judeges-model-and-data-analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model for the Judge Panels in the US Appellate Court"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we implement a model for the voting pattern in the U.S. Appellate Court as analyzed by _C. Sunstein_ in the book [Are Judges Political?](https://www.amazon.com/Are-Judges-Political-Empirical-Judiciary/dp/0815782349), where he test four hypothesis, (which are?), about the judges behavior and arugment how the court dicisions support them.\n",
    "\n",
    "The model was designed to use the Entropic Dynamics for learning agents and the code is based on the implementation for the opinion-distrust agent models.\n",
    "First we present Sunstein's data and perform some analysis of our own, then we implement the class to control for the initial conditions and interaction details, them we proceed to investigate if and how the his hypothesis show up in the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data and some analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data  represent the percentages individual and panel liberal votes in fourteen case types here and can be\n",
    "found at pages 27 and 28 from the book \n",
    "[Are Judges Political?](https://www.amazon.com/Are-Judges-Political-Empirical-Judiciary/dp/0815782349), from\n",
    "where we did a straight copy and paste to this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:08.582107Z",
     "start_time": "2017-09-04T16:20:07.622701Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>Panel composition</th>\n",
       "      <th colspan=\"2\" halign=\"left\">dd</th>\n",
       "      <th colspan=\"2\" halign=\"left\">rd</th>\n",
       "      <th colspan=\"2\" halign=\"left\">rr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Apointee party</th>\n",
       "      <th>D</th>\n",
       "      <th>R</th>\n",
       "      <th>D</th>\n",
       "      <th>R</th>\n",
       "      <th>D</th>\n",
       "      <th>R</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Case type</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Affirmative action</th>\n",
       "      <td>0.81</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.83</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NEPA</th>\n",
       "      <td>0.71</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11th Amendment</th>\n",
       "      <td>0.73</td>\n",
       "      <td>0.44</td>\n",
       "      <td>0.54</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NLRB</th>\n",
       "      <td>0.75</td>\n",
       "      <td>0.55</td>\n",
       "      <td>0.57</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.50</td>\n",
       "      <td>0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sex discrimination</th>\n",
       "      <td>0.76</td>\n",
       "      <td>0.44</td>\n",
       "      <td>0.52</td>\n",
       "      <td>0.37</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ADA</th>\n",
       "      <td>0.50</td>\n",
       "      <td>0.38</td>\n",
       "      <td>0.45</td>\n",
       "      <td>0.29</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Campaign finance</th>\n",
       "      <td>0.62</td>\n",
       "      <td>0.37</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Piercing corporate veil</th>\n",
       "      <td>0.60</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EPA</th>\n",
       "      <td>0.76</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.54</td>\n",
       "      <td>0.55</td>\n",
       "      <td>0.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Obscenity</th>\n",
       "      <td>0.44</td>\n",
       "      <td>0.33</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.29</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Title VII</th>\n",
       "      <td>0.54</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Desegregation</th>\n",
       "      <td>0.71</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.77</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.71</td>\n",
       "      <td>0.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FCC</th>\n",
       "      <td>0.80</td>\n",
       "      <td>0.66</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Contract clause</th>\n",
       "      <td>0.50</td>\n",
       "      <td>0.38</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.27</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Commercial speech</th>\n",
       "      <td>0.53</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.50</td>\n",
       "      <td>0.57</td>\n",
       "      <td>0.49</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Panel composition          dd          rd          rr      \n",
       "Apointee party              D     R     D     R     D     R\n",
       "Case type                                                  \n",
       "Affirmative action       0.81  0.69  0.83  0.46  0.60  0.34\n",
       "NEPA                     0.71  0.42  0.42  0.06  0.10  0.20\n",
       "11th Amendment           0.73  0.44  0.54  0.46  0.58  0.26\n",
       "NLRB                     0.75  0.55  0.57  0.42  0.50  0.23\n",
       "Sex discrimination       0.76  0.44  0.52  0.37  0.42  0.30\n",
       "ADA                      0.50  0.38  0.45  0.29  0.35  0.17\n",
       "Campaign finance         0.62  0.37  0.39  0.26  0.35  0.31\n",
       "Piercing corporate veil  0.60  0.34  0.36  0.26  0.30  0.21\n",
       "EPA                      0.76  0.58  0.58  0.54  0.55  0.40\n",
       "Obscenity                0.44  0.33  0.34  0.29  0.35  0.20\n",
       "Title VII                0.54  0.34  0.47  0.30  0.34  0.39\n",
       "Desegregation            0.71  0.72  0.77  0.67  0.71  0.56\n",
       "FCC                      0.80  0.66  0.61  0.41  0.47  0.54\n",
       "Contract clause          0.50  0.38  0.31  0.27  0.26  0.17\n",
       "Commercial speech        0.53  0.69  0.64  0.50  0.57  0.49"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from collections import OrderedDict, namedtuple\n",
    "\n",
    "book_data = OrderedDict({\n",
    "'Affirmative action':     OrderedDict({('rr','R'):.34,('rr','D'):.60,\n",
    "                                       ('rd','R'):.46,('rd','D'):.83,\n",
    "                                       ('dd','R'):.69,('dd','D'):.81}),\n",
    "'NEPA':                   OrderedDict({('rr','R'):.20,('rr','D'):.10,\n",
    "                                       ('rd','R'):.06,('rd','D'):.42,\n",
    "                                       ('dd','R'):.42,('dd','D'):.71}),\n",
    "'11th Amendment':         OrderedDict({('rr','R'):.26,('rr','D'):.58,\n",
    "                                       ('rd','R'):.46,('rd','D'):.54,\n",
    "                                       ('dd','R'):.44,('dd','D'):.73}),\n",
    "'NLRB':                   OrderedDict({('rr','R'):.23,('rr','D'):.50,\n",
    "                                       ('rd','R'):.42,('rd','D'):.57,\n",
    "                                       ('dd','R'):.55,('dd','D'):.75}),\n",
    "'Sex discrimination':     OrderedDict({('rr','R'):.30,('rr','D'):.42,\n",
    "                                       ('rd','R'):.37,('rd','D'):.52,\n",
    "                                       ('dd','R'):.44,('dd','D'):.76}),\n",
    "'ADA':                    OrderedDict({('rr','R'):.17,('rr','D'):.35,\n",
    "                                       ('rd','R'):.29,('rd','D'):.45,\n",
    "                                       ('dd','R'):.38,('dd','D'):.50}),\n",
    "'Campaign finance':       OrderedDict({('rr','R'):.31,('rr','D'):.35,\n",
    "                                       ('rd','R'):.26,('rd','D'):.39,\n",
    "                                       ('dd','R'):.37,('dd','D'):.62}),\n",
    "'Piercing corporate veil':OrderedDict({('rr','R'):.21,('rr','D'):.30,\n",
    "                                       ('rd','R'):.26,('rd','D'):.36,\n",
    "                                       ('dd','R'):.34,('dd','D'):.60}),\n",
    "'EPA':                    OrderedDict({('rr','R'):.40,('rr','D'):.55,\n",
    "                                       ('rd','R'):.54,('rd','D'):.58,\n",
    "                                       ('dd','R'):.58,('dd','D'):.76}),\n",
    "'Obscenity':              OrderedDict({('rr','R'):.20,('rr','D'):.35,\n",
    "                                       ('rd','R'):.29,('rd','D'):.34,\n",
    "                                       ('dd','R'):.33,('dd','D'):.44}),\n",
    "'Title VII':              OrderedDict({('rr','R'):.39,('rr','D'):.34,\n",
    "                                       ('rd','R'):.30,('rd','D'):.47,\n",
    "                                       ('dd','R'):.34,('dd','D'):.54}),\n",
    "'Desegregation':          OrderedDict({('rr','R'):.56,('rr','D'):.71,\n",
    "                                       ('rd','R'):.67,('rd','D'):.77,\n",
    "                                       ('dd','R'):.72,('dd','D'):.71}),\n",
    "'FCC':                    OrderedDict({('rr','R'):.54,('rr','D'):.47,\n",
    "                                       ('rd','R'):.41,('rd','D'):.61,\n",
    "                                       ('dd','R'):.66,('dd','D'):.80}),\n",
    "'Contract clause':        OrderedDict({('rr','R'):.17,('rr','D'):.26,\n",
    "                                       ('rd','R'):.27,('rd','D'):.31,\n",
    "                                       ('dd','R'):.38,('dd','D'):.50}),\n",
    "'Commercial speech':       OrderedDict({('rr','R'):.49,('rr','D'):.57,\n",
    "                                       ('rd','R'):.50,('rd','D'):.64,\n",
    "                                       ('dd','R'):.69,('dd','D'):.53})\n",
    "})\n",
    "\n",
    "judges_data = pd.DataFrame(book_data).T\n",
    "\n",
    "judges_data.index.name = 'Case type'\n",
    "judges_data.columns.names = ['Panel composition', 'Apointee party']\n",
    "judges_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of cases, from presidents Eisenhower to Bush, can be found in the pages 118 and 119, although the data from the previous table uses mostly data from the period of 1995 to 2004."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Number of cases</th>\n",
       "      <th>Fraction</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Case type</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Affirmative action</th>\n",
       "      <td>481.0</td>\n",
       "      <td>0.029171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NEPA</th>\n",
       "      <td>273.0</td>\n",
       "      <td>0.016556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11th Amendment</th>\n",
       "      <td>318.0</td>\n",
       "      <td>0.019286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NLRB</th>\n",
       "      <td>216.0</td>\n",
       "      <td>0.013100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sex discrimination</th>\n",
       "      <td>2144.0</td>\n",
       "      <td>0.130026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ADA</th>\n",
       "      <td>2253.0</td>\n",
       "      <td>0.136637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Campaign finance</th>\n",
       "      <td>195.0</td>\n",
       "      <td>0.011826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Piercing corporate veil</th>\n",
       "      <td>345.0</td>\n",
       "      <td>0.020923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EPA</th>\n",
       "      <td>543.0</td>\n",
       "      <td>0.032931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Obscenity</th>\n",
       "      <td>484.0</td>\n",
       "      <td>0.029353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Title VII</th>\n",
       "      <td>1089.0</td>\n",
       "      <td>0.066044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Desegregation</th>\n",
       "      <td>739.0</td>\n",
       "      <td>0.044818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FCC</th>\n",
       "      <td>327.0</td>\n",
       "      <td>0.019831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Contract clause</th>\n",
       "      <td>233.0</td>\n",
       "      <td>0.014131</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         Number of cases  Fraction\n",
       "Case type                                         \n",
       "Affirmative action                 481.0  0.029171\n",
       "NEPA                               273.0  0.016556\n",
       "11th Amendment                     318.0  0.019286\n",
       "NLRB                               216.0  0.013100\n",
       "Sex discrimination                2144.0  0.130026\n",
       "ADA                               2253.0  0.136637\n",
       "Campaign finance                   195.0  0.011826\n",
       "Piercing corporate veil            345.0  0.020923\n",
       "EPA                                543.0  0.032931\n",
       "Obscenity                          484.0  0.029353\n",
       "Title VII                         1089.0  0.066044\n",
       "Desegregation                      739.0  0.044818\n",
       "FCC                                327.0  0.019831\n",
       "Contract clause                    233.0  0.014131"
      ]
     },
     "execution_count": 259,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cases_data = pd.DataFrame({'Affirmative action': {'Number of cases': 481.},\n",
    "                           'Abortion': {'Number of cases': 435},\n",
    "                           'ADA': {'Number of cases': 2253},\n",
    "                           'Campaign finance': {'Number of cases': 195},\n",
    "                           'Capital punishment': {'Number of cases': 624},\n",
    "                           'Contract clause': {'Number of cases': 233},\n",
    "                           'Criminal appeals': {'Number of cases': 2795},\n",
    "                           'EPA': {'Number of cases': 543},\n",
    "                           'Federalism': {'Number of cases': 960},\n",
    "                           'Piercing corporate veil': {'Number of cases': 345},\n",
    "                           'Sex discrimination': {'Number of cases': 2144},\n",
    "                           'Takings': {'Number of cases': 654},\n",
    "                           'Title VII': {'Number of cases': 1089},\n",
    "                           'Punitive damages': {'Number of cases': 264},\n",
    "                           'First Amendment': {'Number of cases': 290},\n",
    "                           'Obscenity': {'Number of cases': 484},\n",
    "                           'Gay and lesbian rights': {'Number of cases': 65},\n",
    "                           'NEPA': {'Number of cases': 273},\n",
    "                           'Desegregation': {'Number of cases': 739},\n",
    "                           'Standing': {'Number of cases': 762},\n",
    "                           'FCC': {'Number of cases': 327},\n",
    "                           '11th Amendment': {'Number of cases': 318},\n",
    "                           'NLRB': {'Number of cases': 216}}).T\n",
    "\n",
    "cases_data = cases_data.loc[judges_data.index].drop('Commercial speech').assign(Fraction=cases_data['Number of cases']/cases_data['Number of cases'].sum())\n",
    "cases_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f933483a438>"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zDARsBpzsnMYqS/oZaZx+2xPtWrjWSFLiuyNst51Ur+Hns5CuPEmXkIaEzmPl\n5EF7kGfC7ECjJJdGXx/XqP//W4N0J/HhPHoB6pXxQe6tQOMPd7N9A1GfQ2PDXo4NmO3rlDIY7p6V\n+fGcHyT2JK/8IIV8/q4bh589nDycdHv7APCDdspu8DQwT9L1rDpPIpegJmkEaRjfYaTgeTUpq2cu\nxffwutn2QE0Exrug1qCktUmDCxbkWa7t47KXBzZrlORwiWvIfsYl/cD2ITmU2ehLda+Xk7oJ3533\nRUoT9JVyjWxCw4gF0tj03p6s94d7eN1sux2bkIaSDQX2koTtH+ZYfjNt1b/ozz+bVVrLsPkIqU9c\ntt/cbtkNpmd/inIHKUBMs/2bnMvuxM/n3cArSSO/cqW6tQyAscppLYMGRTUK679Uc32wWlPAz3pT\npQn6pMkcxwCbkr4Ra/8JTwK59GWSstt9Iiu79ppse1QeF5D0HVJOjVUeJAJtB331vJCHSGmd21H/\n+dcvCLKMfD7/35MmHx1keyGApH/LodxVuPg0v68pqpUMbC/pSbKH9Nlrsu08WrMAI4F7JP2OVe+E\n8gjMp1HMWgadaBT29oWbG0lvB7al7v/TOaTXqFeaoJ/9sl4k6RDbed7u1/sWK3Pd17+GlHEwD7vn\nOfywQW8LeXy1nYI78PkfTOoSuVHSz0ljufPqslghGzP+f6RnKvW/WLm03goM+OTxXKAFpxVYdiFr\nGWSKbpT09oXb1si4GknfIH1BvZkUbw4lremRqzI+yP1f4AyvmjDr323nnne6CJLOJ43rvafbdRmo\nIlsjktYBJpO6efYhLQpzte1rcyr/18CpwJnAO0gLhayR97C4Msseqm9l+xfZPJIhziE/Tvazfz1p\nMt8hpIlIw2x/qN2y665RZKOwUJLutL1d3d/rAj+z/cZcr1PCoN8sYVZeIxd6+8W37c/mcI29SX3K\nfyXdPtdaCtvlUHYn6t+0NWL72HbLbnKtl5Me5r6nfiRVm2XOsb2zpLu8cvZyYZlPy0bSB4DjSOPD\nt8jujL6Rx+effYF8mpV5oWYCn81j5F3DdQrvIimCpNts7ybpt6Q736WkFA9b5nmd0nTv1BkiaXht\nnHU2GmB4TmX/o8m+dUj59DcC2g6apLS7R5KyJOa9FFon6r9nXWvkM5K+BPwsh3Jfwmlx7vOyP3l5\nVtmCIJKOJ6VKaPd5xwrZA+lzgY2dZlxvB0yyncdCLZ3wUVK/+20ATiuYvSKPgp1SnHw6+1OITnWR\nFOQnkjayeadBAAAbv0lEQVQAvkDK3WTy61ZeoYwt/f8k3ZZfkO16HymN7Rk5X2c90ipRx5Jm4n0p\nj0kYkn5je492y2nhOkXVvyOtkaIoTZu/l5Sf5bOk3Cxn2P5tTuXfRMqA+U3nnFq5E+r+f2+3vaOk\noaTEbgO+E1UHl0vsVBdJ0SQNB9ay/UTeZZeupW/7dEl3kma1Qro9nJlX+ZI2JCVEOwK4CNgpa3Hm\n5XZJ3wV+zKqjI3IZstmB+nekNVIU27Oyl0+RGgx5e5nt3zU8rFxewHWKcpOkT5EeVu4PfIT0s9qO\nTi6XWFvz4mlJryY1Sl7Vwev3m6SDezmW+3Du0gV9ANs/o4AuBaXFww8mdSdMKGjW5tqkYP+Wun15\nDdksvP51zwV+IOknFNQaKUrW/XIiL024lscaxQCPKKXWcHa9QylgzHuBTiLdHd5FStE9gza/1J3l\nrJL0cdurjCJTWpO37ZxWdcrYKHlHL8dyiQ31yti9sztprcptSJM8hgD/yGnI1IukgLycVW9HcxuW\nVaRO1V8lzM1SowLXKM7Kfw3pS3dP4DHSjOIjnNPKX0XLRk89Y/uFbHsIMNw5rPfbbMBFs4EZeSmy\ni6TMytjSP5s0nvtKVma5G5dHwbZzz59fI+kseu/XbDsNQJH1r1EPuVlIQyvLYLntcwss37b3y4Ln\nGraX5TUBqUOuB/YjdX9BujO9lvQlNiBK6Y4PJ83CrZ8NvR4r897nollXiaQnSEs+FpYYLQ+dGo5e\nxqCP7YWShmStkQsk3U5a7m0wm539/XrSxKBafu8ppEyMZVFobpYO+LGkj1DcGsU/ID1HqR9JdRVQ\nliGha9V3C9p+Khtq2Y5bSV1cI1k1v8wy0kpXeToW2IOUTx/gTaS7urGSptnOZTGeghzoukypth+T\n9DZSgsbclDHoPy1pTVLSrDNIP0yFt3Dblc1oRdKHgTfYXp5tf4OUfqAsCsvN0iFHZ3+fWLfPtJlP\nRdJrSWPD129obY4gvxQJnfAPSTs5S0UsaWdWPhwdkKxr60FSMC7aUGAb238DkLQx6S50N9KCSIM5\n6Bc5HH2FMgb9I0lB/njg30ipd4vIeFeUl5MCQa1luW62ryyKzM1SONtFdbVsDRxEGgpa/2BuGWkx\n87I4gbRk4p9Jz4JeSVp0ZsAk/dr2GyQto/hnZZvVAn7m79m+RyU9n+N1inAZcL2k+uHoueeKKt2D\n3LKT9D5SfpP65dxOc/GJwHKhHlYXcw6rihVJ0j62b+hpeFyOQ2b3cP7ZNTtK0jDSlxjAAtttBcsi\nH9Y2udbXgdGkZ36QJmc9RLqz+4k7lMlyoCQdQHqmAnBdnsPRV1wjgn7nKWUE3C3bvM05rfEbeibp\nNNun1bWi6tn2+3O6zlqkfuXGNAC5lF80SVOAn2cPoP+LlJL4c25vYfRC1mru4VoiDVt+Q7brFtKy\nlRHoMmXs3lkdDAGWkD7/cZLGOaeFuYvS4Vv0ItQmqJ1v+9cFXucSUprotwLTSJPk7i3wenn7b9tX\nSnoDaQLkF0lpJXbr/W29qk9T/hK2v9zTsf6ybUmzgSe8MmHcuqRutkCJg76kl+UxdrjT1MPC3KSH\nTIOW7Tdkf/eWvnkwex8pvfTXyGeVtZ5saXuKpMm2L8pmX5fpQX1tGO7bgW/Z/qmkdvMGDSEF3txT\nZTdSXcI40tDiTUjzMnJJ2Lc6KF3QzyYGfZv0QzRa0vbAB21/pLs1a9k7ga1d4MLcRcvGD2/GqpOz\n2l54umD3Svoj8OosjUdNbllOM7X+78clvY6UTTWXhGUd8rCkbwL7A6dnE5zaHR33F3cuy2VhCeOK\n1tOM5cZ97Spd0CflQX8r2ZJ3tu+QtFd3q9Qv9wPDqBv5UiaSPktarOJ+Vr1TySuNQSFsT82epcwE\nihxpdF72pfhfpJ/RdYH/LvB6eXs3cADwRduPS3oVqw5vHYjCW/h1nrX9XC33UZYwriz9+Ufz0sWO\njmmyry1lDPrYfqghodULPZ07CBW6MHcHvBvYwvZz3a5If2UPzLcvqnyllM1PZgnubqagtVSLZPtp\nSYuAA7ORJLe4/QVsOtm1UkTCuEJ1csYylDPoP5R18TgbWvZxyvWgrOiFuYt2N2ks+qCe0t4Ntl+U\n9ElSKutSUlqIZwork3xdIOlKt7EeQI6znVuRe8K4DujkjOXyDdmUNJJ0u7Mf6bbxWuDjtpd2tWL9\nkM20G217Qbfr0l+SJgI/IgX/0k3OKpqkzwOPkNJsrEjF0OHAN2CSFgDbO1vNKvtZnWd7697f2X1Z\ncriLbR/R7boMRJas788Nn/3GthfleZ0ytvRV1v9UAEnvIA2DW5N0O7cDMK1EQfMi4HSKWflrdVCb\nvfrRun1tp3nooD+T5hfUljAcTlpdbNCz/YKkzSWtWcbuR9IdYn1iuxdIk8x2yfMiZQz6t2R9jleQ\nJl083uX69NdppNEFvwSwPS/7hi+Lp21/rduVGCgVnE+/wDQPharLAvsEMF/Sddmh/SjPcoOQBhjc\nkvWN199p5TYXoEBD67+ssgfSa+Z+kbwLLJrtcZJ2JaVX/rSke4DLbV/a5aq16nnbTzQ8iC5Ti/lX\nkv6P9FyivntnsA/ZrLmSNG77WxQwACB7zvRhUnoNSF/u32w3lUEH1LLA3kNKr2zSugw39viOwem+\n7M8apAehZbJE0iTb0wEkTSZ1FeaqdH369bL+/S+TFqkY0u36tELS+aRfqpNIieL+FRhm+0NdrViL\nJDULAs6rpVw0SXNsF5bmWNK3SUNya7mUjgResP0vRV0zD9mX1f8A7ydlxBQph80FwKdK8KVVekor\nrl0GvJr0+T8EHGV7Ya7XKVvQlzQCeBeppb8FKS/6953TykdFy6aFf5q0XKJI48Y/W3t4E4ol6TTS\nyKNC8ulLusP29n3tG2wknUmaU/AJ28uyfSNIz5+etn1CN+vXKjVfhP0J0p3MN8vwe6a0mDsuZrnW\nUgb9B4BrSIG+1NkMy0TSe21f2lMOlZL0mdZ+fhrZdi7PVSTNBabYvi/bfg1wVacSjg1UNlt5XGNi\nsmxEzO9tb9WdmvWPpK8Co4DvZbveAzxJ+iIYYfvIbtWtFZLezkuT9eU6m7l0ffrAa8qcMS8b8vgp\nXrrGbF5pAIqyTvZ32fpJV9GBB60nAjdKup90J7c5Ke/PYOdmv1fZiJgy/b7tabt+tMuPJc2yvYuk\n+V2rVQuUFlR6GfBm0tyCQyngIXppgr6kr2S3mNOb/RCWaMjjZaTAUKohj7a/mbX6nrR9ZrfrM1A9\n5NPPbQ1V29dL2opV89GXIeXGPZKOcsMC95LeS8oaWhbrShpt+08AkkaTuq0ABvswzj1tbyfpTtuf\nkfQl4Gd5X6Q0QZ+Vy5x9sau1aN+S2tP5sslafVNJ+Y/KqtA1VJXy6X+ElM/dpNFO3yhBX/JHgR9K\nej/p84C0HvLapGdoZfHvwK8l3Ue60xoLfERpofrBvlBR7WfkaUmvBpYCr8r7ImXs0+9IJrqiSNoX\nmEoawVP/IDGXlZuKlj3wG8ZLZ5yWYsimpJmkERGNa6hOBW62/bo2y/8+afp8bQjx4cAGtqe0U26n\nSNqH1KcMcI/t67tZn4HIMoO+NttcUIIvXAAk/TdwFilX0TmkRsO3bJ+S63VKGPRfsgqPOrgcW7sk\nXUr6gVwln77Ls7JS2Yds3mN7fN22gPm2x+fxc9RYfk/7QjGy0XGfADa3/YFaV5vtn3S5ar3KkvXt\nbvvWbHs4sJbtJ/K+Vmm6dzqdia5Au5Qhj0lPPMjXGG3BLyX9hJVrqB6S7VsHyGN291xJu9v+LYCk\n3Vg58SkU7wJS99Qe2fbDpP/rQR30s2R95wA7ZtvPUlD69dIEfTqcia5At0oab/uebldkICT9L3BG\nLf2FUu74f7f9X92tWcs+Sgr0r8+2L2blGqp5fKHtTPo//lO2PRpYIOku8l2sJTS3he33ZI3EWqro\nTubzb8f1kg4BfljkCMXSde+UnaR7SZPKHiB9k+e9clOhmnWBNOtyqypJm/d23PaDnapLFUm6ldQn\nfovtnbJZrt+zvWuXq9YnpfWn1yGlv3iGgtafLlNLHwBJu5MedmxDylQ5BPhH3h9MgQ7odgXaNETS\n8NowxCz96/Au16lP6sDC7tmQ1pm2X9vnyaEopwI/BzaTdBnpju6YrtaoRe7Q+tOlC/rA2aQUDFeS\nhpQdBYzrao36ob6ll/Ujv4s0cuTtXatU/1xGug29INt+H4N/KFxHFnbPhrQuqB8nHjrL9nXZrOjd\nSV/oH7ede9KyIki63va+fe1r+zpl696RNNv2xGwCw3bZvjKN3lmTFOAPJ631+wNSH96gXtKtntIy\nevtlm9fZntnN+gyE0mLZ9VPdcwnSkm4mPYz7HasOaS3L5MFSk/R60qIv/8gmlu0EfHUwd6tlczte\nRpo78iZWrik8Avh53neOZWzpP50FznmSziA93F2jy3Xqk6S3kFr0byH9515MGslThin6K2R3J9fa\n/rmkrYGtJQ1zSbIwSppEGgjwalLitc1Jy21u29v7+qFMi6Cvjs4Ftpe0PWno5vmk37W9u1qr3n0Q\nOIH0MzmHlUH/SVLPRq7K2NLfnPTLOgz4N2B94OvOOf1o3iS9CPwKOMb2A9m++/NK9NUpkuYAbwRe\nDvyaNBzxOZdkNTNJdwD7AL+wvaOkNwPvtX1sjtfYmJWrHf0uj/QOoTW1QQVKa/0+bPv8sgw0kPQx\n22cVfZ3StfTrbtP+CXymm3Xpp51IzyJ+kSXjupz0ELpslA2DOxY41/YZkuZ1u1L98LztpZLWkLSG\n7RslfSWvwiW9G/gCafEUAWdJOtH2VXldI/RqmaSTSesYvDGb9DSsy3Vqie2zJO3JS5MxXtzjmwag\ndEFf0kHAZ1m53F0hw5ryZnseMA84KfuPnQoMk/Qz4Grb53W1gq2TpD2AI0h5bKBcX16PK+Ur/xVw\nmaS/U9f3noNPk7rt/g4gaRTwCyCCfme8h/S87P22/5olXPtCl+vUEkmXkIZzz2Plqm4mdU/ld50S\ndu8sBA4mZUUsV+UbZK2Q/YDDSpSGYW9SUqtbbJ+ulC/+BNv/2uWqtSR7JlEbA30EqXvwMttLcyr/\nLtsT6rbXAO6o3xeKlXUBb2X7F1lahiHOFoYZzLI5POOLjmtlDPo3AvvaLk1a4jC4SHolaXF6A7Ns\n/zXHsr8AbMeqi3jcZfuTeV0j9EzSB4DjgA1tb5Hl3vlG3sMeiyDpSuBfbf+l0OuUMOjvQureuYlV\ns1SWYuWmslK2noGaL0dXmiGJkv4FOAW4gdTa3xuYZvs7OV7jYFJqZYBf2b46r7JD77LnS7sCt9WG\ncTfefQ1WWYN2B9Jw3/rYluvvVun69EmLNz9FGmO9ZpfrUiWry3oGJwI71rpzJG1EyuuUS9CXNBaY\n4SxVtqS1JY2xvSiP8kOfnrX9XC3djqShNGmkDFKndeIiZQz6r3abOc+7LZuuvzGrPqEf1DM4nS08\nb/umbtelTUtJSfpqlmX78nIlsGfd9gvZvl2anx5ydpOkTwFrS9qftKBNKSY+2r6pE8N9y9i9cwZp\njPW13a7LQEj6GCk/yN9YNZ/+oE64VssS2dPxwV7/GkkXAxOAH5H+PZNJWVrvhPa7CSXNs71Dw747\nbG/fTrmhNdmD82NJkyAFzAS+XYZBH02G+74RyH24bxmDfi0T3bPA85RkyGZNNvpot7xGi3RKXfbI\nj2Z/17p73kv6/E/qfK36T9KpvR233dbcD0nXAWc5WxJT0mTSw7lB/yBxdZENk8X2km7XpT+yiYP7\nNw73zbvBUKqgn+XF3mywd4X0JntYs7/t5d2uy0BEauXeZal8LyNNqQdYDBxp+77u1Wr1l8WGU4Hj\nWZmW5QXSF/C0rlWsHzo13LdUffq2LemnpNvzUpH0iezl/aSVmn5KOUcfSdLrbd+SbexJCXIf1Uia\nSJpAVZvcB+TXPZUF992zCWDYfiqPckOf/o2URnmXujQnrwHOlfRvts/sau1a83OlNZzrh/v+LO+L\nlKqlDyDpIuBs27O6XZf+6KNbwSVqjexMGumyfrbrcdLsx7IsjL6ANILnLlY+U4nFTUpO0u2kO+hH\nGvaPIiUILEsW3sKH+5Yx6P8e2BJ4kDR9vmwrT02xfWVf+wY7SesDuICFm4ukbDGVbtcj5EvS3T2N\n6uvt2GAgaUtg49rdc93+NwB/ybtrsIxBv+lydGVpqTXr/44+8c6RtC8p79H1rNq99sOuVSq0rbff\nocH++yXpJ8DJtu9q2D8B+F/b78jzeqXp05c0wvaTrDrGujQkHQi8DdhE0tfqDo0grYkZOuN9wGtJ\nmRdXDJkFcgn62e15oydIqRgixXJxtpf0ZJP9om6xnEFq48aAD2D7Lklj8r5YaYI+8F3gINIiA2bl\nQgNk24M9L/2fSbnnJ5H+DTXLSA+hQmfsYnvrAss/FtiDtFAOpJWQ5gBjJU2zfUlPbwwDZ7tMmV4b\nbdDLsbXzvliZgv7ns7+3sf1MV2syALbvAO6Q9F2XZJWpZiR9FvhMbcippBGk5ejKsgLYrZLG276n\noPKHkn5G/wYrFlS5GNgNuJmV8xtCqJkt6QO2v1W/M8sTNaeH9wxYmYL+V4GdSXlSBm3/XF+aBXxJ\nP7N9YDfqMwBDgdskvY+USuJsoPDVfnK0O2mpzQdIffp5DwTYrBbwM3/P9j0qqbRf9qFQJwBXSzqC\nlUF+Iim32LvyvliZgv7zks4DNm3oEwdgsOdzl9TTF5VImfVKwfbJkn4B3AY8BuzlQb5UZYMDCi7/\nl9mDudporEOyfeuQhreGsIqskbCn0tKdtVFGP7V9QxHXK83oHUkjSQuOnE5KjbsK2xd1vFL9IOkF\nUjpoNTm8u+3c++6KIGkv0uLTl5Imyb0cONb2n7tasX6S9ArqHvDlNcs7mxl6CGmiEMAtwA/KkPsl\nVEOZgv7ptv9T0idtn9Ht+vSXpLuBd9n+Y5NjD9nerAvV6jdJvyMt7n5Ptn0waVjZa7tbs9ZImgR8\niZQm4e+kmbn32t62qxULoUNKM30eeFvWijqs2xUZoNPo+fP+WAfr0a496h+CZuPbX9/L+YPNZ0n9\n+n+wPRbYF/htXoVLOljSHyU9IelJSct6GEoYQleUKej/nNSHvF32y/RkmX6pbF9le0EPx67pdH3a\nMFLS+ZJ+DiBpPPDOLtepP57PMpyuIWkN2zeSHprl5Qxgku31bY+wvV5ZMsCGaihN0Ld9ou0NSA84\nRtT9Kf0vVTYSpiwuJOUof1W2/QfS6IOyeDxLhnYzcJmkr5LSeeTlb7bvzbG8EHJVmj79nmT5Kaba\n/mifJw9Skv5ke3S369EKSbNs71KfYrnZwiGDVTaK5p+kBs8RpMRxl+W1vkH2JfJK4BoizUMYhMo0\nZHMFSTsChwNTgAfIaQp9kSTd2dMh0nj3sviH0rqyBpC0OynNwKDWJKnVi8BFWaNhA/JbMnEE8DRp\n5aaa3NI8hNCu0gR9SeNIibKmAo8AV5DuVN7c1Yq1bmPgraTnEvVEmnBWFp8ApgNbSLoFGAUc2t0q\nteQrwMlN9j+RHcslqVWJZiaHiipN0Ad+D/wKOKg2GUhSmXLW/ARY1/a8xgOSftn56gyM7bmS9ga2\nJn1hLShJWolCk1rVhhJLOosmawkP9smDoTrKFPQPJg3XvDEbOXI5zSc6DUq2j+3l2OGdrMtASNoF\neMj2X20vzxZTOQR4UNJpth/tchX7UnRSq9rD29k5lBVCYUr3IDd7EDeZ1M2zDymZ1dW2r+1qxVZz\nkuYC+2U5ZPYifel+jJRCYhvbg7qLR9L3gBt6SGq1v+33dKdmIXRW6YJ+PUkvJz3MfY/tfbtdn9WZ\npDtsb5+9PgdYYvu0bHvQj97Jsl1eDTxHk6RWtv+a03WuA6bYfjzbfjlwue235lF+CO0qddAPnZOl\nkdgh69r5PXCc7ZtrxwbzcnT1GpJazc87qVWzL8D64a0hdFuZ+vRDd30PuEnSI6Rx7r+CFUMhB/2Q\nzZpsBu6NfZ44cC9IGl1L4JYt7xktqzBoREs/tCwbk/8q4Frb/8j2jSONSprb1coNEpIOAM5jZUbV\nN5LuimZ2tWIhZCLoh5CTLCHgpqQ7od2z3b+1/Uj3ahXCqiLoh5AjSXfZntDteoTQk9IkXAuhJOZm\ncxpCGJSipR9CjrKRTVsCD5Kyd+a9Bm8IbYmgH0KOstE6L2H7wU7XJYRmonsnhBxlwX0zYJ/s9dPE\n71kYRKKlH0KOJJ1Kmum7te1xkl4NXGm7TEtKhtVYtEBCyNe7gElkq3HZ/jOwXldrFEKdCPoh5Os5\np9vn2iIz63S5PiGsIoJ+CPn6vqRvAhtI+gDwC+BbfbwnhI6JPv0QciZpf9JyiQJm2r6uy1UKYYUI\n+iGEUCGRZTOEHEj6te03SFrGqlk1a5OzRnSpaiGsIlr6IYRQIdHSDyEHktYCPkRKwXAn8B3by7tb\nqxBeKlr6IeRA0hXA86TFZQ4EHrT98e7WKoSXiqAfQg7qUypLGgr8zvZOXa5WCC8R4/RDyMfztRfR\nrRMGs2jph5ADSS+QpV4gjdhZm5RsLUbvhEElgn4IIVRIdO+EEEKFRNAPIYQKiaAfQggVEkE/rFYk\nvVLS5ZLukzRH0gxJ4wq61jsljS+i7BCKEkE/rDYkCbga+KXtLWzvDJwMbFzQJd8JRNAPpRJBP6xO\n3gw8b/sbtR2277D9K0nrSrpe0lxJd0maDGmRE0k/lXSHpLslvSfbv7Okm7K7hZmSXlV/IUl7klbI\n+oKkeZK2kDS37vhWtW1JiySdkV33d5K2zPaPkvQDSbOyP7GkYihc5N4Jq5PXAXN6OPYM8C7bT0oa\nCfxW0nTgAODPtt8OIGl9ScOAs4DJtpdkXwT/A7y/VpjtW7P3/8T2Vdl7n5C0g+15wPuAC+qu/4Tt\nCZKOAr4CHAR8FTjT9q8ljQZmAtvk9WGE0EwE/VAVAv5X0l7Ai8AmpG6fu4AvSTqdFMB/Jel1pC+Q\n61KPEUOAv7RwjW8D75P0CeA9wK51x75X9/eZ2ev9gPHZNQBGSFrX9lMD/DeG0KcI+mF1Mh84tIdj\nRwCjgJ1tPy9pEbCW7T9I2gl4G/A5SdeTngvMt71HP6//A+BU4AZgju2ldcfc5PUawO62n+nndUIY\nsOjTD6uTG4Dhko6r7ZC0naQ3AusDf88C/puBzbPjrwaetn0p8AVgJ2ABMErSHtk5wyRt2+R6y4D1\nahtZ8J4JnMuqXTuQWv61v3+Tvb4W+FhdXXcY0L86hH6INAxhtZIF8a8AO5P68RcBJwCPAT8G1gVm\nA7uTUiBvTQr2L5KSpn3Y9uwsAH+N9GUxFPiK7W81XOv1pEXPnwUOtX2fpN2Bq4DNbb+QnbcIuCK7\n3rPAVNsLs2cL55D68YcCN9v+UAEfSwgrRNAPIUeS/gNY3/Z/1+1bBEy0/UjXKhZCJvr0Q8iJpKuB\nLYB9ul2XEHoSLf0QQqiQeJAbQggVEkE/hBAqJIJ+CCFUSAT9EEKokAj6IYRQIf8PdM2ZX1DUumQA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9334855080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cases_data.plot(y='Fraction', kind='bar')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To reproduce each of the bar plots in _Sunstein's_ book, we use the function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:09.128965Z",
     "start_time": "2017-09-04T16:20:08.793334Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.6/site-packages/matplotlib/style/core.py:197: UserWarning: In /home/felippe/.config/matplotlib/stylelib/tableau10.mplstyle: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
      "  warnings.warn(message)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "def sunstein_bars(book_df, case_type, ax=None):\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    df = book_df.loc[case_type].unstack(level=1).iloc[-1::-1][['R','D']]\n",
    "    df.plot(ax=ax, kind='bar', \n",
    "            rot=0, fontsize=12, \n",
    "            yticks=[0.2,0.4,0.6,0.8], ylim=(0,1),\n",
    "            color=['#cccccc', '#ffffff'], lw=1, edgecolor='k')\n",
    "    ax.set_title(case_type)\n",
    "    ax.set_ylabel('Percent liberal votes')\n",
    "    for p in ax.patches:\n",
    "        ax.annotate(str(p.get_height()).split('.')[1].ljust(2,'0'),\n",
    "                    (p.get_x() + 0.055, p.get_height() + 0.025))\n",
    "    ax.legend(['Republican appointees', 'Democratic appointees'], \n",
    "               mode='expand', frameon=False, ncol=2, loc=(0,-0.2))\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And all the bar plots are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:15.005586Z",
     "start_time": "2017-09-04T16:20:09.706457Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f934c5454e0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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K2XlELAK+1ED7YySTbRvaZjLQp5j9t6T58+czatQoVq1axerVqznuuOM48sgj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\nUoY5v8wsK7k0Z5dJ2hr4EXA9yUmx5xa0KjMrCvWdq1TT7Nmzm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MzMrIi4OTMzMzMrIm7O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\nkjuBx6rqtim3KEmStAo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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9388adc860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(figsize=(10,33), ncols=2, nrows=8)\n",
    "axs[-1,1].set_visible(False)\n",
    "for ax, ct in zip(axs.ravel()[:-1], judges_data.index):\n",
    "    _ = sunstein_bars(judges_data, ct, ax=ax)\n",
    "    ax.get_legend().set_visible(False)\n",
    "h,l = axs[0,0].get_legend_handles_labels()\n",
    "fig.legend(h, ['Republican appointees', 'Democratics appointees'],\n",
    "           loc='upper center', mode='expand', frameon=False, ncol=2,\n",
    "           bbox_to_anchor=(.5,.115), bbox_transform=fig.transFigure)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to measure the similarity between different panel compositions across the case types, so we make a\n",
    "transformation to the percentual values to convert them to real vectors in a 15-vector representation to use\n",
    "the internal product as such measure.\n",
    "\n",
    "To transform the values, we consider a linear tranformation $y = 2x-1$ and the inverse $\\Phi$ $y = \\Phi^{-1}(x) = \\sqrt{2}\\mathrm{erf}^{-1}(2x-1)$, followed by a normalization of the resulting vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:15.191491Z",
     "start_time": "2017-09-04T16:20:15.009115Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.special import erfinv, erf, erfc\n",
    "from numpy import sqrt\n",
    "from numpy.linalg import norm\n",
    "\n",
    "Phi    = lambda x: erfc(-x/sqrt(2))/2\n",
    "invPhi = lambda x: sqrt(2)*erfinv(2*x-1)\n",
    "linear = lambda x: 2*x - 1 \n",
    "\n",
    "def plot_matrix(df, order=None, ax=None, **kwargs):\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    if order is None:\n",
    "        order = df.columns.tolist()\n",
    "    im = ax.imshow(df[order].T[order].T, **kwargs)\n",
    "    ax.set_xticks(arange(0,6))\n",
    "    ax.set_yticks(arange(0,6))\n",
    "    ax.set_xticklabels(order + [' '])\n",
    "    ax.set_yticklabels(order + [' '])\n",
    "    return ax, im"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:15.253841Z",
     "start_time": "2017-09-04T16:20:15.196801Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "        text-align: right;\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ddd</th>\n",
       "      <th>Rdd</th>\n",
       "      <th>Drd</th>\n",
       "      <th>Rrd</th>\n",
       "      <th>Drr</th>\n",
       "      <th>Rrr</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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       "      <td>-0.509865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rdd</th>\n",
       "      <td>0.292014</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.886943</td>\n",
       "      <td>0.618621</td>\n",
       "      <td>0.731595</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>Drd</th>\n",
       "      <td>0.498231</td>\n",
       "      <td>0.886943</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rrd</th>\n",
       "      <td>-0.354647</td>\n",
       "      <td>0.618621</td>\n",
       "      <td>0.479484</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.933392</td>\n",
       "      <td>0.847378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Drr</th>\n",
       "      <td>-0.083477</td>\n",
       "      <td>0.731595</td>\n",
       "      <td>0.694059</td>\n",
       "      <td>0.933392</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.683850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rrr</th>\n",
       "      <td>-0.509865</td>\n",
       "      <td>0.503100</td>\n",
       "      <td>0.286860</td>\n",
       "      <td>0.847378</td>\n",
       "      <td>0.683850</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Ddd       Rdd       Drd       Rrd       Drr       Rrr\n",
       "Ddd  1.000000  0.292014  0.498231 -0.354647 -0.083477 -0.509865\n",
       "Rdd  0.292014  1.000000  0.886943  0.618621  0.731595  0.503100\n",
       "Drd  0.498231  0.886943  1.000000  0.479484  0.694059  0.286860\n",
       "Rrd -0.354647  0.618621  0.479484  1.000000  0.933392  0.847378\n",
       "Drr -0.083477  0.731595  0.694059  0.933392  1.000000  0.683850\n",
       "Rrr -0.509865  0.503100  0.286860  0.847378  0.683850  1.000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data = judges_data.transform(lambda x, f=linear: f(x)/norm(f(x)))\n",
    "linear_overlaps = trans_data.T.dot(trans_data)\n",
    "linear_overlaps.index = [''.join(reversed(idx)) for idx in linear_overlaps.index]\n",
    "linear_overlaps.columns = [''.join(reversed(c)) for c in linear_overlaps.columns]\n",
    "linear_overlaps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:15.295845Z",
     "start_time": "2017-09-04T16:20:15.258132Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "      <th>Drr</th>\n",
       "      <th>Rrr</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ddd</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307920</td>\n",
       "      <td>0.516455</td>\n",
       "      <td>-0.352026</td>\n",
       "      <td>-0.104686</td>\n",
       "      <td>-0.486709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rdd</th>\n",
       "      <td>0.307920</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876311</td>\n",
       "      <td>0.570710</td>\n",
       "      <td>0.684351</td>\n",
       "      <td>0.500162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Drd</th>\n",
       "      <td>0.516455</td>\n",
       "      <td>0.876311</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.429794</td>\n",
       "      <td>0.635120</td>\n",
       "      <td>0.274509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rrd</th>\n",
       "      <td>-0.352026</td>\n",
       "      <td>0.570710</td>\n",
       "      <td>0.429794</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.947280</td>\n",
       "      <td>0.813282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Drr</th>\n",
       "      <td>-0.104686</td>\n",
       "      <td>0.684351</td>\n",
       "      <td>0.635120</td>\n",
       "      <td>0.947280</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.681111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rrr</th>\n",
       "      <td>-0.486709</td>\n",
       "      <td>0.500162</td>\n",
       "      <td>0.274509</td>\n",
       "      <td>0.813282</td>\n",
       "      <td>0.681111</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Ddd       Rdd       Drd       Rrd       Drr       Rrr\n",
       "Ddd  1.000000  0.307920  0.516455 -0.352026 -0.104686 -0.486709\n",
       "Rdd  0.307920  1.000000  0.876311  0.570710  0.684351  0.500162\n",
       "Drd  0.516455  0.876311  1.000000  0.429794  0.635120  0.274509\n",
       "Rrd -0.352026  0.570710  0.429794  1.000000  0.947280  0.813282\n",
       "Drr -0.104686  0.684351  0.635120  0.947280  1.000000  0.681111\n",
       "Rrr -0.486709  0.500162  0.274509  0.813282  0.681111  1.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data = judges_data.transform(lambda x, f=invPhi: f(x)/norm(f(x)))\n",
    "invPhi_overlaps = trans_data.T.dot(trans_data)\n",
    "invPhi_overlaps = trans_data.T.dot(trans_data)\n",
    "invPhi_overlaps.index = [''.join(reversed(idx)) for idx in invPhi_overlaps.index]\n",
    "invPhi_overlaps.columns = [''.join(reversed(c)) for c in invPhi_overlaps.columns]\n",
    "invPhi_overlaps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:16.248001Z",
     "start_time": "2017-09-04T16:20:15.299603Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f93406ecef0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NM8nVSfb5uk2Sc5JcOEzseba9OMnZLfLu8fn2xLs1yeeTPKefvJJsTPKFYWLPs90FST7Y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\nSZLUnA2GJElqzgZDkiQ19/8BkFdx39V2iOEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9388adcbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy import arange\n",
    "\n",
    "fig, axs = plt.subplots(figsize=(9,3), ncols=3)\n",
    "order = 'Ddd Drd Drr Rdd Rrd Rrr'.split()\n",
    "_, im = plot_matrix(linear_overlaps, order, ax=axs[0], vmin=0, vmax=1, origin='lower')\n",
    "plot_matrix(invPhi_overlaps, order, ax=axs[1], vmin=0, vmax=1, origin='lower')\n",
    "plot_matrix(((linear_overlaps - invPhi_overlaps)**2), order, ax=axs[2], vmin=0, vmax=1, origin='lower')\n",
    "fig.colorbar(im, ax=axs.tolist(), fraction=0.05, orientation='horizontal', aspect=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But since they are almost the same, we keep the linar overlaps for the analysis, as they are simpler.\n",
    "Lets compare the angles between different panel compositions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:16.319539Z",
     "start_time": "2017-09-04T16:20:16.254299Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import arccos, pi\n",
    "\n",
    "def plot_angle(angle_df, x_order, y_order, ax=None, *args, **kwargs):\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    angle_df[y_order].T[x_order].T.plot(ax=ax, **kwargs)\n",
    "    ax.legend(loc='upper right', frameon=True)\n",
    "    ax.set_ylim(0, pi)\n",
    "    ax.set_yticks([0, pi/4, pi/2, 3*pi/4, pi])\n",
    "    ax.set_yticklabels(['0', r'$\\frac{\\pi}{4}$', r'$\\frac{\\pi}{2}$', r'$\\frac{3\\pi}{4}$', r'$\\pi$'],\n",
    "                       fontdict={'size':14})\n",
    "    ax.set_ylabel(r'$\\theta$', fontdict={'size':16})\n",
    "    return ax\n",
    "\n",
    "angle_data = linear_overlaps.transform(lambda x: arccos(0.999*x))\n",
    "\n",
    "def plot_angle_pairs(angle_df, x_order, *pairs, title='', **kwargs):\n",
    "    n = len(pairs)\n",
    "    fig, axs = fig, axs = plt.subplots(figsize=(4*n,n), ncols=n)\n",
    "    for ax,p in zip(axs.tolist(), pairs):\n",
    "        plot_angle(angle_df, x_order, p, ax=ax, **kwargs)\n",
    "    fig.suptitle(title, fontsize=16)\n",
    "    fig.tight_layout(pad=2.5, h_pad=0.1, w_pad=0.1)\n",
    "    return fig, axs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:18.233585Z",
     "start_time": "2017-09-04T16:20:16.322663Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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blCtXDgDQvXt3bN261bcHIyJLOC2OAED79u1RunRpABpXevbsiYiICFSqVAnt2rXz/QGI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\nMzMzM2utfwCDTSqxQ1MxVAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9388add898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_order = 'Rrr Rrd Rdd Drr Drd Ddd'.split()\n",
    "_ = plot_angle_pairs(angle_data, x_order, ['Rrr', 'Ddd'], ['Rrd', 'Drd'], ['Rdd', 'Drr'],\n",
    "                     title='Empirical Data', color=['r', 'b'], style=['-d', '--h'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the angle flag is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9337e2f278>"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ajd3zW4Dzk9htkqQhWdxDm+OAx/ZaHgPeta82VbUryVPAkcAv926UZC2wtlt8NsnDsyl6\nlo6aXE9PFs7fKI9vKgvj+Fo+NvD4pjb743tzL416Cfe+qar1wPpB7nOPJKNVNTKMfQ+Cx7dwtXxs\n4PENSy/DMo8Dx++1vKJbN2WbJIuB1wM7+1GgJGnmegn3HwEnJlmd5HeAS4GNk9psBD7aPf8wcGdV\nVf/KlCTNxLTDMt0Y+jrgO8Ai4OtV9UCSa4DRqtoIfA34RpLtwJNM/AGYb4YyHDRAHt/C1fKxgcc3\nFLGDLUnt8QpVSWqQ4S5JDTLcJalBzYZ7Jhw/fUtJak/TH6gmub+q3j7sOqS9dfdreqCqThp2Lf2W\n5EP7215Vtw6qloPdQK9QHYItSd5ZVT8adiH9lOTT+9teVV8cVC0HQpLbgX32OqpqzQDL6buq2t3d\nZXVlVf2fYdfTZxd3P48G/hlwZ7f8u8D3gQUd7km+wv7fm38ywHL2q/VwfxfwB0keBf4vEKCq6rTh\nljVnR3Q/3wq8k5cvKrsY+OFQKuqv/9z9/BBwDPBfuuXLgF8MpaL+eyPwQJIfMvHeBJr4w/UxgCR/\nD5xSVTu65WOBG4ZYWr+Mdj/fw8Rdcm/uln8f2DaUivah9WGZKW+wU1WPDrqWAyHJ3cAHq+qZbvkI\n4H9U1bnDraw/prpnx3y9j8dMJfkXU62vqv856FoOhCQPVtXJey0fwsRQ1Mn7+WcLRpIfAP+8qnZ1\ny0uA71XVu4db2cua7bl345rfaXFccy//BHhhr+UXunWtODzJCVX1CECS1cDhQ65pzrr35l9U1e8O\nu5YD6I4k3wE2dMv/FviHIdbTb28EXsfEFfkAr+3WzRvNhnvj45p73AT8MMlt3fLv0cap7x5XA5uS\nPMLEkNqbgX833JLmrntv/r8kr6+qp4Zdz4FQVeuS/Ctgz1nk+qq6bX//ZoH5T8CPk9zFxHvzXOAv\nhlrRJK0Py9wNnMHEOHQz45p7S3ImcE63eHdV/XiY9fRbktcAe86+Hqqq3w6znn5J8t+YeG9+l1e+\nN+fNB3Kz1Z2Z/EPjZyYkOYaXv9vinqr6+TDrmaz1cG92XNPpdAtbko9Otb6qbpxq/UKT5A7gQ62d\nmXSdqX2qqi2DqmU6zQ7LwKtDvPtQ57IhldNXjQ87TZ5OdwcTp75NTKeDiRBPsrx7Pj7seg6AZ4H7\nk7R2ZvKF7udSYAT4CRPvzdOYmElz9pDqepUmwz3J64BPMvH1fxuZOPX9JPAfmPif8c3hVddXTqdb\nYLrvFv4csI6JK8STZBfwlaq6ZqjF9detNPBHeLI9Q01JbgXOrKr7u+VTccz9wOvGM38F/C/gfCZ6\ngAE+VVX3DrO2fmp52AnanE7XXYD2fmBtVf3vbt0JwFeBb1fVl4ZZXz+1fGaS5IGqett064ap1XB/\n6bYD3dj0DmBlVT0/3MoOrD3DTlXVxJlJkmuBE3nldLrtVfXvh1fV3CT5MXBBVU3+8vjlwN9X1RnD\nqaw/pjozAZo7M0mygYmz5T0X2P0B8NqqmjfDvq3eOOzFPU+qajcw1lKwJ3ldkv+Y5Nok/7K7Sdo6\n4BHg3wy7vn6pqnXA9cA7usf6hRzsnSWTgx1e6t0uGUI9/XY1E1dvvrOqllXVG5mYUfKeJFcPt7S+\n+hjwAPCp7rGtWzdvtNpz383LY9ABDgV+w8u3H3jdsGrrh4Nl2GmyFs5MkmypqilnXOxv20LR+pnJ\n3ub7sFOT4d661oedpvtAvKouGWJ5czKp4/GKTcDSqlrQvfckW6vq1JluWyimGHYC2M08HHZqcrbM\nQeAVw05Jmhp2Ar7By2cmfwR8honw+72FfmZSVYuGXcMB9sIsty0Uew87veID8SRXz6cPxO25L0AH\nwbBT02cmLTsIzkwWzLCTPfcF6CDo/bV+ZtKsg+C9uc8PxLs7Q84bhrvmo3ckebp7HuDQbrmJMxMt\naAtm2MlhGUnq0UIadjLcJalBrV7EJEkHNcNdkhpkuEtSgwx3SWrQ/wc5qqzOHVnmcQAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f933844cf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "angle_data.T[x_order].T[['Rdd','Drr']].plot(kind='bar', stacked=True, color=['r', 'b'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Y4Ru4Ng1r7NA+/xITaFnYW8uxbX2F9qZtRMYVkF40C2tMdhDPsP8EUhZuj4el\nW0rZUl5DbmoCx4weitnof8vJlkrv9DK7y8FdZ17LpNzRvTqP7lxOFw/8+UXeffFrTjxrMn964FdE\nWP27BawMdguMBHmQSZB3CaUAOxitPb7a+dsoZSKtcGbQaucDXQ5au2mpW0+jbQkttevwDlwrID5j\nGnGph/fZwLX9CUZZaK1prFxK9Y7/4Ha2kTTkOFLyftav7yMYelsWHU4Xn6/dhq2hmfF5GUwsyO7R\n53TJ9tXc/s6/iLVGcf85f2RoSuDTy1qa2rjtt0/w3Zcbufi6U/nNTWdg8HNdc5AgD5QEeZBJkHcZ\n6ADrDUd7NRWbX6C9aRvRSWPIGHYh5gj/l3jcn4EqB3tbJY22xTRWLcPtaMJojt1zx7WIfhq4tq9g\nloXb2ULVjkU02r7FZEnwzT2fEDZdI70pi4bWdj5ZU0xrh4OjRuZTmJnco9e/s+ZzHvzoWQpSc7hv\n5vVBmV5WWVbL7IvnU1Js46Z5v+Rns3reRC9BHhgJ8iCTIO8SjkEOnbXzL6jeschXOz+H+PQpvQ6I\n/iwHj9tOU/VKGm2LvQPXMBCTPJb4jKnEJI4Z8ClcfVEW7U3bsW19BXtrGdFJY0gvPA9LZEpQj9EX\neloW5XWNfLZuO0al+Mn4ItLi/R/UprVmwddv8PzSd5iSP46/Bml62eY1Jcz+1XwcHU7uevJKjjjG\n30lGe5MgD4wEeZBJkHcJ1yDvFKzaeV+Xg9aajuYdNNgW01y9Eo/bjiUyjfiMacSnTwmpgWt9dzcz\nN/VlX1BT8l+09pCc+/9IGnICBoN/fbQDoSdlsXF3Fcu2lhIfFckJ44uIjfS/G8HpdjH3/QV8tHFx\nUKeXffXBKu68egEJybHMe/5ahg7P6vW+JMgDI0EeZBLkXcI9yMFXOy/7guqdi1AGE+kF5xDXw9p5\nX5WDd+DaMhorl+Bos6EMFuJSDyc+YxqRcQUh2cTc158Jp72eqm1v0lzzPZbIdNKHzSI6YXifHS8Q\n/pSFx6NZtrWUTWXVDEmOZ8aYAswm/1tVuk8vu/zoc/nFlNOC8rl4bcEnzL/jVUZOyGPuM9eQlBrY\nl0UJ8sBIkAeZBHmXwRDknRztVb7a+fYe186DWQ5au2mt20CDbTEtdetA+waupU8lNvVwjCZrUI7T\nV/rrM9FSt57K4tdwdtQQl3YkaQVnh1TLBBy8LOxOF1+s2055fRNjctOZVDgEQw9C2NZYw+w3H2B3\nfSV/OvkQiZxCAAAgAElEQVQyTho9PeBzdrs9zL/jVd54+lOOPWUit87/NdYetA4ciAR5YCTIg0yC\nvMtgCnLorJ1/TvXOd7y188JziUubfNAaTjDKwdFeRYNtMU2VS3HtGbg22TdwLXyW/uzf8QIOand9\nSO2ujzAYLKQOPZ2EzKNDZu75j5VFU1sHH68pprndzrQRuQzPSt3vdgeyuXInc958EIfLyd1nXsfh\nub3ru+6urbWDv161gG8/XsOsK37K7/5yDsYe3Mf9x0iQB0aCPMgkyLsMtiDvtHftfCwZwy740dp5\nb8vB47b7lgpdTHvTNsBATNJo4jOmEZM0dsAHrvXGQHwm7G2VVBa/QlvDFqyxeWQUzcIam9uv57A/\nByqLivomPlu7DQUcP66IjMSe3VBl8fbV3PHOo8RZY5h3zg1BmV5WY2tg9q/ms23Dbv5w14Wcfclx\nAe+zOwnywEiQB5kEeZfBGuTQWTv/jOqd7/pq5+cRl3bkfmvnPSkH78C1Ehps3/oGrnVgjkwlIWM6\ncWlHBjwVbqAN1GdCa01T9XKqtr2J29lCQtYxpOafjtEU+Mjt3tpfWWwpr2bx5lLiIiM4YXwRcVE9\n6ypZtPozHvr4Od/0shtIiQn887Jt425mXzyf5oY27njscqafOD7gfe5LgjwwEuRBJkHeZTAHeSd7\nWyW2LQtpb9pOTNJYMoZdiCkifq9t/CkHl6OZpqplNNgWdxu4NtE3cK0wJAeu9cZAfybcrjaqd75L\nQ/lXGC2xpBfMJDZ10oCUb/ey8GjN8uLdbNhVSVZSHMeNLcBi8n9k+V7Ty4aO56+nX02UJfDxEks/\nX89tv32CqBgr8569lmFjcwLe5/5IkAdGgjzIJMi7DPRFu7/sXTs3+/rOu2rnByoHrd201m+iwfYt\nLbVrQXuwxuaTkDHNN3Bt4GqLfSVUPhPtzSVUbn2ZjpZdRCWMIKPo/H5b3a1TZ1k4XG6+XL+d3bWN\njBqSxpFFORgM/n+xcLiczP3gKT7euJjTx8/g+hN/hSkI3S6LXviSB//8IkNHZHHfs9eSltV3iwpJ\nkAdGgjzIJMi7hMpFu794a+cv0N60g5jkcd7auSXuB+XgaK/23nGtcikuRyNGc4x34Fr6NCKiMwfw\nHfS9UPpMaO2hoeIrqne8g/a4SMr5Kcm5J/Xb3HOlFE1tHXyyZiuNbR1MGZbLyCFpPdpHc0crt/zn\nYVbt3sQVx5zLRZMDn17m8Xh44t63ePFfHzD1J2P562NXEBXTt7MhJMgDI0EeZBLkXULpot1ftPZQ\nt/tTana+izJaSC88j4SMybhddpprVtFg+5b2xmJAEZ00moQ9A9dCZSHCvhWKnwmXo4mqbW/SVL0c\nszWF9KLziUkKfBGRg1FK8eKX36O15rixhWQl9Wx6nK2xhpveeICyhkpuPuVyfjpqWsDnZG93cPfv\nn+bz/67krItn8Pu7LsDUg3nrvRWMIF+xYkWayWRaAIwFQmNqQvB4gHUul+uySZMmVe375KFx9ehn\nDvvdGIyTMBomoQw9+4YtwptSBpJzTiQmeSwVm1+gYvOzABQv+bN34Jo1ldT804lLnxL2A9cGC5Ml\njqxRlxCfMY3K4lfYve5fxKZMJK3wnD75N2rtcLB+VyUAESYjJ4wfRnx0z2q8m207mPPWQzhcTh44\n9yYmBmF6WX1NEzdf+i82fL+Dq287j1lXnNgvYwd2OzuCsh+TybQgIyNjVGpqar3BYAitb4sB8ng8\nqrq6erTNZlsAnLHv8xLkfcDpeADvFyhQKheD8XCMxkkYDJMwGA9DqeiBPUHR5yKiMsg77Abqdn8K\nPEpM8ngSMqYRGV80aAauDTbRiSPIn3Qzdbs+oXbXB7TWbyAl7zQSs49FqcBrpQ2t7awrtbHdVofG\nmzM/O2IUEeaeXYa7Ty/7x4VzyE8JfBnXkuIKbvrlfOqqGrnryd8y49TDA96nP75tbeC6ik3B2t3Y\nwRjiAAaDQaempjbabLax+3tegrwPRMXsxuNeg8ezHLd7BR73Ctyu//ieNWAwjMZgPByD4QiMxkko\nw0iUkn+Kwaazdg6QNfLiAT4b4Q+DwUxK3snEpR1BZfGrVG1/g8bKpWQMm0Vk3NBe7bO6sYW1pTZK\nqxswGgyMyE5ldE46l0CPQ/zt1Z/x0MfPUpSWy9yzgzO97PtvN/Pnyx7DbDby8Os3Mnpi795nT2it\neaa+nHurd1BgiQrWbg2DMcQ7+d7bfrsMJD36gFLRGE3TMDKNzmEz2lON2+MNdY97BS7nIuA537NR\nGIyHYTRMwmD0/lEqR2puQgwQS2QKQ8b+juaaVVRte4OSVQ+SkDGd1KFnYDQfvEVNa015XRNrS2zY\nGpqxmIxMyM9k1JA0rJaeD6bzaA///up1Fi77L1OHTuCO068KyvSy919bzH03PUd2fhrznruWrNy+\nXzWuw+Pmlspi/tNUzU9jkvh75nB6dsub0GU0GicNGzas3eVyKaPRqC+44ILa2267rdJo/GGLzuTJ\nk0f8/e9/33Xssce2dX/84YcfTl6+fHn0c889V+rvcSXI+4kypGIynAymkwHvf3Stt3tr675wdzqf\nBKfdu71K8zXFT/I1zR+OUn03/UMIsTelFHGpE4lOHEVNyf+oL/uc5trVpA0964AL53i0pqSqnrUl\nFdS1tBMVYebIoiEMz0rt0WIn3TlcTua+v4CPNy3hjAnH84cTfhnw9DKtNf/34Dv834Pvcvj0Edz9\n7yuJTej7Lr9yp53flW1knb2FPyTncnVyTo/uHx/qIiIiPJs2bdoAUFZWZjrvvPMKmpqajA899FB5\nXx5XgnyAKKVQqhCDoRCT+XwAtHbg8azz1dpX4vYsx+14r9triryD6IyTMBiPwGAYi1KBL1gghDgw\no8lKeuFM4tMnU1n8ChVbXqChcgkZRbP2TBd0uT1ss9WyrtRGc7uduCgrR43MpyAjCaOh9wOo955e\ndh4XTf5ZwC11DruTeTc9zwdvLOGU86dz032/wGzp+yhY1tbI1eWbcGgPT2SP4sSY5D4/5kDKzs52\nLViwYOf06dNHP/DAA+VtbW3qggsuGLphw4bIwsLCjo6Ojj3/kP/85z+TH3rooczY2Fj3mDFj2iwW\nS4+6CCTIQ4hSFoy+2ncnrRvxuL/31to9K/C4P8ftesX3rBmDYZyv1u7rb1eFIbMohBCDiTVmCLkT\nrqfRtpiqHW+zY+W9xGadSK3hcDaU1dDhcJESG8UR4wrJTUkIOHArGquZ/caDlDdWcevPrgzK9LKm\n+lZuufwxVi3ewmU3ncnFvz+1z7vwtNa80FDB3VU7yDFbeSJ7FIURQesX36+KzS/k2NsqgnqQiKjM\ntswRv9jVk9eMHj3a4Xa7KSsrMz311FPJkZGRnu3bt69funRp5FFHHTUaoKSkxDx37tysFStWbExK\nSnJPnz59xNixY9sOtu/uJMhDnFLxGE3HYTQdB3Q2yZd7a+2e5bjdK3E5XwLnv32viMdgnIjReIQ3\n4A2TMBj6945VQgxWShlIyDwKY+xoVm5YynclcbixkRajmDFmOBkJsUEJxs22Hcx58yEcbu/0ssNy\nRga8z7KdVcy+eD4Vu2q57ZHf8NOzpwS8z4OxezzcXrWN1xorOT46kYcyRxBrPDRj5+uvv4657rrr\nqgCmTJnSPnz48DaAL7/8Mnrq1KnNWVlZLoCZM2fWbdmypUcDIA7NEg1j3ib5bAyGbDqnE2rtRns2\n7zWYzul4CHD7XjNkzyA6454pcDED9yaECFNNbR2sK62k2FaD9qQwJNFMiuMLIjq24C4fjyvyXMzW\npICOsXjbKm5/51ESouL4x6w/kZ+cFfB5r1u+jT9d+ijao3no5euZMGVYwPs8mEqXnavKNrGqo5mr\nk3P4Q3Juv/WH97Tm3Fc2bNhgMRqNZGdnu/ryOBLkg4BSRpRxNAbjaDD/EgCt23xT4DoH0y3H7Xob\nJwAGlGEURuPhvgF1R2AwjJIpcEIcQG1zG2tLKiipqkcpRVFmCmNz04mLsqI9Y6kr+5SakvfYvvxu\nUvJOISn7J71aZvbtVZ/y0CfPUZSWy30zbyA5OvDpZZ+9s5y7f/80aZlJ3PfcteQW9n0L3cr2Jq4q\n20irx82jWSM5ObbvR8OHmvLyctPll1+ed+mll1YZDAaOPvroloULFyadccYZzd999511y5YtUQDH\nHnts65w5c3JsNpsxMTHR89ZbbyWOGTOmvSfHkiv3IKVUFEbTVIxM7TYFrga3Z6Wv1r4cl/Nd4Hnf\ns5EYjIdhMHQOppuEUrkyBU4csrTW2BqaWVtio7yuCbPRwJjcDEbnpBEVYdmznTIYSc75KXGpk6jc\n9jrVO972zj0vuoCohCK/juXRHp786nVeXPZfphVM4PbTAp9eprXmxX99wON/e5NxRxbyt6evIiGp\n7yd6vdxg447KbWSaI3g2ZywjIg6dG2DZ7XbDyJEjR3dOP5s1a1bt7bffXglw4403Vl1wwQVDCwoK\nxhQVFXWMHj26FSAvL885Z86c8qlTp46KjY1197R/HORe60EXTvda9/a37/COkHcv9/W7rwa8U+BQ\nKb6m+CO6TYHzv9kwFO+rPRCkHLqEQ1lorSmtaWBtiY2aplasFhOjh6QzIjvVrxu4NNeupbL4NVz2\nOuLTp5A69CxMlh8GaNfqZ07uff/ffLJpKWdOOJ7fB2F6mcvp4sFbXuKdhV9xwplHcvODlxBh7dvF\nYBzaw12V23mx0cYxUQn8M2sk8X72hwfjXuurV6/eOWHChJpA9hHqVq9enTJhwoT8fR+XGvkhzNvf\nXoDBUIDJfC7QOQVuAx73ct8UuBW4HR+C75aSShV2mwI3CYNhHEr17cpIQvQHt8fDdlsd60ptNLZ1\nEGuNYNqIPAozkjEZ/Z8JEps8juiE4dSUvk/d7k9orl1L2tAzic+Y9oMZJU3tLdzy9sOs3r2ZK489\nnwuPDHwUeUtTG7dd+STffbGBX157CpfNPhNDAFPg/FHtcnB1+SZWtDfx26Qh/DElD6O05vUbCXKx\nF+8UuMMwGg/b85jWTftMgfsKt+tV37NmDIax3QbTHYEyFMkUOBE2nC43W8qrWb+rkja7k6SYSGaM\nKSAvNbFH64J3ZzBGeMM7bTK24lewbX2JxsolpBfNwhozZM92V710NxWN1dz2sys5MQjTyyrLapl9\n8XxKim3M+fvFnHbh0QHv82DWtDfzu/KNNLhd/CNzBKfHpfb5McXeJMjFQSkVh9E0A6Npxp7HPJ7O\nKXArcLuX43K+As4FvmfjMBgnDczJCuGnDoeTjbur2Li7CofLTUZCLEeNzCcrKS5oY0MiojPJHf97\nmqqWUbX9LXaunEdi9gzKjN5R43WtjUGbXrZ5TQmzfzUfe7uDvz9/HUcc2/dLsb7RWMlfKotJNVp4\nLXc8o60yG2YgSJCLXjEYsjAYsoDTgc4pcFt9U+CW43Z9BEBH+6VYIu72TZcTYuC1tNtZv6uSLeU1\nuD0eclMSGJuXQVp834SQUor49CnEJI2lYvt/eHrJ+7xfsQiAf/381qBML/vmw9XccdW/iU+K4R8v\n38DQEYHv88c4tYd7q3bwbEMF06LieThzJEmm3vXBa+0M8tkdeiTI+8CfbVvJM0eSb7GSb4kk12wl\nMsDBK6HOOwVuJAbjSDBfhNYdQCRu1/9od32A2TIbs+UqlLIcdF+DhdPlZuPuKgA+X7eNtPgY0uJj\nSIqJ7PM+S/FD9S2+ZUQr6wAozEhibG4GCdGR/XL88pZm7vpuK5tsDo7NjOdLILZtPQQY5K8//Snz\nb3+F4eNymfvMNSSnxQfnhA+g1uXk2vJNLG1v5NeJWcxJHYqply0YWruwd1wW5DM89EiQ94GPW+qo\nde/9LTPdZCHP7A32PLOVvG5/Rw/CkO8cABcZvRSH/c84Hbfjci0kImIeRtPxA3x2fcvudLFpdxUb\ndlVid3lvylPd2MrOqnoATAYDKXHR3mBPiCE1LrrHy1kK/1U1trC2pIJdNY2YjAZGDUljTE460db+\n+VKpteZ/677i4U9fwGQ0cefp1zBj+OHc84v5VO94G6WMJA35SY/363Z7eOSvr/L6U59y9P+bwG2P\nXEZkVN+uvbC+o4UryzZS43bw94zhnB2f1ut9ae3G3vHbbks8i96Sq0cfWFY0hWa3ixJnByWOdkqc\nHez0/f1ZSx3V+4R8qtG8J9j3Dfpwv52hwZCPNfJFXK4PcXTMpqP9LIymM7FE/A2DYcjBdxBG7E4X\nG3ZVsmF3FU6Xm5yUBCbkexfVOO+o8bR2OKhqbNnzZ21pBbrE+9qEaOueGntafAyxkREyhz8AWmvK\nahtZW2KjsrGFCLOJw4ZmMXJIGtZ+/NLU1N7C/R/+H19sXc7EnFHccuoVpMV2TeGMTZlI1fY3QRlI\nyj7O7/22t9m58+oFfP3has6//ESuuvVcjD0YWd8bi5qquNlWTILRxCu54xlv7f2cdK3dODquwu16\nHbPlDuCGoJ3nQOpcxtTtdqucnBz7q6++uiMlJcW973bnnHNO/mmnndZ46aWX1nd//N1334194IEH\n0j/77LPinhw3vFMihMUaTYw1xjB2P4M/Wj3uPQHfPei/bmvgjaaqvbZNNpr3CvZ8SyR5Fiv55kji\nwijkTaaTMEYfi9MxH6fjAdpdH2G23IjZck3Yr+DW4XCyflclG3dX4XJ7yEtNZHx+Jsmxe6/ZEG21\nMNSaxNB074Xc6XZT09RKVUMLVU0t7KyqZ0u5dxqs1WzqCvaEGJJjowJaRetQ4fFodlbVsbbERn1r\nO9ERFiYPy2FYVgrm/awJ3ZdWlm7knv89QX1bE1ceez6zjjjlB/+GWSMvoWyjh6ptr6OUkcSsYw66\n35rKBub86hGK1+/i+nsuZOYlfdvC5dKaedU7eaq+jCMj43gkayQppt63ZmjtwdFxHS7Xy5gtf8ES\ncT2DJci7L2M6c+bM/Pvvvz/1vvvus/X1ccMnCQaRaIOR0daY/Y7wbPO4KXV0UOJsZ2e3vxe3NfCW\ny7HXtolGE/lmb7DnmbsCPs9iJcHYtzd/6A2lrFgibsJknoXDfjNOx524nAuxWOdhMp040KfXY212\nJ+tLbWwuq8bl8TA0LYnx+ZkkxvjX52o2GslMjCMzMQ7w1iIbWjv2qrWX1jQAYFCKlLgo0uJjSPUF\nfKQl9P6NB4rL7WZrRS3rS220dDhIiLZy9Kh8CtKT+n08gtPtYsHXb/Dyd+8xJDGdx35+KyMyhu53\nW2Uwkj3qUso2LKCy+BWUMpKQOf2A+962cTezL55Pc0Mbf3v6ao766fi+ehsA1Lud/L58M9+0NfDL\nhEz+nDYUSwBTS7X24LBfj8v1AmbLHCwRNwXxbEPL1KlTW9esWRMJ4PF4uOSSS3K//PLLuKysLIfZ\nbPZ0bvf666/H3XTTTTmRkZGeyZMnt/TmWBLkISbKYGSkNZqR1h/e1rDD4/bV4r0BX+LoYKeznWVt\nTbztqqb7/bLiDaa9gr170CcaTQPabGsw5GKNXIjL9TGOjtnY28/BZToNS8S9GAy5A3Ze/mq1O1hX\nYmNLeTUerSlIT2ZcXuCDppRSJMZEkhgTyYhs71zcdodzT6hXN7awYVcVntJKAOIiI0iNjyHdF+4J\n0dZDrjne7nSxqayKjbuq6HC6SI2LZsrwXIYkxw9IWZTWVXDnfx9jS2UJZ0w4nqtnXEik5cdbnJTB\nRNbo31C2/t/Ytr6EUgbiM6b+YLtlX6zn1iueIDI6gvlv3siIcXl99TYA2NTRypXlG6h0Obg3vYjz\nEzIC2p/WGof9JlzOZzBbbsBsuTlIZ/pDcyq25GxxtAV1GdPhlqi2+zKH+7UYi8vl4rPPPov9zW9+\nUwPw/PPPJxQXF0cUFxev2717t3ncuHFjLrnkktq2tjZ1zTXX5H/00Uebx4wZYz/ttNMKenNuEuRh\nxGowMiIier/3LrZ7POxyeoO9pFtNfmVHE+82V+Pptm2swdgV7J198r5R9slGc79dAE2mEzFGL8bp\neASn4++0uyZjtvwRs+XakLxbXEu7nbWlNraW16CBogxvgMdF9d25RlrM5KUmkpeaCIDL7aG2uZXq\nxlYqG1soq21km60WAIvJSGp89J4m+ZS46H5vTu4vbXYH63dVeltD3B6GJMczzjeFbCACXGvNO2s+\nZ/5nL2I1W7jnzOs4Zpj/91IwGMxkj7mc3eueoGLLQlBG4tOP3PP8ooVf8eDNC8kbnsm8Z68lPTuw\nFdYO5r3mGm6q2EKswcSLOeOYGBkX0P68IX4zLucCzOZrMVtuG5RfOjvvtV5ZWWkuLCzsOOuss5oA\nvvjii9jzzz+/zmQykZ+f75w2bVozwKpVq6xDhgyxjxs3zg5w0UUX1S5YsKDHd9SRIB8kIgwGiiKi\nKIr44ZdQu8dDmavD21TfrU9+bUcL7zXX7BXyMQbjD/vkfb+n9kHIKxWBJeKPmMzn+0a3343L+aKv\nuf2nQT1WbzW1dbC2xEaxrRYFFGWmMC4vg9jI/u/bNxkNpCfEkp4Qy1i8F8jmdjuVvhp7VWML39eW\nA6AUJMVE7dXXHh0R3tP/Gls7WFdqY5utFq01Q9OTGJuXQVJMUCtfPdLQ1sz9Hz7NV8UrOSJvDH8+\n5XJSYhJ7vB+DwcyQMVewe93jVGx+DqUMxKRM5Mm5/2Hho+8z5fgx/PWxK4iO7bvpcm6teaimhMfq\ndjPRGsu/skeRFkB/OHg/o077rbicj2Ey/w5zxF19HuL+1pyDrbOPvLm52XDccccNmzt3btpf/vKX\nqoO/MjAS5IeACIOBAksUBZYfXuwc2kOZ075nVH2Jo52dzg7Wd7TwQXMN3YdbRinDXtPm8rsFfprJ\nEtBawwZDDtbI53G7PsVun429/Vxcpp/5mtv7tgnxQBpbO1hTUsH2ylqUUozITmVcbka/TVvyh1KK\nuCgrcVFWhmV6l4q0O12+UG+lqrGFLeU1e+azR0dYSEvoGh2fGB3Z69uQ9qeaplbWltgoqa7HaFAM\nz0phTO7AfJnq7rud6/jbe/+mqaOFq4+7kPMmnYQhgD5kg9HCkLG/Zde6x9i55hleeuFjvv5oG2f+\n4lj+cM+FmEx918LS5Hbxh4rNfNFaz6z4dG5PKyQiwPEFWmucjjtxOudjMl+OJeLeQVkT31dsbKzn\n4YcfLj3vvPOK5syZUzVjxozmf//736nXXHNNbVlZmXnJkiWxF154Yd1hhx3WUVZWZlm/fn3EmDFj\n7C+//HKvmlokyA9xFmVgqCWSoZYffst3ag/lTjs7u42uL3G0s9nexictdTi79cpblWGvmvz+Wgb8\nYTT9hEjjtzgdj+J03O9rbr8Bs+X3/dbcXt/SzpqSCnZW1mEwGBg9JJ0xuel7LV3pL6fbBUC7w37Q\nvtJgiTCbGJKSwJAU71rWHo+Hupb2PX3tlQ3N7PDdFMVkNJAa19UcnxofjcUUGpcFrTUV9c2sLamg\nor4Zi8nI+LxMRuWkDfhAP4fLyZNfvc6rK94nLymLeefcwLC04HzhNBgjiMm4iL/ecDdbN23jNzdM\n51c3XNSnAbjV3saVZRvY7bRzV3ohP0/IDMp+nY57cToexGS+BEvEvEMixDsdddRR7SNHjmx/8skn\nk373u9/VffLJJ3FFRUVjs7Ky7BMnTmwBiIqK0vPnzy857bTTiiIjIz1TpkxpaWlp6fG3NVnGNMjC\naRnTQLi0psJp36tPvnPw3S5nBw6t2T7yGOpdjl6PoPd4ynDYb8Htegul8rFY78NkOjm4b6SbuuY2\nVu+soKS6HpPRwMjsNMbkpvc6NJo7WvnL2/N5+IKbOetf1/Hro87mlLHHBLxEZaC01vvMaW+lvqVt\nz9eyxOjIvWrtMVZL0C7A/ixj6tGa0up61pbYqG1uI9JiZkxuOsOzUrH0YY3UXztryrjzv49TXF3K\nWYedwFUzZmE19/xL2oHKorTYxk0XP0yNrZErb0hh3IQGhoy+nJjkscE4/R/4sLmWGyu2EGkw8GjW\nSI6ICs6d4Rz2+3E67sZk/gWWiPk/upCSLGPqH1nGVASVSSlyLFZyLFaO2WfsnVtr/ttczZnAeaVr\neCp7DLmWntemDYZsrJHP4HZd4mtun4XLeDIW61wMhv1P5+mNmqZWVu+sYFdNA2ajkfH5mYzOSQ/o\nxiG2xhrmvPkgu+q9U0gz41O4/8P/45Xl7/PbY87j6KLDB6x2opQiJjKCmMgICjKSAe/tZKubWveE\n+3ZbLZvLqgHvgLu0boPokvpoTrvb42GbrZZ1JTaa2u3ERUYwfaR3GdFQmEOvteY/qz7l0S9eIsps\nZe7Z1zO98LCDv7AHvl+8mVsuewyj0cjDr/2RkRMy2LXmEco2LCB7zBXEJAVvIRSP1syvLeXh2l2M\ns8bwWNYoMnvxhWR/HPaHvCFuugBLxMOyGmIfkxp5kB0qNXJ/KKWYuGUxJqVYkD2a8ZGB3AnKgcv5\nOA77fYATs+V6zJY/oFTvB/5UNbawZmcFu2sbsZiMjM5JZ9SQtIBvl7q5cidz3nwQh8vJ3Wdex6S8\n0Xg8Hr4uXskTX71GaV0F47KHceWxsxiXPSygY/UVj9Y0tLZ7b1bjC/eWDu99DIwGRUpstHfqm+8W\ns1Y/Wy32Vwt1uNxsKfMuI9rucJIcG8W4vExyUxMCGncRTPWtTdz3wVN8u30VU/LH8adTLiM5OiGg\nfe5bFh+8sYS5f3yW7LxU5j1/HVm53jEPbmcrpWvm42ivZMiYK4lOHBHQcQGa3S5utG3h45Y6Zsal\ncXd6UcD94Z2cjkdw2G/BaDqXCOuTKHXwVhSpkfvnQDVyCfIgkyDvopSiuKOV35Stp9rl5J9ZIzgx\nJjmgfXo85Tjst+J2vY5SeVisczEaT+lR7bayoZlVO8qpqG8mwmxiTE46I4ekBaXZdvH21dzxzqPE\nWWOYd84NDE0ZstcF2+Vx87+1X/L0t29R19rIMcMmccXR55IXhBWw+lqb3UFVYyvVjS1UNrZQ19yG\nxx5aps8AACAASURBVPe+4qKsvvns3pp7fNT+57R3L4t2h5ONuyrZWFaN0+UmMzGWcXmZZCbGhlRf\n6tIda7j3vQW02Nu4csb5zJx4YkAD2jp1loXWmmceepenH3iHidOGc8+C3xGbsHczl9vZQumah3G0\nVzNk7O+IThje6+PucLTz27IN7HS08+e0An6VkBm08nY6Hsdhn4PRdBYR1qdQyr8vxRLk/pEg7ycS\n5F06L1Q1LgeXl21gXUcLt6YVcHFi4KHldn2F3X4T2rMRo/EkX3N74QG311pjq29m1c5yKhtasJpN\njM3LYERWKuYg9bu+vfoz/vHxcxSm5TD37BtIifHW2PZXC2132Hl1xfu89N3/sDsdnDruWC6dfvae\n14SDzjntlQ0tVDd5+9rtTu/gvgiTcc8d6DrntJuMBpRSNLV1sL7UxtaKGtweTV5qIuPyMkiJ++H9\nEQaS3eXg8S9f5Y2VHzE0ZQi3/exKClNzgrZ/pRQOu5N5Nz3P+68v5uRzpzH7/l9ituw//FyOZkrX\n/BNnRx05464mKv7An/cD+ayljj9UbMaiFPOzRjI1KnifN6djAQ77HzGaTiPC+gxK+T+2RILcP4M6\nyJVSZwFvAaO01psG+FwkyH26B1ibx831FZv5uKWO3yRm86fU/ICbTbV24nI+gcM+F7Bjtvwes+UG\nlIrqto2mvK6J1TvLqWpsJcpiZmxeBsOzUjAF6WYpHu3h31+9zsJl//3/7J1nfBVV97avOT2NJCQh\njYTQe69CQERApQjSsdGbiAW7DwICNhRBEUGKgqg0aQKKgBQJIEV6Qm/pvef0mf1+CPinhHCSnETk\nzfXFnzBzZmfnsO/Za691L9pUbczUni/gelNOQGEJXpnGbJYd+IWNJ3aiUakZ0OJxBrfshpu+bFpr\nOhMhBFlGMylZ/3fWnmU0A/lz4OPhSs+W9Vi68zASEtUDfGhQJQDPUjTUKS6XUmKYtmUBV1Jj6dus\nC2PbD0CvdW7ZoSRJTOj7KccOnGf4608y9JXu99wZ263ZRJ/4Ars1k5CG43Gp4JgRmBCC+emxfJ56\njXp6N+YH1yVY67x5t1mXYrW8jFr9BHqX74vcrrhcyB3jQRfyVUAQsFMIMaUI96mFEHd0pinhWMSE\nvp8yeNxjtOnU4L4KEZY1twuYLAQzki/zfWYCT7j78FlgLQxOyOBWlMTr4fbVSFJofmc1dXfi0rM5\ncSWe1BwjbnodDasEUCPQF40Tu0RZ7TY+2rqIP84e5MnGj/DKo8/dkZXuSKZ2XGYSi/auZee5g3i5\neDDkoV482fgRtP+hxjgFYbbaSMnOIykzk+TMOLq3DOfQ+bPUD61arHK+0kYIwdpj21mwZzXuelfe\nfnwEbao1dvpzYi4nEVo9gEfCxvHWZ8/zWN87LVnvhs2SSfTJL5CtOYQ0fBGXCmGFXp+nyLyZcJ6t\nuWn09PDjo4AauDixcsJm+xGreTxqdWf0Lj8WqwlSuZA7xgMr5JIkuQPngEeATUKI2lJ+iuRXQCcg\nBrAB3wohfpYk6SqwCugCzAQOA/MAP8AIjBJCnJUkyQ9YANww/35FCLHPgfGIPs3fJDkhg6q1gxg0\npiude7dEp///r8FFQQImhOC7jHg+TLlCU4MH3wTXo6LGOXMj2/dhNr9JbJoXZxPGkWEMwN2go1GV\nQKoHOj/zOduUy/82fsmJ2HOMaT+Ap1t1u+e58L04k3CZBX+u5ljMGYK9KjEyvB+darf6T74QCpGL\nbN+G3b4R2b4dyMO9QjZ5ObXRG5ai1jguXmVBWl4mH/+2mINXT9G2WhPeemwE3m4lsyYtiD2/HuWj\niUv5/dxcjh04R5M2RT/vtlkyiD7xBbI9j9CGL2HwKDjkf81qYmzcGS5ajbzlF8YI72CnfpfstlVY\nzGNQqTticFlZbK+HB0XIb7QxtdvtklqtFoMGDUqbPHlyktqB6N/dWpvezN2E/EGoCegFbBVCnAfS\nJElqDvQBwoB6wHPAQ7fdkyaEaCaEWAksBCYIIZoDrwNfX7/mC2C2EKIl0BdYfLcBSJI0WpKkI5Ik\nHQFYuf8D/vfFMFQqFR9NXMqAh97lx3lbyckyOu2H/q8iSRLDKwYzN6gOpy259Is+wVWrqcSfqwhB\ndFpdtkd+w4FL72OTFVpWnUWPphuoGeT8cqn4zBReWDGDqIRLTOkxjmda3zss6gh1A6sxZ8BbzOwz\nEb1Gx/ubv2bMD+9zNPqME0Zd+giRjd22BrPpGYy51bGYh6HI+9FoB2Fw+eX6VS6YTd2xWec5/IJT\n2uy/dJxhSydxLPYsrz76PB899YrTRdxul5k3/WcmjVpAaPX8BiTFEXEArd6b0EYvoVK7EH1qLubc\n2Duu2ZuXwVPXTpBkt/Jd5fqMrFjZySL+MxbzWFTqcAwuP92X/RHKmhsWrRcvXozcuXPn+e3bt3u+\n/vrrdyQF2Ww2pz73QdiRbwa+EEJslyTpJfJ30BrghBDiu+vXrAN+umlH/rAQ4tr13XwK+Tv6G+iF\nEHUlSUoG4m/6cz+gthCi0DZzN5+RCyE4/GcUK+Zv48jeM7i46en5dHsGjHoU/+CSZW//F7jXTvRv\nUzZj4qKQgG+C69GsGI0ZFEVwJTmdk1cTyDKa8XQ10DgskFBfG7JtKnb7CiSpMjr9h6g1TzplITuT\ncJm318/Grsh80OslmoTUKfT6ouzIb0ZWFLZF7WfJvrUk56TTumojxnYY4NSEK2cgRAZ2+2/Ito3I\n8k7AiiQFotY8iUbTC5W6zT8lSJIkoSiZWMwvINs3o9b0Qm/4Ckly/s7XESw2K1/vWcn6439Qwy+U\nyd3HEuYb7PTnpCZlMvWFRZz46wJPDenIi1P6ozfoSvwiYzWlEn3yC4RiI7TRS+jdghBCsDgjjpkp\nV6mpc2VBcL1i+TgUht22AYt5OCp1Gwwua5CkkiUqPig7cldX16ZGo/HYjf+PiorStW3btl56evrx\nr776ymfDhg3eRqNRJcuydPDgwXO3tzYdOnRoWnF25P/pAzhJkiqSHz5vKEmSANSAID/xrTDyrv9X\nBWQKIQpydVABbYQQ5hKMj1YP16fVw/W5cDqGFd9sY+23O1n77U46PdmCwWMfo2aD+2tRLkuau1Rg\nTWhjRsRG8mzMaT4PrMXjHr4O3asoCpcS0zl5LYEckwVvNxcerl+NKpW8/0mi02gWoLEPxWp5HYv5\neVTqR9AbPkWlKn7tdsTFo0zbPB9vN09m9pl417IxIQQnDl5gy4r805j1y3bT+/mHi/QioVapeKJB\nOJ3qtGLd0R0sP7iJ4cve47H67RjRrg/+Ff69l0GhpGG3b0G2b0SWdwN2JCkEjXY0Gu2TqFQtbzEB\nUYTg24w4AEbHxRLuNpPH9M3wsH+AKS8Sg8tyVGrnmZ04wsXkaN7fPJ9r6fEMaP44o9v3Q+ekY56b\nOXbgHFPHLcKYa+a9uSPo2qe10z5b5+JLaKOXiD4xh+iTc/FrOIGp2TlsyknhCXcfPgmshZuTnQTt\nti1YzCNQqVpgcFlVYhEvDSym8SGKEuXUTjoqVT2j3mVekZqx1KtXzyrLMnFxcRqAyMhI15MnT0b6\n+/vLy5YtK7C1aXHG9p8WcqAfsFwIMebGH0iStAdIB/pKkrSM/J10R+Cn228WQmRLknRFkqT+Qog1\nUv4q20gIcQLYBkwAPr3+uU2EEMeLO9CaDUKYPHcEY97uzZrFO/nlxz/Zvv4QLdrXZfC4rrTsUO8/\neQ5aUqrqXFgT2pgxcVG8GH+W//lVZVjFu++IZEXhYkIap64lkGu2UtHdlUcaVifU16vA+VNr2mBQ\n78Zu+xarZQamvIfQ6saj1b1BfkDGcdYd28GXO3+gln8YHz/1KhXd7rSyTE3KZOuaA2xZuY/YK8m4\neeTvhD5/9ycO7Y7krVnP41WxaMY4eo2Owa260b1hB344uJl1x3aw8+xB+jbrwrOte+BRQO/60kAo\nydjtm7DbN6LIEYCMJIWh1Y1HremFSlWwW12y3cobCeeJMGYCcNlqYmdeBtNoTVeXT5ni+QF2YyeE\n7nM89U+X+s+hCIU1f29j4d41VDC4M6vfG7QMc779qRCCFQu2sfCj9QRV8WP2ylepVsf5u32dix+h\njV7i4OmFjL92jMsaT173rcJYJ4fSAez2rVjMQ1CpmmBw/RlJKr7J0/+PtG/fPtvf31+Gu7c2LQ7/\ndSEfDHxy25+tBeoCsUAU+cluR4Gsu3zGM8B8SZImAVpgJXACeAmYJ0nSSfLn6U9gbEkH7B/sw4tT\n+jPkle788sOfrFnyB689/QXV61Zm0NguPPpky7vWkT6o+Gi0/BDSgNcSzjMj5QoxNjP/q1QN9U2L\nkF1WuJCQyqlrCRgtNnwruNG6ViiVfTzvuVhJkgatbjQazVNYLVOxWedgt61Bp5+BWvPUPe9XhML8\nPatYdWQr7ao3ZXL3cbc0QLHb7BzYeZotKyL4a+dpZFmhcZuaDHm5Ox17NMPFdS4Tpg5gwYfrGNp5\nGpPmDKNFh6LvPiu4uPNCx0H0bdaFJfvWsfLwb2w+tYdnW/egT9PO6EvYbrIgFCUe2b4Ju/0XFHkf\nIJCkGmh1r14X74aFzt8fuWm8nXgBo6Iww78GTwN/VGtBjNVMhDGTiDwfnkn9kimeH9KccWzM3spl\n3qOdWyWauHigc7K1Z2puBh/+togj1yIJr9GMN7sOx8vV+WKUm23kw1eXsnfrcTp2b8bbs4aUavvR\nI0LPK96PYrNbmJZzhH6htUtBxHdgMT2HStUAg+vaf+04xBGKunMuLaKionRqtZrg4GA7gKurq3Kv\ne4rDf/6M/G5IkuQuhMiVJMkHOAS0E0IklsFzi1RHbrPa2b7+ECu/2caVc/H4BXjRf1Rnnnymfan+\nwy8Lino2rAjBxylXWJIRT2f3iswJrI1WwLn4VE5fS8RktVHJ053GYYEEVaxQ7IVKlg9hNb+GopxE\npX4Yvf5TVOqCbS8tNisf/LaQ3ecP06dpZyY88sw/iXPRl5L4ddU+fluzn/TkbCpWqsATA9rSfWA7\nQqr53zEPFyNjmDp+MdcuJDBobFdGv9W7RC9tl1KiWbBnNQevnsLfw4cR4X3oUrdtiRP7FCUG2f4L\ndttGFOVg/s+gqofm+pm3pKp7z7k3KzIfp1xleWYC9fRuzAmsTXW9a4HfCbsQnDKlY7FMo6FmKaet\ntXgt4x2ylUDauHoS7uZFezdvwrQFu8U5yt4LfzNz27eYbVYmPPI0PRt1LJUo2MXIGN4b/Q0Jsam8\nMKkf/Uc+WuJqhrshhGBpZjwfJV+hqs6FL719UZ2Zj6TSEtroZXQujh1V3QvZvguzaSAqVS0Mrr+Q\nf6rpPB7EM/L4+HhN//79q7Zq1Spv9uzZ8V9++aXPkSNH3L7//vtogGXLlnktWrTIb/fu3Rfi4uK0\nDRs2rP/FF19cK84Z+YMs5LsBL0AHzBRCLC2j5xbLEEYIwcFdp1kxfxtH95/DzcNAz2c60H/Eo1QK\n8i6FkZY+xV2olmXE83HiZXpYXGmao8JqsxPg5UHjqoEEeDnHvlMI+Xq4fTqQh1Y7Dq3+rVtChZnG\nHN7dMIfT8RcZ33EwA5o/htlkZffmv9mych8nDl5ArVbx0KMN6TE4nNadGhTYL/rmeTCbLMyb9jMb\nvt9DzQYhTJ03itAaASX6Wf6OjmLBnlWcS7pKdb8QxnYYQKuwwnfKt6Mol7HbfkG2b0RRjgKgUjVE\nrel1PWHN8ezqs+Y8Xkk4xwWrkRHewbzmW+UfH+97fSfstk2YzeOwo2a9eTrf59Qj2pafphKs0f8j\n6g+5ejrcVc9ktfDV7p/YdHI3tfyr8F63saVmifvrqv3MevdHKni58f6C0TRqWeOu15ZUyM2KzKSk\nS6zPTqaze0U+C6iFh1qDOTeW6JNfolIbqNL4FbSGkomubN+L2dQfSVUNF9fNThdxeHCE/Pbys4ED\nB6ZNmTIlSa1Wc7uQK4rCTcluFq1WK4qb7PbACvm/hTOc3c6euMrKb7aza9MRJJVEl96tGTimCzXq\nVXbSKMuG4ixUVrudM7HJnIhORLErxBmgW80wmvo5Z2dxO0JJxWqdit22HEkKvB5u70t8VjJvrJ1F\ncnY6/3tiNP4mP7asiGDHxsMYc81UrlqJHoPDeaxfG3z9C7e5LGge9v5+nE9eW4bFbOOlaQPpMTi8\nRC8oilDYde4wi/auIT4rhWah9RjXYQC1A+7eJU5RLmC3bbwu3icBUKma5Yu39klUKsdcw24ghGBZ\nZgKfpFzBU6Xh08BatHe79SXUoTamyiXMpucQShRa3VskMIF9phz25mWy35hJriKjAhoa3Al386a9\nqxdNXDzQFhCGP5d0lelbFhCTnsiglk8wMrxvqZjsWMw2vpi8kk0/7qVZ29pM+XoUFf0KDz2XRMjj\nbRZeiD/DKXMuL/uE8qJPyC1OieacGKJPfYla40Zo45fR6ou3GZDt+zGb+iKpQnFx2Yyk8ivW59yL\nB0XIS5tyIS8jnGnRmhCTyupFO9iyYh8mo4VWHeszeGxXmofX+U8kxhVlobLY7ETFJHEmNhmrXaay\njyeugZ68nH0FRQi+Ca7rtD7JBSHLR66H249zLuURpvwWgGJU0VVqz9Gt57l8Jg69QcsjPVvQY3A4\njVrVcPh3cLd5SE3MZMbL3/J3xFke7taUN2c+TwXvkiWu2WQ7v5zYxdIDG8ky5fBondaMCu9HkFel\n/AYdylns9o3Y7RsRShQAKlUrNNpeqDU9UamqFOu5qXYrbyZeYE9eBp3cvPk4oBY+BWSAO/qdEMKI\n1TwRu30FanUn9IbFSCof7EJw0pxDRF4me/MyOG7OQQHcVer8MLyrF+Fu3oRqdKw6spXFEWvxdq3A\nu91G0zy0dLLi46NTeW/0As6fiubZF59gxBtPFhiZuZ3iCvlhYxbj489iVhRmBdaii0fB1QumnGvE\nnJyLWutxXcyL5qsuywcxG/sgqQIxuGxBpfK/903FpFzIHaNcyMuI0vBaz87IY8PyPaz9difpKdnU\nbBDC4LFdeaRHczQlbLlZmjiyUJmttn8E3CYrhPp60Sgs8J8GGtFWMyPiIom1mfksoBbdK5TOjgDy\nw+1/RH7Kh4uiUJ+RsJ/XY7dB3SZhdB/Ujkd7tcS9QtErWgqbB0VRWLVwBws/Xo+3jweTvhxOs3aF\n16U7Qp7FxIrDv7L6yFbsip2eDSswsOlBPPVnAAmVui0aTS/Umh6oVCXLpN6dm86biRfIVWTe8Qvj\n2UK6aRVFvIQQ2G1LsVreRJIqoXf5HrW6+S3XZMt2Dhgz84XdmEGMzYLKlEvgib2QEkvtqo2Y8vgI\nKpew5ejd2L/jJNNf+haEYNIXw2nX1XE716IKuRCCnzITmZZ8mcpaPQuC61FTX/j30ZR9mZhT89Do\nvAht/DIanWMJarL8N2ZjLySpEgbXLahUgQ6PsziUC7ljlAt5GVGaTVMsZhvb1x9k5YJtXLuYiH9w\nRfqPfJSeT7fH1f3+c1UqbKEyWW1ERidyNi4Fu6wQVsmbRmGBVHS/c2HKlG2MiTvDEVM2b/qGMbqi\nc20mARJj0/h09vcc2hIFORLuntC513ke75dF7UbvoNb0L/YzHVmwz526xvsvLCb2SjJPj3+Mka8/\nWeyXNCEEinIM2b6RpMwt/HDEld/PVsGgkRjUIoz+LUbhpi+5f4FFUZiZepWlGfHU0rkyJ6g2tfWF\nRxSKswuV5WNYTM8jRAI6/UdotCPv+rv4OWof3+xYjlWxk9egHRmVa6CSJBobPAh38yLc1YvGdwnD\nF21MCks+3cjyub9Rs0EIMxaOJahK0V4yixSxUhSmJl9idVYSHd28mR1YmwoOHhEYsy4Rc2oeWkNF\nQhu9jEZXeJa+LB+7LuLeGFx/LfGLniOUC7ljlAt5GVEW3c8UReHAjlOs+GYbJ/66gLunK72e60C/\nYZ3wDbh/2mAWtFAZLVZORydyLi4VRVGo6l+RRmGBeLkVnqFvURTeSDzPlpxUnvEKYHKl6mhKKOZW\ni429W4+zeUUERyLOgBB41/Vg/PgBPNKtOWrNSazm11GUo6jU7a5nt9cv8nMcXbBNRgtfTlnF5p8i\nqNskjMlfjaRy1UoOPUMIBUU5cv3M+xeEiAY0qNUPo9b0Ii67BYsidrD34lF83LwY3u4pnmjQ/o4G\nL45y3pLHqwnnOGsxMsQrkLf8qv6T0FYYxQ0nC5GOxTQGWd6GWtMfveGLW4xIjFYzc3f9yJZTf1In\noCrvdR9LgFclTphyiTBmEJGXyYnbwvDtXb0Jd/OiShGz4TNSs3l//GL+jjhL98HhvDp9EHqXopf+\nOToXSXYL4+POcsycwwsVQ3jFN/SW0kxHMGZeIOb01+hc/Ahp9BIabcEeCrJ8ErOxJ5JU4fpOPLTA\n65xNuZA7RrmQlxFl3cY08uhlVi7Yxp+/HUOlVtG1T2sGje1K1Vqlk5VbFG5eqPLMVk5dS+B8QipC\nCKr5+9AoLLBILSwVIfg09SoL0+N4xM2bL4LqFMu16tKZWLas2Me2dX+RlZGH3luLpbaJHoPCeb3v\n0FvKt4RQsNuWY7VOBZGFRjsanf4dJMnx8/qiitfuLX8z883l2K0yr8wYzBMDHipQaISQUeSD15uS\n/IIQ8YAOtfoR1NpeaDRP3JFhfCruPPP3rOJ0/EVCKwYypn1/wmsUbORSEDfCux+kXMFNpWZmQE0e\ncXc8i7kkCV5CKNiss7BZP0BS1cZgWI5KXYszCZeZtmUB8ZnJPNu6B8Pa9kZTwG4163oYfm9eJhHG\nDGJtFgBCtHrCXb1p7+bFQ65ehe50Tx2+xJSx35CVmcfEDwbTfVB4sX4WcGwujpqyeSHuDHmKzMzA\nWjzhoPNhQeRlnCM2cgE6F39CG01Arb01eqLIkZhMPZBwvS7iYcV+VlEpF3LHKBfyMqKshfwGcVeT\n8xPjVu7DYrbRplMDnh73GE0eqvWvJcZJkkS20cypawlcTEhDADUC8gXcw6XorQ5v8FNmAlOSLlFX\n78aSyvXxc8AIJS/HxI4Nh9iych9njl9Fq9PQ+tH6xATHEe0Wz0udn6Zfs653vV+IdKyW6dht3yFJ\nfmj109BoBjk0t8URr6S4dD54+VuOHThPp54teP2TZ/HwdEUIO4q877p4b0aIJECPWtPl+pn3Y/d8\nyRBCEHHxKN/sXUN0egINg2sytsNAGgYXbl2bbrfxTtIFduSm08HNm5kBNR2a+5txRu20bN+F2TwC\nWbawIfIlvvvrHD5unkzqNuaevvc3EEJwzWb+52z9L2PWP9nwjQ0etHfLT5prbPBAc33MPy/Zybzp\na/APrsj0hWOp1aBku9V7zcWqzESmJF0iQKvjm+B69zy2cITc9CjiIheidwskpNEE1Jr8oyxFPovJ\n1B0J7XURr17iZxWFciF3jHIhLyP+LSG/QWZ6DuuX7WHdd7vITMuhTuMqDBrTlYe7N3Mok9ZZZBvN\neLq5sHTnYSQkagb50jA0APcSCPjN7MpN56X4s3irtSypXL/ApB8hBCcPXWTzigh2bTqCxWyjWp0g\negxuT71HqjB95wLS8rKY3H0s7Ws2L+ApdyLLx66H24+gUrdBp/8MtbphofcUu2mKrPDT17+z5LON\n+PobeHuWnbpNfwWRBrii1nRFo3kStaZrsawy7YrMr6f+5Nv960nPy6J9zeaMDu9XYI31vrxMXk84\nT6Zi403fMIZ4B91S7uQozhBygITMSGZsmc6pBD0daxp4vesnVHAp/rGSTSicMOWw93ri3MmbwvCt\nhAu2j/dw6fdIwrs25t05w/DwLLmN993mwioUPki+wg+ZCYS7evFFUG2Ha+YdITftNLFRizC4hxDS\ncDySKhazsRsgXT8Tv3vte2nxoAj5jTpyWZalkJAQy+rVq6/4+vrK97pv4sSJQe7u7vK0adOSCruu\nXMjLCEmSxJXUOMJKyXDCUSwmK1t/PsDKb7YTeyWZwFBfBozqTPdB7XBxdY6YFkSuycKJqwlcTEhl\n6KMt+evcNRpUCcBN73z70FPmXEbFRmIRCvOD69LGNX8hT0vO+sfvPOZyEq7uBjr3akn3weHUbRLG\nqbgLvLthDipJxcd9XqVeYNF2H0Io2O0/YrVMAZGBRjsKnf5dJKlgISmOeAlhQZZ3I9s2Enk0go9f\nr09SrDuDXxAMe6UHOkNXJMk5PSFMVgur/97KisO/YrFZ6dawA8PaPoWvuxdWoTAr5RqLM+KoqXNl\ndmAt6hqK5lF/M84Q8j/OHmTW9qXIisyEhw10rLYMtbo1epelqFTO+XeXKds4YMxi68kLHH19HSI2\nm5wRTfF+tjnt3fPP1u8Vhr8XBc1Fqt3K+PizHDFlM8o7mNf9wkqcC1IQOakniTuzGDfvClSssgYk\nGReXLXd1OCxtHhQhv9nZrU+fPmE1a9Y0f/LJJ7c4itpsNrTaW1/MyoX8PkOSJPHwZ0N4rF47hrbt\nTaBn6ZVLOYKiKERsO8GK+ds4feQSHl6uPPV8R/oO73RPw4qiYLLaOHk1gXNxKQDUDvajTe0qpd5v\nOs5mZnhsJNdMRkadV0jdeJoDf5zK9ztvXZPug9rRsUfzf15edp49yIe/LcK/gg+f9n2NIC/HkskK\nQogMrJYPsNuWgOSDTv8+Gs3gW7p+QVFqp03I9p3Xw+a/AdmAJxpNNyyWJ5g7NYWtaw7RoHk13vtq\nJEGhzjXJyTRms+zAL2w8sRONSk2Xpo/yZ1AYUYqdZ7wCeMevKi4l7KRVEiE3Wk3M3rGc36P2UT+w\nOpO6jyHYyx+7bS0W8wSQXDAYlqDWdCzRGG+wff1BZr6xHBc3PWO+HEJaI18i8jL5y5hFnpBRcyMM\nny/sja6H4R3l9rk4acphXPwZMmU7HwXU5MlSLLUEyE7dgpBGolKDi9tvaLQFNYEsGx5EIZ85c6bf\nyZMnXX744YfozZs3e0yZMiXI09NTvnz5suHq1aun33rrrYBVq1b5+vj42IKCgqxNmzY1lgv5hD5N\nQgAAIABJREFUfYIkSeKrXT+x/tgfKEKhV+NOPNumBz6lVMdaFE4dvsTKb7axd+txtDo1Xfu2YdCY\nLlSpUfwaUYvNTmR0IlExychCoUaAL42rBuJu0DstjFoYMZeTWPfTXtatjkBJM2LwceOpAe3oMSj8\nFutTIQQrD//G/D9X0Si4Fh/0fhlPl+LvLG9Glk9cD7cfQqVqhc7wGWr1/9UTFzYPQuQh27dfF+/f\nye+w641G2x21pjdq9cNI0v9FM3ZsPMSst39EUQSvffSMU1ti3iA2I4nJu37g4uWTCJ2BJ1o+wRut\nejjFEa2434nI+ItM37KAxOxUnm/zJM8/1OuWjHtFPofZ/BxCuYBWNwmt7tU7XqgcxWqxMW/aGtYt\n3U3DltWZtmDMLdUgVqFw3JRzvelLBifNuQjAQ6WmravX9TI373v2AL95LtZlJfG/pIv4qnUsCK5L\n/RJEPRxBUaIxG7uhKFkkneuAVteayg3GolI7P3LmCM4W8o+3Lg65nBrr1Dam1XwrG99+fGShzVhu\nCLndbqdnz57VRowYkdqvX7/szZs3e/Tv37/GsWPHIuvUqWPdu3ev64gRI8L+/vvvszabjSZNmtQb\nOnRoSnGF/P51E/kPM77jYPo3f4xlBzay4fgfbDm1h37NuzK4ZbcyazlZEA1bVqdhy3FEX0pi9aId\n/LZmP5t/iqBdl0YMHvdYkdzKbLLMmZhkTkcnYrXLhFXypmm14CJloRcXs8nC7s1H2bwyghN/5fud\nt36kASmPV+XPRh7E+AQS6P9/O227IvPlzh/ZcPwPOtVuzTtPjHRqpzC1ujEG19+x21dgtUzGbOyI\nRjscnX4SknSnNaYQOcj236+L93bABJIvGu2A677m4UhSwWeinXu1okHz6kx7cTHTJyzh4K7TTPzw\naac12MmUbXxoTGdP/da0qNaIimcPs3Xfek5F7mNkeD861W5VpsmTdkXmh782sezARvw8KjJ30Ls0\nDL7T912lro2L604s5pexWaehyIfQuywocP4LIykujffGfMOZY1cZOLoLY9996o56fp2kopWrJ61c\nPZnoW4WM62H4vXkZ7M3L5Pfc/JbSoVpDftKca743vEcBL0I2ofBxSn4tfhtXT74MrFOgI54zUZRY\nzMYeCJGNi9smfEOtJJxbTmzkQio3GINKVbrPf5CxWCyqOnXq1EtKStJWr17d3Lt37+wbf9eoUaO8\nOnXqWAF27drl3q1bt0wPDw8FoGvXrpkleW75jtzJ3J7sFpuRxLf71/PHmb9w07vwdKtu9G3a9ZY2\nmP8WGanZrFu6m/VLd5GVkUe9plUZPK4r7R9vilpd8G5GVhTOx6dy4mo8Zqudyj6eNK0WjI/HnS+/\nztyRCyE4e+Ladb/zQ+TlmKkcVonug9vxeL+H8A3wQgjB56nRfJ0eQ3tXL74KroPaLvP+5q/Zf/k4\ng1t2Y0yH/qic3Brz1nFmYrV8iN22CCRvdLqp6PRDUJQM7PatyPaNyPY/AAuSFIBa0/O6eLdFkhwP\nW9vtMsvn/say2ZupFFyRyXNH0KBFyTKNDxjzE9rS7DZe86vCCO9gJODglZMs+HM1l1NjqeNflbEP\nD6RZaN1iPaMo34mErBRm/PoNp+Iu0KXuQ7za+Xnc7+Fklu8Gtwir5V0kKQi9y/JboiOFcWhPJNPG\nL8Zmk3l71hAe6eFYAuTtz79iM+WXuOXlZ8MbhYIaaOJSgfbXd+wNDR5oVSqejj7JX8YshnoH8bZf\nWImNau6FosRjNnZHiFQMrhv+ccrLTPyLxPM/4uZdl+D6o8pczB+00HpOTo6qY8eONZ966qmMSZMm\nJW/evNlj1qxZ/rt27boIMG3atErp6emaOXPmxAOMHDmyclBQkK08tH6fcLes9Usp0SyOWMe+S8fw\ndq3A822epGejjuhK+e3bEcwmC7+tOsCqRduJu5pCcJgfA0d14YmBD2G4nmWuCMHlxDSOX4kn12zF\n38udZtWC8fe6e7a0M4Q8Kz2XbesOsnllxD9+5x27N6f74HY0aVNwad2qzETeS7pITQF+h7ZxNSWa\nVx59jt5NHi3RWIqCLJ/CankDRT6Ae4VscrN9ABuSFHxTR7FWxQ7/3uDU4UtMn7CY5PgMhr7ag+de\n6nbXl7C7YRMKc1Kj+SY9ljCtC3OCatPgttCurChsi9rPkn1rSc5Jp3XVRoztMIDqfkVziHP0O7Et\naj+zd3wPwKudn6drvbZFeo4sH8ZiGoIQqej0n6HVPX/XaxVFYdkXv/LdrE1UrR3I9IXjCK3uHF9x\nq1A4Zsphb14GEcZMTl8Pw1dQqTleqy11zkUww78GfT1Lz8f8BoqShNnYDSESMbiuR61udcvfZybs\nJ/HCT7hVbEDleiORVGUXsH3QhBxg3759Lv37969x7dq1U7///vstQh4REeE6fPjwsKNHj56x2WxS\nkyZN6g0ZMqTYofVyIXcy9yo/Ox1/kUV713As5iz+Hj4Ma9ubrvXbFdthy5nIssLercdYMX8bUceu\n4OntxlNDH6HNUy04n5JOltGMj4crzaoFO9QPvLhCrigKf0ecZfOKCPZuPY7NaqdO4yp0HxRO596O\n+Z3/HHuGORu/QrKamfDEKAbUaVPkcZQUIQR2+yp0usFYTP9Dre2NStWsxOJ9O7nZRj5/9ye2rz9E\n49Y1eW/ucPyDC26kcTtXrSZeTTjHSXMuAzz9ea9SNVwL+S5a7FbWHd3B8oObyLOYeKx+O0a064N/\nBceed6/vRK7FyOc7vmfHmQM0DK7JpG5jip0wKpRUzOYRKPJuNJpn0Rk+Q5JuPYLISs9l+ktLOLgr\nkq59WvP6J8+WalVHhmxjf14mEcZMPg6sxQljNo1cil46WFSEkoLJ1B2hxGJwWYta81DB44vfS9LF\nVbj7NCa47nCkMlqXHkQhB+jUqVONvn37plepUsV2s5ADlCe73cc4UkcuhODv6CgW7l3D2cQrhFYM\nZGS7vnSo1bxUw76OIoTgxMELbPrlEIZqPvhV88Oea6Fp1SCaNQgrcdevu5EUl8avq/bz66r9JMam\n4eHlStc+begxqB016ju+8zsec5Z3N3yBSq0mvdXj5Hn68HVQXdr9SwmHZZH0B/D72r/4/N2fUKkk\n3vjkOTo9efd1UQjB2uxk3k+6hFZS8WFADR4vgmtYtimXHw5uZt2xHQD0bdaFZ1v3uGcOSGFzcTL2\nPDN+/YaUnHSGtu3NM617lPgFVwgZm/VjbNaZqFQN0bss+8fs5Mzxq7w3egHpKdm89P5Aej3XoUzP\n/8vqeyGUNEymngjlMgaXn1FrCnejS4/bTfKln/HwbUpQ3aFFOvIpLg+KkJc25UJeRhTFEEYIwd6L\nf7M4Yi1X0+Kp5V+FUeH9aBXW8F9tU5qclcvfl2JJyszFoFaTdCyaX+Zuw2ax0/7xJgwe29Wh81hH\nFiqrxUbE7yfYvDKCI3+eQQhBi/Z16T64He0fa4reULSjh+1nDvDRb4sI9vJnZt+JCNcKjIyN5JLV\nxIcBZRPCvJ2yWrAB4q+l8P74xUQdu0K3gW15efogXN1uTUDMlu38L+kiv+ak0trFk88CaxGkLd4u\nNCk7jSX71vF75D7cDa4827oHfZp2vmsyYUFzYVdklu3fyPKDvxBQwZf3uo+lfpBzTUns9m1YTKMA\ngU7/NZtXuDN36moq+lVg+sKx1G0S5tTnOUJZfC+ESMdsfBJFuYDBZZXDpXnpsX+QfHk9FfyaE1hn\niNOjSLdTLuSOUS7kZURxnN1kRWHHmQN8u389CVkpNKpci9Hh/WlU+c7s3NIkLcfIsctxxKZlYdBp\naBwWRK0gX9QqFWnJWaz7bhfrv99NTqaRBi2qM3hcV8K7NkZ1l2YZhS1Ul8/GsXlFBNvW5vudVwry\nptvAdnQb2JbAkKLXRwsh+PHQZhbu/ZmmIXWY0eulf3aHObKd8fFn2WfM5GWfUCb4hDyQO68b2G12\nls7ewvdf/kpwFT8mzxv5j1AdNmYxMeE8yXYrr/iGMrpi5SI34CiISynRLNizmoNXT+Hv4cOI8D50\nqdv2Ft96uHMu4jKTmLHlGyITLvF4/XBeefRZXHXOycC/HUW5RmbaEL6YrGPnL2G07liP9+aOxLNi\n6ZZ63Y3S/l4IkYnZ2AtFiULvsgKNpnOR7k+L2U7KlY1UqNSKwNrPlqqYlwu5Y5QLeRlREotWm2xn\n88k9LPtrI+l5WbSp2piR4X2p5V/FyaO8lSyjmeOX47mSnI5Oo6ZBaAB1QyqhVd8ZUjPmmfl11X5W\nL9xOQkwalatWYtCYLjze76E7OkDdvlDl5Zj4Y+NhNq+M4Myxq2i0asK7NqbH4HBadKhX5CStG9gV\nmdk7lrHp5B661H2Itx4bcUcSoVUoTEq8yNrsZPpWqMSMgBroyugYo6yF/AbH/zrP9AlLSEvOYvjr\nvUgdUIf5mXFU1hqYE1ibxqVwNvt3dBQL9qziXNJVqvuFMLbDgFsiTDfmQgjB1sh9zPljOWqVite6\nDOXROs6vib+Z6IuJTBo9n6vnE3h2wimeGe+Di+sSVKqyj9JA6X4vhMjCbHwKRTmJ3uUnNJq79xEo\njNRrW0m9thlP/zYE1Hq61MS8XMgdo1zIywhneK2bbRbWHdvBj4e2kGPO45HarRjRrg+hFYtv3FIQ\neWYrx6/EczExFbWkol6IP/VD/dE70AfbbpfZs+UoKxZs49zJa3j5eNB32CM8NaTjPzscSZJQFOUf\nv/Pdm//GbLJStXYQ3Qe1o2vfNnj7lExMjFYTU36Zx8Grp3iuTU9Gtut71922EIKv0mKYkxZNO1cv\n5gXVKbC219n8W0IOkJOZx7Q3v+evLcewNPGnzQe9+bBRY9xLMSNZEQq7zh1m0d41xGel0Cy0HuM6\nDKB2QNX8RjqmXGZtX8bOcwdpXLk2k7qNcThZrrjs2vw3H7+2DK1WzeR5I2na9iRW86tIkid6w3eo\nNUXLincGpfW9ECIHs7EPinIUvctyNJpuJfq8lKtbSIv+Da+AdvjXHFgqYl4u5I5RLuRlhDObpuSY\n81h95HdW/70Vq93G4w3CGfpQ7xIvemarjZPXEjkblwwi3061UVggLrqil8IJITh+4Dw/zf+dv3ae\nRm/Q0n1QOx7v3za/Lj18EjGXk3Bx09O5dyu6D2pHvaZVnRLaTs3N4K11n3M5JZbXugyhR6OODt23\nNiuJdxMvUk3nwpLK9Yt9Puwo/6aQb8xOZnLiRbRbL1Jh7iEMOg1vffo8D3drVurPtsl2fjmxi6UH\nNpJlyuHROq2Z2nM8fRe8QlpeFiPa9WFwy253hN+did1mZ/4H61i9aAf1mlZl2jej/8noV+RIzKbn\nEOJqvr2u9sX//JGLEHmYTf1Q5IPoDd+h0fZywmcKUq9uIi1mG16B7fGvMcDp81Qu5I5RLuRlRGl0\nP8vIy+aHQ5vYcHwnAL0ad+K51j3xdiuaV7rVbicyOonImCRkWaF6oA9NwoKc1pHsyrl4Vn6zjW3r\nDmK3yUTEL2Jcr4/pMbg9j/Rs7tSynsspsby5bhY5ZiPTnhxP66qNinT/vrxMXog/g5tKzeLgetQr\nRUvMf0PIc2Q7U5MvsSE7heYuFZgdWAslJotpLy7m7Ilr9HymPROmDijVUqsb5FlMrDj8K6uPbGX7\nq4sZvPgN3us2lrqB1Ur1uSkJGUwZt5BThy/RZ9gjvDi5P1rdrZEIIbKwmMcj2zeh1vREb5hXpF7z\nJcHZ3wshjJhNA1DkfegNi9Fo+zrxswUpVzaQHvsH3sEdqVTt7pGv4lAu5I5RLuRlRGm2MU3KTmPZ\ngY38dnovOo2W/s0fY2CLx+9Z8mOXZc7EJnPq2v/ZqTapGoSXW+kkFaUmZrL/j1P0erZDqQjY39ci\nmbRxLi46PZ/0mUjNSsXLIThnyWN4bCQ5sszc4Do87FY0O09HKWshP2rKZmLCOeJtFib4hDLOJ+Sf\nZh42q50ls37hp3m/E1KtEpPnjaR2w9LNwbhBam4mfh7e5FlMuN7Dh7ykHN13lqkvLMKUZ+Gtz56n\nc+9Wd7023w3uK6yWKUhSGAaX5ajU9Ut1fOBs50MTZtMgFHkPesNCNNoBTvncW58hSL68loy43VSs\n/Ch+VXs7TcwfFCG/0cbUbrdLarVaDBo0KG3y5MlJ6gLyjYpDuZCXEWXRjzw6PYFv961n57mDeBjc\neLpld/o264zhthCxrChciE/lxNUETFYbwT4VaFYtGB+PsvF7Lw0B++10BDO3fUtoxUBm9plY4mOG\nJLuFkbFRnLPkMd2/BgO9Au59UxEpKyGXheDrtBjmpkUTqNXzeWBtmrsUHLU5uu8sM176loy0HMa8\n/RQDRne+a/WBMyntuVCU/B7uiz7ZQEg1f6YvGkvVWo61NpXt+7GYhyFEFjrDHLTaQaU2TnDeXAhh\nxmJ6Bln+A51hHlrtM04Y3d2eJUi6tIbM+D/xCemKb1hPp4j5gyLkNxvCxMXFafr371+tdevWubNn\nz46/+brbW5kW1Nq0IMqFvIwoCyG/wYXkayyOWMuByyeo6Ob5j+2rWqXmSlI6xy/Hk2O2UMnTnebV\nC7dTLQ2c7bW+7MBGvt2/nhZV6jPtyRfv6bvtKLmKnQnx5/gzL4MXKoYw0TfU2WHDMmnnOjHhPEdM\n2Tzp4cc0/+r3TOTLSs9l5pvL+fO3Y7TsUJd35wzD1790TXNKcy5ysox8+Mp3RGw7QaeeLXjrs+dx\ndS/azl9RkrCYh6PIEWi0w9DpP0aSSid64Iy5EMKKxfQssvw7Ov2XaHVDnDS6wp6pkHRhFZmJ+/AJ\nfQK/sO4l/swHUcgBoqKidG3btq2Xnp5+/KuvvvLZsGGDt9FoVMmyLE2ZMiX+9tam9/r88u5nDyA1\nK1Xhkz4TORV3noV7f2bOH8vZFXWS1pXDscsqKrq70rlxTYIdsFO9n7HLdj7d9h2/RUbweP1w3ug6\nzCktNW/grtKwMLguk5Mu8XV6DHE2Mx8F1ERfBjtUZ7A5O4VJSRcRwKyAWvT2dKzHumdFd2YsGsum\nH/fy5ZRVDO08jXdmDaFdV8eajNxPXDgdw6TR80mKS+el9wfSb0SnYn3nVSp/DC4bsVmnY7POQZGP\noXf5HpWqbI4fioIQNizmYddFfFaZiDiAJKnwrzkQIRTSon9DktT4Vnm8TJ7tKB9NXBpy+Vy8c9uY\n1g4yvvP50ELbmN5OvXr1rLIsExcXpwGIjIx0PXnyZKS/v7+8efNmj6ioKNcbrU1LMrZyIX8AaBhc\ni7e7jGfvmYuYrYLUvAxics7RM7jNf17Ecy1GJv/yFUeuRTKsbW+GPuS8c7mb0UoqPvSvQYjWwKzU\nayTarcwProtnGZSnFZdcxc60pMuszU6micGD2YG179kD+3YkSeLJZzvQuE1N3n9hMW8Pm8dTQzoy\n/r1+d/gC3K9sWRnB5/9bQQUvN+b+/AYNW5asC5wkadDp30elaoXFPA5TXgf0LouKXYtdGghhx2Ie\ngWzfjE4/E61uZJk+X5JUBNQajBAyqdc2I6nU+IR0KdMx/Bdp3759tr+/v3zj/29ubVoS7t9VqhyH\nSM7K5djlOBIycnDT62hbJ5C4bMGR/bFM3jSXOv5VGdW+Hy2q1P/PCXpyTjpvrp3FtfQE3nl8FE80\nKNwjuqRIksQLPiFU1up5M+ECA6JPsKRyfSprS7/HelE5YcrhlYRzxNjMjPcJYYJPSIlaYFapEciC\nTW+z6JMNrPxmO8cOnGPKvFHUqFfZiaN2LhaTldmTVrBl5T6atavD1K9H4u1btEqOwtBou6NS78Zi\neh6LqT+K7k20urfLxHu8MPJFfDSyfSM6/QdodWP+lXFIkorA2s+CkEm5shFJUlGxctl1GCyMou6c\nS4uoqCidWq0mODjYDuDq6qrc/Pe3/39xKRfy/ygZuUaOXo4nJjUTg1ZDq5oh1A72Q61SUSvIj/a1\nmrE9aj/f7d/Aaz9/StOQOoxq358GTvawLi0uJkfz5rpZmKwWPu37Gi2qlH4W8Q2erFCJShod4+LO\n0PfaCRZXrk/DUixPKwqyECxKj2V2ajR+Gh0/hTSklatzyqV0ei3jJ/en5cP1+OCV7xjT40PG/a8v\nfYcXL0xdmsRfS2HSqAVciIzh+Ze6Mfz1J4vtDFgYKlU1DK7bsZpfw2adiSwfxmBYjKQquo2wMxBC\nxmJ+Adm+Fq1uKlrdi//KOG4gSSoC6zyPEArJl9eDpKZicMd/dUz3C/Hx8ZpRo0ZVGTZsWHJpJ5KW\nC/l/jGyjmeNX4rmclI5Wo6ZZtWDqVq6EVnPrLkGjUvNEg/Y8WqcNm07uZvlfm3jhp+m0rd6EUeF9\nqe4X+i/9BPfm0JVTTN70FW56V74a/L8i97x2Bm1cvVgd2pgRsZEMjj7Jl0F16OResczHcTMJNguv\nJZznoCmLbh6+zPCvUSqh/1YP12fpjil8PHEZX0xexcHdkbzz+VAq+jlvt1sSIrYd54OXvwNJ4uOl\nL9KuS9E8BIqKJLmgM8xDZWuN1fIGJmMH9C7LUKtblupzb0cIBav5JWT7KrS6Sej0r5bp8++GJKkJ\nqjOUuDMKyZd+RpLUeAe1/7eH9a9gsVhUderUqXej/GzgwIFpU6ZMKbQ1qTMoz1p3MqWVtZ5nsXLi\nSgIXElJRSRL1QirRIDTAITtVAJPVwtpj2/jp0K/kWUw8Wqc1w9o9RYi388utblCcrNzNp/Ywa9tS\nqvpW5pM+r+Ln8e+KZ4rdysjYKKIsuUytVJ1nvItuk+uM7OTfc1J5J/EiNqEwxb86fStUKvVdshCC\n9ct2M2/6z7i5G3h39lDadGpYos8syVzY7TKLP93Ij19tpVbDUKYvHEtQaNnujGX5OBbTcwiRgE7/\nARrt6GL/HooyF0IoWC2vYrctRat7C53+3WI9szQRip24qMXkpp8moOZgvALbOXzvg5K1XtqUl5+V\nEc4WcrPVxqnrdqpCQK1gPxpVCcBVX7xEpBxzHisP/8aav3/HJtvp1rA9Qx7qTaVSEMyiLVSCJfvW\n8f1fv9AqrCHTnhxfal2wikqeIvNK/Fl25mUwumIwb/iGoSrC4l0S8TIqMjOSL7MqK4mGBndmB9am\nahnPy+Wzcbw/fhGXz8bTb0Qnxr7bt8jtZW9Q3LlIT8nm/RcWcXT/OXo+056Xpw0q9hhKihAZWExj\nkeWtqDV90Ru+RJKKfvTi6FwIIbBaXsduW4xWNxGtbvJ9d9RxA0WxERe5iLyMMwTUegavgDYO3Vcu\n5I5RLuRlhLOE3GqXiYpJIjI6EbusUC3AhyZVg/Bwkp1qWl4mP/y1mY0ndqKSVPRu8ijPtu6Ol6vz\nwqeOLlQ22c4nvy9hW9R+ejR8mImdn0dzn2WL24VgWvIlfsxMpLuHL58G1HK4PK244nXanMurCee4\nYjUxpmJlXvYNLbOObbdjMdtY8OFafl6yk2p1g5k6bxRVaztmtHIzxZmLk4cuMHnsQnKyjLz24TN0\nG1j2DU5uRwgFm/VzbNYPkFQ1MRiWo1LXLtJnODIX+SL+DnbbfLTaCWj10+9bEb+BotiIPf0Nxsxz\nBNZ+Dk//u7vq3aBcyB2jXMjLiJIKuV1WOBuXb6dqsdmp4udN02qlZ6eamJXK0gMb2BoZgV6jZ2CL\nxxjQ4nGnmK04slDlmPOYtHEux2LOMCq8H8+27nHfLlRCCBZlxPFJylVauFRgQXBdvNX33hUWVbwU\nIfg2I47PUq7ho9HyWWAtHnItXaMWRznwxyk+fHUpxjwzL77Xn95DHi7S76uoUZrVi3Ywf8ZaAkJ8\nmLFwLDXql32+RGHI9t2YzSNAmNAb5hbJ3/xecyGEwGZ5D5ttLhrtOHT6j+7bfxu3o8hWYk8vwJh1\ngaA6Q6hQqXCNLhdyxygX8jKiuEKuKAoXEtI4cTUeo8VGUMV8O1XfCmVjp3otLZ4l+9ax+/xhKhjc\neKZVD/o07YxeW/xa4nstVIlZqby5bhaxGUm8/fhIutb793dajrAlO4XXE88TrDHwbeX696zdLop4\nJdktvJlwgQhjJl3dffgwoIZDLwtlSVpyFh9NXMrBXZG069KIt2YNcbgdraNzkZdj4uPXlrF7y1Ha\nP96Edz4fioenU/09nIaixGMxDUVRDqLRjkWnn44k3fvfTWFzIYTAZp2Gzfo5Gu0odPpP/zMifgNF\nthBzej6mrMsE1R1GBb+md722XMgdo1zIy4iiCrkQgitJ6Ry7Ek+OyUIlTzeaVatMgHfZ2qne4Fzi\nFRZHrOXg1VP4unsxpE0vujfsUKxQd2EL1bmkq7y17nOsdhsf9HqJpqF1Szr0MuWIMYsxcWdQSRKL\ng+vR2OXuvy9HxWtHbhpvJ17ApChMqlSNQZ7+9+3irSgKa7/dxfwP1uLh5cqkL4bTskO9e97nyFxc\nPhvHpFELiL+Wwuh3nmLw2K737TzcQAgbVstk7LavUalaoXdZikoVXOg9hc2F1fIhNusnaLRD0eln\nl0oP8LJAtpuJPf01ppyrBNcdiYdvwRUG5ULuGOVCXkY4KuRCCGLTsjh6KY6MPBPe7i40qxZMZR/P\n+2LROh5zlkURP3Mq7gJBnn4Mb9eHR+u0KVLv6LstVAcun2Dqpnl4ungws89EwnwLX/DuVy5bjQyP\njSTFbmNOYG26eBTcwOVe4mVSZD5KucKPmYnU07sxJ7A21Z3kI1/aXIyM4f0XF3P1fAKDxnRh1Fu9\n0envHkG411z8vvYvPnvrB1zdDUydP4qmDxXt3Pnfxm5bh8U8ASQ9BsMS1JpH7nrt3ebCavkUm3UG\nGu2z6PRz/7MifgPZbiLm1DzMuTFUrjcSd587Kx/KhdwxyoW8jHBEyBMysjl6KY6U7DwquOhpWi2Y\nsEre94WA34wQgr+unGRxxM9cSI6mqm9lRob3Jbx6U4fGWtBCtfH4Tmb/8T01K1Xh4z6v4uN2f5z9\nFpdUu5XRcVGcNOfyXqVqDPG+MwGsMPE6a87jlYRzXLAaGeEdzGu+Vf4zHu83MJsszJsRTLEAAAAP\n40lEQVT2Mxu+30PNBiFMmTeSKjUKLtO7u3jZmDt1NRu+30Pj1jWZOn9UqTdwKS0U+Txm83MI5Rxa\n3f/Q6l4rUIwLmgurZTY261Q0mkHoDF//6y5yzkK2G4k5+RWWvHiC64/GveKt0ZsHRchvtDGVZVkK\nCQmxrF69+oqvr6987zsd474TckmSAoA5QEsgE0gCXhFCnC+FZ3UEXhdC9CjkmiZAkBDi1xI+665C\nnpKdy9FL+XaqrnotTaoGUSPAp0zaR5YERSjsPneYJfvWEZORSN2Aaoxu34/m93Bbu3mhUoTCwr0/\n89OhLbSt1oTJPcaVek/qssKkyLyacI7tuekM9w7iHb+qt5SnFbRgCyFYmhnPzJSreKo0fBpYi/al\n1A+9rIjYdpyPJy7DbLLy0rRB9Hw6/I4XvoLmIjE2jcljvuHM8asMGtuVMW/3RuOgP8L9ihC5WMyv\nINvXoFY/ht5lAZJ0a4nn7XNhs36F1fI/1Jp+6A0LHxgRv4FsyyP65FysxkQqNxiLm3edf/7uQRHy\nm7uf9enTJ6xmzZrmTz75JPHma25vWaooCkIIHOlZfjch/1cURMr/170e2C2EqC6EaA68A/j/G+O5\nThOgW2l8cEauiZ2nLrLlyFnSc020rBlCnzYNqRXkd9+LOIBKUtGpTmuWDfuQtx4bQVpeJq+umcmr\nqz8hKuHSPe+32m1M37KAnw5toXfjTszo/dIDI+IALio184LqMsQrkG8z4nkx/ixm5e4v4al2K8Pj\nopiRfIVwVy+2hDX7z4s4QHjXJizdMYWGLWvw6ZvLmTRqAVnpuYXec3DXaUY8NoPoS4l88P/au//4\nqKozj+Ofb35NgoQfIlhgwYD8FgKCVbYgpUhxXaELQmr9gVqhLqVK2bU2douVXdkWta9VWKuQ0oor\nq6W2RTG2RVqkKC+pVoQ0BFIEKis1JS1FIgkJyTz7x71jhjEhCcnMZCbn/U8yd+7MnHled+aZc+85\nz1nzZb5y35yET+IAUmcCmd8nI/Bd6uq2UHXy09TVvd3o/qdrVvlJfCaBzNVJl8QBUtPPo3/unWR0\n6sV7e1Zz8nib99nalfHjx588cuRIBkBhYWH2uHHjhk6ZMmXQ4MGDR5aWlmbk5OSMnDVrVs6QIUMu\nOXDgQKtWKIpLj1zSFGCpmU2K2C7gIeAawIBlZrbe71H/O17PfRTwY+D3wFeBLGCmmR2QtBY4BVwG\ndAH+1cwKw3vkks4D/hsYCaQDS4FfAO/4z3UE+A5QGLmfmb3QjPf2UY+8oqqaXYf+xIGyv5KemsrI\n/hcyot+FHyunmmiqa2vYuHsrT+/YyPGqCiYOGsu8Cdd9rJSqJD6orODfXlhB0Xt/YMGkz3PDJ/+x\n3V1CaEtPHjvCf5YfYkxmNqv7jqBHWvoZPa9XPjxGftl+PgzW8Y2eOdzcrXfSxSMYDLK+4FcULN9A\n9x7ZLFl5O2MneL2vUCzq6oKsfaSQpx59iQHD+rCsYAH9Bsbzd3z01NX9juqqWzE7SkbgIdLSb0PS\nR7E4XbOGmuq7SU2bTiBzLVL7mqXQ1mprKjhctILTp47Rb9RCOnUd1OY98tf2Hup3/MOqNh1o0q1z\nVuXE4QPOuhhLqEdeW1vLjBkzBs6bN+8vc+bMOVFYWJidl5c3KLRkaWlpacbw4cNHbd68ed9VV111\nsrltaFc9crzk+FYD26/D6xmPBqYCD0sKXWwbDSwAhgNzgSFmdjmwBrgr7DlygMuBa4FVkiK7ft8E\ntviP/QzwMF6i/haw3szGmNn6hvbzfwQ0qbK6htdL3+VnO4r549FjjOz/CWZ/ahSjB/RJ+CQOEEjL\nIG/cNH70pe8yf+Js3j68l9ufuo8HXlrFkeNnlhVe+Owy9r5/kPunL+TGy69NuqQV6Yvn9+V7fYZR\nUn2SOYd3c6imCoDqYJD/+PMB5h8poUdqOhsuGs3c7n2SMh4pKSncsGAaq168l8xOARZf/wirvvMz\nak/XAnD8WAX3zF3J2kcKuXr2eFa/eG/SJnGA1NTLyOq0jdTUidRUL6bm1ELMKgE4XbPWS+Kp1xDI\nfDLpkzhAWkY2/XMXkR7oznvFT1D5wcF4N6nNhGqt9+zZc3R5eXn6zJkzT4Tui1yytHfv3jUtSeJn\n097OYU0EnjWzOuDPkn6Ddw39BPCmmb0PIOkA8LL/mN/jJdqQH5tZENgv6SAwjDNNAz4n6Wv+7Uyg\noRVEGttvb1Nv4qevFxM0Y0ifCxid0/ucy6m2d50yMrll/OeYOXoKz7z5c366czNbSt9g+qhJfGrg\nGACOV57gkbx8cv9uSJxbGztXZ1/AurQM/vlICXmHdwMw691dlNZUcmu33uT3HJBwA9rOxdBRF/GD\nTUtYef96/vexX/LWq95HZ97Vy/jbXyq458GbmXHTlUn5YyaSUnoQyPoJp2se4nTNgwQriwCoqV5M\naupnCWQ91ay558kiLaML/XLv4nDRCt4rfrzNn7+pnnO0BAKB4L59+0oqKipSJk+ePHj58uW9lixZ\nchSit4QpxC+R7wHmtPAx1WH/B8NuBznzfUReK4i8LWC2mZWesVG6ojn7NUdOr+5tWk61veuS1ZkF\nkz7PnLHTeHrHRl4s2soLu18B4PEb76P/+S1faCTRjc3qwnP+6mkA5XWnWdN3BJ+J8wpqsZbVKUD+\nw7dwxeRLeOjrTwOQmprCEy/kMzT3oji3LrakVDIC3yAl9ZNUV80HICV1MoGsdUgd47siXHqgG/1z\nF3F494p4N6XNZWdnB1euXHk4Ly9vUH5+/tFov168ugVbgICkO0IbJOXiXQO/XlKqpJ7AJOCNFj53\nnqQUSRcDA4HIRLwJuMu/Ho+kULmhCiC7Gfs16coRAzpMEg93Qedu/MvUW1h3+4PccaX3O60jJvGQ\nnIwsnus/GoCf51za4ZJ4uMnXjuPJl78FwJpfLOlwSTxcWtpUss7bBkBm1jN8/Opfx5Ee6E7/3EXx\nbkZUTJgwoWrYsGFVBQUFUf/gx6VHbmYmaRbwqKR8vAFqfwQWA52B3Xg96a+bWZmkyNPjZ3MYL/l3\nARaY2amIU3cP4E17K5I3ufMQMB14BbhX0i68wW6N7ec0oU+3ntx8xQzmxrsh7cD5ad41z55pHee0\naWMu7Ot9n3XpHpuyw+1ZSop3NU9KjMI/0ZSemTw/cENTz0K2bNnyTuj/6dOnV4T+Hzp0aM3+/fv3\ntNXrJlVBGH/UeqGZ/SSObYjKeuSJqC3W4U4GLg71XCzquVjUS5Z55NHW2Kj19jbYLSH5lwjuaHJH\nx3Ecx2ljSZXIzey2OL1uAVAAXo88Hm1wHMdxOqbknwPTSpK6SVoY73Y4juM4ZxUMBoNJO5fRf28N\nTllrl4lcUns6U9ANcInccRynfSsuLy/vmozJPBgMqry8vCtQ3ND9UU2Ykp4H+uEVU1lhZgWS5gH5\neFPNdgPVZnZnWHnVS4Htku6jgRKp8ooQLwcmAwHge2a2ugVlXHsCq6gvArPYzLZLWupvG+j/fdTM\nVvqvdbE/mn2zmd3TxNve47fZ8cYNFMS7Ee2Ai0M9F4t6Lhb1GkxQLVFbWzu/rKxsTVlZ2UjaaSe1\nFYJAcW1t7fyG7ozqqHVJ55vZMUlZwJvA1cB2YCzevO0twO6wRH4B8E9mVifp20CJma2T1A1vStml\nwE1ALzNbJq+KwnYgD7gIeB6vhOsx4CCwxszul/RVYICZLZb0DPC4mb0mqT+wycyG+4l8Gl6VuGy8\n+eefAPrijYRvVnKW9LvWjr5MFi4WHheHei4W9Vws6rlYtE60T2Ev8ueLg9cznwv8xsyOAUh6Dgiv\n3fmcX54VGi+ROg3IlRSqDNcVGAzU0LwyrlOBEWFzy7tI6uz//5KZVQPVko4S39XYHMdxHKdJUUvk\n/qnuqcDfm1mlpK3APrwec2PCC8g3VkpVwF1mtqmB12tOGdcUYLyZnYp4PBGPryPJRvU7juM4ySea\n1xG6An/zk/gwYDxwHvBpSd39AW2zz/L4xkqkbgK+LH+ZIElDmrsqme9lwlZLkzSmif0jS7c2xV3z\nqudi4XFxqOdiUc/Fop6LRStEM5H/EkiTtBdvwNgOvLW+v413vXs7XlnWDxp5/AN4g9yKJO3xb4O3\nbGkJsFNSMbCalvWcFwGXSSqSVIK3NGqjzOyveIPviiU93NST+3PKHVwsQlwc6rlY1HOxqOdi0Tox\nL9EqqbOZfej3yDcAPzSzDTFthOM4juMkiXgM0V/qT+UqxluI5Pk4tKFVJNVJ2uX30l/0R9V3OOca\nB0lLwwYxJrzmxkHS2rBBmuHbJ0sqjH5LYyMsHnsk7ZZ0t7/wUIfSmjg0dqwkopbEQdJWSR8bvS7p\nNkmPRb+1iSnmHy4z+5qZjTGzYWa2KEFXGKny38NIvKluX4ncIbKojTzJ9mXW4jgkqSbj0MGE4nEJ\n8FngGuD+yJ0a+Iwk27FyTnFIQs2Kg3Puki2xxMPreHPNQz2rVyVtBEok5UgqlfQ/eGcg+sWzoVHW\naBz8bd+U9AdJrwFD49jOaAuPgyQ95h8DvwJ6hXaS9A+S9knaCVwXp7ZGnZkdxSt8cqcfj9skbZS0\nBfh1Q8dKMmpGHBo9VpJJA3HIkvQjSXslbcAr3gWApC/63xlvABPi1eZEkOy/BKNKXpW5q4AfhG0e\nC4w0s0OScvDmuN9qZjti38LYaEYcxgFfAMbgHXM7gbdi3tAoayAOs/B+tIzAq0lQAvxQUibwfWAK\n8A6wPvatjR0zO+jHJpScxgK5frGoyYQdK/FqYyw0EYfraOBYiU9LoysiDjcBlX5Rrly87wYk9car\n1DkOb0D0K8DbjTxlh+d65Ocmy7/OX4b3odscdt8bEV9I7yZxEm9uHK4ENphZpZmdADbGuJ3R1lgc\nJgHPmlmdmf0Jr5IhwDDgkJnt9y8trYt5i+Nrc6golC/yM9NRhMehsWMl2U3CP/7NrAgo8rdfAWw1\ns3IzqyHJf+y2lkvk56bKzMbglYUVZ14TPRmxb+TtZNKSOCSzs8Whw5M0EK/A0lF/U0f6jHykGXHo\nEBqIg9NKLpG3gplV4s1Lv7sDDFhpVDPisA2Y6V8PywZmxLSBMdJAHLYB10tK9U8VhsoE7wNyJF3s\n374h9q2NDdUvUvRYgg5sbRPNiENjx0pSaSAO24Ab/ftGArn+rr/FKx7WQ17xr7x4tDdRdNjk01bM\n7G1JRXhfxv8X7/bEy9niYGY7Ja3HW+3uKN4COkkpIg7r8K6DlwCH8QbCYWanJN0BvCSpEniVllUP\nbO9ClxrSgVrgaeC/4tukuGhJHDbQwLGSJM4WhyeAJ+UVDtuLP3bGzN6Xt5DV63grWu6KdaMTScwL\nwjiO4ziO03bcqXXHcRzHSWAukTuO4zhOAnOJ3HEcx3ESmEvkjuM4jpPAXCJ3HMdxnATmErnjOI7j\nJDCXyB3HcRwngblE7jiO4zgJ7P8BxSAJj4MNIxkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9336690240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas.plotting import parallel_coordinates\n",
    "\n",
    "foo = parallel_coordinates(angle_data[x_order].reset_index(), 'index', axvlines_kwds={'ls':'-', 'c':'k', 'lw':1})\n",
    "foo.grid(False)\n",
    "for s in ['top', 'bottom']:\n",
    "    foo.spines[s].set_visible(False)\n",
    "foo_lgd = foo.get_legend_handles_labels()\n",
    "foo.legend(*foo_lgd, loc=(1.05,0))\n",
    "foo.set_yticks([0,pi/4,pi/2,3*pi/4,pi])\n",
    "_ = foo.set_yticklabels(['Complete\\nagreement', 'Agree', 'Different', 'Disagree', 'Complete\\ndisagreement'],\n",
    "                         fontdict={'size':10})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:20:18.756761Z",
     "start_time": "2017-09-04T16:20:18.238349Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f93402d1cc0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YQEOutPWaqglvlqQNwM+BEyimYgF4OXCD7X22fwbcWpY/D9hq+6HyxcHrml3Y9nLbC2wv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\nIwkvIgZGEl5EDIz/DzerIjFp4b6wAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f934c37feb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "order = 'Rrr Rrd Rdd Drr Drd Ddd'.split()\n",
    "_, im = plot_matrix(angle_data, order, vmin=0, origin='lower', cmap='viridis_r')\n",
    "plt.colorbar(im)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These plots will be compared to the model results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model details and implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is fully explained in the paper (cite nestor's judges paper), but for completness we restate some of the relevant information to implement a simulation class for it.\n",
    "\n",
    "Each panel is composed of 3 judges, each judge being an apointee of some U.S. president, so each judge is supposed to be affiliated to either the Democratic Party or the Republican Party. \n",
    "In the model we refer to two distinct political parties, `A` and `B`, and each agent representing a judge belongs to either party `A` or `B`.\n",
    "We assume the relevant elements of the judges decisions to be the Law, the party ideology and a personality component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:29:17.465995Z",
     "start_time": "2017-09-04T16:29:15.278430Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from agents_base import *\n",
    "from numpy import (vstack, split, arange, ones, zeros, \n",
    "                   r_, eye, array, stack, fill_diagonal,\n",
    "                   linspace, cos, sin)\n",
    "from numpy.linalg import norm\n",
    "from numpy.random import randn, choice\n",
    "\n",
    "\n",
    "class JudgePanels(HEODAgentSociety):\n",
    "    N, P = 18, 15  # number of agents, internal dimension and number of issues\n",
    "    panel_compositions = ('Aaa', 'Aab', 'Abb', 'Bbb', 'Bba', 'Baa')  # types of panel by political affiliation\n",
    "    panel_indices = vstack(split(arange(N), len(panel_compositions)))  # agent indices for each panel\n",
    "    panel_map = {c: i for (c, i) in zip(panel_compositions, panel_indices)}\n",
    "    focal_agents = list(range(0,18,3))  # the agent indices corresponding to the capital letters\n",
    "\n",
    "    def __init__(self, K, components_A, components_B, mu0XX, mu0XY, c0A, c0B, s20, \n",
    "                 *args, opinion_norm_scale=1., issues_angular_bounds=(-pi/2,pi/2), **params):\n",
    "        \"\"\"Society of agents representing panels of judges apointed by presidents \n",
    "        of political affiliation A or B.\n",
    "          The society has 18 agents interacting in groups of 3, representing the 6 \n",
    "        possible composition panels: Aaa, Aab, Abb, Bbb, Bba, Baa.\n",
    "          The notation Xyz is to be understood as the focal agent has political\n",
    "        affiliation X in a panel with agents with political affiliations y and z.\n",
    "          The initial opinion state for the judges is composed by a law component,\n",
    "        representing the knowledge of the law and common to all agents, a party\n",
    "        component, represent the political attitude and opposite for A and B, and\n",
    "        a personality component of random charater.\n",
    "          To initialize the society, the weights `alpha_law`, `alpha_party` and \n",
    "        `alpha_person` are used to build the opinion vectors.\n",
    "          The opinion uncertainty is a party dependent multiple of the identity \n",
    "        matrix, with the multiples being the parameters `c0A` and `c0B`.\n",
    "          For the distrust, we use two paramenters `mu0XX` and `mu0XY` to characterize\n",
    "        the distrust attributed between members of party X to members of X and Y,\n",
    "        respectively.\n",
    "          Last, the distrust uncertainty is equal to everyone, being a multiple of the\n",
    "        matrix will all entries equal to 1 and given by the parameter `s20`.\n",
    "        \n",
    "        Inputs:\n",
    "        =======\n",
    "          - alpha_law, alpha_party, alpha_person: floats - weights to initial opinion\n",
    "          vector components of law, party and personality.\n",
    "          - mu0XX, mu0XY: floats - intra and extra-party initial distrust\n",
    "          - c0A, c0B: positive floats - initial opinion uncertainties for each party\n",
    "          - s20: positive float - initial distrust uncertainty\n",
    "          - opinion_norm_scale: (keyword only) float, defaults to 1.0 - the value of\n",
    "                                norm for the agents' opinion vectors\n",
    "\n",
    "        API:\n",
    "        ====\n",
    "          Although you can use any method inside this object, it intended to be used\n",
    "          a iterator with the `dynamics` function, so we only give a description for\n",
    "          the methods provided to this end:\n",
    "          - update(*args, **param): Method to make a random move using the Entropic\n",
    "          Dynamics of Learning. The Options section covers the parameters recognized\n",
    "          - reset(): Method to reset the system to its initial state.\n",
    "          - observables: Propery to compute and return all the observables in this\n",
    "          system.\n",
    "          \n",
    "          There are, also, three more properties to retrieve data about the parameters\n",
    "          and history of interaction:\n",
    "          - describe: dict with the parameters used to initialize the system\n",
    "          - describe_latex: raw string with LaTeX formated names and values of initial\n",
    "                            parameters\n",
    "          - log_book: list of dicts with the history of interactions.\n",
    "\n",
    "          Options:\n",
    "          --------\n",
    "            Initialization Options:\n",
    "            -----------------------\n",
    "              opinion_norm_scale: positive float; default is 1.0 - gives the bound for the\n",
    "                scale for the norm of opinion vectors.\n",
    "                \n",
    "              issues_angular_bounds: pair of floats; default is (-pi/2,pi/2) - the bounding\n",
    "                angles to generate the issue list from the law and party\n",
    "                components.\n",
    "                 \n",
    "            Options for the `update` method:\n",
    "            --------------------------------\n",
    "              constants: tuple with acceptable values 'norm', 'C', 's2', 'bounds'; default \n",
    "                is () - each value keeps the respective variable fixed under the dynamics,\n",
    "                where 'norm' is for the opinion vectors, 'C' is for the opinion uncertainty,\n",
    "                's2' is for the distrust uncertainty and 'bounds' is for the distrust interval.\n",
    "                \n",
    "              issues_probability: (keyword only) 1d-array with 15 entries summing to 1; default \n",
    "              is `None` - the probability mass for each issue in the list.\n",
    "        \"\"\"\n",
    "        assert (c0A >= 0) and (c0B >= 0) and (s20 >= 0)\n",
    "        assert len(issues_angular_bounds) == 2\n",
    "        assert len(components_A) == len(components_B) == 3\n",
    "#         self.alpha_law = alpha_law\n",
    "#         self.alpha_party = alpha_party\n",
    "#         self.alpha_person = alpha_person\n",
    "        self.components_A, self.components_B = components_A, components_B\n",
    "        self.mu0XX, self.mu0XY = mu0XX, mu0XY\n",
    "        self.c0A, self.c0B = c0A, c0B\n",
    "        self.s20 = s20\n",
    "        self.K = K\n",
    "        self.opinion_norm_scale = opinion_norm_scale\n",
    "        self.issues_angular_bounds = issues_angular_bounds\n",
    "\n",
    "        # Building the initial opinion vectors\n",
    "        self.law_vector = ones(K)/norm(ones(K))  # vector repesenting the kwoledge of the law\n",
    "        self.party_vector = r_[(K//2)*[-1.]+(K%2)*[0.]+(K//2)*[1.]]  # vector representing the political attitude\n",
    "        personality_vector = randn(self.N, self.K)\n",
    "        personality_vector /= row_norm(personality_vector)\n",
    "        alpha_law_A, alpha_party_A, alpha_person_A = components_A\n",
    "        alpha_law_B, alpha_party_B, alpha_person_B = components_B\n",
    "        \n",
    "        #             law component                 party compoenent\n",
    "        A = alpha_law_A*self.law_vector + alpha_party_A*self.party_vector\n",
    "        B = alpha_law_B*self.law_vector - alpha_party_B*self.party_vector\n",
    "        # personality weights\n",
    "        alpha_person = array(self.tile_values_for_panels(alpha_person_A, alpha_person_B))[:,None]\n",
    "#         alpha_person = array([alpha_person_A,alpha_person_A,alpha_person_A,\n",
    "#                               alpha_person_A,alpha_person_A,alpha_person_B,\n",
    "#                               alpha_person_A,alpha_person_B,alpha_person_B,\n",
    "#                               alpha_person_B,alpha_person_B,alpha_person_B,\n",
    "#                               alpha_person_B,alpha_person_B,alpha_person_A,\n",
    "#                               alpha_person_B,alpha_person_A,alpha_person_A])[:,None]\n",
    "        \n",
    "#         #            A a a A a b A b b B b b B b a B a a                  personality component\n",
    "#         w0 = vstack([A,A,A,A,A,B,A,B,B,B,B,B,B,B,A,B,A,A]) + alpha_person*personality_vector\n",
    "        #                                                             personality component\n",
    "        w0 = vstack(self.tile_values_for_panels(A, B)) + alpha_person*personality_vector\n",
    "        w0 *= opinion_norm_scale/row_norm(w0)\n",
    "        \n",
    "        # Building the initial opinion uncertainties\n",
    "        I = eye(self.K)\n",
    "        CA, CB = c0A*I, c0B*I\n",
    "#         #            A  a  a  A  a  b  A  b  b  B  b  b  B  b  a  B  a  a\n",
    "#         C0 = stack([CA,CA,CA,CA,CA,CB,CA,CB,CB,CB,CB,CB,CB,CB,CA,CB,CA,CA], axis=0)\n",
    "        C0 = stack(self.tile_values_for_panels(CA, CB), axis=0)\n",
    "        \n",
    "        # Building the initial distrust proxies - X in (A,B), Y in (A,B), i, j, k are agents\n",
    "        #                      i     j     k\n",
    "        muXxx_tile = array([[-10, mu0XX, mu0XX],   # ii==XX, ij==XX, ik==XX\n",
    "                            [mu0XX, -10, mu0XX],   # ji==XX, jj==XX, jk==XX\n",
    "                            [mu0XX, mu0XX, -10]])  # ki==XX, kj==XX, kk==XX\n",
    "        muXxy_tile = array([[-10, mu0XX, mu0XY],   # ii==XX, ij==XX, ik==XY\n",
    "                            [mu0XX, -10, mu0XY],   # ji==XX, jj==XX, jk==XY\n",
    "                            [mu0XY, mu0XY, -10]])  # ki==XY, kj==XY, kk==XX\n",
    "        muXyy_tile = array([[-10, mu0XY, mu0XY],   # ii==XX, ij==XY, ik==XY\n",
    "                            [mu0XY, -10, mu0XX],   # ji==XY, jj==XX, jk==XX\n",
    "                            [mu0XY, mu0XX, -10]])  # ki==XY, kj==XX, kk==XX\n",
    "        mu_map = {c: mt for (c, mt) in zip(self.panel_compositions,[muXxx_tile, muXxy_tile, muXyy_tile]*2)}\n",
    "        mu0 = zeros((self.N, self.N))\n",
    "        panel_pairs = stack([vstack([[i,j] for i in p for j in p]) for p in self.panel_indices], axis=0)\n",
    "        for panel, indices in self.panel_map.items():\n",
    "            pair_indices = vstack([[i,j] for i in indices for j in indices])\n",
    "            I, J = split(pair_indices, 2, axis=1)\n",
    "            mu0[I, J] = mu_map[panel].reshape(I.shape)\n",
    "            \n",
    "        # Building the initial distrust uncertainty\n",
    "        s20 = s20*ones((self.N, self.N))\n",
    "        fill_diagonal(s20, 0.0)\n",
    "        \n",
    "        # building the issue_list\n",
    "        thetas = linspace(*issues_angular_bounds, self.P)\n",
    "        self.issue_list = vstack([cos(t)*self.law_vector + sin(t)*self.party_vector\n",
    "                                  for t in thetas])\n",
    "        \n",
    "        # some info about the state and interactions\n",
    "        self.interaction_counter = 0\n",
    "        self.log_book = []\n",
    "\n",
    "        # let the super class prepare the remaining of the object\n",
    "        super().__init__(w0, C0, mu0, s20)\n",
    "    \n",
    "    @staticmethod\n",
    "    def tile_values_for_panels(vA, vB):\n",
    "        #       A  a  a | A  a  b | A  b  b | B  b  b | B  b  a | B  a  a\n",
    "        return [vA,vA,vA, vA,vA,vB, vA,vB,vB, vB,vB,vB, vB,vB,vA, vB,vA,vA]\n",
    "    \n",
    "    def pick_issue(self, *args, issues_probability=None, **params):\n",
    "        k = choice(len(self.issue_list), p=issues_probability,\n",
    "                   size=len(self.panel_compositions), replace=True)\n",
    "        x = self.issue_list[k]\n",
    "        return x, k\n",
    "\n",
    "    def pick_agents(self, *args, **params):\n",
    "        pairs = vstack([choice(p, size=2, replace=False)\n",
    "                        for p in self.panel_indices])\n",
    "        return pairs\n",
    "\n",
    "    def update(self, *args, constants=(), **params):\n",
    "        \"\"\"Method to update the state of the system by running the sequence:\n",
    "            1. pick_issue\n",
    "            2. pick_agents\n",
    "            3. interaction\n",
    "           Each step receives the params dict to enable fine control, but a few\n",
    "           of the keyword parameters are emphasized, as described below:\n",
    "        \n",
    "           Keyword only Inputs:\n",
    "           --------------------\n",
    "             constants: tuple with acceptable values 'norm', 'C', 's2', 'bounds'; default \n",
    "               is () - each value keeps the respective variable fixed under the dynamics,\n",
    "               where 'norm' is for the opinion vectors, 'C' is for the opinion uncertainty,\n",
    "               's2' is for the distrust uncertainty and 'bounds' is for the distrust interval.\n",
    "\n",
    "             issues_probability: (keyword only) 1d-array with 15 entries summing to 1; default \n",
    "               is `None` - the probability mass for each issue in the list.\n",
    "        \"\"\"\n",
    "        xs, ks = self.pick_issue(*args, **params)\n",
    "        pairs = self.pick_agents(*args, **params)\n",
    "        for ((i,j),x, k) in zip(pairs, xs, ks):\n",
    "            self.interaction(i, j, x*self.opinion_norm_scale,\n",
    "                             *args, constants=constants, **params)\n",
    "            self.write_to_log_book(((i,j),k))\n",
    "            \n",
    "    @property\n",
    "    def opinions(self):\n",
    "        u = self.w[self.focal_agents, :]\n",
    "        h = (u/row_norm(u))@self.issue_list.T\n",
    "        return (self.panel_compositions, h)\n",
    "        \n",
    "    @property\n",
    "    def observables(self):\n",
    "        if not hasattr(self, '_observables'):\n",
    "            self._observables = 'opinions'.split()\n",
    "        return {n:getattr(self, n) for n in self._observables}\n",
    "    \n",
    "    @property\n",
    "    def describe(self):\n",
    "        if not hasattr(self, '_info'):\n",
    "            self._info = dict(\n",
    "#                 alpha_law={'value':self.alpha_law, \n",
    "#                            'descr':r'$\\alpha_L={}$'.format(self.alpha_law)},\n",
    "#                 alpha_party={'value':self.alpha_party,\n",
    "#                              'descr':r'$\\alpha_P={}$'.format(self.alpha_party)},\n",
    "#                 alpha_person={'value':self.alpha_person,\n",
    "#                               'descr':r'$\\alpha_\\eta={}$'.format(self.alpha_person)},\n",
    "                components_A={'value':self.components_A,\n",
    "                              'descr':r'$\\alpha_A={}$'.format(self.components_A)},\n",
    "                components_B={'value':self.components_B,\n",
    "                              'descr':r'$\\alpha_A={}$'.format(self.components_B)},\n",
    "                mu0XX={'value':self.mu0XX,\n",
    "                       'descr':r'$\\mu_{0,XX}=$' + '${}$'.format(self.mu0XX)}, \n",
    "                mu0XY={'value':self.mu0XY,\n",
    "                       'descr':r'$\\mu_{0,XY}=$' + '${}$'.format(self.mu0XY)},\n",
    "                c0A={'value':self.c0A,\n",
    "                       'descr':r'$c_{0,A}=$' + '${}$'.format(self.c0A)},\n",
    "                c0B={'value':self.c0B,\n",
    "                       'descr':r'$c_{0,B}=$' + '${}$'.format(self.c0B)},\n",
    "                s20={'value':self.s20,\n",
    "                       'descr':r'$s_0^2=$' + '${}$'.format(self.s20)}\n",
    "            )            \n",
    "        return self._info\n",
    "    \n",
    "    @property\n",
    "    def describe_latex(self):\n",
    "        info = self.describe\n",
    "        info_str = ', '.join([v['descr'] for v in info.values()])\n",
    "        return info_str\n",
    "    \n",
    "    def write_to_log_book(self, ij_x):\n",
    "        (i,j),x = ij_x\n",
    "        n = self.interaction_counter\n",
    "        entry = {'interaction': n, 'agents': (i, j), 'issue': x}\n",
    "        self.log_book.append(entry)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just to test out the model, lets do a simple dummy simulation and look for the respctive plots we did above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:31:04.642205Z",
     "start_time": "2017-09-04T16:31:04.633495Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "K = 5\n",
    "#aL, aP, aE = 5., 1., 1.\n",
    "alpha_A, alpha_B = [5.,1.,1.], [5., 1., 1.]\n",
    "mu0XX, mu0XY = -1., -1.\n",
    "c0A, c0B = .1, .1\n",
    "s20 = .001\n",
    "judges_model = JudgePanels(K, alpha_A, alpha_B, mu0XX, mu0XY, c0A, c0B, s20, issues_angular_bounds=(-pi/2,pi/2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:31:05.126704Z",
     "start_time": "2017-09-04T16:31:05.111684Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cols, vals = judges_model.opinions\n",
    "initial_opinions = pd.DataFrame(vals.T, columns=cols).transform(lambda x: x/norm(x))\n",
    "initial_overlaps = initial_opinions.T.dot(initial_opinions)\n",
    "initial_angles = initial_overlaps.transform(lambda x: arccos(0.999*x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:31:07.301347Z",
     "start_time": "2017-09-04T16:31:05.627464Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dmGiMeQq4xVpbEE0gxpg6wEFr7SFjTHdgRTSvp5RyneaPMFgL+/dD3bpQWAgD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\nCQ8AALAVctueaB3bhTMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9334e262e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_order_agents = 'Aaa Aab Abb Baa Bba Bbb'.split()\n",
    "_ = plot_angle_pairs(initial_angles, x_order_agents,\n",
    "                     ['Aaa', 'Bbb'], ['Aab', 'Bba'], ['Abb', 'Baa'],\n",
    "                     title=judges_model.describe_latex,\n",
    "                     style=['-d', '--h'], color=['r', 'b'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:31:07.814795Z",
     "start_time": "2017-09-04T16:31:07.305647Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f9334a39710>"
      ]
     },
     "execution_count": 289,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RsbFfmfXJIGZWeyIbtpFny+HbwMo+z18AnJG2tcC1gwp0QjOzQspagjsi/g3Y3eeUVcCN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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9335b41668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, im = plot_matrix(initial_angles, x_order_agents, vmin=0, vmax=pi, origin='lower', cmap='viridis_r')\n",
    "plt.colorbar(im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:31:10.975304Z",
     "start_time": "2017-09-04T16:31:07.819108Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_ = record_trajectory(judges_model, 300, record_step=lambda n: n==False, in_place=True)\n",
    "cols, vals = judges_model.opinions\n",
    "agents_opinions = pd.DataFrame(vals.T, columns=cols).transform(lambda x: x/norm(x))\n",
    "agents_overlaps = agents_opinions.T.dot(agents_opinions)\n",
    "agents_angles = agents_overlaps.transform(lambda x: arccos(0.999*x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:31:12.926497Z",
     "start_time": "2017-09-04T16:31:10.979625Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ItgFQJdYNcMgcQQiLffv2oUqVKmjSpAmUUqEPiAKICEePHsW+ffvQtGlTp80JimiHEO2I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\ny5AhjppFNGUKG/LAA+Efq/UGNWpkS0S2sghWvp0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wNPBWPP4c2Er16nLj8ba1wA/89wIM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\naIMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9334b7dcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_order_agents = 'Aaa Aab Abb Baa Bba Bbb'.split()\n",
    "_ = plot_angle_pairs(agents_angles, x_order_agents,\n",
    "                     ['Aaa', 'Bbb'], ['Aab', 'Bba'], ['Abb', 'Baa'],\n",
    "                     title=judges_model.describe_latex,\n",
    "                     style=['-d', '--h'], color=['r', 'b'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:31:13.398326Z",
     "start_time": "2017-09-04T16:31:12.928091Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f933577a128>"
      ]
     },
     "execution_count": 292,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f93384ea320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, im = plot_matrix(agents_angles, x_order_agents, vmin=0, vmax=pi,origin='lower', cmap='viridis_r')\n",
    "plt.colorbar(im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:08:01.872599Z",
     "start_time": "2017-09-04T16:08:01.863711Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'agents': (0, 1), 'interaction': 1, 'issue': 0},\n",
       " {'agents': (4, 3), 'interaction': 2, 'issue': 0},\n",
       " {'agents': (6, 7), 'interaction': 3, 'issue': 11},\n",
       " {'agents': (9, 10), 'interaction': 4, 'issue': 10},\n",
       " {'agents': (13, 12), 'interaction': 5, 'issue': 4}]"
      ]
     },
     "execution_count": 293,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "judges_model.log_book[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model simualator class is built to be easy to specify the initial conditions matching each of the following intuitive scenarios:\n",
    "  1. Courteuos and Certain: $\\mu_{0,XX} = \\mu_{0,XY} < 0$ and $s_0^2 \\approx 0$\n",
    "  2. Courteous and Uncertain: $\\mu_{0,XX} = \\mu_{0,XY} < 0$ and $s_0^2 > 0$\n",
    "  3. Discourteous and Certain: $\\mu_{0,XX} < \\mu_{0,XY} $ and $s_0^2 \\approx 0$\n",
    "  4. Discourteous and Uncertain: $\\mu_{0,XX} = \\mu_{0,XY} < 0$ and $s_0^2 \\approx 0$\n",
    "  \n",
    "We can also impose the distinction between liberals and conservatives through the specification of liberal index $\\rho_{0,X} = \\frac{1}{\\sqrt{1+c_{0,X}}}$, where $c_{0,X}$ stands for the opinion uncertainty for members of party $X$.\n",
    "The liberal index is closer to $1$ when the agent is more liberal and closer to $0$ when its more conservative.\n",
    "As in the paper [For whom will the Bayesian agents vote?](http://journal.frontiersin.org/article/10.3389/fphy.2015.00025/full), the empirical data from MFT suggests values of $\\rho$ between $0.76$ and $0.91$ for american citzens, which correspond to values of $c$ $c_{0,A} = 0.74$ amd $c_{0,B} = 0.21$.\n",
    "Notice the relative value conservatives and liberals is of order $3$, so we could choose different values of $c$ keeping this relation if we would like to retain the opinion learning time scale.\n",
    "\n",
    "The last thing to control is the relative importance of the initial components of the law, the party and personality.\n",
    "\n",
    "Lets proceed by simulating each o the four cases:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Courteous Certain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:46:35.965303Z",
     "start_time": "2017-09-04T16:45:44.402362Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# distrust settings\n",
    "mu0XX, mu0XY = -1., -1. # courteous \n",
    "s20 = .1  # certain\n",
    "\n",
    "# opinion settings\n",
    "K = 5  # internal dimension\n",
    "#aL, aP, aE = 4., 1., 2.  # law, party and personality weights\n",
    "# initial opinion vector components: [alpha_law, alpha_party, alpha_person]\n",
    "alpha_A, alpha_B = [5., 2., 2.], [5., 2., 4.]\n",
    "# the following is to account for the difference between liberals and conservatives\n",
    "rho_C, rho_L = 0.76, 0.91  # most conservative and most liberal indices\n",
    "ratio_cC_cL = (1/(rho_C**2) - 1)/(1/(rho_L**2) - 1)  # ~ 3.5\n",
    "c_base = 0.75\n",
    "c0A, c0B = c_base*ratio_cC_cL, c_base # A is conservative, B is liberal\n",
    "# c0A, c0B = c_base, c_base*ratio_cC_cL  # A is liberal, B is conservative\n",
    "\n",
    "# the angular bouds used to generate the issue list from the law and party vectors\n",
    "angular_bounds = (-pi/2, pi/2)  #  unbiased\n",
    "# angular_bounds = (0, pi/2)  #  A party biased\n",
    "# angular_bounds = (-pi/2, 0)  #  B party biased\n",
    "\n",
    "# simulation\n",
    "judges_sims = [JudgePanels(K, alpha_A, alpha_B, mu0XX, mu0XY, c0A, c0B, s20, \n",
    "                           opinion_norm_scale=sqrt(K), \n",
    "                           issues_angular_bounds=angular_bounds)\n",
    "               for _ in range(50)]\n",
    "for sim in judges_sims:\n",
    "    _ = record_trajectory(sim, 100, constants=(), record_step=lambda n: n==False, in_place=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:46:36.055068Z",
     "start_time": "2017-09-04T16:46:35.970233Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# take mean after the overlaps\n",
    "# agents_opinions = [pd.DataFrame(sim.opinions[1].T, columns=sim.opinions[0]).transform(lambda x: x/norm(x))\n",
    "#                    for sim in judges_sims]\n",
    "# agents_overlaps = [ot.T.dot(ot) for ot in agents_opinions]\n",
    "# agents_angles = [ot.transform(lambda x: arccos(0.999*x)) for ot in agents_overlaps]\n",
    "# mean_angles = sum(agents_angles)/len(agents_angles)\n",
    "\n",
    "# take the mean before computing the overlaps\n",
    "agents_opinions = [pd.DataFrame(sim.opinions[1].T, columns=sim.opinions[0])\n",
    "                   for sim in judges_sims]\n",
    "mean_opinions = (sum(agents_opinions)/len(agents_opinions)).transform(lambda x: x/norm(x))\n",
    "mean_overlaps = mean_opinions.T.dot(mean_opinions)\n",
    "mean_angles = mean_overlaps.transform(lambda x: arccos(0.999*x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:46:37.829616Z",
     "start_time": "2017-09-04T16:46:36.059676Z"
    }
   },
   "outputs": [
    {
     "data": {
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u03HuTu7ffnGXt3sATHFve0/vNWstvzrPrfV9rjW/hQBGu/e5HcATYO/D5+CuFzrvYVVo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9334ad4cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_order_agents = 'Aaa Aab Abb Baa Bba Bbb'.split()\n",
    "_ = plot_angle_pairs(mean_angles, x_order_agents,\n",
    "                     ['Aaa', 'Bbb'], ['Aab', 'Bba'], ['Abb', 'Baa'],\n",
    "                     title=judges_sims[0].describe_latex,\n",
    "                     style=['-d', '--h'], color=['r', 'b'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-04T16:46:38.277342Z",
     "start_time": "2017-09-04T16:46:37.832574Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f93340482b0>"
      ]
     },
     "execution_count": 297,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f93340feeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "agents_order = 'Aaa Aab Abb Baa Bba Bbb'.split()\n",
    "_, im = plot_matrix(mean_angles, agents_order, vmin=0, vmax=pi, origin='lower', cmap='viridis_r')\n",
    "plt.colorbar(im)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}