{
 "metadata": {
  "name": "",
  "signature": "sha256:a965d3379a5cdf9ac058d265f5b3def6ce1aa745940143cde5e5c0db58abc0b3"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#In this notebook I ask a question how does diffusion simulation converge or does it converge at all?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##todo\n",
      "\n",
      "1. write about purpose of this notebook\n",
      "2. write about assumptions\n",
      "3. write about steps\n",
      "4. write about results and conclusion\n",
      "5. roadmap to future?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from hypergraph import utils"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 10\n",
      "k = 3\n",
      "f = 0.8\n",
      "HG = utils.create_graph(n, k, f)\n",
      "utils.plot_different_representations(HG.nodes(), HG.hyper_edges())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Drawing different representations of hypergraph\n",
        "Bipartite graph\n",
        "Graph of hypereges as nodes"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Clique graph"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wMCAKQT4yaC8H1Go16uvrUV9fDyA9g7a7uxvHjh27pDJom5ubce7cOezfvz+r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\nIiMKrIQQQoiM/j9vQEgMd0EP9gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f87398a6810>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SwsIogoKC8PHxYdOmTXh4eDB06FA++uijdz7u3r176dq1KzNnzqRz586ZUGnm\ne/jwIY0aNdI/q5ybPuyzWmJiYrqtWI1Gk2Yrtnjx4jmuFfu2EhISGDduHEuWLGHmzJl07NjR2CWJ\n10gIi2yjKAo7d+5k6tSpXLx4kcGDB/Ptt9+SP3/+TDn+smXLGDFiBKtXr+aLt5heLTuFhYXRuHFj\nmjdvzpQpUySIX4iMjEyx9fryn+/fv4+Tk1Oardj8+fPL3xM4ffo0np6efPTRR8ybN4/ChQsbuySR\nAglhkeXi4+NZvnw5Pj4+qNVqhg8fTufOnTNtAnZFUZgyZQrz589n27ZtVHyLeX2N4cmTJzRt2pQv\nvvgCHx+fXB8ciYmJhIaGptmKTUxMTLcVm1n/3eRWWq2WyZMnM3v2bHx8fOjWrVuu/28rJ5MQFlkm\nLCyMOXPmMHfuXGrUqMHw4cNp0KBBpn4gJCYmMnjwYI4ePcrWrVspVqxYph07O4SHh9OsWTNq1arF\njBkzUpxoIqeIiIhItQV79+5dHjx4QKFChdJsxebLl08C4x2cP38eT09PChcuzMKFC6UHcg4gISwy\n3aVLl5g2bRpr1qyhY8eODB06lAoVKmT6eWJiYujSpQsajYY1a9Zgl8bIPaYsIiICNzc3KleuzNy5\nc00yiLVabbqt2KSkJIOW6+ut2GLFikkrNoskJibyxx9/MHXqVKZMmULv3r3ly0wOISEsMoWiKOzb\ntw8fHx9OnTrFd999x4ABA9J8XvFdPHr0iJYtW1KpUiUWLFjw1o8ymYqoqCjc3d358MMPWbRoUbb2\nQlUUxaAV+3oL9u7duzx8+JDChQun2Yp1dHSUD34juHLlCp6enuTNm5fFixdTunRpY5ck3oCEsHgn\nGo2GlStX4uPjg1arxcvLi27dumX6SECvunbtGm5ubnTr1o1x48blmg/+mJgYWrVqRbFixVi6dCkW\nFpkzqqxWq+XevXtptmIVRUm3FZvTv+jkNjqdjunTpzNp0iTGjx/PgAEDTPIqikibhLB4K0+fPmX+\n/PnMmjWLSpUq4eXlRbNmzbI8EF9OQ/jzzz/Tp0+fLD2XMcTGxvLVV1+RL18+li1blm7wKYrCs2fP\nUm3B3r17l0ePHlGkSJE0W7EOMvhCjnLjxg169eqFoigsWbIkUx7vE8YhISzeyPXr1/nzzz/x9/en\nTZs2DBs2LNkk4lllw4YNfPvtt/j6+uLm5pYt5zSG+Ph42rdvj5WVFb6+voSFhaXZilWpVOm2YjOr\nVS2MS6fmpwwGAAAgAElEQVTTMW/ePMaMGcOPP/7IkCFDZACNHE7+zxTpUhSFgIAAfHx8OHz4MN9+\n+y0XLlygaNGi2VbD7NmzmTx5Mtu3b6dGjRrZdt6spCgK4eHhKbZgnzx5QmBgIPb29pQoUcIgWF1c\nXGjdurVBK1bkfnfv3qV3795ERUUREBDAJ598YuySRCaQlrBIlVarZe3atUydOpWIiAiGDRuGp6cn\nNjY22VaDTqfjP//5Dxs3bmT79u05auozjUZDSEhImq1YCwuLVJ+LLVq0KN7e3sTGxrJu3TqjTkAh\njOflJecffvgBLy8vvL295cpGLiIhLJKJiIhg4cKFzJgxg7JlyzJ8+HDc3d2zvdNHQkICPXv2JDg4\nmI0bNxplGsLUKIrCkydP0gzYx48fU6xYsVTvw5YsWTLdVmxiYiJff/01YWFhbNy4MVu/AAnjCw0N\n5ZtvvuH+/fv4+vpSuXJlY5ckMpmEsNC7ffs206dP199z9fLyMtql32fPntG2bVsKFizIsmXLsr0V\nmJCQkG4r1tLSMs3RnYoWLZop9+uSkpLo1asXwcHBbN68GVtb20x4h8KUKYqCv78/Xl5eDBgwgNGj\nR0vv9FxKQlhw7Ngxpk6dyr59++jTpw+DBg2iZMmSRqvn7t27tGjRgsaNGzN16tRM73iiKAqPHz9O\nM2CfPHlC8eLF02zF2tvbZ2pdaUlKSqJfv35cvnyZbdu2Zeu5RfZ69OgR/fv35+rVq/j6+uaaPhAi\nZRLC76mkpCQ2btzI1KlTuX//PkOHDqVXr15GH3UqMDCQli1b4uXlxbBhw97qGPHx8em2Yq2srNJs\nxRYpUsTkep3qdDoGDhzI2bNn2b59O46OjsYuSWSyNWvWMGjQIHr27Mn48ePfm9me3mcSwiYuKSkJ\nzZUrEBYGWi1YWqJycsKyfPm3ukcbHR3N4sWL+fPPPylSpAjDhw+nbdu2JhE4u3fvplu3bsyePTvV\nKdcURUn3kZ3w8PB0W7HG/rLxthRFYejQoRw5coSdO3dm2gxUwriePHnCoEGDOH36NL6+vtSpU8fY\nJYlsIiFsorQREWiDgjDbsYM8M2eiiorSr9M5OKAZMgRd06ZYVq6MRQYuTYaEhDBz5kz+97//0bBh\nQ4YNG0bdunWz8i28ET8/P7y9vVm+fDmlS5dOdUL24OBgbGxs0mzFFi5c2CS+VGQVRVHw9vZm7969\n7N69m4IFCxq7JPEONm/eTP/+/enUqROTJk2SznfvGQlhE5Rw9y74+GA5fTppjWGkqFRofvgBBg4k\nT4kSKW5z+vRpfHx82LZtG56ennz//fdGe8xHURQePXqULFh3797N9evXsbW1JTo6mhIlSqTZipWO\nSc//lqNHj2bLli3s2bOHQoUKGbsk8YaePXvG0KFDOXToEEuWLDH5ObBF1pCHzUxMQkgIqv/8B0t/\n/3S3VSkKeaZMQfP4MZqJE7EsUgR4fu9w69at+Pj4cOPGDb7//ntmz56d5YM6xMXFERwcnOqk7MHB\nwdja2uoDtUSJEpw8eZK4uDjWrVtH9erVKVy4sIx/mwEqlYpJkyZhaWnJl19+yd69e7N18BTxbnbu\n3Mk333xDy5YtCQwMlC+W7zFpCWeSiRMnolarGTVq1FsfIykpCe0ff2D1FseImzEDXe/eLFu2jGnT\npmFnZ8fw4cPp0KFDhh9tOH/+PH379uXo0aPJ1ul0umSt2NdfERERlCxZMs1WbN68eYHn96a7dOlC\nYmIiq1evzrH3aE3Bzz//zLJly9i3b5/MH2vioqKiGDFiBDt27OB///sfjRs3NnZJwsikJZwJIiMj\nmTdvHlevXgWe987t1q0bJ06cICQkhH///ZfatWunexzN5cvkmTyZ6cBS4ALQB5j72naHgf7AdaAa\nsBgoN2ECc4KD2XP1KosWLaJevXppDsh/69YtKlWqRP369dm+fTuxsbGo1WoURWHw4MHkz5/foBUb\nEhKCnZ1dsnux9erV0/9eqFChDLViHz58SMuWLalcuTLz58+X5x/f0U8//YSlpSX169dn3759lCpV\nytgliRTs37+f3r1706BBA4KCgmS4UQFICGeKlStX0qBBA30rT6VS0aBBA7y9vWncuHGGZqdRFAXO\nnMEsMpKSwETgb0h2TzgSaA2MA3oAvwBtgYuPH9O9alUG/vprsvPpdDoePnxo0GqdOXMmtra2HDly\nBCcnJ6KioihZsiSWlpZs2LCB3r17U69ePTw8PPSt2MzoMHL16lXc3Nzo0aMHY8eOlZl7MsnIkSMN\ngjgnDe+Z28XGxjJq1CjWrVvH/PnzcXd3N3ZJwoRICGeCrVu30qpVK/3vefLkYdCgQQAZDpnEyEjU\nc5+3edu9WLYTSHxtuy1APmDwi98nAHOAfwHXpUvZbG3NybNnDSYFCAkJwcHBQd9ijY+Px9HRkXr1\n6nHz5k3Wr1+Pk5MTZmZm3L9/n7Jly/LTTz9legv1yJEjtGvXjkmTJuXKaQiNbejQoajVav09Ypne\nzviOHDlCz549qVWrFkFBQfJImUhGQjgTBAYG4u3t/U7H0EVFob5zJ93tLgAur/yeB/jkxfI6d+7w\n6OZNzMzMqF+/vsG92JfDPkZGRlKzZk3279+Pr68vT548oXDhwvrjFS1aFGtray5evEjVqlXf6T29\nav369fTr1w8/Pz+aN2+eaccVhgYOHIilpSUNGjRgz549lC9f3tglvZfi4+MZM2YMy5YtY/bs2bRr\n1y79ncR7SUI4Ezx9+vTdhxFMSno+GEc6YoDXuzA5ANEAWi09unUjTxq9ZP/zn//Qr1+/NHvSOjg4\nEB4enpGqM2TmzJlMmTKFHTt2UL169Uw7rkjZN998g1qtpmHDhuzevZuKFSsau6T3ysmTJ/H09KRC\nhQoEBQXh5ORk7JKECZMQzgT29vbExMS80zFUNjYo+fLBo0dpbmcLBL+2LILnwaw4OrL3yBGKffgh\nzs7OyaY7O3nyJAEBAcyYMSPNc0RHR2fK2MQ6nY4ffviBLVu2cPjwYcqUKfPOxxQZ07NnT9RqNY0a\nNWLnzp1UqVLF2CXlehqNhokTJ7JgwQL+/PNPunTpIn0eRLokhDOBs7Mz165de6cRqCwKFEDTowfm\nP/1ksPz1/4UrASte+T0euPJi+dOvvmLznj38M3o0ISEhVK9endq1a1O7dm3q1KnDqVOnOHfuXLJ7\nvTY2NsTGxgLPW/URERHvPGF4QkICnp6e3Lt3j8OHD8u9MCPo1q0barWapk2bsm3bNrkKkYUCAwPx\n9PSkZMmSnD17Vp7ZFhkmoyJkgqZNmxIQEJBs+ctHsF9/FHvlypXJZikyMzND17AhyivfnJUXr1e1\n5HnLdwYQDowBigN1zM2xc3Ojfv36xMTEEBwczE8//YS9vT1Lly6lWrVqTJgwgbZt2/LLL7+wb98+\nxo0bR7NmzfQBDHDo0CHq1q37Tj2hw8PDadq0KUlJSezevVsC2Ig6derE3LlzcXNz48SJE8YuJ9dJ\nTEzk559/pnHjxgwdOpRNmzZJAIs3o4h39ujRI6VYsWJKQkKCflnx4sUVlUqlmJmZ6X9euXJFURRF\n+e2335TOnTsnO44mMlLRtG2rjAZF9drrP6AoL14BoDiDkgeUuqBcBiWhRw9FGxub6rF1Op1y48YN\nxd/fXxkyZIhSp04dRa1WK7a2tkrfvn2VhQsXKkFBQUrnzp0VPz+/t/5b3L59W6lQoYIybNgwJSkp\n6a2PIzLXpk2blEKFCilHjhwxdim5xoULFxRXV1elSZMmyt27d41djsihJIQzybBhw5S5c+dmaNtW\nrVopQUFByZbrdDol5vRpJalYMX3gZuSVWKaMEhMYqOh0ulSPnZL4+Hjl2LFjyowZM5Ru3boppUuX\nVszMzJQvv/xSGTVqlLJ+/XolNDQ0w3+DM2fOKMWLF1emTZuW4X1E9tm+fbvi5OSkHDp0yNil5GiJ\niYnK77//rhQsWFCZN2+eotPpjF2SyMFk2MpMkpCQQGRk5Dv3hFQUhbjjx8nTpQvmt2+nu31SuXIk\nLF+OdY0a79wJJCYmhocPH3LlyhWOHTvGsWPHOH78OHnz5tXfW65duzY1atRIdrl6165ddO/enTlz\n5tChQ4d3qkNknT179uDh4cGqVav48ssvjV1OjnPt2jV9p7clS5bIoCjinUkImyBFUYg/fx7Vrl1Y\n/v47Zg8fJttGV6wYCSNHQpMmWFWokGW9MBVF4fr16/pQPnbsGOfPn6d8+fL6UA4NDWXGjBmsXbuW\nevXqZUkdIvMcOHCAjh07snz5cpo0aWLscnIEnU7H7NmzGT9+PGPGjGHQoEEy0YjIFBLCJkyn06G5\ndYuwf/4h9soVStrZocqXD6VUKcyqVMGydGmjfBDEx8dz5swZjh49yuLFi7l8+TJWVlbUqVPHoMUs\n0+uZroCAANq1a4evry9ubm7GLsek3b59m969exMfH8/SpUspV66csUsSuYiEcA4wcOBAfH19iYiI\nwMzMzCSePUxMTGTAgAGcPn2arVu3YmZmxvHjxw0uY+fLl88glKtVq6YfuUsY39GjR2ndujWLFi2i\ndevWxi7H5CiKwsKFCxk9ejTe3t4MHz4cc3NzY5clchkJ4RygXr16+nGgTUF0dDSdOnVCURRWr16d\n4lyoOp2Oq1evGlzGvnTpEhUrVjR4dvnjjz82iS8V76uTJ0/i7u7OnDlzaN++vbHLMRkhISH07duX\nx48f4+vrS6VKlYxdksilJIRzgEKFClG+fHkOHTpk7FJ48OAB7u7uVKtWjblz577RJA+xsbGcPn3a\nIJijoqKoVauWPphr1apFwYIFs/AdiNedOXMGNzc3pk+fTufOnY1djlEpioKfnx/e3t4MHjyYUaNG\nyVSbIkvJiFkmLjIykoiICJOYEefKlSu4ubnRs2dP/vvf/75xC9bGxoZ69eoZdN568OCBPpCnTp3K\nyZMncXJyMriM7eLiQp48eTL77YgXqlWrxu7du2nWrBlarZbu3bsbuySjePDgAd9++y137txh165d\nuLi4pL+TEO9IQtjEXb58mQIFChh9ovbDhw/Tvn17fvnlF3r16pVpxy1SpAht2rShTZs2ACQlJXH5\n8mV9MC9evJhr167h7Oysv4Rdu3ZtypYtK5exM1HlypXZs2cPTZo0QavVZuq/45zg77//5vvvv+eb\nb75hzZo1WFpaGrsk8Z6QEDZxFy9exMbGhhIlShithrVr1zJgwACWLVtGs2bNsvRc5ubmVKpUiUqV\nKtG7d2/g+T3oU6dOcezYMdauXcvIkSNJSEhIdhk7X758WVpbblexYkX++ecfGjVqhFar5dtvvzV2\nSVkuLCyMgQMHcv78ebZs2ULNmjWNXZJ4z0gIm7iLFy+iUqmMFsLTp0/n999/Z+fOnVSrVs0oNdja\n2lK/fn3q16+vX3bv3j19a/mXX37h1KlTFCtWzOAydpUqVaRF84bKlSvH/v379UE8cOBAY5eUZdav\nX893331H9+7d8fPzw8rKytglifeQdMwycS1btiQoKIht27bh7OycbefV6XR4e3uzfft2tm/fTunS\npbPt3G8jMTGRixcvGnT6unnzJlWrVjW4jF26dGm5jJ0Bt2/fpmHDhgwePJhhw4YZu5xMFR4ezvff\nf8+///7L0qVLZYAZYVQSwiaubNmyPHr0iJCQEBwdHbPlnPHx8Xh6evLgwQM2bNiQYy/zRkZGcvLk\nSYNg1ul0Bq3lmjVr4uDgYOxSTVJwcDANGzbkm2++YeTIkcYuJ1Ns376db775hq+++oopU6aQN29e\nY5ck3nMSwiYsJiYGJycnVCoV0dHR2dKCe/r0KW3btqVo0aL4+vrmqkt0iqIQHBxsEMpnzpyhVKlS\nBsFcuXJlLCzkTg08v+zfqFEjunfvzk+vzXWdk0RGRuLl5cWePXtYvHgxDRs2NHZJQgASwibt9OnT\ndO3aFTMzMy5dupTl57t9+zZubm64u7vz22+/vRdj42q1Ws6fP28QzHfv3qV69eoGwVyiRIn39jL2\ngwcPaNSoEe3bt2f8+PE57u+wd+9e+vTpQ9OmTfnjjz+wt7c3dklC6EkIm7C//vqLRYsWoVar2b17\nd5ae68yZM7Rq1YqRI0fy/fffZ+m5TN2zZ884ceKEQTBbWFgYhLKrqyt2dnbGLjXbhIWF0bhxY1q0\naMHkyZNzRBBHR0fzww8/sGnTJhYuXEjz5s2NXZIQycg1NxN28eJFHB0ds/ye7M6dO+nRowfz5s2j\nXbt2WXqunMDR0ZEmTZroZxhSFIXbt2/rA3n06NEEBgZStmxZgyE4K1asmGvHFnZycmLfvn00adIE\njUbDH3/8YdJBfOjQIXr27Em9evU4d+5ctvWnEOJNSUvYhLVt25Y8efJQvnx5JkyYkCXnWLx4MT/+\n+CNr167ls88+y5Jz5EYajYagoCCD1vL9+/epUaOGQYu5WLFixi41U4WHh9OsWTNq167NjBkzTC6I\n4+LiGD16NCtXrmTu3Ln6QWCEMFUSwiasXLlyVKlShaZNm2b6wAmKojBhwgR8fX3Zvn075cuXz9Tj\nv4+ePn1qMJPUsWPHsLGxMQjlGjVq5PgeuREREbi5uVGlShXmzJljMn0Hjh07hqenJy4uLsyaNUvG\nIBc5goSwiYqPjydfvnx8/vnnDB06lBYtWmTasbVaLf379ycwMJAtW7ZQpEiRTDu2+H+KonDjxg2D\nUD5//jwff/yxwWXsTz75xGSCLKOioqJo0aIFH3/8MQsXLjTqZfiEhATGjRvH4sWLmTlzJp06dTJa\nLUK8KQlhExUUFETXrl1RqVSsWLGCypUrZ8pxo6Ki6NSpE2ZmZvz9998pTkMosk5CQgJnz541COaw\nsDBq1qxp0GIuXLiwsUtNV0xMDK1ataJ48eIsWbLEKI91nT59Gk9PTz788EPmz5+fI/5uQrxKQthE\nrVy5krVr17Jr1y5u376dKZ2z7t+/j7u7O66ursyZM0eehTURYWFhBpexjx8/joODg0EoV69eHWtr\na2OXmkxsbCxt27alQIEC+Pn5Zdu0f1qtlsmTJzN79mx8fHzo1q2byd2fFiIjJIRN1JgxY9BoNMya\nNYuoqKh3/oC5dOkSLVq0oE+fPowePVo+sEyYTqfj2rVrBq3lixcvUrFiRYNg/vjjj03iMnZ8fDzt\n27fH2toaf3//LB+v+/z583h6elKoUCEWLVpE8eLFs/R8QmQlCWET1aFDBz799FMWLFjA5cuX3+lY\nAQEBtG/fnt9++w1PT89MqlBkp7i4OM6cOWMQzM+ePTOYSap27dpG64yUkJBAp06dUKlU/P3331ky\n/3NiYiJ//PEHU6dO5ZdffqFPnz7yZVLkeBLCJqpixYoMGTKE1atXs2fPnrc+zurVqxk4cCDLly/X\nP/cqcoeHDx8ahPKJEycoWLCgQShXq1YtSwIxJRqNBg8PD+Li4li7dm2KQ57qdDp0Oh0AKpUKMzOz\nDAXplStX8PT0JG/evCxevNjkJxQRIqMkhE2QRqPBwcGBP//8k6NHj7JkyZK3Os60adOYOnUqW7Zs\nwcXFJZOrFKZGp9Nx+fJlg2C+evUqzs7OBsH84YcfZlkLMjExkR49evDkyRM2bNiAjY0NiqKQGBuL\n9tw5zAICMDtxAtWzZyiFCpH0xRdQsyaWFStinsJlbJ1Ox/Tp05k0aRLjx49nwIABJnEJXojMIiFs\ngi5evMhXX31Ft27d0Gq1TJw48Y321+l0DB8+nF27drF9+3ZKlSqVRZUKUxcTE8Pp06cNgjk2Ntbg\nMnatWrXInz9/pp0zMTGR3r17ExISwqaNGzE7cwaLGTNQr1+P6kUr+FWKtTWavn1J6tkT62rV9F8Q\nbty4Qa9evVAUhSVLlvDRRx9lWo1CmAoJYRO0Zs0ali9fTsGCBXF1daVfv34Z3jc+Pp4ePXoQFhbG\n+vXrc+w0hCLrhIaGGoTyqVOnKFKkiMGzy1WqVHmnDlZJSUn84O1NnzJl+GTUKFRxcenuoytShPg1\na8hTpw7z589nzJgx/PjjjwwZMiTXDgcqhISwCZowYQIJCQmcPn2awYMHZ3igjqdPn9KmTRtKlCjB\n0qVLs+1eoMjZkpKSuHjxokEw37hxg6pVqxpcxi5TpkyGL2MrikLs7t3YtGqFSqPJcC26QoU4OG4c\nPyxdiq+vL5988snbvi0hcgQJYRPUpUsXWrVqxS+//IK/vz9VqlRJd59bt27h5uZG69atmTJlitw3\nE29t4sSJ6HQ66tevrw/lo0ePkpiYaBDKtWrVwsHBIcVjJISEYNGoEeZXr77x+SO7dCHPwoXkeYeB\nZM6fP0/fvn05evToWx9DiOwgn9Qm6OUzoSEhIZQoUSLd7U+dOkW9evUYNGjQezMPsMgakZGRzJs3\njxEjRvDll1/yww8/0LZtW2xtbYmOjubcuXOcPXuWiRMnUrx4cSpUqEDPnj2ZN28eZ86cITExEUVR\nSDp3DvOrV5kOVAMsgQEZrMFu7Vp0ly8TGBhIkyZNyJ8/f4oDlURFRdGlSxdsbW0pWbIk8+fP169z\ndnamQIECbNq0KTP+LEJkGfm0NjGJiYlcu3aNYsWKodVq072nu337dtzc3Jg1axaDBg3KpipFbrVy\n5UoaNGign2Ti8uXLfPvtt8ycOZPw8HDGjh3Ljh072LJlC8+ePWPFihXUrVuX48eP0717dxwdHRnQ\nty9JCxYAUBKYCHQGMtofW6XVwuHDqNVqunfvzqxZs1LczsvLi7CwMG7evMlff/2Ft7c3AQEB+vXd\nu3c3CGYhTJIiTMqVK1eUsmXLKhcvXlTKlSuX5raLFi1SChcurBw5ciSbqhO5XevWrZWFCxfqf1+3\nbp1StmxZg20sLS2VwMDAFPd/9uyZcmnfPiUpXz5FAf1rECj9X/k9vZemYUNFo9EoiqIoJ06cUKys\nrAzOo9FoFFtbW+XQoUP6ZX379lX69u2r/z00NFSxsrLSH0cIUyQtYROTkUvRiqIwduxYJk+ezMGD\nB6lbt242Vylyq8DAQIPOUPXq1SMqKoodO3YQFxfH//73P0qWLEmFChXQaDQ8fvyYW7duERgYyKFD\nhwgICCAxNhZVZOQ71aEKD0eJj091/e3bt4mJiTF4/r1q1apcuHBB/3vRokWxtrbm4sWL71SLEFlJ\nRvA3EcqL/nGvhnDJkiWTbafVaunXrx/nzp3jyJEjMmuMeCOKohAXF0dkZGSKr4cPH7Jq1Sq2bNmi\nX1ayZElatGiBoiiYmZlhZ2eHnZ0diYmJODg4YG9vb/Dq27w5laytITr67eu0tkaVxiNS0S+O/eos\nYA4ODkRFRRls5+DgQHh4+FvXIURWkxA2IkVR0ISEkBQUhCo0FGJj8dDpMKtYkYsqFR988IHB9lFR\nUXTs2BG1Ws3+/ftz/OTwIuN0Oh3R0dGphuebvNRqdbLgfPkyNzfn2bNnFC1alJIlSxIaGsrWrVuZ\nNWsW1apV48KFC3h7e3Py5EkqVaqU7JGlxMRELh8/jvbjj7E8c+bt32/NmmnO8vUyfKOjo/X/HBER\ngZ2dncF20dHR2Nvbv3UdQmQ1CWEjUBSFhCtXUPbvx/K338hz65Z+XZkXP4uWLYtL//7EX75MnvLl\nefDgAS1atKBWrVrMnj1bpiHMIbRabZqBGBUVlaHgjImJIW/evKmG58tXkSJF+Pjjj1Ndb2dnl+Yg\nHM2bN6dx48Z8/fXXAIwePZrGjRvz3XffAVC3bl3mz5/P8ePHcXZ2BuDx48fs2LGDrVu3smvXLj76\n6CNWd+9OqddC+E0Gykxq1Yo8aQzQUaZMGWxsbDhz5gyff/45AGfPntXXBM+fm4+IiJBnjYVJk0/y\nbKYoCnGnT5Pn668xT+NelfrmTYqMHEnSsmWEzZrF571707t3b/7zn//IzDFZTFEU4uPjM6XVqdVq\n0w1Oe3t7ypQpk+Z6W1vbbHn0rGnTpgQEBOhD2MXFhQULFnD8+HGqVKnC3r17OX/+PFZWVkyePJml\nS5dy/fp1Wrdujbu7O3/88QfFixcn7vx5FDs7VC8uDysvXq+zArYBDV9ZlujqikXlymnWqVar6dq1\nK2PHjmXFihVcunSJVatWsX37dv02hw4dom7dutjY2LzT30SIrCSDdWQjRVGIO3eOPF99hfnNmxne\nT/PBB9yYMYMKLVtmYXU5n06nIyYmJlPC08LCIs1QtLOzy1C4Wltb56gvTWFhYbi4uHDr1i19i3ni\nxIksWrSIBw8e6N9P/vz5cXd3Jy4ujoiICFatWmVwnKTERDQzZzLJy4vJr51jFDAZCAPKAreBAi/W\nKSoVcZs2Ye3uzo0bNyhXrhzwfMYlRVEoUqQIoaGhwPNLzX379mXz5s3ky5ePMWPG8O233+rP07Vr\nV1q0aEGPHj0y+a8kROaREM6giRMnolarGTVq1FsfIzE2Ft2332K5fPkb76vp2ROzOXOwSGHQgowy\n1VGEtFpthi/LpnUpNzo6GhsbmwyFY3oBm9UT05syLy8vypUrR7Nmzdi6dStbt24lICAAV1dXWrZs\nibu7O+XLl0elUtG6dWsmTZpE5RRarppHj1B+/pk8M2emeJ61wL/AHy9+V4D4efOw/PprzN/hv3OA\nO3fu0KpVK86ePSuD1wiTJiGcAZGRkVSoUIGrV6/qO0P5+fnx888/c+/ePT766CN+/fVXmjdvnuZx\nYk+cwLpuXWYkJbEUuAD0Aea+tt1hoD9wneejDS0GyqvVxB85grWra7r1+vn5MWnSJO7cuUPp0qX5\n66+/qFmzJgDu7u7069eP1q1bv8mfIBlFUUhISMiUVqdGo3mn1uarl2xloP+3p9VqOXLkCBs3bmTr\n1q08e/YMNzc33N3dadq0aapDVKZF8/AhuqVLyTN+fJqTOOjy5yd+1iwsW7fGIhM6HMbExKDVanF0\ndHznYwmRleSecAakNorQxo0b+fLLL/H396dDhw6Ehoam2hNTp9NhdvAgqqQk/ShCf5O8s0ok0BoY\nB/l3CvQAACAASURBVPQAfgHaAhdfjCKkq149zW/2W7ZsYfTo0Sxbtow6depw9+5dg17UHh4ezJ49\nmxo1arxV6/PVl5mZWYbCsVixYrnqkm1u8vjxY7Zv367vVPXBBx/g7u6On58fNWvWfOdWpGXhwiR5\neRHfrBmcOIHlb79hdv06Kp5fek6qUwftkCGoXFyw+vjjTGu1ypMDIqeQlnAGtGnThlatWtG3b18A\n1q9fz4gRI7hx44Z+mzx58nDixIlUJ1vQhIdj9sUXWJw/r182GEjEsCXsD4zheSsYIAEoCOwAalet\nyqM1a3iSxnOec+fOpUKFChQqVCjVS7iKolC0aFEcHBzeuLX5aitVZmnKeRRFITAwUH+Z+cKFCzRs\n2BB3d3datGhBsWLFsvTcmvv3ORcQgCYmhmp16mDu5IS6QAH5EibeW9ISzoDAwEC8vb31v786ilD9\n+vXx9/fXjyKUGiU6GrOnT9M91wXA5ZXf8wCfvFhe5+lT5k+bxrqDB1MMRhsbGx4/foyDgwN79uxB\nURQaNWrEnDlzKFiwoP6SrZOTE9u3b6dq1apv+ycROUhMTAx79+5ly5YtbNu2DSsrK1q2bMn48eP5\n4osvsu3LlEqlIk+xYmy7fBmtVsunvXply3mFMGUSwhnw9OlTg8vMTk5OTJ8+nbZt2+rvZ65fvx61\nWp36QczMUDJwvzIGsHttmQMQDaBW8+N//8v4IkVS3PfmzZtMmjSJ8PBwLl68SEJCAq1bt2b9+vVM\nmDDh/48nowjlejdv3tS3dg8fPkytWrVwd3dn+PDhlCtXzqgtz9jYWLlXK8QL0m0wA+zt7YmJidH/\nfuDAAYYNG8aBAweIi4tjxYoVtG/fnuvXr6d6DDN7e5RSpdI9ly3P7wu/KoLnwawrUQIzu9cj+v+9\nnO5t5MiRFC1alDJlyjB06FCDZydBRhHKjbRaLfv378fb25uKFStSt25dTp8+Td++fQkJCWHv3r14\neXnpezUbU0xMjDy7K8QLEsIZ4OzszLVr1/S/79q1i88//5zatWuTJ08e3Nzc+PDDDzl48GCqx7Cw\ntUXbv3+y5a9/HFYCzr7yezxw5cXyCw0a4DVqFAcOHECn0yU7VtGiRSlYsCCv3uZXFMXgQ1dGEco9\nwsLC8PPzo3PnzhQqVIgRI0ZgY2ODr68v9+/fZ8mSJXTo0OGtejVnpdjYWAlhIV6QEM6Al6MIveTi\n4sL+/fs5fvw48fHxbN26lfPnz+s7Za1cuTLZ5AsqlQqqVUN5pSWb0ihCLXne8p0BhPO8k1ZxoLa9\nPUWbNycsLIwmTZpQsmRJhg4dytGjRw1C9//au/f4GM/8/+OvICckBIlISL8IFZKIQ7qJw6aoBCOK\nSDJltXSxVK2lW23ZsouuatVK+W1b3d32Ubs1kzi1Eqc4RXQ16rAIIlR0HZIoIZPzJDP37w81ayRE\nNHJP+DwfjzyYO/fc9zXDY95zX9fnvq6JEyfy/vvvk52dzYULF1i5cqXV7Ugyi1D9pSgKR48eZfHi\nxYSEhODr68umTZuIiIjg1KlTHDp0iD/96U+1UtX8KBUXF0v1shA/kTHhBzB+/HiCgoIwGo04ODgQ\nHR1NRkYGMTEx5Obm4uPjQ1xcHL1/uof34sWL9O3bt9JxHLp0oeyNN1j8hz9YzSL0Cf+bRcgF+Ipb\n9wnPAXoCm4DyuXNxf+YZevXqBcCCBQvQ6/VMnDiRkpISYmJi0Gq1LFy4kBkzZtClSxecnZ0ZO3Ys\nb7zxhuVcOp3OUuUtbF9hYaFVUVXjxo0ZPnw4ixcvpn///vWyQl2uhIW4Qx2tW1zvzZo1S/noo48e\naN/IyEjl+PHjVf6u9L//VYxRUQ+8uLkCSllsrFJ68WKVxzabzcp//vMf5a233lI6dOig+Pr6KvPm\nzVNOnDhR6dwXLlxQAgICFJPJ9BDvgKgr586dU+Li4pTw8HCladOmyqBBg5Tly5crZ86cUbtptWLQ\noEHKjh071G6GEDZB7hN+QLdnh3J3d//5x8rKwu7dd7Ffvfq+K8sogHHaNJgzB8f/+79qj6soCocO\nHUKv1xMfH4+LiwuxsbHExsby9NNPyyxCNqq8vJz9+/dbqplv3LjBsGHD0Gg0DB48+LErouvTpw/L\nli2jT58+ajdFCNVJCKuk/Pp1yo8fp+GmTTh8+qnVlH5K48YYp0zB9Pzz2AcGYt+iRY2PbzabOXDg\nAHq9noSEBDw9PS2BfPc6xaLuXb161TJTVXJyMr6+vpZ5mXtWMytafRcUFMTnn39OUFBQ9TsL8ZiT\nEFaZqbwc4+nTXEhLQzEacXRxIauoiAGTJtHwfvcd1+QcJhP79u1Dr9ezfv16OnTogFarJTo6mrZt\n29bKOcT9KT8VVSUlJZGYmMiZM2d47rnn0Gg0DB06FM973Pv9OOrUqRNJSUmWFZKEeJJJCNuIuXPn\n0rRpU8xmM8XFxfz5z3cvAFc7ysvL2b17N3q9nk2bNtGtWze0Wi1jxoyhdevWj+ScT6qCggJ27txJ\nUlISW7ZswcXFBY1Gg0ajoX///k/sSk3e3t6kpaXJF0AhkBC2Ga+++ipdunQhPT2d7t27M23atEd+\nzrKyMnbs2IFerycxMZFevXqh1WoZPXo0LVu2rP4AopJz585ZxnYPHDhASEiIJXg7deqkdvNsgpub\nG+fPn8fNzU3tpgihOrlFyUYYDAZcXV25ePEiGo2mTs7p6OhIZGQkkZGRlJSUsGXLFvR6Pb///e/p\n06cPWq2WkSNH2txkD7bEaDRaFVXl5+czbNgwpk6dyvr163G5zwxnTyq5RUmI/5EQthEGgwEXFxcu\nXbpUaaKPuuDs7ExUVBRRUVEUFhayefNmdDodM2bMYMCAAWi1WiIjI2natGmdt83W5ObmWhVVde7c\nmeHDh/Ovf/2LHj16PNZFVT9XRUUFFRUVT2xXvBB3kxC2EQUFBbi6unLp0iXVx8qaNm3KCy+8wAsv\nvMDNmzf56quv+OKLL5g6dSoRERHExsYybNgwy1zVjzuz2czRo0dJTEwkKSmJzMxMBg8ejEajYdWq\nVTKWXgO3Z8tSe/5qIWyFjAnbiODgYJYvX054eDjFxcU2+SF1/fp1NmzYgE6n4/DhwwwfPpzY2FjC\nw8Pr5cxN91NQUEBycrKlqKpZs2aWsd1+/frJldxDysnJISgoiJycHLWbIoRNkH4zG2EwGCgqKqJt\n27Y2GcAALVu2ZPLkyezatYuMjAxCQ0N57733aNOmDS+//DLbt2+nvLxc7WY+tLNnz7JixQoGDx6M\nl5cXH3/8MYGBgaSmppKRkcEHH3zAwIEDJYB/BllBSQhrEsI2wmAwYDAYVO+KflCenp5Mnz6d1NRU\njh8/TkBAAPPnz8fb25upU6eyZ88eTCaT2s28L6PRaLXEX1hYGOnp6UyfPp3s7Gx27NjBzJkz8fX1\nVbupjw1ZvEEIazImbCMKCgq4ceNGvQnhO7Vt25ZZs2Yxa9Yszp8/T3x8PLNnzyYnJ4fo6Gi0Wi0h\nISE2UbCUk5PD1q1bSUxMZNeuXXTp0gWNRsPatWvp0aOHzfZCPC6kMloIaxLCNsBkMlFSUsKPP/6o\nSmV0berQoQNvvvkmb775JmfOnEGv1zNp0iQKCwuJiYkhNjaW3r1711nYmc1mjhw5YimqOnfuHIMH\nD2bEiBF89NFHeHh41Ek7xC3SHS2ENfUvTQQFBQW4uLhw+fLlenklfC9PP/008+fP5+TJkyQlJeHk\n5MTYsWPx9fVl7ty5HDt2jEdRF2gwGFi/fj0vv/wyXl5ejB8/nsLCQt577z2uXr1KfHw8L730kgSw\nCqQ7WghrciVsA27fI3zx4kWGDh2qdnNqnZ2dHQEBAQQEBLBo0SKOHj2KTqdjxIgRNG7c2LKwhJ+f\n30OfIzMz0zJhRlpaGn369EGj0TBv3jw6duxYi69G/BzSHS2ENQlhG3DnPcL1vTu6OnZ2dvTs2ZOe\nPXuydOlS0tLS0Ol0PPfcc7Rq1coSyNUFp9FoZN++fZYFEYqLi9FoNMyYMYNNmzbJpCI2SkJYCGsS\nwjbg9pSVmZmZj1V3dHXs7OwICQkhJCSEDz74gP3796PX6wkNDeWpp55Cq9USExNj+WKSk5PDli1b\nSExMZPfu3fj5+aHRaIiPjycoKEiKquoBGRMWwpqEsA0wGAw0btyYoqIiWrVqpXZzVNGwYUPCwsII\nCwvjww8/ZM+ePeh0Ovz9/XF1dcXOzo78/HyGDBnCyJEj+eSTT3B3d1e72aKGZExYCGsSwjbAYDDQ\nqFEjm56oo64YDAZ27NhBUlISW7duxcvLCz8/P4qKijh48CBXr16lpKTkiX+f6ivpjhbCmlRH2wCD\nwYCdnd0T1RV9m6IonDlzhuXLlzNo0CC8vb3529/+Rq9evThw4ACnT59mw4YNbN++nezsbH7729+y\nZ88eOnbsSEREBJ999hk3btxQ+2WIByTd0UJYkythG1BQUICiKE9MCJeVlVkVVZWWlqLRaJg5cyaD\nBg26Z3elk5MTo0aNYtSoURQVFZGYmIher2fmzJmEhYWh1WoZMWKELB9ow4qLi/Hx8VG7GULYDAlh\nG2AwGDAajY91ZXR2drZVUVW3bt3QaDSsX7+ewMDAGncvN2nSxFJJbTAY+Oqrr1i7di2vvPIKgwcP\nJjY2Fo1GI1ddNka6o4WwJiFsAwwGA6WlpY/VlbDZbOa7776z3LublZVFeHg4UVFRfPrpp7VagObq\n6sr48eMZP348eXl5bNy4kdWrVzN58mSGDRtGbGwsQ4YMeexWeqqPJISFsCZjwjbg9gpK9f1KOD8/\nn4SEBCZMmGBZWamsrIy//OUvXL16FZ1Ox69+9atHWgHeokULfv3rX5OcnExmZib9+/dn+fLleHp6\nMmHCBLZu3VqvV3qq74qKiqQ6Wog7SAjbgIKCgnq1gtJtiqJYLfHXtm1bPvvsM4KDg0lLS+PkyZMs\nXbqUX/7ylzRqVPedLh4eHkybNo2UlBTS09Pp0aMHCxcuxMvLiylTprBr1y6bX+npcSNXwkJYk+5o\nG2AwGMjLy6sXIVxWVkZKSoqlqMpoNKLRaJg1axYDBw602ascb29vZs6cycyZM/nhhx+Ij49nzpw5\nXL58mTFjxhAbG0vfvn1tYqWnx5mEsBDW7JRHMYO+qJE+ffpw+PBhSktLbfL+1ytXrljGdvfs2YO/\nvz8ajQaNRvNQRVW25OzZs8THx6PT6bhx44ZlpadnnnmmXr8uWxUYGMiaNWvo3r272k0RwiZICNuA\nLl26UFRUxMWLF9VuCnBracU7i6p++OEHwsPDGT58OEOGDKFly5ZqN/GROHnyJHq9Hr1ej9FotFRf\ny5SYtcfX15dt27bh6+urdlOEsAkSwjagTZs2+Pj4kJaWplobbt68aTVTVevWrS1Xu6GhoaqM6apF\nURSOHTuGTqdDr9fj4OBAbGwsWq2Wrl27qt28es3Ly4tDhw7h5eWldlOEsAkSwjbAxcWFiIgI1q1b\nV2fnvF1Udftq9/Dhw/Tv398SvE899VSdtcWWKYrCd999h06nIz4+Hjc3N8sVcqdOndRuXr3TvHlz\nLly4QPPmzdVuihA2QUJYJabycoxZWSiFhaxLSOApPz/6xsTQyMnpkZ2ztLSUlJQUEhMTSUpKoqKi\nwhK6AwcOlIKZapjNZv7973+j0+lYt24d3t7elkCWLy0Pxt7enuLiYuzt7dVuihA2QUK4DimKQvn1\n61ScOEHDTZtw+PRT7EpKbv3O3p7yceOoGDuWhv7+OHh61so45OXLly1Xu3v37iUgIACNRsPw4cPx\n9/eXsc6HZDKZSElJQafTsWHDBjp16oRWqyU6Olq6Wu+hvLycxo0by33aQtxBQriOKIpCyfHj2P/u\ndzTau5f7RV9FUBDGTz7BOTi4xiFpMpk4ePCgJXj/+9//MmTIEDQaDREREY9tUZWaysvL2blzJ3q9\nnq+//pqAgAC0Wi1RUVF4eHio3TybkZ+fj4+PD/n5+Wo3RQibISFcBxRFoeQ//8Fx1Cga/vDDAz3H\n3KIFpZs34xwaWm0Q37x5k+3bt5OUlMS2bdvw9PS0dDOHhIQ8UUVVaistLWX79u3o9Xq2bNlCcHAw\nWq2WUaNG0aJFC7Wbp6orV67Qu3dvrly5onZThLAZMjNBDS1atIh33323Rs8pO38exwkTHjiAARrk\n5eEUE0PpyZOVfqcoCqdOneL9998nLCwMHx8f1qxZQ2hoKIcOHeL48ePs3buXZs2aSQDXMScnJ55/\n/nm+/PJLrly5wpQpU9i6dSvt27dHo9GwZs0aDAaD2s1UhUzUIURlEsI1YDAY+Pjjj5kxY4Zl2xdf\nfEHnzp1p0qQJ3bt3Z9u2bVbPURQF5cgRGh4/brW9HPgN0BFoAgQBm+86X4PLl2H/fhRFobS0lG3b\ntvHqq6/SoUMHhg4dSlZWFnPmzCEkJIQtW7YQFRVlWSZu9uzZLFiwoLbfAlEDjRs3Jjo6mnXr1nHp\n0iXGjh1LQkIC7dq1Y9SoUej1eoqKitRuZp2REBaiMgnhGtDpdAwYMMAyNWNGRgZTpkxh5cqV5OXl\n8bvf/Y4xY8ZYXemU37iB/cqVlY5lBJoBicB1YA4QC3x/1372773HZ0uX0rp1a9555x3atWvH5s2b\nuXDhAn/9618pLCzEbDZX6rKOjIwkJSWF7OzsWnwHxMNycXFh3LhxfP3111y4cIERI0bw2Wef4eXl\nhVarZePGjZSWlqrdzEdKQliIyiSEayApKYlnn33W8vj06dN4e3sTERGBo6MjEydOpLy8nAsXLlj2\nMZ08ScPU1ErHagK8B/gBTsBYoB1w5K79GmVlMdjbm6ysLFJTU3njjTcsVc35+fn88Y9/ZNmyZdw9\ntO/k5ERwcDA7duyoldcuao+bmxsTJ05k27ZtnDt3jgEDBrBy5UratGnDiy++SFJSEkajUe1m1jpZ\nQUmIyiSEa+DYsWN06dLF8rhfv34UFBSwbds2SkpK+Pvf/067du3w8/P735Py8u5bCX3bZSAL8K/i\nd63s7Kos6pk7dy6vvPIKnp6eVR6za9euHD169AHOLtTi7u7Ob37zG3bv3s2pU6cIDg5myZIleHl5\nMWnSJJKTk6moqFC7mbVCroSFqExCuAby8vJwdXW1PHZ3dycuLo6RI0fSpEkTXnvtNT799FPriQge\n4AO0DHgB+DW3rozvdvPHH9m4cSMHDhwgKyuL4uJi0tLSSEtL49VXX73ncZs1a8aNGzce+PUJdbVp\n04YZM2awf/9+jhw5gp+fH/PmzcPb25tXXnmFlJQUzGaz2s18aBLCQlQmpbM14OrqalVIk5KSwqxZ\ns0hJSSEoKIjdu3cTFRXFwYMH/zdBvaPjfY9ZDkQDrYD/d499CsvL+fzzz8nJySE3N5fs7GwqKirw\n8vIiLCyMZs2aoSgKK1aswNfXl9atW+Pp6Ul2djYuLi618dJFHfPx8eG1117jtdde4/vvvyc+Pp6Z\nM2fy448/Eh0dTWxsLCEhIfVqshXpjhaiMrlPuAaGDBnC2LFjefHFFwGYN28emZmZJCQkWPYJDg5m\n2rRpvPzyywCUHD+OU2godsXFlY5XAWiBYuBrqv5GpNjZUfLNNzQODbVsKykpqfLDTFEUwsLCcHZ2\nJicnh9OnT1NeXk6LFi3w9PS0hPOdP3dua9mypayna+MyMjLQ6/XodDpKSkosSy/27NnT5gN51apV\nZGRksGrVKrWbIoTNkCvhGggPD2f//v2WEA4KCmL16tUcPHiQwMBAdu3aRXp6OoGBgcCtaurXX3+d\nc5Mn4xgXZ3UsBZgA3ACSqPofwgn4OiSEAf7WI8XOzs5W3ZK5ubm0adOG3NxcywxNJpMJLy8vvvnm\nG1xdXcnJybH83L6aPnr0qNX2goIC3N3d7xnYd253dXW1+Q/9x1GXLl1YsGAB8+fP58SJE+j1emJi\nYmjQoIFlpSd//6oqC9Qn3dFCVCYhXAPjx48nKCgIo9GIg4MD0dHRZGRkEBMTQ25uLj4+PsTFxdG7\nd28ALl68SN++fTGNHIkSF2dVoPUD8CVgB9z5sbQC+C3wI2AP+E2fTqOmTe/bLkVRKgXizp078ff3\nt3SLe3h4WL4c3IvRaOTq1auVAvvs2bOkpqZaba+oqKjyarqqwHZ2dq7+zRU1YmdnR2BgIIGBgSxe\nvJjDhw+j1+sZNmwYLi4uloUlnn76abWbalFcXCzd0ULcRbqja2j27Nl07tyZqVOnVrvviBEjeOed\nd/Dz8aFi+XKcFi584POsB/b7+7M0ORmHe1Q/309ERARvv/02/fr1q/FzH0RRURG5ubmVAvvOx7d/\nnJyc7tkFfuc2Dw8PWV3nZzKbzXz77bfodDoSEhLw9PS0BHL79u1Vbdvrr7+Oh4cHr7/+uqrtEMKW\nSAjXUFlZGQaDAXd39xo9z5idjbJsGY7Llz/Y/uPGoSxciGOHDg/TTC5fvoy3t/dDPbc2KYpCfn5+\nleF8d2hfu3aN5s2bP1Bgy/h19UwmE6mpqZaVntq3b29Z6alt27Z13p7p06fTtWtXpk+fXufnFsJW\nSQjXofLr1ynfuROHJUtodOxYlfuYOnbEOHcuDSIicLSBEK1LJpOJ69evP1BgGwwGPDw8qg1sT09P\nXFxcnvjx64qKCnbv3o1Op+Orr76ia9euaLVaxowZQ+vWreukDRMnTiQsLIwJEybUyfmEqA8khOuY\noigYc3MxnThBgz17aHD+PCgKSrt2mAYOpGFAAA5t2z7xoVGdsrIyrl69WmUX+N3b7hy/ru4K+0kY\nvzYajezYsQOdTkdiYiK9evVCq9UyevToR7LUpdlsxmw2s2DBAvr27cvQoUPl/7cQP5EQVtHtDye4\nVWjToEED+XB6BAoLC8nNzb3nmPWd2+8ev75XaHt4eDwWK1SVlJSwdetWdDod27dvp0+fPmi1WkaO\nHEmzZs0e+riKomAqLsZ48iQNvvmGBv/+N8q1a5hbtoRnn4XQUOy7daORk1PtvRgh6iEJYSF+oigK\nN2/evG+R2e3t165dw83Nrdp7rz09PWnRokW9GL8uLCxk8+bN6PV69uzZw7PPPotWqyUyMpKm1VTo\n38lsNlP67bc0WrkS+4QE7EymSvso9vaUjxtHxdSpOD/zjHz5FE8sCWEhHoLJZOLatWsPFNgFBQV4\neHhUeyuXLY1f5+fns2nTJvR6Pd988w0RERHExsYybNiw+3bZm81mSrdvxzkmBrvCwmrPY27enNL1\n63F69tl68UVFiNomISzEI3Z7/Pp+t3Ld3mYymR7o3uu6HL++fv06GzZsQK/Xc+jQIYYPH05sbCzh\n4eE43jEtq6IolOzbh/OwYVXOEHcvZldXSrdtw7meTcMpRG2QEBbChtwev67u3uvc3FycnZ2rLTR7\n2PHrRYsWYW9vz5tvvmm1PTc3l3Xr1qHX60lPT2fkyJHExsYycOBAlJs3aTB8OI0OHqzx6y4fOhTW\nrsW+huPQoaGhrF69moCAgBqfUwhbICEsRD105/h1dYF9/fp13NzcHmiGsxYtWlBYWIifnx+ZmZmW\nGa6++OILFi9ezOXLl/H19WXp0qX4+/uTkJCAXq/n/Pnz7Fy0iMAqJrE5A7wCHARaA0u4tWiJ1eux\ns6MkNZXGfftabV+zZg2rVq3i1KlTuLq6otVqeffddy2TuiQkJLB27Vo2bNhQ22+xEHVCQliIx9yd\n49fVhXZhYSFNmjShQYMGhIaG0rp1axo1asQ//vEP5syZw8CBA/nuu+8sgXy7gvqHrCya/fnPNP/b\n36zOXcGtNbKfB+YDaT/9/QCV184unT8fhwULrMaGV6xYQbdu3QgJCeHKlSuMHj0arVbL22+/fes5\npaV4e3uTnp5OmzZtHs0bKMQjJCEshLAoKysjMjKS4OBgQkJCyMnJYffu3WzZsoXBgwdbwvr777/H\n0dERLy8vPD09Ga/RMOXvf6dhVpbV8U4C3YEi4PbocQzgAyy769wVQUGY9+7F4T5d0kuWLCE1NZUt\nW7ZYtg0ZMoQXXniBl1566ee/AULUMSlHFEJYODo6kpmZydChQ4mMjGTy5Ml8+OGHODo6MmnSJJKT\nk3nrrbfo2LEj2dnZJCcn8/777xPasyd2BkOl4yl3/Xn778erOLddfj5KScl925eamlppIZKuXbty\n9OjRGr1OIWxF/Z9tQAhRq/Ly8nB1dbU8dnd3Jy4ujpEjR2I0GnF1dWXjxo24ubnh5uZGx44dKbt0\nCaqYeKMLt656/wj8AfgO2Ar0qOK8irMzdg4O92zXRx99RHp6Ov/85z+ttjdr1ozz58/X/IUKYQPk\nSlgIYcXV1ZWioiLL45SUFGbNmkVKSgolJSWsXbuWqKgozp07Z9mnQfPmmKpYx7gRsBHYz62irLeA\nsUBVy0eYe/SgwT0mBfnyyy9ZuHAhycnJtGjRwup3BQUFP2t2LyHUJCEshLDi7+/P2bNnLY937NhB\n//79+cUvfoGjoyNDhw6lY8eO7Nu3z7JPoyZNKJ8ypcrjdedWCBcB3wLngWeq2K9i3DgaVrGU5bp1\n65g1axbbt2+vcn3kzMxM/Kv4AiBEfSAhLISwEh4ezv79+y2Pg4KC2Lt3LwcPHqS0tJSkpCTS09Mt\nY7M6nQ4fHx8adO+OuYq1r48CN4A8YCmQAdx5I5MTkOzlRcOAgEqTdSQlJTFt2jSSkpIqjQXDrcrv\ntLQ0Bg8e/HNfthCqkDFhIYSV8ePHExQUhNFoxMHBgejoaDIyMoiJiSE3NxcfHx/i4uLo3bs3ABcv\nXqRv3744tG9P2ZIlOE+caHW8TcBKoBToD+wCbs/19SNgD3RZvBiHKpbuXLZsGXl5eTzzzP+unYOC\ngjhy5AgAO3fuxN/fn/bt29fyuyBE3ZBblIQQlcyePZvOnTsztYrJN+42YsQI3nnnHQICAii/cQNT\nXBxOf/rTA51nHbA/LIxlmzfTyMWlxu2MiIjg7bffpl+/fjV+rhC2QEJYCFFJWVkZBoMBd3f3aux6\nHAAAAghJREFUGj+3PC+PCp0OpzffxK6g4J77mZs1o2zFCuxHj6bRHdXYNXH58mW8q7iCFqK+kBAW\nQtQ6k8mE8fRpOHIE+w8+oOGJE9gpCkqDBph69qR89mzo0QPHzp1l9STxRJMQFkI8MoqiUH71Kqa8\nPDAawcGBhq1aYd+qlayYJAQSwkIIIYRqpB9ICCGEUImEsBBCCKESCWEhhBBCJRLCQgghhEokhIUQ\nQgiVSAgLIYQQKpEQFkIIIVQiISyEEEKoREJYCCGEUImEsBBCCKESCWEhhBBCJRLCQgghhEokhIUQ\nQgiVSAgLIYQQKpEQFkIIIVQiISyEEEKoREJYCCGEUImEsBBCCKESCWEhhBBCJRLCQgghhEokhIUQ\nQgiVSAgLIYQQKpEQFkIIIVQiISyEEEKoREJYCCGEUImEsBBCCKESCWEhhBBCJRLCQgghhEokhIUQ\nQgiVSAgLIYQQKpEQFkIIIVQiISyEEEKoREJYCCGEUImEsBBCCKESCWEhhBBCJRLCQgghhEokhIUQ\nQgiVSAgLIYQQKpEQFkIIIVQiISyEEEKoREJYCCGEUImEsBBCCKESCWEhhBBCJRLCQgghhEokhIUQ\nQgiVSAgLIYQQKpEQFkIIIVQiISyEEEKoREJYCCGEUImEsBBCCKESCWEhhBBCJRLCQgghhEokhIUQ\nQgiVSAgLIYQQKvn/UjgvSdkgadIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f87397cb250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WA3XStVPy5QMvL5t6zULkVhLCNkCr1WLXuTPJAwY803q6hg35o1Ejmvr5cTmL\niTzi/1lTTzgzly9fZtSoUVSsUoVLDRtmWO5EygjIRsADaETKDOnJ6dolDxqE40svmbtcIUQOSAjb\nCMeSJVE++YSkkSPJSVTo2rZFv3Qpb7z7Lj179qRx48aEhISYvU5bZW3D0Y8pisLevXt58803adiw\nIfb29hw/fpyaXbqg69AhQ/smwEFSTk+7S8pM6bT3XFLy58fQrRt2efh2e0JYE5mYZUOcypZFN2EC\nCZ06Ybd+PY7ff48mISF1uWJnhy4gAH2/ftjVqYPLfxdjCA4OxsfHh+7du/PHH38wbdo0nDI5ppiX\nWdvQrE6nY82aNcycOZMHDx4wYsQIli5d+sTpQglffYXh2jWcT5zI0TYVR0cSfvkFZ29vc5UthHhG\nGsUaP/6LbBmSk0k+e5bjW7ZQydOTQkWLQrFi2NesiX2+fJmGyoMHDxgwYACRkZGsWrXqidvh5XVt\n27YlKCiIdu3aqVrH/fv3WbRoEd988w1VqlQhODiY9u3bZzqbfPHixdhdv06PkydxXLfuqdeQNpYs\nSeKSJTi//jpaOSVJCKshw9E2ys7REZc6dejzww889PbGpV07XBo1wiF//ix7da6urqxbt45+/frx\nyiuvsDrNaU95ndrD0efOnSMwMJBKlSpx9uxZQkND+eOPP+jUqVOmAbxjxw4+/PBDvLt3R/vddyTs\n2UPSuHEoae4kpAC6li2JX7+e5L17cWnZUgJYCCsjf5E2TFEUbt68ScmSJXO8jkajISgoiFdffZVu\n3brxxx9/MHPmzDx/bV81hqMVRWHXrl3MnDmTv/76iyFDhnDmzJls/z9PnjzJW2+9xbp166j238x3\nB19fDK+8QlL//iixsWAwgLMz9mXL4lK4sNUNtwshUkgI27CHDx9ib2//XJcVrF+/PseOHWPQoEF4\ne3uzevVqqlataoYqbYelesKJiYmsWLGCWbNmYTAYCA4OZu3atbi4uGS77o0bN+jQoQNz5szB19f3\niWV29vbYyeloQtgUGY62Yc/aC06vcOHCrFq1iiFDhuDj48OKbO7WlJtZoqd4584dJk6cSPny5Vmz\nZg3Tpk3j1KlTDBw4MEcB/PDhQ9q3b09gYCA9MjlPWAhheySEbditW7coVarUC21Do9EwbNgwduzY\nwcSJExk0aBAJaWZc5yXm6gmHh4czYMAAqlevzq1bt/jjjz/YunUrrVq1ynH463Q6unXrRuPGjRk3\nbpxZ6hSIuf9FAAAgAElEQVRCWJ6EsA17fAccU6hbty5Hjx4lLi6ORo0aERERYZLt2gpTT8wyGo1s\n3rwZPz8/2rRpQ+XKlblw4QLffvstNWrUeKZtKYpCYGAgWq2WefPmyfFdIXIROSZsw150ODq9ggUL\nsnz5cr7//nt8fX2ZPn06ffr0Mdn2rZmpgi0uLo6lS5cye/ZsChQoQHBwMN26dcPR0fG5tzllyhSO\nHj3K7t275Y5HQuQy8hdtw27dukXp/y7IYSoajYZBgwbRuHHj1NnT33zzDfnz5zfpfqzRi/SEr1+/\nzjfffMMPP/zAa6+9xnfffYevr+8Lh/uKFSv49ttvOXDgAAXTnH4khMgdZDjahpm6J5yWl5cXf/31\nFwaDgUaNGnH69Gmz7MdaPO9w9JEjR+jVqxdeXl4kJCRw8OBB1q9fT5MmTV44gHfv3s3IkSMJDQ19\n4WP/QgjrJCFsw0wxMetpChQowNKlSxkzZgzNmjVj8eLFVnl9ZVN4lsA0GAysW7eO1157jS5dulC/\nfn0uX77M7NmzqVSpkknqOXv2LN26dWPFihXUrl3bJNsUQlgfGY62YaacmJUVjUZD//79adSoUerw\n9IIFC57r3GRrl90HjJiYGH744Qfmzp1LqVKlCA4OpnPnziY/Tnvnzh3at2/P1KlT8fPzM+m2hRDW\nRXrCNsycw9Hp1axZk8OHD+Pg4ECDBg04efKkRfZrKU/rCV+6dImRI0dSoUIFjhw5wqpVq9i3bx9d\nunQxeQDHxcXRsWNHevfuTb9+/Uy6bSGE9ZEQtlGPHj0CsOhknfz587N48WI++ugjWrRowaJFi3LV\n8HTa16IoCmFhYQQEBNCoUSOcnJw4ceIEv/zyC40aNTLL/g0GA7169aJGjRpMnDjRLPsQQlgXGY62\nUY97wWqcM9q7d28aNmyYOjz97bffUqhQoexXtGKPJ2YlJyen3kLw4cOHjBgxgmXLlpl9+F1RFIKD\ng4mNjWXNmjVyLrAQeYT0hG2UuSdlZad69eocOnSIggUL0qBBA44fP65aLaaQnJxMSEgIFStWZPHi\nxXzyySdEREQwfPhwixz/njVrFr///jvr1q17oXOKhRC2RULYRlliUlZ2XFxcWLRoEZ9++imtWrVi\n/vz5Njc8HRERwdChQ9m+fTs3b95k8+bN7Nq1i44dO6LVWubPY926dUybNo3Nmzfj6upqkX0KIayD\nhLCNsuSkrOz07NmTffv2sWjRIrp160ZMTIzaJT2Voijs2LGDdu3a0bRpUzw8PGjVqhWBgYHUqVPH\norUcOHCAoUOHsmnTJsqVK2fRfQsh1CchbKPUHo5Or2rVqhw8eJDixYtTr149/vrrL7VLyiAxMZEf\nfvgBLy8vgoODefPNN4mMjOTTTz/N0V2MTO2ff/4hICCApUuXUq9ePYvvXwihPglhG2VNPeHHnJ2d\nmT9/PlOmTKFt27bMmTPHKoan79y5wyeffEK5cuUICQlhxowZhIeH88477+Ds7JzazpK13rt3j3bt\n2vHJJ5/Qrl07i+1XCGFdJIRtlDUcE85Kt27dOHjwIEuXLuXNN98kOjpalTpOnDhB//79qV69Onfv\n3mX37t1s3ryZli1bZph9bOq7KD1NYmIinTt3xt/fn6FDh1pkn0II6yQhbKOsbTg6vUqVKrF//348\nPT2pV68ehw8ftsh+jUYjmzZtokWLFrRv356qVavyzz//sGDBAqpXr57lepY6JchoNNKnTx88PT2Z\nMmWKRfYphLBecp6wjbLG4ej0nJycmDNnDs2aNaNDhw588MEHBAcHmyXw4uLiWLJkCbNnz6ZQoUIE\nBwfTtWvXZzrdxxI94Q8++IBbt26xY8cOi82+FkJYL3kXsEGxsbHo9XoKFy6sdik5EhAQwKFDh1i5\nciVvvPEG9+/fN9m2r127xrhx4yhXrhy7du3ihx9+4MiRI7z11lvPFMCW6AkvWLCAX3/9lQ0bNjxx\nLFoIkXdJCNugx8eDbemqShUqVGDv3r1UrlyZl19+mf3797/Q9g4fPkzPnj2pU6cOycnJHD58mJCQ\nkBe6h685e8KhoaFMmjSJLVu2ULRoUbPtRwhhWySEbZA1T8p6GkdHR2bMmMHcuXPx9/fnq6++wmg0\n5nh9vV7PmjVr8PHxoXv37jRq1IjLly8zc+ZMKlas+EK1mXNi1tGjR+nfvz/r16832a0OhRC5gxwT\ntkHWPikrO506daJOnTr06NGDP//8k2XLllGsWLEs28fExPD9998zd+5cPD09GTVqFG+88YZJ72Bk\nrlGFyMhIOnXqxKJFi/D29jbLPoQQtkt6wjbIFiZlZadcuXLs2bOHWrVq8fLLLxMWFpahzcWLFxkx\nYgQVKlTg6NGjrFmzhr179/Lmm2+a/BaCYPrh6AcPHtCuXTvef/99/P39TbptIUTuICFsg2x1ODo9\nBwcHvvrqKxYuXEjXrl2ZPHkyBoOBPXv24O/vT+PGjXFxceHkyZOsWLGChg0bmq0WUw9HJycnExAQ\ngJ+fHyNHjjTZdoUQuYsMR9ugmzdvUqtWLbXLMJn27duzf/9+2rRpw5dffom7uzujR4/m559/Jn/+\n/BapwZTD0YqiMHDgQAoXLsyMGTNMtl0hRO4jPWEblFt6wpBy+cYvvvgCX19fypQpQ5s2bUhISKBG\njRoWC+DHTNUTnjhxIufOnWP58uXY2dmZZJtCiNxJQtgG2frELICzZ88yZMgQqlSpwsWLF9m6dSu7\ndu1i9erVLF68mJ49ezJp0iQMBoNF6jFVT/jHH3/k559/ZtOmTeTLl88k2xRC5F4SwjbIVidmKYrC\n9u3badu2Lc2bN6dkyZJERESwePFivLy8Utu1bt2ao0eP8vvvv9O6dWtu375tsfpexM6dO/nwww/Z\nsmUL7u7uJqpKCJGbSQjbmPj4eBITE3Fzc1O7lBxLSEjg+++/p3bt2owZM4auXbty5coVJk6ciIeH\nR6brlCpVip07d/Lqq69Sr149du3aZdYaX3RiVnh4OL169WLNmjVUq1bNhJUJIXIzCWEbY0tXy7p9\n+zYTJkygfPnybNiwgdmzZ3PixAkGDBiQo8s22tvbM2nSJJYtW0bv3r2ZMGGC2YanX+Tf88aNG3To\n0IE5c+bg6+trwqqEELmdhLCNsYVJWX///Td9+/alRo0a3Lt3jz179hAaGkqLFi2eK+z8/Pw4duwY\n+/bto0WLFty8edMMVT/fcPSjR49o3749w4YNo0ePHmaoSgiRm0kI2xhrDWGj0cjGjRtp3rw5HTp0\noEaNGly8eJH58+ebZHi2RIkSbN++nddff5369euzbds2E1T9/55nOFqn09GtWzcaN27MuHHjTFqP\nECJvkPOEbczNmzetamZ0bGxs6i0EXV1dU28h6ODgYPJ92dnZMWHCBJo0acJbb71F3759mTRpkkmu\nnvWsPXRFURg+fDgA8+bNs4nDA0II6yM9YRtjLT3ha9euMXbsWMqXL8+ff/7JkiVLOHz4ML169TJL\nAKfVrFkzjh8/zl9//UXz5s25fv26Sbb7LD3hL7/8kiNHjrB69WqzXEJTCJE3SAjbGLV7wgcPHqRH\njx7UrVsXvV7PkSNHWLt2LT4+PhbtDbq7u/Pbb7/Rtm1bGjRowJYtW15oe88yHL1ixQoWLlzI5s2b\nKViw4AvtVwiRt0kI2xg1esJ6vZ7Vq1fzyiuv0KtXL7y9vbl8+TIzZsygQoUKFq0lLa1Wy/jx41m9\nejVDhgxh7Nix6HS659pWTj9A7Nmzh5EjRxIaGmpVhwWEELZJQtjGWDKEHzx4wLRp06hUqRJz587l\n/fff58KFC4wcOZJChQpZpIacaNKkCceOHePUqVM0bdqUq1evPtd2susJR0RE0LVrV1asWEHt2rWf\nax9CCJGWhLCNscRw9MWLF3nvvfeoWLEif//9N+vWrSMsLIyAgACrvRZy8eLFCQ0NpXPnzjRs2JCN\nGzc+0/rZ9YTv3LlDu3btmDp1Kn5+fi9SqhBCpJIQtiGJiYnExcVRtGhRk29bURR2795N586d8fb2\npkCBAoSHh/Pzzz/ToEEDk+/PHLRaLWPHjmX9+vUEBQUxatQokpOTn7qOoijo9XpqV61KiaJF0ev1\nGXrEcXFxdOzYkd69e9OvXz8zvgIhRF6jUUx9J3NhNpcvX6ZZs2ZERkaabJvJycmsXLmSWbNmER8f\nz8iRI+nTp4/N33wgKiqK/v37c+fOHVauXJnh2LXRaCTp3Dk4fhz75cvR3L4NdnYYK1RA37MnWi8v\nHMuXR1EUAgICcHV1ZcmSJXIqkhDCpOTcChtiyuPB9+7dY+HChcyfP5+aNWvy+eef06ZNG7Ta3DE4\nUrRoUX799VdmzpxJ48aN+fbbb/H390dRFJIuXoTly3GaORNtTMyTKx45guPq1RhLlSLxf/8jRKcj\nNjaWNWvWSAALIUxOesJWTFEUkm/exHjqFPz7L4+io7kXF0f5pk1xqFkT+4IFnzkYzpw5w6xZs1iz\nZg0BAQGMHDky108yOnToED169KBjx45MHjwY5+HDsd+zJ0fr3vX3x3HKFFzlpgxCCDOQELZCiqKQ\nePYs7N+P49dfY3f+/JPLNRr0HTqgGzgQ+0aNcCxRItvtbd++nZkzZ3LixAmGDRvG0KFD89Tt9qKj\no1m/YAFvbttG4TQBPBtYApwG3gEWZLJu0siRaCdMwMGG7lwlhLANEsJWRlEUEg4fxqlXL+wuXcq2\nfXKfPhgnTMC5UqUMyxISEvjpp5+YNWsWDg4OBAcH07NnT5ycnMxRulVTFIWE1avJl+4mCyGAI7AK\nKAjMz2L9+F27yPf66+YtUgiR58gxYSuiKAoJx47h3KkT2rt3c7SO47JlJCcmkjR9Ok6enkDKseN5\n8+axaNEiGjduzDfffEPz5s3z9DFNXVQUjrNmZXg+4L+v2wD9U9a327ABg68vdma+JKcQIm/JHbNw\ncgndvXs4vvtupgG8DKgGOP/39UiaZY6rV2PctIkTJ07Qp08fXnrpJaKjo9m7dy+bNm3i9ddfz9MB\nDKAPD8fu4MHnXt/x++9JPnPGhBUJIYT0hK2KPjycfJkERSjwEfAT4A1cBfKna+M4eTLbunalVq1a\nzJo1iyJFipi9XluiuXaNF/kYoklIgFu3oE4dk9UkhBASwlbCkJyMXUhIpssmAJOBZv/9XDWTNnbX\nrzO8WTPydexoc71eo9FIUlJSlo/k5OSnLs9J2ym1avHCV7lOTDTFyxVCiFQSwlZCFxmJ05IlGZ5P\nAk4A/wAlAQPQFZgBpJ9eZb91K8b27Z96aUmDwfBMwWaKAMyurV6vx8nJKdOHo6Njlssya+vi4oKr\nq2uGZfnv3cv2/yDbjy5yPFgIYWISwlZCSUhAExeX4fkbgAL8DhwjJZQ7AV8Ak9K1NVy8yKD+/fn7\n77+zDD+DwfBMofa05fnz56dIkSLPFZZpf3ZwcDB77z1+69anLlf+e2S5XKuF4sVNWpMQQkgIW4ss\nQsjlv69jSekJA4wk5XzW9CGstbdn9OjRAFkGoL29vc0NV5uCXa1aGCpVwu7ixSee/x8pQ/2PfQt8\nkO45AJ2/P/Y1a5q3SCFEniMhbCU0Li4YCxVC+/DhE8+XBIrxZC9NIfOhU02VKtSqVctq73SkJkdP\nTxLHjcNl8OAnnv/8v0d29P3742Lj19MWQlgfOUXJSjiUL49u6NBMl/UHvgZuAVeAuaQMSadnyEXX\nfjY1jUYDr72GoUqVZ15X16YNdnXr5skRBCGEeck7tpWws7fH0L59psclPwNqANVJOUXpdWBcujaG\nqlWxq11bguIpnKtXJ2n5coylS+d4HX3DhuhnzMDpGdYRQoickhC2Iva1aqFv0ybD847AIiAGuE3K\nzOj083STx4/HUYLiqTQaDS4NGpAYGoqudeunT8SysyO6Z090P/2Ec/XqFqtRCJG3SAhbEQc3N3Rf\nfYWhYsVnWu9W9+5E1a8vveAc0Gg0uNSpAytXkhAWRuL48RhLlkRxdERxccFQvjyJ06YRt3cvQxMT\n2XHunPy7CiHMRm7gYGUURSHhxAkcBwzA/vjxbNsnjRnD/oYN6T1qFL/99hu1atWyQJW5R2RkJD9P\nn86od99Fo9GgyZ8fhxIl0Gq17Nq1i4EDB3L69GnyyaQsIYQZSE/YyjzuqenXriV+zRr0TZpkGDZV\nnJ1JCgwkfudOtOPH07xbN77++mtatGjBoUOHVKnbVoWHhxN2/jwuVaviXKUKTqVKpU5ua9GiBd7e\n3kyenP6EJSGEMA3pCVsxRVHQRUdjOH0aoqJApwNnZ/D0xLFmTewcHZ9ov3nzZvr3788vv/xCixYt\nVKratnz55Zfcu3ePadOmZbr85s2beHl5sW/fPqpVq2bh6oQQuZ2EcC6ze/duunbtyqJFi+jcubPa\n5Vi9t99+Gz8/P/r165dlm5kzZ7Jlyxa2b98ux4eFECYlw9G5TNOmTdm6dSvDhg3jp59+Urscq3fq\n1Klsj6MHBQVx9+5dVq9ebaGqhBB5hfSEc6mzZ8/SunVr3n//fYKCgtQuxyrp9XoKFizIvXv3yJ8/\n/c0hn7Rv3z66d+/O2bNnKViwoIUqFELkdtITzqVq1KjBnj17mDNnDp999hnyWSujf/75h9KlS2cb\nwAA+Pj60atWKiRMnmr8wIUSeISGci5UvX56wsDDWrFnD6NGjJYjTyclQdFpTp07lp59+Ijw83IxV\nCSHyEgnhXK5EiRLs3r2bgwcPMnDgQAwGg9olWY1Tp05Ru3btHLcvXrw4kyZNYtiwYRiNRjNWJoTI\nKySE8wA3Nze2b9/O1atX6d69O0lJSWqXZBWetScMMGjQIJKTk1m2bJmZqhJC5CUSwnlEgQIFCA0N\nRVEUOnXqRFxcnNolqe55QtjOzo758+fzwQcfEB0dbabKhBB5hcyOzmP0ej2DBg3i/PnzbN68GVdX\nV7VLUkViYiJubm7ExMTgmO6iJzkRGBgIwPz5801dmhAiD5GecB5jb2/PDz/8QMOGDWnWrBl37txR\nuyRVREREULly5ecKYIAvvviC9evXc+TIERNXJoTISySE8yCtVsvMmTPx9/fH19eXyMhItUuyuOcZ\nik7Lzc2NL7/8ksDAQJnsJoR4bhLCeZRGo+GTTz5h+PDh+Pr6EhERoXZJFvWiIQzQp08fXFxcWLRo\nkYmqEkLkNRLCedyIESP47LPPaN68OceOHVO7HIsJDw9/4RDWaDTMmzePTz75hLt375qoMiFEXiIh\nLOjbty/z58+nTZs2hIWFqV2ORZiiJwxQu3Ztevfuzbhx40xQlRAir5HZ0SLVzp076dmzJ0uXLqVd\nu3Zql2M2Dx8+pGTJkjx69Cj13sEv4tGjR9SoUYOVK1fy2muvmaBCIUReIT1hkcrPz49NmzbRv39/\nVq1apXY5ZnP69GleeuklkwQwQMGCBZkxYwbDhg1Dp9OZZJtCiLxBQlg8wdvbmx07djBq1Ci+++47\ntcsxC1MNRafVtWtXSpYsydy5c026XSFE7mavdgHC+nh5ebF7925atmxJdHQ0Y8eOVbskkzJHCGs0\nGr755hteffVVunfvTunSpU26fSFE7iQ9YZGpypUrs3fvXpYsWcL48eNz1R2YzBHCAFWrVmXo0KGM\nHj3a5NsWQuROMjFLPNW9e/do06YNjRo14ptvvjHZcVQ1eXh4cOzYMbP0VuPj46lZsybfffcdfn5+\nJt++ECJ3sf13VGFWxYoV4/fff+fMmTP07t3b5ice3b17l+TkZEqVKmWW7efLl485c+YwfPhwuVuV\nECJbEsIiW4UKFWLr1q3ExMQQEBBAQkKC2iU9t9OnT1OrVi00Go3Z9tGxY0eqV6/OtGnTzLYPIUTu\nICEscsTFxYX169dTqFAh2rZty8OHD9Uu6bmcOnWK2rVrm30/s2fPZubMmVy5csXs+xJC2C4JYZFj\nDg4O/PTTT9SoUYMWLVpw7949tUt6ZuaalJVe+fLlCQ4OZsSIEWbflxDCdkkIi2ei1WqZP38+LVu2\npEmTJty4cUPtkp6JpUIYYMyYMURERLBp0yaL7E8IYXtkdrR4bl999RULFixgx44dVK5cWe1ysqUo\nCq6urly6dImiRYtaZJ87d+5k0KBBnD59mnz58llkn0II2yE9YfHcxo4dy4cffkizZs0IDw9Xu5xs\nXb9+nfz581ssgCHlUqCNGzdm8uTJFtunEMJ2SAiLFzJ48GCmT5+On58fBw8eVLucp7LkUHRa06dP\nZ+HChZw/f97i+xZCWDcJYfHCunfvzo8//kinTp3YuXOn2uVkSa0QLl26NOPHj2f48OG56spjQogX\nJyEsTKJdu3asW7eOXr16sX79erXLyZRaIQwQFBTEnTt3WLNmjSr7F0JYJwlhYTK+vr789ttvBAYG\nsnTpUrXLySA8PFy1EHZwcGD+/PmMGjWKR48eqVKDEML6yOxoYXIRERG0atWKMWPG8N5776ldDgAG\ng4GCBQty9+5dChQooFod/fv3p0iRIkyfPl21GoQQ1kNCWJhFZGQkLVu25O233+bjjz8262Uic+L8\n+fO0adOGS5cuqVrH3bt3qVWrFrt27bLIlbuEENZNhqOFWZQrV46wsDBCQkIYNWoURqNR1XrUPB6c\nlru7O59++imBgYEySUsIISEszMfDw4M//viDQ4cO8c4776DX61WrxVpCGFJO60pMTGTZsmVqlyKE\nUJmEsDArNzc3duzYwc2bN+nevbtqt/ezphC2s7NjwYIFfPDBB0RHR6tdjhBCRRLCwuzy58/Pxo0b\n0Wg0dOzYkbi4OIvXYE0hDNCgQQP8/f356KOP1C5FCKEimZglLEav1zN48GAiIiLYvHkzbm5uFtlv\nUlISrq6uPHjwACcnJ4vsMyeio6N56aWX2LRpEw0aNFC7HCGECqQnLCzG3t6e77//Hm9vb5o1a8bt\n27ctst9z585RoUIFqwpgSBmqnzJlCoGBgRgMBrXLEUKoQEJYWJRWq2X69Ol06dIFX19fIiMjzb7P\nU6dOWe3pQH369MHJyYnvvvtO7VKEECqQEBYWp9Fo+Pjjj3nvvffw9fXl7NmzZt2ftR0PTuvx/Zkn\nTJjA3bt31S5HCGFhEsJCNUFBQXz++ee8/vrrHDt2zGz7seYQBqhduza9e/dm3LhxapcihLAwmZgl\nVLdhwwYGDx7M2rVradKkicm3X7FiRbZt20aVKlVMvm1TefToETVq1GDVqlX4+PioXY4QwkKkJyxU\n17lzZ3755Re6dOnCli1bTLrt2NhY7ty5Q8WKFU26XVMrWLAg06dPZ9iwYape1EQIYVkSwsIqtGjR\ngk2bNtG/f39Wrlxpsu2eOXOG6tWrY2dnZ7Jtmku3bt3w8PBg7ty5apcihLAQe7ULEOKxxo0bs3Pn\nTtq2bUtMTAxDhgx54W1a+/HgtDQaDd988w0+Pj5069aN0qVLq12SEMLMpCcsrErt2rXZvXs3U6dO\nZerUqS+8PVsKYYBq1aoxdOhQRo8erXYpQggLkBAWVqdSpUqEhYWxbNkyPvzwwxe625CthTDA+PHj\nOXToELt27VK7FCGEmUkIC6tUunRp9uzZw86dOwkMDHzuWyGGh4fbXAjny5eP2bNnM3z4cNVueCGE\nsAwJYWG1ihYtyq5du4iIiODtt99Gp9M90/r37t0jPj4eT09PM1VoPp06daJq1apMnz5d7VKEEGYk\nISysWqFChdiyZQuxsbH4+/uTkJCQ43VPnz5NrVq10Gg0ZqzQfGbPns2MGTO4cuWK2qUIIcxEQlhY\nPRcXF9atW4erqytt2rTh4cOHOVrPFo8Hp1WhQgWCg4MZMWKE2qUIIcxErpglbIbRaCQoKIhDhw7x\n22+/UaxYsSeWG/R6ks+dg6goSE4m/Px5FHd3GgYEoNXa5ufNpKQkvLy8mD59Oh06dFC7HCGEiUkI\nC5uiKAr/+9//WL9+Pdu3b8fT0xNddDS68HDsQkNxXLAATWxsantjsWIkjx6NsVkzHL28sM+XT8Xq\nn8+OHTsYMmQIp06dIp8N1i+EyJqEsLBJ06ZNY968eexfu5aiixbhsGgRTzvyq2i1JE2ahHbgQBw9\nPCxWp6l0796dqlWr8tlnn6ldihDChCSEhc3at24dL82fj9vvv+d4naTRo9F+8AEO6Yayrd2NGzeo\nU6cO+/fvp2rVqmqXI4QwEds8UCbyPENyMvWPHs0QwHpSfqnTP4L/W+40fTr6zZtf6AIgaihdujTj\nx4/n3XfftbnahRBZkxAWNin5zBmcZs7M8Lw9YEzzeATkB7qmaeP48cckXb1qiTJNKigoiFu3brF2\n7Vq1SxFCmIiEsLA5iqLAoUNoEhOzbbsWKAW8muY5u2vXMJ48aXM9SgcHB+bPn09wcDCPHj1Suxwh\nhAlICAubo7t3D8c5c3LUdgnQJ5Pn7VeswGAwmLIsi/D19cXPz49PP/1U7VKEECYgE7OEzUm8eBGn\nl19Gk01vMBKoDFwCyqRbpq9XD+XPP3EoWNBMVZrP3bt3qVWrFr///rtNX4xECCH3Exa2yGgEvT7b\nZkuBpmQMYAB0OjZv3Ei8RkOJEiUoWbIkJUuWpHDhwlZ/mUt3d3c+/fRTAgMD2b17t9XXK4TImoSw\nsDkaZ2cUNzc02VxHehkwMYtlRjc3rty9y8FDh7h9+za3bt3i1q1b6HS61FBOG87pv3d3d8feXr0/\nn8GDB7N48WJ++ukn+vTJbMBdCGELZDha2ByDXo9+3DicZszIsk0Y0B64A7hksvzChAlsK16cjh07\nUq5cudTn4+LiUkM5bTin/z4qKoqiRYs+Nagff2+uq1wdOXKETp06cebMGdzc3MyyDyGEeUkIC5sU\nv3s3Ls2aZXmVrEGknKL0QybLFBcXLq1bx5R16/j1118pV64cAQEB+Pv7U6NGjRztX6/Xc/fu3acG\n9ePvHR0dUwP5aWFdpEiRZx5aHjZsGFqtlnnz5j3TekII6yAhLGxSclQU2oAA7PfseeZ1k4KCsJ8+\nHZ1Cn2gAAAsgSURBVDsHB/R6PXv37iUkJISQkBAKFixIQEAAb775Ji+//PILH29VFIUHDx7kKKzj\n4+Px8PDIdijcw8MDR0dHAO7fv89LL73E5s2bqV+//gvVKoSwPAlhYZMURSHhyBGc27ZFe/9+jtcz\nVK9O8tq1uNSsmWGZ0Wjkr7/+IiQkhHXr1qHT6fD39ycgIIBXX30VOzs7U76EDBITE3M0FH737l1c\nXV1TwzkuLo5Lly7x/vvvU7p06SdCu0CBAjJxSwgrJiEsbJaiKCTs24dzt25ob93Ktr3By4ukJUtw\nqVs322BSFIXTp0+n9pBv377NG2+8QUBAAM2bN0/tiarBYDBw79691HC+ceMGn332GRUrVqRo0aJP\nhDaQ7TB4iRIlKF68uM3e7lENiqKgf/QI/fnz8OgRKArky4ddxYo4FC8uH3xEjkkIC5umKAqJJ06g\n2bwZxxkzMu0VGzw9SR43Do2fH07Vqj3XG+SlS5dYv34969atIyIigvbt2xMQEEDr1q2t4vaCJ0+e\nxM/Pj9OnT1O8eHEg5d8mNjY222Hw27dvExMTQ/HixbMN6xIlSuDs7Kzyq1WPoigkRUZiPHECh0WL\nsN+6FU2at1B9/froRo2Cl1/GqVo1+WAjsiUhLHIFo9FI8oULGMPD0Vy/jiYmBsXNDaVCBbReXjiW\nKWOyN8SbN2/y66+/EhISwuHDh/Hz8yMgIID27dvj6upqkn08j1GjRvHgwQMWL178zOsmJydz586d\nbI9d37lzh/z58+doVrgtnHP9LB4fAnHq0we7c+ee2tZYpAiJK1bg1KIFdiqeyiasn4SwyHUURUFR\nFDQajdlDICoqitDQUEJCQvjjjz/w8fEhICCAN954A3d3d7PuO72HDx/y0ksvsWrVKnx8fMyyD6PR\nyP3793M00cxWzrnOCUVRSDh8GOf27dFGReVsHUdHEtatw7ldO+kRiyxJCAthIrGxsWzdupWQkBC2\nbt1KnTp18Pf3x9/f/4lzkc1p5cqVTJkyhaNHj6oebLZ0znV2Ei9cwKFNG+wuXXri+WHAJuAe4A68\nBXzB/1+UXylQgISdO8nXuLElyxU2REJYCDNITExk165dhISEsHHjxtRzkQMCAqhevbrZ9qsoCi1b\ntqRDhw6MHDnSbPsxJWs55zoriqKQuGYNLt27Z1j2N1AWKAxEAG2BycDbadokfvopjv/7n/SGRaYk\nhIUwM71eT1hYGCEhIaxfv55ChQqlBrIpzkVO79y5c/j4+HDy5ElKlSpl0m2rSVEUYmJicjTRLC4u\n7pnPuc5K8r17aDt1wv7AgSzbGIHzpITwD8DraZe5uZG8fz/OZvzwJWyXhLAQFmQ0Gjly5EjqqU86\nnS41kF955RWTnYv80Ucfcen/2ruf0KjuBIDj35lkkkxSTWBNZoVWEGxFV9GWGkRQI1Rba1xiinvr\ndquFtXSlmFq6hx7cw0IXPOzBLehaCurW7W6NrbpiSwousYvUpYc2BQ+1yx4snYRg8U8yk8zM20Mw\nm78mVpNfMn4/l0zevDfzJpdvfu+937xvv+X48ePAQMDy+fzgufJ4PF7UI7PJzrnu6uqiurr6jqH+\nWSbDT555ZtxvZ/sN8DYQA/4A7B1jnd4TJ0g2N0/Vx9UsZoSlQKIooqOjYzDI6XSapqYmmpubaWho\nuKe5yD09PSxdupS/HD3KE3PnwqVLlHz6KbF0mqimhsKqVRTWryexbBmlc+YU1VXMd2PknOuxQv37\np55i3b59d3ydHPBP4BfACaBhxPO977xDcseOqfgImuWMsDRDXLlyhZMnT9La2srly5dpbGykubmZ\nTZs23fUFSVEU8Z9z56g8fpzUBx+MecepKBYjt2UL/S0tlK9d+8BPpbl16xadnZ2k0+lhP7c99BBL\nJ3l+fTeQAf48YnnvoUNUvPTSA/vPjsZnhKUZ6OrVq4NzkS9dusTGjRsH5yJXV1ffcdsoiui9eJHy\n7dspuXp1wveKysroPXaM8qYmShKJ+/URgisUCnR3dw8L6niP0+k0hUKBVCpFKpWirq6Ouro6UqkU\nv1q0iMd27pzUe/6agbt2/XHE8t4jR0g+//z9/ogqAkZYmuG6u7s5ffo0ra2tnD9/fsK5yD1ffEHF\n1q3Ev/tu0u8RlZbS+9FHJDdvntGjtUwmM25ERy7r7u6murp6WFBHPh66bLzv2c588w1la9YQ7+oa\ntvwmcAxoAuYCbQxMUToDrB+yXhSP0/vZZ1SuXj1VfxbNYkZYmkVu3LgxOBf53LlzrFixYvA2jAsW\nLCCXzZJ/9VXKDx4ctW0jcHbI7zXA0C/5zD/yCP3t7VRM05xmGBi1X7t2bcKg3n6czWYnFdRUKsW8\nefNI3IeRfaFQoG//fireeGPY8h6gGfg3A4egFwO/BbaP2L5/2zY4epREVdU974uKjxGWZqlMJkNb\nW9vgXOSFCxdycM8eHt+xg1g2O2r9rQwE4pd3eM2eU6dINjbe02i4r6/vjod+hz7u6uqiqqpqwqDe\n/jl37twgI/Wezz8nuWYNsXz+7rc9c4bks8/O6CMMCufBvhJDmsUqKipobGyksbFx8L7Ite3tYwb4\nton+404cPkyuoYHEnDn/3yaKuH79+qTOq3Z2dnLz5k1qa2vHDOry5cuHLautraW8vPw+/UWmTvnK\nlWQOHaJi585xpyqNJbt3L4nVqw2wxuVIWCoSuVyOwnPPUXbq1JjPbwUuAH3AY8DvgJ+PWCeqrOQf\n+/fz9unTg5Ht7OykrKxs0oeBa2pqinIOcu76dfrfe4+KV14hVihMuH62pYXYnj2UPfzwNOydZisj\nLBWJ/mwWGhpIXLw45vMXgUVAJfA3YBfwL+CJIetEQMeHH/LfkpJhcU0mk1O897NDPpMhe+ECpe++\nS+L990cdno6A3IYN9O/eTWLtWhLz5oXZUc0aRlgqErlcjmjzZhJtbZNavwlYCewbsixKJMh89RXJ\nxYunYA+LQxRF5Ht76e/ogK+/Jvb995DLEdXVES1ZQuny5SRqajwErUnxnLBUJOLxOH319ZOOMDDq\n/Gbh0UeJTzAP+UEXi8UorayktL6eaNUqgGm7daaKT/GduJEeUPF4nMLTT4958VUP8Fegi4H5rUeA\njxl9TrjvtdcoS6WmdkeLyO3wxuNxA6wfxQhLRaR02TLy69aNWh4Bf2LggqyfAgeAvwOPD12nqgqe\nfNKYSNPIc8JSEYmiiN5PPiG5Zctdz2nNvPUWiZaWovrqSmmmcyQsFZFYLEb5hg1kDh8muosRbXbX\nLuIvvGCApWnmSFgqQvlMhuzZs1S8/DLxzs5x14uSSbJvvkn8xRcpmz9/GvdQEhhhqWgVCgX6rlyh\n8OWXJA4coLS9nVg+TxSLUVi0iL7XX4f6esqWLKHkHu5dLOnHM8JSkYuiiP4ffiCfTkM2C4kE8Zoa\nyubP9yIsKTAjLElSIF6YJUlSIEZYkqRAjLAkSYEYYUmSAjHCkiQFYoQlSQrECEuSFIgRliQpECMs\nSVIgRliSpECMsCRJgRhhSZICMcKSJAVihCVJCsQIS5IUiBGWJCkQIyxJUiBGWJKkQIywJEmBGGFJ\nkgIxwpIkBWKEJUkKxAhLkhSIEZYkKRAjLElSIEZYkqRAjLAkSYEYYUmSAjHCkiQFYoQlSQrECEuS\nFIgRliQpECMsSVIgRliSpECMsCRJgRhhSZICMcKSJAVihCVJCsQIS5IUiBGWJCkQIyxJUiBGWJKk\nQIywJEmBGGFJkgIxwpIkBWKEJUkKxAhLkhSIEZYkKRAjLElSIEZYkqRAjLAkSYEYYUmSAjHCkiQF\nYoQlSQrkf40crguWY/emAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f87397af7d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from hypergraph import diffusion_convergence_analytic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "\n",
      "\n",
      "def diffusion_on_hypergraph(hypergraph, markov_matrix,\n",
      "                            t_max, plot_results=False):\n",
      "    \"\"\"Simulate numerically diffusion on a hypergraph,\n",
      "\n",
      "    Diffusion is simulated using markov chains.\n",
      "\n",
      "    \"\"\"\n",
      "    nodes = hypergraph.nodes()\n",
      "    hyper_edges = hypergraph.hyper_edges()\n",
      "\n",
      "    most_common, most_common_nodes, states = simulate_diffusion(\n",
      "        nodes, hyper_edges, markov_matrix, t_max)\n",
      "\n",
      "    if plot_results:\n",
      "        return plot_diffusion_results(most_common, most_common_nodes,\n",
      "                               hyper_edges, \"hypergraph\")\n",
      "    else:\n",
      "        return utils.get_names_and_occurrences(most_common_nodes)[1]\n",
      "\n",
      "\n",
      "def plot_diffusion_results(most_common, most_common_nodes, edges, name):\n",
      "    plt.figure(figsize=(8, 4))\n",
      "    utils.plot_hyperedges_frequencies(most_common, edges,\n",
      "                                      ('Ocurrences of hyperedges in'\n",
      "                                       ' a {}').format(name),\n",
      "                                      normed=True)\n",
      "\n",
      "    plt.figure(figsize=(8, 4))\n",
      "    return utils.plot_nodes_frequencies(most_common_nodes,\n",
      "                                        'Nodes in a {}'.format(name),\n",
      "                                        normed=True)\n",
      "\n",
      "\n",
      "def simulate_diffusion(nodes, edges, markov_matrix, t_max):\n",
      "    engine = DiffusionEngine(markov_matrix)\n",
      "    most_common, states = engine.simulate(t_max)\n",
      "    most_common_nodes = count_nodes(nodes, edges, most_common)\n",
      "    return most_common, most_common_nodes, states\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from hypergraph.diffusion_engine import DiffusionEngine\n",
      "from hypergraph.markov_diffusion import (create_markov_matrix,\n",
      "                                         count_nodes)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t_max = 100\n",
      "markov_matrix = create_markov_matrix(HG.hyper_edges())\n",
      "nodes = HG.nodes()\n",
      "edges = HG.hyper_edges()\n",
      "engine = DiffusionEngine(markov_matrix, t_per_walker=20)\n",
      "most_common, states = engine.simulate(t_max)\n",
      "most_common_nodes = count_nodes(nodes, edges, most_common)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "states"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "[[2, 5, 1, 4, 3, 4, 1, 6, 1, 4, 2, 4, 2, 0, 2, 4, 3, 6, 1, 5],\n",
        " [0, 2, 0, 2, 6, 5, 6, 1, 5, 2, 6, 2, 6, 4, 6, 1, 3, 4, 2, 6],\n",
        " [7, 5, 1, 6, 5, 2, 6, 5, 6, 2, 0, 5, 6, 0, 5, 6, 0, 5, 0, 5],\n",
        " [1, 4, 3, 4, 3, 6, 5, 7, 0, 5, 6, 1, 5, 0, 7, 5, 2, 4, 3, 6],\n",
        " [5, 0, 7, 0, 7, 5, 1, 2, 6, 4, 2, 4, 1, 2, 6, 1, 3, 1, 2, 6]]"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "most_common"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[(6, 19), (5, 17), (2, 16), (1, 13), (4, 12), (0, 11), (3, 7), (7, 5)]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "most_common_nodes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "Counter({1: 63, 8: 51, 10: 48, 7: 33, 6: 30, 4: 28, 2: 19, 5: 16, 9: 7, 3: 5})"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_diffusion_results(most_common, most_common_nodes, nodes, 'Hyper 100')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lh7XYtImIiHRCU7+Iduh8kb1LqFVDf67xxsxLm79e1VASMgByZl4S1kNCBkBG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\naRMREenE/we3KF30nQqaowAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f8739761f10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f873973d390>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[0.21,\n",
        " 0.06333333333333334,\n",
        " 0.016666666666666666,\n",
        " 0.09333333333333334,\n",
        " 0.05333333333333334,\n",
        " 0.1,\n",
        " 0.11,\n",
        " 0.17,\n",
        " 0.023333333333333334,\n",
        " 0.16]"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_diffusion_results(most_common, most_common_nodes, edges, name):\n",
      "    plt.figure(figsize=(8, 4))\n",
      "    utils.plot_hyperedges_frequencies(most_common, edges,\n",
      "                                      ('Ocurrences of hyperedges in'\n",
      "                                       ' a {}').format(name),\n",
      "                                      normed=True)\n",
      "\n",
      "    plt.figure(figsize=(8, 4))\n",
      "    return utils.plot_nodes_frequencies(most_common_nodes,\n",
      "                                        'Nodes in a {}'.format(name),\n",
      "                                        normed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import get_cmap, cm\n",
      "import numpy as np\n",
      "\n",
      "\n",
      "def plot_comparison_bars(x, ys, labels=None):\n",
      "    plt.figure(figsize=(12, 8))\n",
      "    colors = [\"crimson\", \"burlywood\", \"#65df25\", \"#dcab11\", \"magenta\"] + [\"blue\"] * 50\n",
      "    N = len(ys)\n",
      "    width = 1.0 / N - 0.04\n",
      "    \n",
      "    colors = cm.get_cmap('jet', N)\n",
      "    if labels is None:\n",
      "        labels = [''] * N\n",
      "    print(width)\n",
      "    for i,  y in enumerate(ys):\n",
      "        \n",
      "        plt.bar(np.array(x) + i * width, y,\n",
      "                width=width, color=colors(i),\n",
      "                label=labels[i], alpha=0.7)\n",
      "\n",
      "\n",
      "    plt.legend(loc=0)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_comparison_bars(range(4), [range(4), [1, 2, 5, 2]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.46\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/att/Projects/hypergraph/py3/lib/python3.3/site-packages/matplotlib/axes.py:4749: UserWarning: No labeled objects found. Use label='...' kwarg on individual plots.\n",
        "  warnings.warn(\"No labeled objects found. \"\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AEBy+TdkCZdmpZelnjm5m6WaWfuboZg8OXwAAhuDwbcoWKMtOLUs/c3QzSzez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\n/w+8mfkstJuXdAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f8723fa7d50>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t_max = 100\n",
      "markov_matrix = create_markov_matrix(HG.hyper_edges())\n",
      "nodes = HG.nodes()\n",
      "edges = HG.hyper_edges()\n",
      "engine = DiffusionEngine(markov_matrix, t_per_walker=30)\n",
      "most_common, states = engine.simulate(t_max)\n",
      "most_common_nodes = count_nodes(nodes, edges, most_common)\n",
      "\n",
      "most_common_to_t_max = {}\n",
      "for t_max in [100, 300, 600, 800, 900, 1200, 1300]:\n",
      "    most_common, states = engine.simulate(t_max)\n",
      "    most_common_nodes = count_nodes(nodes, edges, most_common)\n",
      "    most_common = list(most_common)\n",
      "    most_common.sort(key=lambda x: x[0])\n",
      "    print(most_common)\n",
      "    _, occurrences = zip(*most_common)\n",
      "    \n",
      "    \n",
      "    most_common_to_t_max[t_max] = utils.get_names_and_occurrences(most_common_nodes)[1]\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(0, 11), (1, 14), (2, 13), (3, 7), (4, 8), (5, 16), (6, 14), (7, 7)]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(0, 38), (1, 47), (2, 36), (3, 33), (4, 31), (5, 40), (6, 57), (7, 18)]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(0, 92), (1, 76), (2, 70), (3, 55), (4, 56), (5, 93), (6, 101), (7, 57)]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(0, 62), (1, 119), (2, 111), (3, 96), (4, 132), (5, 72), (6, 170), (7, 18)]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(0, 117), (1, 96), (2, 128), (3, 81), (4, 99), (5, 149), (6, 162), (7, 68)]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(0, 165), (1, 155), (2, 169), (3, 108), (4, 117), (5, 177), (6, 234), (7, 75)]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(0, 147), (1, 177), (2, 162), (3, 153), (4, 178), (5, 188), (6, 216), (7, 69)]\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "most_common_to_t_max.values()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "dict_values([[0.17735042735042736, 0.09743589743589744, 0.007692307692307693, 0.10384615384615385, 0.03418803418803419, 0.08162393162393163, 0.06495726495726496, 0.22094017094017093, 0.041025641025641026, 0.17094017094017094], [0.20694444444444443, 0.0625, 0.020833333333333332, 0.07944444444444444, 0.06666666666666667, 0.09222222222222222, 0.11583333333333333, 0.17055555555555554, 0.03, 0.155], [0.20592592592592593, 0.06666666666666667, 0.025185185185185185, 0.08407407407407408, 0.06851851851851852, 0.09074074074074075, 0.1237037037037037, 0.1622222222222222, 0.03, 0.14296296296296296], [0.18423772609819122, 0.0855297157622739, 0.017829457364341085, 0.08785529715762273, 0.05581395348837209, 0.09431524547803617, 0.10439276485788114, 0.18708010335917313, 0.03953488372093023, 0.1434108527131783], [0.19777777777777777, 0.06166666666666667, 0.03166666666666667, 0.07, 0.08277777777777778, 0.09388888888888888, 0.13444444444444445, 0.16, 0.030555555555555555, 0.13722222222222222], [0.2, 0.05555555555555555, 0.025925925925925925, 0.07777777777777778, 0.06666666666666667, 0.1111111111111111, 0.1259259259259259, 0.15925925925925927, 0.025925925925925925, 0.15185185185185185], [0.19, 0.07111111111111111, 0.02, 0.07444444444444444, 0.06222222222222222, 0.09666666666666666, 0.10666666666666667, 0.18666666666666668, 0.03666666666666667, 0.15555555555555556]])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from hypergraph import analytical\n",
      "from pylab import cm\n",
      "to_compare = list(most_common_to_t_max.values())\n",
      "nodes, predictions = analytical.analytical_hypergraph_diffusion(HG)\n",
      "to_compare.append(predictions)\n",
      "plot_comparison_bars(range(len(nodes)), to_compare)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.08499999999999999\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zUO/rddG5sbFireP24WhbPFqjigDOXs4wU2hmz0iRC1LkghS5IA/OMAPMEMfm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\nAwBABg0zAABk+P/pDlCUP2SSygAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f8761676210>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It look like it does converge. However, what is the impact of number of walkers?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "markov_matrix"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "array([[ 0.        ,  0.        ,  0.16666667,  0.        ,  0.        ,\n",
        "         0.33333333,  0.16666667,  0.33333333],\n",
        "       [ 0.        ,  0.        ,  0.16666667,  0.16666667,  0.16666667,\n",
        "         0.16666667,  0.33333333,  0.        ],\n",
        "       [ 0.16666667,  0.16666667,  0.        ,  0.        ,  0.16666667,\n",
        "         0.16666667,  0.33333333,  0.        ],\n",
        "       [ 0.        ,  0.25      ,  0.        ,  0.        ,  0.5       ,\n",
        "         0.        ,  0.25      ,  0.        ],\n",
        "       [ 0.        ,  0.2       ,  0.2       ,  0.4       ,  0.        ,\n",
        "         0.        ,  0.2       ,  0.        ],\n",
        "       [ 0.33333333,  0.16666667,  0.16666667,  0.        ,  0.        ,\n",
        "         0.        ,  0.16666667,  0.16666667],\n",
        "       [ 0.125     ,  0.25      ,  0.25      ,  0.125     ,  0.125     ,\n",
        "         0.125     ,  0.        ,  0.        ],\n",
        "       [ 0.66666667,  0.        ,  0.        ,  0.        ,  0.        ,\n",
        "         0.33333333,  0.        ,  0.        ]])"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}