+YFWaTHlFXfVsxwd+vGoe23XqD0Amk+GhmZP59qQbqlKevpMvD7BY37/DVptE\nS7PoDaxsqfmrNnZVBmkB7t7mvoBCgqbRfkBkPe+XAWOB84AO2Y43376AbYBXCAoYPwSOCbffAYwN\nX58NvApcF+43ExgBnEOwivwS4NvRaEHl+Sf+x08+4gHv3nkHL0iUebvS3r7vbpf7Ly9c6XvseHFd\nLFY8nqB7LRKe+2Xg3AbxnAt8RLCi/bNAv3D7TQSLQDaM/Unghy30czoGOCTbf1+bEO/5wMBWEEd3\n4GJgNFAAJIqiid8XxwpWD23fe83wbkNXd0iUVHZIlLwDHJjtePXV+r6A/Vvy/x4wa3P/LQIlYN8p\nSLT7LBqJ15hFkpFI/BNg72z/HHPxKy9aijaVB7Meb3CYpbuXm9ndwF7ABWb2rLtrHacmENbJjAdu\nBQ4G9gWeMLPd3P2cRrsPB/5JsGDqbwlme36MIKHdH3iyf8990t27bE9N3RqOPehmunbahqUrPuK+\nCaPp3nkHRuz8w/i0D/91yNfEcyzwc4Lu0Rnh6/sJhmTfCTxuZpe6u4cTex5EkCy3hFeAi8zsTXdf\n00LX3CxmVgx0BeZlMQYDdiNoHZ7o7u81ePuXZvabz9Ys2I2gaHq2N1rvUKSBwQT//1o1M+uZiJdM\n6d1t9+577vS9kh5dduLZyT+mpm7N0MXL338uES+5vi5Z+fNsx5lL8rWmaIt5YCpwDzDSzEabWUG2\n48oDewIl7v5Hd0+5+8sEC6Getp59Z7n7XR48Dj1EULPyW3dPuvvzQKRvzz1KAPr32puunbYBoFvn\nbdl2yPHMXfQqxUWd6dxx6Netbn0h8Ad3/9SDrtI/ADuZWV93fwtYQ5AIAZwKvOzuLVKU60FtzjSC\nBLC1q5/5N5WNi5tZEXAysAtwW6OECAB3r3P3qe7+vBIi2ZDwc747QYt0SxpuZtPNbKWZ3R5ORHq2\nmU1uFF/GzAaZmZlFP+rUfsiASCRW8u+JY/l01pN8Ovtp5i6caqlUbbG7XxqJxM42s23CASarzOzD\nhoOGwlrOm8IJT9ea2etmNqiF773VaJMtRZvC3ReZ2T8JJoi70Mwe9aAQVjZPL77amjCHoA+/sYbF\nr9UAX05ILJPJpAFYsGQaL7/xW5at/IR0po50uo5tBh8HQMSiXxdPf+BvZnZto+29wzjHAWMIanzG\n8NUZz5vbqwQj6rq5+9IWvvamyFo9kZn1A04APgYeyVZiJnljADDfg1nmW4oBpxNMAVNF0Jr+K77+\n/9TIWLSgdNXaWZHD9vkTfXoMJ5WuZf6SN2lX2puRu/+COQtfjT749Km/TaYq61h/6/xn4blOIRhl\n/S5wF/B71v+gmvfUUrQRwifM8cBzwKlmNjKHJ9fLtoVA30ZLWfQH5m/6qbxu0dJ36gAef/HbDB1w\nJN8/80N+eu5sdtn2bNwzJJNVLF/1aWF4QPv1nGQu8G1379jgq8TdXw/fvwc41sy+BQwDHt/0ODdf\n2NU7hS9aq1qd8O+yxZMiM4uY2X4ELURPufuzSoikCQyi5UedOXCjuy/wYCLSb0xKCuJl53fpuHVs\n6wFH0afHcABi0aAzI2hch349RxCLFnQB2n9D6/yj7j7N3dPAvcBOTXt7uUO/2DeBu3/M/2fvvMOj\nLLP/fZ/JTApJqNJBehNQsetaECwIKPYCoq51Lbu6bnPd6s/d9bvrrlssa1/B3lFR7NJBQFGaVOlV\npKZPJuf3x3kGhhBIm2QmyXNfVy5C5i3PTCbzft5TPgcew+4krhGRpgffw1MGM7E7oV+KSEhEBmL1\nPC9V9AAWNpbegK5cPyklJ28L4XAu6WlNSUlJZf3mL1i4/HVEhK+XvKASSInaGd/o/ImysQJcgEeB\nu6ODfkWkiYhcEj2Xqq7DUlhjgddUtbB6T79KzAZai0inBJy7IrQGCt2Hea0gIo2xZoiuwOMxd7we\nT3XpRmJGe8RG0NdgUfUDEkgJtU8NZZGddeDNRIT0tKaKNZHEsjrm+Mr+Ufmsii66vuFFUSVR1V3Y\nBXIJVoTdL8FLqlO4kPS5wDmYC/VDwOgyLmpleQmpE0M3YnU2+ar63HNvD8879di7mTz7Pu5/6lCm\nfvl3+nQ7n5056/hk5h9yw+Hcu92x/gFMxgTRYOeJtAbrcHtJRHYC83HDQWMYg7VsPxuXF6GSuOjH\npyTvsNhajRKJSE/sPfAtMNb9TXo81caJ7Ubs62heWxxa6vsNQK5bDwAisscWpqSkeEu4uCzHgL0f\nEapKYXg3QIsyovO1MZ+wzuFriqqAK/ydJiIrgYtEpDswIUFRhDqHqi6inOJhVR2DiZFoeiYI3OL2\nmwgsUdVHRUR25axf+dG0u+7q2vGMlM7tTw6Fi/OZt+SF3btyNuQUF+efr6qzgGhh0TKgv+uC646J\nnTbA/2GCaImqli7MXg2sVdVJ1X7yVWc+ZknQG6udSSa6Y7VPNYqIBLGaiD7AK6pa24WwnvpPV6zB\no7Z9qQS4VUTGY5Ga32DR86+Bvi59vwT4o9s+tbBo1+dbty+5uEuHgfsEN7IatWLHrtUArN88m3A4\ndxd7o/MPYJ21w2OOlYw3WgnDi6JqoKob3IylIcBNrgi7CrUxnrJwYqgXcBr2hzsREy17PrDc9/eI\nyISlq969bdX6iQUlJZH84kjBBOBDPcBgUhex+gb4xnWb9MLmjQ0XkeWYf9Iyd947gCdq6nlWBGcJ\n8DEwRESWHOh51TbutWuHCceaPE8L4GJsNuGjWncMLT11i0SN9lCsludD7O9pHPAnVS0Qkf+HNXrk\nYULmBszHbXa4OD9v/eY5mcQImyN6X8kbH/6Qvz/dGdWSSCRS+CfMm+0RzHJkHftG58uMytfM00x+\npPYFcf3E1aQMAz4HpibLRasuUhExVMY+5wFbYgqkq3ruRlgkoh8WRboVm383KNFpGve6XAUsUHNY\nTzgunXmcqo6twXMcgaU0PwPmJOAu3tMAcH9fPweeUNXSg8ETiohkYb55R2E3c1NVdZuIdA4FG03v\n3umspicccVtG25YDKC7OZ9GKcUyec19uQeGOF4rCuTf5v5mK40VRHHH56AuwWq03kt1wL9moihiK\n2QAT3uUAACAASURBVO9O4H+qWrqgsDrryQb6YgKpGeZ6vQBYk6gPGRFpj/klPVhGmi8R6xmOjUOY\nXgPHTsNuNNpiRe7lzSfzeKqMiLQGLlPV/yR6LVFEpAmW7uqPpdCnlb6uiEizQCD0o2BK6u1F4bxW\ngmhqava0wqKdfwXe84KocnhRFGdcq/5JmKp/T1UXJnhJSU9VxVDM/u2AC1X1oRpcYzNMHPXDhgwv\nxD6kNtb2h47rjtukqlPK3bhm1yHA7cAL8fZQcr/Ti7HxBx8kgwD01G9E5ESghaqOT4K1NAdOxqLW\nXwIzVDWnAvsFgYgXQlXH1xTFGZc2m1pGEbb/UC9FdcVQDD2AGm3Jdu3mU4ApItIKE0cXA4jIAmB+\nbTldY51o14nIF1pLAysPQAssKhq35+3eEydgFwR/U+GpTbphAiRhuM+WU9xaZmMR4Qr/jXufrurj\nI0U1iIikYq3nnTCnXd8CSVzFUPR4NwAfqeqqeK2xgucVLLXTH0uz5WPptQU17dkjIsOAYlX9oCbP\nU84ajgdaq+rbcTpeJnA+Fol7vTZ9jzwNGxdh+QXwr0QU8bvI6ClAR8zLbbbvZk4MPlJUg7jo0Fsi\n0hcYKSIzsZxwgyzCjrcYcsfMwiIWtT56xa17A7BBRD7EvEX6AdeLyHZMIC1Um2EWbyZhLbyfJ7Ao\ntDs2FqDaiEgXrB5vHjZfLhKP43o8FaQDsLW2BZHYiJpTgVbAdKwWtTbHi3hK4SNFtYQrmLvA/ffN\nhlSEXRNiKObYA4DuqvpqdY8VL0QkBeiCCaTewEZMIH0Tz3SXcwNvrqpvxOuYlTh3COvU+afaKJKq\nHieATbU/EhinqolwEvY0cERkEHY9/KQWziXY58Op2OihqcDXPvWVHPhIUS2hqjtFZCzWSXCjiLzr\nTAzrLTUphmLoCSyO4/GqjYtyLAeWu7B8D0wgnSUia9hrElnd8PgMbFhsG1WtbQfeQ4HN1RRETbFB\nroXAYxUpJPV4aohumBdQjeE+D3tiYigNq1Gc31AzB8mKF0W1iHvzTxGRb9lbhP1+fSvCriUxFK0D\n6IpNlE5K3N1faZPIfsAwEVmBCaTlVQmZq2qhiEzGXJ6fi+OyK0K1RnvE+HpNwzprfMjakxBEJANo\nSQ2l4F00tA8mhhQbNbTYi6HkxIuiBKCq650T9jmYE/brqroh0euqLrUlhmLohBk2JrIDq8K4yNA8\nYJ77IO4DHAeMEJElWIrt20rW03wBnCAiXVW1Np14uwNvVnYnl3Y7G7szf8E3H3iSgM6Y91hc01cu\njd4f66QsAD4BlvkbgOTG1xQlGLGBsudgqZBpdfEPJiYsPJDaEUPR854D5CTar6e6OJPIw7AP0Obs\nNYlcXZHX0L2HTsKceGv8/ePSXjcAf6/M+Vy78cXYRO7xvrvGkwy4Ts7t8TIgdRHsIzExtB2LDK2q\ni5/tDREfKUowqrpARNZhRdjdRORNrSNTvxMlhkqd+6WaPldN47rTPgc+dyaRfbF5epnOA2kBsOEg\nr+tCTBQd5r6vaboBKyphrinA0cAg4CPgK3+B8CQR3YBXqnsQZ8FyNPa3uAmzlaj1rlhP9fCiKAlQ\n1R0iMga7s7hJRMararJNQt9DIsVQDIdgxoFxdVJONM6bZypmANoSqz+6CHvZoyaRW0rtoyLyEXCu\niCyuhXb27lidVLmISDpwHhYBe1pVt9bkwjyeyuCinmlY9LKqx0gHjsVMR1djaeGN8Vmhp7bxoihJ\ncEV3k0sVYSfVeIMkEUNRegJL63PEwTlkfyYiEzGTyH7AlSJSwF6TyG1u25Uisg27U51VU2uKsRso\ndxSCiHTEBN0SzH/Ftxx7ko2uWB1fpT9HxIZHnwAcgzUdPFOLrvaeGsLXFCUhrktpKNAeC8Em9K4j\nycRQdE0/xCZFL0vUGhKB+110xOqPDgN24EwigUbAldhogBqp1xGRTsAQVX3sINsEMOuJE4B3VDWp\nLBM8nigicjGWCq6wCamrATwRGIDV/03TOA6i9iQWHylKQtwF7U0R6Y9FBqYD02tbhCSjGII9LbRt\ngFWJXEcicK/9GmCNiExgr0nkqVgKQLDfV02N/zhoK767YFwApGDeQ3WiPs7T8HCfb12xOreKbN8U\nE/v9sC7SRxuSCW9DwYuiJEZV54vIWuBCrAh7XG1cZJJVDMXQDevMatB2+C7lugJYISLvYoLlOOAO\nEWmPtesvjnPUqDvwflkPiEgPYAQwB5jsfVg8SU4bIK88YSMiLbB6z97Y39TD3mi0/uLTZ3UAl444\nBSvmG19T6Yg6IIYAEJELMV+ROYleSzIiIsOxFNsOzIPlW8wkcll1hKSbM3cbcH9sMberMzoDS+e9\noaqrq756j6dyiMg1wHWqeko526UC5zdLy7q9RPVQAc0tLpgcLon8oqwSBRFpjX3udsXq9D7XBAyL\n9dQuPlJUB3B33JNcEfaFMUXYcYmU1BUxBHsEYg9q2JK/jvMpJl5eBvIxk8hjgPNEZCkmkCpkEiki\nA7JC6T9KC4R6NkltpDuL8r7Guv4i7vHmmPfQbixdVieMND31FxEpweYhfhvzs7ZZofRJvZt2bPPz\nIy/I7te8E9sKdvP04o8ufnn5lAtEZKSqvuW2bY+JoQ6Yf9w73lOr4ZDUkSIReQZYq6q/K2e7I1JD\nWT8NBIIngmgkUjQpXJz7r2Rua68srh37FszPZhjQjgMUYYtIGyAbm021S0R2A/1VdVWp7eqMGIoi\nNlV6qKo+mui1JDMicirQWmMG5YrIauCv2KyxFlhbfdQksqTU/lmNQ43eSE0J/uC2/sPTDm/eOeX7\ngt08tmhC3qLta3PziguHAMWYn9JEYHYyv2889ZfSkSIninqoGy4sIsGsUMbCnx4+ous9x44K2sfe\nXr74bjkD37orPydccDnQGJtYPw34sqGn6BsiyR4pUvdVJiISCAUzH01Pazrq2P43pXbrOCioqixb\n/UG3LxY+OTo11OjhcHH+L+vDh7Wq9ov57xsicjgwWkSmYnczACObpGb+NjOY3iUrlB7eUZQbapqW\n+T5wcqwgqotiKIaewNJEL6IOMBMbFts+ZpRGCfZ7/sQVjfbFRm5kishCTCCtB8gOZbw3rNOxx44Z\n9NN0ESEYSAHg+sPObvT6immNRn/yj6n5kaK/YcWmtT2M1tMAEZG7gOsx0bIW+I2qjiu1zWT37dci\nosC1QK+C4qIeWaEMaf3MlQQDKTxy6s2kBoLcMe0Jvi/YzaB2R6R/tmHeX3eH86/E6vT+BfQWkXzg\ndeDOqEByoutm4GfYzLTnVfW2mn8FPLVBsosisIt2mYSCmX9p0bT7yFHnvtUoPa3xnp93aHNc8PjD\nbwmOfWvozTt3r92K3R3XK1R1XmwRdlYo/Yx2jZpf9I+Trs8859CjSQmkpG0vzOHpbz469w+znztT\nRC7AuizqqhiK0hN4O9GLSHZUtcj5G50hImOBsdhk+3dEJAL8P8w/6MeY9cNKzHtoKxDKKy48+fAW\nneXo1+5g2c4NLLjsYXq8cCNPDvwx98x5kZYZTTK2F+Z03x3OHyoiP8eKVmcBN6rqGgAR+ScwEkjH\nTO2uUNXacNz21E+WYzd4m0TkUuA5V0qwB1U91YmWw6Pps6xQxtyCSJEUlYTZePVY/rf4Y66f+CBn\ndxzA3Ev+w+rdWzjmtTukRLUL9nfQGbgdaxjoCEzAovT/jjnVMCwl3QT4QkTeUdWa6vj01CaqmjRf\nmO/Dl8AubHzDi8C97rHhwFfYLJlpwIkpKWl5Pxm9UJtkddTBJ/4/bdWir6alNtbDul2gv7pho958\n+WwNBEJ5wDrgTqxleQNwjTvmsZgdu8Ss4UJsDEHCX49Sr80qYLB7/rvdVw529/9go2BaJCuUrlmh\nDM0KZWhAAjpm0E9Vbx6vgmhqIJTvXoPbgKexi9Qm4L9AeqKfXwVfg6bAL2J/X/7roK9XwP2+u7v/\nrwQGue97uvfPYKx9/hfAMqBD41Cjmc3TsnXAId103ehntODGN3XlqKdUEL2612DNu+F1XXXlUxoK\npBRiF6pe7ly/wTxbwCJQc4DG7v+9gDaJfk38V/35AuZibulXA1Nifl4CdI3+PyuUvj4tJaQlP3pH\n9ebxuuu6V1QQnXXRA6o3j1e9ebwe3bK7Nk/LygMOK+M8d2ANBLHHPynm/y8Dv0r06+G/4vMVqKB2\nqnFcZ8A4YAzQDHgVc8NVERkAPIUNoWwOPAa806X9aSXZmW1BhG9WvMUVw17j1lFfsWXbQuYteZHm\nTbvRokl3xe5iG2N1ONcBD4tIE1WdDXyPfYBHGe3WkGwoZlPTTFWzVTUb+A8wuXGo0ZmvnnVXYPf1\nr7H7+ld55cxf0bZRMwa3P2LPzoM7HB5IkUAbrJ29OXAE1l7dHvh97T+dKtETP2W6wqjVCX0CnCml\nCyngMqyT8RO1guu/AxlA15RAoGV6Soif9D+X9lmHkJYS2rPTH48ZSUYwjU7ZrREkBRvdscSd6z7g\nSFf3VYTVtfURkYDbxqfZPFVGRK4Skbkisl1EtmN+QYeUu6OSnx3KIPonkBFMA6B1RtM9m6SnpJJX\nXJgKnCYiV4jIJyKyUUR2An/GavBiiX0v5wFZVX9mnmQimdJnJwBBVY2GKF8XkdlYmucGrLNltnts\nrIg8kJnRMjO687H9byKrUWsAenQawuat8wFo1qRb+nfbv4ka3o3GVH4xcLuIrAC+Bn4jIk0wR+Bz\nsBTDhW5bjfk62P8rs21VjhUE2opIV/f/YZh78bUllIwfcujRACzdsZ5rPvsXbw75De2z9n5eXN7t\n1NQZmxYP2VGU2xULLe8AEJH7gOeBuyv2a0ooPbFIoqfiLMYM5/qX+nlb7G8C2DM/bS0mksMlKB2z\n9r/eRH+mqhSXRALA3SLyi1KbtVPVz0TkIeBhoJOIvAH8XG34rcdTKZyT+uPYUOEZ7v06l4OUV0TJ\nLS78oFhLbj7YtjsKcxBkKzZ3cCwmeh4FtmEZjKOc2Pczzeo5ySSK2uGKPGOI+p10Aq4WkR/HPNZo\nd+7GCBb6J6tRqz0PBFPS2R02IV9YtDMMFGBtyuK+dmGphNlYwd67WOpghPvZnJhtAzHfl/f/QMy/\nwSrue6D/p2F3RkH3evwc+AdwQraly9hZmMuICffy5+NGc1KbPvu8kM3SsijRksaY8PsiJnAQPVdS\n4yKJHbEIoqeCuIvHR5jLdGyEbQMxQilmfMj6/OLCN4pLIncJ+0WX9txtT9u0CBEpQvUGVX3xAOd+\nEHhQbLDtK1iKrq5EJT3JRSb2/t0KBETkKuzzEPYXO5uxiPi3YvP3KIgUycT18xjY/vD9DryrKI8V\nuzaWFETCb6gZ5hYB07EI0YlYQXUO1mnZ0u12hoh8if0dJf3np6fiJJMo2ojdpcbSCesEWAv8WVX/\nEn1ARPqu3zJndiRSlHGgAxaFc1m3aZZgrqWrYvYtBtar6lJgqRujcRhWX/GIqs6L15OKFyLyJ6xQ\negFW0Hqtqr4mIk23Feb8dkdhDqM+/juDOxzB9Yedvd/+y3ZtICCBldgf9WFa96Y4d8F+Z94vpJKo\n6moR2QLkYheLTzFxeZeIDAKmYIWlBcD0gkj428JI+K61OWXPtgxHivnljP8VlWjJJCzK+rWqLnLR\n1rNU9VUROQa7YfkSSy8U4LyNPJ7K4t5f/8A6bUuwaM5U9o2oR/kjlk3IxjrHPgO2DHvvnqzfHX15\n+jW9BgdEhOKSEt5aOZOfT38qtyhSvNsdD+yG83Hgl1jd0hjgdFV9XESCWJPCZux6dSwmzlqIyDBM\nJG0AvlPv6F4nSSZRNB0oFpGfYMW/52JvuE+AJ7BZYB9jkZxGQGdVnTdt7j+PpsznoUya/ZciCQS+\nooR25Zx7LHAXdqf8RpyeT00gwGvAc6r6GoCq7mialvXJJR/839BijfCvH9xY5o5PLPogd0dR7oPY\njKx/ichtqvqdMyrrq6of1taTqCI9sWiep2p8DJwJ/FZE/gbcixsei324zwXOVdViEdmukPvjqY+m\nNU3LCg3vdCxgUaJF29Zw+7TH8xZsW/25Wm3fBViqux2wE/gQE1yNgX9ibsAF2GiQ+2vzCXvqF6r6\nW+C3B3h4DOwxd/0SeACbTzbR3Ug9IyJ97/vy1T/8cc4L5zVPyyru98qtwbRAcPmOotw/Ay9FaxVV\ndQpmeBrLH9xjxbjsRBQReQqrW22Hvd9PBrJFZBMmkNa7f7f5esjkJ6nMG0XkaEwAdQfew9T/MlX9\nvYicjX2Q98BceqcAd4eCjaaISNshJ/+d/r0uA+D9Kb9k+ZoPS/Lyv18dLs69A3hIVQ+NOc9KzOzr\nU/f/DCyH/Iaq/rDWnnAlcGv+E/b65LH3zkiBywXGp6aEJBTYqw8fP+02Lu9+KimPnkt6Suq2/EjR\niVhK8vfA5ViR4nosOvZQLT6dSuFSO3cCz6jq94leT11FREYAOar6yUG2yQauwowd05ukZt4fDAQ6\n9WzSvnhb4W5Zm7NVS1T/UxApuldVwyLSE+sMXQx8rKpFtfJkPJ5SuBu8YUAYeE9VNx9gu0zM6yhX\nVbfU0FrSMZEU/WqPlUBsiPlaD+zyQim5SCpRVBVEpGUomPEbVb0uPa2JqqoUhneXoPpocaTgvmhB\ncQWOswy4KSqU6hoiMiwjJfXlC7ueFLiuz1kZzdOyWLhtDX//+o3dy3Zu3JhjpmSnYqm3qXXpD1FE\n2gIXuxoVTxVx6a0fYSJ4v4Jn9/hVwNeqOjnm54dhHkc5wKzSwsfdVAxx24xTP/vMU4uISCOs9KEn\nVmIwPxk/35wYiwqk6L+wbzRpg1Zz2Ky7iRwM8nYomJ4fCAQLVPWzonDOA6r6pdtmAXBL7N+5x6jz\noiiKU+adsMjJqsrcsbpOs/9T1Z41tb7aQERahQIp12eHMq4sUc0UkdXbC3P+A7zl7uobA5dgkaY3\nVbUgsSuuGCJyGual5M3RqomInIm9lu+U+nkzTBDNVtXpVTx2L+xO/RvgEx818tQk7uJ/FNaRtgD4\nrK58psGe9UetYmLFUiH7RpM2agUH0YpIWmoo682M9OanFBXlZJ1x0r20aXkEy1ZNiMz8+pHCSKTw\nsXBx3s+SUTQmC/VGFFUV5/rbGxitqh8leDk1jthE87OwNOTLBwoxJxMicgOWmlmZ6LXUdVxU58eY\nv9BW97MWmCCapqqz4nD8c7Bhmm/5qJGnJnA1bMOwout364sHlhNKzdgrkNph9hk5xESTMKG0301H\nemrj59q3OfbCS4Y8n/HoS8czfOB/6Nz+VADyCrYxdtyQ3J271/0+XJz/QC09pTpHg28lVNWBqtqm\nIQgiAFWNqOoEbMTH1WIz1JIWEcnCjNPWlLetp3zcHec0LN2Aa5e/BitIrZYgih5fVd8APgAuFpEh\nIhIqbz+PpyKISIaIDMfGx8zGxH29EESOlcCN7J3ocApWNP4SJpCeBxYBy0TkTyJyvogcKyJrReQv\nheGckWs2TMsIyL69R1u3L+F/rw/myN6jM0XkdyKyynWeIiJ/FJFXRGSMiOwSkQWuvhf3+K9EZJ17\nbHF0v/pKgxdFDRVnOzAGGCgiQ10EKRnpAaxwrsue+DALaC8iR2EjEj5S1bnxPIGqLgEewTpFb3bG\ndx5PlRBjAHArFh16WFW/qqdpoJFYNL8bVif1Gyxy9FvMiT4La5a5CrOyaYv9nd3Wp9sFkZ9du4pA\nYO/H+cbvvubFdy/h7JP/xglH/pjmTbsHsHmEsZyLibAm2GzJh2BPSvxW4BhVbezWtaomnnSy4EVR\nA8alzh7H/hCucTVHtYaIPCMi97rvTxGRxe77NBEZICLHYW6yS0vt956IjK7NtdYn1KZ9L8BsKN6r\nKV+umKjRh8AlPmrkqQqu0eI64GhsIv17Fa2xqYMo1i29XlW3YwaSVxAz1UGNMVhtaKqqvg3sCgRC\nX3ZofUwwmJK252CrN0zj1fdHMWLQo3TvdCYArZofFmR/G5spqvq+E5nPYWOgwLzF0oC+IhJS1TXq\nBu3WV5LJp8iTAFS1QERewrw1bhCR12ONLmv69O4LVZ0iIsc0CqbdnxFMval1RjNNDQR1Tc6WzNRA\n6D0R+YUz20RVh9bS+uolLmpzJBaGr/EInKouFpE1WK3Rj0TkLVX16VDPQXHNM4OAvphf3dx6Ghkq\nzdqY79dgabOypjqE3GMAqEY25OZv2TPlAVXmLhpDp3Y/4NB2J+3ZKSd3cwSLtsUSW1uaB6SLzSxc\nLiJ3YIaYfUXkA+DOOmj+W2F8pMiDu/OYgg3kvVhETnIFf7WBgPnjZIcyPh/e+bjbvrrkweyVVz7V\neMnIx5qsv2ps8FcDLh6eEUybIyJH1tKa6i0i0gULwb8OvICNK6jxzwFVzVPV1zETyUtE5GwfNfKU\nhUuVHQnchl2jHlLVLxuIIAKztoj9fgMmjv6sNhA8+pWlqi9HN1QtmfTVN88WlpS4+xwRzjn1AXbm\nrOWj6b8BICdvC2s3zQhhXn8VQlVfVNVT2Nvd/ddqPr+kxosizx5UdQVmDtkPu3CllbNLhRCRPiIy\nUWy69QIRObf0NukpoVciWnLYy2f+Kv3NlTO45IP7AGiens3dR18aOK1tv+ygpEwVkRR3rOvcsbuJ\nyKcislVEvhOR55zfjqcUItIDuBh41f2ul2F3hUccdMc4oqrfYI712VjUqGNtnduT/IhIG+CHwHHA\ni6o6vh6nyspCgFtEpL2INMfqiV4CnsT+Xo5zojFTRIa5RpQoyyKRosXT5j5QHP1BWmoWlw99jTUb\nZ/DpzHv4YOov8wOB1BfZP1JU9mJEeorIIHctKKQBjOvxosizD6q6E3gau5O4wXUnVRkXDXgHG/PQ\nEmsHf17MCTm6TdOIlgxqmpqJiHB591N5b80ccsL2WRgpifD19ytpn9kc4Gz2n3X0Z6zYsA82quWP\n1VlzfUREegPnY+MMVoFFCDGzu9NrM2rjokavYVGjy0TkLB81atiISLqIDAFGA18DT6pq6QHhDQHF\nIrgfYnM/lwF/UtUvsLqih4Bt7udXse/nIIXh3efNmPvvzW9/enNhSUkYgLTUbE475tfMWfBEydJV\nE7YXhXffVsY5S0fhov9PA+4DvsOKug8Bfh2XZ5qkNHifIs+Bcd0eZ2I+IAureIxTgFdUtW3Mz14A\nlgCdgXXAnH7NOj2/oyg3c+1VzwBwypu/5MbDhjC61yA+WjuXmyc/wi39hvKH2c8/lRMu6AY8q6pP\nl3G+84Hfq+pRVVlvfURE+mGO0y+o6oYyHr8MWKeq0xKwtkbAUGx21FuquracXTz1CJem7499zizF\nTD/zEruqxCGlRlBV8RgtUlJS7xRJuTUgwVTV4oBIytZwcf4/VCOPqB+qfVB8obXngKjqXLGhhpeK\nSAfMQLGyodN27Fs4CDZ/rX3M/zOyQumyoyh3zw9G9hjIi8snMbrXIF5YNolRPQbSJDWToKRkxx5I\nRFoD/8YNYcSin9squcZ6i6vNGIyJyAMZdX4CXCsiX9Z2qsJdAF8TGyVymYjMw5yJw7W5Dk/tIyKt\nMAPGVMxIdl2Cl1QvUJsP+RsR+QMW2SkBvmtANVnVwqfPPAfFdRk8jqW+riqVw64IG4COpQq3O2Hu\nrFFWLtu1cZ/C7ou7/YCJGxawPmcr41bOYGSP05i9ZWlhXnHhN6WO/xcsx91PVZtg4Xf/vmbPgOVB\nwJiDOZc7Z+tvMKO4hKCqi7BaoybATU6Ee+ohznLjbMwjawHwhBdE8UdVi1V1k6pu8YKo4viLh6dc\nXPTgeZzbaiWN+GZixby/FJGQiAzEpqq/iOs8A2blFxfuLIjsda1vmdGEge36cc1n/6Jr4za0adSM\nZ5d+pkUlxU+WOn4WkAvsEpuS/YuqPMf6hoicgImcZ6LjPMphIjAgkUXqqpqrqq8CnwGXi8iZIuKj\n2fUEVyDcHzMDTMcGE89W1QoV/TYEVLVLdVJnnurjRZGnQri2/YlY0fRlInJ8Rdr2XRrkXMyj5jus\nUHC08xzS6KHzigsf2lawW5ds33vDOLLHQD5Z9zUXdf0B5074f3kpEni+jDvKe7ChkDvd2l5n/6LB\nBoWInIx17zyjqhVKJarqbmxswuk1ubYKrmUhFjVqhkWN2peziyfJcQ0bVwE/wLof31LV3HJ283hq\nHV9o7ak0YhPVL8NEzjsap2nooUDw2mAg8PDF3U7Wy7ufmpGeEmLyhoXFDy54p6QoEp6WW1x4lqoW\nl3+khokTqadhlgpjVXVXJfdPx7oDxx4s3VabiEhfTFB/hc1n87//OoSIpGLvyQHAJMBHhjxJjRdF\nnirhWqiHYYXUL7vivngct3VqIHhjdihjOEKwKFI8d3c4/1Hsg/U19VPXy8QJojOA7lhRdc4BtusM\nfAsEy7o4iciTQC+sW20Y8AzQ3/kaJQQRyXRraQmMa6Ct2nUK9348DLPQWInN1yvzPenxJBNeFHmq\njPvgOxpLubyjqotr8Fy9sA/YR+MVmaovuN/DEMyj6bmDtTRXQBT9JYBcl5oSzO7RpH04K5SuC7et\nSQ2IzN9RlHtnItr23boEG/dwDjAXHzVKWkTkEMxmIRObredvZDx1Bi+KPNXG1XxcCswHPq2p8LiI\nXAjkq+qEmjh+XcSJheFAK2xYZkE523fmAKJIRLJCgeCKdo2aHTJxxP8FOjduDUBRJMzLy6dwy5RH\n8nLCBRcn8vV33Y/DsFZjHzVKIlyq7FSsxm8yMMunyjx1DV9o7ak27sL0OJZKu9KlO2qCCcBh7sLe\n4BGbWXY+JhDaAAtEZJeILHQmlrixKH93I1BWYIIi9hhdRGSSiOwSZGGnrJYtTmnbN9C5cWtW7dpM\n4L/nEgykMLrXIG7vf14jgXfdOb4VkZHuGCIivxWRVSKyWUTGiEhj91hnESkRkatEZLVbx91Vfc4u\nBfMKdtEdKSKDfYdaYnG//z5YV1lj4L+qOtMLIk9dxIsiT1xwnSTPYf5DN9ZEx5CzBhgPjHB3Fd8j\n2gAAIABJREFUpQ0WEUkBLsIsCZ7DHMJPVtXGWEfec2JzpG7AhNCRwDHY7LPY8PALWNdZh1AgpeWm\nvO0pZTUV5oYLeHDBeE5qc1ieIHcCJ2LFz2Czqq4GBgJd3ZoeKnWIHwA9MSPJ34uNHakSrhNyPtah\n1hJ7v7UrZzdPDSAiLYBRWAr9TVV9w3Uyejx1Ei+KPHFDVUtU9RMsojNSRI6pSNt+Jc+xBJsYfUY8\nj1uXcJGRS4AQNjQzrKqvqeomAFV9BZuNdJzb7p+qul5Vt2Nml+KOcygmlH4HHNmjSbui87ocf0A/\ngwDCMS27ZzZNbXSpqm52hotgF8V/qOoqJ45/jfkMxX6+3KOqhao6D5ttVe0htC5q9DIwBRglNrjS\nR41qAec5Ngi4DkvHPhadqefx1GW8KPLEHVdw/TR2UR4h8R/2+T7QuyGm0dxreTlm3f9ytNjYpafm\nish2EdmOteUfwv5jVtbEfN8O2O4icKmZoXQ6ZbUq87yZoXRePutXTNwwn+1FuaeLyHhX/A42jDe2\nmHYNNkKodczPNsV8n4cV4VabUlGjVljUqG05u3mqiEuV9cZSZc2xxofpVRj/4/EkJV4UeWoE16L/\nJJACXOe8jeJ17AaZRnPPdSQmKl6LXohEpBNW03Ur0FxVm2HjEwSbbB3rQB77/UagmdhQ1mWLtq9J\n+3bXJg4U2jur41Gc1WFAJD0QmoClSZ9wD23AhvvGnqMYqDWvo5io0VSsrm2QSzF64oSINMfef2cA\nb7voZKW8sDyeZMeLIk+N4Vrn38BaqK8XkR5xPPZSGlAazRkrjga2Y11XsUWsmVid0FYgICI/xCJF\nYEXJPxGR9k6Y3hXdybVKz8FqkHJKVDe/verzMs+/JW8HLy+fzKMLJ4QLSsKvAh2AtiIyBIvc/dQV\nVWdhKbqXyim0jWtaFfZEjeYBj2JRKh81igOydzzP9cAqrJD624QuyuOpIbwo8tQo7kL1OXYXf66I\nnF6q1qQ6RNNoXeJ0vKRERDKwEQmbMD+ofcSGq+35BzDDbdMPi5goFs35AKvjmcP+Y1CuAs4C1ucV\nF+aFSyLFm/N2xJ4bgN3hPG6a9FDJ7uL8FOA/QHRNBUA+sAKYhV008zBn7D1LLONp1ZgXiCv0fQmY\njkWNTvdRo6ohIj2BW7DU5GOqOs2nyjz1Ge9T5Kk1XBThEiAMvO7SYNU9Zk/M0O+/9dHU0dkbjMaK\nWT/SOP3BxjgOnwWsc8feISJnpKekvnFC615yTa8zsrJC6czYvDj8+KL3I8Cru8P517l5dqWP18od\nry+QBiwEFgHr4rXmqiAi2djsvcZYhG1TObt42DPKZwhWl/ZeIh3NPZ7axIsiT63i7tjPAPpghcIb\n43DMC4AiVX23usdKJtwF/SpMXEyMoyBqi13w0oAJpR2HXWTqsuZpWReJBDLyiwvn5xUXPqKqyyp4\n/FiBlOrWvxBYnwiB5ATg4ZgAnA1M8dGOsnHdez8AjscijzO8c7inIeFFkSchiA36HIZFKOZW81gZ\nwM2YT8rKeKwv0YhIE8z7Z66qTonTMTOBQdhss8/csWvUYM8JpL7uK0QCBZIzlByOjxqViYh0x8Zz\nbAY+UNUd5ezi8dQ7vCjyJAwRaQlchrVzT6jOHalLow0FHqnraTSXurga+FxVZ8TheCmYPcIpWG3R\npPLGgcQbF61pyb4CKZpiqzWB5NZxBHAmPmoEgIg0xeYKtsb+DisUEfR46iNeFHkSioikASOAJsAr\nqrqzGsc6HwjX5TSa2DDNq7CL9ew4HK8HdsHbAbyvqlure8zq4oRJbIotiImjWhNILmp0Lua+PU5V\na80+IFlwqbIT3dfnwDSfKvM0dLwo8iQcd5E8ETgJeKOq7b6ubf0W6mgazaWaRmNDdaubUmyB1Q01\nx8RQUt79xwikaAQphb0ptg01KZDcuY/EatxmAVMbStRIRLphkdWt2Ptje4KX5PEkBV4UeZIG11p/\nIXsvUJV+c7rIyDDqWBrNFT+Pwmo55lfjOOnYpPIjsbb8z+vKhT5RAslFjc7D/J7qddTI1aqdjbmQ\nT3B+Xx6Px+FFkSepcBeoSzCvmzerUvtS19JoItIBuAIYr6rfVPEYAUwIDQKWYtGmnPitsnY5gECK\n1iDFXSDFRI3OxFJJ9Spq5OrKotHYWViqbD9rBY+noeNFkSfpcB/gZwPdsbb9St2516U0mhvRcSnw\nVlXv2t0xhmD+TxPiYXOQTDjB0pq9NUhRgbQQ2BhPgeQiKedSj6JGLgI7DHNDn6Cq2xK8JI8nafGi\nyJO0iMjh2MX+fTe+oTL7RtNo/1XVwppYX3URka7Axdgcs0rXUbkL+JlAR+AjYGEijRJrgxiBFI0g\nCXtTbHERSO4cA7Bao5lY1KhGrQtqAhd1PQsbyfI+sKS+vz88nuriRZEnqRGR1ljb/nKs3qbCKQ0R\nGQFEVHV8Ta2vqjjRdj7Wcbe6vO1L7RvCDPaOowGnQg4gkKIptmoLJCc6z8NGmoxT1S3VW3Ht4CKt\nxwMnY6NdpjTE94fHUxW8KPIkPS4ddgHQCHhVKziZOyaNNi6ZBliKSB/MRPBFVV1Xif0Eu/ifCazF\njC+rbGFQn3CvTRv2ptiiAmkhsKmqAskd9yhgMObwPC2Zo0Yi0hmLkO7EUmXfJ3RBHk8dw4siT53A\nXZxOxqIjr6vqqgrul1RpNBHph6UEn69M7U/MaI5ULJ1YqehSQyJGIPXFRFK1BZKLGo0A0knCqJEb\nCXMm0AlLlS32qTKPp/J4UeSpUzh/lQuwCegzKvLBnyxpNBE5Eos4PFvRi2qp0RyfAl8lc6Qi2Sgl\nkPoCyt4UW6UEkjvW0djvIymiRq7r8DjMhuFLYHJdsqLweJINL4o8dQ43luBSzKX5rfIiQC6NdrPb\nNiFpNBE5Brtwja2Iq3QyjOaobzhR05a9KbaoQFoIbK6oQHLvv/OwgbrjVPW7mllxuevohBkw5mKT\n7BPuVu7x1HW8KPLUSdyIgnOwdMHL5V2Y3LDL4SQgjSYiJwAnYIKo3HZol/IbAmzDisv9xS7OxAik\naIqtUgKpVNRoOjC9tqJGIpKFpcq6AB8Ai3yqzOOJD14Ueeo0IjIAu0C8q6oLy9n2PEBV9Z1aWZyd\n8xSsvXtMeUXRbu7Z2ST5aI76RimB1BeIsLfN/6ACyUWNRmC1XjUaNXKpsmOB04C5WPTQp8o8njji\nRZGnzuOKkC/DLmQfH+iOPSaN9raqrqjhNQkwELvIjlHV3QfZNh270B0BTAFm1Sc35bqE+721Y2+K\nLcLeGqQyBZLb5xjgdGAaVusW16iRiHTEGgbysVRZQlJ2Hk99x4siT71ARBphc9OCmBlimSMuXBrt\nXGw2Wo2k0dxF8kygG5Yyyz3AdgEsinQ6sAQbzVHmtp7a5yACaSGwpbRAEpFmWNQoiEWNqp32dIX2\nZ2DvpQ9pAAadHk8i8aLIU29wIuM0TGi8pqprDrBdjaXR3IX0HMxF+FlVzT/Adp3cdoVYqqxejeao\nb8QIpGiKLczeFNsegeS2Oxb4MyaihpaOGrmaoCOxcSWLyxol4t7LR2PRxnnAxGSwlPB46jteFHnq\nHSLSE7tjn4ylokrf0adhpo5xTaO5C9lwoCXmQ7Rft5jzu4mOXmgQoznqGwcQSNEU2xZVVRG5D+s2\nfBrretwqIs1TQ5l/LSkpHtW0cZeilECI73cuT0sJhD4tLNp1p6ouccfvgKXKirBauaTyRPJ46jNe\nFHnqJSLSHGvb/w54p3RBqvM7Og/rRqt2q7sTROcDjYEXyjifH81RD3ECqT17U2xRgTQU80d6EIv2\nzA8FM//br8fFbU8++uepjbPaA1BYtIsvF43RyXP+L6e4OP8soBXQAxPM871g9nhql0CiF+Dx1ASu\n9f0poAS4XkRalHp8BTZP7azqnst5Cl2MTVZ/PlYQidEPuA04BHhMVSd6QVQ/cKJlFBYRuge4A0uf\n9cMMNzOBcSkpaQ+mpIQ6fbNiXOrbn97M1u1LAUhLbYxqRNJCWdmYIeSDwBpVneciTteIyFQRuV9E\ntonItyIyJAFP1eNpEHhR5Km3OOExDovMXCsivUtt8iHQzRVfVwnnl3QpVh/yYqzYcV1xP8QiRG+o\n6mt+Vln9QkR6AbcCx6hqY8y36DVgJjafLhW4NRIp7DZ84EP89JrldDv0DF6ZMJKSkmIAmjXuwnUX\nT6JZ4y65wFjgf24QcpTjgMVAC+BvmNj3eDw1gBdFnnqNGnOAF4FzRGSwS3XhClffBs51bfGVwqXE\nrsAKal9R1WL38yxXzD0K+Ap4ws8qq7dEMGfrviISUtU1zjVdgDxV/QBom5nRqrhXl6EEAimccMSP\nKY7ks3bT5wD06TaC7Mw2HNH7ykbBlPQmwDJsyn2U1ar6lItKjQXaikirWn2WHk8DwYsiT4NAbRr9\n41iB85Wu1bnKaTQRScVETy7W6RYRkRQROQkr4i4AHlLVLxM9H8tTc6jqcixl9kdgs4i86CKEsRyS\nltp4T22QiNA4qz05uZsAmLfkJZ589TSmfvF3KY4U/AhLvcVGijbFnC/PfZsV/2fj8Xi8KPI0GJwH\n0LPABuBGEWnvHqpUGs1FlUZjYzjeVNUS1/F2C9AZeFpVP/SzyhoGqvqiqp6CjZxR4K/u3ygrduWu\n39PUoqrsyllPdmZbdu5ey3uTf8qQU/5Gj05DCkGeAzYCQ0TkTuBEoKmIHCUiHasS0fR4PBXHiyJP\ng0JVS1T1Y+B9YJQb1FpEBdNoziTyKuzC9Q7QQkSuxCJN76vqC35WWcNBRHqKyCBn81CIRQhLu5H/\nu7g4P/j5vIeJRMJ8/vVDBFPS6dDmOIrCuQgCCEtXvaegc7GRI+8C/wO+xZoFDsV8re50xzxfRIZ4\nseTxxBffku+pt4jIKuA6Vf3kAI+3wMaDbMAuQkOADJCm6WlNb0RLmiOypaBwx3+BV7CbiKuwdNsU\nrNX6cPxojgaLiPQHngT6YO3404AbgZswF+o/Y2LmVJHA+aFgI2nb8kiGnHI/hzTrBcDH03/HrPmP\nohopAB4BjsKMP58Wkaux9/Cp7nwCFGOO6YWYJ1b0qxCzoNji/v0O+O5ABqIej2d/vCjy1FtEZCV2\nQfn0INukYn5FhwDLgynpbx3a7iSO7nt9I0tvrGbW/MdzNn33VV64OO8xYCKwEz+aw3MQnEnnOZhY\neVdVvw0Egj8MBIIP9+w8VA/rdn6jQCDEynUTi+cteb64REvGFRfnzwGeUdXvq3A+AZqwr0iKfhUR\nI5Jwoqm2xZJbYxpQVF6dnYh0xqJkQV+T56lNvCjy1FsqIorcdgIMDaZkvDZi8H/Te3c9b89jqiWI\nBJi7aKx+NP3u3eHivHuA7fjRHJ4ycJ5VJ2A2DJ9jJp3FMY+3CEjwurTUxueABovCuSWRkqI7VHWu\niByFjakZ43y24rEewQxFowKpVcz3YUoJJUws5ZV9tCqvoW16SuodAj8qKinOVFXJTm00cWdR7n0u\nlV3WPp3xosiTALwo8tRbYkWRiPTBUmR3AxcBJwMZwNfAzcGU9GuO6D3y9nA4PzUYTGfn7rWs2TiD\nS895nhZNe/DB1F+xfPWHREqKdgK/U9UHRaQdlkprr6rb3TkHYIXbbXw6rWEhIodiY152YZPsyxU2\nInI+sEFVZ7n/H42NB3km+p6qobUKkM2+IikqmooplYLDxpccVCyJSDBWALqfHd4omDZpdM/TM24/\nfERan2YdyQ0X8OKySfxu1rN5u8L5D+aGC+4q41id8aLIkwCCiV6Ax1PTuDvwN4GbVfU9V5R6DZZW\n+BvwPCJdjul3Y+qMuf9m4fLXuXzoK3Rocxzh4nzGjhtKry7DOK7/j3hpwmU54XDuHSKyRFU/FJEZ\nmMh60p1uJPCqF0QNB1d8fyZWQ/QBsKgS4zmWYcNhZwGo6hdOsFwtImNqShi59e1yX8ujP48RS1GR\n1Barm2spIhH2T8NNAh4GrgR6iMgZwP1YjdWatEDo0CcG/qTJyB6nyc7CXK777N9MWPMFARFG9hjY\n6LUVU28TkbnAq9jf4tVuTQ/UxPP2eMrDiyJPfec04FpglKpOBlDVZ2DPBeCvwO3Fxfm0aNoDgF6d\nh9GhzXEAbPl+IXkF33Py0T+noHAXkUjRIdg4h8uxiNALmBB60h3vMvd/Tz3H/b4HAIOB+cDDVZhk\nvwI4zxk/hgFUdY4zGL1aRJ5R1R1xXfhBKCWW9gxLds81i72RpdaYn1Jj4Hbg78BWLBp7O/A68LuI\nlvzi7I4DBOCaz/5Jm4xmrBj1BDnhAoa/dw/ndj4+87llE/+4syi3GTYE90ggD3iDfW0NPJ5awYsi\nT73EfYgHgJuB2UCeiAwCmmIi6Xjsjth98Aa0sGi3IJCd2W7PcXbuXktO3ib+8XQXVEsoKQmnAr8G\nJrtN3gAeFJE22KyrElWdWhvP0ZM43BiOYdh4l+eqWl+mqgUisgnzOFoe8/NZMRGjZxI9HsaJpd3u\nK1Ys/Q67sfgQswv4AntNbm2amnlJp+xW8u7q2Zzd8SgmrPmCHde+THowlYxgGnccPoLHF70P9tyv\nAv6pquvdcf+C3dB4PLWKF0X1kPJa0UttmwpE6lK6x10sMrC71Cbu37K+srFW+sHAb4F/YdPMe2G+\nQovccbaFghmT5y99+TRsPMMemmR3oGl2J26+YjaTZt9X8vnXD38WLs67QlW/A1DV7SLyIRYhOgwb\nJ+Kpp7i/l4HAEcBnQDwcy5cDPYgRRQCq+rl7r1+TDMLoICxT1W9ddOskzFKAnUW5jZfuXM+mvO2s\nyfmOcEmEtmNG79mpBOXQrJYckt64aGdRbltsVlyUNbX6DDwehxdF9RPlIKFnEclOkcANjYJpPwuI\ntEGRZmlZX+8oyv0rNsMrYYWN7iLQiPIFT5i9Yf7o1yqsXX4Xdkd7PSaKfgV8ApyNffDmYBegIPAX\ngHBx7lNT5vz1pM7tT0mNXU+7VkeTGsri0xl/ZM7CpwrDxXkvAL8Ske3A88BqLIV2F2awd3r8XxVP\nonHvy15Ym/1q4L+qmhOnwy/DhgpPKP2Aqs4sFTHaFadzxpPoZ80azF/pRoDm6dmf/OsHNwy6qtdg\nNuZuIy0lxPfXvkhA9noGF0XCtPjfFWmYV9ihMceM/d7jqTW8KGpgiEirrFD69NPa9W9391GXZpzY\nujfFJRHeWT3ryN/Peu7JtTnfjRSRC0t3kcTp3AJkslfYHEj0FLK/4PmWGMGjqkUVOB8AqrpTRM7E\n7uw/xS5q64Hvgd9jRns9iopzX1i2+oMru2kkGIkUkZKSSnGkkP49L+OTmX+IlJSEw1jtxBLgGazT\nKAzMAbpjgzvnV+9V8iQbItIUGAo0B8ap6so4n2IzEBKRFmV5FKnqjFIRo2QURgDPAbNF5CzsJuTJ\ne+e8dMLg9kc0ap91CGd1GMCd057k3uOuJDOUzspdm3l26WcEJWURNn7nJyIyHqsp2q8jzeOpDXxL\nfj3EtaJfj83nWquqv3M/HyjwwS8HXCz3HX91aF3uVm6f+jhTNy6iBOWybqcw7/tVeVM3LQwAx6rq\nArdfK2AlcOiBjOVc6Lw8wZONjUEoLXh2sa/gCdfE63KAdfcCRgAfqupXIjI8LbXxA5FIuHN6WpOC\ngsIdaYFAaENRePdNqvphqX0F6InNp2oGzMTSKZUttvUkIc5z6EQsJTQTmF4TNwvuXCOATar6+UG2\nORkr7H5GVXfXxDoqS2kvMBE5Dusi6w9EUiSQ9eujLk2997grU3YV5XHXzGd4Z9Usdofz6ZDZgjU5\n3xXuDudfgNUk3Y/VFu0E/gE8CIR8S76nNvGiqB4SI4quBNbFiKIbAshjRTeNE4CjXrudMzocyZ+O\nG01AAnzx3XJaZzSl14s3hSNa8h9V/bnb7w6s5fgmDix6soB8yhc8NXJRqSxO0JwCHIOlDNfF/Pyn\n2Gw0xTpqzgCWqOqXBzleO+zi2Q2YC3yexDUgnnIQkU5YJHAH5jlUY55B7nyHAUep6nPlbHcKVs80\nJlmE0cEQkS6ZwfSpA9v3b/KzIy7IPKJFF3YU5fLskk+LH/h6XFFRSfjX+cVF/0n0Oj2eKD591oAI\nSsoZGcFUSQmkMGPTN2zM3c79J167J8d/Ups+APRo0i6yeMe6G0RkMSZ4fgZ8jNVTxIqdDewreOpE\nsbYrlh2BdaI9Ueri0hYbQ7AoZvs5WK3QAUWRqm4AXnOpluOBH4nIMmCGd76uO4hIJnYD0BUTxt9U\nwnOoOnyLDXkNHSxSqqpTStUYxauuqUZQ1ZUi0nvCmjlXT9246I6CSFG7oAQKAxJ4a3c4/wFVnZfo\nNXo8sXhR1IAIBVKaBZ0AWpuzlU7ZrfYpeozSt/mhunjHuiJM8HwF/A64oSJ1PMmOEy2XY3Uc/ysj\nctUHWFzqZyuAYSLSzomfA+I8ZT4QkUnA0cAVIvI9MB1YXksXWE8lcULjKGAQMI+qeQ5VGdeavwHo\njBVeH2zbyaWEUVLP3nM3HQ+5L48nqfGiqH6Ti3VyAVBUUpyXEjAR1DHrENbkfEekJEJKIGWfnZbv\n3BgGxmPdWpsxh+b6IIg6AZdgk8xnHkCg9Abeiv2Bqpa4aNGxpR87EKpaAEwTkZmYyd1g4CwRmQ7M\nT5Y0ogecx9QwzI7hWVXdlKClRFvzDyqKAFR1UozB45hkF0YeT11h/zCBpz7xFTBURJqJSJuIlnTO\nDRdqUSTMca160rZRM+6aOYa8cAEFxUVM3/QNC7etZtnODQrcC1wIjALGJvRZxAEROQZrex6nqjPK\nEkQi0gJIxzrTSjMX6CMiGZU5r6pGVPVr4DGs5bovcIeInOrGQ3gShIikicjZWEPCV8BTCRREYGKo\nh0TbJstnIhbVvMq/lzye+OBFUf1FsTbXrzH/nveBZ0ALb578SKGI8M7Q37N81wYOfe5aOj57Dc8t\n/YyRH9+fq6p/VdVvsRqaOu3QLCIpIjIcq/N5WlWXH2Tz3lhB9X6Cyd2JL8eKXCuNGt+6QtqxWLfa\nj0VkqIg0r8oxPVVDjMOAWzHzzkdU9YskSG1uwdygW1RkY7fez4ClWMTICyOPp5r47rMGhog0yQ5l\nfNq7aYeevz7qkqzT2vWnMBLmzZUz9C9fvpK3syj3pZxwwQ2qqiLyFLBeVX+f6HVXBVc0eynme/R6\neTUiInIdMFFVVxzg8U7AuVi9SbX/cEQkGzgOqz1ajbV8rz34Xp7qICLNMM+hpsB4VV2d4CXtg4ic\nh02kn1mJfQTrkOyGdaXl19T6PJ76jhdFDRDXfXVx09TMX+ZHinoGkEhqSmjazqLcvwGfOUHUGUsZ\nHZlsF46K4OpELscGdX5WnteJEyi3AvcfqIvOXXxuAd5V1VVxXGsqNgjzRMxtezoWsfL+LHFCRIKY\nZcIJ2Os7Ixm7JUWkD3CMqj5byf0E65rrAoz1wsjjqRpeFHn2Q0TuBe4A/qKq9yV6PZVFRPpihbPv\nRQ0oK7DPMUAnVX29nO2Ox0wsX63+Svc7dgBL4Z2EFcjPBL6qD0XuiUREumDvh23Ye6LWps5XFhFJ\nwyww/l7Z37sTRmdhA1af9cLI46k8XhR56g3uojAQi7q8VBl/IBG5EpirqgvL2S4dE4wP1aRHjIh0\nxMRRJ2yMyKxk96RJNkQki70iYQIHqBdLNkTkaiyStbQK+wrWNdoRE0YF8V6fx1Of8aLIUy9wd9gX\nYBGWVyojIJzQ+SnwQEW8aVzdx3ZVnVLV9VZibS2wlE8/rNNohqpuqenz1mWcMDga8xz6CqsTqzPR\nNhH5AdBUVd+t4v4CDAE64IWRx1MpfPeZp87jureuw3yZxlQhohId5lpRs745wDEu3VWjqOr37uL4\nILAda78eJSJdK9G63WAQkbbYiJvDsffCh3VJEDkq25q/Dy4a9j7mOH+lu2HweOKKiARFpIeIlLhu\nznqBF0WeOo2IdMUE0Rysm6gqxbO92d/F+oA4V+scTEzVCqqap6qTgX8B32AjV24SkcPFBpc2aJzn\n0BBs3t8czK18c4KXVVW+w4wkD6nqAZwweg/YhBdGnjIQkVUiMqgK+2UGU9LuCQUbbWmUcchcQFIC\nqV+khrIeF5H2NbDUWsWLIk+dxHnNnIAZTL6qqrOqUi/iupK6Y14vlSHqcF2rqGqx2mDaR4BPsKnp\nt4vISS4N2KBw74O+WOdgGmaXMLcu1A4dCLf25VRTdLvjvIv5H41yXY4eTxTFxHeFEZHs1FDWzK4d\nB/3y6vPfb/bTq5dmgjDq3HHpAw67+ppQMONrEan0+9Z9DicFXhR56hzuD+g8TBA8Vc32+C6YL0xl\nU24LgPZis9RqHWcGuUxVxwAvYoNsbxeRs0WkSSLWVNu4tOko4DTgNVV9S1XzEryseLEMG/lRLZww\nGg9sxQsjj0NEngUOBd4Rkd0i8gsRWVtqm1UiMth9nyIid4NsKI4U9NuduzE9I32v52xWZhvOPOlP\noQF9rmkG8o2InOr2u1ZEFonINhF5X0QOjTl+iYjcIjY4e0ltPO+K4EWRp07h/ISuwcZxPKWq26t5\nyEqlzqKoTTKfhxX0JhRV3eisBB7F7v5+JCIXiUi7BC+tRnC1DKdhtUMrgcdUdU2ClxVvVgId4iFi\nnDB6B7MkGOmFkUdVRwNrgOGqmg3MLmsz9wVwJzAqEAiGfjJ6EcNPf4hQcN+JRyvWfMzilW8HGqU3\nDwMRERkB/BprgDkEmILdwMUyAou4J01NkhdFnjqDy1ffgN1Fv1LdAlpXKN2LKogixxxgQLLU9Kjq\nTlX9EPg3sBG4TESuEZGe9aUo29WQ3YxFxh5T1WnJaMJYXVzR/zoskhmP4ynwNrADuEJEQvE4rqfB\ncD0wvlO7HxRlZhxC6xZ9yUhvtufBRcvfZMLkn3H50Fc5uu91aSkpaRcBPwLuU9WoEe19wJHObiTK\nfaq6oxJNLjWOF0WeOoGIHI6lSiao6qQ41Yy0B3JVdVtVdlbVrVhRbJ84rCVuqGqBqk6ydOf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wGKpNOAV8xscq7OuYo2xAm5Gze3h2RFSd8F3jKz5lxjrl2TdCAh+fWVPJy7c8dk8ZV1mdTR2/UY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\nNkTSkIJY4pTiROHg2kxqYVWq5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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10d291160>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"colors = {\"M\": \"mediumslateblue\",\n", | |
" \"F\": \"hotpink\"}\n", | |
"node_colors = [colors[node[1][\"sex\"]] for node in G.nodes(data=True)]\n", | |
"\n", | |
"pos = nx.spring_layout(G, k=0.075, scale=4)\n", | |
"fig, ax = plt.subplots(figsize=(10, 10))\n", | |
"nx.draw_networkx_nodes(G, pos, node_size=100, node_color=node_colors, ax=ax)\n", | |
"nx.draw_networkx_edges(G, pos, alpha=0.5, ax=ax)\n", | |
"nx.draw_networkx_labels(G, pos, ax=ax)\n", | |
"\n", | |
"ax.set_xlim(-0.25, 4.25)\n", | |
"ax.set_ylim(-0.25, 4.25)\n", | |
"_ = ax.axis('off')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Building the ERGM\n", | |
"\n", | |
"Now comes the important part: building and fitting the ERGM with PyMC.\n", | |
"\n", | |
"To start with, we need to know what model we're actually fitting. I use the simplest one, explaining the network in terms of the number of edges and whether those edges are between nodes with the same gender.\n", | |
"\n", | |
"We need two NxN matrices, one for each network statistic. Each cell in each matrix indicates how the presence of that potential edge would change that statistic, holding the rest of the network constant. \n", | |
"\n", | |
"For the edge count, the matrix is just all 1s -- since any new edge, by definition, increases the edge count by 1.\n", | |
"\n", | |
"Gender matching is a specific example of attribute matching: we want a matrix $M$ such that $m_{i,j}=1$ if nodes $i$ and $j$ have the same attribute value (e.g. their gender), and otherwise $0$.\n", | |
"\n", | |
"Now, here's one change we make here from the Social Abstractions tutorial. Unlike the prison friendship network, the hookup graph is undirected -- if $i$ has hooked up with $j$, then $j$ has obviously also hooked up with $i$. That means we really need only one half of each matrix, either the upper or lower triangle. We can zero out the other triangle, to make sure that we can only realize one edge per dyad. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 15, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def edge_count(G):\n", | |
" size = len(G)\n", | |
" ones = np.ones((size, size))\n", | |
" # Zero out the upper triangle:\n", | |
" if not G.is_directed():\n", | |
" ones[np.triu_indices_from(ones)] = 0\n", | |
" return ones" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 16, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def node_match(G, attrib):\n", | |
" size = len(G)\n", | |
" attribs = [node[1][attrib] for node in G.nodes(data=True)]\n", | |
" match = np.zeros(shape=(size, size))\n", | |
" for i in range(size):\n", | |
" for j in range(size):\n", | |
" if i != j and attribs[i] == attribs[j]:\n", | |
" match[i,j] = 1\n", | |
" if not G.is_directed():\n", | |
" match[np.triu_indices_from(match)] = 0\n", | |
" return match" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 17, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"# Create the gender-match matrix\n", | |
"gender_match_mat = node_match(G, \"sex\")" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Now we bring in PyMC stochastic variables for the coefficients on both statistics matrices. The prior for them can be pretty arbitrary, but we want them to be able to take on any value, either positive or negative, and be centered on 0. So, normal distributions it is.\n", | |
"\n", | |
"The actual term for each statistic is the coefficient times the matrix; since these values are wholly dependent on stochastic variables, they are PyMC deterministic variables themselves." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 18, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"density_coef = pymc.Normal(\"density\", 0, 0.001)\n", | |
"gender_match_coef = pymc.Normal(\"gender_match\", 0, 0.001)\n", | |
"\n", | |
"density_term = density_coef * edge_count(G)\n", | |
"gender_match_term = gender_match_coef * gender_match_mat" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 19, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"term_list = [density_term, gender_match_term]" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Next, we create the probability matrix, where $p_{i,j}$ is the probability of an edge between $i$ and $j$. This is another PyMC deterministic variable, since the probability is based on the two terms defined above.\n", | |
"\n", | |
"We set the upper triangle to 0 here, so that there is only one probability associated with each dyad." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 20, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"@pymc.deterministic\n", | |
"def probs(term_list=term_list):\n", | |
" probs = 1/(1+np.exp(-1*sum(term_list))) # The logistic function\n", | |
" probs[np.diag_indices_from(probs)] = 0\n", | |
" # Manually cut off the top triangle:\n", | |
" probs[np.triu_indices_from(probs)] = 0\n", | |
" return probs" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Finally, we create the outcome variable: it's a matrix of Bernoulli random values, one for each potential edge, each realized with probability as determined by our mode. This matrix is actually observed as the network's adjacency matrix. It's this outcome that PyMC will maximize the probability of the model generating." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 21, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"# Get the adjacency matrix, and zero out the upper triangle\n", | |
"matrix = nx.to_numpy_matrix(G)\n", | |
"matrix[np.triu_indices_from(matrix)] = 0" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 22, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"outcome = pymc.Bernoulli(\"outcome\", probs, value=matrix, observed=True)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In order to view sample networks drawn from the posterior distribution, I add one more random variable: a simulated outcome. This takes the same form as the outcome matrix above, but isn't set as observed. Instead, the value of each potential edge will be randomly drawn based on the probs matrix." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 23, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"sim_outcome = pymc.Bernoulli(\"sim_outcome\", probs)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Fitting the model\n", | |
"With all the variables finally set, we can plug them all into a model object, and start the MCMC process." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 24, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"model = pymc.Model([outcome, sim_outcome, probs, \n", | |
" density_coef, density_term, \n", | |
" gender_match_coef, gender_match_term])" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 25, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
" [-----------------100%-----------------] 50000 of 50000 complete in 31.8 sec" | |
] | |
} | |
], | |
"source": [ | |
"mcmc = pymc.MCMC(model)\n", | |
"mcmc.sample(50000, 1000, 50)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The estimated coefficients and standard errors are computed from the traces:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 26, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Density: -2.314, 0.154\n", | |
"Gender: -3.430, 0.804\n" | |
] | |
} | |
], | |
"source": [ | |
"density_trace = mcmc.trace(\"density\")[:]\n", | |
"gender_match_trace = mcmc.trace(\"gender_match\")[:]\n", | |
"\n", | |
"print(\"Density: {0:.3f}, {1:.3f}\".format(np.mean(density_trace), np.std(density_trace)))\n", | |
"print(\"Gender: {0:.3f}, {1:.3f}\".format(np.mean(gender_match_trace), np.std(gender_match_trace)))\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"These are pretty close to the coefficients and standard errors computed in R, suggesting that the model was specified and fit correctly." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Diagnostics\n", | |
"\n", | |
"The R ergm package can plot some diagnostic charts automatically, to help us make sure the model is not degenerate and that chain is mixing well. I plot similar charts below:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 27, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.text.Text at 0x10effb160>" | |
] | |
}, | |
"execution_count": 27, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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ICMA1AGYy84Sk+rSInjtXhUgzRZ0tLNrbwyzRgLoQJkXnSLPYaszEDeWaxW9b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\n45g2ZOijH63eBkEQBKFv0VQi2hzUF4fe7hI3PpGSlCvYbtcnxkM80S+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wxeWJNpd7eyun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\nAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10d291940>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure(figsize=(12,6))\n", | |
"ax1 = fig.add_subplot(221)\n", | |
"ax1.plot(density_trace)\n", | |
"ax1.set_title(\"Density\")\n", | |
"ax2 = fig.add_subplot(222)\n", | |
"ax2.hist(density_trace)\n", | |
"ax2.set_title(\"Density\")\n", | |
"\n", | |
"ax3 = fig.add_subplot(223)\n", | |
"ax3.plot(gender_match_trace)\n", | |
"ax3.set_title(\"Gender_Match\")\n", | |
"ax4 = fig.add_subplot(224)\n", | |
"ax4.hist(gender_match_trace)\n", | |
"ax4.set_title(\"Gender_Match\")" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Checking the goodness-of-fit\n", | |
"\n", | |
"One way to inspect the goodness-of-fit of the model is to take a random realization of the network from the posterior distribution, and see how it compares to the observed network. This is one of the things we can do with the sim_outcome variable we added to the model. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 28, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"realization = mcmc.trace(\"sim_outcome\")[-1] # Take the last one" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Or you can fix the coefficients and draw at random:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 29, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"# density_coef.value = np.mean(density_trace)\n", | |
"# gender_match_coef.value = np.mean(gender_match_trace)\n", | |
"#realization = sim_outcome.random() " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Convert the realized matrix to a full network, and add the node attributes:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 30, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"sim_g = nx.from_numpy_matrix(realization)\n", | |
"sim_g = nx.relabel_nodes(sim_g, {i: names[i] for i in range(44)})\n", | |
"for node in node_attributes:\n", | |
" name = node[\"name\"]\n", | |
" for key, val in node.items():\n", | |
" if key == \"name\":\n", | |
" continue\n", | |
" sim_g.node[name][key] = val" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"And visualize. We don't care about the individuals here, since our model was only looking at the gender matching:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 31, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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fTKTyVdSWfDOLpZJ186bt8+3djjjwB1tMAzS3ruKGOz/Vsq5x8cXuhZuiqLEn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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10f2b24e0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"colors = {\"M\": \"mediumslateblue\",\n", | |
" \"F\": \"hotpink\"}\n", | |
"node_colors = [colors[node[1][\"sex\"]] for node in sim_g.nodes(data=True)]\n", | |
"\n", | |
"pos = nx.spring_layout(sim_g, k=0.075, scale=4)\n", | |
"fig, ax = plt.subplots(figsize=(10, 10))\n", | |
"nx.draw_networkx_nodes(sim_g, pos, node_size=100, node_color=node_colors, ax=ax)\n", | |
"nx.draw_networkx_edges(sim_g, pos, alpha=0.5, ax=ax)\n", | |
"#nx.draw_networkx_labels(sim_g, pos, ax=ax)\n", | |
"\n", | |
"ax.set_xlim(-0.25, 4.25)\n", | |
"ax.set_ylim(-0.25, 4.25)\n", | |
"_ = ax.axis('off')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"This graph looks 'about right' (a really scientific assessment), and the model seems to be capturing a lot of the tendency towards heterosexual pairings (though there appear to be more same-sex pairs, and especially pairs of women, than observed in the actual data). There are also more singletons than observed in the actual data -- though about as many as produced by the R model." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"#### Degree distribution\n", | |
"\n", | |
"Another way of assessing the goodness-of-fit is comparing the degree distribution of the simulated networks to the observed one. The R ergm package has that built in, but here we have to do it ourselves.\n", | |
"\n", | |
"To do it, we count the number of nodes of each degree in the observed network, and across all of the simulated networks, and plot them together." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 32, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"from collections import defaultdict, Counter" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Observed degree distribution:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 33, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"obs_deg_freq = Counter(nx.degree(G).values())\n", | |
"x = list(obs_deg_freq.keys())\n", | |
"y = list(obs_deg_freq.values())" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Simulated degree distributions:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 34, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"deg_freq = defaultdict(list)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 35, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"# We don't care about node properties here, just the degree.\n", | |
"for realization in mcmc.trace(\"sim_outcome\")[:]:\n", | |
" sim_g = nx.from_numpy_matrix(realization)\n", | |
" for deg, count in Counter(nx.degree(sim_g).values()).items():\n", | |
" deg_freq[deg].append(count)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 36, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"vals = list(deg_freq.values())\n", | |
"labels = list(deg_freq.keys())" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"And finally, plot: black dots for the observed degree count, box-and-whiskers plots for the distributions." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 37, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.text.Text at 0x10f401128>" | |
] | |
}, | |
"execution_count": 37, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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zv78/JfobgBMBGBy8kauuWkF/f3/+DagQz7O3ZpSZ7A+MiL2BNwDvl3RQiW2p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\nmVWAk72ZWQU42ZuZVYCTvZlZBfx/3mwvTDg6HOkAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10f587978>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig, ax = plt.subplots()\n", | |
"\n", | |
"h = ax.boxplot(vals, positions=labels)\n", | |
"ax.scatter(x, y, s=40)\n", | |
"ax.set_xlim(-1, 10.5)\n", | |
"ax.set_ylim(0, 30)\n", | |
"ax.set_xticklabels(labels)\n", | |
"ax.set_xlabel(\"Degree\")\n", | |
"ax.set_ylabel(\"Frequency\")\n", | |
"ax.set_title(\"Degree distribution\\nObserved vs Simulated\")" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"As we can see, there are far more simulated singletons than in the observed model, and fewer degree-one (monogamous, in this case) nodes. More importantly, for our purposes, this looks pretty similar to the results produced by the R model." | |
] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.4.2" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 0 | |
} |
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