notebooks/sepp_2_testbed.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Allow us to load `open_cp` without installing\n",
    "import sys, os.path\n",
    "sys.path.insert(0, os.path.abspath(\"..\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The EM algorithm for Hawkes processes\n",
    "\n",
    "Here we explore the optimisation algorithm for parameter estimation given in\n",
    "\n",
    "1. Mohler et al. \"Randomized Controlled Field Trials of Predictive Policing\". Journal of the American Statistical Association (2015) DOI:10.1080/01621459.2015.1077710\n",
    "2. Lewis, Mohler, \"A Nonparametric EM algorithm for Multiscale Hawkes Processes\", preprint (2011) see http://math.scu.edu/~gmohler/EM_paper.pdf\n",
    "3. Laub et al \"Hawkes Processes\" arXiv:150702822v1 [math.PR]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Checking the simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import open_cp.sources.sepp as source_sepp\n",
    "process = source_sepp.SelfExcitingPointProcess(\n",
    "    background_sampler = source_sepp.HomogeneousPoissonSampler(rate=0.1),\n",
    "    trigger_sampler = source_sepp.ExponentialDecaySampler(intensity=0.5, exp_rate=0.05))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Background rate\n",
    "\n",
    "Should be a homogeneous Poisson process of rate 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "totality = []\n",
    "trials = 50000\n",
    "for _ in range(trials):\n",
    "    result = process.sample_with_details(0,100)\n",
    "    totality.extend(result.backgrounds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFACAYAAABz+RVqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsCRJkiRpTDAAliRJkiSNCf8fzaYwsxQ4AUIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f6208710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(0, 100, 21)\n",
    "counts = np.histogram(totality, bins)[0]\n",
    "counts = counts / (trials * (bins[1] - bins[0]))\n",
    "\n",
    "fig, ax = plt.subplots(ncols=2, figsize=(16,5))\n",
    "ax[0].plot((bins[:-1] + bins[1:])/2, counts)\n",
    "ax[0].set(xlim=[0,100], ylim=[0,.15])\n",
    "ax[1].plot((bins[:-1] + bins[1:])/2, counts)\n",
    "ax[1].set(xlim=[0,100])\n",
    "for i in range(2):\n",
    "    ax[i].set_xlabel(\"time\")\n",
    "    ax[i].set_ylabel(\"intensity\")\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aftershocks\n",
    "\n",
    "Should be exponential, with an \"exponential weight\" on 0.05, and \"intensity\" of 1.0.  So the conditional intensity function should be $\\theta \\omega e^{-\\omega t}$ with $\\theta=1, \\omega=0.05$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "totality = []\n",
    "trials = 10000\n",
    "for _ in range(trials):\n",
    "    result = process.sample_with_details(0,100)\n",
    "    totality.extend(result.trigger_deltas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6oAAAE/CAYAAABPSD7HAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJEmSJHXK/w+jbtJb049uzgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f6600278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=2, figsize=(16,5))\n",
    "\n",
    "bins = np.linspace(0,1,11)\n",
    "xcoords = (bins[:-1] + bins[1:]) / 2\n",
    "\n",
    "y = np.random.exponential(1 / 0.05, size=100000)\n",
    "x = 1 - np.exp(-0.05 * np.asarray(y))\n",
    "c = np.histogram(x, bins)[0]\n",
    "ax[0].scatter(xcoords, c / 10000)\n",
    "ax[0].set(xlim=[0,1], ylim=[0,1.1], title=\"Direct simulation from numpy\")\n",
    "\n",
    "y = np.asarray(totality)\n",
    "x = 1 - np.exp(-0.05 * np.asarray(y))\n",
    "c = np.histogram(x, bins)[0]\n",
    "ax[1].scatter(xcoords, c / trials * 10)\n",
    "ax[1].set(xlim=[0,1], title=\"From our process, showing edge effects\")\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We only sample the process in a finite time interval, so we'll miss aftershocks which occur after the end of our time window.  \n",
    "To correct for this, using the extra (normally hidden) information we have about our simulation, we can discard aftershocks which occur near the end of our time window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "totality = []\n",
    "trials = 1000\n",
    "total_points = 0\n",
    "for _ in range(trials):\n",
    "    result = process.sample_with_details(0,1000)\n",
    "    mask = result.trigger_points <= 900\n",
    "    totality.extend( result.trigger_deltas[mask] )\n",
    "    count = np.sum(result.points <= 900)\n",
    "    total_points += count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7AAAAFACAYAAACFsJDyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5861be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=2, figsize=(16,5))\n",
    "\n",
    "y = np.asarray(totality)\n",
    "x = 1 - np.exp(-0.05 * np.asarray(y))\n",
    "c = np.histogram(x, bins)[0]\n",
    "ax[0].scatter(xcoords, c / trials)\n",
    "ax[0].set(xlim=[0,1], title=\"From our process, corrected for edge effects\")\n",
    "scale = 1 / ((bins[1] - bins[0]) * total_points)\n",
    "ax[1].scatter(xcoords, c * scale)\n",
    "ax[1].set(xlim=[0,1], title=\"Normalised to estimate $\\\\theta$\")\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the normalisation correct above, we need to think about what the \"intensity\" parameter $\\theta$ represents.\n",
    "\n",
    "- Each background event gives rise to $n$ aftershock events, where $n$ is distributed as a Poisson random variable with mean $\\theta$.\n",
    "- Each of these initial aftershocks gives rise to further aftershocks, again with the same distribution.\n",
    "- And so on.\n",
    "\n",
    "The total number of events, counting also the initial event, is then\n",
    "$$ 1 + \\theta + \\theta^2 + \\cdots = \\frac{1}{1-\\theta} $$\n",
    "supposing $\\theta<1$.  This is a standard result in the theory of Branching Processes, see e.g. [Lectures notes, page 9](http://wwwf.imperial.ac.uk/~ejm/M3S4/NOTES2.PDF)  So let $\\alpha$ be the count of aftershock events, and $\\beta$ the count of background events, $\\alpha + \\beta$ is the total number of events.  Then\n",
    "\n",
    "$$ \\frac{\\alpha}{\\beta} = \\frac{1}{1-\\theta} - 1 = \\frac{\\theta}{1-\\theta} \\implies\n",
    "\\theta = \\frac{\\alpha / \\beta}{1+\\alpha/\\beta} =\\frac{\\alpha}{\\alpha+\\beta} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The EM algorithm\n",
    "\n",
    "Here we implement the \"EM\" algorithm described by Mohler et al (2015)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1891,), (922,))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_time = 10000\n",
    "result = process.sample_with_details(0, total_time)\n",
    "points = result.points\n",
    "points.shape, result.trigger_deltas.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.48451346371327142, 0.049659928352839541, 0.097478504011820372)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def p_matrix_col(points, col, theta=0.5, omega=0.05, mu=0.1):\n",
    "    p = np.empty(col + 1)\n",
    "    p[col] = mu\n",
    "    dt = points[col] - points[0:col]\n",
    "    p[0:col] = theta * omega * np.exp(-omega * dt)\n",
    "    return p, np.sum(p), dt\n",
    "\n",
    "def m_step(points, total_time, theta=0.5, omega=0.05, mu=0.1):\n",
    "    omega_1, omega_2, mu_e = 0.0, 0.0, 0.0\n",
    "    for col in range(len(points)):\n",
    "        p, norm, dt = p_matrix_col(points, col, theta, omega, mu)\n",
    "        wp = p[0:col] * dt\n",
    "        omega_1 += np.sum(p[0:col]) / norm\n",
    "        omega_2 += np.sum(wp) / norm\n",
    "        mu_e += p[-1] / norm\n",
    "\n",
    "    return omega_1 / len(points), omega_1 / omega_2, mu_e / total_time\n",
    "\n",
    "theta, omega, mu = m_step(points, total_time)\n",
    "theta, omega, mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def apply_algorithm(points, total_time, steps=200, theta_in=0.5, omega_in=0.05, mu_in=0.1,\n",
    "                    convergence_criteria=None, func=m_step):\n",
    "    theta, omega, mu = theta_in, omega_in, mu_in\n",
    "    thetas, omegas, mus = [theta], [omega], [mu]\n",
    "    for _ in range(steps):\n",
    "        theta, omega, mu = func(points, total_time, theta, omega, mu)\n",
    "        diff = max(abs(thetas[-1] - theta), abs(omegas[-1] - omega), abs(mus[-1] - mu))\n",
    "        thetas.append(theta)\n",
    "        omegas.append(omega)\n",
    "        mus.append(mu)\n",
    "        if convergence_criteria is not None and diff <= convergence_criteria:\n",
    "            break\n",
    "        \n",
    "    return thetas, omegas, mus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.49052987372188317, 0.041711314767587958, 0.09634080087919196)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thetas, omegas, mus = apply_algorithm(points, total_time, 100)\n",
    "thetas[-1], omegas[-1], mus[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAFACAYAAABEN9peAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nN/8/v2iJ5SS+6gwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5879048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_convergence(thetas, omegas, mus, inv_omega=False):\n",
    "    fig, ax = plt.subplots(figsize=(16,5))\n",
    "\n",
    "    x = list(range(len(thetas)))\n",
    "    ax.plot(x, thetas)\n",
    "    legend_txt = [\"$\\\\theta$\"]\n",
    "    if inv_omega:\n",
    "        legend_txt.append(\"$\\\\omega^{-1}$\")\n",
    "        ax.plot(x, 1 / np.asarray(omegas))\n",
    "    else:\n",
    "        legend_txt.append(\"$\\\\omega$\")\n",
    "        ax.plot(x, omegas)\n",
    "    ax.plot(x, mus)\n",
    "    legend_txt.append(\"$\\\\mu$\")\n",
    "    ax.legend(legend_txt)\n",
    "    ax.set(xlabel=\"Iteration\")\n",
    "\n",
    "plot_convergence(thetas, omegas, mus)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a largish sample size, this is typical behaviour-- we converge to an estimate which under-estimates $\\theta$ and slightly over-estimates $\\omega$ and $\\mu$.\n",
    "\n",
    "- So we think there are slightly more background events than there really are\n",
    "- For the aftershocks, we underestimate the mean value of the exponential (so believe aftershocks occur closer in time than they really do) and underestimate the total aftershock intensity.\n",
    "\n",
    "I cannot rigourously justisfy this, but I believe this is due to edge effects-- events which occur near the end of our time window are likely to trigger aftershocks which we do not observe (because they fall after the time window) and so we underestimate the intensity of aftershocks, and so compensate by overestimating the background rate.\n",
    "\n",
    "It must be said that with repeated runs, you can also get the opposite behaviour-- $\\theta$ being over-estimated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For a small sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((208,), (111,))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_time = 1000\n",
    "result = process.sample_with_details(0, total_time)\n",
    "points = result.points\n",
    "points.shape, result.trigger_deltas.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAFACAYAAABEN9peAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5929390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_convergence(*apply_algorithm(points, total_time, 200))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a slightly extreme graph, but it can certainly occur."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using a window of data\n",
    "\n",
    "If our model is correct, then note that \"real-world\" will not start from time 0, but will instead be a window onto an on-going process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAFACAYAAABEN9peAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmcXHWd7//3t7auXqvXdCfdSTohG9lJwqogCoKAggyI\ngBd19A7DXMdxdp3x/mZxZnSW3+jMHRF1XNDrqCiKwLiAKwIC2chCgOxbd5be966u7Xv/OFXVVZXq\ndCfp7tPL66n1OOd8z/ec86kOSr/zPed7jLVWAAAAAAC4weN2AQAAAACA2YtQCgAAAABwDaEUAAAA\nAOAaQikAAAAAwDWEUgAAAACAawilAAAAAADXEEoBAAAAAK4hlAIAAAAAXEMoBQAAAAC4xufWhaur\nq21jY6NblwcAAAAATKBt27a1WWtrRuvnWihtbGzU1q1b3bo8AAAAAGACGWOOjqUft+8CAAAAAFxD\nKAUAAAAAuIZQCgAAAABwjWvPlAIAAAAAskWjUTU1NSkcDrtdypgFg0E1NDTI7/ef1/GEUgAAAACY\nIpqamlRaWqrGxkYZY9wuZ1TWWrW3t6upqUmLFi06r3Nw+y4AAAAATBHhcFhVVVXTIpBKkjFGVVVV\nFzSySygFAAAAgClkugTSlAutd0yh1BjzNmPMXmPMAWPMx/Lsv9YY022M2ZH8/NUFVQUAAAAAmBVG\nfabUGOOV9KCkt0pqkrTFGPOEtfbVnK7PWmvfPgE1AgAAAABmqLGMlF4m6YC19pC1NiLp25Jum9iy\n3BWJJfSDl5u143iX26UAAAAAwIw2llBaL+l4xnZTsi3XVcaYXcaYHxtjVuU7kTHmfmPMVmPM1tbW\n1vMod3J4PUYff2y3Htve5HYpAAAAADDp4vG4PvKRj2jVqlVas2aNDh06NGHXGq+JjrZLWmCtXSvp\nPyT9IF8na+0XrbWbrLWbampqxunS48/rMVpVH9Ku5m63SwEAAACASfepT31Kixcv1p49e/QHf/AH\n+tznPjdh1xpLKG2WND9juyHZlmat7bHW9iXXfyTJb4ypHrcqXbC2PqRXT/QoGk+4XQoAAAAATJr+\n/n499thj+shHPiJJWrRokQ4cODBh1xt1oiNJWyQtNcYskhNG75Z0b2YHY0ydpNPWWmuMuUxO2G0f\n72In05qGkIZiCe0/3aeV88rcLgcAAADALPO3T+7Rqyd6xvWcK+eV6a/fkfdpy7Sf/exnOn78uNav\nXy9J6ujo0PXXXz+udWQadaTUWhuT9PuSnpL0mqTvWGv3GGMeMMY8kOx2p6RXjDE7Jf0fSXdba+1E\nFT0Z1jaUS5J2NzPZEQAAAIDZY8eOHfrEJz6hHTt2aMeOHbrhhhvSAXUijGWkNHVL7o9y2j6fsf5Z\nSZ8d39LctbCySKVBn3Y1devdl7pdDQAAAIDZZrQRzYnS2dmpRYsWSZJisZiefvppffzjH5+w643X\nREczjsdjtKY+pFeY7AgAAADALLJs2TK9+OKLkqTPfOYzuuWWW9IhdSIQSs9iTX1Ir53sVSTGZEcA\nAAAAZod77rlH27dv15IlS7Rr1y59+tOfntDrjen23dlqTUNIkXhC+073anV9yO1yAAAAAGDCVVRU\npEdKJwMjpWextt6Z7GhXE7fwAgAAAMBEIJSexfzKQoUK/czACwAAAAAThFB6FsYYrW0IMVIKAAAA\nABOEUDqKNfUh7T3Vq3A07nYpAAAAADDjEEpHsbYhpFjC6vVTvW6XAgAAAAAzDqF0FGsanMmOdjfx\nXCkAAAAAjDdC6SjmhYKqLA5odzPPlQIAAADAeCOUjsIYozX1THYEAAAAABOBUDoGaxtC2t/Sp8EI\nkx0BAAAAmPmeeOIJ3XHHHVltDz30kD784Q+P+7V8437GGWhNfUjxhNWrJ3u0cWGF2+UAAAAAmA1+\n/DHp1O7xPWfdGummfxy128c//nF961vfymq76KKL9L3vfW986xEjpWOylsmOAAAAAMwSO3fuVCKR\n0OrVq3X06FE99NBDkqRoNCpjzLhfj5HSMagtK1BdWVC/Odiu979hkdvlAAAAAJgNxjCiORF27Nih\njRs3SpJ++tOfav/+/ZKkV199VevWrRv36zFSOgbGGN20pk6/2tuq7sGo2+UAAAAAwIRJJBLq6+tT\nPB7X97//ffX29mpwcFAPP/yw7r333nG/HqF0jG5bX69IPKGfvHLS7VIAAAAAYMLcfPPNOnTokNav\nX68HHnhAe/bs0aZNm3T//fdrw4YN4349bt8do3UNITVWFenxHSf07ksXuF0OAAAAAEyI2tpa7dix\nI7196623Tuj1GCkdI2OMbltfrxcOtetUd9jtcgAAAABgRiCUnoPb1s+TtdKTO0+4XQoAAAAAzAiE\n0nOwuKZEaxtCenxns9ulAAAAAMCMQCg9R7etr9crzT060NLndikAAAAAMO0RSs/RO9bOlcdIj+9g\ntBQAAAAALhSh9BzNKQvqqouq9fiOE7LWul0OAAAAAExrhNLzcNv6eTrWMaCXj3e5XQoAAAAATGuE\n0vNw4+o6BXwe/eBlbuEFAAAAgAtBKD0PZUG/3rqyVk/uPKFILOF2OQAAAAAwrq699lq9/vrrkqT2\n9natXr16wq7lm7Azz3B3bmzQD3ed1C9eb9HbVte5XQ4AAACAGeafNv+TXu94fVzPuaJyhT562UdH\n7XfgwAEtW7ZMkrRr1y6tWbNmXOvIxEjpebp6SbVqSgv06LYmt0sBAAAAgHFz9OhR1dfXy+Nx4uKu\nXbu0du3aCbseI6Xnyef16LcuqdeXnzustr4hVZcUuF0SAAAAgBlkLCOaE2Hnzp1ZIXTbtm1697vf\nPWHXY6T0AtyxsUGxhNXjO064XQoAAAAAjIsdO3YoHA5Lkvbv36/HH3+c23enqmW1pVrbEOIWXgAA\nAAAzxs6dO5VIJLRu3Tp94hOf0MqVK/W1r31twq7H7bsX6M6NDfqrx/doz4lurZoXcrscAAAAALgg\nu3bt0vbt21VaWjop12Ok9AK9Y+08BbwefW8b7ywFAAAAML319vbKGDNpgVQilF6wiuKArrt4jh7f\n0axonHeWAgAAAJi+SktLtW/fvkm9JqF0HNy5sUHt/RH9am+r26UAAAAAwLRCKB0H1yyrUXVJgb67\n9bjbpQAAAADAtEIoHQd+r0d3bKjXL15vUUtv2O1yAAAAAExj1lq3SzgnF1ovoXScvPvS+YolLK+H\nAQAAAHDegsGg2tvbp00wtdaqvb1dwWDwvM/BK2HGyeKaEl2+qFKPbDmuB665SB6PcbskAAAAANNM\nQ0ODmpqa1No6fearCQaDamhoOO/jCaXj6O7L5uuPHtmpFw+166ol1W6XAwAAAGCa8fv9WrRokdtl\nTCpu3x1HN62eq7KgT9/awoRHAAAAADAWhNJxFPR79VsbGvTUK6fU0R9xuxwAAAAAmPLGFEqNMW8z\nxuw1xhwwxnzsLP0uNcbEjDF3jl+J08vdl81XJJ7Q97cz4REAAAAAjGbUUGqM8Up6UNJNklZKuscY\ns3KEfv8k6enxLnI6WVFXpvXzy/XtLcenzYxZAAAAAOCWsYyUXibpgLX2kLU2Iunbkm7L0+/Dkr4n\nqWUc65uW7rlsvg609Gnb0U63SwEAAACAKW0sobReUubMPU3JtjRjTL2k2yU9dLYTGWPuN8ZsNcZs\nnU5THJ+rt6+dp+KAV9/azIRHAAAAAHA24zXR0b9J+qi1NnG2TtbaL1prN1lrN9XU1IzTpaee4gKf\nbrukXv+964Q6mfAIAAAAAEY0llDaLGl+xnZDsi3TJknfNsYckXSnpM8ZY945LhVOU/ddsVBDsYQe\n3caERwAAAAAwkrGE0i2SlhpjFhljApLulvREZgdr7SJrbaO1tlHSo5L+l7X2B+Ne7TRy8dwyXdpY\noW+8dFSJBBMeAQAAAEA+o4ZSa21M0u9LekrSa5K+Y63dY4x5wBjzwEQXOJ3dd2WjjrYP6Jn9M/f5\nWQAAAAC4EL6xdLLW/kjSj3LaPj9C3/dfeFkzw9tW1am6pEDfeOGo3rx8jtvlAAAAAMCUM14THSGP\ngM+jey6br1/sbdHxjgG3ywEAAACAKYdQOsHuuWyBjKT/eumY26UAAAAAwJRDKJ1g88oL9daVtXpk\nyzGFo3G3ywEAAACAKYVQOgnee2WjOgei+uGuk26XAgAAAABTCqF0Elx1UZUW1xTr6y8ckbW8HgYA\nAAAAUgilk8AYo/df1aidTd3afqzT7XIAAAAAYMoglE6SOzY0qCzo01eeO+J2KQAAAAAwZRBKJ0lx\ngU/3XL5AP37lpJo6eT0MAAAAAEiE0kn1visbZYzR135zxO1SAAAAAGBKIJROonnlhbp5zVx9e/Nx\n9Q3F3C4HAAAAAFxHKJ1kH3zjIvUOxfTdrcfdLgUAAAAAXEconWTr55dr48IKffX5I4oneD0MAAAA\ngNmNUOqCD75xkY51DOhnr512uxQAAAAAcBWh1AU3rKxVfXmhvvzcYbdLAQAAAABXEUpd4PN69IE3\nLtLmwx3afqzT7XIAAAAAwDWEUpfcfel8hQr9+vyvDrpdCgAAAAC4hlDqkuICn953VaOefvW0DrT0\nul0OAAAAALiCUOqi91/VqKDfoy88c8jtUgAAAADAFYRSF1UWB3T3pQv0gx3NOtk96HY5AAAAADDp\nCKUu+59XL1LCSl9+lpl4AQAAAMw+hFKXNVQU6dZ18/TNzcfUNRBxuxwAAAAAmFSE0ingd9+0WAOR\nuL7+wlG3SwEAAACASUUonQJW1JXpuhVz9NXnD6t/KOZ2OQAAAAAwaQilU8SH3rJEnQNRfeNFRksB\nAAAAzB6E0iliw4IKXb20Wl/89SENRBgtBQAAADA7EEqnkD+8fqna+yP6rxePuV0KAAAAAEwKQukU\nsnFhpd64pFpf+PVBDUbibpcDAAAAABOOUDrFfOT6pWrri+i/XuLZUgAAAAAzH6F0irm0sVJXXVSl\nL/z6kMJRRksBAAAAzGyE0inoI9ctVWvvkL75Es+WAgAAAJjZCKVT0OWLq3TF4ko99AzPlgIAAACY\n2QilU9Qfv3W5WnuH9PUXjrhdCgAAAABMGELpFHXZokq9aVmNHnrmoHrCUbfLAQAAAIAJQSidwv7s\nxuXqGojqP399yO1SAAAAAGBCEEqnsNX1Id2ydq6+/NxhtfYOuV0OAAAAAIw7QukU9ydvXaahWEIP\n/vKA26UAAAAAwLgjlE5xi2tKdOeGBn3zpWNq6hxwuxwAAAAAGFeE0mngI9cvlYz07z/b73YpAAAA\nADCuCKXTwLzyQt13xUJ9b3uT9p7qdbscAAAAABg3hNJp4vffvEQlBT598kevuV0KAAAAAIwbQuk0\nUVEc0IffslTP7GvVM/ta3S4HAAAAAMYFoXQaee9VC7Wgskif/OFriies2+UAAAAAwAUbUyg1xrzN\nGLPXGHPAGPOxPPtvM8bsMsbsMMZsNca8cfxLRYHPq4/dtEJ7T/fqO1uPu10OAAAAAFywUUOpMcYr\n6UFJN0laKekeY8zKnG4/l7TOWrte0gckfWm8C4XjptV12rSwQv/69D71DcXcLgcAAAAALshYRkov\nk3TAWnvIWhuR9G1Jt2V2sNb2WWtT95MWS+Le0glijNHHb7lYbX1D+sIzB90uBwAAAAAuyFhCab2k\nzHtFm5JtWYwxtxtjXpf0QzmjpZgglyyo0K3r5uk/nz2k5q5Bt8sBAAAAgPM2bhMdWWsfs9aukPRO\nSX+Xr48x5v7kM6dbW1uZQfZCfPSmFZKkf/jhqy5XAgAAAADnbyyhtFnS/IzthmRbXtbaX0tabIyp\nzrPvi9baTdbaTTU1NedcLIbVlxfqQ9cu0Y92n9Jz+9vcLgcAAAAAzstYQukWSUuNMYuMMQFJd0t6\nIrODMWaJMcYk1zdIKpDUPt7FItvvXLNYCyqL9NdPvKJILOF2OQAAAABwzkYNpdbamKTfl/SUpNck\nfcdau8cY84Ax5oFktzskvWKM2SFnpt53Z0x8hAkS9Hv11+9YqYOt/frab464XQ4AAAAAnDPjVnbc\ntGmT3bp1qyvXnmk+8PAWvXSoXb/802s1pyzodjkAAAAAIGPMNmvtptH6jdtER3DPX719paJxq0/9\n+HW3SwEAAACAc0IonQEaq4t1/zWL9djLzXrhII/yAgAAAJg+CKUzxIfevETzKwv18cd2KxyNu10O\nAAAAAIwJoXSGKAx49Q/vXKNDbf363K8Oul0OAAAAAIwJoXQGuWZZjd65fp4e+tUB7T/d63Y5AAAA\nADAqQukM87/fvlLFBT79xfd3K5HgrTwAAAAApjZC6QxTXVKgv7z5Ym092qlvbznudjkAAAAAcFaE\n0hnoXRsbdMXiSn3qx6+ppSfsdjkAAAAAMCJC6QxkjNEnb1+jSCyhv3xst6zlNl4AAAAAUxOhdIZa\nXFOiP7txuX72Wosee7nZ7XIAAAAAIC9C6Qz2229YpE0LK/Q3T+zRaW7jBQAAADAFEUpnMK/H6F/e\ntU6ReEJ/8X1u4wUAAAAw9RBKZ7hF1cX68xtX6Bevt+jRbU1ulwMAAAAAWQils8D7r2rUZY2V+sST\nr+pE16Db5QAAAABAGqF0FvB4jP7lXWsVt1Z//J0diie4jRcAAADA1EAonSUWVhXrb25dpRcPdeg/\nnz3kdjkAAAAAIIlQOqu8a2ODbl5Tp399eq92N3W7XQ4AAAAAEEpnE2OMPnn7GlWXFOgj335ZA5GY\n2yUBAAAAmOUIpbNMeVFA/3rXOh1u79ff/fdrbpcDAAAAYJYjlM5CV11Urd+95iJ9a/Mx/Xj3SbfL\nAQAAADCLEUpnqT9+6zKtm1+uP390l46297tdDgAAAIBZilA6SwV8Hn32nkvk8Rh96JvbFY7G3S4J\nAAAAwCxEKJ3F5lcW6dN3rdMrzT36+x++6nY5AAAAAGYhQuksd93FtfrdaxbrGy8e0+M7mt0uBwAA\nAMAsQyiF/vTG5dq0sEJ/8f3dOtDS53Y5AAAAAGYRQink93r0H/deokK/V7/7f7eqNxx1uyQAAAAA\nswShFJKkuaFCPfieDTrSPqA/emSnEgnrdkkAAAAAZgFCKdKuWFyl/++Wi/Wz107r33++3+1yAAAA\nAMwChFJked9VjbpzY4P+/ef79fSeU26XAwAAAGCGI5QiizFGf//O1VrXENIff2en9p/udbskAAAA\nADMYoRRnCPq9+vx9GxX0e/WBr21Re9+Q2yUBAAAAmKEIpchrbqhQX3rfJrX0DOn+/7tN4Wjc7ZIA\nAAAAzECEUoxo/fxyfebd67XtaKf+/NFdspYZeQEAAACML0IpzurmNXP1529brid2ntC//YwZeQEA\nAACML5/bBWDq+703XaTDrf3695/v14LKIt2xscHtkgAAAADMEIRSjMoYo3+4fY2auwb10e/tUlVJ\nQNcun+N2WQAAAABmAG7fxZgEfB594b6NWlZbqt/7xna9fKzT7ZIAAAAAzACEUoxZadCvhz9wqWpK\nC/SBh7foYGuf2yUBAAAAmOYIpTgnc0qD+voHLpPXY/TeL2/Wqe6w2yUBAAAAmMYIpThnjdXF+ur7\nL1PXQET3ffkltfcNuV0SAAAAgGmKUIrzsqYhpC+971Id6xjQfV/erO6BqNslAQAAAJiGCKU4b1de\nVKUv3LdR+1t69b6vblbfUMztkgAAAABMM4RSXJBrl8/RZ+/doN3N3frgw1s0GIm7XRIAAACAaWRM\nodQY8zZjzF5jzAFjzMfy7H+PMWaXMWa3MeY3xph1418qpqobV9Xp03et0+YjHfqdr28lmAIAAAAY\ns1FDqTHGK+lBSTdJWinpHmPMypxuhyW9yVq7RtLfSfrieBeKqe229fX65zvW6vmDbfrg17ZoIMKt\nvAAAAABGN5aR0sskHbDWHrLWRiR9W9JtmR2stb+x1nYmN1+U1DC+ZWI6eNem+fr0Xev04qF2vf+r\nW9TPM6YAAAAARjGWUFov6XjGdlOybSQflPTjfDuMMfcbY7YaY7a2traOvUpMG7df0qDPvHu9th7p\n0Pu+wuRHAAAAAM5uXCc6Msa8WU4o/Wi+/dbaL1prN1lrN9XU1IznpTGF3La+Xv9xzwa9fLxL7/nS\nS+oaiLhdEgAAAIApaiyhtFnS/IzthmRbFmPMWklfknSbtbZ9fMrDdHXL2rn63Hs26LUTPbrrCy/o\ndE/Y7ZIAAAAATEFjCaVbJC01xiwyxgQk3S3picwOxpgFkr4v6T5r7b7xLxPT0Y2r6vTwb1+q5s5B\n3fHQb3S0vd/tkgAAAABMMaOGUmttTNLvS3pK0muSvmOt3WOMecAY80Cy219JqpL0OWPMDmPM1gmr\nGNPKVUuq9c3fuUL9QzHd+fkX9NrJHrdLAgAAADCFGGutKxfetGmT3bqV7Dpb7D/dq/u+vFn9kZi+\n8D826qol1W6XBAAAAGACGWO2WWs3jdZvXCc6AkaytLZU3/tfV2luKKj3fXWzHnu5ye2SAAAAAEwB\nhFJMmvryQn33gau0cWGF/uiRnXrwlwfk1kg9AAAAgKnB53YBmF1ChX597QOX6aOP7tK/PLVXTZ0D\n+sRtq+X38vcjAIDpwVorKytrrRJKSFZKKOFs24QkKWETshrul+qbeazVmf0T1jlfaj23b+Z21vUz\nj1fG8cm+WXVnnCN1ray2jL65x+Xrn9WeeVxyO3N9xLaM9hFrzfnZZ7alzzdK/9zvkNsnX1253y3v\ndUeoK+93G2P/zGvnHjfizyJ5THo9z5/DiP1yz+OsnNGW72efuz/zzyN1nrPVkjtIMeZ+eWoeqaZ8\n9WWeJ7fmrH5j+JnmO3fefqP8TPN+t7P8TL/7ju9qScUSTXeEUky6Ap9Xn3n3etVXFOrBXx7U4bZ+\nPfSejaooDrhdGgCMyFqruI0rYRPpT2o7vUzE87fbeDqwJJRQIpHICjGZgSIVJBLKWE9dM7dtjOc4\n63nPco6znfd8jjnbdaU8QSzjWtKZwStvSBshyCkjOKb7jhYS8+zL/cURM4ORkTFGqf84/zXZ7cZk\n9U2vZ/bPOEdu/3Rfp3Fs/U3GMVL+/jnnzj0mty1vv/Qi+zyZ/XPbjBn+3ul+GefJ97PK/O4j1TLm\nfiajrjw15/1uObVktmWe64x+5/AzzVfTmH+m+fqN8jMtD5ZrJiCUwhXGGP3ZjSu0ZE6JPvq93brt\nwef15fdt0tLaUrdLA2adVJiK2ZjiibjiNq5YIqa4jZ+1PXM7dznW43L7jTXc5WtPJEYIijl94jYu\nK3vWa6RDZ0afmR5GPMYjjzwyxjjrxiMjZz3V5jXeM9pGOibzk9lmjJFHzrokeT1e+Ywv6xdwj/Gk\nfyFNHZ+5L/eXdo+c/ul9uf3NmW2p75zvXMZkh4Ws/hnXO1s9WdvJ48/on6fviPXlfv9RvmO+elLy\n9ZPODDy5vxCPtX/uL9fp7TEGsdRxZ9Sa2T/ftVPfL/dnkFNXbsgE4D5CKVx1+yUNWlhVrPu/vk23\nf+43+j/3rNdbVtS6XRYwJtZaRRNRReIRRRNRxRIxxRKx9HrmMrctX7+z7c93zrOdZ8SQmBEMo4mo\n4gn3w1YqrPiMLx18PJ7kMrkvtZ7ZdkZ7xjE+j08BEzjjOK/Hmw5Smf1HvFaePmOtYaT+WZ+zBLrM\n8JavbaRQONq5co/zGi+/nAMAXMUrYTAlnOga1O98fatePdmjP7xumT78liXyePglCWey1mooPqSh\n+JDCsXB6PRKPKJKIOMvkejQezWpLBcjR2kY6PrctmohO6Hf1Gq/8Hr98Hp98Hl/e9bO2GZ+8Hq+8\nxiufxyev8ebd9hnn+JH2pdrT23n2pY5JnWes104FNgAAMPOM9ZUwjJRiSphXXqhHH7hKf/nYbn3m\nZ/u0s6lLn7lrvUJFfrdLwxhYaxVJRDQYHdRgbFADsQENxpLr0QGF4+EzQmRqPb2MhzUUG8paTx2X\ntR4fGpea/R6/At6AAp6A/F6/Ap6As53RVuwvVqW30tmfbA94A8PHZrSlwuA5B8ectsx2whoAAJgN\nCKWYMgoDXn36rnW6ZEG5PvHkq7r1wef00Hs2auW8MrdLm1FiiZj6o/3qj/arN9KrgdiABqIDw2Fy\nhGCZXh+hPW7j51xL0BtUga9ABd6C9HrQG1SBt0ChYEi13lpnny+Y1Se3f2Y4zA2L6dCZEyq5XREA\nALguHpMifVJ0QIr0O+uRfikykLHeL0X7h9cjfcn9/dLbPyOF6t3+FheMUIopxRij917ZqFXzyvR7\n39iu2z/3vP7m1lW6+9L5sz5EJGxCfdE+9UZ61RfpU3+0X33RPvVF+tQXHd5Ohc30diTZL7lvMDY4\n5msGvUEV+gpV6CtUkb8ovR4qCjnr/kIV+Yry9slsD/qC2YHSF1TAE5j1f6YAAGCasFaKhaWhvuyw\nGMm3nRMwozkBMzNwnssdYMYrBUqkQLEUKHKWsfDEfedJxDOlmLJae4f0R4/s0HMH2vSOdfP0ydtX\nqzQ4vW/ntdZqIDagnqEe9UR61D3UrZ6Is94z1KPuSHfefd1D3eqL9qVfVTASI6MSf4mKA8Uq8Zec\nue4vVkmgJGs79ckNlkFvUF6Pd5J+MgAAAOPknAJkf55+I/Qd5fewYSYZHJMff3H2dtanRPIXDa+n\nA2fJmX18BdI0+wt9ninFtFdTWqCvfeAyPfSrA/r0T/dpV1OXHrx3g1bXh9wuLS2eiKs70q2ucJc6\nwh3qHOpUZ7jTWQ8766m21PrZJsfxGq/KAmUqKyhTKBBSebBcC8oWqCxQplBByNkXKFNJIBkwM8Jl\naaBUhb5CRh8BAMD0MSUCZIlUkBMCS+ZIgcU5YbFYKig9M1RmBchiyVcoeZgX4lwwUoppYfPhDv3B\nt15We/+Q/vSG5fqfVy+Wd4Jm540n4uoc6lTbYJtaB1rVNtjmrA8665mBszvSPeLoZam/VBXBCpUH\ny1VZUKmKYIWzXVCeFTzLCsrSobPIV0SoBAAAU9NUDZB5l6MFyOTSXzjtRh+nk7GOlBJKMW109Ef0\nF9/fpaf2nNYViyv1r3etV3154ZiPt9aqN9qrU/2n0p/TA6fPCJ8d4Y68k/aUBkpVXVitymClKoOV\nqiioSAd17QsgAAAgAElEQVTNymClygvKnfZghSoKKuT3Tu9bjQEAwDRn7XDwG+qTIr3DQTG1nRke\nh3oz9hEgceEIpZiRrLX67rYm/e0Te+TxGP39O1fr1nXzZIxROBbWib4TTuAcGA6dmSF0IDaQdT6P\n8agyWKmawhpVF1arpqhGVcEq1RTVpNtSn6Av6NK3BgAAs0LWSOS5BMh828mlxvi7vr8oI0SWZIRE\nAiTOH6EUM07CJtQ60KqmvibtOnVYD2/ZptP9zaos71Mg2Kn2cFtWfyOjqsIq1RXVqa54+FNbVJte\nry6sls/Do9UAAOA8xSJ5QuH5BMhkCB3rK9a8BTkBMjNQlkiB0rFvB4olJjfEBGCiI0xLCZvQ6f7T\nOtx9WId7Dutoz1E19Tapqa9Jzb3NiiQi6b7Gb1RRVa3u3lJ5+xbr+iW36LolKzS3ZK5qi2pVW1TL\nLbQAACBb5mjkUI8TELM+PSMHxnzb8cjo15Qkj+/MAFlQKpXNPbcAmVryOw5mEEIpXBGOhXW056gO\n9xx2Amj3YR3pPqIjPUey3qNZ4i/R/NL5WlK+RG9qeJMaShrUUOp85hbPVcAb0IGWXv3Jd3fpsV92\naaClVn976yrVlXKrLQAAM0oiPjzKmBkgh5IB8Yy23owRyZz2RGz06xnP8G2pmYGwqPrcRiBTIXQa\nvs4DmCzcvosJFYlHdKj7kPZ17tO+jn062H1Qh7sP60TfCdnkMw5GRvNK5qkx1KhFZYu0KDT8qQpW\njWk22lg8oS89d1if+ek++b0e/fFbl+m9Vy6Uz8t03AAAuMZaKTZ0ZijMFxTT4TLf6GWvFO0f2zX9\nRU4QTI9IlkoFZcNtBcnQeEZbaTJQJvf7iwiRwAXimVJMKmutWgZatLdzrxNAO/dpf+d+He4+nJ7J\nNuAJaFFokRaHFmcFzwVlC1ToG/ssumdztL1ff/X4Hj2zr1Wr5pXp79+5WpcsqBiXcwMAMGukbnEN\n9zghMdwjDXUnl5mjkHnCYzpsJoPnWd7PnWa8OeGxJCcwluWEzNygWTIcKr3cCAhMFYRSTKi2wTbt\nadujPe179Gr7q9rTvkdtg8MTDc0rnqdlFcu0tGKpllUu07KKZVpQumBSJhWy1urHr5zS3z65Ry29\nQ7r3sgX68xtXKFTEsxcAgFnAWmckMhUoh3pzQmVPnn09Urg7Y98Yw2TmqGQ6NOYZgcz7KRsOmczU\nCsxIhFKMm4HogHa37daOlh16pf0Vvdr+qloGWiQ5r1RZHFqslVUrtbJqpVZUrtDSiqUqC5S5XLXU\nNxTTp5/ep4d/c1iVxQF9/JaL9c719WO6HRgAAFck4sMjjWcEyDxt+YLnUO/o75I0nmQwDEnBMicg\nZi1LM9Zz+5QyKglgTAilOC/WWp3sP6kdLTv0csvL2tm6U3s79yqR/JfbotAirapapZVVK7WqapVW\nVK5Qkb/I5arP7pXmbv3vH7yiHce7dOXiKv3VO1bq4rnuh2YAwAyTSDi3s4a7cz7nEC4jfaNfx+M/\nM0ieESozA2Se4BkoZmQSwIQjlGJMrLU63HNYm09u1pZTW7SjZYdaBp1R0EJfodbWrNX6mvVaP2e9\n1tasnRIjoOcjkbD61pZj+uef7FVPOKp3bWzQn9ywXLVlzNILAEgaMVSe7dOVHT41yu9VvmD+ADli\nqMzT5gsSKAFMC4RSjKipt0mbT23WSydf0pZTW9Q62CpJqi2q1YbaDbpkziVaX7NeSyuWTsozoJOp\neyCqz/5yv772m6Pyeox+55rF+t1rFqu4YGZ9TwCYlSYjVAZKpWDoHD5lzrIg5Ixa+gKT8qMAgKmA\nUIq0nkiPXjjxgp5rfk6bT27Wif4TkqTKYKUur7tcl829TJfVXab5pfNnzfOWx9oH9M9Pva7/3nVS\n1SUF+pMbluldGxt4hQwAuC02JA12OWFxsEsa7BxezwqQkxUqMz4FZTxDCQDngFA6i1lrtb9rv55t\nelbPNj+rHS07FLdxlQZKdXnd5bq07lJdPvdyLQ4tnjUhdCTbj3Xqkz98TVuPdmrpnBL95c0X69rl\nNbP+5wIAFyQePXuwPFtbbPDs5yZUAsC0QSidZQZjg3rhxAt6tvlZPdv0rE4PnJYkrahcoavrr9bV\nDVdrTfWaGXc77niw1uqpPaf0jz9+XUfaB3RpY4X+8PpluuqiKsIpgNkrHhseiRzszAiPGWEyM1Bm\nBsto/9nPHSiRguVSYblUWOEExsLynLbkerBiuI1QCQDTCqF0FuiP9uvZpmf19NGn9VzzcxqMDarY\nX6wr516pqxuu1hvmvUG1xbVulzltRGIJPbLlmB785UGd6gkTTgHMDPFYMlR2SoMd0kDH8PpgZ3K7\nI6NPt7OM9J79vP6iEULkaG0hyct7owFgNiCUzlA9kR49c/wZ/fToT/V88/OKJCKqClbp+oXX67oF\n12lT7Sb5+Zf9BRmKxfWdLcfT4fSyxkr94fVLdSXhFICbEomMUcvOEcJlbvDsdF4zMhLjdYJiUaVU\nWDlCmKzIHyx9BZP33QEA0xKhdAYZiA7o58d+rh8d/pFePPmiYomYaotqdf3C6/XWhW/V+pr18nq8\nbpc544SjcX1n63F9jnAKYDxZKw315g+QI4bLDufW2BEn8TFOUCyqTIbIyuz1dPCsyF4vKOPVIgCA\nCUMoneYSNqEtp7boiYNP6KdHf6rB2KDmFc/TDY036PqF12tN9Rp5DDPFTobccHrJgnLdf/Vi3bCq\nTl4Pv8wBs5q1UqRPGmhPfjoy1pOf/rbh9tSoZiI28jkDpVJRRZ5AmRsuM4JnMCTxl5MAgCmGUDpN\nHeo+pP8++N968tCTOtV/SsX+Yt3YeKNuvehWXTLnEoKoi8LRuL679bi+9NxhHW0f0MKqIn3wjYt0\n58YGFQWYeAOYEaLhM0NlvqCZ+YlH8p/LeKWiqoxPhbMcbSSTRzAAADMEoXQaGYgO6IeHf6jH9j+m\n3W275TEeXTXvKt160a168/w3K+gLul0iMsQTVk/vOaUv/PqQdhzvUnmRX++9YqHuu7JRNaU8YwVM\nGakJfgbaxhg0O5xRz5EUVuSEzMqc7ers9mCIW2MBALMaoXQaONR9SI+8/oieOPiE+qJ9WlK+RO9c\n8k7dvOhm1RTVuF0eRmGt1bajnfrCrw/pZ6+dlt/r0R0b6vXbb1ikZbWlbpcHzDyJuBMy+9uk/lbn\nM9A+vN7fNrxvoM3pO5JASU6gHCloVknF1c4kP7yKBACAczLWUMq/YSdZNBHVr47/So+8/oheOvWS\n/B6/bmi8QXcvv1vratYxgc40YozRpsZKbWqs1MHWPn35ucN6dFuTvrX5uC5fVKn/ccVC3biqTgEf\nt1wDeVnrvAczK2RmBMvMZWq00ybynMg4YbK4xhmtrF2VXE8GytygWVgp+bkDBQCAqYKR0knSOtCq\nR/c9qkf3PaqWwRbNLZ6ru5bfpduX3K6qwiq3y8M4ae8b0ne3Nem/Xjqq4x2Dqi4p0N2Xztc9ly9Q\nfXmh2+UBEy86KPW1ZIxepj7teYJnm5SI5j9PMOQEzOIaJ1gWp9ZTYbNmeF9hJaOYAABMQdy+O0Uc\n6T6ih/c8rCcOPqFoIqo31L9Bdy+/W1fXX81rXGaweMLq1/ta9Y0Xj+oXe1tkJF13ca3uu2Kh3rik\nWh5m7cV0khk0+1qkvtMjrLdIkd785/AXZwTLjJCZFTyTy6JqyReY3O8IAADGHbfvumxX6y599ZWv\n6ufHfi6/x6/bl9yu9656rxaWLXS7NEwCr8fozSvm6M0r5uh4x4C+tfmYHtlyXD999bQaKgp1x4YG\n3bmxQfMri9wuFbNVNCz1t0h9rclgOdJ6qzTUk/8cwXKpZI5UPEeauy65XiOV1CbXM4JngH/WAQBA\nfoyUjiNrrZ5rfk5feeUr2np6q0oDpbp7+d269+J7VV1Y7XZ5cNlQLK6fvHJKj25r0nMH2mStdMXi\nSt25cb5uWl2n4gL+jggXKB5zAmXvyeGRy/6W4fX0dqs01J3/HMGQEyqL50glyYBZXOOEzMz14hrJ\nx2zTAABgZNy+O4kSNqGnjjylL+3+kvZ17tOcojl678r36s5ld6rYX+x2eZiCmrsG9dj2Jj26rUlH\n2gdUFPDq5jVzdefGBl3WWMntvcgWDTujln2npd5TyeVJqfe01HdqeNnfJinP/6cHQ8mQOWd4ZDMd\nOHPCJ0ETAACME0LpJLDW6hfHfqHP7visDnQd0OLQYv326t/WLYtukZ+Xn2MMUq+V+e7WJv1w90n1\nDcVUX16ot6+bq3esnadV88qYkXkmG+rLCJqnskNm78nhfeGuM4813uHRy9K5UmmtVFI3vEzfQlvD\nTLMAAMAVhNIJZK3V8yee13+8/B96tf1VNZY16kPrP6QbGm+Qx/D6D5yfgUhMP3nllJ7YeULP7m9T\nPGG1uLpYb183T+9YO1dLeffp9JB6zclIo5mZy3yTAnkDGeGyViqtS24nP6m2oiqJydIAAMAUNq6h\n1BjzNkn/Lskr6UvW2n/M2b9C0lclbZD0cWvt/z/aOadrKN1yaos++/Jntb1lu+pL6vXAugf09sVv\nl8/D84AYPx39Ef3klVN6cucJvXi4XdZKK+pK9Y5183TLmrlqrOa2cFfEo07Y7Dkp9Z7IWZ6Uek44\ny+jAmcf6izICZu0IyzqpsEJidBwAAMwA4xZKjTFeSfskvVVSk6Qtku6x1r6a0WeOpIWS3impc6aF\n0o5wh15rf00P73lYL558UXMK5+j+tffrt5b+FrfpYsK19IT1o90n9eSuk9p2tFOSE1BvWFmrG1bV\ncYvveLDWmWF2tLDZ16Izntn0BpKjmPOksrkZy7kZI521UkEpYRMAAMwq4xlKr5T0N9baG5PbfyFJ\n1tpP5en7N5L6pnsojcaj+tTmT+lg10Ed6j6kriHnea7KYKU+uPqDumv5XQr6eEYLk6+pc0BP7Tmt\np/ac0tYjHUpYqb68UG9dWasbV9Xp0sYK+bzcQp4lHhu+lTYVLs9YnpSi/WceW1iRHTLL5p25LKoi\nbAIAAOQxnu8prZd0PGO7SdLl51nU/ZLul6QFCxaczykmhd/r15ZTW1QRrNB1C67TReUXaXFosS6Z\nc4mK/LxrD+5pqCjSB9+4SB984yK19w3p56+16OlXT+mbm4/p4d8cUXmRX29ZMUdvWTFHVy+tUahw\nho/kxyLJUNksdTdLPU3J5Ynhkc7+Fskmso/z+JOhcq5Uu1paekNO2EyGUH+hO98LAABgFpnUByGt\ntV+U9EXJGSmdzGufqydvf9LtEoCzqiop0F2Xztddl85X/1BMv97XqqdfPa2fv9ai729vltdjtHFB\nha5dUaM3L5+jFXWl0+s233jMmRAoFTZ7TuQEz+b8t9MGQ1JZvRMqa1flua02ObrpYUQZAABgKhhL\nKG2WND9juyHZBmCKKC7w6aY1c3XTmrmKxRPa2dSlX77eql/ubdE//2Sv/vkne1VXFtS1y2t07fIa\nXXlRtbujqImEM4KZGzK7k+Gzp9kZAc0d4QyUOIEzVO8EzlDD8HZZgzPSWVDizncCAADAeRlLKN0i\naakxZpGcMHq3pHsntCoA583n9WjjwkptXFipP71xuU73hPXM3lb9al+LfrjrpL695bg8RlrTUK43\nLqnSG5ZUa8OCCgX94/R6EWul/rbssJm+vTa57D0hJWI5hRcmw2W9tPhaJ2CW1WcHz2BofGoEAADA\nlDHWV8LcLOnf5LwS5ivW2n8wxjwgSdbazxtj6iRtlVQmKSGpT9JKa23PSOecyhMdATNVNJ7Q9qOd\nev5gu54/0KYdx7sUT1gF/R5d2lipNyyp1hsuqtbKeWXyeka41TcedcJl13Gp+7gzutl1zFnvSm7H\nh7KP8QaSIbNhOHhmjm6GGngVCgAAwAwzru8pnQiEUsB9veGoNh/u0HMH2vT8gTbtO92nQoW1LNil\na+eEtbG8T8uCnZqTaJWnu8kJnvluqy2plULzpfL5TsAMzc8OnsXVBE4AAIBZZjxn3wUwU1grDXRI\n3cekruMq7T6u67qO67r+41LRcSXKj8sT7nD6tjifqPWqWVXqDc6VKb9EZYvu0JyGJfJXLRwOn35e\nkQQAAIDzQygFZpJE3BnJTN1am3tbbfdxKTqQfYy/ODnCOV+e+o3JEc8FUmi+2n1z9GKrX5uPdOml\nwx16/WivdFTybzVaOdenSxaEtWFhhy6ZX66GisLpNbsvAAAApgRu3wWmk2g4GS6PZQTPjGVPs2Tj\n2ccUVWXcWrsgHUDTy3N4lrOzP6ItRzq0/ViXXj7WqV1N3RqMOterKS3QhgXlumRBhTYsqNDahtD4\nTZ4EAACAaYdnSoHpxlop3J0TNI9lb/e3Zh9jPM57N3ODZiqAhhqkQNGElRyNJ7T3VK+2H+vUy8e6\ntP1Yp462OyOxPo/RxXPLtGFBudY2lGtNQ0gX1ZSMPIESAAAAZhRCKTDVJBJS3+mzj3RGerOP8QWH\nJw7KN9JZOk/yTq278Nv6hrQjGVC3J0dTByLOaGrQ79HKuWVaUx/SqvqQVs8LaWltifxej8tVAwAA\nYLwRSoHJFos47+bMfH6z6/hwAO1pluKR7GOC5cMhM99I5wyYtTaesDrY2qdXmru1u7lbe5p7tOdE\nt/qTQTXg8+jiulKtrg9pdX1Ia+qdoFrg49ZfAACA6YxQCoy3od6Md3MeP3Oks/eUpMz/PRmptO7M\nV6UkJxFS+XypoNStb+OqRMLqcHu/XmnuzgqrvUMxSc6tv4trirW8rkwr6kq1oq5Uy+tKVV/OZEoA\nAADTBaEUOBfWSn0tw7fWdmeOeCZHOsNd2cd4/E7QzHx+M3Oks6xe8hW4832moUTC6ljHgHY3d+u1\nkz3ae6pXr5/qVXPXYLpPaYFPy5MB1QmqZVpeV6pQod/FygEAAJAPoRTIFBtybp/NvLU261UpTVJ8\nKPuYQGnO7bQ5I50ltZKHZyEnWk84qn3JgOoE1R69fqpXveFYus/cUFBL5pToopoSXTSnREtqSrRk\nTomqSwKMrAIAALiEUIrZw1pnFDN3dDNzu++0sm+tlVRSl/E8Z0MybDYMbxeWu/J1MDprrU52h9MB\ndf/pPh1o6dPB1r70pEqSFCr0J8NqsZbMcYLqkppS1VcUMgswAADABCOUYuZIxJ3nNbuTAbPrWMZo\nZ1P+WWu9BRm30zbk3F7bwK21M1QqrB5oGQ6pqWVb3/AkUwGfRwsri9RYXaxF1cVaWFWkRVXFaqwu\nVl1ZUB4CKwAAwAUbayidWu+SwOyTSEgDbU647Dnh3GLb0+ysdzc7s9n2nJASsezjCiudcFm5WFp0\nTcZoZ3Lks7hm2s9ai3NnjNG88kLNKy/UNctqsvZ1DUTSIfVQa78Ot/XrSHu/ntnXqkgske5X4PNo\nYVWRGqucwNqYDK3zK4o0NxSUj9fXAAAAjCtCKSbOSIGzOxk6e5qknpNSIpp9nDcglc1zRjPnX3Hm\naGeoQSoocec7YdoqLwpo48JKbVxYmdWeSFid7AnrSDKkHmnr1+G2AR1q69ev9rYqEh8OrD6P0dzy\noOZXOCF1fmWh5lcWqaGiUPMrilRTWsAzrAAAAOeIUIrzk4hL/W3Do5rnGzjL5iVvp022ldXPiHdz\nYvrweIzqywtVX16oNyypztoXT1id6BrU0fYBHe8c0PGOATV1Dup454B+/nqL2vqyJ8cq8HmcgFo5\nHFobkgG2vqJQFUV+QisAAEAOQimyxWNSf6vUd8p5jjP16Tsl9Z6Wek86kwb1nZZsIvtYAidmGK/H\nOAGzsijv/sFIXE2dTmBt6hzU8Y4BHe9wQuv2o53qCWffdl7g82huKKi5oULNLQ9qXs5ybqhQZUEf\nwRUAAMwqhNLZIhZxbqXNCpm5ofOUE0hzw6bkPKNZUieV1kl1q4fXCZyYxQoDXi2tLdXS2tK8+7sH\no05o7RjUia5Bnewe1InusE52DeqFg+063RNWImeuueKAV3PLCzU3lB1a60JB1ZYFNae0QOWMuAIA\ngBmEUDpdJRLSYKcTIgfanGV/atl65na4O89JjBM2S2ul0rlS3VpnmdpOBc+SOZLXP+lfEZjuQoV+\nhQpDWjUvlHd/LJ5QS++QE1a7wlnLk91hvXay94xbhCVn9uA5pQWaU1qg2rJkWC0r0JzSoGrLCtLh\nNVRIeAUAAFMfoXQqiEWcgHnGpyN7e6BjOGgOtEs2nudkRiqqcsJmcbVUtya5ntwuqRsOncVzJC//\nCABu8Xk96dmCNy7M32coFtfp7iGd7g3rdE9Yp3uG1NIbVkvPkE73hLW/pU/PHWhTb86twpITXmuT\nYXVOaYGqS5xPVUlA1SUFqikNqKq4QNWlBSoOeAmwAADAFSSS85FISLHw8Cc6KMWGpEi/NNQjDfUO\nfyJ9Z7alPuFuJ2xG+ka+lvFIhRXOK1AKK6SKRqlhU3bQTK/XSEWVksc7aT8KABOrwOfVgqoiLajK\n/1xrymAkrpZeJ7Se7gmrpXdILT3h9Pr+lj69cKhdXQPRvMcH/Z50QK0udkJrdUZorS4OOMuSApUX\n+nmXKwAAGDeE0pF85SYnLMbCUjScHULjkXM7l69QKijN/pQvdJZFlcnAWZ4MnxXJtuR6oFTy8F5E\nAGdXGPBqYVWxFlYVn7VfNJ5QR39Erb1DausbUntfxFn2R9TWO6TWviGd7A5rd3O32vsjiuc+9Cpn\nAqjK4oAqiwKqKParsjig8qLUdkCVxf70dmWx08ZILAAAGAmhdCTBkPPxByVfxie9XeCETV+B5E8u\nAyVO0EwtUx+exwQwRfi9nvRzqKNJJKy6B6Nq63PCairApsJsR39EXQNR7Tvdp87+iDoHImdM3JQS\n8HpUXuQE2IpkWM3dDhX6FSryJ5/FdT5+L38pBwDATEcoHcm933a7AgBwlcdjVJEc6RxphuFMiYRV\nTziqzoGoOvoj6uyPqGMgoq6BiDr6o1nbr5/qUedAVF1nCbKSVBTwZoXUzE95MsCWndEeUFnQJx+B\nFgCAaYFQCgAYFx6PUXmRcyvvouqz30ackgqy7f0RdQ9Gnc9AdHg9+ekaiKpnMKqj7QPptsFovsne\nhpUU+DJCq7NeGvSrNOhTaYFveD29dNbLgj6VBH0q9HPLMQAAk4FQCgBwTWaQPVdDsbi6B52wmhle\ncwNtKuQebutXbzim3nBMfUNnzlacy+cxKkmF1QL/GaE1O9A6y5ICn4oCXpUU+FRc4GwX+DyEWwAA\nzoJQCgCYlgp8Xs0p9WpO6ejPx+aKJ6z6I7FkSI3mLM9s7xuKqSccU3PXoF5PtvcNxfJOBJXL6zEq\nDnhVnAyqTlj1qjiQ2nb2lQSGg2xRqq3Ap+LAcBshFwAwExFKAQCzjtdjVBb0qyzol1R4Xuew1mow\nGk8H155wTANDcfUNxdQ/FFN/JDa8PhTPaHPW2/sG1B9x9vUNxRSJJcZce3FyNLYw4FVRILV0PoV+\nZ7S2MOBVoT+jPTDcXuT3po8pDPjS2wReAIAbCKUAAJwHY4yKAj4VBXxjms14NNF4wgm1ESfIDgfa\nZKjNCbl9QzENRuIaiMQ0EImroz+ips64BiNxDUad9nB0bEE3xWOUDrmpQFuYE3ZzA2/Q71WB39kO\n+j0K+py2oN+TXOas+zxMQgUAyEIoBQBgCvB7PQoVeRQqGr/XiCUSNhlQnbA6EI0NryfD62Ay1Ga3\nZ7cNRuPq6B9M93XOFR/T7cv5v6tR0OeE2eHA6kkGW68KfPnbnX3DAbcw5/gC33Af5+NVgd+jgNcj\nj4cRYACYqgilAADMUB6PST/HOt6stYrEEwpHExqKxhWOJhSOxRWOOqE1HEsoHHW2h5L7BiPZ/VLH\nDkaHt/uGYmrri5zRHo7FZc8vA0tygnCBz6tAOrB6sreT4TUzyBb4c/rkHu/3ZvTLCMI+T7Jf5joj\nxAAwEkIpAAA4Z8aYZOjySoXjN7o7kswQHM4Mq6n1WEKDkbiGYnFFYgkNJT/Oejx7PZpQJJ7QUNTZ\nTq33DMby9He2o/ELSMRJXo9RwOuEVL/XCap+r5E/o214/3B75jHDbdnH+X0eFXg98vuMAl6vc3y6\nLfPcOddLnt/v9cjLaDIAlxBKAQDAlJcZgkOTEIJzJRJ2OMjG48lAOxx0xxyEk22ReELR1DKeUCRm\n022D0bh6whn94glFM/YPxRNjnhjrXHg9Jh2GCzJCcKrN7/XI5zXye5LL5D5fcjuQ3O/zeuT3mGT/\n4T5+3/CxPq8TrH1Z5xr5/KkaUu0+jxO60+fzGCbpAqYxQikAAMAoPB6joMd5ZlWa/FCcy1qreCIV\nVK2G4s5obiroRmKpsJtQNG4ViccVidmMtsx+Nt0WTQbnzH7RuE3viyWGz9E/FFM0bhVLJBSLO7XE\nktupY2Jxq2gicUG3Xo+V/4yQOxxofRkB2+dxtjOXXo9JL1OjxiNt5x4z2vao50jVnW87VW9ym2ej\nMVMRSgEAAKYZY0x6xFEBaSoE5bOJJzKCbTKoRuNWsWTojSWccB1NBtxYMjSPFHJj6aCcPEcitX+E\n8yWc0ehY1nZCAxFnwq5YwjlPaj1Vb+b28LGTkLBHYIyyQmoqtHo9w4E8HY5ztr3pj0deo4zt4TZP\nRl+PMekgnFp6R2jzeoavk9uW/mS0pa+Tp82T/Gfba0Zpy9iXujaj5dMXoRQAAAATygkeqZHm6c1a\nq4RVVkjNDK3DQdYJyGfbTh2fdzs5Mp0+fzx5jnzb8Yxr5GzHUn2tVTSaUDzhBPF4wiphnX6JjOvk\ntiUSzrGZbVNVKrR7ckPxCCHZk7n0SF7jBNvh/UoH9NQ5naWctoxzO32UDthna/d4km3pa5vktYf/\nssBjzt7uMU4NV15UpdLg1P5LqbEglAIAAABjZIxJjjR6NQETW08LqaCaCrdx6wThrLbMfWdpSwfi\njHOkA7EdDvG5balPZnA+52un16WEHd5OLxNyRtBt5jWGb5/PbE8kzxHPqdFapa85vH/8/iye/qNr\nCBTpkYkAAAk5SURBVKUAAAAAZhePx8gjoxkw8O2azCCdGVYTuWE31ZbRnrBKH7egssjtrzIuCKUA\nAAAAMIkI9tl4izMAAAAAwDWEUgAAAACAawilAAAAAADXEEoBAAAAAK4hlAL/r707jZWrLuM4/v2l\nLBJEQSEEAS0kRYMkFgIIsqSJgEAIRV5IKxEQk4IBFI1BwBcSXlUQE00MBAMRElZFtDHIFmURAxSa\nUiiLlC20llLEsIhhKY8v5hSnt3cut3iZM535fpKbO+c/Z2aee58855xnziZJkiSpNTalkiRJkqTW\nTKopTXJ4kieSLEty9jjPJ8kvmueXJNlr6kOVJEmSJA2b921Kk0wDfgkcAewOzE2y+5jZjgBmND/z\ngIunOE5JkiRJ0hCazJ7SfYFlVfV0Vb0FXAvMHjPPbODK6rgX2DrJDlMcqyRJkiRpyEymKd0ReL5r\nenkztqHzkGRekgeSPLB69eoNjVWSJEmSNGQ26eeHVdWlwKUASVYnea6fn/8BbAu81HYQWoc5GUzm\nZfCYk8FkXgaPORlM5mXwmJPBszHk5DOTmWkyTekKYOeu6Z2asQ2dZx1Vtd1kAmxTkgeqau+249D/\nmJPBZF4GjzkZTOZl8JiTwWReBo85GTzDlJPJHL67EJiRZJckmwFzgAVj5lkAnNBchXc/4JWqWjnF\nsUqSJEmShsz77imtqneSnA7cAkwDLq+qpUlObZ6/BLgJOBJYBrwBfPPDC1mSJEmSNCwmdU5pVd1E\np/HsHruk63EBp01taAPh0rYD0HrMyWAyL4PHnAwm8zJ4zMlgMi+Dx5wMnqHJSTr9pCRJkiRJ/TeZ\nc0olSZIkSfpQ2JRKkiRJklpjUzqOJIcneSLJsiRntx3PqEqyc5K/JHk0ydIk323Gz0uyIsni5ufI\ntmMdJUmeTfJw879/oBn7RJLbkjzZ/N6m7ThHSZLPdtXD4iSvJjnTWumvJJcneTHJI11jPWsjyTnN\neuaJJF9pJ+rh1yMvFyZ5PMmSJDcm2boZn57kP101c0nvd9YH1SMnPZdX1kp/9MjLdV05eTbJ4mbc\nWumDCbaFh27d4jmlYySZBvwdOBRYTueWOHOr6tFWAxtBSXYAdqiqRUm2Ah4EjgG+BrxeVT9tNcAR\nleRZYO+qeqlr7ALg5aqa33yRs01V/bCtGEdZswxbAXyRzpXQrZU+SXIw8DpwZVXt0YyNWxtJdgeu\nAfYFPgXcDuxWVWtaCn9o9cjLYcCfmzsM/ASgyct04I9r59OHo0dOzmOc5ZW10j/j5WXM8xfRue3j\n+dZKf0ywLXwSQ7ZucU/p+vYFllXV01X1FnAtMLvlmEZSVa2sqkXN49eAx4Ad241KPcwGrmgeX0Fn\ngal2fBl4qqqeazuQUVNVdwEvjxnuVRuzgWur6s2qeobOLdX27UugI2a8vFTVrVX1TjN5L7BT3wMb\nYT1qpRdrpU8mykuS0NkpcE1fgxpxE2wLD926xaZ0fTsCz3dNL8dGqHXNN3J7Avc1Q2c0h11d7qGi\nfVfA7UkeTDKvGdu+qlY2j18Atm8nNAFzWHejwVppV6/acF0zOE4G/tQ1vUtzOOKdSQ5qK6gRNd7y\nyloZDAcBq6rqya4xa6WPxmwLD926xaZUAy/JR4EbgDOr6lXgYmBXYCawErioxfBG0YFVNRM4Ajit\nOdznPc19iz0voAVJNgOOBn7TDFkrA8TaGDxJfgS8A1zVDK0EPt0s474PXJ3kY23FN2JcXg22uaz7\nhae10kfjbAu/Z1jWLTal61sB7Nw1vVMzphYk2ZROEV5VVb8DqKpVVbWmqt4FfsVGcljCsKiqFc3v\nF4Eb6fz/VzXnPaw9/+HF9iIcaUcAi6pqFVgrA6JXbbiuaVmSk4CjgOObjTqaQ97+2Tx+EHgK2K21\nIEfIBMsra6VlSTYBjgWuWztmrfTPeNvCDOG6xaZ0fQuBGUl2afY6zAEWtBzTSGrOX7gMeKyqftY1\nvkPXbF8FHhn7Wn04kmzZnGhPki2Bw+j8/xcAJzaznQj8oZ0IR94632RbKwOhV20sAOYk2TzJLsAM\n4P4W4htJSQ4HzgKOrqo3usa3ay4WRpJd6eTl6XaiHC0TLK+slfYdAjxeVcvXDlgr/dFrW5ghXLds\n0nYAg6a5Et/pwC3ANODyqlraclij6gDgG8DDay9BDpwLzE0yk86hCs8Cp7QT3kjaHrixs4xkE+Dq\nqro5yULg+iTfAp6jczEE9VHzJcGhrFsPF1gr/ZPkGmAWsG2S5cCPgfmMUxtVtTTJ9cCjdA4fPW1j\nuDrixqhHXs4BNgdua5Zn91bVqcDBwPlJ3gbeBU6tqslekEeT1CMns8ZbXlkr/TNeXqrqMta/VgFY\nK/3Sa1t46NYt3hJGkiRJktQaD9+VJEmSJLXGplSSJEmS1BqbUkmSJElSa2xKJUmSJEmtsSmVJEmS\nJLXGplSSpHEkeb35PT3J16f4vc8dM/23qXx/SZI2JjalkiRNbDqwQU1pkve7D/g6TWlVfWkDY5Ik\naWjYlEqSNLH5wEFJFif5XpJpSS5MsjDJkiSnACSZleTuJAvo3LicJL9P8mCSpUnmNWPzgS2a97uq\nGVu7VzbNez+S5OEkx3W99x1Jfpvk8SRXJUkL/wtJkqbc+32TK0nSqDsb+EFVHQXQNJevVNU+STYH\n7klyazPvXsAeVfVMM31yVb2cZAtgYZIbqursJKdX1cxxPutYYCbwBWDb5jV3Nc/tCXwe+AdwD3AA\n8Nep/3MlSeov95RKkrRhDgNOSLIYuA/4JDCjee7+roYU4DtJHgLuBXbumq+XA4FrqmpNVa0C7gT2\n6Xrv5VX1LrCYzmHFkiRt9NxTKknShglwRlXdss5gMgv495jpQ4D9q+qNJHcAH/k/PvfNrsdrcB0u\nSRoS7imVJGlirwFbdU3fAnw7yaYASXZLsuU4r/s48K+mIf0csF/Xc2+vff0YdwPHNeetbgccDNw/\nJX+FJEkDym9ZJUma2BJgTXMY7q+Bn9M5dHZRc7Gh1cAx47zuZuDUJI8BT9A5hHetS4ElSRZV1fFd\n4zcC+wMPAQWcVVUvNE2tJElDKVXVdgySJEmSpBHl4buSJEmSpNbYlEqSJEmSWmNTKkmSJElqjU2p\nJEmSJKk1NqWSJEmSpNbYlEqSJEmSWmNTKkmSJElqzX8Bl9muovXM724AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5f45128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "total_time = 2000\n",
    "result = process.sample_with_details(0, total_time)\n",
    "points = result.points\n",
    "points = points[points>=1000]\n",
    "\n",
    "plot_convergence(*apply_algorithm(points, 1000, 200))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a typical graph, though more extreme behaviour can be observed as well!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAFACAYAAABEN9peAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f65a3748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "total_time = 11000\n",
    "result = process.sample_with_details(0, total_time)\n",
    "points = result.points\n",
    "points = points[points>=1000]\n",
    "\n",
    "plot_convergence(*apply_algorithm(points, 10000, 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Choosing different parameters\n",
    "\n",
    "The above work is all performed with $\\mu=0.1, \\omega=0.05, \\theta=0.5$.  The choice of $\\omega$ is problematic, as this means that the average time between event and aftershock is $20$ time units, 2 times longer than the expected time to the next background event.\n",
    "\n",
    "So let's repeat the work, but with $\\omega=1$ say."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7QAAABZCAYAAAAO9WhvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5244ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "process = source_sepp.SelfExcitingPointProcess(\n",
    "    background_sampler = source_sepp.HomogeneousPoissonSampler(rate=0.1),\n",
    "    trigger_sampler = source_sepp.ExponentialDecaySampler(intensity=0.5, exp_rate=1))\n",
    "\n",
    "points = process.sample(0, 1000)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(16,1))\n",
    "ax.scatter(points, np.random.random(len(points))*.02, alpha=0.3)\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1967,), (1005,))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_time = 10000\n",
    "result = process.sample_with_details(0, total_time)\n",
    "points = result.points\n",
    "points.shape, result.trigger_deltas.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAFACAYAAABEN9peAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA42U/slEafBPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5c2dbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_convergence(*apply_algorithm(points, total_time, 200, theta_in=0.5, omega_in=1, mu_in=0.1), True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally try with $\\omega=10$ and a small(er) sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7QAAABZCAYAAAAO9WhvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5f732e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "process = source_sepp.SelfExcitingPointProcess(\n",
    "    background_sampler = source_sepp.HomogeneousPoissonSampler(rate=0.1),\n",
    "    trigger_sampler = source_sepp.ExponentialDecaySampler(intensity=0.5, exp_rate=10))\n",
    "\n",
    "points = process.sample(0, 1000)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(16,1))\n",
    "ax.scatter(points, np.random.random(len(points))*.02, alpha=0.3)\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((192,), (102,))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_time = 1000\n",
    "result = process.sample_with_details(0, total_time)\n",
    "points = result.points\n",
    "points.shape, result.trigger_deltas.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAFACAYAAABEN9peAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n5UGbxr6aQCUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5d1f160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_convergence(*apply_algorithm(points, total_time, 200, theta_in=0.5, omega_in=10, mu_in=0.1), True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recreation of Lewis and Mohler\n",
    "\n",
    "The EM algorithm which we're using originates in:\n",
    "\n",
    "Lewis, Mohler, \"A Nonparametric EM algorithm for Multiscale Hawkes Processes\", preprint 2010, see http://math.scu.edu/~gmohler/EM_paper.pdf\n",
    "\n",
    "In Figure 1 of that paper, they carry out simulations (10 times) with $\\mu=1, \\theta=0.5$ time in $[0,2000]$ and with $\\omega^{-1} = 0.01, 0.1, 1$ and $10$.\n",
    "\n",
    "By comparison, if we rescale to $\\mu=0.1$ as used above, the paper considers time in $[0,20000]$ and $\\omega^{-1} = 0.001, 0.01, 0.1$ and $1$ which are more extreme values than we considered before!\n",
    "\n",
    "As in the paper, here we run the algorithm until the difference (in $L^\\infty$ norm) between iterations is less than $10^{-5}$.  We are only varying $\\omega$ which controls the \"scale\" of the aftershocks.  As $\\omega^{-1}$ increases, aftershocks becomes more spread-out in time, and thus, at least intuitively, it becomes harder to tell background events apart from aftershock events."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "all_results_dict = {}\n",
    "for omega_inv in [0.01, 0.1, 1, 10]:\n",
    "    results = []\n",
    "    for _ in range(10):\n",
    "        process = source_sepp.SelfExcitingPointProcess(\n",
    "            background_sampler = source_sepp.HomogeneousPoissonSampler(rate=1),\n",
    "            trigger_sampler = source_sepp.ExponentialDecaySampler(intensity=0.5, exp_rate=1/omega_inv))\n",
    "        points = process.sample(0, 2000)\n",
    "        convergents = apply_algorithm(points, 2000, 2000, theta_in=0.5, omega_in=1/omega_inv, mu_in=1,\n",
    "                                 convergence_criteria = 10**(-5), func=m_step)\n",
    "        convergents = np.asarray(convergents)\n",
    "        # (theta, omega, mu), iterations\n",
    "        results.append((convergents[:,-1], convergents.shape[-1]))\n",
    "    all_results_dict[omega_inv] = results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "thetas = {key: [result[0][0] for result in all_results_dict[key]] for key in all_results_dict}\n",
    "mus = {key: [result[0][2] for result in all_results_dict[key]] for key in all_results_dict}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8EAAAF+CAYAAACiSxiJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f5c60710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=2, figsize=(16,6))\n",
    "\n",
    "def plot(ax, data, true_value):\n",
    "    x = list(data.keys())\n",
    "    y = np.asarray([ np.mean(data[k]) for k in x ])\n",
    "    ax.scatter(x, y, color=\"black\")\n",
    "    yy = np.asarray([ np.std(data[k], ddof=1) for k in x ])\n",
    "    for x, y, dy in zip(x,y,yy):\n",
    "        ax.plot([x]*2, [y-dy,y+dy], color=\"black\")\n",
    "    ax.plot([0.001,100], [true_value]*2, color=\"black\", linestyle=\"--\", linewidth=1)\n",
    "    ax.set(xscale=\"log\", xlim=[0.001,100])\n",
    "\n",
    "plot(ax[0], thetas, 0.5)\n",
    "plot(ax[1], mus, 1)\n",
    "ax[0].set(xlabel=\"$\\\\omega^{-1}$\", ylabel=\"$\\\\theta$\")\n",
    "ax[1].set(xlabel=\"$\\\\omega^{-1}$\", ylabel=\"$\\\\mu$\")\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Except when $\\omega^{-1}=10$ these look like the graphs from the paper.\n",
    "\n",
    "Reading more closely, we see from the paper:\n",
    "\n",
    "> To investigate the convergence of (14) we simulate realizations ...  run the EM algorithm (with boundary correction)\n",
    "\n",
    "This is misleading, as (14) refers to the uncorrected algorithm.  By \"boundary correction\" we mean computing the likelihood without applying certain approximations.  This leads to a variant on the \"M step\":\n",
    "\n",
    "$$ \\theta = \\frac{\\sum_{i<j} p_{ij}}{n - \\sum_{i=1}^n e^{-\\omega (T-t_i)}}, \\qquad\n",
    "\\omega = \\frac{\\sum_{i<j} p_{ij}}{\\sum_{i<j}(t_j-t_i)p_{ij} + \\theta \\sum_{i=1}^n(T-t_i)e^{-\\omega(T-t_i)}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def corrected_m_step(points, total_time, theta=0.5, omega=0.05, mu=0.1):\n",
    "    omega_1, omega_2, mu_e = 0.0, 0.0, 0.0\n",
    "    for col in range(len(points)):\n",
    "        p, norm, dt = p_matrix_col(points, col, theta, omega, mu)\n",
    "        wp = p[0:col] * dt\n",
    "        omega_1 += np.sum(p[0:col]) / norm\n",
    "        omega_2 += np.sum(wp) / norm\n",
    "        mu_e += p[-1] / norm\n",
    "\n",
    "    from_end = total_time - points\n",
    "    exp_from_end = np.exp(-omega * from_end)\n",
    "    corrected_n = len(points) - np.sum(exp_from_end)\n",
    "    corrected_omega_2 = omega_2 + theta * np.sum(from_end * exp_from_end)\n",
    "        \n",
    "    return omega_1 / corrected_n, omega_1 / corrected_omega_2, mu_e / total_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "all_results_dict = {}\n",
    "for omega_inv in [0.01, 0.1, 1, 10]:\n",
    "    results = []\n",
    "    for _ in range(10):\n",
    "        process = source_sepp.SelfExcitingPointProcess(\n",
    "            background_sampler = source_sepp.HomogeneousPoissonSampler(rate=1),\n",
    "            trigger_sampler = source_sepp.ExponentialDecaySampler(intensity=0.5, exp_rate=1/omega_inv))\n",
    "        points = process.sample(0, 2000)\n",
    "        convergents = apply_algorithm(points, 2000, 2000, theta_in=0.5, omega_in=1/omega_inv, mu_in=1,\n",
    "                                 convergence_criteria = 10**(-5), func=corrected_m_step)\n",
    "        convergents = np.asarray(convergents)\n",
    "        # (theta, omega, mu), iterations\n",
    "        results.append((convergents[:,-1], convergents.shape[-1]))\n",
    "    all_results_dict[omega_inv] = results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8EAAAF+CAYAAACiSxiJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f0f6600eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = {key: [result[0][0] for result in all_results_dict[key]] for key in all_results_dict}\n",
    "mus = {key: [result[0][2] for result in all_results_dict[key]] for key in all_results_dict}\n",
    "\n",
    "fig, ax = plt.subplots(ncols=2, figsize=(16,6))\n",
    "\n",
    "plot(ax[0], thetas, 0.5)\n",
    "plot(ax[1], mus, 1)\n",
    "ax[0].set(xlabel=\"$\\\\omega^{-1}$\", ylabel=\"$\\\\theta$\")\n",
    "ax[1].set(xlabel=\"$\\\\omega^{-1}$\", ylabel=\"$\\\\mu$\")\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is definitely an improvement, but despite having tried this a number of times, I cannot reproduce the graphs from Lewis and Mohler."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing the likelihood\n",
    "\n",
    "From (3) Theorem 3 we know that if $\\lambda^*(t)$ is the conditional intensity function, then the likelihood of the process is:\n",
    "\n",
    "$$ L = \\Big( \\prod_{i=1}^n \\lambda^*(t_i) \\Big) \\exp\\Big( -\\int_0^T \\lambda^*(s) \\ ds \\Big) $$\n",
    "\n",
    "were $(t_1,\\cdots,t_n)$ is a sample of the process in the time window $[0,T]$.  Taking logs, this expands to\n",
    "\n",
    "$$ l = \\log L = \\sum_{i=1}^n \\log\\Big( \\mu + \\sum_{j=1}^{i-1} \\theta\\omega e^{-\\omega (t_i-t_j)} \\Big)\n",
    "- \\int_0^T \\lambda^*(s) \\ ds. $$\n",
    "The integral can be split into parts:\n",
    "\\begin{align*} \\int_0^T \\lambda^*(s) \\ ds &= \\mu T + \\sum_{i=1}^{n-1} \\int_{t_i}^{t_{i+1}} \\sum_{j=1}^i \\theta\\omega e^{-\\omega (t-t_j)} \\ dt + \\int_{t_n}^T \\sum_{j=1}^n \\theta\\omega e^{-\\omega (t-t_j)} \\ dt \\\\\n",
    "&= \\mu T + \\theta \\sum_{i=1}^{n-1} \\sum_{j=1}^i \\Big( e^{-\\omega (t_i-t_j)} - e^{-\\omega (t_{i+1}-t_j)} \\Big)\n",
    "+ \\theta \\sum_{j=1}^n \\Big( e^{-\\omega (t_n-t_j)} - e^{-\\omega (T-t_j)} \\Big)\n",
    "\\end{align*}\n",
    "Many terms in the double sum cancel out, leaving\n",
    "\\begin{align*}\n",
    "& \\mu T + \\theta \\sum_{i=1}^{n-1} e^{-\\omega (t_i-t_i)} - \\theta \\sum_{j=1}^{n-1} e^{-\\omega (t_n-t_j)}\n",
    "+ \\theta \\sum_{j=1}^n \\Big( e^{-\\omega (t_n-t_j)} - e^{-\\omega (T-t_j)} \\Big) \\\\\n",
    "&= \\mu T + n \\theta + \\theta - \\theta \\sum_{j=1}^n e^{-\\omega (T-t_j)}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def likelihood(points, time_range, theta, omega, mu):\n",
    "    n = len(points)\n",
    "    first_sum = np.empty(n)\n",
    "    first_sum[0] = mu\n",
    "    for i in range(1, n):\n",
    "        dt = points[i] - points[:i]\n",
    "        first_sum[i] = mu + theta * omega * np.sum(np.exp(-omega * dt))\n",
    "    second_sum = np.sum(np.exp(-omega * (time_range - points)))\n",
    "    return np.sum(np.log(first_sum)) - (mu * time_range + n * theta + theta - theta * second_sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "omega_inv = 10\n",
    "process = source_sepp.SelfExcitingPointProcess(\n",
    "    background_sampler = source_sepp.HomogeneousPoissonSampler(rate=1),\n",
    "    trigger_sampler = source_sepp.ExponentialDecaySampler(intensity=0.5, exp_rate=1/omega_inv))\n",
    "points = process.sample(0, 2000)\n",
    "convergents = apply_algorithm(points, 2000, 2000, theta_in=0.5, omega_in=1/omega_inv, mu_in=1,\n",
    "                         convergence_criteria = 10**(-5), func=corrected_m_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.48739324904421333, 0.092978204725401775, 1.060589789400499)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "convergents = np.asarray(convergents)\n",
    "theta, omega, mu = convergents[:,-1]\n",
    "theta, omega, mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1131.105486019007"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood(points, 2000, theta, omega, mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1131.8470624938977"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood(points, 2000, 0.5, 0.1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the algorithm is doing what it should be: finding a maximal likelihood!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}