comparisons.ipynb

{
 "metadata": {
  "name": "comparisons"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "source": [
      "SDM/Hopfield Comparison Code"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\"SDM/Hopfield Comparison\n",
      "\n",
      "This code compares SDM networks and Hopfield networks on various\n",
      "properties, including appropriate parameter values, storage capacity,\n",
      "\"prototype\" retrieval, and sequence retrieval.\n",
      "\n",
      "Authors: \n",
      "  Jessica Hamrick (jhamrick@berkeley.edu)\n",
      "  Josh Abbott (joshua.abbott@berkeley.edu)\n",
      "\n",
      "\"\"\"\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "'SDM/Hopfield Comparison\\n\\nThis code compares SDM networks and Hopfield networks on various\\nproperties, including appropriate parameter values, storage capacity,\\n\"prototype\" retrieval, and sequence retrieval.\\n\\nAuthors: \\n  Jessica Hamrick (jhamrick@berkeley.edu)\\n  Josh Abbott (joshua.abbott@berkeley.edu)\\n\\n'"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import scipy.stats\n",
      "import sdm as sdm\n",
      "import hopfield as hop\n",
      "import util as util\n",
      "import metrics as metrics\n"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 1,
     "source": [
      "Parameters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# SDM Parameters\n",
      "# --------------\n",
      "#   n : length of inputs\n",
      "#   m : number of addresses\n",
      "#   D : hamming radius\n",
      "\n",
      "\n",
      "# Hopfield Parameters\n",
      "# -------------------\n",
      "#   n : length of inputs\n"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# print extra information\n",
      "verbose = True\n",
      "\n",
      "# length of inputs\n",
      "n = 16**2\n",
      "# number of simulations to run\n",
      "iters = 10\n",
      "# step by which to test storage capacity\n",
      "k = sorted(set(np.round(\n",
      "    np.logspace(\n",
      "\tnp.log(5)/np.log(10),\n",
      "\tnp.log(200)/np.log(10),\n",
      "\tnum=20, base=10),\n",
      "    decimals=0).astype('i8')))\n",
      "\n",
      "# hamming distance encompasses 2.5% of addresses\n",
      "D = float((n / 2.) - (np.sqrt(n*(0.5**2)) * 1.96))\n",
      "#D = 105\n",
      "# address spaces for the SDM\n",
      "M = np.array([500, 1000, 2500, 5000, 10000])\n",
      "\n",
      "# corruption levels to test\n",
      "noise = np.array([0.0, 0.025, 0.05, 0.10, 0.15, 0.20])\n",
      "\n",
      "# colors for plotting\n",
      "colors = ['#FF0000', # red \n",
      "\t  '#FF9933', # orange\n",
      "\t  '#FFFF00', # yellow\n",
      "\t  '#00FF00', # green\n",
      "\t  '#00FFFF', # cyan\n",
      "\t  '#0000FF', # blue\n",
      "\t  '#660099', # violet\n",
      "\t  # '#FF00FF', # magenta\n",
      "\t  '#FF0099', # pink\n",
      "\t  ]\n",
      "# alpha value for error regions in plots\n",
      "alpha = 0.3\n"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 1,
     "source": [
      "Uncorrupted Storage Capacity"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# How many random, uncorrelated inputs can the SDM store?\n",
      "sdm_capacity = np.empty((len(M), len(k), 2))\n",
      "for midx, m in enumerate(M):\n",
      "    print \"SDM (M=%d)\" % m\n",
      "    sdm_capacity[midx] = metrics.test_capacity(\n",
      "\t(int(n), int(m), float(D)), \n",
      "\tk0=k, iters=int(iters), verbose=verbose)\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "SDM (M=500)\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "24:  0.001 +/- 0.000\n",
        "29:  0.001 +/- 0.000\n",
        "35:  0.002 +/- 0.000\n",
        "42:  0.004 +/- 0.001\n",
        "51:  0.004 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "62:  0.009 +/- 0.000\n",
        "76:  0.015 +/- 0.001\n",
        "92:  0.022 +/- 0.001\n",
        "112:  0.036 +/- 0.001\n",
        "136:  0.046 +/- 0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "165:  0.059 +/- 0.001\n",
        "200:  0.077 +/- 0.001\n",
        "SDM (M=1000)\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "24:  0.000 +/- 0.000\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.000 +/- 0.000\n",
        "42:  0.000 +/- 0.000\n",
        "51:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "62:  0.001 +/- 0.000\n",
        "76:  0.003 +/- 0.000\n",
        "92:  0.005 +/- 0.000\n",
        "112:  0.010 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "136:  0.016 +/- 0.001\n",
        "165:  0.025 +/- 0.001\n",
        "200:  0.034 +/- 0.001\n",
        "SDM (M=2500)\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000\n",
        "24:  0.000 +/- 0.000\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "42:  0.000 +/- 0.000\n",
        "51:  0.000 +/- 0.000\n",
        "62:  0.000 +/- 0.000\n",
        "76:  0.000 +/- 0.000\n",
        "92:  0.001 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "112:  0.002 +/- 0.000\n",
        "136:  0.004 +/- 0.000\n",
        "165:  0.007 +/- 0.000\n",
        "200:  0.012 +/- 0.001\n",
        "SDM (M=5000)\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "24:  0.000 +/- 0.000\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.000 +/- 0.000\n",
        "42:  0.000 +/- 0.000\n",
        "51:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "62:  0.000 +/- 0.000\n",
        "76:  0.000 +/- 0.000\n",
        "92:  0.000 +/- 0.000\n",
        "112:  0.001 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "136:  0.002 +/- 0.000\n",
        "165:  0.003 +/- 0.000\n",
        "200:  0.007 +/- 0.000\n",
        "SDM (M=10000)\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "19:  0.000 +/- 0.000\n",
        "24:  0.000 +/- 0.000\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.000 +/- 0.000\n",
        "42:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "51:  0.000 +/- 0.000\n",
        "62:  0.000 +/- 0.000\n",
        "76:  0.000 +/- 0.000\n",
        "92:  0.000 +/- 0.000\n",
        "112:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "136:  0.001 +/- 0.000\n",
        "165:  0.002 +/- 0.000\n",
        "200:  0.005 +/- 0.001\n"
       ]
      }
     ],
     "prompt_number": 103
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# How many random, uncorrelated inputs can the Hopfield net store?\n",
      "print \"Hopfield\"\n",
      "hop_capacity = metrics.test_capacity(\n",
      "    int(n), k0=k, iters=int(iters), verbose=verbose)\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Hopfield\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000\n",
        "24:  0.000 +/- 0.000\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.001 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "42:  0.002 +/- 0.000\n",
        "51:  0.004 +/- 0.000\n",
        "62:  0.006 +/- 0.000\n",
        "76:  0.008 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "92:  0.011 +/- 0.000\n",
        "112:  0.014 +/- 0.000\n",
        "136:  0.017 +/- 0.000\n",
        "165:  0.019 +/- 0.000\n",
        "200:  0.021 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 104
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot corruption as a function of items stored\n",
      "util.set_fig_properties()\n",
      "for i in xrange(M.size):\n",
      "    util.plot_error(k, sdm_capacity[i], colors[i], alpha, 'SDM M=%d' % M[i])\n",
      "util.plot_error(k, hop_capacity, colors[i+1], alpha, 'Hopfield', linestyle='--')\n",
      "\n",
      "plt.xlim(k[0], k[-1])\n",
      "plt.xlabel(\"Number of stored items\")\n",
      "plt.ylabel(\"Mean fraction of corrupted bits\")\n",
      "plt.title(\"SDM and Hopfield Capacities for Ideal Inputs (N=%d)\" % n)\n",
      "plt.legend(loc=0)\n",
      "\n",
      "util.save(\"figures/capacity.svg\", width=8, height=6, f_close=False)\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Saving figure to 'figures/capacity.svg'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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HIDDwliO+NgSp9CUSiUQiaQpyc0XQHbUaWrYU0/exscKI75NPRNq1ayI4T79+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\nIntjOfS5HGIukBE8O1YL1JYBVgjrC2H9zli7P1/ta7KmP3fuXNasWcP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/eOABddxTzg2b\nVWr2edvFPtcvVMS7tgwOLIfigzKC132EZI0amvSs0G0IhPYBT++2/ik6JK1S0zcajSxZsoTf//73\nzJ07l4ceeqjZL9hSqOgrSj0Wi/jpb9oEkZEi9F9+CT//LI17x49r455y9jjZ54aLeFvNMoKXuUbM\nc/pe5RjBqy0TF77wfrL5TjvyXYpLRb+2tpZvv/2WTz75hMzMTKZMmcLdd99NrBtECyr6igJUVcEP\nP0B2tvjpGwzw6aeS4p8/X+r78fFwxRVax1fOjKUOCvZB0X5ZcOMTJD0hBbth31IIjIaB1znq86Zq\nqfEHxUC3oQ5DHsWluEz077zzTnbv3s3kyZO59dZbGepmNp0q+kqn59gx+M9/5I05IkIa9958E2pq\npJYPYrt73XVax1dOj80G5TmyCc9ikkY9g4fM4e/7GmpL6kfwBsr5ZqNE974hEJ0kS3OUVsNlou/h\n4UFAQMBpX7S8vLzZL9oSqOgrnRarFXbtgp9+km78gAAZy3vlFbjwQpgxA+rqpHHvpptkk56inApj\nhdTtK4+Bb5ik7E01cGgV5G6W3fY9x0rDXkOTXhcR++A4bdJrA3ROX1E6EzU1sHatiHz37tK0t3o1\nLF4Ms2bJtrzaWigo0MY95fScaJ/rGyLNeDmbID1FNtwlTK5P8dd75NussuY2rK826bUhLt+ypyiK\nm1BQIOn82lro0UPq9e++K1H/Sy9Bz55QWipfnzxZBV85Naeyzy3NlC14Hp7OI3i1ZTK2Fx4vDnve\n/m166R0dk0mSdCc+amslcVdTc/6voaKvKO6OzQb79onhTlAQREXJDcArr0gt/403pHaflweBgXDj\njZL2V5TGnGifGxApjXgHlkPRgUYjeB71TXoV0rwXNVS33zWDEwXc/nltrfTfVlc7/qypkY9rauTr\n4eH1k5CNAvrqavjww/O/Lpem91euXMmjjz6KxWLh3nvv5cknnzzpnDlz5rBixQr8/f356KOPSE5O\nJisri+nTp3P8+HEMBgP3338/c+bMcb5wTe8rnYG6Ohm9271b0vne3rB9uzTsXX893HCD1Phzc6Ff\nP7jsMmjjvRiKm3Eq+1ybRcbvMlMhbkz9CJ6vdPDXlMhNQXQSBEa19dW7BWbzqSNwo1HE2i7e9kdt\nrUzSGo0i5OHhIuA2m4i5t7d87f33pf+2vFwenp6yG+svf5GbBLNZHjabfH7gALzzjpvW9C0WCwMG\nDOD7778nNjaWCy64gCVLlpCYmNhwTkpKCgsXLiQlJYUNGzbwyCOPkJaWRl5eHnl5eQwfPpzKykpG\njhzJ119/7fS9KvpKh6ekBFatkpR99+7yP//LL2H5cvjd72TuvqZG3PfGjIHkZNC110pjTmWfW7BH\nuvIDusGA6yTit1qgpljq+1HDpEnP7p/fwbBYzl7Aa2rkT4tFvtd+Tteujufz8pKH1Qpvv+0s4gYD\ndOsm9+h1dSLgdjG3WCSBFxjoePj7S19uQIDjWFCQ3Mf7+MgjIsJNa/obN24kPj6e3r17AzBt2jSW\nLl3qJNzLli1jxowZAIwZM4bS0lLy8/OJjo4mOlr2MgcGBpKYmEhubq7T9ypKhyYjQ9z1/Pzk1r+q\nSjz0S0pkRW5kpHxsNMI110CvXm19xYo7YbfPLcmQXfWB3aDquMzbVxfCwBsgMrHeSa/Y0aQX3leE\nv51wJgFvnD5v/LBa5XsNBjm3vFxE3GCQSNvTUyJxDw8Ra7uAl5bK94WGwnvvyWubTM6PsWNFpO2P\nLl3kucxm2WLdWOB9fSVRZxdzHx+5eXA1LnuJnJwcevTo0fB5XFwcGzZsaPKc7OxsoqIcKaXMzEy2\nbdvW4P/fmLlz5zZ8PH78eMaPH99yP4CitAVms6zA3b5davc+PmKv+/LLMHy4zN97e0v9PjgYpkyR\ndyFFgZPtcwMiJWW/f5l05ve9EpJnSsRvLJdmvrC+cgPQxk16dgE/VTPbqVLoNTXy3wUcvlNGozS8\nhYbKfxMvL8efvr6wcCEUFUFZmTysVploff99EfnGAm42w0UXOaLtwED572gwyA1AYKB8b+OvT54s\n53TpIn/6+spNxPmQmppKamrq+T1JI1wm+me7lOfENEXj76usrOSmm27i7bffJjAw8KTvbSz6itLu\nqaiQ6D4vD+Li5F1o7VpYtAjuvltc9cxmyMqS9biXXirvLIoCJ9vnenjKrH16ihjrXPKErLY1VUN1\nkdTre451eZOe1eoQ6qoqiZpPlUY3meR8uwTYbCL4FRUSidsjYS8vEVV/f4nE8/MdIm6xiBAvWCAi\n3FjAa2rExsLbW+6Xg4Md/30KC+XjgACpv9uj8csucxZx++N8hfxcODGgnTdv3nk9n8tEPzY2lqys\nrIbPs7KyiIuLO+M52dnZDRa/JpOJG2+8kTvuuIPrr7/eVZepKO5BdraM43l6iuCbTPD//p/46T//\nPPTtK++ORUVw8cWQlKS2uopwon1uYJRE+3v/DRgg+W4I6SnnVeaL8PcaBwFRLfY7ZDI5p9OLi6X6\nVFQkkbe9gc1ikc/DwiQKtkfifn7yq79ggdzT2tPpJpOI8xtviPDbbI66uNEorSyeniLWQUHyPAaD\nIyXv6ytfs6fWhw+XzxsLuP3RWdphXNbIZzabGTBgAKtXryYmJobRo0efsZEvLS2NRx99lLS0NGw2\nGzNmzKBr16689dZbp75wbeRTOgIWi6Ty09Jk/M7fX94pX31V3p0ef1zerYqL5d1u0iS5KVCUU9nn\n1lXCgW/lBiDhGogZKefVFIOHN0QPg+AezWrSq611CHtlpfxK2sW9ulpE0/6W7O0tQvrzz1Kdys+X\nBNbx4yLMr74qvan2H8Mu5Nu3y/P4+sqvvV3E7ecZDHKscaNbYOCphbxLl44p5G7tyLdixYqGkb17\n7rmHp59+mg8++ACAWbNmAfDQQw+xcuVKAgICWLx4MSNGjGDdunVceumlDBs2rCHd//LLL3P11Vc7\nLlxFX2nvVFfDf/8LR4/KO6CnJ/zyizTq/epXcPPN8i6XlydFykmT1FJXEU60z/XwhCM/wuEfIHY0\n9JsgO+1rSgArRCTKFrwzNOlZrY558epqSZfbo3V71O3hIfep9nR6SYkI/1VXOUS8McuWiaCHh8uv\ncEiIoy4OzkJuF297fdzf31nA7R939gSXW4u+K1HRV9o1eXmSzrdYpBPfZoOlS2Uk77HHYMQIebc8\ndgwGDBB7XV2ao9jtc4/vFp983xAo2CsjeP4RsgUvoFujJr0+IvhdZI+K2exsDFNaKqJeUiIibsdm\nc0TcjevY77wjHlGBgdJnGh0tCaqxYyWFXlcnNw+NhTkoSNL59seJUXmXLirk54KKvqK0J2w2sc1d\nt07eAQMDJbx65x0R+KeekndTe/1+7FgYOlTfFRWozINjWx32uTXFsH8pVBWI2EcOAlMNxopKqgzR\nVAcOptIc2hCt29PwjaPs/HxpJykuFpNHexr+7rvh8svlPLvJjNEo6Xm7WNvffv39JYIPC3M0wfn7\ny8PPr2Om2NsSFX1FaS/U1sKPP0J6uoRI3t7yjvvyyxLNz54tYY+9fn/11eqfr5xkn2vDgOnA93jl\nbaC06wRyfa6ksKgLJYW1lFQHYQroBV2CqTUaKCyUaD42Fvr3l1+5xixfLr+OEREi2PZoPDjYUaP3\n9naO1IODRcztwt4as+WKAxV9RWkPFBaKu15VlQg+SJfTu+/C9OkwcaK8wx47Jm3KEyfKu6vSKbFY\noKrCQnXuEaqy0imt8KGoOoTgyk0MNXxOtmkoG6tvpcoSgoepCh9f8I2IY+PuSJaneJCfLwmk6GhJ\nHF15JQwZItF6XZ1E+waDpOI9PSVSDw111N7tgu7vr1Uld0NFX1HcnX37IDVVipvBwfKO/vHHkuJ/\n8kmZuTeZRPATEyWlr++0HZ7GrnFVVY5u+OJiqC6pgLIs6qqN5JWHYq4sxq9yL1mFkfxSNJzEgVZu\nvPKI2OcGx2HyjcFo9uboUUnld+0qQm5P5QcGOkTdXle3i7qvr1aP2hMq+orirjRelhMdLUJeWgqv\nvSbh1e9/LzcB9nf8ceMkHNN34A5FTY2zoNvH3Orq5OvFxXIfGBsLvt51+Biz6GI8Bl6+rN8axL+/\nDSIh4jCB4UF4h0QSFlRDdNdKukYHQVB3bJ6++PmJqNuFPSjIUVP399e6ekdCRV9R3JHSUvjuO3lH\n795dhHzfPhlQvuIKuO02Ef6iIknrX331qWeelHaFzSamMMXFkJMjRjNlZY50enExrF4t1Z78fPkz\nJATGjbVx23XHMR7Pwmj0wOrhw2C/70j2/5oDtZexo+56AvwhzL+M8G4BBPdNwD88VOvqnRAVfUVx\nNw4fFjtdHx/JpdpskJICn3wCDz8Mo0c76vcREVK/Dwpq66tWmoHZLFF7YaEIfHa29GsWFYmHkn2x\nCkhkn50tJothYfJP37UreNuqMFQcJdi7lLBIX3oF/ELfqk+x+oRh7DsV3+AQfGwl4rYXPVx23Gs2\nqNOioq8o7oLZLO/oW7fKPk1fXync/s//yI3A00/Lxjx7/X7oUNnocWJLteK22FP1+fniNHf8uIh8\nZqZ8fuiQdMP36wfPPCPOdRaL3OMFBjrG2kJDIcDHiH9NOv41B/AL8sFgNcoWvMo8GHg9dB0gfvoe\nntBtCIT2kkU5SqdGRV9R3IGKCvjhBxHz6GhJ3R87JuN4vXvDgw9K5F9ZKaHh+PEwaFBbX7VyBk5M\n1R896tiRbvd79/aGmTOhRw8R+l69ZE1CQIDc9/XqJd3z4eFSX3c8cSP73C4B4qSXnQa9x0OvS2VM\nz2qCrv2hawJ4+bblX4XiRqjoK0pbk5sr7nogOVuAjRvFcGfaNNm3aTBIDthgkPq9fWx3v08VAAAg\nAElEQVRPcRtMJoftrD1VbzTKvdvRo2JWEx7uOLeyUiJ/i0V6NGNioGdPMVgMDz9NAsdYDnk7xD7X\nJxQKdsOB5RAeD/1/DQYP2YIX0kOi+y4nbxdVOjfnq32aK1KU8+HIEVixQvK2/v6iAEuWSNT/xz/K\nCJ7VKjcGUVEwYYLkeZU2x74NLj9fRP34cTluT9NnZEjvZWCgeCcVFIjIGwyStOnRQ0TePh53xnWr\nZiOUZDjscy0m2LpIbHWTpkNQd6gtA/+uEHeh/KkoLkAjfUVpLocOSYQfGSn1+/Jy2QFqMsEf/iCF\nW3v9ftgwqd9rm3WbYLNJF31xsUTwWVlSkWmcqg8IkM+XLJHhi169oE8fx+71Xr1krM4+EndWvXQ1\nJVCaCaWH5SI8u8Ch/4j4J0yWxjxjGXj5Q3QSBMVok55yRjS9ryhtwf790qEfFSVhX3o6zJ8Pl1wi\nDnuenpL/LSuT+v3AgW19xZ0Ke6q+sFCi+JwcOVZQIJ9nZsp92Pjx9e539QY59reUiAgR+ehoEXl/\n/3N4cYtJ9tYX7YOaUvD0ls777DTI+B5iRkHfq8BcKwIfOVgW42iTnnIWqOgrSmuzZ4+sxLUb7qxe\nDYsXwwMPiOiDqI2Hh6zI7datba+3E9A4VX/kiIi7nWPHxAF53z7R2MREabZLSJB/Gg8PsUjo1ctR\nj2+WIaKxHEqPQvFBSdv7BEpDXnYa5G6SPfb9r5WmPEudNOlF9NcmPeWcUNFXlNZkxw6xz+3eXVL1\nS5aIxe6zz0qR12oVlYmJEcPzgIC2vuIOh9Xq2OWenS2Re1WVTEz6+Di2vNmz5IcOyX1ar15Sf+/S\nRf6p7J+HhjZRjz/jxVig6jgUp8ufHl4S1Rfug6z10rAXMwriLgJvP7kJCOkh0b2PejMo546KvqK0\nFlu3wvr1Iugg8/dHjsCf/yzKUVcne0mHD4cxY7R+30KYTBLF2w1wcnIcpjj2VP3+/fLX/frrEvVX\nVEjaHuS+q1cvMcsJD5f6/HmXzeuqoDxLdttb6kTQzUaJ6nM2yk77HheJuJtqwFoHvmFSt/ePON+/\nEqUTo6KvKK7GZhPTnU2bpJPLaIRXXpGZrCeekCa+igpp5LviCtlhqjQb+yoCe1e9PVVvMDgi+Mcf\nl076QYMkVd+jhzy8vSV6b1yPb7Fki80K1YWSvi/PFdMc7wAoPiBRfXl2fVR/IfgEQ12FjOCF9hFj\nHd8wbdJTzhsVfUVxJVYrpKXB9u0S4ZeWwrx5Uhi+/37JCxcUiNpcfbUUhZVzwmKRcbnMTEnFV1VJ\ndJ+VJc12jTvlzWbpjzx82Lke37OnfB4eLin+FsVcC2XZIu6m6vqavAlyNkhU79e1PqofIl+3mcE3\nFML7Q1C0dOwrSguhc/qK4iqsVqnf//KLRPhZWfD889Kcd+ONkgHIzpa88ZVXnmOLd+fGaJRI/tAh\nedTVyVx8ejocOCCi3rMnxMfLDUBtfaO7t7f8dY8aJfdXoaEuqqLYbFBTLLP15VlyzMtf6vZZP0PZ\nUeg+EkbNlqjeWAmmKgjrWx/Vh7rgohTl/NFIX1FOhcUCa9ZIsTg2FnbtkpW4994Ll13mUK3kZKnf\nN7sTrPNQWSk9jvv3i1eR1SqVkdBQcSsuLYWkJEnN9+ghEbu/v3M9vvGOeJdgqYOKXCjcD8YK8Ooi\naf2cjZC9AfzCpCmv2xCp1dvM4BcuUX1glIznKYoL0fS+orQ0ZrOM5B08KIK/Zg38v/8n9fthw6R2\nX1Eh0X1CQltfrdtiszk67PfvF3tbq1WEOzBQUvNWq/xVlpZKxB4WJqsKuncXkW8188LaUjHRKcmQ\nC+8SACWHIXu9/Nl9BPS4WDruTdXg4Q1h/aQT3zeklS5SUVT02/oylI6GySSmO0eOSA3/iy9g5Urp\n0O/VS+v3TWCxyF/RkSOSpq+oENHft0+GH4YNg7vuEpE3mSRqt6fxo6Nb2aHYahYTncL9UFssQm6z\nwbHN0oXvEyxRfdTQ+qjeIp33XftLd76a6ShtgIq+orQUdXViq2v3yV+0CPbuheeekxA0N1fr96fA\nXunIyJDkiNksYr9qlQi9vz+MGCG9j716SUo/IUEi+m7dmmmEc14XXCE1ebuJjrcflGVJVF98CLon\nQ+yFEsGbayVlH54AwXE6W6+0OSr6itIS1NZKRF9QIEXm116TUPSpp6Rer/V7JyorxZLgwAHpb7TZ\nRMxDQiRNX1Yme4gGDBBhDwuTj2NjZaTOw6OVL9hqgeoCmauvzJdxO4MBcrdIVN8loL5WPxQsRonq\nA6Jkra1/hEb1itugoq8o50tNDaSkSM65Sxd44QXJOT/4oHytvLzT1+9tNvnrycmR+nxhoaMp78Yb\npenObBaxNxrle2JjxbIgOloMcdoEU7VE8UUHpEnPswtU5klUX5QuZjlxF0q3valWNuB17Q/BsbrW\nVnFLdGRPUc6HqipYvlz+rKuDZ54Rg51p00TZvL1F1Tph/d5icSys2b9f7n0OH5b6/LZtkhwZOVJq\n9r6+8lcVHy+b6ex7iNoEmxWqi6DkEJTn1Lf7e0D+TonqvXxlrj5xKpjrAJt04Mf0q4/qNZOjdFw0\n0lc6LxUV8M03EpoePy4ue3feKVF9J63f19U56vP2+XkvL6l4LFwoNwDDh0t9Pi5O0vkDBsiIXdeu\nbVz5MNeKyBcdEJtcLx9J5Wevl2NRQ+vd8kLFFtfLH7rGS63eu/P8GyvtESNQAGRhMFys6X1FOWfK\nymDZMpkZ27cP3n0XHnsMhgyRYvWIEZ2mfl9VJT9yerqIutkMfn4O4xuLRVL7FRUSzcfESKUjJkZE\nv02x2aC2RMbqSo8ANrG+zd8pYu/hLVF9t6GS3gcR+bC+4N9VzlUUt8MCFAN5wEHgOGADumAw3KPp\nfUU5J0pKRPANBnHc++orsdbt1k3y2ZMmdfj6fUmJJDP275fIPidHBhV27pT0/P33y1y92SzC37cv\n9Osnf0V+fm199YgNbsUxKNoPxjIweIn4Z6fJhrtuQ2DINPG7t5okZR85HIJipFtfUdyOCiSazwAy\nATPgAQQB3ZFof/d5v4pG+krnoqhIBN/TE778UorTzz3n8HjtoPP3VqtjS529Pl9RIZYE27bJX0dy\nsmPXfOO0fWSkGyU8assamehYwOAJx3eJ2GMQA51uQ2QUDyCkJ4T1EX98XXajuBVGoBDIRqL5ivrj\n/oC98/UgsAPYXv9xPwyG3ZreV5Sz4vhxqeF7eIjDXmkpPP20KGAHrN/X1cmPfPiwzM8bjRK1h4RI\n411lJfz73yL03btLl33//pK2Dw11I420m+gUHYCaIsBTzHRyNkLBbllfG3dhfVRvlln6rv0hqLs0\n7SmKW2DFkbI/VP8nSMI9BOgCHMMh8ruAcGA4kAQMAfwwGKao6CtKk+TlieDbbPDXv0JEBDzwgET+\nHah+X13tqM8fOSKiv2cPXHONjM3V1Tnc8Dw9xSAnPl667d3ufqeu0jFuZzUBHlC4R9bYYnN44Nus\ncocS0kuiel1hq7gNlTin7E2AAUnZByLR/U5E5LfXf90u8klAV6AWKEfS/TYMhgdU9BXljOTkyFie\n0QivvioCf8MNEuq28/l7+/y8vT6flycravftgx07pF9xxAhZDBgUJMKekCDOeN26uWhD3fnQYKJz\nEKryAQMYSyWqP/4LRCRC3Bjwi5Co3jdEDHQCu0u3vqK0KXU4p+zL64/7ISl7G7AXh8jnAIMRgR8O\n9ETEvRwRe/sNQh+gBxCBweDnvqK/cuVKHn30USwWC/feey9PPvnkSefMmTOHFStW4O/vz0cffURy\ncjIAd999N99++y3dunVj165dJ1+4ir5yNhw5IsY7JSXwxhtw880wenS7rt/b/e3t9fnKSglsg4Ph\no49E8IcNk7S93eq2f3+pYIS5axBsMYk1buE+8bk3IJ742evlRiDuQonqQTruw/pIZO8X1qaXrXR2\nrEAJkqrPAHIRYW+csj+CQ+T3IeI9vP4xAGnWqwCq65/TB+gN9AIikYyAA7d15LNYLAwYMIDvv/+e\n2NhYLrjgApYsWUJiYmLDOSkpKSxcuJCUlBQ2bNjAI488QlpaGgA//vgjgYGBTJ8+XUVfaR4ZGWKt\ne/QovPeeOOz16NEu6/cn7p+vrXWspfXxkbR9WZmM33XpIpF8QoKk7Vt1ic25Yq6VxrzC/SL8deWQ\nuxnyd0HEAIgdDX6RgEXS9l37Q2C0rrBV2hB7yj6z/mHEOWVfhEPkdyCNefaU/bD6z6sQobffIPRE\novlI5Gbh9HfmbuvIt3HjRuLj4+nduzcA06ZNY+nSpU6iv2zZMmbMmAHAmDFjKC0tJS8vj+joaMaN\nG0dmZqarLk/p6Bw4IK3pO3bA55+Lh35QkCxsbyf1+4oKsbq1+9sfOeIYq+vVC2bNguJi6cz395fI\nvmdPiey93V0T66qkA78oXWryFTlwZK3U8eMuhDFzJCVh8IJw+wrb0La+aqVTYkJS9jlIyr60/rgv\nItAmpOnOLvJliLgPB+4EopAovrzRI6b+nCikWa/13o9cJvo5OTn06NGj4fO4uDg2bNjQ5Dk5OTlE\nR0ef1WvMnTu34ePx48czfvz487pmpYOwZw/88IM80tLgT38SVXTz+r3VKiKekyMp+pISh0vwjh0Q\nECBp+xtvlFl6Hx8YOlS67d02bX8itWWy3a40E7CJ6B9ZK7PzvS4T4xxsYocbngCBUbrsRmllbEjK\nPh/pss/BEZEHI0J9AFiLCH0m0B+J5B8H+iI3AuVIjT8HiABGImLfFTj7u/LU1FRSU1PP94dqwGX/\nmwxn+Q50YpribL8PnEVfUQAJg//7X5lFy8+HJ5+E8HC3rd+bTNJhb98/X1srSYjgYFlYU1kpKfpH\nH5WxOrfutj8TNcVSr6/IBYsZCn6Boz9JBD/wBvG+9/CUpryQnrLLXlFajSocKfvDiFiDpOujkFG6\nTYjI7wa6IZH8NGAQUpe3N9/lIan+RCAOEfzmG0KdGNDOmzev2c8FLhT92NhYsrKyGj7PysoiLi7u\njOdkZ2cTGxvrqktSOjrbtklK/+OPRREfeECcZtysfl9dLfcj6ekyQ3/kiCQnbrhBovbKSunILymR\nevxjj0naPjLSDbvtz4TNJp34BXugqkDq98e2Ss2+2xAYfpestPXyh4iBEBInW/AUxeWYkNq7PWVf\nUn/cnrKvQlL19pl5EJG/FHgIEfWK+vMK67+vN6drvnMnXPYWMmrUKNLT08nMzCQmJoZPP/2UJUuW\nOJ0zZcoUFi5cyLRp00hLSyM0NJSoqChXXZLSUbHZYNMmWLUK/vY3GDxYIvtRo9ymfm+3vbXX5/fv\nd9Tnu3SRtH1enmzy7d5dWg/cziTnbLFaZNzu+G6oLYW6CsjeAIV7pTFv1GwRd78wiBwke+t1s53i\nUmxILd6ess/GkbIPQqLxPTga8I4jo3TDgamIDW41DqE3Is13vRGRD+VMzXfuhMtE38vLi4ULFzJp\n0iQsFgv33HMPiYmJfPDBBwDMmjWLyZMnk5KSQnx8PAEBASxevLjh+2+77TbWrFlDUVERPXr04Pnn\nn2fmzJmuulylvWKxSN3+229h0SLxzR87Fq66qk3r9yeupW08Vvef/0iEP3gwPPSQDBP06ydJCbfx\ntm8OVrNsuSvYLY16Vcch62eoPAY9x0Hvy6U+HxwraXy1xlVcSjWSsj+CjNPZ594DkfR8Jg6RP4B0\nzw8HZgMJSIq/Apmbz6ctm+9aEjXnUdovVVWwerU8/vEPmDYNLrmkzer39rG6jAyxvS0vF5EPDZVo\nvqJCxN9qdXjbx8WJOaAbJCOaz/9v78yj4yrvu/+ZkWY00sxotTZLlm0s23iRJYNtSt4Y7ICP2SKz\nvKXJoQTHZu3CoQ007jntCbSF0AO0paFJaWOaQE/LenB4EwMuiR22YhsjB7ABbzKyNmuxRjMazWi2\n5/3jN88skrzLWCM933vuuXdm7r26uleaz/2tTzQEnhax5HUJXsu78hAw/TIonCGj3RVfAEWzpE2u\nkdGYK4K42tsRl/2x+PsOJAHvGEnIf4y48XW9/EIE4l7E9a8Q6/8CxMovQWruz7/GbZ3+uZaB/iRX\nd7c03dmyRZbr1sGKFV95/D4QgNZWcds3N8tyzx5x28+fD9/9rjwMQHJI2srKcTAk7VgoHBDA934h\n68f2C+wdhTDt/4BrKtgcUm9fUGP64BuNsRRSHteFuOyPIM1yshDIxxC467j8IEnI1yPQ18l3IB6A\nWYxF8t25lIG+0eTTvn0C+1dflWy49eth1aqvLH4fDkv9/OefC+h9PnjhBUnGmzZNYF9XJ7X0tbWS\ncV9eLiV2E0KhATh2EPoOihu/e4+Mcld0QbyZTolk35fOl0FvTMmd0ZgpQLrLPoC47J1IJ7sDJK35\nI0gGvYZ8NRKP153v7IhLfzoC+czwQBnoG00e6fj9u+/Cs89K8Pvb34ZrrpHONOdQsZg4Fw4ckAS8\nSEQcCvn5Av3f/EZgX1MjbvuqKigpkQH9JoyCHqmr9xyW5LyOJujcDRX1UHExONzgLJNM/LxSE683\nGgNFkCz7DgToPQjk7QikO0k2xdkDVJHe4jaEdNBTiAegGnHZZ1byXaoM9I0mh3T8fudOydBftgy+\n+U0ZPm7q1HP2Y/v6xJr/5BNx2dfUyBwMSttbkLj83LkyNK07M4yF09Ngj7TJ9XVICV77TrH0qy+B\nsjqw5UncvniW6ZpndJZSiMs91WUfRerg8xFXvHbX/w6Bf2qL22wk+S6KAL0ccdlndvJdqgz0jSa+\nurvh9dcF+M8+CzffDCtXytBxRWM/4IrfL1n3GvQffgi7dollf8stAv3ycnEuTJsmnfImnJSS7Htd\nY+9rExd+4JjE66fMlRj9lAuhcLqA38jojBRALPgWBPSDCLDzEIjrUel+hyTjLSI5Kl0x6cl3xQjk\ndee78ZF8N5Yy0Dea2Nq3Tyz8bdtkeccdcOmlEsMfw9q2UEja3+7dK3X0n38Or7wiFv2SJXDxxRKn\nX7BAoJ8/URvGxaJi0XfHa+z7DkrZncUK074GBTMkXm+a6RidsaIkXfYHEavegrSmdSHw13H5Q0At\nSWu+BonL6/I7J+Kul2Fnx2vy3VjKQN9oYkrH73fskJa6nZ2SCv+1r0kd/hi0potG5bD79kk+YCwm\nHfAcDqmt7+uTpjk6Ka+4eAx+r/GqWAS8rdC1FwJ90Pu5DGubVybJee6p0g+/dJ7E7U0zHaNTUgxx\nt3uQBLzW+FK77N2Ipa4t+Y8ReOu4/IVIXN8fP54daYgzg0xKvhtLGegbTTwNDopVv2cP/PSnUuN2\n443i0q+vP6sEMaWkac6hQ9K1d88eseJdLqmrHxoS6M+fL81ypkyZ4PlokSHo/xK6P4dgHxz9WNrk\nFs+GqReDs1QGwSmeDXkl5/tsjca1FOmAb0Oa2sRIdr9zIhD/lKQ1HyEJ+UWIxT88+W4m0lAnM5Pv\nzkQxYgwyiC8+dcenGyw3jM+hdY2Mzkg6fr9vH/zrv4ob/7LLpNPeBRec8WG9Xjh8GHbvFufBhx9K\nzH7WLEnCi0Zhzhypoy8rm2BZ96MpPAh9zVJb7++STPyuT6FyMTTcJgl5RbMkOc8+fvuIG50vKQTM\nHsRV34oAPhL/PAtxtUeR8rrmlHmAZIvbRiT2PhDfdggBex1QwURJvjuRokQZiE/99Cfg3kcfMWKJ\n7ezYUZy9oWssfaPxo337pPbt44/hv/4L1q6FhgYpySsrO+3D6cY5n34qnfI2b4bf/lYOdfHFEqu/\n6CKBfUVFhg1mc6Ya8kmcvu8Q9LdCx4fQ3wJVl0hdfW5xPF4/zTTTMUrRANIIp4ck4HXyXBZinfcw\nEvA65j4jvpyJQH2A5Eh2OvmuEnHZT8w8kQgRfPgYYAAPngTcPXiwYEGhsGDBjp0oUbrpppVWjqRM\nAwwQtASNe98owxWNwvbtYn7/5jcSy7/7bsmaW736tLLmdOOczz4Ty16pZBndzp3irl+6FC68UKIG\n9on5/TJSQQ/07gPPl3DsEHTslAeA6kuhZI647ksXgLvCNNOZ9PIjgNej0LUjgAeJw4eR5LtUwHci\nGfMa7DORmvlsJDtfx/BjSOndDMRtX8pES74LEUrAvY8+uuiim24GGEhsY8GCAwdhwnTRRQstaXAP\nEmQa06ihhmnxqZxynDhZa1lroG+UwdLx+wMHxLoPBuE735HsuZUrT6mNXSwmY9IfPAjvvw+9vRKT\nz86WxjlKSSn//PnSNCdjB7Q5XSkFgV7o/kxK7no+l9Hush2SnFd0gSToTZlrmulMWgVIuujb43O8\nb3QiRt+JZNRrwA+Rbr1PQ1z0kfis4e5E4vDlQBGSdOdGvAKZryDBBNx76U1Y7oMMYonnHVix4sBB\nkOCocI8QSQN7DTWUU04uuQQJprnz3bgpo4xVllUG+kYZKh2/b2+HH/9YCt+vvfaUhsTVHfIOH5Ya\n+vffF0dBa6sMsKfH3FmwQJrnuCZTWDoaknr6rr0C+65PoW2HjG5XeTHkT4OimaaZzqRTEAH8MZKA\n1zXxIcQ9nwr4L5H+9Np6r0Fc8Hkkm9/EEEu9LD6XkIR75rvRFIoAgQTcu+mmhx666CKc8H5AFlk4\ncBAgQCedI+AOUBOfUi33HHKOC/dSSimiCDduXLiwxR+WTPa+UWZKx++PHBHg33STBNgvv1xIPYqi\nUQF9c7PU0Xs88MwzYuHPmyfPCl//uiT4T58+QQa1ORXFIuK+H+wVyAeOieu+owmO7oaSCyVBz1Up\nVr1ppjMJNIQA3kPSRa/dy/1Idn0HScB3kxwffgbiqi9F3PMWxOq3k4S7LpdzI6PYZbaOlynfQw9R\noontbNhw4GCAAdpp5whH0gBvxz6qW96GjSBBYsQSXgA3bkoppYyyUeGupVMmfUhx4zwDfaOMko7f\nf/QR/O538NJLcM89kpl/9dVilg/bvKtLQP/FF1JSZ7eLi97rlcPopLwZMyZ4Lb1WLApD3jjk26VN\nbnRI6ux9bdB3WNz6lYuhvEHi9KXzwV0FWRPDtWqUqhBJwGsL3otY4UfjcwdiuR9GMDITgXsVkiVf\nggBeIe73KQjcS0nCPfPjYqeTKZ9DDl68tNOeBvZWWskld1S4Z5NNgMAZw30QgbsPyZroQvwvsZTt\n7jbQN8oY6fh9Swv88pdSJP/HfywB92uvTRA7EknG6HftErd9XZ10wvP5kk105s0Ti76kZIKHo1VM\nIB/ok255/k6IhgX4vjYZAMfXLm77wungqhLQO0sF9nmlppnOhFEYgXs/ScB7ENd9K+Ke1xZ8CwLt\nGUjS3FTSa92tJOFeRhLueWR6LfxomfJddNFPf2IbnSmfQw4ePLTRloB7Cy200YYbdwLsellGGVas\nZwx3kLulLfduknAPp2xjRx6zHKQXLTYa6BtlhHT8vq8PNm6UBL1bbhHzfNUqIjlOjh6VfD4N+t27\n4csvJQHvmmukhl6PZDehQa+UDF8b6IOBDhjolCY6A50C+f4vof8IuCpkoJv8Khm7PtsugM+vktI7\nE6/PcEUQuHsQkLcjCXceZCAa/V5L/L2a+FyFJM9NRbBhQcriNNzzEbg7yXS4n06mvA0bffQlLHYN\n+HbaKaJohOVeSikWLKPCfQpTKKf8pHAPkYR7L+Jz6UagbyXpV8mNz8Mfzb3Io1xbfG4FdhjoG417\n6fh9fz/80z9J7/xvfIPw7Pl0zl7OgS9tHDiQ9Py/+CIsXAiLF8tgeg0NyTa4Exb0Ib/E5Qc6xWqP\nBKVpjq8NPC3gaZayusKZAnV3NWTnyHvuasgrlp74ptwuQxUlCfijyNd7FwL2VgTubYiLXreirUIS\n66oQmFuRLHkN9wIE8M74Z5mr42XKBwgktrFiJZdcssiil94RcO+kkxJKRoW7TthLhbsLF6WUnhLc\nIyTd8seQO9iFFD9quOt2Rbmk1y9EEP+Mhnoq4GPI3a2OL6uARw30jcZM4XDSf67U6S8jEVmPRpNL\nr1eK5ltb4Sc/IfKHa2mvvJj9JZdwKGsO0ZgFh0Na3/p8MDAgCXgTHvThQBzyRwXyYb8k4HlbwXtE\nmufY3ZJl766WVri2XMgtkth8XolY8gbyGagoYsNpwLcjMD8SnzXgOxB4T0Osdv31n48AXcO9ELHc\nXWRy97rTyZTXcO+iKw3sLbTQRRdllI1wy5dQQoxYGtwVKuGW13B34cKNe1S4R0km1em7dzT+WstK\nEu66fkEPGJwKdL3ehQRZNNSrU5YFjPTFGPe+0diopUXa1Q0OplN2+DVWaiSF9TYWi8y6h63VChYL\nkbe2weub2dX4IFs9F/FRaCGtHjf33ivPBLGYNNDRrvsJCfrIkEDe3w2+Vgj6YKg/DvlW6ZKXZZPa\n+fxqic/bnOAokNd5U2TdjGqXYdLR2wHEsXsE+Bxxyeuv/lYkhUvDvTq+rhPsypHYfDFJuGfuw97p\nZMrnkosFCx10jLDce+mlgooRlnsJJUSIJOBuxUqM2GnBPYZY6do1r+Hel7KNhSTcdTeRMKNb7W3x\nY6Za7Hq9kpGdCyJI/cUQ8hekf57CJPKd79PIfPX3S5H7oUMSKD/VweFjMXlA0PPAQHLd7yfmH2Sw\nN0hw/xFajjl5vPqf2NFZw1G/i0X1VhoaZMC8BQtkTPoJB/poWKDu7xEXfdAjZXTeFvC2iSWvonHI\nTxOwOwrB7hTL3lkqkDetcDNEqXDvRb769yMWfEd87kSgn4dAvSplWYNAPvMb2SgUQYIMpkx98cmD\nBx++tLp0O3ZyyUWhEmVwqXDvo4+pTB0B92KKCRMmQCDRwvZ04T5axvxR5A6mZsw7SCbVgQRiRrPa\nuxGrfTS4D7fah1Lm0LDPbMgjXlF8mY/81TgBp4G+0RkpHJbs+Q8+kKS6KVOk083evWnwTixT1wcH\npXOewwF5efKgEF9GHE68FNA+VMyAtYCYK5+79t5LQX6MxZfls/TrDhYtEou+qL0h/sIAABzqSURB\nVGgCgT4WgWC/lMp547XyIX+8jK5VBrcJDwrkC6YJ2HOLwZ4n7npXuUDfQH6cazjcO4AvkFI4nTmv\nlzYE5BWIPVeJjA1/AQJ3bblnViOb04U6iNWeQw527IQJ00bbCLe8Fy/VVKfBvYYaCikkRCitzv10\n4Q7Se1DD/XgZ8zkk4R5F7uJocIfRwV5B8jEtRjrYda9CuYbirylEfDnFCNA12E/012Ca8xidvlpb\n4e23xbdeVgZtbfD88xJ7X7pU6uFSQJ5Y6vW8PCmUj3fMUwq6+u18djiXL1pyIRoj3xbAPwjhsKJg\nWiHz/+98ambnTJw6el0rHzgWr5Xvlji9ty0J+WCfJN5pyDvLwOaQ1reuCoG8aZIzTjUc7u3AZwjc\ndRy+Mz7nkQS7XtYitfDaLe+Kz+P/oe5Moa4HivHipZdeeuhJLPXUSy8AVVSNiLnnk5+w3M8G7iHE\nJe8jPWN+KGUbnTHvQO5waqBFg70HuXujwT0fsczDpFvrqVfFikC9CLH+U631PM48+8JA3+jU5fOJ\nZb9/v5jZvb0C+z17ZLz6q68evdd9JAKhkHgHwmFZB4bCVg4fc7P9UClvfV5Nls3CFYv7GMBFtjOH\n+QsszJmXzZSG6hO21M0IqZi454N94G0H/1Epq/O1S1md50vJti+YDoU1ceu9Qix3VwW4K+Pu+8nU\nDzgTNBzurcAexC3ficBd52Lnk261TwXmIq75UuQrXsN9/LrlzxTqMWL48NFPP73xScfiNdwViinD\nphJKEuvFFGPDxhBDCbjrc0qFeyGFuOPT8eB+vIz5wZRtskgCVo8PONxyt5IOdg33ciRzIkQS7Kle\nARDPQKobXnc5cCIPFOfCkWmgb3RyRSLitt++XZLrBgfhhRcE9jfcILC326WGfij+PGyxJBP0cnIk\n087lgvx8emNFfN6Rz//8r4vf7nDwYZONmTNhxUoLK1fCokUSp8/oEeyG18r7OuKu+1Z53X9EYvYF\nccC7p8qsIe+qlEx7u2sCxTAyWcPh3gJ8SjrcO+OfFZMO9ypgPoIC3cRGw338lcKdCdQjRPDjx4s3\nAfWeYZMGegkllFKaBvMiiiigABs2woSJEElLytNWexZZOHEyhSlpTWxOBPfUjPk+knD3kUxusyKQ\nDcU/G81qL2Nk+Vs1AuhUN7weVUDLjUC9JL7Ulnoe5ycoY6BvdGK1t4sr3+OROPwrr8Annwjsr7lG\n4NYXz0mtrYWZM0nU0DkcAvysLMJhiQrs3i2J/k89BT09UnK/YoW0zJ89O8Pb4IYGJOHO1yEWvLdN\nyuc05FUs3vFuqtTKO8sE8s7SuLu+CHLcYBl/IJg8Gg73ZgTuh0m2o21HUrGmkLTYK4DpwAIEByUk\nwT6+OtSdLtRTa9z76ceDJ81S76WXKNERFnoqzPPJTwA9tZZdn48NG06ciVr2Agpw4SKHHBw4Ekv7\nCTCZmjHvIdmGto8k3C2I1a5HDziZ1a7XSxCYa7CnKguBuQb7cDf8ePtvNtA3Gl0DA7Bjh4xMMzAg\nbW8//hiuv17GqA8GZS4okBFqZs6UWP0weTwSDfj4Y/HsOxyy/OwzGdzmootkuFrb+PVmHl/hwWRD\nHM+X0gCnP96/3tcmdfL51WLJF1QL1PNKwVWWBLyJyZ8nDYf7QeBjxILXlnsHgpEyBOw65l6LWO5T\nSbrk3SQLr86vTgfqQYL00Zcof+unnz760mLqESIj3O3FFCdgrq1sDXJdvw6QQw5OnOSTjwsX+eST\nR14ayHPIOa6VPvrvl8yY121oR8uYH4q/143cTQ32XuSODnfJlyFBFZ00px8UFAJv7YLXtRHaWs+0\nEQUM9I3SFY0K6N9/Hzo74X/+Jwn7lSsF9ABz5kjz+vLyEe7naFRy+3btkra4hYUSkh8aEugvWgSz\nZsn7GaVIMF4r3wU9++DY/uQgNf4usdzdVfE6+Spx0TvLpEY+xx131Y+35/6JrlS49wD7gE8Qt/xR\nBAOdyFd9BQJybbnPReBejhRMjY8a91OFepAgHjz00Yc3PvXTzzGOJaAeJkwppQmYF1FEIYUUUJBw\nmztxYolP2krPIw9XfHLjJp98cskdAfOsk6SbxZA4dyhlqech5JErgEB+ELmbgyThrkcSGA3u2aSD\nvZJkE+FI/Bip31wFJK31QtKt9Uy0SY4nA/3JqFhMkulS53BYqLx7N3z6KWzdKm78xkb4vd8TsOtW\ndzNnSvZ9isJhSeY/cgTeeEPGxdm+XcL9K1dKjL6uTsbGyc6UviCRIYm7D3RB1yfQ84W4672t4srP\nr0o2wtE97J1l0s7W7jYj0n0l0vnPGhNBBO6fkYR7asxdkYS7jrcvAC4kfUS4r771rEIlSsv0cogh\n/PgZYAAv3gTUtYWuQd8fn1Jd7xroxRRTQgkFFFBIIfnxqZjiBNAVCitW8shLuNi1dZ5LbhrIc8jB\nOsq1GQ3e+u4MpswBkiAPk4ypg4A4dTu9fzBl9iN3shVx3ada7RUk6x2GBwKySbfWC0iCPZfx54Y/\nVzLQn2iKRiWr3uNJr5EPBOR1ICCEhqSFHgjAsWOy30cfSdLeNdfAJZcI3LVVX1aGwoLfL4D3eODo\nUXEItLXBzp3yzNDRIbH6K6+EVatk1Nv8/PN3SU5ZuiGO7yh07IKezwTy/UfkWukmOIUzoHResmwu\nJ9/Ux4+ZYqTnO+v1QcSmS82I7yFZXDUQX9epWjaS8fZypNf8QmA2ybHcXSQHlDk30iAfGjYNMsgA\nA/jwJaCu3ex66FbtcvfHpwEGOBafQoQoiU+FFFJEEfnkJ9aLKSYPCR1lkZVmletptHi5BQtRRod3\niCSMhy91B/tofF3DWX+e2h0uQDr4/SlzMH5HnKPM2pWeh4BbW+TahlDx7VKT5nRGRR6ZUOz41chA\nfyKovz85aHxLi2Tbg5jUVqvE5D0eSbjr65MMuu5uWXZ1iaVfWioNdmbNkmB7ZSWRhQ14i6bjDefS\n1SVe/v37BeIgzxe6a67XC5s3Sy7fmjXiEKisHKeVdkqJqz4SkNp4fze074TuvdDfIol3drfUx+fX\nQNl8KJ4DzikCeFuecdOfloZb43rdQ7JHvM6p7iMd4t74+gBJJLhIjvQ2fK4A6pC4u/7adzHW8faT\ngVz3fu+mGy/eESAfYCABch8+vHgBEjFybW0745N+r5hiCikkjzxyyElsl7pPEuI5ZOFAYRsBb/0Y\npd3nGsD6yqe+lwr4VIt7OPj98eMmOr+RHvfW4NX17Y74XdHlac74ayvJeHqqbIj1noNY6aO54TPF\niXg+ZaCfiQoEBNhHjsig8YODAjKfT7LtDxyQ7nhdXWLBu1zSREeDvahIXPVut5jgbjeDYRvemAtP\n0Uw63bW0DhTx0ssW2tvlkN3d0ltn+nT4oz+SCIHdLocqKZHZ7Zbse9d4KSWPBGUODwrYjx1Mjh0f\n6JU56BE3vrNMyueKa6HyImmK48iXOLwZlGaYUq3xVJB7SfYg60Qg3ovkSuu0K10ZnWrX6US44SAv\nQpy1ZSRbzOrcaPso89mFU8KER4A8QAAvXnz46KSToxyliy68ePHjT0A8FeR6PYusEQAfbm2nvldA\nAXnxKZfcxLqDXKzYsZKDFQcW7FhxECWLMEkw+0kmtvUhj1TDrerUZXCU98Okw1oDO7VHfCrEh0Pd\nThLYGtKpc84osw2BdTaSCZ89ypzFeKp/yGyNa+i/8cYb3HfffUSjUW6//Xa+//3vj9jm3nvv5fXX\nXycvL4+f/exnLF68+JT2zSjox2Liem9vF8h3dQngW1vlvUOHZPhZ7YqfPVvi7gUFQmo9il38UL7s\nIrx55RwKVPK/+6dQNtWGL+xgMGxLdMfNzZXYfFUVXHihxONragToLpck6jvOkb9s27ZtrFix4tQ2\njobEWo8EpE/9sf0Cdm8bBHpgsFfa20aHpBe9o0hGmHOWi6u+aCYUzEgCflK56RXyNR9JmcMpy0GS\nRU2dJHuTeUiCfDSIO9EQ37YtyooV00jaZqUIvHUNez6jA9zOWERZI0TSIB6MTx48dNBBO+0c5Wia\nRa6hnWqh+/Fjx54A9HDrWi9duCimmDLKcFOAnTxycGIjjxzyyCIHCzYs8YcUCzbC2AiQTT+WtCvb\nH7+qA8ij1WiQHh4j15nmw2Gd6uJ2km55621TaxBs8aUG9Z5t2/jaihUjIH0iUBtIj0+dLfvOmQkU\njUb5kz/5E9566y2qqqpYunQpjY2NzJs3L7HN5s2bOXDgAPv372f79u3cc889fPDBB6e077hXNCpw\nP3xYEur275f11laBvN8vcJ81Swrd//AP00vmrFbCriK8eRX055TRFSrgtW357P4shy9brLS2St7e\n1Klw990C9IoKcQi43fKscM89ozfYO9caAf1Y5DhgPyKvA8ek010sDDkpYC+aBTNWxPvVTxe3vC1X\nwJ7R1rtidFAHEVuvP748lrI+3NpOtQF1tFUvQymvNcRTrfF8pEVsCUkrXEPcRSq4t217nBUrHuJ0\nvyqkOUuySYtepq5roPfTn7C2PXjojE+99CY+SwW6Hz8BAjhwJFznqW71KZQxnVryKaKIUooop4QK\ncnFjx0kWuQRwMEgOfmz4sTFINn6y8JJFJ1a2p1xBbVWnXuHRBkvRkNVub8cocy4Sz9YQ14PkFpIc\nIFfvn5NyzNEs5+HvnegRa+u2bTSc6oO40YTWOfvm3LFjB7W1tcyYMQOAb33rW/ziF79IA/drr73G\nbbfdBsAll1yCx+Ohs7OT5ubmk+47LhUOS2bc9u3w1lsC+uZmyZKrqpJg+rx5cNVVUFZGWGUTzHIS\ncJUykFtKa7CElmMu8gpzCGU56D1mZbBVvP/Z2fC/TfJccN11sGyZxN0LC8XD/5XUycci6XNkCEI+\naU871C8W+ZBP4uvvPSYZ8kNe6WqnXfGxMOQUSre6vBIomSNueT0QjS0XsjXYx0tCgUJSnPQcJhmn\nHkBsND0+up77SIJap0RpWy8VIcOH5Ei1zzQ6Utd1RLUAyXd2DZs1RgoQmOemHC/VCpeM79GgLBnn\nYi230MGb/DrNFa5j2dqC9uNnkMFE1rq2ykPDpjDhxFJPurFLNrZ4//YcXLhx4sZFIU4KyaeaCipw\nMBUbFdipJIsSwrgYwk6AbPxkE8SKjyx6sDKEhSEsowI6Qrq7OhXUuSlLR/yKlpOMceurrAsA9dXW\njXe1FZ2VMmcPW08Ft5HRV61zBv22tjamTZuWeF1dXc327dtPuk1bWxvt7e0n3fcrUSwiXdgs1uNb\nln4/bN1K9LVfoXbtInLgSwZCNvqqFtJXWUdv3U2U3FRCTnkRfVml9MSK8eMkNJTDi/8vj0/3WvH5\nJMyfmytW+u//vjgB8vMlsa6iQmLuf/qn4pq3nsxrGovKeauYrEcC6YlvkYDEycPxZeL9oIwMF/LF\n34/H1KND8fUhccdHQ/JeLCrju2fZpbwtKweycySZrnuvrGc5oPRCsdSLZolL3pYrc1bOGbaoVSmz\nfh1BwKpBrN3W3pTX/pTPZV0xiIrbb2pEnDtZdawIESVEjDBRIsTIJoJtxBzDThg7UWxEyIm/7yCK\ngzDFRMklQh5hcomSQwhbfKn3kW7kEWLxx4sYUVS8D5oiTJQYUSJEiREjTIQYQSL4idGRQLe0VQ0w\nSJggEYJEGSLCEDGGiBImRghFBEWIGBFU3O+g4s1SHWSRR4x9vAhYySULB1Zy43HpAqyUYSEXC/b4\nMifu/tZxa0GqBTsObDji7nCNR0U2CisKC1EsxIAoFnxY6QVCWBgCsrCkWb6pj0EazrkkLWUNZp1Z\nkB//TD8KaUCfCMypnxkZTSSdM+hbTvHL/KwSEsZzT/ODbXDwzdPaRVfn/ehH5+icvkI99OKn5/sU\nzrG0az5wsg0zUtqnARB56PzeS32l/ef1LDJfDz300Pk+BaNxoHMG/aqqKo4cOZJ4feTIEaqrq0+4\nTWtrK9XV1YTD4ZPumzFJfEZGRkZGRuNE56xYecmSJezfv5/Dhw8TCoV44YUXaGxsTNumsbGRZ599\nFoAPPviAwsJCysvLT2lfIyMjIyMjo9PTObP0s7Ozeeqpp1i9ejXRaJT169czb948nn76aQDuuusu\nrrnmGjZv3kxtbS1Op5P/+I//OOG+RkZGRkZGRmchZWR0lpo+fbqqq6tTDQ0NaunSpUoppXp7e9WV\nV16pZs+erVatWqX6+vrO81kajabvfve7qqysTC1cuDDx3onu3SOPPKJqa2vV3Llz1Ztvvnk+Ttlo\nFI12H3/wgx+oqqoq1dDQoBoaGtTmzZsTn5n7OD7V0tKiVqxYoebPn68WLFignnzySaXU2P5PGugb\nnbVmzJihent709574IEH1N///d8rpZR69NFH1fe///3zcWpGJ9Hbb7+tPvroozRYHO/e7dmzR9XX\n16tQKKSam5vVrFmzVDQaPS/nbZSu0e7jgw8+qJ544okR25r7OH7V0dGhmpqalFJK+Xw+NWfOHLV3\n794x/Z80DciNxkRqWGJlag+G2267jU2bNp2P0zI6iZYvX05RUVHae8e7d7/4xS/49re/jc1mY8aM\nGdTW1rJjx46v/JyNRmq0+wijJzyb+zh+VVFRQUNDAwAul4t58+bR1tY2pv+TBvpGZy2LxcKVV17J\nkiVL+Pd//3cAjh49Snl5OQDl5eUcPXr0fJ6i0WnoePeuvb09rYpG99UwGr/60Y9+RH19PevXr8fj\n8QDmPmaKDh8+TFNTE5dccsmY/k8a6Budtd577z2ampp4/fXX+Zd/+RfeeeedtM8tFsv47qlgdFyd\n7N6Z+zp+dc8999Dc3Mzu3buprKzke9/73nG3NfdxfGlgYICbbrqJJ598ErfbnfbZ2f5PGugbnbUq\nKysBKC0t5YYbbmDHjh2Ul5fT2dkJQEdHB2VlZefzFI1OQ8e7d6P11aiqqjov52h0cpWVlSUAcfvt\ntyfcvuY+jm+Fw2Fuuukmbr31Vq6//npgbP8nDfSNzkqDg4P4fD4A/H4/W7Zsoa6ujsbGRn7+858D\n8POf/zzxx2s0/nW8e9fY2Mjzzz9PKBSiubmZ/fv3s2zZsvN5qkYnUEdHR2L91Vdfpa6uDjD3cTxL\nKcX69euZP38+9913X+L9Mf2fPIeJiEaTQIcOHVL19fWqvr5eLViwQD3yyCNKKSkxueKKK0zJ3jjX\nt771LVVZWalsNpuqrq5WzzzzzAnv3cMPP6xmzZql5s6dq954443zeOZGqRp+Hzdu3KhuvfVWVVdX\npxYtWqTWrFmjOjs7E9ub+zg+9c477yiLxaLq6+sTpZavv/76mP5PWpQy/WyNjIyMjIwmg4x738jI\nyMjIaJLIQN/IyMjIyGiSyEDfyMjIyMhokshA38jIyMjIaJLIQN/IaAxltVq5//77E68ff/xxHnro\noTE59tq1a3nllVfG5Fgn0ksvvcT8+fO54oorTmn7Rx555Jydy4MPPsgTTzwx4v2nn36a5557DoCf\n/exnaeVpRkZGx5eBvpHRGMput/Pqq6/S29sLjG2ns7M5ViQSOeVtN27cyE9/+lN+/etfn9L2P/zh\nD0/rXJQM9HVK2x7vd77rrru49dZbAalbbm9vP61zMDKarDLQNzIaQ9lsNu68807+8R//ccRnwy11\nl8sFwLZt27j88su5/vrrmTVrFhs2bOC5555j2bJlLFq0iEOHDiX2eeutt1i6dClz587lV7/6FQDR\naJQHHniAZcuWUV9fz7/9278ljrt8+XLWrFnDggULRpzPf//3f7No0SLq6urYsGEDAH/zN3/De++9\nx7p16/iLv/iLtO07Ojq47LLLWLx4MXV1dbz77rts2LCBQCDA4sWLExD+h3/4B+rq6qirq+PJJ58E\npI/43Llzue2226irq+PIkSM89thjiXN+8MEHEz/n4YcfZu7cuSxfvpwvvvhi1OusPQCvvPIKH374\nIbfccgsXXXQRwWCQXbt2sWLFCpYsWcJVV12V6GS2YsUK/vzP/5ylS5cyb948du7cyQ033MCcOXP4\n67/+a0AaTF177bU0NDRQV1fHiy++eLxbbWSUmTpXTQaMjCajXC6X8nq9asaMGaq/v189/vjj6sEH\nH1RKKbV27Vr18ssvp22rlFJbt25VhYWFqrOzUw0NDampU6eqH/zgB0oppZ588kl13333KaWUuu22\n29TVV1+tlFJq//79qrq6WgWDQfX000+rv/u7v1NKKRUMBtWSJUtUc3Oz2rp1q3I6nerw4cMjzrOt\nrU3V1NSonp4eFYlE1De+8Q21adMmpZRSK1asULt27RqxzxNPPKEefvhhpZRS0WhU+Xy+tN9DKaU+\n/PBDVVdXpwYHB9XAwIBasGCBampqUs3Nzcpqtart27crpZR688031Z133pk41nXXXafefvvtxP6B\nQEB5vV5VW1s76vCwqcPGpp5vKBRSl156qerp6VFKKfX888+rdevWJbbbsGFD4rpWVlYmrnl1dbXq\n7e1VL7/8srrjjjsSP6e/v3/EzzYyymRln++HDiOjiSa32813vvMd/vmf/5nc3NxT2mfp0qWJUbRq\na2tZvXo1AAsXLmTr1q2AuLpvvvnmxDYXXHABn3/+OVu2bOGTTz7h5ZdfBsDr9XLgwAGys7NZtmwZ\n06dPH/Hzdu7cycqVKykpKQHglltu4e2332bNmjXA6EOyLl26lHXr1hEOh7n++uupr68fsc27777L\njTfemPi9b7zxRt555x0aGxuZPn16okXoli1b2LJlC4sXLwbEwt6/fz8+n48bb7wRh8OBw+GgsbHx\nlEIBepsvvviCPXv2cOWVVwLiBZk6dWpiu8bGxsR1XbhwYeKaX3DBBbS2trJo0SLuv/9+NmzYwHXX\nXcfXv/71k/5sI6NMknHvGxmdA913331s3LgRv9+feC87O5tYLAZALBYjFAolPsvJyUmsW63WxGur\n1XrCeLyOeT/11FM0NTXR1NTEwYMHE9BzOp3H3S8VpkqptPj5aLH05cuX884771BVVcXatWsTiXSn\netzh5/KXf/mXiXPet28f69atS+yTuv+pSP8MpRQLFixIHPfjjz/mjTfeSGyXel2HX/NIJMLs2bNp\namqirq6Ov/qrv+Jv//ZvT+nnGxlligz0jYzOgYqKirj55pvZuHFjAkgzZsxg165dALz22muEw+HT\nOqZSipdeegmlFAcPHuTQoUNceOGFrF69mh//+MeJh4N9+/YxODh4wmMtXbqU3/72t/T29hKNRnn+\n+ee5/PLLT7hPS0sLpaWl3H777axfv56mpiZA8hj0z16+fDmbNm0iEAjg9/vZtGkTy5cvHwHv1atX\n88wzzyQeitra2uju7uayyy5j06ZNBINBfD4fv/zlL4+bzKeP6Xa78Xq9AMydO5fu7m4++OADQEYs\n27t37wl/r9TjdXR04HA4uOWWW7j//vv56KOPTmlfI6NMkXHvGxmNoVIB9b3vfY+nnnoq8fqOO+5g\nzZo1NDQ0cNVVVyUS+YbvN/x4+jOLxUJNTQ3Lli3D6/Xy9NNPY7fbuf322zl8+DAXXXQRSinKysp4\n9dVXTzjudmVlJY8++igrV65EKcV1113HN7/5zRP+btu2beOxxx7DZrPhdrt59tlnAbjzzjtZtGgR\nF198Mc899xxr165NuPHvuOMO6uvrOXz4cNq5rFq1is8++4xLL70UEHD/53/+J4sXL+YP/uAPqK+v\np6ys7IQjhunjrV27lrvvvpu8vDzef/99Xn75Ze699176+/uJRCL82Z/9GfPnzz/udU1975NPPuGB\nBx7AarVit9v5yU9+csJrYmSUaTID7hgZGRkZGU0SGfe+kZGRkZHRJJGBvpGRkZGR0SSRgb6RkZGR\nkdEkkYG+kZGRkZHRJJGBvpGRkZGR0SSRgb6RkZGRkdEkkYG+kZGRkZHRJNH/B2pcS2Uqxkr6AAAA\nAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 109
    },
    {
     "cell_type": "heading",
     "level": 1,
     "source": [
      "Noise Tolerance"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# How many random, uncorrelated inputs can the SDM store and be able\n",
      "# to retrieve even with corruption?\n",
      "m = M[-1]\n",
      "sdm_tolerance = np.empty((len(noise), len(k), 2))\n",
      "for nidx, err in enumerate(noise):\n",
      "    print \"SDM (M=%d) w/ %.2f%% corruption\" % (m, err*100)\n",
      "    sdm_tolerance[nidx] = metrics.test_noise_tolerance(\n",
      "\t(int(n), int(m), float(D)), \n",
      "\tk0=k, noise=float(err),\n",
      "\titers=int(iters), verbose=verbose)\n",
      "    "
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "SDM (M=10000) w/ 0.00% corruption\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "24:  0.000 +/- 0.000\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.000 +/- 0.000\n",
        "42:  0.000 +/- 0.000\n",
        "51:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "62:  0.000 +/- 0.000\n",
        "76:  0.000 +/- 0.000\n",
        "92:  0.000 +/- 0.000\n",
        "112:  0.000 +/- 0.000\n",
        "136:  0.001 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "165:  0.002 +/- 0.000\n",
        "200:  0.005 +/- 0.001\n",
        "SDM (M=10000) w/ 2.50% corruption\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "24:  0.000 +/- 0.000\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.000 +/- 0.000\n",
        "42:  0.000 +/- 0.000\n",
        "51:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "62:  0.000 +/- 0.000\n",
        "76:  0.001 +/- 0.000\n",
        "92:  0.003 +/- 0.000\n",
        "112:  0.006 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "136:  0.011 +/- 0.001\n",
        "165:  0.016 +/- 0.001\n",
        "200:  0.023 +/- 0.001\n",
        "SDM (M=10000) w/ 5.00% corruption\n",
        " 5:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000\n",
        "24:  0.000 +/- 0.000\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "42:  0.000 +/- 0.000\n",
        "51:  0.001 +/- 0.000\n",
        "62:  0.003 +/- 0.000\n",
        "76:  0.006 +/- 0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "92:  0.010 +/- 0.001\n",
        "112:  0.018 +/- 0.001\n",
        "136:  0.023 +/- 0.001\n",
        "165:  0.035 +/- 0.001\n",
        "200:  0.046 +/- 0.002"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "SDM (M=10000) w/ 10.00% corruption\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000\n",
        "24:  0.001 +/- 0.000\n",
        "29:  0.003 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "35:  0.004 +/- 0.001\n",
        "42:  0.009 +/- 0.001\n",
        "51:  0.016 +/- 0.001\n",
        "62:  0.022 +/- 0.002\n",
        "76:  0.031 +/- 0.001\n",
        "92:  0.045 +/- 0.002"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "112:  0.057 +/- 0.002\n",
        "136:  0.078 +/- 0.002\n",
        "165:  0.092 +/- 0.002\n",
        "200:  0.103 +/- 0.003\n",
        "SDM (M=10000) w/ 15.00% corruption\n",
        " 5:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000\n",
        "13:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "16:  0.001 +/- 0.000\n",
        "19:  0.003 +/- 0.000\n",
        "24:  0.008 +/- 0.001\n",
        "29:  0.016 +/- 0.001\n",
        "35:  0.022 +/- 0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "42:  0.029 +/- 0.002\n",
        "51:  0.044 +/- 0.002\n",
        "62:  0.063 +/- 0.003\n",
        "76:  0.074 +/- 0.003\n",
        "92:  0.095 +/- 0.002"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "112:  0.107 +/- 0.002\n",
        "136:  0.131 +/- 0.003\n",
        "165:  0.144 +/- 0.003\n",
        "200:  0.163 +/- 0.003\n",
        "SDM (M=10000) w/ 20.00% corruption\n",
        " 5:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.003 +/- 0.001\n",
        "11:  0.005 +/- 0.002\n",
        "13:  0.008 +/- 0.001\n",
        "16:  0.015 +/- 0.002"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "19:  0.025 +/- 0.002\n",
        "24:  0.038 +/- 0.001\n",
        "29:  0.052 +/- 0.003\n",
        "35:  0.066 +/- 0.002\n",
        "42:  0.082 +/- 0.003"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "51:  0.102 +/- 0.003\n",
        "62:  0.124 +/- 0.002\n",
        "76:  0.142 +/- 0.002\n",
        "92:  0.166 +/- 0.003\n",
        "112:  0.181 +/- 0.002\n",
        "136:  0.198 +/- 0.002"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "165:  0.220 +/- 0.003\n",
        "200:  0.230 +/- 0.002\n"
       ]
      }
     ],
     "prompt_number": 110
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# How many random, uncorrelated inputs can the Hopfield net store and\n",
      "# be able to retrieve even with corruption?\n",
      "hop_tolerance = np.empty((len(noise), len(k), 2))\n",
      "for nidx, err in enumerate(noise):\n",
      "    print \"Hopfield w/ %.2f%% corruption\" % (err*100)\n",
      "    hop_tolerance[nidx] = metrics.test_noise_tolerance(\n",
      "\tint(n), k0=k, noise=float(err),\n",
      "\titers=int(iters), verbose=verbose)\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Hopfield w/ 0.00% corruption\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.000 +/- 0.000\n",
        " 9:  0.000 +/- 0.000\n",
        "11:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000\n",
        "24:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "29:  0.000 +/- 0.000\n",
        "35:  0.001 +/- 0.000\n",
        "42:  0.002 +/- 0.000\n",
        "51:  0.004 +/- 0.000\n",
        "62:  0.006 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "76:  0.008 +/- 0.000\n",
        "92:  0.011 +/- 0.000\n",
        "112:  0.014 +/- 0.000\n",
        "136:  0.017 +/- 0.000\n",
        "165:  0.019 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "200:  0.021 +/- 0.000\n",
        "Hopfield w/ 2.50% corruption\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.000 +/- 0.000\n",
        " 7:  0.001 +/- 0.000\n",
        " 9:  0.001 +/- 0.000\n",
        "11:  0.000 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "13:  0.000 +/- 0.000\n",
        "16:  0.000 +/- 0.000\n",
        "19:  0.000 +/- 0.000\n",
        "24:  0.001 +/- 0.000\n",
        "29:  0.001 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "35:  0.002 +/- 0.000\n",
        "42:  0.004 +/- 0.000\n",
        "51:  0.006 +/- 0.000\n",
        "62:  0.009 +/- 0.000\n",
        "76:  0.013 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "92:  0.018 +/- 0.000\n",
        "112:  0.022 +/- 0.000\n",
        "136:  0.027 +/- 0.000\n",
        "165:  0.030 +/- 0.000\n",
        "200:  0.034 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Hopfield w/ 5.00% corruption\n",
        " 5:  0.000 +/- 0.000\n",
        " 6:  0.001 +/- 0.000\n",
        " 7:  0.001 +/- 0.000\n",
        " 9:  0.001 +/- 0.000\n",
        "11:  0.001 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "13:  0.001 +/- 0.000\n",
        "16:  0.001 +/- 0.000\n",
        "19:  0.001 +/- 0.000\n",
        "24:  0.002 +/- 0.000\n",
        "29:  0.002 +/- 0.000\n",
        "35:  0.003 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "42:  0.006 +/- 0.000\n",
        "51:  0.009 +/- 0.000\n",
        "62:  0.013 +/- 0.000\n",
        "76:  0.019 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "92:  0.025 +/- 0.000\n",
        "112:  0.031 +/- 0.001\n",
        "136:  0.038 +/- 0.000\n",
        "165:  0.043 +/- 0.000\n",
        "200:  0.047 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Hopfield w/ 10.00% corruption\n",
        " 5:  0.002 +/- 0.000\n",
        " 6:  0.002 +/- 0.000\n",
        " 7:  0.002 +/- 0.000\n",
        " 9:  0.002 +/- 0.000\n",
        "11:  0.002 +/- 0.000\n",
        "13:  0.002 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "16:  0.002 +/- 0.000\n",
        "19:  0.003 +/- 0.000\n",
        "24:  0.004 +/- 0.000\n",
        "29:  0.006 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "35:  0.010 +/- 0.001\n",
        "42:  0.014 +/- 0.000\n",
        "51:  0.020 +/- 0.000\n",
        "62:  0.027 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "76:  0.037 +/- 0.001\n",
        "92:  0.047 +/- 0.001\n",
        "112:  0.056 +/- 0.000\n",
        "136:  0.065 +/- 0.000\n",
        "165:  0.074 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "200:  0.080 +/- 0.000\n",
        "Hopfield w/ 15.00% corruption\n",
        " 5:  0.004 +/- 0.001\n",
        " 6:  0.003 +/- 0.000\n",
        " 7:  0.003 +/- 0.000\n",
        " 9:  0.003 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "11:  0.003 +/- 0.000\n",
        "13:  0.003 +/- 0.000\n",
        "16:  0.004 +/- 0.000\n",
        "19:  0.005 +/- 0.000\n",
        "24:  0.009 +/- 0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "29:  0.015 +/- 0.001\n",
        "35:  0.022 +/- 0.001\n",
        "42:  0.029 +/- 0.001\n",
        "51:  0.038 +/- 0.001\n",
        "62:  0.051 +/- 0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "76:  0.063 +/- 0.000\n",
        "92:  0.075 +/- 0.001\n",
        "112:  0.087 +/- 0.001\n",
        "136:  0.099 +/- 0.001\n",
        "165:  0.110 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "200:  0.119 +/- 0.000\n",
        "Hopfield w/ 20.00% corruption\n",
        " 5:  0.004 +/- 0.001\n",
        " 6:  0.003 +/- 0.000\n",
        " 7:  0.004 +/- 0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 9:  0.004 +/- 0.001\n",
        "11:  0.005 +/- 0.001\n",
        "13:  0.006 +/- 0.000\n",
        "16:  0.008 +/- 0.001\n",
        "19:  0.012 +/- 0.001\n",
        "24:  0.020 +/- 0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "29:  0.029 +/- 0.001\n",
        "35:  0.040 +/- 0.001\n",
        "42:  0.051 +/- 0.001\n",
        "51:  0.066 +/- 0.001\n",
        "62:  0.083 +/- 0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "76:  0.097 +/- 0.001\n",
        "92:  0.113 +/- 0.001\n",
        "112:  0.127 +/- 0.001\n",
        "136:  0.140 +/- 0.001\n",
        "165:  0.152 +/- 0.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "200:  0.163 +/- 0.000\n"
       ]
      }
     ],
     "prompt_number": 111
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the storage capacity as a function of address space size\n",
      "util.set_fig_properties()\n",
      "\n",
      "for nidx, err in enumerate(noise):\n",
      "    util.plot_error(k, sdm_tolerance[nidx], colors[nidx], alpha,\n",
      "\t\t    \"SDM %d%% corruption\" % (err*100),\n",
      "\t\t    linestyle='-')\n",
      "    util.plot_error(k, hop_tolerance[nidx], colors[nidx], alpha,\n",
      "\t\t    \"Hop %d%% corruption\" % (err*100),\n",
      "\t\t    linestyle='--')\n",
      "\n",
      "plt.xlim(k[0], k[-1])\n",
      "plt.xlabel(\"Number of stored items\")\n",
      "plt.ylabel(\"Fraction of corrupted bits\")\n",
      "plt.title(\"SDM (M=%d) and Hopfield Error Tolerance (N=%d)\" % (m, n))\n",
      "plt.legend(loc=0)\n",
      "\n",
      "util.save(\"figures/tolerance.svg\", width=8, height=6, f_close=False)\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Saving figure to 'figures/tolerance.svg'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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YPe9/tB0+Pj5GU0uGmJmZMWfOHGbPnm30PJVdrVH2Y2iVSk5OplevXrz//vvqNFV18PT0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      }
     ],
     "prompt_number": 112
    },
    {
     "cell_type": "heading",
     "level": 1,
     "source": [
      "Prototype Retrieval"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# How well can the SDM/Hopfield net store prototypes?\n",
      "m = M[-1]\n",
      "kp = 3\n",
      "prototype_noise = noise.copy()\n",
      "prototype_k = np.array([10, 25, 50, 100])\n",
      "\n",
      "sdm_prototype = np.empty((prototype_noise.size, prototype_k.size))\n",
      "hop_prototype = np.empty((prototype_noise.size, prototype_k.size))\n",
      "for nidx, err in enumerate(prototype_noise):\n",
      "    print \"Noise:\", err\n",
      "    for kidx, k in enumerate(prototype_k):\n",
      "\tprint \"SDM\",\n",
      "\tp = metrics.test_prototype(\n",
      "\t    (int(n), int(m), float(D)), \n",
      "\t    kp=kp, ke=int(k), noise=float(err),\n",
      "\t    iters=int(iters), verbose=verbose)\n",
      "\tsdm_prototype[nidx, kidx] = p\n",
      "\tprint \"Hop\",\n",
      "\tp = metrics.test_prototype(\n",
      "\t    int(n), kp=kp, ke=int(k), noise=float(err),\n",
      "\t    iters=int(iters), verbose=verbose)\n",
      "\thop_prototype[nidx, kidx] = p\n",
      "\n",
      "\tprint\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Noise: 0.0\n",
        "SDM  3 10:  0.000 +/- 0.000\n",
        "Hop  3 10:  0.000 +/- 0.000\n",
        "\n",
        "SDM "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 25:  0.000 +/- 0.000\n",
        "Hop  3 25:  0.000 +/- 0.000\n",
        "\n",
        "SDM  3 50:  0.000 +/- 0.000\n",
        "Hop  3 50:  0.000 +/- 0.000\n",
        "\n",
        "SDM "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 100:  0.000 +/- 0.000\n",
        "Hop  3 100:  0.000 +/- 0.000\n",
        "\n",
        "Noise: 0.025\n",
        "SDM  3 10:  0.000 +/- 0.000\n",
        "Hop  3 10:  0.000 +/- 0.000\n",
        "\n",
        "SDM "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 25:  0.000 +/- 0.000\n",
        "Hop  3 25:  0.001 +/- 0.000\n",
        "\n",
        "SDM  3 50:  0.000 +/- 0.000\n",
        "Hop  3 50:  0.000 +/- 0.000\n",
        "\n",
        "SDM  3 100:  0.000 +/- 0.000\n",
        "Hop "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 100:  0.001 +/- 0.000\n",
        "\n",
        "Noise: 0.05\n",
        "SDM  3 10:  0.000 +/- 0.000\n",
        "Hop  3 10:  0.001 +/- 0.000\n",
        "\n",
        "SDM  3 25:  0.000 +/- 0.000\n",
        "Hop "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 25:  0.001 +/- 0.000\n",
        "\n",
        "SDM  3 50:  0.000 +/- 0.000\n",
        "Hop  3 50:  0.001 +/- 0.000\n",
        "\n",
        "SDM "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 100:  0.000 +/- 0.000\n",
        "Hop  3 100:  0.001 +/- 0.000\n",
        "\n",
        "Noise: 0.1\n",
        "SDM  3 10:  0.001 +/- 0.000\n",
        "Hop  3 10:  0.003 +/- 0.001\n",
        "\n",
        "SDM "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 25:  0.000 +/- 0.000\n",
        "Hop  3 25:  0.002 +/- 0.000\n",
        "\n",
        "SDM  3 50:  0.000 +/- 0.000\n",
        "Hop "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 50:  0.001 +/- 0.000\n",
        "\n",
        "SDM  3 100:  0.000 +/- 0.000\n",
        "Hop  3 100:  0.003 +/- 0.000\n",
        "\n",
        "Noise: 0.15\n",
        "SDM  3 10:  0.009 +/- 0.001\n",
        "Hop  3 10:  0.007 +/- 0.001\n",
        "\n",
        "SDM "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 25:  0.001 +/- 0.000\n",
        "Hop  3 25:  0.002 +/- 0.001\n",
        "\n",
        "SDM  3 50:  0.000 +/- 0.000\n",
        "Hop  3 50:  0.003 +/- 0.001\n",
        "\n",
        "SDM "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 100:  0.000 +/- 0.000\n",
        "Hop  3 100:  0.003 +/- 0.001\n",
        "\n",
        "Noise: 0.2\n",
        "SDM  3 10:  0.030 +/- 0.002\n",
        "Hop  3 10:  0.020 +/- 0.002\n",
        "\n",
        "SDM "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 25:  0.004 +/- 0.001\n",
        "Hop  3 25:  0.007 +/- 0.001\n",
        "\n",
        "SDM  3 50:  0.002 +/- 0.001\n",
        "Hop  3 50:  0.004 +/- 0.001\n",
        "\n",
        "SDM  3 100:  0.000 +/- 0.000\n",
        "Hop "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3 100:  0.004 +/- 0.001\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vmin = 0.97\n",
      "vmax = 1\n",
      "plt.clf()\n",
      "\n",
      "gs = plt.GridSpec(1, 3, width_ratios=[10, 10, 1])\n",
      "\n",
      "plt.subplot(gs[0])\n",
      "im = plt.imshow(\n",
      "    1-sdm_prototype, \n",
      "    cmap='gray', interpolation='nearest', \n",
      "    vmin=vmin, vmax=vmax,\n",
      "    origin='lower')\n",
      "plt.xticks(np.arange(prototype_k.size), prototype_k)\n",
      "plt.yticks(np.arange(noise.size), noise)\n",
      "plt.title(\"SDM (M=%d)\" % m)\n",
      "plt.xlabel(\"Exemplars\")\n",
      "plt.ylabel(\"Exemplar Percent Corruption\")\n",
      "\n",
      "plt.subplot(gs[1])\n",
      "plt.imshow(\n",
      "    1-hop_prototype, \n",
      "    cmap='gray', interpolation='nearest', \n",
      "    vmin=vmin, vmax=vmax,\n",
      "    origin='lower')\n",
      "plt.xticks(np.arange(prototype_k.size), prototype_k)\n",
      "plt.yticks(np.arange(noise.size), [])\n",
      "plt.title(\"Hopfield\")\n",
      "plt.xlabel(\"Exemplars\")\n",
      "\n",
      "sp = plt.subplot(gs[2])\n",
      "plt.colorbar(im, cax=sp)\n",
      "sp.set_ylabel(\"Prototype Accuracy\")\n",
      "\n",
      "plt.suptitle(\"Prototype Retrieval from Stored Exemplars\", fontsize=15)\n",
      "\n",
      "util.save(\"figures/prototype.svg\", width=8, height=6, f_close=False)\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Saving figure to 'figures/prototype.svg'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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mTZuGuLg4HD16FJ07d8aTJ09KFGtZjufmzZuFHqOVlVWB8+Dl1xcAtLS0CqzT1tYuUbza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\nQkRERE7pfwFGILxXgPle2gAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 114
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diff = hop_prototype-sdm_prototype\n",
      "diff = np.sign(diff)*(1.5**np.log(np.abs(diff)))\n",
      "diffmax = np.max(np.abs(diff))\n",
      "plt.clf()\n",
      "\n",
      "gs = plt.GridSpec(1, 2, width_ratios=[20, 1])\n",
      "\n",
      "plt.subplot(gs[0])\n",
      "im = plt.imshow(\n",
      "    diff,\n",
      "    cmap='RdBu', interpolation='nearest', \n",
      "    vmin=-diffmax, vmax=diffmax,\n",
      "    origin='lower')\n",
      "plt.xticks(np.arange(prototype_k.size), prototype_k)\n",
      "plt.yticks(np.arange(noise.size), [])\n",
      "plt.xlabel(\"Exemplars\")\n",
      "\n",
      "sp = plt.subplot(gs[1])\n",
      "cb = plt.colorbar(im, sp)\n",
      "cb.set_ticks([-diffmax, 0, diffmax])\n",
      "#sp.set_ticks([-diffmax, 0, diffmax])\n",
      "sp.set_yticklabels(['Hopfield better',\n",
      "\t\t    'No difference', \n",
      "\t\t    'SDM better'])\n",
      "\n",
      "plt.suptitle(\"Difference between Hopfield and SDM prototype retrieval\", fontsize=15)\n",
      "\n",
      "util.save(\"figures/prototype-diff.svg\", width=8, height=6, f_close=False)\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Saving figure to 'figures/prototype-diff.svg'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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p0KCBGTp0qPn888/d+xISEszGjRu95r/++uvNnDlzjDHGhIeHm6+//trcdNNN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\n"
      }
     ],
     "prompt_number": 115
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.io as io\n",
      "\n",
      "b = 20\n",
      "m = M[-1]\n",
      "nex = 9\n",
      "\n",
      "data = io.loadmat('numbers.mat')\n",
      "zero = data['zero']\n",
      "one = data['one']\n",
      "two = data['two']\n",
      "three = data['three']\n",
      "four = data['four']\n",
      "five = data['five']\n",
      "six = data['six']\n",
      "\n",
      "inputs = np.hstack([zero,one,two,three,four,five,six])\n",
      "\n",
      "vec = six.copy()\n",
      "cvecs = util.corrupt(vec * np.ones((n, nex), dtype='i4'), b)\n",
      "ex = util.corrupt(vec.copy(), b)\n",
      "\n",
      "mem1 = sdm.SDM(n, m, D)\n",
      "mem1.writeM(cvecs, cvecs)\n",
      "r1 = mem1.readM(ex)\n",
      "\n",
      "mem2 = hop.hopnet(cvecs)\n",
      "r2 = mem2.readM(ex, 1000)\n",
      "\n",
      "for i in xrange(nex):\n",
      "    plt.clf()\n",
      "    plt.imshow(cvecs[:, i].reshape((16, 16), order='F'),\n",
      "\t       cmap='gray', vmin=0, vmax=1, interpolation='nearest')\n",
      "    plt.xticks([], [])\n",
      "    plt.yticks([], [])\n",
      "    save(\"vi_ex%d\" % i)\n",
      "\n",
      "plt.clf()\n",
      "util.plot_io(ex.reshape((16, 16), order='F'),\n",
      "\t     r1.reshape((16, 16), order='F'))\n",
      "save(\"vi_sdm\")\n",
      "\n",
      "plt.clf()\n",
      "util.plot_io(ex.reshape((16, 16), order='F'),\n",
      "\t     1-r2.reshape((16, 16), order='F'))\n",
      "save(\"vi_hop\")\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Saving figure to './vi_ex0.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_ex1.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_ex2.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_ex3.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_ex4.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_ex5.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_ex6.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_ex7.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_ex8.png'... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done\n",
        "Saving figure to './vi_sdm.png'..."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " Done\n",
        "Saving figure to './vi_hop.png'..."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " Done\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.io as io\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import sdm as sdm\n",
      "from util import corrupt, plot_io, save\n",
      "\n",
      "#data = io.loadmat('sequencePatterns.mat')\n",
      "#face = data['face']\n",
      "#x = data['x']\n",
      "#hi = data['hi']\n",
      "#a = data['a']\n",
      "#b = data['b']\n",
      "#c = data['c']\n",
      "#d = data['d']\n",
      "#e = data['e']\n",
      "#f = data['f']\n",
      "#g = data['g']\n",
      "#h = data['h']\n",
      "#i = data['i']\n",
      "\n",
      "#inputs = np.hstack([face, x, hi, a, b, c, d, e, f, g, h, i])\n",
      "\n",
      "\n",
      "data = io.loadmat('numbers.mat')\n",
      "zero = data['zero']\n",
      "one = data['one']\n",
      "two = data['two']\n",
      "three = data['three']\n",
      "four = data['four']\n",
      "five = data['five']\n",
      "six = data['six']\n",
      "\n",
      "inputs = np.hstack([zero,one,two,three,four,five,six])\n",
      "\n",
      "\n",
      "\n",
      "#clean the input to be 0/1\n",
      "inputs = ((inputs + 1)/2).astype('i4')\n",
      "\n",
      "# length of input patterns, number of unique patterns\n",
      "lenPatterns, numPatterns = inputs.shape\n",
      "\n",
      "# figure size (sqrt(lenPatterns))\n",
      "figSize = (np.sqrt(lenPatterns)).astype('i4')\n",
      "\n",
      "# number of sequences ( this is similar to # of exemplars )\n",
      "numSequences = 10\n",
      "\n",
      "# percentage of bits to corrupt\n",
      "numCorrupt = 25\n",
      "\n",
      "\n",
      "# number of addresses in SDM\n",
      "numStorage = 10000\n",
      "\n",
      "# hamming radius\n",
      "D = 112\n",
      "\n",
      "\n",
      "reload(sdm)\n",
      "mem = sdm.SDM(lenPatterns, numStorage, D)\n",
      "print \"Addresses in hamming radius:\", mem._select(inputs).sum(axis=0)\n",
      "\n",
      "\n",
      "\n",
      "for curSeq in xrange(numSequences):\n",
      "    # store copy of inputs in addresses\n",
      "    addresses = inputs.copy()\n",
      "\n",
      "    # corrupt the patterns\n",
      "    for curPat in xrange(numPatterns):\n",
      "        a = addresses[:,curPat].copy()\n",
      "        d = corrupt(addresses[:, curPat], numCorrupt)\n",
      "        addresses[:, curPat] = d\n",
      "#        plt.figure(curPat)\n",
      "#        plot_io(a.reshape((figSize, figSize), order='F'), d.reshape((figSize,figSize), order='F'))\n",
      "\n",
      "\n",
      "    # write data to address curPat with address curPat+1\n",
      "    data = np.empty((lenPatterns, numPatterns)).astype('i4')\n",
      "    data[:, :-1] = addresses[:, 1:]\n",
      "    data[:, -1] = addresses[:, -1]\n",
      "        \n",
      "    mem.writeM(addresses, data)\n",
      "\n",
      "    # plot what we just wrote\n",
      "    for i in xrange(numPatterns):\n",
      "        plt.figure(50+curSeq)\n",
      "        plt.subplot(1,numPatterns,i+1)\n",
      "        plt.imshow((1-addresses[:,i]).reshape((figSize,figSize), order='F'),cmap='gray',interpolation='nearest')\n",
      "        plt.xticks([],[])\n",
      "        plt.yticks([],[])\n",
      "\n",
      "    figName=\"storedSeq\"+str(curSeq)\n",
      "    #save(figName, ext=\"png\", close=True, verbose=True)\n",
      "\n",
      "\n",
      "# now read sequentially with no noise used as input\n",
      "#addresses = inputs.copy()\n",
      "#for curPat in xrange(numPatterns):\n",
      "#    a = addresses[:,curPat].copy()\n",
      "#    d = mem.read(addresses[:,curPat]).reshape((figSize, figSize), order='F')\n",
      "#    plt.figure(numPatterns+curPat)\n",
      "#    plot_io(addresses[:,curPat].reshape((figSize, figSize), order='F'), d)\n",
      "\n",
      "\n",
      "\n",
      "#\n",
      "# read until converge, using retrieved data as the next address\n",
      "#\n",
      "# first initialize some things\n",
      "addresses = inputs.copy()\n",
      "lastTrial = np.zeros((lenPatterns,1))\n",
      "# just start with a particular corrupted pattern someone in the sequence\n",
      "d = corrupt(addresses[:,0],25)\n",
      "i=0\n",
      "startAddress = d\n",
      "\n",
      "# loop till convergence\n",
      "while (((d == lastTrial).all() == False)):\n",
      "    # save lastTrial\n",
      "    lastTrial = d\n",
      "    i+=1   \n",
      " \n",
      "    # use lastTrial as the address to read from\n",
      "    d = mem.read(lastTrial)\n",
      "#    plt.figure(i)\n",
      "#    plot_io(lastTrial.reshape((figSize, figSize), order='F'),d.reshape((figSize, figSize), order='F'))\n",
      "\n",
      "\n",
      "# how long this look to converge\n",
      "numTrialsTillConverged = i\n",
      "\n",
      "d=startAddress\n",
      "for i in xrange(numTrialsTillConverged):\n",
      "\n",
      "    plt.figure(0)\n",
      "    plt.subplot(1,numTrialsTillConverged,i+1)\n",
      "    plt.imshow((1-d).reshape((figSize,figSize), order='F'),cmap='gray',interpolation='nearest')\n",
      "    plt.xticks([],[])\n",
      "    plt.yticks([],[])\n",
      "\n",
      "    lastTrial = d\n",
      "    d=mem.read(lastTrial)\n",
      "\n",
      "\n",
      "figName=\"finalSeq\"\n",
      "#save(figName, ext=\"png\", close=True, verbose=True)\n",
      "    \n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Addresses in hamming radius: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[281 244 241 243 246 273 266]\n"
       ]
      },
      {
       "output_type": "display_data",
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      },
      {
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      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAAA3CAYAAACvkJk/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAEIUugAgRKELAEIUugAgRKELAEJ/AToZQrWtoVtHAAAAAElFTkSuQmCC\n"
      },
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}