ntf_school.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Revealing mesocale structures of time-varying networks through non-negative tensor factorization\n",
    "\n",
    "In this notebook we show how the method presented in [[1]](#1) can be applied to data about face-to-face proximity relations collected in a school.\n",
    "\n",
    "The data were collected by the [SocioPatterns collaboration](http://www.sociopatterns.org) using wearable proximity sensors that sense the face-to-face proximity relations of individuals wearing them. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A few libraries are required in order to run this notebook. The Python Pandas library is used for data loading and manipulation, the `sktensor` library is used to represent the 3-way tensors and the `ncp` script contains the algorithms for the non-negative tensor factorization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "\n",
    "import pandas as pd\n",
    "import sktensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.simplefilter(action = \"ignore\", category = FutureWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import ncp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following we load the expected structures (classes) that are used as a validation for the methodology.\n",
    "\n",
    "The population of the school consisted of 231 children, organized in 10 classes, and 10 teachers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "241\n",
      "['cm1a' 'ce2b' 'cm2b' 'cm1b' 'ce1a' 'cm2a' 'teachers' 'cpb' 'ce1b' 'cpa'\n",
      " 'ce2a']\n"
     ]
    }
   ],
   "source": [
    "classes = pd.read_csv(\"data/classes.csv\", index_col=0, squeeze=True)\n",
    "print classes.size\n",
    "print classes.unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data collected through the SocioPatterns platorm is represented as triples $<t, i, j>$ where $i,j$ is a pair of nodes that were in proximity during the interval between time $t$ and $t+20$.\n",
    "\n",
    "It represents 2 days of activity in a school. We selected only the hours when the kids were at school, for a total of 18 hours (two intervals of 9 hours per day concatenated as a single interval, thus removing the night)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t</th>\n",
       "      <th>i</th>\n",
       "      <th>j</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>228</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   t  i    j\n",
       "0  0  0    1\n",
       "1  0  0    2\n",
       "2  0  0  222\n",
       "3  0  1  222\n",
       "4  0  2  228"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"data/school.csv.gz\", compression=\"gzip\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "18.0277777778 hours\n"
     ]
    }
   ],
   "source": [
    "print data.t.max() / 3600., \"hours\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the timeline that shows the sum of number of contacts for each 20 seconds interval, we see that there is a small interval with no activity between the two 9 hours interval, in order to show where one day ends and starts the other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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lE+UgIDvIgme87O7vd995uIrOQzYDSZXN3T/s6vREquxVPEbZibzODHIHeaCV\nzgJ5UDZZ6zT/IfK0pk5oXttnl1HGahpmGpcXGT9IyEnxvUYBueYpUQzKYUV9R3QiDy5yOnh2Pchr\nX/D7ZZHXipM1eyL5l9pm3PEEcxR8Q9T72DyUV1P/KTYn8mkQO2g2cw79gLX8ki0GCNkA3m0Me4a4\nk9bFKnQQbOKDggZNkNpFko61LzjabgX+I7LVyrNkpo6VZ2zZKQV46OL8o1TZ3PVmsvpXhVuN0s4d\nNvkO8lPpR8FDgrz8+0eBHyALtDJRII8IP8kyvp05WyGK9OsR9AysqaHpeZK9B2FSHlA4HkjyYo2O\nHTeAxDztyDSGGEt43fVVMp10L+XjePyOwxbyI2li9JBWEJfIgo69BDxHZvr/drKdsvNk7gRe7sjd\njTurAmrVyQE7QfCNHiwFfL3fPE55lxWqCxKYYNb3ceBvgafIOt6ryA5DfIDsVO89QMRZNT1bzJ+x\nmyg6/Q1ylbeLVehJ8iB31K118k18bwc9OFcyheAAFANSHKijSbiaR+7YuyHoca7B+4VdSOIBRRo5\nDYe8ME77DjHFaaIBIqZE60byZNzV7G7LqjywzCmTC/fsdzsw0V32LnRsJM+52ZFpWS9Jq3Whfypp\nWEUPilYQh0U+8ligMB1y73m5f6z6+3E5UKU3x9Spgw+ctKypS13QlDeGkqrmRONmeBPwTeBV7no7\n8F+Rrd5+xN37KPDJNoUJiCzNzJKmav0StpMzOnwep2MTiwYD/pKZIhVRj4Iyr5JHdDw1rwrL0UOa\nrch0pElHpWzKcZYssuaI9om2qD2/r05BVvFT03eHnBahDkNOFBcnjoY8pEnTEFMoF5rI177L3COt\n6sYBq+QToctk0Zp9ROxQ58t3Gg9kKZtOWrDXEnp3e0SntjVFleez7qjinYo8ZnLmXax9NPWTxh1v\n9NWG05ig3QB8jSxCz3XALjJn0GeB17hnXgs826YwAbFW3WDjMAOdONDBKrTL40JMwKWYLbh3zv09\n6elEhY29LHNEgPr8k+HRh5aIT878IdWnw7qJd1IDgf1gD1IOGxwqnPAg0Crbe3/vPNkRAJfBrhEo\nyKBtfBmPhPnNW4rRRFOn9A378brSWdPQk+NTS3a8zBrxxcbed3qHkBK6R05gYmMIrwsvkU2kHgpo\nfDnM0+Ub1f/kvmZ16RJZ+H2vu07TchznyiCtWXYGvzfSKY5/pu6/HWufoC46eeue5qlFC7+Q0Gpj\np6oNp1sou3vDAAAgAElEQVRmbPL58T/EPyfzXToC/JG7d0L8buS1uJ8szKyJNZREeWWqztlW3nsk\nIri9YDxbJRQpri49IfKPTty6q2+n29myrJfIgqGskHBeTvEWkYFASPsmSiGRj793SnzXUmFeGpRx\nrgfccZqoeVuH9B28tUG83MoDy5zAPgxrUh7OXSCkGdIqNg6Q4wZ59qeUBaHO8TSWi5fHKvRjTEf6\nid1VsH8pnjsbKcPFMJ9y3cpyICjD8ZAfYjqlgnZTn+RXjQ1i4w1N9TzQgOZ1mxc7WuY39YXkeJmx\nqefHChJijHkz8GEyU8fXAf+hMeafyGesK804+Tv07sQ+Q/i6ngb+jKLTc8wRWjrgnnD3JJ3eShbu\n9ses5YUKR9nbgZ1kjsQyoIZ0DH4FeP2AjzzwZT0O3GwtW23mVHwbcIjAOdqdU7LFXY5Cv9t40BFP\n56fJaHSd+ztyfDaGdWN42NNH5hMEgLmD3BkbMgfu/e5/H6RlVYTVl6H9f9zOSWAQKDtmJ2ir6A6p\nfqxQDBmnxf9P0jIQ0qwCQAzhSAri44An3N+r4rmvko0h7iGLD/BdwW+exo+6e8eBn7LxAFiQH3t0\niCzA2PcBt7pn3gL8Arns+Uv3zin393HgL8T/pXFcpo/v+d0IbaVe/8mQH5rqFKfv7yELZDJNVAWs\nWaax7CwRo6u890Fo1X/HDTrUBr58V4Gfrz3mY8zZ7m3AvxPX/xT4PeAZ4LXu3o0kTByBVeATLn0Y\nuJXR1t8XHoXNWxkFSPjiU9m9PLgAYra9GNdffCqfVW/f2+79zVuzdzx9PrvLOV47szluddcu/y+9\nWP49zH/zVkaOwV98Sqxybh8GvcL6f+lFRr57m7f63zN+WrOu/EeynagHz4r67CjnV0e/PSccPzpT\nkVH+gj6f3eVWSi6K33eCXYH7j8CfPMLIpHHPCfH+EfH8N7PrHY/D5q3DoXeTa0mvtvys15Nfj/jv\nXth2X31/12u9nv11xo/3HYIHTjLyl8p+D8cDiff3CXm5fXrlHaY8y+i1d0Poj3MV+u/FgL5uVyl/\nPs9/231k7iXn4U//Fr4sTCHXLGzfmy7P9r3wrtsYmeqH45OwPvfsF+V/Lrv+wqOMrGBi5WtzXcj/\ncqZv33Vbd+0RGy9Ex1PbVf5Og/+/9KIbP69nY7Idj8PnHyry25D67+at8G+uwG/ZLP3qWSp20KI3\n6xLZQYR/Q7Y6Y8jCrf53ZEFCPuqe+RgtgoQEW38+sEPlOV2LksbdWiVug7svpFmQf8zOP+lzNm7Z\nZkCzVKCUQ4IWMgCLDdJlgiAgDeh3OviOJbeTrzIR9c/VBW056P4/SdF09RxzFMlxqDyzLCngv/Pi\n/1YmH5o0tUkxfdTgHcmrzyVkesI0rpHJ+cT+P0OWZ+Rm8htOZ6wLXRE7n8zr+otkpoOFwGRUB9yy\n7r2kLgrpXUd/asYmHdDH539F5H0hLMu4fEKN+WIX/KepMf2j7TC0/kvggtT5BC37CB8hD7P/h2Qn\n098APMgYYfapHgQPgrCRMnfS+RjDRjoiSGOTMXlApA/XXgo6EWHyUeTDccrWgHdu7YD20kH6cFD+\n0GbeK6ow4pT0AbuYdZYR/Y4IRbTNXcsIeSvB+ztEuxxLfM+CPUNRgfkyrlL0FzgUebczxTXlflHL\nM13wgKa4DApkwHHBO6Gjfa+DB+WBxUqBzNrZ7J0vPCp4NVxoq5t8NZAznRyFk/xO/31oFCJfLuiN\ndFJY7gq9YikHwvI7Z14vXaUYuCM2IdlXkV8pzD2jXbduI0q7djnnyusno1WD+LH4hPJ44Ywr/xEi\ngcZmzR/zksbRBRTHWj4V/ClzHhtOoCGCYy2mMkGboCGihaE8mJYn1Q+CsJEy99b5gm+PmDLFjMHz\n64HQlkEGzky7Th1N0GTH3EWFQnc0Cc9teYxyVKp1QT85WDgSPhPQLTXZDb95lkhQl0R7rog6nQy/\nM+9JB+dd0bE64I3g8VLwkL4HD8oDi5UCmdxot7Zo/lWQp53o/piM7rjOgxiAi3pW6grKA9rL8nmR\nzzGwW1wbrFA+l7Y0EI7ROxhbJCZ13Ep5kXgiWkbyO0ge6TI2RhjXiik2XpBjhUHt3gw1jTlBC9v4\nGAON+F5Td5v67dsYCGzmlPfjwM+QBVN4gWxnbtrOnZOgT+dP6UQ7cvK1aedZWdYfJw9ycS/wIXJH\n30fEc1Opk7V2XwfZeAfpJ8l8IG8h7eB5p/j/PC4QC/Ar5IE7zgEPk9Hg7S4/yIKkXCe+5Wl3CPh5\nYMO96/Em9/cU8BX3/98ALwI/Rjyoiy8XuPYE/iXZWYMvAT9XUbfBwTnlHjKGY8awRwY/8U66HfGA\nIiKDvAwg68s/A1jgR4CvB07JvTqvKw8sHKRM/mCzV575ReA1ZIGUPkQWiOIy8AfAHSl5NyDH/6EE\ngDhCFhDrSVwgK5sHqhrJYrJAIR4ngX9AHgjrRbLjki6R+c78C7K2+QPygFaQ6bAwsIgsxwXgh12+\nHyLTYZCgkZMDbxK3vuqfC9u5RbvL/M4D7yCLi5DihbH4xD17CvhRd+uK+3uOTG/fTs7T2wYaaK13\n1OkC0e6joGzkgdTOAC+T8eQLUy7qbDGk2SJFk73a8Kx9JzrYOqXeRjv6O5lJwBEanlMWljW18kfR\nHHKwdtNNae/oJ0MQfyn4fYVs1/CRyOpiuAv2PKPgH6Xn/O6FXEkbmZiIdtxDFjAkuQ1P2nx18Pbs\nkbKHNBxkX57XFOsHgk82gnawCP+LLuSXJk0+jcNPoR6KXHtelr5Vm1L6K/GN8EDnzmToLPpQndxP\n6YsIfb1Oep7MXF+ecRY+tx7c2yHerfJBC00ovU7zZvzReoR6syl/VNBM5rdrynwvy/QlhPlarA6z\n6IuLliL86Xmy6qiiQY+X8vJhk8/MvlAVhSk6z625/xd6a7iu86Z+n7TTk5syboDdUvHNkT9ahzxw\n64xoG5sslHwjIp0/NrB9grgZgyWbAL5MNsGTfmqps2VKtvgVZT5GPmmTE81BBnxICFIb0mRWPLBM\nSSik2EJDYdDUd1mVB5Y3UQhK9YCXdZfJFr78Ys5RJ29jvHyIxBmXie+F+sz/L4OSDHaMEZT/POUD\npOXv4ZlmpTMSI/RYp+ijdY6iP3bKhD883HofxcW4QkARIj6K2Xv37CfiGx+U3/t4RZ+L8JfnmwsI\nn7Aptc+6+9bJ2DdidNQU0qhaF1A2lb1E2Sy6yoQ/Oebqr86+fNjUM4MxcXQYnd8F/BJzZNY1AaIm\nEuIMrVtiv6fek4iYmsnt9Wvu73XAn0nTAeDN7rerwKuB9wGfGqt2U0QDc4ebgevF9VeBX4s852n5\nikunIs+8QH5uj99at+7vdwI/QBYk5/vJTERSJqaQmVoU6GkMzxjDSeCfiTJfBu4nMz/5Nfed0SuR\nMnaOMc4AelPk3t8gzG66LaECRuf9/ArwTjI+hIxfvQmv7+99m2IpFDeTycAb4LrryfTMdwCvcn89\n3kHOy1Im30hmsls44zKGyLmX3lTvceAwWX8ZpH4T8LrjDFnk7BvITBE/Ffx+nExf3CPktT8j8Vtk\npofbKJqGvRp4A9n5ZrhnbrGZqVjM7C817riZjJa+/SzZ2OId5PS9QTz/s658N8P1P+HKcYCyjvBl\n+LrL69XAWYTJYGj+Bvxj8a1XAd/r3nuIjuH4y+vr6ym6U4R1UP03BhyNvxcK5ypfJDehTZmQVo65\n+kJkbJ9GDzPl5GxxGRNjBPWoeq8ij3DFKwj1WXj2aPDeIFd+Uqt54ne/unIc7O6KFbeYo+8B8uiQ\n3uHZPxdGzJI7XtEgK8EKYmy1J9zp84FCwja0YPfPqj3qaBx5XtLwXBXdNU2tneQOsDezXamTF5o0\nzSJR3tUJI+wdpxjcxp0hWZCfjUKyB/1ih9SbzMnOhiizDGolj3WRdYrK6wgdZH6Ng1CRHq94Wkr9\nF+52lCIpNm2D4LmHgzxiOtJSjAi+wRR20KjYvdQ0FRqHKWn2Ss2YayD1Wa+aE/VQuHRhXOGTZ3It\nUwoE0tecEG21TU/EvEH8toKzlaZoEnBUCNL9RPylhpLqhDsRfzoq7JLD/IQyWg14MjZ4cAd7p01v\nSCu3u8hNQwqTmqANL4O9b5btEaMxCb+Q4Pkj4W+aZtJOx1gS83BNw0hVMjXx/Caw3yT3g9orZNyG\nuy4tKED7yZV47rLTa2fJTd62hN/oon5TpPMmIv5jwTNRc7uEHPf0XHE0ueTotBaR9TF9KX/z7eX1\nn18kugr2cfeMl0uj8UhKJybq7nXxsSAPXzfvAnDK6dA94v7nUzprwjaRcndl0vw0VdI4XMQO27/x\nmCvxnan3c4pjbVd+bPL52RM7XRhXgeSuzzIkIsEkAsZcb5HXJvKJQ5USk7bhr4j/p+LnREe+JzQI\nlBLwU6WTMcUBgJyEyPPJLMH5MsGzjzh6rgS/JSeIQZl2ifLc5ZSJ9D2b9XEOsSAUsRWtMMR75Qp3\nVzyw7CkhL9oE0Olt4Kk8sBipSqbWv7Nmwb5ENqCWlhuVPiMUB+xJHnbPycPaZWqkS8ep3xRoHPMv\n9f5o8rDp1DEuVcGE7o3ouOddG8jd+ILPXowu4jtbKJ/P5gON7CyWo7kcCL7pzx5ddbSQZT1PNiE/\nTNoSpWrntZFsJF8EPswSbSp0rTuqeIB8nLfXyYkXEIsUTfVdS96a0hFTMf7FJp+ffcOmC+MqkNz1\nWYaUEHr+/I4rBAE9OvqmFPp+MjC11fcOJ2i1HYryrpg8EL3pxE6m0iGaiWd3Rn47EtDaB2A5664L\nAVsi+T5Gx1HIxqT7vaK80X4a0n1aPLDsqWEfiO14rlJc+Ok8GFB92ZUHFiHV9fXqd9ZGvBvo/kaD\npIb8Hws0cjaU413Wbwo0DnXB6UidLC1MuoI8rwb5XAuuj1E2LaylS+qZokzac5yGk5swP+KBwMKy\nPyd44FRYHuoXTWPBUFLPTm1wP6TUpN+1y69ygrYvaMtoxNIO6jT1fh77xrxN0ELzh2WboMVMEaKr\nYh1+M3pgc9+0qCivF5JNIjqFK617KK7U1k3svDCQQv8yxSha4YTFK9CTZJNqK/7GFKxUjmfJzSl9\nOb0pZavw0lOk/yaK0dBKO60Eq1oxxaapk7aoGgB5Pgp9P2zQfht989SipWXi97CvV9EB7DPkpnRy\nMXCVbAJwUdyritLn84yalAfPvCj4+xmyQ4tXuqjfDGns+7nXBaHO9jRYqSsrZf3pU6ijpH5aCWUN\nZd0aM4Ns4mMfTqZii0k+/0L9KvLxKYy+/ArCwiWSh/9+KqpkbAE93FTofRF1hvw49UWL4FuyLSt9\n/mjpLjWLfi6/kfdDbPL52TdsRWGqt/GXYrIWY5K6zsCEgwH3Tb/y5m31B0vvQEheoIGyDd6pXWUU\n7eAVQmyQ6wX0qhPo3jz0KOVVPJ+8X58cWIShieXzhcnyLAVjDT1lOVaFIPTBVapCQeskoLt2iJrY\nEB+4yGAAnv/UZ2067bKw/B7TNykdFNDhHOVJwHqgfyzZBKpp8KuCuXniGbkg18psv6JeST/cKdHc\n6xhp1uWDWEV9xSvaSe5AeOscP7k7F7TPNXIfshUiZ6TGeD1FH9KTQ1+P2FE28tlDFOvi9eVligua\nu8kXNaXVTKlPUtRlh8UzB4MyRxcECFxJYvRYtMQMFy3IdZw8ZqHW54+yDhxUW+TlwyafmX2hKgpT\nv40/KALPsCErO0MXAoHyrsjU6M2Epk0UV6walTMQwitthQvlFUsZRUvS3yukUMkUBgiyTcmd5PdT\nnAgeD8s4S8HYlCcj/bbUNpRWX9W8rcO2KCmioI/4AdyKaLNNsf9nW+7F5YGQ3/suT8d1iw3Iozoo\nIquDAfnmre45uShbOYlqQtvgmWTgpnHqGrk/9fFJguatxwXBPR8pWO5ISd3lA3xIuVK1g5Q6Ly31\nvpscro3aXeQVW0yqqot/PzZZD6NghrtiUhaW+JAGCwLL0venx9+156CFY6wmQT8G7S6Vlw+bfKaH\nhkgXpnobv+T703eiJzOW8LsJAdm6bLNi6A4maK3DpzLGIDSg4TayFbqXCULHC7r5yIUXBB3PpGhK\nvgV/nGyn+BHyVcCrYE+QjtY1Vd5rkr94Rtb3dKy+If0XeXA+60Qeuc0NekeTrucZsKn4IvPAOPJm\nXlJC36RMbaWs9iaNV8F+GbFQI3R9rYlYE9rKZ6qer5NzFfWKTSSmuYM2gZ9ftJ2iOxDh72EeiTxj\n0ZKj9KGoK1/OeGHNkh9MvsfJrVGwrYCHYnUZjQ9T7enunyfbEUzuvgR8WMnbKR5a5L7v6vsMY0QV\nr86z8UHVbfi/UZC8GdItwSfY5DuzL2RFYeLb+LX+Qj0S+tgkZUsJkwbvFVaxhED4mug4L4tnGpl1\nCIZ+3gnLmZhvjNkGYwnBNjQP6Cx3Fwtmt6IssZ2zL4VCgmzidYW0GWR4P+akPBHvteWxBs/49Ap5\nVLZB8cw8pLYywT0vI7DtEL+F/Du4fqxp/lIoe8mjzRZ8eyLPS1/qMCKgnFBJc8dLsTwnLL/sYzXR\nZpM+VH5S8kiq3tOkeUV9ojtDTfJJtG3ltfh+IXCDeG4l8X4YWVOO86Su9XxyltyMcRu5P7nUg4eC\n9ryGOzIgoquuISYYgoZ+gignm6UJaECzWl25SIkxo4pPi/8bvDsIf+AUn8zTBE1W4JBrlOi5Hn2m\nSGcfa/VsnI5N0e66sKsYdBwZeGLnhPWbW8ETds42NCduJhM1uw3a5VoV7Uk7Y8fy309RGXbCew3o\nllyxouxHcDJS9srIV5qSdK/kzxp+PkZxkWatql00aeoiUZxQ+ei1kk/9jpiXF0coLiqEx52EURfX\nu5QhlMcZlmzCcIrckiH0meptYC7K4BdMQ7+uzsoxDp0jMqhu4fOuQEdeomh+KP+PLXpeDd6Vvx2K\nPB+LEFqYYAR1iE0QkwuijLG7M89J0KdxJNQp9IVx+bM3/RfySV4XbPKd2ReyojDlTrSTmhWungl9\nGnfORhcNJu43VQrhQFh2nIfc/61NFUW5pmK+QYemTXUdNuycbYQpxZWzPZTNblN+aKXfg7J6BXON\nXFH9bSR/S7D7Sb5g4Q/jnJZ5Y9WKuKzrGfJVZB8t7RLFQU5JQHbJA4uU6vizgp+9SZJcpLno2mVt\nGv148roqDyxCot5vRw54Ax/dB05FdJyUgVcd/3YyDqB4UOwZMv/fnZTPAbNk0U2vpb4r+t4Vsp2d\nlY7pGrOWqJp8TNy/Y7K6wTuVZpM137gG9x1y9L9Idn7aKrklleeFjUjdw4VO718uA23tJ48Qepji\nhE4GQIlNEK9StmbZID/0eilMGiPtt+L6cWf83lQXhPxJecEyFhhnEBPokE8YLSZgk+/MvpAVhckq\nIDvQjqEQN1JOqXQmCcxRF4EqpRRiE4BRx5lEaIh3V6YheDqeoNXtOKRCA4+1+kLCrjlol1RULZnX\nBsWdjQOC9kn/OmawYNGSprI80kylcgChg/Mk7etMkCr5Wcglucpc69jeT12VBxYhUe+3syfgWTGg\nf9dtkfw2gd1FcSzQyue4oqyxhbTtot/4QX9oyXApIos3UYzA26m5V6Ss4SRlLJ1W881xfX3a6NR7\nBU23wINnJQ2DenvZtYXc1/mJQNccp+hCsEIWTXg35QXC2A5bQUZSHt+FSU4AB7FpMO+pxQQt1H/h\n+CyyGDzMCTSjhRds8pkJCLoJ+BPgGeBp4GeAG4AHgK8De4DICnC6MK7QBWE/YOJK00tvE92F+UW4\nwldw8CdbDTrvhNtepnzmBgM3T6tTKJPwT9AWlTuRJCZuibIeIVvN86tz5yiaqqYm7pW8MQXevoKz\n4U/QdFWU5zL5YKVwGOhQ+/A8pjpaki/S+N3Mk+TO86UzYYbevzUNP8V4MpARo9148t35c2R+0skj\ndALZviLyG5tfRZ5+p9nL4hNkE4B73D05AdgAuyWS111C5hVkeEd0DYOmyWi/Uwl80EZWp2RHnUwJ\nv0HR8mcbCZ0r3xM66nKsbWr4yB8lsCHuhzpOLriGu2jHU+8tQ5q1zgh0l9/x9rxTcIGiPIEbrH5j\nNNfBJp8ZP3P+EPig+/864HrgTuAj7t5HgU9G3ksWxhV6LgZzFHcOWu+mVQi36Apfxe8xe+kmkfea\nBiGo3E3pO9XxyyQdNKj7jjb5hc9RNBuUzvIW7K4xytNpmwTlDcvXJkiIJVv9rmuTxgdIahqrPQs7\nrZRXjo/SIEiCprHpP9iBwTTLHry7StkiJrWD0ShAR5U+inw7pl99ntuc7gzPt5TlPUjFodZBWRrJ\n8Ja0jAXo8Cb3vQfwSrVFVRvF+Mu1xUXKpqzJ4GYR+VblFhLSUb67LnhF0nTF6bENsgXHcJKWDPUu\nytJ7G82y3SfMs41bjxznyrGKDE4Tcz1pXNaq8nRYzxWwFzqfoLnJ2Dcj958FXuP+fy3wbOSZZGHm\nKVGcqR90/zcOZFIh3MIVvtMUV7xDE0cZvEIqm6jQIuLQXcWYQT07YVQmD7M/biTGVsIkVveAflUK\npPDd4FoOAhr7CIry+Pc7C5wTlO9QXfkoBkXZaFOf7FtrlYOzZUx0GL445F3KB6D75O8X5Mxs6ru4\nJo6TyJ2+U0QW+AUmeRh9aeBJ+hBkn56nZKa3VikzXJ+4RLZTskbFmWZBuY8E/zdZCJXJW/BUDRxn\n7n6RKHcv/JWqfx1dwr4B9+yP6J6qM+7CgFwnKI59fNCRlN6SVh/HKU/SLdku28Nlfs15o2UbtQrU\nNuQ0Cd+n+lPAA3VuPXKCHeUX8Z0j45SV4hjocFf9OyKjLk9jgvYW4CvAZ4Angf8L+G7ghHjGyGtx\nP1mYeUkEQRRosZpTx+TkKwArRHbmCEzpiNtL++3e0iCBmgNBw3dEeQYTJCRWr4pnJxEmsRVcSb+k\n0A2/K66lb8PBlkJj1bX1iab1b5G3NBXYQr25ZrgSfoAgPHE1bdYaKbtlSnQYvjjkXYqDkKtB2/Xi\nU7HgE7TB+U6PUXapB1ITmtTOyVWKg9sTFPXkCbC74fMPER9Y+QXCk8H3/O78KuXFx5jfm/QR2xmp\n4+ngmYJupGJBLqYfptgmqci5vfFXqv5VdCHiNgBfeFTUxe9sliZY5IsEsUlTJW8meDRMTfL1k78S\n/0V4S+Z3NPbsPKZJ+J7kxkSBB2L8JMe80lWkcMyF6CdSp7UaZ7l8wsA8XY2zZGAhlzc2+fx4H+Gn\ngQ3gre76d4H/NZyQAccj71pgFfiESx+Wihq4dfjXcra/fW+RuTZvLf9ezi9n8s1bU99jNJDd9Qwj\nJRQrz+j7p7Pn17xSjby/43G5alnO7wuPut8fi/8+hOuQ3lXPb96atUEV/dpc19Ev3r759ej91vRl\ntPO0ZpvXv9k1o8HTmoXtexs8fyx//oHTrn6yfNvT72/emgvcbsq/CNeZwlmz8OCFXOF0kz+jAesD\np2HXs7l8euBUxpPd8tOyXzeR78O93ryV0cRk1zPu+t68v4+COhT4Jdc3azbnrzULX77MyD9kzfFc\nir/v2S/e3w57ThTz+/xDjr77QnmV0Xz7XldeR/8HTov3dwTtcyRe3t1fy/XFA6fE7zt75CdR3/tf\nZuSTN2/8VWjfHYLf3GJw2P6V+s+K6/1gD4vruvHNScHP5/P8vnzJ/b6R/77XL2jJ8dWRtL4c1Wdv\nOf/4eHB5ruPjy3byckTfh8vjjQL/uN8+/9AY/W1PXB5MWv/NW+F3zsBv2SzdfokpTNBeCzwvrv9j\n4M/IAoa81t27kQU1caS8OyKdVxsHlqjI368C+NDudSZj/vthtKwq5+3Uzoh07t7HAFd96uow5G+L\n979GS3M2wXdPZMrCnmrzfk3e6y7vaGCQyPMH3PNXiYcqHhTPzENiKuGLy7JE8NExshXr5JEKmiam\n++DkZ8Pyx/yf/Cr2SkwGumf8jtNJwWMrsTwT3w116wr5arOY2BVW0ZO79kQiTEa+dZosYMl9lA8p\n9u8frfrODHhp6sGhZlSXuqOFvFlsyXxf6Cj/+31kkRqlNdHzrq1SJo6rjmf2gn3Bfc/voF4m29nd\nIN/9OksemCIWir9kGh6Rua1dYOYhjSPjKB6h0MZ6qFH4fMq7l/vH6SsEu3ZT6gPuaBxs8tnxP8Jf\nADe7/z9BFiDkTuCj7t7HGCNIyDwkyhOyEeMQCSzRMu/Qjv8aDc9YoYECbFGOSl+1yfLOVxQ6ao+5\nGwwxhjlbwHeN30/RJ7gfBgaRviexd2MHiD7fVPh2zQPzngSd1+lwIEjczFny0dT6eX3ZFpcHYnRf\nhuR46jkC06OmPJDQrdI81/sG7XHyRp5fVvI9qtKJlN0DSmG6xfu9BdMhbpY3lzwVaw8KO4TpOpII\nIBLoqMp2SnynSZK8sOq+cyVRnpCHFioQk6B38vDuhrwsTBw/u4uKMVydHgv4S+xYTha8hw7HliQ2\nXqY1QfsJ4HHgq8AOssAhNwAPMkGY/USlBhvxLWCcQxRXWVbJB12Hm9ShQoAcnCUtqPFVmyzvzido\nczcYohhaeKXluzK88wb5odCS32Skr4IgTQjYWHS16LkirgxhwJJLFAdLqciP7ttfeHRofblnfmg0\nCGurMCjvSIQTQel/05kzdLM6L+YEjWIQg0Y70ouQiPsIlQJ01PFAQj7F0qXE/UZ8TNQfqn3gi7Z9\ncgya+jKeSpVhnpOboIXB0UqHf1e0TTgGS9JI5BEech1L1xLfi+nK3YlyroY81je9O+DJUFe1OTMv\ntut1V3AWXu15tjXfkHKj5PvXpr8y4diS9OLBIaY5QRu/cdOFacgMh+qIOmNmDR2q5YGHqclWMpCI\nyC90XL5EZoYh73nltxrm1YYJE/VKmoYMJYk6jhWpp+eyrzCmOVvAV9IZNnZQtEynKAeP8W284nj3\nsOCth0mYnJCvXoU8aZ2ATJnQzt1keko8G/bV2kEY5d31JP1IrtaNzgBKpaVrkym0cXSxow1PDCXR\nYs3vfpgAACAASURBVFEwIldkMJrGQRIi+RwVecUCOcSCfNTycfAdHxRknMAXU5NpQd7JACnzngR9\nV0gc/l3RNuE5Z01cOEJd+RTFgf1VsD8b5uX6Q4wHd8bKGciCzo9i6KmtpKtFKxPAWBsGPB4dO1T1\nv8izfux6JtYv2/RXWkwME+/HFg98cuN3bPL92TduujA1BBrkICLohKlVNzmo8it1qZ0JKajCwa9U\neOEqZSGvNkxYUa9Bn0cX1HF9yGXtuN5SaEjzHz+5Ohn8LfSdSJ+S5hkxk54kH1Fe5R75nDQo+1K0\nV1D/Ur8kPgirGwgmJ8Gp77j7VZHKlrJNptDGYZ9oE5Z7MLotUrbK8gVy5TjFaLON60d5ABjKogvB\n7ytgX2pK78h3JuL7acq0WN5D5peO6tzKuoQxxiqOZw6Q+bHFfHOj3w1o7yeSVcdENIr6PE9pHHrX\n5FdL9zHLF/WJb9NfJ60r5cUDP1cQ0byxqfe/jeHjdmAn8LK7fhy4o6/CGMNdxrDPGNaN4WFgG/B2\n4G7gPcCd7vd7gZPAUbKjCP4M+BZwwb1z2WV5FHi9MdxrDJus5SRwiuwg8K+K584BR9z/G8Cj4v3r\n3P9PktPmvPs7Fr2s5aS13ObK0ymMMbd2lJWs449Po6wDxRGydr+R7HgLAAv8B2T95OfI+PEnyGkE\nGT/dQdanXnL3Hgc+6B/w7Q6cdreuuL8bwPuN4aIxHDeGPcawCXhC5H0P8GZreaGi7LdnZfvcceBp\nYzgm8loGxPqlvPdPK/qdf+4K8O/H+A4wyvcauWx5kqzt3jPLPtShHBgafJ84SSb331VD14lkdZcQ\n+u1e1yel/DgLfJ8xrBrDIdd3DxjDw8ZwBngHcBU4QaavPM64v6X6JXjAyQjeZS2/RC6LIOPVzfJ3\nJ29+lGyccA/19A6/8x5rORnqdvH33hr5VMinwXfbIJb3YPilC0R44K3AAeDHanQJMN5YxVpesJY3\nWMt7yXTpPWTjqDod5ml/HPgHwN/hxnQJHvGy4Eng15qWb8gQY9R7GvSNJrgd7l6jfuzQtnx/j2yc\n88sBb5T6lOv7h8LxSFveishPP1Y7Cfw28E1XJs8Xj9dUZtaz7/RscZaz9glm5/uqVgWD3+XO1nMU\ndzS+SebMuBHmQ3lFfZ0s2pr08fGmlCnH2U7oxRTMb5jQ94Si+dbz9BRdqyf+C83cYmnk91HDH8+l\naEdmRhMzHSrwveCz1TZ8EhxMuVArwVV9hkgUq9i9RL6loAY1z8bMgVYomsX2tvM8qRwYamore7uQ\n1V3I6YhsuQb2IbJIeUeD+1VyIUyvkK0cbwvL2IQHHH2mElEtoF2Vz1unftgTlvdrTjY3Ch42tBTy\nalM50AWPJ/KV4606U+SXyNxNXiTi3x15ZxDj1im0YSOaNW3DLnVBRI61NXceezwS0oX0fEC4QmGT\n+c2+YdOFqSH4ObLJTK9CibLZog+z6sOmXxKN4c3PrlAc7B6jbLYxMlmi3qyh8tm6zjAJw/VF94oy\nNRqwLkoK6h4bKEnn5+0Bf/hJVCx4yEWKPmaxhQiZLlc838TfRrbbYP0cO2ijMBJZ6bfg3nNVfbaq\nv7co31Kbmc6g/WfqU8YYA5JEPjHfOS9H1hO/eRnkFxq9/LkUXHuZ0amspugjd4CKYFxgnyFytElE\n1p2MlP35WbZpTZ1bRwAeUqLi8O+a96YyFhHysBAyP+zHNTpxqWTpuDokbENqfFzHkaXBNy4SLELH\n8hT1mWg8EtIluE6YXGKT+c2+YdOFqah0qDgu9NUZKPqIyUGmVD7XSK8yurMPCgyxgYj0RWTVhVxB\nXga7JShPdCekC4E2bkecchvUMn3wfO9O+F2VQdRd7ryepexb5AOCrJLt1F6MPBOm9ch3ZLTIMGqa\niERUzSfEV6kPMKVV8QHxZ8qhfTQYCJ6vCxMd9nc/6W6jwKqOCem9r8xzIpsESNk/9Z0XEot3Y+QT\n20HaT3kn3lLWb18i01FbHG+Fx3acnrSMRBZqqR40y8WOVYoTrpiskz5t28l0sr8/k1Dpif5YGMAy\nQQTgISRqouxV0GIqY5GApiO9RnkyIcds3popGShjkWUpY+4Mhm0Y6b9+0XKSUP7+G1ept1CTIfu/\niThDb5z2C+lCUdfG9O76IkzQYoqj992SgNm8CcjVSFljA1pvtnG0SZ2oUBAxhot1hjHr2PkWPZOb\nOEaZvuL53ncBuyqDqK+cmMYCenilUrcT5vm1oOzFd1YoKq8L4Tea8Em5HLue6ZKnhpSqaEHETDHg\n59o+G9Byoh3kkC9n2VcmlQNDTJTNj6ceGEDwzERO9kKmPEVmwrVb6Cs5OD1BPnnxg9TUQoQfwO6J\nlbEND0Rk2TrxQbP/rpSLsp9sJGRdMnJjk37ZUVtW9Ud/b4WOD7SfZaIUZW8tKmsitJiauWDAR/57\n4WRCmtqu1JVllrJ0XlLYhjmN1wpyJML3bUL5hzrWy53KxeSavjfF6KzY5HOzb6B0YSoq4zv01baN\nNStmE0JTKi6vDCyJE82bCH4i57U0yWOaAm1CHrh1xu3U+y5g12UgPniQiwP7g998uhY8s4UaZR+U\nfRv5TlpjUwCKA7bn4YtPsYAri+PwAsVV8r3U7CoG73vZWDDPqfm+XBncE5RlZn1lQSdocmDgTdnH\n2umsaLPkRGLCstctLDxPtkBz3PHp7hivurI+jDioOpV3ywmalGXnyHSuL9dRV6YXyFfBD7pnT5JN\nOL2M/NkxaF+oT5v2afktX8fwmJPkGGKeUkBLN1aKL9YJWtTKtnHpL97bQ/mIGX9Eie+78jzbA9T4\nvs9Sls5rYjTp/fxDkkaCdkdFf27TrmFE2RXx2yoRn++wvabZfiLvk4swQZOr+b1NOGJCgMJWpT3s\nmCEM/nFGdOyzZCt9R4SCabMScz4UDE3yWOY0BPpMWoYa3vOKRB7LsEsow5fIwglLZX+VbHJWNfAr\nnaUV8GIb/wFpmid3xCsPsp3HVEXTGC9QNuGuO5sl3EFutYsWtOFRGgykNTVu+xWywdtuijs4Uf+r\nOl5JtNnMV+OJByc67e6dJzNpjPnqdOkrtMnJtYOkfcjkItUrAZ9XlomyLvdmheFOXMwcuBMTSNH/\nDov8WsvboaZQf1TJmjaybVyeS5Sn0JaUd3PClOKnhZelTeVX3fORvnfRycwTdXSuoH00sFDQntIM\nujC/oONgPEHd/bdW5n6CNi4zTIEZZcPG7JRjaYPiWVUyNfKlI34WXC+Kemipb57oifdittRHKA4C\nj1KeCIVRGderFBvFiYMfjF0S162ceiN95Urq2/OcqmiaeF6200aMrlU0puVKH8WV6b4H/QvbdxN0\nLvhfNeWVtm08hbrE9FwsyqsMKHKSGZjhie9dCcpyWNCsia9ySpcfiuR/jqJJZa1VQRt+p+zWsRC7\nMBPIKmltEBvghzuPTScMsYBsqZ0UuUBxqk09Fi2JdmjlI5aSdxV9L8r/bfpSTZvLhZAdwXOdBuNJ\n1x2bfGf2DZsuzLgVnCFTxuyUvXKIBWBocm93g+9uEkrCM83cCgacWcsknWwoPNED70lF4mz4Sw77\nZ4Pr08G1H2CsBPmuOj67SLaoIFejU0FvmvpD3kUhvPvawg0+Um1VxefuN7+AU3JobsLztFypFc/7\nQasc1KxO2ieb06lw1MJC9F3iq6RR/6sYrzRos6m0SQMe9QMxPyk7Kv73Exe/aCMDhNTsBrcycUwN\nzmM+uKfJA5b4neZTCOuVSP6xAEzHKfvhVun05C5XSjYm6uh3/PazQIGUYnxcxQPh8wENQ5/+0u5X\nA17aE9I38k1pweV3ZbbR4GiUyPd8BOW5XpSiPKFqcuhzyVUnp8sev1MW7tI/FeP/Jn0pQnu/oOnb\nczXouzuDd7x8u4oI4tfmW8Fv4VjLPYdN5jf7hk0XpkHl+15FlBMlP/iSAsGbkHmhukf8ZslMM7YE\n9w60+HbvZp4d8cCtrk4TT6765okZ814Y2fNUwEs++VWh0EH/jHhmV5hvROjWpaoohVUOuNZN0BZq\n8JFqqyo+D347nKLrNHie+KBmZsdWwBceXbS+G2vrWN9N8cqQyp34bVeEZ75EOQpew0Hb2EFCYsGw\nnqBo1hjWo3JFXLTFXvfMyHdFfMMP2nxex8j9zifut0EdezujcLa8N7YfYqyNmy54TDT2aPt+Wf+N\n992hpKDPNdLhAQ12FO+teX5foWiOHF3waKMDK+SGvH+cyvHKWO0c8mZirIVN5jf7hk0XpkHlV2mx\natEy79rdHOLOz3Jr/RHK/hwlZSUYcLBhcpvQo4N8a81OGuSxwgAGOD21kR8UbZAPHJ4IaeL48Dny\nnZoz5E7OckXPO9Vbka+lPBE8h4jwFpQpFREtjAIXfX/eeTyWJ/nEeAPs5ymu5klFk+TlCM+XjtYY\ntz5BGcbqk2PSahCTk47rFNvpHrwpZ6zcNXUKTcqOiGemIpODb0ofMdkfjlTUo1F4eiEvR/1L8Kqv\nm9xBaVTfJvxe1Q6a0mOqNjTugs5N3ic+1vE69QxTGMfOsB1aj8UDmn2NzCzYW+Y8Qb6r5PtpMjhM\nqp1jslZ8Nzznzt+vsmxoZbGWkJVVZXps7idojGnv2vIb0t8mGhqZ6tVRuaIY23qXpk57CRyd65hs\n9u00NUfvwipKE2E6q7LNWyKPHCpNinaI3yUfxZzOmyS/qiVXyHeNUdZVsoWJwy6/heTxQI48774h\nzSguBv9/nkDRBbTxSkvKvueIHEzcpD4xugcyaiaTpiG0/5TqFZP3su0ODbG+otxfIzjMOcYTxPVe\ncseni/YmHxSGPt1hIIdoOUiEpw/LRoODv8O+1hU/J/hnofpIh7zaCZ2n9T7lsU7MTHYq8mBavNNW\nppFYTKdsyrgjoJfUk+MGfZFjdBkg7Xny8xQvIs4VFvl4WbPXPd/ILJXIxLWiTI4W2GR+0+hA1RVI\nF6Yh0S3F2XYnDBgwXOttVfFbUmhTHLxNZKs+/Xaazkpelu/aRPlOq2zzmiivEMUG9ZfE/5a0T5lM\nVSvmbXdpJE8fgQfkrlxfPC6DC6x1IVMoH8Iq6XmVsvN/SRGVaVV4fgPs40E7rlHejWtiQtXb4kZW\njrXeyzH9OhbaLlrfUE9MsTxNrESknDjYIK/kjlXw/DmR7+78/kTnoPmxwCbGCExCYuE3+E70UO2g\nr61SM6Fr2840mCQuSmrDA/OUQnksrsPJSedtOy05TznicB3PR8sR6LX9sHlrQK8D7n+vm2t3ymI0\nF/er9PJ6JG/ZRkmz/7AcsfqmyiT43ybpPXumTRemAaPLgc61FNHGZDy/BV0VhanOl8Azrx/EhlH0\nZNCFZHCQugadTTtNZyU9y3f73knynVbZ5jU5ehwJeE32l8fI/SS839crwTPhJOAw8cNcxwonTXES\nacXgvE8eD4MLTOx/RdHf76ios+z78nDwNUEHP0GUg97Qj9UGecmB5VyYUDFyFl+rlLfzngStn6DC\nv5AZTZopr1CvBG2yj6JefYVE4Jggr1pfKYq7yAfy+5UBIlLRSp8gOIMt6Ms+dHZlQAbKEz7fB73e\nLpyfFLyb8t2NTuhS7RzWMfFsbWTXeU5dTNBSdOy3XiVf5K+RuSK8Qn4kzlTk8LTkPMUx7YW6b8TK\n4drqEbLJ1/GMtzdvDfpUqJsLu3QpmRnSXNyX43upU8+RmSunJlk+YFpUV4XloLxwU7lT5/jfJuk9\ne6ZNF6aG0WOhbisF4iSdKfHMMwTmH4k8QuaKRdGr2kFb6AnIEIXpvKdAMOwRfOdNCkNlsUI8SmNl\nJMFxBb/4vhSUvQYIIV91t2QT14n9ryhPlsPJ1GNkgYLOkCnp466NtlFctbtCpsT2UG+eepmGZqN1\nsiWVB3Gzy7H6LxFn8UVMFM1dVkj7DcrIZmPTtq79KS90rot3Lga/yUiwkp/95KfRzpn4dmu/a8qD\nn6oF0lTo7CayTMrJ1rxJLkcukxiERcqYNH8Knm0U2XXZU4qOQ0oU5fsFxtR/Xcj5Ceog9fdK7Bsk\nzBoTbRXKFa9fQkuTVP9oKn9k5MaHXX8/FOnzcpJ1jOBs2Ui+4S5pVdC16LFaU5ugAd8O/DXgIsJx\nA/AA8HVgD9CqMA0JLLcnTzDDIBs0PBeB4kqfjKJ3Stxf2onJPAjTeUuBYAgnCSnzg5iwrZykTCr4\np6U4xiyLXEjZ0VXZKA+EpSyIDczCQXCYdpBFz5O7G+HELzTNGncHMDVg3Jco6zgR0HrfxZsRf4WK\nP7aDUpgQTNKGde86/vYTsbOUByc+HQzkgPy/kc9Z5NsrRPy/uuKTQP41OkOMiJwchzdpHto95suX\nMskKF7QWuq9MmuZBpkRkfKcyekZ1aOt7V7UwIgNwpCIJR3fpmpSjadlC3qmQJaXYFFXlID4OiNAD\nmyzvZI3F/wT8MfCn7vpO4CPu/48Cn2xTmIYEXiGzT515FDjBONfIJofS3yfqdO+u/UpqK4fDRU2L\nGF57KImEbwiRVbfEgGFGQSI+uyssTw+0ikZ36iBfueN/1CmZ48QjSFmKZhdhGO9R2USbboD9WcpH\nfkw8SEnRJMh7okFjzmObt8b4clFSRPFXRUP09B6btk3an2CiJN4pLB5SHKR4/TVR+eLlaX4GVuKZ\nmFzzZfTm3E1Nfv3q+igSc1d0ryh76XvU7EAsWqrigRa0nNnC37gyy7Wln3CMrXMa9vPe5CoJf1By\nC7SjZOP3EW8HY0IpYzrl/1jZqniH4iJ20wWbu1yfPu7k5kVRn9nsoAE/CDwI/CPyHbRngde4/18L\nPNumMENPjllCUxA5249Gs6E4a5cr39FokR2Wt7NOOklegmGdPe/OJ53iLE1uZ1mnRUwUnXgPkg9a\nJA8+1wcNi233xadEefoKEhLdaRT86sN4jzsJeY7yEQX+G6sUo1qGYbxXKPsVvkgWxGGNYBAtvtlF\ndDNpRr47zLuL72R5fnYXCxwIQfDAebJJ9SsEC4sRHtwh6NxK1jVtF+ITgORAiPIuX4cDpuY+aIln\nYivijfkz4OtSXi3aeZzV/GjQsKAcR2Ytp2edupigzba8jaLlFtxhBC/voRhRsLWJdxN+G5eXG3w7\ntiASmr9HA4CRsEDL3v/iU+Qmh8mIslXlaFj+0m53VV5Chjc+0oZyIJVvkumAwiKt4H+bLO/4DcXn\ngZ8E3ikmaCfE70ZeNylMQ+bwA32fopWekPH8xKHkZExx5fsUuZN/sjME78jUqnPWMEXJP66rTko8\nqk2bSdW+SN13BvcbhZulwXEIy5wobslfJlcQctUtaZIzruAbgw8aH2Y7zfIRWY2M8Ou4pijngnwu\nO3l1gIQSC+p4RLwX9p/tsT7fUTtJv5dkJL+O+aETX+KhJcrKOnZAcsrMbVqDrGi+qb6VKt8MaNdk\nINxZ2SbJq61ccs/LfrYzUo7TdfXXNPsk2icZ0ZhgMhLw8qVYu0+pjJ3ussX6JOUFBSnT5Vja67Fz\nFHfWUvIo6VI0jmyk7O/rF8EqFwkb1DnU33ITZ4PIsSDF57HJMo/X+GwFfs/9f2tsguauj0fetcAq\n8AmXPoxYQXH5Ra8ZhWZeE5UdXW+ve7/qOif4moU9J9L5b94KD4gG/fxfwP0+It5j2e9h/pu3MlLU\nD56V0cvK5fnsLrhnv+80FfXfHpT/ZF7e+1/OO+mahV3PMBp8jkOfe/bn9d17RYbHbvb+aPta0nNH\nXr66/EbmcOvB93eM296Le73j8XL/uP9lCmZl0pwg5Nd79rdv38b9dz3L+8GzZIEytsf7S9V11+Xb\nvNVFFV3NeOwLj2Y09PR78Ly7bth/Cv13o0Jeif4U5n+/iLB5/1F44HTx/T0nyHberon81rvjp5F8\nuwr3/DVs3joNfs35Ye8GLrjC9PvHrK8fOCXa+wq867by85u3MtrFGclzEely99di/Jc9c/8r8OXL\njBYr7z/iVqOd/ojpE9n/t90HX77gBhJXpXyuKl+C3yO/T8QfDfTXqP9OoN9G33MRhuv4XeqjLz7l\n6Plw3j+/fJHR7nsm3xgNhr/wqKPnvvz5vVcYmTHf+4Jrz6tZe9bVX69nfz3qDw9XjMfOO/l+FX71\n1xhNmPZehb3el/ip9vqv8XhW6PtG4+nE+Dns3194VB6TRFGenM50x5p1/L8S6Gv3rT/5y2J/GOnb\nI6I/bQJ7wfWPq6F+yOm565mm+gnsIVHf3VkZRuNxV+YYvcrjpervf/lysb6y/g+ehTf+Nvn8ZxWw\n/v0wRW/WJeBfAQeA54GXgHPAH5GZOL7WPXMjHZs4kt6JmjjoBsUVB293Kp0YkyuKeWeo3HIOTZga\nm2ykvhv85lcuRlGympSrJW2OUQwL3nTVZRPZhMxFxMkGHC7V7qRQ3tGwmfJavBX3SRNlk6kNyuYB\nTaOhdb2DJnbutu+dkBe7Dh8seWyHSzIgUdNVOpmPXCmNpWiENgLHZMo+NWGU2FIbT0iLFcY8KLTd\nd/o3c512Em13iYoIf3X82OCZWEoFJqmKNDbiuzHKOUbAmMl80Hpq0xjNvB4LIzZHV9yFHNsI7p8M\n3l8fWv27p+d8mTgKPqgajz0StGuoly3iuImhlV88E/Jtym/9SIxnxTcKY+lQvrlFloeDbxVoGJSr\ntWwgOOuYsq5eSbzXylef8o7ZExSPNZruDlqQ+TvJd9DuBD7q/v8YHQcJIR/o73bpBbJBVBcmjjEf\nixX3d5XiOQnRxqEb35WqTl/FFCu0jJLVokyrFMNFS5qs0/yUdVf+bfcJOu2luSO37+THplHPRUmC\nXq0GhXU81mG5HpOrThPwYpcTtKoADm0WI6R50l+Q+xs8QR6y10+05HEIMiBHwTE5rDPFharWbdyg\nDiVTEPGbNKssnB/T/jv3e3oUnMkXKTXpT8T9OtZD2lA2w4+For4k3xO8EjXHCnjJ+x5K85+kPqvi\nk+b06X5wHqNnx/nHBp3bHI0vBPRcC/psuKgrAyKsUjRn3j+N8g8tzfEErdVCZ9DXCmZ+UyhblTuM\n9Id7PiYXquqRyMtP0I6QWXd4meH7RWGcF8o3CrtS1suxh6q+PQY9/KKj75cH3fVlRjt0cbeBFD0p\ny+RDog8fI5+fJIMrzWKC5qM43kAWOOTrdBxmP8EUcpX38CSNWMPQjVYJKa+sjROCenCrhkG9vP9Z\nuIrfuL6U/TIq3xM0WSHisKkpSq/B0akL3m7aF7soW115YzKD8mqiDPogF4F8BLdLYX0izxVs5MkX\nqqZyjlxA44JcpXxWm/+/tS9FIEMa+aAuYgrofci1rzzL6wKZspf6Tu7uvkh+cPMjQV4rjMyxinwm\neO0Fl/dfUH0URLiKLX+vOtdzpoGdpiUjApoVrGEitJLptOvn18gGnTL4wRaRh9SLLy1rf1iERFqf\n7CKbGKxM+fvJPkB5PJfsKxFdFOo7mZc81Dkmp2RwslBO+YVI+e65kIYd0aOqbHJHe72CZn5CJvXh\n+Yr8k8GVpjpBa0+odGEmJPZESj7I8xxicEvDlXSKKwDJFcUYow85UdwVkLS2RMxA6+pHcaBxknzl\nIbnzKPKUq8YLaRbVUZtNdZDSY71KOwsd5h0LFNQqgpy7Xxu+PyLDUiuU8rmZBNII5FhYN6/Qr1Jc\n7d8R5NEkAl/4nbkO+hOrs7hXsjSgvPosZWs40AmTn8ClzO8LbUdRhxV4uwEfR/VZEz6v6icz4N/O\nzKDr+Fl8Uy5a+BQG+ZHnGcpBoNSLpUNxNS1GaiIbO/hGUk8Gv72Yei6SZ6kfEx8bxuTUZYqTn9Ii\nfeTeQx3231Au7iff1TpC2R3hKvnut7QUOJPo18coyuzjNDySZBEnaDH7bdnwrSdGkQb0yZ9hdLgB\nAzda2Y4x+pATmUI/T35EwCXHdIcQK4Cp+lEa+O6VSuwSxdUU32HCgUxom69nqFW3WS+R1xqW7S7p\neNzy3UaHwo5ZLqkgLqf4sY7GTg7I1bTS7oJ49ygRM23H8zIK5CiQxgzaR67mX3HlW3G/bYvIyP2R\nstdGKnPO9lIWzPWglEiEWcqDDjm4kXLyQvDMy5H3pPL3pkMh36wK2o8mVeQr4fJ3yyhYU5KPk/qM\n8m5x60iLTMfEsVMLAhpEMRb0DY/V2E9xJV2mgu8oxQHe0S7KPg9pGjww5MQMxn9UR2p+OOCzRmWJ\n9WPB93tEPj6dITNtDGWbCyAi4w9s3krcZLsT+rhyyro+T34GYShr5VFY4cTxWvDXOnm6Imjg5XOj\nMxUXcYIWKoaQAVKKItkxXJ51Tv1dMctgB88N6FZLk7B+lLaH18I8ZPudCfMO3j/OlEy7FikJwTk4\nOjGKHhXnn5p3pxnEJKYgooE86mgc5FWaoIh3U6ZnsT43s8UcVz45SV2vKFe4exY+kwhywa0UB6Xz\nvoN2LKxzhKdSPo4rgf7ZRT4wkO1w3D2b2vXaF5ahpm12TiIrmvTH6n4yncF5ij4d5JWUB+7ZcDd0\nB/HzU0eR6cS7foBX0oGLnJZwgjb18V/VN4LfGu3yuPeq9N0mweNnA7l3Kfh/JczP6QJfllNNyzQB\nTR5OlO9kSJOIDJfpWLw+zeXPwk3QIsReoVk0wEqTDIpO+2HDecfCVSbcnq5i9Ip3ejOLpLy7uFFD\nx1XiQQ2kQPDpGtgnyWzudxMJnEC+JT9y5tQ0bJ5pyE/jnDc0zSAmnvc8f18E64/ciJoshzQW10er\n3qujRaTPzTRggKuHnxh4c49VysrKH7Y9Mk8W/dX34xWR56Hg2UJAlL55syP+kTtXYQTOpI+jePYo\n2QBij3tnhWzF9yhxmRrjm9jATDrK+4HURMF2ptkfJ2yLRuaXLfOqjWLs2upC+O2gT5wgW2EP+0K4\nG5E8Z0vT/KZZ9Jmqb8jfmpaFClNt8fsjjve3UDSj9ME+/OJSKuBGybdzWjQR5btCvkjoyxeOX+WY\n9ap4775UGSkFQamy3sMmyzx75kwXZhIGDImaeGeVCtOlCIOEpnf+nUYz446Zq3JGzvQOrfXBwBz5\nSwAAIABJREFUDF6iuNqdDMNNacfMHiAbXBwg206+RNkUxIrOcyS4p8EEpsAzPZZrLAVVJeQ6LJfk\nPWnqEDW/o2j+EIbuXae4oFNa3EnRwt3fRb4aOdEgcwwax1YNJW1eJB7y/xRlP5zYTrjvyysUzdFW\nifijTrvtp8XX4l7IB4ecDPWO9XuoCOgRkal+8ibp433XSub4xM3Eo3owyG9mvDflvjy2/INmA1rB\no3somlMdoag7z1HWf9dcOkbuNjA1c25NM+fH1EJeJ/Js3Pzq3qNaH0j3lTCAkeT3QoAMBjAuoay3\n1lPlc+3lTb0fa1J2ymPWCpNTbDKf2RMmXZgJiP0MxUFBysRRDqakqcJlxMRGMF1orvAELbaEO65j\nXbhTqXzXO/yuZNaLogxROpB2qBRpTV77csdWG6+QDQRDh/moT5CmdjzTb9nam7UE/XeHuN9UycQC\nNIT3jgnekzwXM1O8i+IkbndIc8oDa///c+H3g3z94Fjy/iwCLISTKLlieEzWzT0vdwb2Ux54yt2k\nYFdwzSvAlO/fqM4MQKl3SNewjiFPeD6JmUOejtEh0m7yt9jk7HTL/CaKktylHGhB85kGCwloljoX\nLZZCWXOBil3SRUvT5IGhpFB+VcmzKh5L/R7I0Er/RXL/5o1AFoUyIzYx8+PmmH6LpViQkkjAouxw\n6hb0nGiCS1EXSR0lrQxOVZT9MvnCWqyN1gM6JC38FmqCFjaMuw6DTqQYUzKbZ0z5rheM4aTkZbJQ\nxNLsZNZmhnUhv0sHVXf03dDU6gLZSm+4g+kHlXLi6yP4eFNR99uaZ/7dFE1CLPFV+ZQym7uB2pB4\npt+yjTVBk6t0u8X9ysF77PcG90KeWysL1tLzzxM4BlNURnJRo8qJO1aOmZgAivImFlfsQcdXfsde\nKvhLoq9fJVBg7j2xs7D3ivs9FbHwFfKdtZLpc988PCZdUwP2UxSd1a+SOdhL2j0naBWeTyfl9AWX\n3xGw3yAeWXBXi/ymJm9DOUCHOwt0LP+oWQgWNDtCZn1ziNwk8gmKRyf45HfOSrTuuvxDTUsyQQsX\n7qpMkcNFvaqAaV53hT6OlvQiZmx8FZ7FWTXxkrtN4UQklsJAcSuCv9131lK6O2UOOdaCHcVdbn80\nicw3eQQU8aNxvOwuWK8FNPZBURY/zH7YMMH1NSp8lIg74YbE3k5cmfZ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f2sFw72Ohrs3Z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\nCCGEEEKIiiAFTQghhBBCCCEqwv8DzqC44GmelyAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec6ac10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.groupby(data.t).t.count().plot(linestyle='None', marker='.', figsize=(15,4));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NR_NODES = classes.index.unique().shape[0]\n",
    "NR_INTERVALS = 150"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purpose of this experiment, we divide the timeline in 150 different intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data_binned = data.groupby((data.t / ((data.t.max()+1) / float(NR_INTERVALS))).astype(int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "t  i  j  \n",
       "0  0  1      15\n",
       "      2      15\n",
       "      222    15\n",
       "   1  219     4\n",
       "      222    15\n",
       "dtype: int64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def create_adj(g):\n",
    "    return g.groupby(['i','j']).size()\n",
    "\n",
    "school_adj_series = data_binned.apply(create_adj)\n",
    "school_adj_series.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We transform the $<t, i, j>$ triples in a 3-way binary tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "triples = array([(i, j, t) for t, i, j in school_adj_series.keys()] + \n",
    "                [(j, i, t) for t, i, j in school_adj_series.keys()])\n",
    "\n",
    "X = sktensor.sptensor(tuple(triples.T), ones(len(triples)),\n",
    "                      shape=(NR_NODES, NR_NODES, NR_INTERVALS))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tensor is factorized using the alternating non-negative least squares algorithm with the block principal pivoting method, proposed in [[2]](#2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.seed(4)\n",
    "\n",
    "X_approx_ks = ncp.nonnegative_tensor_factorization(X, 14, method='anls_bpp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of the factorization is a set of loading matrices $\\mathbf{A, B, C}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = X_approx_ks.U[0]\n",
    "B = X_approx_ks.U[1]\n",
    "C = X_approx_ks.U[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then group the rows of $\\mathbf{A}$ by class and sum the values, in order to check how much of each class is represented in each one of the factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DLwd+WHX7A8CdETEZeBP4VD/23czMGtRsN848YEVEtANExB5J84FJVWddHi1pVET8FkDS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\nrAQc9mZmJeCwNzMrAYe9mVkJ/D889Hz6XmVlSAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec50f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfa = pd.DataFrame(A).groupby(classes).sum()\n",
    "dfa = dfa[dfa.index!='teachers']\n",
    "\n",
    "plt.pcolormesh(dfa.values, cmap=plt.cm.Greys)\n",
    "plt.xlim(0, dfa.shape[1])\n",
    "plt.yticks(arange(10)+0.5, dfa.index)\n",
    "plt.xticks(arange(14)+0.5, arange(1,15));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The activity timeline of each factor is represented in $\\mathbf{C}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ODkZxfX191q6ri+d+6b41NMQf0erq6sraBw4ciHIzZsyI4u7u7qx95MiRKJfu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\nAAAAcjBZAgAAyMFkCQAAIMf/B9HDbL6NxXd5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a539d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(10,4))\n",
    "plt.pcolormesh(C.T, cmap=plt.cm.Greys)\n",
    "plt.xlim(0,C.shape[0])\n",
    "plt.yticks(arange(14)+0.5, arange(1,15));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also reorder the factors to show better the results of the factorization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "factor_order = [1, 0, 7, 5, 3, 8, 12, 2, 11, 4, 6, 13, 9, 10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a3ac90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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R9BtDMQAAwCkp92M4d7+xQNU145ALAABAxWEFbwAAgBxMlgAAAHIwWQIAAMjB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ba3910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfa = pd.DataFrame(A).groupby(classes).sum()\n",
    "dfa = dfa[dfa.index!='teachers']\n",
    "\n",
    "figure()\n",
    "plt.pcolormesh(dfa.values[:, factor_order], cmap=plt.cm.Greys)\n",
    "plt.xlim(0, dfa.shape[1])\n",
    "plt.yticks(arange(10)+0.5, dfa.index)\n",
    "plt.xticks(arange(14)+0.5, arange(1,15));\n",
    "\n",
    "figure(figsize=(10,4))\n",
    "plt.pcolormesh(C[:, factor_order[::-1]].T, cmap=plt.cm.Greys)\n",
    "plt.xlim(0, C.shape[0])\n",
    "plt.yticks(arange(14)+0.5, arange(14,0,-1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "References:\n",
    "\n",
    "<a name=\"1\"></a>[1] L. Gauvin, A. Panisson, C. Cattuto. [Detecting the Community Structure and Activity Patterns of Temporal Networks: A Non-Negative Tensor Factorization Approach](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0086028#pone-0086028-g001) PLOS ONE 9.1 (2014): e86028.\n",
    "\n",
    "<a name=\"2\"></a> [2] Kim J, Park H (2012) Fast nonnegative tensor factorization with an active-set-like method. In: Berry MW, Gallivan KA, Gallopoulos E, Grama A, Philippe B, et al., editors, High-Performance Scientific Computing, Springer London. 311–326."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}