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     "cell_type": "markdown",
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     "source": [
      "W define our hypergraph: \n",
      "$H = \\{V, E\\}$\n",
      "\n",
      "\n",
      "\n",
      "In this notebook I introduce two models of hypergraph traversal.\n",
      "\n",
      "First model assumes that we start with the node and then choose one of the hyperedges\n",
      "from hyperedges which contain our node. From node we have the same probability to go to all nodes which\n",
      "are contained in hyperedge.\n",
      "\n",
      "So for example traversal may look like:\n",
      "- start in node `1`\n",
      "- go to hyperedge `{1, 2, 4}`\n",
      "- choose one of nodes `1, 2, 4` -> `4`\n",
      "\n",
      "and so on.\n",
      "\n",
      "Second model is a bit different. It assumes that the basic unit of traversal is hyperedge.\n",
      "\n",
      "So we can traverse from one hyperedge to another hyperedge having a probability of traversal $j \\rightarrow k$ dependent on nodes that are in both hyperedges.\n",
      "\n",
      "Let's begin with first model \n",
      "\n",
      "#Traversing on nodes\n",
      "\n",
      "\n",
      "$C$ and $D$ are two matricies of sizes (m, n) and (n, m) where:\n",
      "- m - number of nodes\n",
      "- n - number of hyperedges\n",
      "\n",
      "We can define probabilities of travering from any node to any other node $A$ by\n",
      "product of the two.\n",
      "\n",
      "C - probability of going from the node `j` to edge `i`:\n",
      "\n",
      "$C(j \\rightarrow i) = \\frac{I_{c_j}(i)}{\\|\\{E_k :\\  V_j \\in E_k \\}\\|}$\n",
      "\n",
      "where:\n",
      "\n",
      "$I_{c_j}(i)$ - is edge i in set of edges that j is in.\n",
      "\n",
      "D - probability of going from edge `i` to node `k`:\n",
      "\n",
      "$D(i \\rightarrow k) = \\frac{I_{E_i}(k)} {\\| E_i \\|}$\n",
      "\n",
      "$I_{E_i}(k)$ - is k in set of nodes in edge E_i ?\n",
      "\n",
      "$A = CD$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Probability of going from node j to k\n",
      "\n",
      "$P(j \\rightarrow k) = \\sum\\limits_{i=1}^{n}{\\frac{I_{c_j}(i)}{\\|\\{E_w :\\  V_j \\in E_w \\}\\|}}\\ \\frac{I_{E_i}(k)}{|E_i|}$\n",
      "\n",
      "It can be rewritten as:\n",
      "\n",
      "$P(j \\rightarrow k) = \\frac{\\gamma(j \\rightarrow k)} {\\Phi_k}$\n",
      "\n",
      "Where \n",
      "\n",
      "${\\Phi_k}$ - is a norming factor for k - sum of all possible ways to k.\n",
      "\n",
      "$\\Phi_k = \\sum\\limits_{j=1}^{m} \\gamma(j \\rightarrow k)$ \n",
      "\n",
      "\n",
      "This should result from ergodicity of probability distribution of traversal.\n",
      "\n",
      "$\\sum\\limits_{j=1}^{m}P(j \\rightarrow k) \\pi_j = \\pi_k$\n",
      "\n",
      "$\\nu_n = \\frac{\\pi_n}{\\Phi_n}$\n",
      "\n",
      "$\\sum\\limits_{j=1}^{m} \\frac{\\gamma(j \\rightarrow k)} {\\Phi_k} \\pi_j = \\pi_k =  \\Phi_n \\frac{\\pi_n}{\\Phi_n}$\n",
      "$\\sum\\limits_{j=1}^{m} \\gamma(j \\rightarrow k) \\nu_j  = \\Phi_k \\nu_k = \\sum\\limits_{l=1}^{m} \\gamma(l \\rightarrow k) \\nu_k = \\sum\\limits_{j=1}^{m} \\gamma(j \\rightarrow k) \\nu_k$\n",
      "\n",
      "\n",
      "\n",
      "$\\sum\\limits_{j=1}^{m} (\\gamma(j \\rightarrow k) \\nu_j - \\gamma(k \\rightarrow j) \\nu_k )= 0$\n",
      "\n",
      "In special case:\n",
      "\n",
      "$\\gamma(j \\rightarrow k) \\nu_j = \\gamma(k \\rightarrow j) \\nu_k$\n",
      "\n",
      "$\\nu_j = \\frac{\\gamma(k \\rightarrow j)}{\\gamma(j \\rightarrow k)} \\nu_k$\n",
      "\n",
      "$\\gamma(j \\rightarrow k)  = \\gamma(k \\rightarrow j) $\n",
      "\n",
      "$\\pi_j = \\frac{\\gamma(k \\rightarrow j)}{\\gamma(j \\rightarrow k)} \\frac{\\Phi_j}{\\Phi_k}\\pi_k =  \\frac{\\Phi_j}{\\Phi_k} \\pi_k $\n",
      "\n",
      "\n",
      "$\\sum\\limits_{i=1}^{m} \\pi_i = 1 \\Rightarrow (\\sum\\limits_{i=1}^{m} \\Phi_i) \\frac{\\pi_k}{\\Phi_k} = 1$\n",
      "\n",
      "$\\pi_k = \\frac{\\Phi_k}{\\sum\\limits_{i=1}^{m}\\Phi_i} =  \\frac{\\|\\{E_p :\\  V_k \\in E_p \\}\\|} {\\sum\\limits_{i=1}^{m} \\|\\{E_p :\\  V_i \\in E_p \\}\\|}$\n",
      "\n",
      "The code:\n",
      "\n",
      "```\n",
      "def analytical_hypergraph_nodes(hyper_graph):\n",
      "    \"\"\"Predict probabilities of being in a node in a hypergraph\n",
      "\n",
      "    Parameters:\n",
      "        hyper_graph: instance of `hypergraph`, should have `nodes` and `hyper_edges`\n",
      "            methods implemented\n",
      "\n",
      "    Predict using bipartite model from perspective of nodes.\n",
      "    \"\"\"\n",
      "    nodes = hyper_graph.nodes()\n",
      "    hyper_edges = hyper_graph.hyper_edges()\n",
      "    all_nodes = []\n",
      "    for hyperedge in hyper_edges:\n",
      "        all_nodes += hyperedge\n",
      "\n",
      "    c = Counter(all_nodes)\n",
      "    for node in nodes:\n",
      "        if node not in all_nodes:\n",
      "            c[node] = 0\n",
      "\n",
      "    xs, ys = zip(*c.items())\n",
      "\n",
      "    sum_of_ys = sum(ys)\n",
      "    ys = [y / sum_of_ys for y in ys]\n",
      "\n",
      "    return xs, ys\n",
      "    \n",
      "```"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Traversing on hyperedges\n",
      "\n",
      "###probability of going from hyper_edge j to k:\n",
      "\n",
      "$P(j \\rightarrow k) = \\sum\\limits_{i=1}^{n}{ \\frac{I_{E_j}(i)}{|E_j|}  \\frac{I_{c_i}(k)}{\\|\\{E_z :\\  V_i \\in E_z \\}\\|}}\\ $\n",
      "\n",
      "$P(j \\rightarrow k) = \\frac{\\gamma(j \\rightarrow k)} {\\Phi_k}$\n",
      "\n",
      "Summing on nodes\n",
      "\n",
      "$\\Phi_k = \\sum\\limits_{j=1}^{n} \\gamma(j \\rightarrow k)$ \n",
      "\n",
      "And by analogy to similar computation on nodes:\n",
      "\n",
      "$\\pi_j = \\frac{\\gamma(k \\rightarrow j)}{\\gamma(j \\rightarrow k)} \\frac{\\Phi_j}{\\Phi_k}\\pi_k =  \\frac{\\Phi_j}{\\Phi_k} \\pi_k $\n",
      "\n",
      "$\\sum\\limits_{i=1}^{m} \\pi_i = 1 \\Rightarrow (\\sum\\limits_{i=1}^{m} \\Phi_i) \\frac{\\pi_k}{\\Phi_k} = 1$\n",
      "\n",
      "\n",
      "###Resulting probability\n",
      "\n",
      "$\\pi_k = \\frac{\\|\\{V_i :\\  V_i \\in E_k \\} \\|} {\\sum\\limits_{i=1}^{n}{ \\|\\{V_z :\\  V_Z \\in E_i \\} \\|}   } $\n",
      "\n",
      "\n",
      "```\n",
      "def analytical_hypergraph_edges(hyper_graph):\n",
      "    \"\"\"Predict probabilities for edge model.\n",
      "\n",
      "    :param hyper_graph to predict diffusion on :\n",
      "    :return: list of probabilities of ergodic state\n",
      "    \"\"\"\n",
      "    phis = []\n",
      "    all_phis = 0\n",
      "    for edge in hyper_graph.hyper_edges():\n",
      "        edge_cardinality = len(edge)\n",
      "        phis.append(edge_cardinality)\n",
      "        all_phis += edge_cardinality\n",
      "\n",
      "    pis = [phi / all_phis for phi in phis]\n",
      "    return pis\n",
      "```"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Below are numerical solutions simulations based on former models.\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# import generators\n",
      "from hypergraph import generators\n",
      "\n",
      "# generic_hypergraph creates hypergraph with 6 nodes, with hyperedges described by tuples\n",
      "HG = generators.generic_hypergraph(6, ((3, 4), (4, 3), (5, 1)))\n",
      "\n",
      "# we can print out how the generated hypergraph looks like\n",
      "print(\"Nodes:\", HG.nodes())\n",
      "print(\"Hyperedges:\", HG.hyper_edges())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Nodes: [1, 2, 3, 4, 5, 6]\n",
        "Hyperedges: [{1, 4, 5}, {2, 3, 4}, {1, 2, 5}, {1, 3, 4}, {1, 2, 5, 6}, {2, 3, 5, 6}, {1, 2, 3, 6}, {2, 3, 4, 5, 6}]\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But let's concentrate on a specific example:\n",
      "\n",
      "![Imgur](http://i.imgur.com/HXlFjoW.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's create the hypergraph from the image above."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from hypergraph.hypergraph_models import HyperGraph\n",
      "\n",
      "HG = HyperGraph()\n",
      "\n",
      "HG.add_nodes_from(range(1, 14))\n",
      "HG.add_edges_from([{1, 10, 8}, {8, 13, 11, 9, 2}, {9, 7, 6, 12, 5, 2}, {2, 5, 3, 4}])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can later represent it in different ways, such as \"custom\" representation and bipartite graph."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np                                                                                                                                                                      \n",
      "import networkx as nx\n",
      "from matplotlib import pyplot as plt \n",
      "\n",
      "from hypergraph.converters import (convert_to_nx_bipartite_graph,\n",
      "                                   convert_to_custom_hyper_G)\n",
      "from hypergraph import utils\n",
      "\n",
      "\n",
      "G = convert_to_nx_bipartite_graph(HG.nodes(), HG.hyper_edges())\n",
      "\n",
      "utils.plot_bipartite_graph(G, *utils.hypergraph_to_bipartite_parts(G))\n",
      "\n",
      "hyper_G = convert_to_custom_hyper_G(HG.nodes(), HG.hyper_edges())\n",
      "\n",
      "plt.figure(figsize=(6, 6)) \n",
      "nx.draw(hyper_G,\n",
      "        node_size=3000, cmap=plt.cm.Blues, alpha=0.6)\n",
      "\n",
      "plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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X33qRmBLDMG/g1vgt/vuP/jvFOcV85PRHnnwBA6TWpWKybi4QzWYzJSUl1NfX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DEtGAyi+5/dGPr+0v3c6xrrUHW0ChVPVkx4u0PaEJb/eTk+Kf4EskmGbbYNCfdH38f9SvZ5PBx5\nia6YYRjoPNgJvU1MDdbRWGZYkPgHVrghupH0NfWh90jvpG8nbkUcYtLFDO5PE8dbwYKZTCY4M52X\n/XRwdBsBnJlOhirRDcaR5oD51sntjGFONcOewgH4ryUG6ySIvS0WVs/kDY5v/60dzjTnpK2fiCaH\nbJahLFIuq/dAVKyAskh8nVeaGAbrJJAkCa4FLpjixB9e0zQTlN8pbK0S3aDsSXbEeCfnNm3MwhjY\nE9lavdYYrJPE6rIiLicOkiIuAE1uE9w5blhiOCAE0Y1KkiQocxU45ol98NDhdcB1l4sX3dcBPrw0\nydROFT8d/wl655U9zCQny3AvdcMWbxP0zojoWjIMA71f9aL/i/6ROsuXwww4FzgRNy+OoXqdYLBe\nBZqqwX/Kj4GvBoCJ1jo3A867nYi9KzastiIR3fiCwSAG2gbgP+mH3jHxdJWny3AtdsH+GztD9TrC\nYL1KgsEg1E4V6n9VqA3quFVwpBgJ9tvtcGQ4YJtm44eG6CamDWroP9sPtVGF9j9t7H7wJsB8qxkO\njwOOmQ5ecF+HGKxXWTAYhNavYahzCJpPg/aTBmNouBlrsplgdpthdpthu8UG2S4zUImmkAsX4IGe\nAHSfDr1PR9AIQjJJkGNlyG4ZlgQL7IlsoV7PGKzX2MWHnx8UIroYzw83JgYrERGRQOxuQ0REJBCD\nlYiISCAGKxERkUAMViIiIoEYrERERAIxWImIiARisBIREQnEYCUiIhKIwUpERCQQg5WIiEggBisR\nEZFADFYiIiKBGKxEREQCMViJiIgEYrASEREJxGAlIiISiMFKREQkEIOViIhIIAYrERGRQAxWIiIi\ngRisREREAjFYiYiIBGKwEhERCcRgJSIiEojBSkREJBCDlYiISCAGKxERkUAMViIiIoEYrERERAIx\nWImIiARisBIREQnEYCUiIhKIwUpERCQQg5WIiEggBisREZFADFYiIiKBGKxEREQCMViJiIgEYrAS\nEREJxGAlIiISiMFKREQkEIOViIhIIAYrERGRQAxWIiIigRisREREAjFYiYiIBGKwEhERCcRgJSIi\nEuj/T4/88YTi4dYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a93e9e8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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m3DkcPXoUWVlZt32eWCbTtm2wpaVxWNrFent7YbFY0Nra2l+y1/98/f9dXV0I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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a8e29b0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Markov Chain Transition matrices"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from hypergraph.markov_diffusion import create_markov_matrix_model_nodes\n",
      "from hypergraph.markov_diffusion import create_markov_matrix_model_hyper_edges"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "```\n",
      "def create_markov_matrix_model_nodes(hyper_graph):\n",
      "\n",
      "    # create N x N matrix with zeroes\n",
      "    number_of_nodes = len(hyper_graph.nodes())\n",
      "    markov_matrix = np.zeros((number_of_nodes, number_of_nodes))\n",
      "\n",
      "    node_hyper_edges = populate_node_hyperedges(hyper_graph)\n",
      "\n",
      "    # fill transition matrix with all possible ways to get from V_i to V_j\n",
      "    for node in hyper_graph.nodes():\n",
      "        for hyper_edge in node_hyper_edges[node]:\n",
      "            for node2 in hyper_edge:\n",
      "                markov_matrix[node - 1, node2 - 1] += 1 / len(hyper_edge) / len(node_hyper_edges[node])\n",
      "\n",
      "    return markov_matrix\n",
      "\n",
      "\n",
      "def create_markov_matrix_model_hyper_edges(hyper_graph):\n",
      "    node_edges = np.zeros((len(hyper_graph.nodes()), len(hyper_graph.hyper_edges())))\n",
      "\n",
      "    for node in hyper_graph.nodes():\n",
      "        node_edges[node - 1] = np.array([node in edge for edge in hyper_graph.hyper_edges()])\n",
      "\n",
      "    number_of_edges = len(hyper_graph.hyper_edges())\n",
      "    markov_matrix = np.zeros((number_of_edges, number_of_edges))\n",
      "\n",
      "    for i, edge in enumerate(hyper_graph.hyper_edges()):\n",
      "        for node in edge:\n",
      "            for j, contained in enumerate(node_edges[node-1]):\n",
      "                markov_matrix[i, j] += contained / len(edge) / sum([edge for edge in node_edges[node - 1] if edge])\n",
      "\n",
      "    return markov_matrix\n",
      "```"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nodes_model = create_markov_matrix_model_nodes(HG)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "edges_model = create_markov_matrix_model_hyper_edges(HG)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "\n",
      "def plot_transition_matrix(matrix):\n",
      "    \"\"\"Helper function for plotting transition matrix as gray grid.\n",
      "    \"\"\"\n",
      "    \n",
      "    conf_arr = matrix\n",
      "\n",
      "    norm_conf = []\n",
      "    for i in conf_arr:\n",
      "        a = 0\n",
      "        tmp_arr = []\n",
      "        a = sum(i, 0)\n",
      "        for j in i:\n",
      "            tmp_arr.append(float(j)/float(a))\n",
      "        norm_conf.append(tmp_arr)\n",
      "\n",
      "\n",
      "    fig = plt.figure(figsize=(12, 10))\n",
      "    plt.clf()\n",
      "    ax = fig.add_subplot(111)\n",
      "    ax.set_aspect(1)\n",
      "    res = ax.imshow(np.array(norm_conf), cmap=plt.cm.gray, \n",
      "                    interpolation='nearest')\n",
      "\n",
      "    width = len(conf_arr)\n",
      "    height = len(conf_arr[0])\n",
      "\n",
      "    for x in range(width):\n",
      "        for y in range(height):\n",
      "            ax.annotate(\"%.2f\" % (conf_arr[x][y]), xy=(y, x), \n",
      "                        horizontalalignment='center',\n",
      "                        verticalalignment='center')\n",
      "\n",
      "    cb = fig.colorbar(res)\n",
      "    index = range(1, len(matrix) + 1)\n",
      "    plt.xticks(range(width), index)\n",
      "    plt.yticks(range(height), index)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# So, what is this exactly?\n",
      "\n",
      "When I'm traversing from one node to another from one hyperedge to another, I can model it as a Markov Chain, because history is not\n",
      "important, when I choose (randomly) where I would do next.\n",
      "\n",
      "How do I compute it?\n",
      "\n",
      "So the most important thing here is generation of corresponding Markov Chain.\n",
      "Markov chain can be further represented as \n",
      "\n",
      "In this course, we will only consider finite Markov chains which are also time-homogenous.\n",
      "In this case, it is convenient to store all information about the transition in a Markov chain in\n",
      "the so-called transition matrix P which is a |\u2126| \u00d7 |\u2126| matrix defined by:\n",
      "\n",
      "$ P_{x,y} := Pr [ X1 = y | X0 = x ]$\n",
      "\n",
      "Below there are examples of transition matrices:\n",
      "\n",
      "How are they computed?\n",
      "\n",
      "The lighter is the field, the bigger probability."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"Nodes model\")\n",
      "plot_transition_matrix(nodes_model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Nodes model\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dX7TlpqYm6urqQuV33nmHKVOmDKn/3HPP8fDDD/PFL36RvLy8sMeLi4spKChg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\nUaNGUVxcTF5eHjNmzOjSYAsLCxk/fjyNjY09HufDDz+kuLiYkSNHpjt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4zO8gOrPW1hpj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\nREREREREpCf/H7LI6RyYqPLlAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a89ba20>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"Edges model\")\n",
      "plot_transition_matrix(edges_model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Edges model\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mEC5kBhGmKe0MHjlyZCpPhxj46Ec/WuwpREZXV5dqa2uLPY1I2LJlS7GnEBm7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\n2q21ziViiWXiKWWM+b6kn0m6yBjTaoz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       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a718cf8>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Comparison between atomistic simulation, raising matrix to the Nth power and analytic prediction for both models."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "from functools import partial\n",
      "from matplotlib import pyplot as plt\n",
      "\n",
      "from numpy import linalg as LA\n",
      "\n",
      "from hypergraph import generators\n",
      "from hypergraph.analytical import prediction\n",
      "from hypergraph.diffusion_engine import DiffusionEngine\n",
      "from hypergraph import utils\n",
      "from hypergraph.markov_diffusion import create_markov_matrix_model_nodes\n",
      "from hypergraph.markov_diffusion import create_markov_matrix_model_hyper_edges\n",
      "\n",
      "\n",
      "# Define model's definitions\n",
      "ALL_MODELS = {\n",
      "    \"node\": {\n",
      "        \"analytical\": partial(prediction, model='hypergraph_nodes'),\n",
      "        \"numerical\": create_markov_matrix_model_nodes,\n",
      "        \"name\": \"node\",\n",
      "    },\n",
      "    \"hyperedges\": {\n",
      "        \"analytical\": partial(prediction, model='hypergraph_edges'),\n",
      "        \"numerical\": create_markov_matrix_model_hyper_edges,\n",
      "        \"name\": \"hyperedges\",\n",
      "    }\n",
      "}\n",
      "\n",
      "# Constants for atomistic simulation\n",
      "t_max = 1000000\n",
      "\n",
      "def slugify(text):\n",
      "    return text.lower().replace(' ', '_')\n",
      "\n",
      "\n",
      "import pykov\n",
      "from collections import Counter\n",
      "\n",
      "\n",
      "def transition_matrix_to_pykov_chain(matrix):\n",
      "    chain = pykov.Chain()\n",
      "    \n",
      "    for i, row in enumerate(matrix):\n",
      "        for j, column in enumerate(row):\n",
      "            chain[(i, j)] = column\n",
      "    return chain\n",
      "\n",
      "def atomistic_with_engine(markov_matrix):\n",
      "    engine = DiffusionEngine(markov_matrix)\n",
      "\n",
      "    frequencies, states = engine.simulate(t_max)\n",
      "\n",
      "    connected_elements = [freq[0] + 1 for freq in frequencies]\n",
      "\n",
      "    if len(frequencies) < len(markov_matrix):\n",
      "        missing_nodes = set(HG.nodes()) - set(connected_elements)\n",
      "        for missing_node in missing_nodes:\n",
      "            frequencies.append((missing_node, 0))\n",
      "\n",
      "    frequencies = [(node, frequency) for node, frequency in frequencies]\n",
      "    frequencies.sort(key=lambda x: x[0])\n",
      "    xs, ys = zip(*frequencies)\n",
      "\n",
      "    ys = np.array(ys, dtype='float')\n",
      "    ys /= sum(ys)\n",
      "    return xs, ys\n",
      "\n",
      "\n",
      "def atomistic_with_pykov(markov_matrix):\n",
      "    chain = transition_matrix_to_pykov_chain(markov_matrix)\n",
      "    pykov_chain = pykov.Chain(chain)\n",
      "    steps = 1000000\n",
      "    \n",
      "    states = pykov_chain.walk(steps)\n",
      "    freqs = Counter(states)\n",
      "    for x in range(len(markov_matrix)):\n",
      "        if x not in freqs:\n",
      "            freqs = 0\n",
      "        else:\n",
      "            freqs[x] /= steps\n",
      "    xs, ys = zip(*freqs.items())        \n",
      "\n",
      "    return xs, ys\n",
      "\n",
      "\n",
      "def show_models(HG):\n",
      "    \n",
      "    def show_model(model, title):\n",
      "        markov_matrix = model[\"numerical\"](HG)\n",
      "        xs, ys = atomistic_with_engine(markov_matrix)\n",
      "\n",
      "        width = 0.2  \n",
      "\n",
      "        ys_prediction = model[\"analytical\"](HG)\n",
      "\n",
      "        plt.figure(figsize=(10, 8))\n",
      "        plt.bar(xs, ys, width=width, color='crimson', label='Atomistic')\n",
      "        freqs_matrix = LA.matrix_power(markov_matrix, 40)[0]\n",
      "        plt.bar(np.array(xs) + width, freqs_matrix, width=width, label='Transition matrix to power N')\n",
      "\n",
      "        plt.bar(np.array(xs) + 2 * width, ys_prediction, width=width, color='#44de44', label='Analytical')\n",
      "        plt.legend(loc=0)\n",
      "        plt.title(title)\n",
      "        plt.savefig('../figures/%s.png' % slugify(title))\n",
      "        plt.savefig('../figures/%s.eps' % slugify(title))\n",
      "        \n",
      "    show_model(ALL_MODELS[\"node\"], 'Comparison of results for node model')\n",
      "    show_model(ALL_MODELS[\"hyperedges\"], 'Comparison of results for hyperedge model')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HG = HyperGraph()\n",
      "\n",
      "HG.add_nodes_from(range(1, 14))\n",
      "HG.add_edges_from([{1, 10, 8}, {8, 13, 11, 9, 2}, {9, 7, 6, 12, 5, 2}, {2, 5, 3, 4}])\n",
      "\n",
      "show_models(HG)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Pb5H5h27cuHG67LLLNGDAAPXo0UNXXHHFbn9U0/dJv9Kzfv163XDDDVq9erXa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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a1e9390>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mzNBFF11U5TSh2/7btGlT4csR69atU+3atSskv7G+/fZbfffdd9HltWvXqnXr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\n0gsAAAAAAAAAAAAAAAAAAAAAAAD81wcdwuhjhSQBkgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a8a2550>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HG = generators.generic_hypergraph(22, ((3, 8), (4, 4), (5, 5), (6, 8)))\n",
      "show_models(HG)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XX+SGG25g27ZtXH755Rw8eJCLL7446af+unbtSocOHTjllFM45phjePTRR+nX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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a2a76d8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lS5dq3759Ovjgg9W4ceOEn+Rr27at1q1bp7KysoTjjho1SjNmzNBnn32m3bt3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\nZYxpLK/gesZaOytyMc8/R8Tk92xlfpk+/xpC0RX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       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a381780>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(HG.hyper_edges())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[{18, 21, 6}, {2, 6, 14}, {10, 18, 15}, {2, 21, 14}, {17, 3, 20}, {17, 18, 22}, {2, 12, 20}, {2, 19, 13}, {17, 20, 5, 13}, {11, 12, 20, 7}, {10, 4, 21, 6}, {1, 18, 12, 21}, {20, 4, 21, 5, 12}, {10, 18, 20, 22, 7}, {8, 16, 11, 13, 14}, {7, 4, 21, 5, 14}, {16, 9, 18, 3, 7}, {1, 19, 20, 6, 22, 9}, {1, 19, 20, 5, 7, 10}, {16, 17, 4, 8, 10, 15}, {16, 19, 20, 7, 13, 14}, {17, 19, 4, 20, 8, 14}, {17, 3, 20, 21, 7, 8}, {1, 19, 20, 22, 9, 12}, {2, 19, 4, 5, 22, 12}]\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HG = generators.generic_hypergraph(36, ((3, 10), (4, 14), (5, 15), (6, 11)))\n",
      "show_models(HG)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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t2bNHY8aMic/VkqQhQ4Zo4sSJGj58uCorK/XOO+/U+vrVj91+++3q27evpk6d\nKkl67LHHNHbsWJ155pkaMGBAje0OPvhgXX/99TrnnHNUXl6u559/XpdeeqmKi4t13nnnac+ePfrO\nd75T57f+evTooUMPPVRHH320Dj74YN13330aNMjrg3fffbdmzZql4cOHq127drrssst0ySWXxLc9\n9dRT9cILL8SvbJ122ml6+OGHaxRd06ZNU1VVlS644AIVFRWpe/fumjhxYjyndAqnxHU6deqka665\nRrfffnvK7Vo65qLYyMVGLjZyCUZkfgWuz81RgTA19s1bmwLvKwA4MA25OSrDiwBaNOai2MjFRi42\ncgkGRReQBuZFAQAOVGQ+SRheBMLD+woADgzDiwAAABFF0QWgRWMuio1cbORiI5dgUHQBAACEgKIL\nQIvG/YVs5GIjFxu5BIOiCwAAIAQUXRE1d+5cTZs2rUHbLlu2TCeffPIBt+HYY4/VX//61wN+HbRM\nFQXFKs9fqfL8laooKG7q5tSKuSg2crGRi41cgtEs/wzQlootKqksabTX79amm3pm9qzXNt/97ne1\natUqffLJJzrooOD/jFBdunbtqvfff1/9+/eXJJ1yyinKz88PpA3cnwq1qSzaptIpsyVJnZ6+S5m5\nvVJsAQCtW7MsukoqSzRn15xGe/1bO95ar6KroKBAK1asUE5OjpYsWaJx48YdcBvq8welG7I+0Fow\nF8VGLjZysZFLMBheDMCCBQs0atQoXXTRRVqwYEH88RkzZmjmzJm6+OKLlZubq7PPPlufffZZ/Pmf\n/exnOuaYY9SvXz+dddZZWr58eY3Xrb7KNGnSJP3mN7+p8dzIkSP1yiuv6Pzzz5cknX766crNzdWi\nRYuUl5enb33rW/F1N23apO9///saMmSIBg0apFmzZkmSNmzYoHHjxmnQoEEaPHiwrrzySu3cuTPQ\nbNA6bOnaTR8WlurDwlJt+KZQq8pXaVX5Km2p2NLUTQMarGjnHvo0AkXRFYCFCxdqwoQJGj9+vN56\n6y2VlOwf+vzjH/+oWbNmacOGDRo4cKDuvPPO+HPHH3+83n77bW3YsEEXXHCBfvCDH2jv3r3x56uv\nXk2ePFl/+MMf4o9//PHHKi4u1r//+7/r5ZdfliS9/fbbKigo0Pjx42u0raKiQpMnT1Zubq4+/PBD\nrVq1ShMmTIg/f/3112vNmjVavny5Nm/erLlz5wYbDlqFkooMzVy8TjMXr9PWCu9K9Jxdcxp1GkC6\nmItiIxfhu4/tAAAgAElEQVRbYi5by/ZGsk83BfpLMCi6DtDy5ctVVFSkMWPG6PDDD9cRRxwh13Xj\nz59//vk67rjjlJmZqQsvvFArV66MP+c4jg499FC1adNGM2bM0J49e7Ru3TrfPsaMGaNPP/1UGzZs\nkOQVeRMnTlRWVurR4ffff19btmzR7bffrg4dOqhdu3YaMWKEJGnAgAEaNWqU2rZtq65du+qqq67S\nO++8c6CRAAAAA0XXAXruued05plnqlOnTpKkcePG1Rhi7N69e/zfHTp00K5du+LLDz30kEaMGKH+\n/ftrwIAB2rlzp7744gvfPtq3b6/x48dr4cKFqqqq0gsvvKCLLroorfZt3rxZffv2VZs2/lO9detW\n/fCHP9TQoUPVr18/XXXVVdq+fXvaxw40B8xFsZGLjVxs5BKMZjmRPiq+/vprLVq0SFVVVTrqqKMk\nSXv27NHOnTu1atWqOrddtmyZ5s2bp0WLFsW3HThwYK0T4i+++GJNnz5dJ598sg4++GCdcMIJabWx\nT58+2rRpkyoqKpSZmVnjuTvuuEOZmZl65513lJ2drVdeeSU+3wsAAASLK10HYPHixcrKytKyZcu0\ndOlSLV26VMuXL9eIESNqXO2ylJWVKSsrS127dtXevXt1zz33qLS0tNb1TzrpJGVkZOiWW27RpEmT\najzXo0eP+NBjsuOPP149e/bUnDlztHv3bn3zzTfx20ns2rVLBx98sDp16qTCwkI99NBD9UwAiD7m\notjIxUYuNnIJRrO80tWtTTfd2vHWRn39dCxYsECXXHKJ+vTpU+PxH/3oR7rpppt0xhln+O5zVb38\nne98R2eddZZOPPFEdezYUdOmTVNOTk6N9ZK3nTRpkn7xi1/o2WefrfH4rFmzNGPGDH399dd64IEH\n1K1bt/i2mZmZmj9/vm666SYNGzZMGRkZuvDCC3XyySfrxhtv1PTp09W/f38NHDhQjuPo0UcfTS8k\nAGiBBhx0iMrzvbm3VT0Oa+LWoKWJzJ0v33jjjarhw4f7Hi8sLNRhh9HxJW8C/X//93/rlVdeaeqm\noJkL4n1Vnr8yfnPUgpce141vF0mS7picqXvLvW/p3trxVg1tO/TAGguEyOrX9GlYVqxYodGjR9er\njmJ4sZnYvXu3nnjiCV122WVN3RQAANAAFF3NwJtvvqkjjjhCvXr10oUXXtjUzQGaFeai2MjFtmPH\njqZuQiTRX4LRLOd0tTbf+c53tHHjxqZuBgAAOABc6QLQonF/IRu52LKzs5u6CZFEfwkGRRcAAEAI\nIl90tWvXTl988UWtNw0FkL6qqip98cUXateuXVM3JTTMRbGRi405XTb6SzAiP6era9euKisrU2Fh\noe++Va3Bjh07uNxtIBdbqlyqqqqUnZ2tQw45JMRWAQCkZlB0SdIhhxzSaj8kuEeZjVxs5OLHXBQb\nudiys7NV+98Gab3oL8GI/PAiAABAS0DRFXGMo9vIxUYufmRiIxcbc7ps9JdgpBxedBxnjKQHJGVK\nesJ13buNdR6UdI6k3ZKmuq77QezxzyTtlFQhqdx13ZOCazoAAEDzUeeVLsdxMiXNkzRG0tGSJjuO\nc1TSOudKGuS67mBJV0h6JOHpKklnuK57HAVXwzCObiMXG7n4kYmNXGx8QcdGfwlGquHFkyStc133\nM9d1yyUtkDQuaZ2xkp6SJNd18yUd6jhOz4TnW99XDgEAAJKkKrr6SEr8+zObYo+lu06VpDccx3nP\ncZz/dyANba0YR7eRi41c/MjERi425nTZ6C/BSFV0pXtH0tquZo10Xfc4efO9ZjiO8691vUjiSc3L\ny2OZ5VqXV65cGan2tMblxA+nffv2qS5RaC/LNZdXrlwZqfZEaTlZcv9u6vbRX6K1XB91Dv05jjNC\n0m2u646JLd8kqTJxMr3jOI9K+ovrugtiy59IGuW67pak17pVUpnruvda+3rjjTeqhg8f3qCDABC+\n8vyVKp0yW5JU8NLjuvHtIknSHZMzdW/5nZKkWzveqqFthzZZG4H6svo1fRqWFStWaPTo0fWaQpWV\n4vn3JA12HKe/pEJJkyRNTlrnRUlXS1oQK9K+cl13i+M4B0vKdF231HGcjpL+TdKc+jQOAACgpahz\neNF13X3yCqpXJa2WtNB13TWO41zpOM6VsXUWS1rvOM46SY9Jmh7bvJektx3H+YekfEkvu677WiMd\nR4vV0EuYLR252MjFj0xs5GJjTpeN/hKMVFe65LruEklLkh57LGn5amO79ZK+faANBAAAaAm4I33E\ncW8UG7nYyMWPTGzkYuM+XTb6SzAougAAAEJA0RVxjKPbyMVGLn5kYiMXG3O6bPSXYFB0AQAAhICi\nK+IYR7eRi41c/MjERi425nTZ6C/BoOgCAAAIAUVXxDGObiMXG7n4kYmNXGzM6bLRX4JB0QUAABAC\niq6IYxzdRi42cvEjExu52JjTZaO/BIOiCwAAIAQUXRHHOLqNXGzk4kcmNnKxMafLRn8JBkUXAABA\nCCi6Io5xdBu52MjFj0xs5GJjTpeN/hIMii4AAIAQUHRFHOPoNnKxkYsfmdjIxcacLhv9JRgUXQAA\nACGg6Io4xtFt5GIjFz8ysZGLjTldNvpLMCi6AAAAQkDRFXGMo9vIxUYufmRiIxcbc7ps9JdgUHQB\nAACEgKIr4hhHt5GLjVz8yMRGLjbmdNnoL8Gg6AIAAAgBRVfEMY5uIxcbufiRiY1cbMzpstFfgkHR\nBQAAEAKKrohjHN1GLjZy8SMTG7nYmNNlo78Eg6ILAAAgBBRdEcc4uo1cbOTiRyY2crExp8tGfwkG\nRRcAAEAIKLoijnF0G7nYyMWPTGzkYmNOl43+EgyKLgAAgBBQdEUc4+g2crGRix+Z2MjFxpwuG/0l\nGBRdAAAAIaDoijjG0W3kYiMXPzKxkYuNOV02+kswKLoAAABCQNEVcYyj28jFRi5+ZGIjFxtzumz0\nl2BQdAEAAISAoiviGEe3kYuNXPzIxEYuNuZ02egvwaDoAgAACAFFV8Qxjm4jFxu5+JGJjVxszOmy\n0V+CQdEFAAAQAoquiGMc3UYuNnLxIxMbudiY02WjvwSDogsAACAEFF0Rxzi6jVxs5OJHJjZysTGn\ny0Z/CQZFFwAAQAgouiKOcXQbudjIxY9MbORiY06Xjf4SDIouAACAEFB0RRzj6DZysZGLH5nYyMXG\nnC4b/SUYFF0AAAAhoOiKOMbRbeRiIxc/MrGRi405XTb6SzAougAAAEJA0RVxjKPbyMVGLn5kYiMX\nG3O6bPSXYFB0AQAAhICiK+IYR7eRi41c/MjERi425nTZ6C/BoOgCAAAIAUVXxDGObiMXG7n4kYmN\nXGzM6bLRX4JB0QUAABACiq6IYxzdRi42cvEjExu52JjTZaO/BCOrqRsAAADCUVFQrMqibWrTu7sy\nc3s1dXNaHa50RRzj6DZysZGLH5nYyMXW0ud0VRZtU+mU2aos2lav7egvwaDoAgAACAFFV8Qxjm4j\nFxu5+JGJjVxszOmy0V+CQdEFAAAQAoquiGMc3UYuNnLxIxMbudha+pyuhqK/BIOiCwAAIAQUXRHH\nOLqNXGzk4kcmNnKxMafLRn8JRsr7dDmOM0bSA5IyJT3huu7dxjoPSjpH0m5JU13X/SDhuUxJ70na\n5Lrud4NqOAAAQHNS55WuWME0T9IYSUdLmuw4zlFJ65wraZDruoMlXSHpkaSX+bGk1ZKqgmp0a8I4\nuo1cbOTiRyY2crExp8tGfwlGquHFkyStc133M9d1yyUtkDQuaZ2xkp6SJNd18yUd6jhOT0lyHCdH\n0rmSnpCUEWTDAQAAmpNURVcfSRsTljfFHkt3nfslzZRUeQBtbNUYR7eRi41c/MjERi425nTZ6C/B\nSFV0pTskmHwVK8NxnPMlbY3N70rrKlfi5cu8vDyWWWY5wsuJwzD79u1TXaLQXpZZTnc5WXL/DnJ/\nFQXFKnktTyWv5amioDi040t8/zZ13s19uT7qLIYcxxkh6TbXdcfElm+SVJk4md5xnEcl/cV13QWx\n5U8knSHpWklTJO2T1F5SZ0n/47ru9619vfHGG1XDhw9v0EG0ZHl5efyGYSAXW5i5lOevVOmU2ZKk\ngpce141vF0mS7picqXvL75Qk3drxVg1tOzSU9tSGvmIjF1vJa3lqc/U9kvb368bs04nvo05P36W2\nJx8T2GvXtb/67ov+4rdixQqNHj26XlOnslI8/56kwY7j9JdUKGmSpMlJ67wo6WpJC2JF2leu6xZL\nujn2nxzHGSXpp7UVXAAAAC1dnUWX67r7HMe5WtKr8m4Z8VvXddc4jnNl7PnHXNdd7DjOuY7jrJO0\nS9IPank5vr3YAM3xN4uinXu0tWyvJKlzl1LtzvxS3dp0U8/MnoHtoznmEgZy8QsiE6tPSwq8X4eJ\nvmLLzs5WaRPte0vXbvqisDSUPla9Lym9Pk1/CUaqK11yXXeJpCVJjz2WtHx1itf4q6S/NqSBaH62\nlu3VzMXrJMWGmr65U7d2vLXZfjgBVp+WRL9GoEoqMnTj4nWh9LHqfUn06TBxR/qIa+hkvZaOXGzk\n4kcmNnKxcZ8uG/0lGCmvdAHpqCgoVmXRNklSVY/Dmrg1AABED0VXxDWXcfTKom3xb+DopccbfX/N\nJZewkYsfmdjIxdaUc7qijP4SDIouADBw9RZA0JjTFXGMo9vIxUYufg3NpPrqbemU2dLe8oBb1fTo\nKzbmdNnoL8Gg6AIAAAgBRVfEMY5uIxcbufiRiY1cbPztRRv9JRgUXQAAACGg6Io4xtFt5GIjFz8y\nsZGLjTldNvpLMCi6AAAAQkDRFXGMo9vIxUYufmRiIxcbc7ps9JdgUHQBAACEgKIr4hhHt5GLjVz8\nyMRGLjbmdNnoL8Gg6AIAAAgBRVfEMY5uIxcbufiRiY1cbMzpstFfgkHRBQAAEAKKrohjHN1GLjZy\n8SMTG7nYmNNlo78Eg6ILAAAgBBRdEcc4uo1cbOTiRyY2crExp8tGfwkGRRcAAEAIKLoijnF0G7nY\nyMWPTGzkYmNOl43+EgyKLgAAgBBQdEUc4+g2crGRix+Z2MjFxpwuG/0lGBRdAAAAIaDoijjG0W3k\nYiMXPzKxkYuNOV02+kswKLoAAABCQNEVcYyj28jFRi5+ZGIjFxtzumz0l2BQdAEAAISAoiviGEe3\nkYuNXPzIxEYuNuZ02egvwaDoAgAACEFWUzcAdWvoOHpFQbEqi7ZJktr07q7M3F5BNqvJMb/ARi5+\nZGIjF1t2drZKm7oREUR/CQZFVwtVWbRNpVNmS5J2L35MXxR6P0Y6dynV7swv1a1NN/XM7NmUTQSQ\nIPEXpW19c7Qt9uO5+j0rKeX7tmjnHm0t21tjO97rQHQwvBhxQYyjl1RkaObidZq5eJ22VpRozq45\nKqksCaB1TYf5BTZy8WsumVT/olQ6Zba2lu7xvWfTed9uLdub9nu9ueQSNuZ02egvwaDoAgAACAFF\nV8Qxjm4jFxu5+JGJjVxs3KfLRn8JBkUXAABACCi6Io5xdBu52MjFj0xs5GJjTpeN/hIMvr0IAM1Y\n4rceq3oc1sStAVAXiq6IYxzdRi42cvFr6Zkk3h5GLz2e9nYtPZeG4j5dNvpLMBheBAAACAFFV8Qx\njm4jFxu5+JGJjVxszOmy0V+CQdEFAAAQAoquiGMc3UYuNnLxIxMbudi4T5eN/hIMii4AAIAQUHRF\nHOPoNnKxkYsfmdjIxcacLhv9JRgUXQAAACGg6Io4xtFt5GIjFz8ysZGLjTldNvpLMCi6AAAAQkDR\nFXGMo9vIxUYufmRiIxcbc7ps9JdgUHQBAACEgKIr4hhHt5GLjVz8yMRGLjbmdNnoL8Gg6AIAAAgB\nRVfEMY5uIxcbufiRiY1cbMzpstFfgkHRBQAAEAKKrohjHN1GLjZy8SMTG7nYmNNlo78Eg6ILAAAg\nBBRdEcc4uo1cbOTiRyY2crExp8tGfwkGRRcAAEAIKLoijnF0G7nYyMWPTGzkYmNOl43+Eoyspm4A\nAKSjoqBYlUXbJEltendXZm6vJm4RANQPV7oijnF0G7nYWnIulUXbVDpltkqnzI4XX+loyZkciJae\nS0VBscrzV6o8f6UqCorT3o45XbaW3l/CQtEFAGhxGlqkA42JoiviGEe3kYuNXPzIxEYuNuZ02egv\nwWBOFyKjaOcebS3bq85dSrU780tJUrc23dQzs2cTtwxRs6VrN31RWCpJ9BekVN1fWmJfqf65KfFe\naA640hVxrWkcfWvZXs1cvE5bK0o0Z9cczdk1RyWVJea6rSmX+mgtuZRUZGjm4nVp9ZfWkkl9taZc\nqvtLOj9bmsucruo5a1u+KEv7vXAgWlN/aUwpr3Q5jjNG0gOSMiU94bru3cY6D0o6R9JuSVNd1/3A\ncZz2kv4qqZ2kgyT9r+u6NwXZeAAAWqPqOWt66fGmbgrqoc4rXY7jZEqaJ2mMpKMlTXYc56ikdc6V\nNMh13cGSrpD0iCS5rvuNpDNd1/22pGGSznQch0HhemIc3UYuNnLxIxMbudiY02WjvwQj1fDiSZLW\nua77meu65ZIWSBqXtM5YSU9Jkuu6+ZIOdRynZ2x5d2ydg+RdKdseVMPRMiR+rbtqz96mbg4AAI0m\nVdHVR9LGhOVNscdSrZMjeVfKHMf5h6Qtkv7suu7qA2tu69PSx9ETv9atveVpb9fSc2kocvEjExu5\n2JrLnK6w0V+CkaroqkrzdTKs7VzXrYgNL+ZIOt1xnDPq1zwAAICWIVXRtVlS34TlvvKuZNW1Tk7s\nsTjXdXdIekXSCXXtLLGSzsvLYzkvLz6OXt/tU/22tmPnjkDbe6D7k6R9+/bVur21fhTOT9SWG9pf\nGrKceM7rOndNvb+RI0e26OOrTeJrWPsLuv1RW06V546dO2qsX729Nacrefug29uQ/aXzM7eu/SXu\nI539pXq+NS/XR6pvL74nabDjOP0lFUqaJGly0jovSrpa0gLHcUZI+sp13S2O43STtM913a8cx+kg\n6WxJc+raWeJEveRJeyzXbzk7O1ulql1252wNHTm0yfdXnr8y/lhWVu3dsanzZNm/XJ6/Mn7O6zp3\n7K/x92fJysqSyoNrX3NbTpVndufsGuvXJTHLxmhvQ/aXeHyWVMeXmEljH19LXV6xYoXqq84rXa7r\n7pNXUL0qabWkha7rrnEc50rHca6MrbNY0nrHcdZJekzS9NjmvSW9FZvTlS/pJdd136x3C1u5hlbT\nLR252MjFj0xs5GJjTpeN/hKMVFe65LruEklLkh57LGn5amO7lZKGH2gDAQAAWgLuSB9x3BvFRi42\ncvEjExu52LhPl43+EgyKLgAAgBBQdEUc4+g2crGRix+Z2MjFxpwuG/0lGBRdAAAAIaDoijjG0W3k\nYiMXPzKxkYuNOV02+kswKLoAAABCQNEVcYyj28jFRi5+ZGIjFxtzumz0l2BQdAEAAISAoiviGEe3\nkYuNXPzIxEYuNuZ02egvwaDoAgAACAFFV8Qxjm4jFxu5+JGJjVxszOmy0V+CQdEFAAAQAoquiGMc\n3UYuNnLxIxMbudiY02WjvwSDogsAACAEFF0Rxzi6jVxs5OJHJjZysTGny0Z/CQZFFwAAQAiymroB\nqBvj6DZysZGLX9iZVBQUq7JomySpTe/uysztFer+00UutuzsbJU2dSMiiJ8twaDoAtCihf1hX1m0\nTaVTZkuSOj19V2SLi7CRC8DwYuQxjm5r6blUFBSrPH+lKgqK67VdS8+lIb78ZJ1Kp8xW6ZTZ8eIL\n9JXaMKfLRn8JBkUXEEHVVwVaYpFQXVA2pKgEgOaM4cWIY96FjfkFtuaQS9jDTMzRsTWHvtIU6C82\n+kswuNKFGqo/EFvqVRYAAJpKJK90Fe3co61leyVJnbuUanfml5Kkbm26qWdmz6ZsWujy8vKa7DeM\nLV276YtC73e+6vMQlXPQlLlU988w+qZ1DuraX1Pm0hD1Pb6G2LFjR/y3yzD2lyjs/dVHEH3F+lmd\nzrFF+WdLYn9pqDB/RoSlur/w+XxgInWlq3qex5YvyjRz8TrNXLxOWytKNGfXHM3ZNUcllSVN3cRW\npaQiw3ceOAfS1rK9ofVN6xy0pPMQ9vG19P2Frfq9UN+fES39Z0uYPyPCZp3zlnR8jS1SV7qq53no\npcebtiER0pyuWoSJXGzk4sccHRt9xUZ/sdFfghGpK10AAAAtFUVXxHFvFBu52MjFj/su2egrNvqL\njf4SDIouAACAEFB0RRzj6DZysZGLX3Z2dlM3IZLoKzb6i+2U3EEqz1+pqj17m7opzVqkJtIDUZV4\n09iqHoc1cWuApsN7oXWK39SYL7odEK50RRzj6Lawc0m8aaz2loe67/qgv/gxR8fW0L7SXN4LDUV/\nsZFLMCi6AAAAQsDwYsQx78JGLjZy8eO+Szb6iq2h/aWlD7vyPgoGRRcAAAco8Q+5M+8JtWF4MeKY\no2MjFxu5+DEXxUZfsdFfbOQSDIouAACAEFB0RRzzLmzkYiMXP+67ZKOv2OgvNnIJBkUXAABACCi6\nIo55FzZysZGLH3NRbPQVG/3FRi7BoOgCAAAIAUVXxDHvwkYuNnLxYy6Kjb5io7/YyCUYFF0AAAAh\noOiKOOZd2MjFRi5+zEWx0Vds9BcbuQSDogsAACAEFF0Rx7wLG7nYyMWPuSg2+oqN/mIjl2BQdAEA\nAISAoivimHdhIxcbufgxF8VGX7HRX2zkEgyKLgAAgBBQdEUc8y5s5GIjFz/motjoKzb6i41cgkHR\nBQAAEAKKrohj3oWNXGzk4sdcFBt9xUZ/sZFLMLKaugGo24CDDlF5/kpJUpve3ZWZ26uJWwQAABqC\nK10R16MqU6VTZqt0ymxVFm1r6uZEBvNRbOTix1wUG33FRn+xkUswKLoAAABC0OyLroqCYpXnr1R5\n/kpVFBQ3dXMCxzi6jfkoNnLx4z1ko6/Y6C82cglGs5/TVVm0TaVTZkuSdi9+TF8UlkqSOncp1e7M\nLyVJ3dp0U8/Mnk3WxqBs6drNd3wt5dgAIJWinXu0tWyvJH4Gonlq9le6EpVUZGjm4nWauXidtlaU\naM6uOZqza45KKkuaumkNljiObh1fcz62A8F8FBu5+DEXxdYc+8rWsr2N/jOQ/mIjl2A0+ytdAICW\nq6KgOP4loqoehzVxa4AD06KudLVEjKPbmI9iIxc/3kO25tJXqqeQlE6ZLe0tb/T90V9s5BIMii4A\nAIAQUHRFHOPotuY4HyUM5OLHe8hGX7HRX2zkEgyKLgAAgBBQdEUc4+i25jIfJWzk4sd7yEZfsdFf\nbOQSDIouAACAEFB0RRzj6Dbmo9jIxY/3kI2+YqO/2MglGBRdAAAAIUjr5qiO44yR9ICkTElPuK57\nt7HOg5LOkbRb0lTXdT9wHKevpP+W1ENSlaTHXdd9MKjGtwY7duygMjbk5eXxm7qBXPx4D9noKzb6\ni41cgpEyQ8dxMiXNkzRG0tGSJjuOc1TSOudKGuS67mBJV0h6JPZUuaSfuK47VNIISTOStwUAAGgN\n0ilcT5K0znXdz1zXLZe0QNK4pHXGSnpKklzXzZd0qOM4PV3XLXZd9x+xx8skrZHE33GoB8bRbfyG\nbiMXP95DNvqKjf5iI5dgpFN09ZG0MWF5U+yxVOvkJK7gOE5/ScdJyq93KwEAAJq5dIquqjRfK6O2\n7RzHOUTS85J+HLvi1SA7du6/T0heXp7vPjP79u0z/22t31yWE++NUp/jS3VPlR07d9S5/6beX7Lk\n9R955JFQz4d1fIntTXV8Ye2v+rEw+mdtfdNine/6Hl9D91db32ys/dWmKfdnnb9HHnmkzudTvV/r\nu79Ux5fq53tY+0v13gt6f5b67s8S9OdlYWFhg/fX0pfrI52J9Jsl9U1Y7ivvSlZd6+TEHpPjOG0l\n/Y+kZ1zXXdSgVsZkd95/ebP60nh5/sr4Y1lZWTX/nfC3UZMvpTeX5ZLX9p/Y+hxfdna2SlW77M7Z\nGjpyqG/7huYZ9P6SJe/vmGOOqfFYY58P6/gSM6nt+MLeX/UPgjD6Z3n+yngb6zp31vaWVMfH/hq+\nv6DPf0P2l+r4rJ/vUdlfOp8nTbk/S6r91ffzMvGzqL77a6nLK1asUH2lU3S9J2lwbHiwUNIkSZOT\n1nlR0tWSFjiOM0LSV67rbnEcJ0PSbyWtdl33gXq3DimLmdaK+Sg2cvHjPWSjr9joLzZyCUbK4UXX\ndffJK6helbRa0kLXddc4jnOl4zhXxtZZLGm94zjrJD0maXps89MkXSrpTMdxPoj9N6YxDgQAACDK\n0rpPl+u6SyQtSXrssaTlq43t8sQNWA8I90ax5eVxjyELufjxHrLRV2z0Fxu5BIMMAQAAQkDRFXHc\nG8XGb+g2cvHjPWSjr9joLzZyCQZFFwAAQAgouiIu1b1YWquG3iOlpSMXP95DNvqKjf5iI5dgUHQB\nAACEgKIr4hhHtzEfxUYufryHbPQVG/3FRi7BoOgCAAAIAUVXxDGObmM+io1c/HgP2egrNvqLjVyC\nQdEFAAAQAoquiGMc3cZ8FBu5+PEestFXbPQXG7kEI60/AwSgZasoKFZl0Ta16d1dmbm9mro5ANAi\ncaUr4hhHtzWX+SgVBcUqz1+pioLiUPa3+e//aND+Kou2qXTKbFUWbWukljUd3kO26r4SZv9sDugv\nNnIJBkUX0IjCLmbafVXWYosnBKu6r9BfgPAwvCipaOcebS3bK0nq3KVUuzO/lCR1a9NNPTN7hrJd\nbdtkZ2ertGGH1aKdkjtI5fkrJUnb+uZom7LqdQ7CtqVrN31R6J3JxmxndX9p6P7CameYeA/ZEnOx\nzntzPucHgv5iI5dgcKVL0tayvZq5eJ1mLl6nrRUlmrNrjubsmqOSypLQtku1DWqqvoJUOmW2tpbu\nqfc5CFtJRUaD+krY+wu7nYgG67xzzoHgUXRFHOPoNnKxkYsfmdjIxUYuNnIJBsOL9VT9LS9Jqupx\nWJTBLQIAAA5cSURBVKNvBwAAWoZWW3Q1tAiqHtaSJL30eKNvxzi6jVxs5OJHJjZysZGLjVyC0WqL\nroYWQQAAAA3BnK6IYxzdRi42cvEjExu52MjFRi7BoOgCAAAIAUVXxPH3rmzkYiMXPzKxkYuNXGzk\nEgyKLgAAgBBQdEUc4+g2crGRix+Z2MjFRi42cgkGRRcAAEAIKLoijnF0G7nYyMWPTGzkYiMXG7kE\ng6ILAAAgBBRdEcc4uo1cbOTiRyY2crGRi41cgkHRBQAAEAKKrohjHN1GLjZy8SMTG7nYyMVGLsGg\n6AIAAAgBRVfEMY5uIxcbufiRiY1cbORiI5dgUHQBAACEgKIr4hhHt5GLjVz8yMRGLjZysZFLMCi6\nAAAAQkDRFXGMo9vIxUYufmRiIxcbudjIJRgUXQAAACGg6Io4xtFt5GIjFz8ysZGLjVxs5BIMii4A\nAIAQUHRFHOPoNnKxkYsfmdjIxUYuNnIJBkUXAABACCi6Io5xdBu52MjFj0xs5GIjFxu5BIOiCwAA\nIAQUXRHHOLqNXGzk4kcmNnKxkYuNXIJB0QUAABACiq6IYxzdRi42cvEjExu52MjFRi7BoOgCAAAI\nAUVXxDGObiMXG7n4kYmNXGzkYiOXYFB0AQAAhICiK+IYR7eRi41c/MjERi42crGRSzAougAAAEJA\n0RVxjKPbyMVGLn5kYiMXG7nYyCUYFF0AAAAhoOiKOMbRbeRiIxc/MrGRi41cbOQSDIouAACAEFB0\nRRzj6DZysZGLH5nYyMVGLjZyCQZFFwAAQAgouiKOcXQbudjIxY9MbORiIxcbuQSDogsAACAEFF0R\nxzi6jVxs5OJHJjZysZGLjVyCQdEFAAAQAoquiGMc3UYuNnLxIxMbudjIxUYuwaDoAgAACAFFV8Qx\njm4jFxu5+JGJjVxs5GIjl2BQdAEAAIQgK52VHMcZI+kBSZmSnnBd925jnQclnSNpt6Sprut+EHv8\nd5LOk7TVdd1jgmp4a5Gdna3Spm5EBJGLjVz8yMRGLjZysZFLMFJe6XIcJ1PSPEljJB0tabLjOEcl\nrXOupEGu6w6WdIWkRxKe/n1sWwAAgFYrneHFkyStc133M9d1yyUtkDQuaZ2xkp6SJNd18yUd6jhO\nr9jy25K+DK7JrQvj6DZysZGLH5nYyMVGLjZyCUY6RVcfSRsTljfFHqvvOgAAAK1WOkVXVZqvldHA\n7dK2Y+f+SjsvL095eXk1nt+3b5/5b2v9dKr2MPe3Y+eOGutXb594b5Qw9peoKfeXzFo/WeL2qfZX\n32Xr+Oqzv7qOLcj9VfeXMPaXuE1992dprP3Vdn+hlnJ86ezP6t+1rZvYxiD3l+r4orI/q7+k+vkX\n9PHVd3+WID+/Up2LVPtr6cv1kc5E+s2S+iYs95V3JauudXJijwUqu/P+N8PIkSMlSeX5K+OPZWVl\n1fx3uXzrx18rjUmBYe4vu3O2ho4cyv5qkc7+EttY2/4autzQ/VUfX13H1lz3V56/Mr5NffdnYX+N\ntz+rf6fan/Xzr7XuL9XPv6benyXV/urz8/1A99dSl1esWKH6Sqfoek/SYMdx+ksqlDRJ0uSkdV6U\ndLWkBY7jjJD0leu6W+rdGvjs2LGD+3oYyMVGLn5kYiMXG7nYyCUYKTN0XXefvILqVUmrJS10XXeN\n4zhXOo5zZWydxZLWO46zTtJjkqZXb+84znOS3pE0xHGcjY7j/KARjgMAACDS0rpPl+u6SyQtSXrs\nsaTlq2vZNvmqGOqBe6PYyMVGLn5kYiMXG7nYyCUYXC0EAAAIAUVXxHFvFBu52MjFj0xs5GIjFxu5\nBIOiCwAAIAQUXRFX2z2GWjtysZGLH5nYyMVGLjZyCUZaE+mBlqho5x5tLdurzl1KtTvT+0tV3dp0\nU8/Mnk3cMgBAS8SVrohjHN3W0FwqCopVnr9S5fkrteWLMs1cvE5bK0o0Z9cczdk1RyWVJQG3NFz0\nFz8ysZGLjVxs5BIMrnShVaks2qbSKbO9hZceb9rGAABaFa50RRzj6DZysZGLH5nYyMVGLjZyCQZF\nFwAAQAgouiKOcXQbudjIxY9MbORiIxcbuQSDogsAACAEFF0Rxzi6jVxs5OJHJjZysZGLjVyCQdEF\nAAAQAoquiGMc3UYuNnLxIxMbudjIxUYuwaDoAgAACAFFV8Qxjm4jFxu5+JGJjVxs5GIjl2BQdAEA\nAISAoiviGEe3kYuNXPzIxEYuNnKxkUswKLoAAABCQNEVcYyj28jFRi5+ZGIjFxu52MglGBRdAAAA\nIaDoijjG0W3kYiMXPzKxkYuNXGzkEgyKLgAAgBBQdEUc4+g2crGRix+Z2MjFRi42cgkGRRcAAEAI\nKLoijnF0G7nYyMWPTGzkYiMXG7kEg6ILAAAgBBRdEcc4uo1cbOTiRyY2crGRi41cgkHRBQAAEAKK\nrohjHN1GLjZy8SMTG7nYyMVGLsGg6AIAAAgBRVfEMY5uIxcbufiRiY1cbORiI5dgUHQBAACEgKIr\n4hhHt5GLjVz8yMRGLjZysZFLMCi6AAAAQkDRFXGMo9vIxUYufmRiIxcbudjIJRgUXQAAACGg6Io4\nxtFt5GIjFz8ysZGLjVxs5BIMii4AAIAQUHRFHOPoNnKxkYsfmdjIxUYuNnIJBkUXAABACCi6Io5x\ndBu52MjFj0xs5GIjFxu5BIOiCwAAIAQUXRHHOLqNXGzk4kcmNnKxkYuNXIJB0QUAABACiq6IYxzd\nRi42cvEjExu52MjFRi7BoOgCAAAIAUVXxDGObiMXG7n4kYmNXGzkYiOXYFB0AQAAhICiK+IYR7eR\ni41c/MjERi42crGRSzAougAAAEJA0RVxjKPbyMVGLn5kYiMXG7nYyCUYFF0AAAAhoOiKOMbRbeRi\nIxc/MrGRi41cbOQSDIouAACAEFB0RRzj6DZysZGLH5nYyMVGLjZyCQZFFwAAQAgouiKOcXQbudjI\nxY9MbORiIxcbuQSDogsAACAEFF0Rxzi6jVxs5OJHJjZysZGLjVyCQdEFAAAQAoquiGMc3UYuNnLx\nIxMbudjIxUYuwaDoAgAACAFFV8Qxjm4jFxu5+JGJjVxs5GIjl2BQdAEAAISAoiviGEe3kYuNXPzI\nxEYuNnKxkUswslKt4DjOmP/f3v2GSlHFYRz/qmj/Q0LSyltKGVQYXgqVrLyGhVpZUb9KqOxFJVQi\nEVH6onxXEZVIIJYWaaH2FKlRFN0iiyBDMor0jaSQZSqhlUhgtr2Yuddlnf1zye6snOcDlzszewbO\n/nh2OZyZnQMsAgYByyQ9W9BmMTAdOAjcK2lzq+eamZmZpaDhTFdEDAJeAqYBFwOzIuKimjYzgAsk\njQEeAJa0eq415+voxVyXYq7L0VyTYq5LMdelmOtybDS7vDge2CZph6RDwGrgppo2M4HXASRtBIZG\nxIgWzzUzMzNLQrNB1znAT1X7O/NjrbQ5u4VzrQlfRy/muhRzXY7mmhRzXYq5LsVcl2NjQKMXI+JW\nYJqk+/P9u4AJkuZWtXkPeEbSl/l+N/A4MKrZudW6u7s/Ayb/1zdkZmZm1g82TJ06tasvJzS7kf5n\noKNqv4NsxqpRm5F5m8EtnNurrx03MzMzO540G3RtAsZExCjgF+AOYFZNm/XAw8DqiJgI7Je0OyJ+\na+FcMzMzsyQ0vKdL0t9kA6qPgC3AGklbI2JORMzJ23wA/BgR24ClwIONzv3f3omZmZmZmZmZmZmZ\nmZmZmZmZmdnxr+EjI/qLlwsqFhE7gD+Aw8AhSePL7VH/i4hXgeuBPZLG5sfOANYA5wE7gNsl7S+t\nkyWoU5eFwH3A3rzZfEkfltPDckREB7ACOBOoAC9LWpx6ZhrUZSGJZiYiTgQ2ACcAQ4B1kuY7K3Xr\nspBEs1ItX21nE7BT0o19zUvpC157uaCGKkCXpM4UB1y518iyUe0J4GNJFwKf5PupKapLBXghz0tn\nil+IwCHgEUmXABOBh/Lvk9QzU68uyWZG0l/AFEnjgEuBKRFxJYlnpUFdks1KjXlkPw6s5Pt9ykvp\ngy68XFAzbTEbWRZJXwD7ag73Lj2V/7+5XzvVBurUBZyXXyV9m28fALaSrYSRdGYa1AUSzoykg/nm\nELIrLftIPCtQty6QcFYAImIkMANYxpFa9CkvzZ7T1R+KlhGaUFJf2k0F6I6Iw8BSSa+U3aE2MVzS\n7nx7NzC8zM60mbkRcQ/Z9PejKV0WqZU/I7AT2Igz06uqLl8Bk0g4MxExEPgGOB9YIumHiEg+K3Xq\nchsJZyX3IvAYcHrVsT7lpR1muirNmyRrkqROYDrZ5YCryu5Qu5FUwRnqsQQYDYwDdgHPl9ud8kTE\nqcA7wDxJf1a/lnJm8rq8TVaXAySeGUn/5JfRRgJXR8SUmteTzEpBXbpIPCsRcQPZPbSbqTPj10pe\n2mHQ1cpSQ0mStCv/vxd4l+xSrMHuiBgBEBFnAXtK7k9bkLRHUiX/4C8j0bxExGCyAddKSWvzw8ln\npqoub/TUxZnJSPodeB+4DGelV1VdLndWuAKYGRHbgVXANRGxkj7mpR0GXb1LDUXEELLlgtaX3KfS\nRcTJEXFavn0KcB3wfbm9ahvrgdn59mxgbYO2ycg/8D1uIcG8RMQAYDmwRdKiqpeSzky9uqScmYgY\nFhFD8+2TgGuBzTgrhXXpGVjkksoKgKQFkjokjQbuBD6VdDd9zEtb3BQXEdM58siI5ZKeLrlLpYuI\n0WSzW5Dde/dminWJiFXAZGAY2fXyJ4F1wFvAuST4k24orMtTQBfZ1H8F2A7MqbrXIAn5r6w+B77j\nyDT/fOBrEs5MnbosIFsPN8nMRMRYshufB+Z/KyU9lz8CIOWs1KvLChLNSq2ImEx2T9vM1PNiZmZm\nZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmdiz8C+GSI3XD1qcLAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a253b00>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8slq3bq3OnTvrueee00knnRRbJz8/X9ZarV69OvZv3bp1sVO2qfYjmXbt2mni\nxImxXsFsnmP0rbiL7NxGfuFCMRaw6KUv2rRpox9++EH3339/tTGpfml+8MEHWrZsmcrLy3XggQeq\nadOmSd9Z2LFjR61fv15lZWVJt3veeedpxowZ+uqrr7R7927dfffdOu6446ocIcpWTd6ZuGfPHu3Z\ns0ft27dXkyZNNG/evCrN/R07dtQPP/xQpYE+2fbjb4u+qeF3v/udHn30URUXF+uvf/1r0vuP3u/q\n1atjt40ZM0aPP/64ioqKtGPHDt19990aM2ZM2ktfTJ06VWVlZVqwYIHmzZunkSNHqkmTJho1apTu\nvfde7dixQ2vWrNHjjz8uY0xsvVNOOUVPPfVU7JRkdPnkk0+OjZkwYYLuueee2CnjzZs3a+7cuSnn\nksmkSZP08ccfa8WKFbybEgAaiEZ1XYVOBzbTH8/u4+v26yrxF+DEiRN1xRVXqG/fvuratauuuuqq\nar9s49eJPzK0ceNG/eY3v9H69evVqlUrjR49WuPGjat2n0OGDNFhhx2mww47TLm5uVqxYkWV7Q4Z\nMkS33XabLr30Um3dulUnnniinn766ZRzTnVb4vxSjY0ut27dWlOnTtVll12m3bt3a/jw4bFeMEnq\n16+fxowZo4EDB6qiokIfffRRyu1Hb/v973+v7t27a8KECZKk6dOna8SIETr99NPVq1evKusdcMAB\nuuGGG3TWWWeprKxML7/8si666CJt2LBB55xzjnbv3q0zzzwz7bsQO3XqpIMOOkhHHHGEDjjgAD34\n4IPq08d7Dt53332aMmWKBg4cqObNm+vSSy/VhRdeGFv35JNP1iuvvBI7EnbKKafoscceq1KMTZw4\nUZWVlTrvvPNUXFysjh07asyYMbHHKZuCKn5M69atdc011+j3v/99xvUk+lZcRnZuawj5lRdtUEXx\nJklSk64dlVvQJcMaqC0n/jTO9qKvwP7k90Vpg8BrCvBPtLhxpbApW7RE2y++XZLU+vl71fTEIwOe\nkTtqetFXTlMCSIm+FXeRXcNTUbxJ2y++PXa0KR3yCxeKMaAO6LsCANQVxRhQS4MHD45d862xagh9\nK6gdsnMb+YULxRgAAECAKMYApETfirvIzm1+5VdetEFli5aobNESlRdtyLwC9otGdWkLAACQWvRN\nBJL3DkkX3tXZEPh9mQ+OjAFIib4Vd5Gd28ivYYkWsdm+G7amKMYAAAACRDHmmKlTp2rixIm1WnfB\nggU68cRIdGKwAAAgAElEQVQT6zyHo446Sv/85z/rvB00fPQduYvs3EZ+4dKoesZKyku0uWKzb9vv\n0KSDOud2rtE6P//5z7V06VJ9/fXXatas/j9OKZ327dvr008/Vc+ePSVJJ510khYtWlQvc+D6WgAA\n1I9GVYxtrtisu3be5dv272h1R42KsaKiIi1evFj5+fmaO3euRo4cWec51OSDuGszHohH34q7yM5t\njT0/1z4aym+cpvTRzJkzNWTIEI0dO1YzZ86M3T558mTddNNNuuCCC1RQUKBhw4bp22+/jX3/lltu\n0ZFHHqkePXrojDPO0MKFC6tsN3pUaty4cXrqqaeqfG/w4MF64403dO6550qSTj31VBUUFGj27Nkq\nLCzUz372s9jYtWvX6pJLLlG/fv3Up08fTZkyRZK0evVqjRw5Un369FHfvn115ZVXatu2bfX62ABA\nWJW076Av1m/X6p/Wa2nZUi0tW6qS8pKkY4u37a7x2PjxqcYmm0d9jU2cc7Kx0Yb44j2Vtd5ufT0W\nfj5u2aIY89GsWbM0evRojRo1Su+99542b953CvXvf/+7pkyZotWrV6t379665557Yt879thj9cEH\nH2j16tU677zz9Mtf/lJ79uyJfT96tGv8+PH629/+Frv9q6++0oYNG/Rv//Zvev311yVJH3zwgYqK\nijRq1KgqcysvL9f48eNVUFCgL774QkuXLtXo0aNj37/hhhu0fPlyLVy4UOvWrdPUqVPr98GBE+hb\ncRfZNVyby3N005yV2ljunc25a+dd1Vpsovlt3LEn49io6Nj48eladxLnUV9jE+fs13br67Hw83HL\nFsWYTxYuXKji4mINHz5chxxyiA499FBZa2PfP/fcc3XMMccoNzdX559/fpWP1THG6KCDDlKTJk00\nefJk7d69WytXrqx2H8OHD9c333yj1atXS/KKvzFjxigvL/PZ508//VQlJSX6/e9/r5YtW6p58+Ya\nNGiQJKlXr14aMmSImjZtqvbt2+uqq67SRx99VNeHBAAAJEEx5pOXXnpJp59+ulq3bi1JGjlyZJVT\nlR07dox93bJlS+3cuTO2/Oijj2rQoEHq2bOnevXqpW3btun777+vdh8tWrTQqFGjNGvWLFVWVuqV\nV17R2LFjs5rfunXr1L17dzVpUv0psHHjRv3qV79S//791aNHD1111VXasmVL1vuOxqOx9600ZmTn\nNvILl0bVwN9Q/Pjjj5o9e7YqKyt1+OGHS5J2796tbdu2aenSpWnXXbBggaZNm6bZs2fH1u3du3fK\nRvwLLrhAkyZN0oknnqgDDjhAxx13XFZz7Natm9auXavy8nLl5uZW+d7dd9+t3NxcffTRR2rbtq3e\neOONWD8ZAKBhiTbDV3Y6mHk4iiNjPpgzZ47y8vK0YMECzZ8/X/Pnz9fChQs1aNCgKkfHktmxY4fy\n8vLUvn177dmzR/fff7+2b9+ecvwJJ5ygnJwc/e53v9O4ceOqfK9Tp06xU5iJjj32WHXu3Fl33XWX\ndu3apZ9++il22YudO3fqgAMOUOvWrbV+/Xo9+uijNXwE0FjQd+QusnPbuv/+XGWLlqhy956MY2Mf\ncbSnbD/MrGHPI/rZm9k8bg1Jozoy1qFJB93R6g5ft5+NmTNn6sILL1S3bt2q3H755Zfr1ltv1Wmn\nnVbtOl3R5TPPPFNnnHGGjj/+eLVq1UoTJ05Ufn5+lXGJ644bN05/+MMf9OKLL1a5fcqUKZo8ebJ+\n/PFHPfzww+rQoUNs3dzcXM2YMUO33nqrBgwYoJycHJ1//vk68cQTdfPNN2vSpEnq2bOnevfuLWOM\nnnjiieweJABAnTXfukPbr75feu3JoKfilFhB6Njj1qiKsc65nWt8UVY/xDfqxxs1alS1dzVKXm9A\ntIG/SZMmevTRR6scjbr22mtjXyc7Xdi9e3cNGjRIBQUFVW6fMGGCJkyYUOW2+DcK5Ofn6/nnn6+2\nvcMOO0zvvfdeldsmT54c+/rzzz9PtntohOhbcRfZua1t27ZKfU4EjQ2nKR23a9cuPf3007r00kuD\nngoAAKgFijGHvfvuuzr00EPVpUsXnX/++UFPB40QfUfuIju3lZaWBj0F7EeN6jRl2Jx55plas2ZN\n0NMAAAB1wJExACnRd+QusnNb27Ztg54C9iOKMQAAgAA5XYzl5uZq165dQU8DaBR27dpV7QLA9B25\ni+zcRs9YuDjdM9apUydt3LhRW7duDXoqSKG0tJTD7Y7Izc1Vp06dgp4GAISO08VYTk6OOncO/rpi\nSO3gg/lYDJfRd+QusnMb1xkLF6eLMQAA0LiF4TMvne4ZQ8NH34rbyM9dZOc2esb2aQifeem3jEfG\njDHDJT0sKVfS09ba+5KMeUTSWZJ2SZpgrf3MGNNd0n9K6iSpUtKT1tpHIuPvlHS5pE2RTdxqrX2z\n7rsDAADglrRHxowxuZKmSRou6QhJ440xhyeMOVtSH2ttX0lXSHo88q0ySddba/tLGiRpsjHmsMj3\nKiU9aK09JvKPQqyRom/FbeTnLrJzG2988l950QaVLVqiyt17gp5KxtOUJ0haaa391lpbJmmmpJEJ\nY0ZIek6SrLWLJB1kjOlsrd1grf08cvsOScsldYtbL6c+dgAAAKCmGtLpz0zFWDdJ8Z+3s1ZVC6pU\nY/LjBxhjeko6RtKiuJuvMcZ8YYz5izHmoJpMGu6gb8Vt5OcusnMbPWPhkqkYq8xyO4lHuWLrGWMO\nlPSypF9HjpBJ3qnMXpKOllQs6YFMdxD/g6WwsJBllllmmWWWnVuWpL179yqVxPHJxpZuK60yPl3h\nVrqttMr2ko2Nv49k800392z2L3G+6fYvcb7J9i9+nfrYv/jv1/f+ZSvtqUJjzCBJd1prh0eWb5VU\nEd/Eb4x5QtL71tqZkeWvJQ2x1pYYY5pKel3SXGvtwynuo6ek16y1R6aaxzvvvFM5cODAmu0ZAAAN\nSNmiJdp+8e0qeu1J3fxBse4en6sHyu6RJN3R6g71b9q/XsZKio1PNVZStW3XZWy6Ofs1tr4ei/p+\n3CRp8eLFGjp0aNbtWJmOjH0iqa8xpqcxppmkcZJeTRjzqqRLpFjxtjVSiOVI+oukZYmFmDGma9zi\naElLsp0wAABAY5K2GLPW7pV0taS3JC2TNMtau9wYc6Ux5srImDmSVhljVkqaLmlSZPVTJF0k6XRj\nzGeRf8Mj37vPGPOlMeYLSUMkXV/ve4YGoTaHa9FwkJ+7yM5t9IyFS16mAdbauZLmJtw2PWH56iTr\nFSpFsWetvaRm0wQAAGicuAI/fMW1jtxGfu4iO7dxnbFwoRgDAAAIEMUYfEXfitvIz11k5zZ6xsKF\nYgwAACBAFGPwFX0rbiM/d5Gd2+gZCxeKMQAAgABRjMFX9K24jfzcRXZuo2csXCjGAAAAAkQxBl/R\nt+I28nMX2bmNnrFwoRgDAAAIEMUYfEXfitvIz11k5zZ6xsKFYgwAACBAFGPwFX0rbiM/d5Gd2+gZ\nCxeKMQAAgABRjMFX9K24jfzcRXZuo2csXCjGAAAAAkQxBl/Rt+I28nMX2bmNnrFwoRgDAAAIEMUY\nfEXfitvIz11k5zZ6xsKFYgwAACBAFGPwFX0rbiM/d5Gd2+gZCxeKMQAAgABRjMFX9K24jfzcRXZu\no2csXCjGAAAAAkQxBl/Rt+I28nMX2bmNnrFwoRgDAAAIEMUYfEXfitvIz11k5zZ6xsKFYgwAACBA\nFGPwFX0rbiM/d5Gd2+gZCxeKMQAAgABRjMFX9K24jfzcRXZuo2csXPKCngAAAH4qL9qgiuJNkqQm\nXTsqt6BLvYwF6gtHxuAr+lbcRn7uIrt9Koo3afvFt2v7xbfHCq36GOsnesbChSNjAJCF6BETV46W\ncIQHcAdHxuAr+lbcRn77RI+YBHm0pCZ++HplgzjCg9qhZyxcKMYAAAACRDEGX9G34jbycxc9R24j\nv3ChZwwA6plf/WWu9a0ByA5HxuAreo7cRn6141d/WU22S8/R/lFetEFli5aovGhDvW6X/MKFI2MA\nGqXibbu1cccetWm3Xbtyf1CHJh3UObdznceWtO+g79dvr9VYSSnHR+cgKeO2o9vNZmxN5+zX45Y4\nNpvHor4ft5o+FtmMjRbIu+ZMz3q7QCKOjMFX9By5zeX8Nu7Yo5vmrNTG8s26a+dd2lyxuV7Gbi7P\nqfXYdOOjc8hm29Htphsb33NUkzn79bgljs3msUg3NnpEquT7HVk/bjV9LPwamw16xsKFYgwA0CBE\nC6zK3Xsyjo0ekdKesv0wM8BfFGPwFT1HbiM/d9W056gmhZBfKLD2oWcsXCjGAAAUQkCAaOCHr1zu\nOYJ7+cV/BFBlp4MDnk2w2rZtq+1BTwK1Rn7hQjEGoNGIHd2RpNeeDHYyAJAlTlPCV/Qcua2x59cQ\n+qT8Qs+R28gvXCjGAIRWQ+iTaswFodT49w+oDxRj8JVrPUeoivz851dB2FCuU9UQCl4XNZT8sH/Q\nMwYAqJHoGyXC/iYJoL5wZAy+auw9R40d+bnLz54jjnb5j56xcKEYAwAACBDFGHxFz5HbyM9d9By5\njfzChWIMAAAgQBRj8BU9R24jP3fRc+Q28gsXijEAAIAAUYzBV/QcuY383EXPkdvIL1woxgAAAAJE\nMQZf0XPkNvJzFz1HbiO/cKEYAwAACBDFGHxFz5HbyM9d9By5jfzChWIMAAAgQBRj8BU9R24jP3fR\nc+Q28gsXijEAAIAAUYzBV/QcuY383EXPkdvIL1zyMg0wxgyX9LCkXElPW2vvSzLmEUlnSdolaYK1\n9jNjTHdJ/ympk6RKSU9aax+JjG8naZakHpK+lTTWWru1XvYIAADAIWmPjBljciVNkzRc0hGSxhtj\nDk8Yc7akPtbavpKukPR45Ftlkq631vaXNEjSZGPMYZHv3SJpnrW2n6R3I8tohOg5chv5uYueI7eR\nX7hkOk15gqSV1tpvrbVlkmZKGpkwZoSk5yTJWrtI0kHGmM7W2g3W2s8jt++QtFxSt8R1Iv+PqvOe\nAAAAOChTMdZN0pq45bXaV1ClG5MfP8AY01PSMZIWRW7qbK0tiXxdIqlz9lOGS+g5chv5uYueI7eR\nX7hkKsYqs9xOTqr1jDEHSnpZ0q8jR8iqsNZWZnM/8adLCgsLWWaZZZaTLifau3dvleVk4xPHlG4r\nTTk+2djE+SSeYopfJ3F8stNR8eMzzbeh7V/i9tKNzXa+6cYnG5u4f/FzyLR/Nc2joe1fsrF1fb6l\nm3vQz7eG/nrKVqYG/nWSusctd5d35CvdmPzIbTLGNJX0/yS9YK2dHTemxBjTxVq7wRjTVdLGTBON\n/ws98a91lhvucmFhYYOaD8uNP79EeXl5XgdrmvF5eVV/FLZts++oRHR82aIlKcf2H9y/yviyRUu0\nPcUcEse3bdu2ytjE8Znmm2r/Nr9dGPtre3/uX+J8E/evNnnEyzTf6JxTzTfT/tU0D7/2L5pfTfcv\n2di6Pt9SjU01vjG+nqLzzXb/Fi9eXO1+0slUjH0iqW/kNON6SeMkjU8Y86qkqyXNNMYMkrTVWlti\njMmR9BdJy6y1DydZ51JJ90X+ny0AAIAQSnua0lq7V16h9ZakZZJmWWuXG2OuNMZcGRkzR9IqY8xK\nSdMlTYqsfoqkiySdboz5LPJveOR7UyUNM8askHRGZBmNED1HbiM/d9Fz5DbyC5eM1xmz1s6VNDfh\ntukJy1cnWa9QKYo9a+0WSUNrNFMAAIBGiCvww1e1aWREw0F+7uI6VW4jv3ChGAMAAAgQxRh8Rc+R\n28jPXfQcuY38woViDAAAIEAUY/AVPUduIz930XPkNvILF4oxAACAAFGMwVf0HLmN/NxFz5HbyC9c\nKMYAAAACRDEGX9Fz5Dbycxc9R24jv3ChGAMAAAgQxRh8Rc+R28jPXfQcuY38woViDAAAIEAUY/AV\nPUduIz930XPkNvILF4oxAACAAFGMwVf0HLmN/NxFz5HbyC9cKMYAAAACRDEGX9Fz5Dbycxc9R24j\nv3ChGAMAAAgQxRh8Rc+R28jPXfQcuY38wiUv6AkADU150QZVFG9Sk64dlVvQJejpNEo8xgCwD0fG\n4CsXe44qijdp+8W3q6J4U9BTCZxf+fEY+4+eI7eRX7hQjAEAAASIYgy+oufIbeTnLnqO3EZ+4UIx\nBgAAECCKMfjKxZ4x7EN+7qLnyG3kFy68mxIIGd7JCAANC0fG4Ct6jhqemryTkfzcRc+R28gvXCjG\nAAAAAkQxBl819p6j8qINKlu0ROVFG4Keii8ae36NGT1HbiO/cKEYA+qAi5cCAOqKBn74qiY9R9HG\nckk0l9eAn48bPWPuatu2rbYHPQnUGvmFC8UY9ovibbu1ccceSVKbdtu1K/cHdWjSQZ1zO8fGRI8y\nSdKuOdP1/frtKccm23Z9jy1p36HKHCSlHF+Tsdk8FjWZc20ft8Q5+/UYZ/O4pXssosXmpu752hT5\nkZXNPADAFZymhK+iPUcbd+zRTXNW6qY5K7WxfLPu2nmXNldsTrne5vKcrMdGt51ubLS3q+T7HbWe\nQ7rxNRlb08cim/1LNY+6jk3MrzbzzeZxS7ftaLG5cfvuGj1uYUfPkdvIL1woxuCkaHFVtmiJKnfv\nyTg+dvRoT9l+mF3j0avZgVk/xgCA2qEYg6/86jmKFlcUWP7qVJnLY+worlPlNvILF3rG4Ktov09l\np4ODngoAAA0SR8bgqx++XsmRlYjoqVWXTvnRt+IusnMb+YULxRiwn9C3BgBIhmIMvqLvwW3k5y6y\ncxv5hQs9Y0ADFH8hV1f67egPBIDa4cgYfEXfQ+00lHeL1iQ/TsM2LLz23EZ+4UIxBgAAECCKMfiK\nvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5Bcu\nFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7\ncBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIx\nBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3\nkZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4ZKXaYAxZrikhyXlSnraWntfkjGPSDpL0i5J\nE6y1n0Vu/6ukcyRttNYeGTf+TkmXS9oUuelWa+2bddsVAAAA96Q9MmaMyZU0TdJwSUdIGm+MOTxh\nzNmS+lhr+0q6QtLjcd9+JrJuokpJD1prj4n8oxBrpOh7cBv5uYvs3EZ+4ZLpNOUJklZaa7+11pZJ\nmilpZMKYEZKekyRr7SJJBxljukSWP5D0Q4pt59R61gAAAI1EptOU3SStiVteK+nELMZ0k7Qhw7av\nMcZcIukTSTdaa7dmni5cU1paSmOiw8jPXWTnNvILl0xZV2a5ncSjXJnWe1xSL0lHSyqW9ECW9wMA\nANCoZCrG1knqHrfcXd6Rr3Rj8iO3pWSt3WitrbTWVkp6Wt7p0LQKCwurfM2yG8vRvoe9e/fGvh//\ndbL1k40p3VZaZXz8O42SjU2cT+I7k+LXSbz/dGOznW+68cnG1mX/kr3rqr72L1l+yeZbl/1LNrYu\n+5dubKrxddm/mj7f6mP/snk9xfcc7c/94/VUP/uX6rUXnXP8eF5P/r+eUo2PziHd+GxkOk35iaS+\nxpiektZLGidpfMKYVyVdLWmmMWaQpK3W2pJ0GzXGdLXWFkcWR0takmmigwcPTvo1yw1/WZLy8vKq\nfl1WfXzZoiVJx0tS2zZtq4wvW7RE29OM7T+4f8rxiXNInG/btm1Tjs1m/xIl7l+ysXXZv8T5Js7Z\nj/1LnK9U+/1LNrYu+5d07j7uX02fb/Wxf/X9eqrP/eP1FOz+JRvL62n/v54WL15c7X7SSXtkzFq7\nV16h9ZakZZJmWWuXG2OuNMZcGRkzR9IqY8xKSdMlTYqub4x5SdJHkvoZY9YYY34Z+dZ9xpgvjTFf\nSBoi6foazRrO4Fo5biM/d5Gd28gvXDJeZ8xaO1fS3ITbpicsX51i3cSjaNHbL6nBHAEAABot3qwB\nX3GtHLeRn7vIzm3kFy4UYwAAAAGiGIOv6HtwG/m5i+zcRn7hQjEGAAAQIIox+Iq+B7eRn7vIzm3k\nFy4UYwAAAAGiGIOv6HtwG/m5i+zcRn7h4kwxVrZoicqLMn32OAAAgFucKca2X3y7Koo3BT0N1BB9\nD24jP3eRndvIL1ycKcYAAAAaI4ox+Iq+B7eRn7vIzm3kFy4UYwAAAAGiGHNMedEGp97MQN+D28jP\nXWTnNvILF4oxx1QUb+LNDAAANCJ5QU8A7ikv2qCK4k1q0rWjcgu6pB1bWlpKxe8w8nMX2bmN/MKF\nrFFjHJ0DAKD+UIzBV/Q9uI383EV2biO/cKEYAwAACBDFGHzFtXLcRn7uIju3kV+4NLoG/po0lwMA\nAASt0R0Zo7m8YaHvwW3k5y6ycxv5hUujK8YAAABc4tRpypL2HfT9+u1q0267duX+oA5NOqhzbuda\nj42e0tzUPV+blBcbK6na+MSxkjLOo3jbbm3csSersfHj62v/arPdxLHJHotUc0g2lmvluI383EV2\nbiO/cHEq683lObppzkptLN+su3bepc0Vm+s0NnpKc+P23VXGJhufODabeWzcsSfrsfHj62v/arPd\nxLHpxifOIdO2AQBAdU4VY/BP9DMvK3fvqdft0vfgNvJzF9m5jfzChWLMB34VNn6KHvnTnrKgpwIA\nQKhQjPmAwmYfrpXjNvJzF9m5jfzCxakG/sYo+sYASarsdHDAswEAAPsbxVjAYkfRJOm1J4OdjA/a\ntm2r7UFPArVGfu4iO7eRX7hQjDVi0aNuHHEDAKDhomesEWsIvWv0PbiN/NxFdm4jv3ChGAMAAAgQ\nxRh8xbVy3EZ+7iI7t5FfuFCMAQAABIhiDL6i78Ft5OcusnMb+YULxRgAAECAKMbgK/oe3EZ+7iI7\nt5FfuFCMAQAABIhiDL6i78Ft5OcusnMb+YULxRgAAECAKMbgK/oe3EZ+7iI7t5FfuFCMAQAABIhi\nDL6i78Ft5OcusnMb+YULxRgAAECAKMbgK/oe3EZ+7iI7t5FfuFCMAQAABIhiDL6i78Ft5OcusnMb\n+YULxRgAAECAKMbgK/oe3EZ+7iI7t5FfuFCMAQAABIhiDL6i78Ft5OcusnMb+YULxRgAAECAKMbg\nK/oe3EZ+7iI7t5FfuFCMAQAABIhiDL6i78Ft5OcusnMb+YULxRgAAECAKMbgK/oe3EZ+7iI7t5Ff\nuFCMAQAABIhiDL6i78Ft5OcusnMb+YULxRgAAECAKMbgK/oe3EZ+7iI7t5FfuFCMAQAABIhiDL6i\n78Ft5OcusnMb+YULxRgAAECAKMbgK/oe3EZ+7iI7t5FfuFCMAQAABCgv0wBjzHBJD0vKlfS0tfa+\nJGMekXSWpF2SJlhrP4vc/ldJ50jaaK09Mm58O0mzJPWQ9K2ksdbarXXeGzQ4paWlVPwOIz93kZ3b\nyC9c0mZtjMmVNE3ScElHSBpvjDk8YczZkvpYa/tKukLS43HffiaybqJbJM2z1vaT9G5kGQAAIHQy\nFd4nSFpprf3WWlsmaaakkQljRkh6TpKstYskHWSM6RJZ/kDSD0m2G1sn8v+o2k0fDR19D24jP3eR\nndvIL1wyFWPdJK2JW14bua2mYxJ1ttaWRL4ukdQ5w3gAAIBGKVMxVpnldnJquZ6stZU1GS9Je/fu\nrbJcWFiowsLCtGNKt5WmHJ84Ntn4dNd8Kd1WWmV7ycbG30ey+aabe33vX+J8k+1f/DqZ9i/dfKNj\n48fUx/7Fz6Gu+5d4/zXZv1Rj0o2v6fMt0/7V9PlW1/ySzZfXU/29nhLHZ5pvqv3L9Bzya/94PdXP\n/qV67UXnHD+e15P/r6dU46NzSDc+G5ka+NdJ6h633F3eka90Y/Ijt6VTYozpYq3dYIzpKmljNpON\nysvLk8r2LQ8ePDj5mDht2+w75BsdX7ZoSdKxycaXLVqi7Snm07ZNW/Uf3H/fctu21cbGzznZfFON\nTTW+LvuXON9k+xc/h0z7V9P5phofnW82+xc/37ruX+J867p/ier6fMu0fzV9vtXH/vF6Sj3fur6e\nEsfX9vW0+e3CpOP93j9eT/Wzf9H8eD01jNdTTX4/SdLixYur3U86mY6MfSKprzGmpzGmmaRxkl5N\nGPOqpEskyRgzSNLWuFOQqbwq6dLI15dKml2jWcMZ9D24jfzcRXZuI79wSVuMWWv3Srpa0luSlkma\nZa1dboy50hhzZWTMHEmrjDErJU2XNCm6vjHmJUkfSepnjFljjPll5FtTJQ0zxqyQdEZkGQAAIHQy\nXmfMWjtX0tyE26YnLF+dYt3xKW7fImlo9tOEq7hWjtvIz11k5zbyCxeyBgAACBDFGHxF34PbyM9d\nZOc28gsXijEAAIAAUYzBV+muf4OGj/zcRXZuI79woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAA\ngABRjMFX9D24jfzcRXZuI79woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzc\nRXZuI79woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZuI79woRgDAAAI\nEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZuI79woRgDAAAIEMUYfEXfg9vIz11k\n5zbyCxeKMQAAgABRjMFX9D24jfzcRXZuI79woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABR\njMFX9D24jfzcRXZuI79woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZu\nIwuyI/sAAAvCSURBVL9woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZu\nI79woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZuI79woRgDAAAIEMUY\nfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZuI79woRgDAAAIEMUYfEXfg9vIz11k5zby\nCxeKMQAAgABRjMFX9D24jfzcRXZuI79woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX\n9D24jfzcRXZuI79woRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZuI79w\noRgDAAAIEMUYfEXfg9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZuI79woRgDAAAIEMUYfEXf\ng9vIz11k5zbyCxeKMQAAgABRjMFX9D24jfzcRXZuI79woRgDAAAIUF6mAcaY4ZIelpQr6Wlr7X1J\nxjwi6SxJuyRNsNZ+lm5dY8ydki6XtCmyiVuttW/WeW/Q4LRt21bbg54Eao383EV2biO/cEl7ZMwY\nkytpmqThko6QNN4Yc3jCmLMl9bHW9pV0haTHs1i3UtKD1tpjIv8oxAAAQChlOk15gqSV1tpvrbVl\nkmZKGpkwZoSk5yTJWrtI0kHGmC5ZrJtTHzuAho2+B7eRn7vIzm3kFy6ZTlN2k7QmbnmtpBOzGNNN\n0sEZ1r3GGHOJpE8k3Wit3VqDeQMAADQKmY6MVWa5nZoe5XpcUi9JR0sqlvRATVbeu3dvleXCwkIV\nFhamHVO6rTTl+MSxycan+yuldFtple0lGxt/H8nmm27u9b1/ifNNtn/x62Tav3TzjV4rJ35Mfexf\n/Bzqun+J91+T/Us1Jt34mj7fMu1fTZ9vdc0v2Xx5PdXf6ylxfKb5ptq/+OtU7c/94/VUP/uX6rUX\nnXP8eF5P/r+eUo2PziHd+GxkOjK2TlL3uOXu8o5wpRuTHxnTNNW61tqN0RuNMU9Leq1Gk87Lk8r2\nLQ8ePDj5mDht2+z7wRQdX7ZoSdKxycaXLVqSspmybZu26j+4/77lJI2X8XNONt9UY1ONr8v+Jc43\n2f7FzyHT/tV0vqnGR+ebzf7Fz7eu+5c437ruX6K6Pt8y7V9Nn2/1sX+8nlLPt66vp8Tx++P1VJ/7\nx+sp2P1LNpbX0/5/PS1evLja/aST6cjYJ5L6GmN6GmOaSRon6dWEMa9KukSSjDGDJG211pakW9cY\n0zVu/dGSlgiNEn0PbiM/d5Gd28gvXNIWY9bavZKulvSWpGWSZllrlxtjrjTGXBkZM0fSKmPMSknT\nJU1Kt25k0/cZY740xnwhaYik6+t/1wAAABq+jNcZs9bOlTQ34bbpCctXZ7tu5PZLajZNuIpr5biN\n/NxFdm4jv3DhCvwAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfgq/lpHcA/5uYvs3EZ+4UIx\nBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3\nkZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMA\nAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5\nuYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAA\nECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7\nyM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAAB\nohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs\n3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCK\nMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t\n5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiD\nr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+\n4UIxBgAAECCKMfiKvge3kZ+7yM5t5BcuFGMAAAABohiDr+h7cBv5uYvs3EZ+4UIxBgAAECCKMfiK\nvge3kZ+7yM5t5BcueZkGGGOGS3pYUq6kp6219yUZ84iksyTtkjTBWvtZunWNMe0kzZLUQ9K3ksZa\na7fWxw4BAAC4JO2RMWNMrqRpkoZLOkLSeGPM4QljzpbUx1rbV9IVkh7PYt1bJM2z1vaT9G5kGY0Q\nfQ9uIz93kZ3byC9cMp2mPEHSSmvtt9baMkkzJY1MGDNC0nOSZK1dJOkgY0yXDOvG1on8P6rOewIA\nAOCgTMVYN0lr4pbXRm7LZszBadbtbK0tiXxdIqlzDeYMh9D34DbycxfZuY38wiUn3TeNMedJGm6t\n/b+R5YsknWitvSZuzGuSplprP4wsvyNpiqSeCeteLOl4a+21xpgfrLX/EreNLdbadqnm8c4777wv\naUjtdhEAAGC/+ufQoUNPy3Zwpgb+dZK6xy13l3eEK92Y/MiYpkluXxf5usQY08Vau8EY01XSxnST\nqMkOAQAAuCRTMfaJpL7GmJ6S1ksaJ2l8wphXJV0taaYxZpCkrdbaEmPM92nWfVXSpZLui/w/u+67\nAgAA4J60PWPW2r3yCq23JC2TNMtau9wYc6Ux5srImDmSVhljVkqaLmlSunUjm54qaZgxZoWkMyLL\nAAAAAAAAAAAAAAAAAAB/pb20RdCy+SgmNBzGmL9KOkfSRmvtkZHb+OgrBxhjukv6T0mdJFVKetJa\n+wj5ucEY00LSPyU1l9RM0n9Za28lP3dEPrXmE0lrrbU/Jzt3GGO+lfT/t3c/LzZGARjHv0am/CqL\nKdRYWCuZ1CTj1yiKZPeUBStZWcjCgoV/gT/AJE1SnjSlbOTHwkpNjQhLCwtkIT+SwlyL9x1uU8y9\nq3tOns/mvvecu3jr6a1zO+fe5xPwE/hue7zf/IotCu+liimKc5Umr26pvqrDd+Cs7S3ADuB0+7wl\nvwrY/gZM2t4GbAUmJe0i+dXkDM2P3Trt+2RXjw6wz/aY7fF2rK/8il2M0VsVUxTE9iPgw6LhVF9V\nwPZb20/a6y/AS5rGjORXCdtf28thmt2EDyS/KkgaBQ4DV/izY5Xs6rJ4p7Gv/EpejPVSxRTlS/VV\nZdr/BhwDHpP8qiFpSNITmpwe2n5O8qvFJeAcMN81luzq0QHuSZqVdKod6yu/khdjnaU/EjWx3SG5\nFk3SGuAWcMb25+655Fc22/PtNuUosEfS5KL55FcgSUdoztnO8Zdz3MmueBO2x4BDNEc8dndP9pJf\nyYuxXqqYonzvJG0A6KX6KgZH0gqahdi07YVWjORXGdsfgTvAdpJfDXYCRyW9Am4A+yVNk+yqYftN\n+/oemKE5ZtVXfiUvxn5XMUkapqlTuj3ge4r+LVRfQaqviiVpGTAFvLB9uWsq+VVA0oikde31SuAA\nMEfyK57tC7Y32d4MHAMe2D5BsquCpFWS1rbXq4GDwDP6zG+pbsqBsf1D0kKd0nJgqqtOKQok6Qaw\nFxiR9Bq4SFN1dVPSSdqf9w7uDuMfJoDjwFNJc+3YeZJfLTYC1yQN0XzJnrZ9v80y+dVlYTsrz14d\n1gMzkqBZU123fVfSLMkvIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIi4r/2CxTP\ngGkEFh3tAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a84b438>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Ok, everything looks fine in this demonstration.\n",
      "\n",
      "# To make things more fun, here is a uniform hypergraph generator"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from IPython.html.widgets import interact\n",
      "from hypergraph import generators, utils"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HG = None\n",
      "def create(number_of_nodes=(5,30), number_of_edges=(5,30), cardinality=(1,10), plot=False):\n",
      "    global HG\n",
      "    HG = generators.uniform_hypergraph(number_of_nodes, number_of_edges, cardinality)\n",
      "    \n",
      "    if plot:\n",
      "        utils.plot_different_representations(HG.nodes(), HG.hyper_edges())\n",
      "\n",
      "    return HG"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(create)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "<function __main__.create>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "\n",
      "fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(14, 4))\n",
      "\n",
      "axes[0].plot([1, 2, 3], [3, 2, 4])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7faa9a89bd30>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JiOSKVm5aKSxI8c8XjGXMgJ7c+nw1B442Or1/x/uOI+PLOJdtbaDhaBOzJw3s\n9r/1ZYziF1/rSrnd8jW3uONrjSi3W77mDiovmxuAglSKL58/hlOG9Oarz1Wz/4jbBkfiIZ1O8+jy\nGq4rH0FhgXdPJoqIiIhIN+RtcwOQSqX44kdGM6OsH19ZXM3ew8ed3G9S9jb6MM433ttHY3Oa8yeU\nBvr3PoxR/ONrXSm3W77mFnd8rRHldsvX3EHldXMDLQ3OF2aN5MNj+3Pzomp2H3LT4Ej0mtNpHl1W\nw/UzyyhIadVGREREJN/lfXMDLQ3O588ZyYWTBnLTonXsPHgs1PtLyt7GuI/z1Q17KSkq4Nyx/QPf\nRtzHKH7yta6U2y1fc4s7vtaIcrvla+6gEtHcnHDN2SOYe8pg/vnZddQ1hNvgSLSamtMsrGxZtUlp\n1UZEREQkERLV3ABcOWM4n5g2lJsWrWP7/qOh3EdS9jbGeZwvVu+mtFcRM0f1O6nbifMYxV++1pVy\nu+VrbnHH1xpRbrd8zR1U4pobgE+eMYyrZgznpkXr2LL3SNRxJMcam9P8uKqWG2aO1KqNiIiISIIk\nsrkBuPz0IVxXXsZXFlezac/hnN52UvY2xnWcS97dxcj+PZhe1vekbyuuYxS/+VpXyu2Wr7nFHV9r\nRLnd8jV3UIltbgDmnjqYv501klsWV7N+16Go40gOHGts5vGqWq6fWRZ1FBERERFxLNHNDcDFkwfx\nxY+M5tbn1vPujtw0OEnZ2xjHcS5au5NJg3px+rA+Obm9OI5R/OdrXSm3W77mFnd8rRHldsvX3EEl\nvrkBuGDiQL78F2P42pL1rKk/GHUcCehIYzM/XVmnVRsRERGRhFJzk3HeuFJuvnAsX39hA6tqD5zU\nbSVlb2PcxvnM6h1MG96XyUN65+w24zZGyQ++1pVyu+VrbnHH1xpRbrd8zR2UmptWZo0ZwK2zx/Fv\nSzdSta0h6jjSDQePNWFX1nNt+Yioo4iIiIhIRNTctFE+qj+3Xzye77y8iT9s2R/oNpKytzFO4/zl\n2zuYOaof4wf2yuntxmmMkj98rSvldsvX3OKOrzWi3G75mjsoNTftmF7Wj29cMoG7X9nMG5v3RR1H\nutBwtJGn39KqjYiIiEjSqbnpwLThfbnj0onc99p7vLpxT7f+bVL2NsZlnD9fVc9540oZNaBnzm87\nLmOU/OJrXSm3W77mFnd8rRHldsvX3EGpuenEqUP7cOe8SXzvt1t5qXp31HGkHXsPH+fZNTv53Nla\ntRERERFxQ2+fAAAYAklEQVRJOjU3XZg0uDd3zpvMD36/jRfe3ZXVv0nK3sY4jPNnK+u5aOJAhvcr\nCeX24zBGyT++1pVyu+VrbnHH1xpRbrd8zR2UmpssTBjUi7vnT+GR5TUsWrsz6jiSsevQcZa8u4vP\nnqVVGxERERFRc5O1saU9uWf+FJ5YUcvTb+/o9Nyk7G2MepxPrqjlY1MGMbhPcWj3EfUYJT/5WlfK\n7ZavucUdX2tEud3yNXdQam66YdSAHtx72RR++VY9dmVd1HESra7hGC+t38OVM4ZHHUVEREREYkLN\nTTeN6NeDey+fwuK1u3i8qrbdc5KytzHKcf5kRS2XnTaEgb3CW7WB5DyW4pavdaXcbvmaW9zxtUaU\n2y1fcwel5iaAoX1KuPfyKby8fg+PLNtOOp2OOlKibNt3lNc37eXTZw6LOoqIiIiIxIiam4AG9y7m\nnssm87v39vHw7/+8wUnK3saoxvl4VQ2fmDaU/j2LQr+vpDyW4pavdaXcbvmaW9zxtUaU2y1fcwfV\n5V+HxpgxwEJgGJAGfmCtfaDNORcBvwI2ZL71lLX2jtxGjZ+BvYq5e/4Ubnmumod+t42/P3cUqVQq\n6lh5bfOew/xhawOPXDkm6igiIiIiEjPZrNwcB/7RWjsNOBf4B2PM6e2c94q19uzMf3nf2JzQv2cR\nd8+fzNr6gzzw+haa0+nE7G2MYpyPVdby6TOH0aek0Mn9JeWxFLd8rSvldsvX3OKOrzWi3G75mjuo\nLpsba22ttXZF5usDwBpgZDunJnbJom+PIv593mQ27znCfa+9R1OzXoMThvW7DvFW7QGumDok6igi\nIiIiEkPdes2NMWY8cDbwZpsfpYHzjDF/NMYsNsZMzVE+b/QuKeTbcydRd+AYN/98WSIaHNd7OBcu\nr+WqGcPpVexm1QaSt09V3PC1rpTbLV9zizu+1ohyu+Vr7qCybm6MMX2BnwNfyqzgtFYJjLHWzgD+\nE3i6s9tq/UuuqKjIm+NexYXM61tH/d4DfOflTTQ2p2OVz+fjtfUHWbfrEAN3v+v0/letWhWL8bs6\nFhEREfFZVlvJjDHFwLPAc9ba+7M4fyMw01q7u+3Pli5dmi4vL+92UJ8ca2zmjpc2kiLF1y4eT0mh\n3pTuZN36XDUfHV/K5adrS1oYKisrmTNnjndbS5Mwn4j4RHOJiORK0Pmky7+6jTEp4EfA6o4aG2PM\n8Mx5GGNmAan2GpukKCkq4PaLJ1BYkOKbv97I0cbmqCN5bVXtAbbuO8qlpwyKOoqIiIiIxFg2Swof\nBa4BZhtjqjL/zTPGLDDGLMic82lglTFmBXA/8JmQ8nqhoqKC4sICvvaX4+nbo5Cvv7Cew8eboo6V\ncy62M6XTaR5ZVsO15SMojmAFTFu2JAy+1pVyu+VrbnHH1xpRbrd8zR1Ul59zY62toIsmyFr7IPBg\nrkLli8KCFF+5cBz/8dp7/MuSDXzrYxPp7egtjPNF1fYG9hw+zsWTtWojIiIiIp3Ti0FC0Pr9xAsL\nUvzzBWMZPaAHtz2/noPH8mcFJ+z3TW+9alNYEM0W7qS9N7y44WtdKbdbvuYWd3ytEeV2y9fcQam5\ncaAgleLL549hypBefHVxNfuPNEYdyQtvbtnPkcZmLpw4MOooIiIiIuIBNTchaG9vYyqV4osfGc30\nsr58ZXE1ew8fjyBZboW5h7M5nWbh8hqum1lGQSq6N95J2j7VsBlj5hpj1hpj1hljvtrOzz+X+bys\nlcaY140x06PIGTZf60q53fI1tyuaT/ytEeV2y9fcQam5cSiVSvGFWSP58Nj+3Ly4mt2H/G9wwvL6\npn0AfHTcgIiTSK4YYwqB7wJzganA1caY09uctgG4wFo7HfgW8AO3KUXEB5pPRKQjXb6hgHRfZ3sb\nU6kUnz9nJMWFBdy0aB13z5/MkD4lDtPlTlh7OJuaW1ZtvvDhkaQiXLWB5O1TDdksoNpauwnAGPMk\n8HFgzYkTrLVvtDr/TWC0y4Cu+FpXyu2Wr7kd0XyCvzWi3G75mjsordxE5JqzRzD3lMHctGgddQ3H\noo4TK7/ZsIc+JYV8aHT/qKNIbo0CtrQ63pr5Xkf+BlgcaiIR8ZXmExFpl5qbEGS7t/HKGcP5+NSh\n3LRoHTX7j4acKvfC2MPZ1Jzmscparj+nLPJVG0jePtWQpbM90RgzG/hr4AP76Ntq/RhVVFR4cXzi\ne3HJk+3xQw89FKs8+n3H79ihnM8nUf/uVNvxP9bvO5rj7nL+1+PSpUvT5eXlru/WqYqKim4tAT67\nZidPrKjlrvmTGT2gZ4jJcqu748zG8+/s4sXq3dxz2ZSc3m5QYYwxjiorK5kzZ06o84Ex5lzgG9ba\nuZnjW4Fma+1dbc6bDvwCmGutre7sNn2dT3ytK+V2y8fcLuYSyP18ornELeV2y9fcQecTveYmBN0t\noMtPH0JxYYqbF1Vz57xJjB/YK6RkuZXrC+VYUzOPV9Vyy0Xjcnq7J8PHySDGlgFTjDHjge3AVcDV\nrU8wxoyl5Q+Ra7pqbHzma10pt1u+5nZE8wn+1ohyu+Vr7qC0LS0mLj1lMH87ayS3LK5m/a5DUceJ\nxPPv7GJMaQ+mjegbdRQJgbW2EbgRWAKsBn5qrV1jjFlgjFmQOe3rwEDgIWNMlTHm9xHFFZEY03wi\nIh3RtrQQnMzy36sb9vDd327ljksnccrQ3jlOllu5XOY82tjMDT9bzTcvmRircfu6lNtdrraS5Jqv\n84mvdaXcbvmYW3OJWz7WCCi3a77mDjqfaOUmZi6YOJAv/8UYvrZkPWvqD0Ydx5ln1+zk1KG9Y9XY\niIiIiIhf1NyE4GS74/PGlXLzhWP5+gsbWFV7IEepci9XzwIcPt7Ez1bWcf3MspzcXi75+EyHxJ+v\ndaXcbvmaW9zxtUaU2y1fcwel5iamZo0ZwK2zx/FvSzdSta0h6jihevrtHUwv68uEQX68kYKIiIiI\nxJOamxCczHtzt1Y+qj+3Xzye77y8iT9s2Z+T28ylXIzz4LEmfvHWDq4tj9+qDTj/3AZJCF/rSrnd\n8jW3uONrjSi3W77mDkrNTcxNL+vHNy6ZwN2vbOaNzfuijpNzT62qZ9aY/owt9efzfUREREQkntTc\nhCDXexunDe/LHZdO5L7X3uO1jXtzetsn42THuf9II8+s3sE1Z4/IUaLcS9o+VXHD17pSbrd8zS3u\n+Fojyu2Wr7mDUnPjiVOH9uHOeZN48LdbeKl6d9RxcsKurOP8CaWU9e8RdRQRERERyQNqbkIQ1t7G\nSYN7c+e8yfzw99t54d1dodxHd5zMOPccOs7id3bx2bPiu2oDydunKm74WlfK7ZavucUdX2tEud3y\nNXdQam48M2FQL+6aP5lHltewaO3OqOME9uTKOi6ePIhhfUuijiIiIiIieULNTQjC3ts4trQn9142\nhSdX1PH02ztCva/OBB3njoPHWLpuN5+ZMTzHiXIvaftUxQ1f60q53fI1t7jja40ot1u+5g5KzY2n\nRvbvwb2XTeGXb9VjV9ZFHadbnqiqY+4pgxnUuzjqKCIiIiKSR9TchMDV3sbh/Uq49/IpLF67i59U\n1Tq5z9aCjLOm4SivbNzDlR6s2kDy9qmKG77WlXK75WtuccfXGlFut3zNHZSaG88N7dPS4Ly8fg+P\nLq8hnU5HHalTP6mq5YqpQxnQsyjqKCIiIiKSZ9TchMD13sbBvYu5+7LJvLF5Lz/6w3ZnDU53x7l1\n3xF+995+PnXG0JAS5V7S9qmKG77WlXK75WtuccfXGlFut3zNHZSamzwxsFcxd8+fQuW2Bv7v77bF\ncgXnscpaPjltKH17aNVGRERERHJPzU0Iotrb2L9nEXfPn8ya+oP85+tbaQ65wenOODfuPkzVtgY+\nMc2fVRtI3j5VccPXulJut3zNLe74WiPK7ZavuYNSc5Nn+vYo4t/nTWbTnsPc99p7NDXHYwVn4fIa\nrpw+jN4lhVFHEREREZE8peYmBFHvbexdUsi3506i7sAx7nllc2gNTrbjfHfnIdbuOMTlU/1atYHo\nH0vJT77WlXK75WtuccfXGlFut3zNHZSamzzVq7iQb31sEvuPNnLny5tojHAFZ+HyGj4zYzg9i1Ru\nIiIiIhIe/bUZgrjsbexRVMA35kzkWFMz33pxI8eamnN6+9mM8+26A2zac5h5pw3O6X27EpfHUvKL\nr3Wl3G75mlvc8bVGlNstX3MHpeYmz5UUFXD7xRMoTKX45q83crQxtw1OVx5dXsPnzhpBSaFKTURE\nRETCpb84QxC3vY3FhQV87S/H07dHIV9/YQOHjzfl5Ha7GueK7Q3UHzjGJaf4uWoD8XssJT/4WlfK\n7ZavucUdX2tEud3yNXdQam4SorAgxVcuHMeQPsX8y5INHDqWmwanI+l0mkeX13DN2WUUFaRCvS8R\nEREREVBzE4q47m0sLEjxzxeMZfSAHtz2/HoOnmSD09k4l21toOFoE7MnDTyp+4haXB9L8ZuvdaXc\nbvmaW9zxtUaU2y1fcwel5iZhClIpvnz+GKYM6c1XF1ez/0hjzu/jxKrNdeUjKNSqjYiIiIg4ouYm\nBHHf25hKpfjiR0YxvawvX32umr2Hjwe6nY7G+cZ7+2hsTnP+hNKTiRkLcX8sxU++1pVyu+VrbnHH\n1xpRbrd8zR2UmpuESqVSfGHWSGaN6c/Ni6vZfShYg9NWczrNo8tquH5mGQUprdqIiIiIiDtqbkLg\ny97GVCrF588ZyYUTB3LTonXsPHisW/++vXG+umEvJUUFnDu2f65iRsqXx1L84mtdKbdbvuYWd3yt\nEeV2y9fcQam5Ea45ewRzTxnMTYvWUdfQvQantabmNAsrW1ZtUlq1ERERERHH1NyEwMe9jVfOGM7H\npw7lpkXrqNl/NKt/03acL63fTWmvImaO6hdGxEj4+FhK/PlaV8rtlq+5xR1fa0S53fI1d1BqbuRP\nPnnGMK6aMZybFq1j674j3fq3jc1pHqus5YaZI7VqIyIiIiKRUHMTAp/3Nl5++hCum1nGzYuq2bzn\ncKfnth7nknd3UdavB9PL+oYd0SmfH0uJL1/rSrnd8jW3uONrjSi3W77mDkrNjXzApacM5m9njeSr\ni6tZv+tQl+cfa2zm8apabjinzEE6EREREZH2qbkJQT7sbbx48iC++JHR3Pb8et7d2X6Dc2Kci9bu\nZNKgXpw+rI/LiE7kw2Mp8eNrXSm3W77mFnd8rRHldsvX3EGpuZEOXTBxIF86fwz/8vx61tQfbPec\nI43N/HRlHdfP1KqNiIiIiESrqKsTjDFjgIXAMCAN/MBa+0A75z0AzAMOATdYa6tynNUbFRUVedMl\nnzeulKKCFF9/YQNfnzOBM0e8/5qaiooKtvefwtRhfZk8pHeEKcOTT49lHBhj5gL3A4XAw9bau9o5\nJ+/nEl/rSrnd8jW3K5pP/K0R5XbL19xBZbNycxz4R2vtNOBc4B+MMae3PsEYMx+YbK2dAvwd8FDO\nk0pkZo0ZwK2zx/FvSzdStb3hT98/2gR2ZT3XzRwRYTrxhTGmEPguMBeYClytuUREgtB8IiId6bK5\nsdbWWmtXZL4+AKwBRrY57Qrg0cw5bwKlxpjhOc7qjXzsjstH9ef2i8fznZc2sWzrfgBq+k9m5qh+\njB/YK+J04cnHxzJCs4Bqa+0ma+1x4Eng423OScRc4mtdKbdbvuZ2RPMJ/taIcrvla+6guvWaG2PM\neOBs4M02PxoFbGl1vBUYfVLJJHaml/XjG5dM4K7fbGbput08/VY915Zr1Uay1t48MSqLczSXiEhb\nmk9EpF1ZNzfGmL7Az4EvZVZw2mr7yY3pkwnms3x+P/Fpw/vy7Usn8dDvtjKx5xFGDegZdaRQ5fNj\nGYFs54S8n0t8rSvldsvX3I5oPsHfGlFut3zNHVSXbygAYIwpBp4CfmytfbqdU7YBY1odj858rz2v\nVFZWXtitlJ7p3bs3lZWVUccI1demARTl/TiT8FhmvOLgPtrOE2NoeSa1s3M6m0vA0/nE17pSbrc8\nze1iLoHczyeaSxxSbrd8zU3A+SSbd0tLAT8CVltr7+/gtGeAG4EnjTHnAnuttXXtnThnzpyLggQV\nEe8tA6ZktrduB64Crm5zTtZzCWg+EUmwnM4nmktE8kfb5doPMMacD7wKrOT95dzbgLEA1trvZ847\n8a4lB4HPW2u9bBFFJDzGmHm8/9atP7LW3mmMWQCaS0SkezSfiIiIiIiIiIiIiIiIiIiIiIiIiIhI\nyLp8zU0Qxpj/B1wG1Ftrz+zgnAeAecAh4AZrbVUYWcLS1RiNMRcBvwI2ZL71lLX2DncJc8MYMwZY\nCAyj5TVXP7DWPtDOed4+ntmMMR8eT2NMT1reeaQHUAL8ylp7azvnxeqxNMbM5f199Q9ba+9q55xY\nZT6hq+zGmM8BX6FlLm4A/t5au9J50D/P1OXvO3Peh4A3gCuttb9wGLFdWdbJRcB9QDGw01p7kcuM\n7cmiRoYAPwZG0PImQPdaax9xnbNNJm//H+/rfOLjXAKaT1zTfNKiWx/i2Q3/RcsL+NpljJkPTLbW\nTgH+DngopBxh6nSMGa9Ya8/O/OfVH8KtHAf+0Vo7DTgX+AdjzOmtT8iDx7PLMWZ4/Xhaa48As621\nZwHTgdmZNwz5k7g9lsaYQuDEC4KnAlf7Un/ZZKelWb7AWjsd+BbwA7cp/1yWmU+cdxfwPCE9SdYd\nWdZJKfAg8FfW2jOATzsP2kaWv+8bgarMdXsR8L+NMVl9jEOIvPx/vK/ziY9zCWg+cU3zyftCaW6s\nta8Bezo55Qrg0cy5bwKlxpjhYWQJSxZjhBhcpCfLWltrrV2R+foAsAYY2eY0rx/PLMcI+fF4Hsp8\nWULLMzu725wSt8dyFlBtrd1krT0OPAl8vM05cct8QpfZrbVvWGv3ZQ7fJPpPT8/m9w3wv2j5UOcd\nLsN1Ipvcn6VlxXUrgLV2p+OM7ckmdw3QP/N1f2CXtbbRYcYP8Pj/8b7OJz7OJaD5xDXNJxlRdWuj\ngC2tjrfSciF2+HkWHkoD5xlj/kjLh4bdZK1dHXGmk5L5PIGzaZk4W8ubx7OTMebF42mMKQAqgUnA\nQ+2MIW6PZXt5PpzFOXGov2yyt/Y3wOJQE3Wty8zGmFG0/A/zL4EPEY9PfM/mdz0FKDbGvAz0A/6P\ntfYxR/k6kk3uHwIvGWO205L7SkfZTobP12Qcs/s4l4DmE9c0n2SEtS0tG22fBY9DQedSJTDGWjsD\n+E/g6YjznBRjTF9anln5UmZ1oy3vH88uxpgXj6e1tjmzHD0auCCzZ7itOD2W2d53nDKfkHUGY8xs\n4K+Br4YXJyvZZL4fuMVam6bl9x6HFc1schcD5cB84FLgdmPMlFBTdS2b3LcBK6y1I4GzgAeNMf3C\njZUTPl+Tccvu41wCmk9c03ySEVVzsw0Y0+p4dOZ7ecNa23BiC5C19jlaOvxBEccKxBhTDDwF/Nha\n294f9d4/nl2NMZ8eT4DM9oVFwDltfhS3x7JtnjG0PGvT2TlRZz4hm+wYY6bT8mzaFdbarra6hi2b\nzDNp+cT3jcCngO8ZY65wlK8j2eTeArxgrT1srd1Fy4dTz3CUryPZ5D4PsADW2vXARuBUJ+mC8/ma\njGN2H+cS0HzimuaTjKi2pT1Dy4uanjTGnAvstdZGvVydU5n9gPXW2rQxZhaQsta2fX1D7BljUsCP\ngNXW2vs7OM3rxzObMebD45l5l5RGa+1eY0wv4BLgm21Oi9tjuQyYktkuuB24Cri6zTlxy3xCl9mN\nMWOBXwDXWGurnSf8oC4zW2snnvjaGPNfwH9ba59xGbId2dTJr4DvZl5024OW7Rr/4TJkO7LJvRaY\nA7yemYdO5f13bYwrb69J4pndx7kENJ+4pvkkI6y3gn4CuBAYQsueuH+lZQkPa+33M+eceEeHg8Dn\nrbWVYWQJS1djNMb8A/D3QCMtb133T9ba30UUN7DMu2m9Cqzk/WXA24CxkB+PZzZjzIfH0xhzJi0v\nyivI/PeYtfYeY8wCiO9jaYyZx/tvbfkja+2dcc98QlfZjTEPA58E3sv8k+PW2lnRpG2Rze+71bkn\n/hiJw1u3ZlMnNwGfB5qBH9p23tbetSxqZAgt7yY0lpbr9k5r7U8iC4zf/4/3dT7xcS4BzSeuaT4R\nERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERERFJ\niP8PDH5c6VrTy7IAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a6ed7f0>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "axes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([<matplotlib.axes.AxesSubplot object at 0x7faa9a002c88>,\n",
        "       <matplotlib.axes.AxesSubplot object at 0x7faa9a6c8c50>,\n",
        "       <matplotlib.axes.AxesSubplot object at 0x7faa9a8acda0>], dtype=object)"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# The next thing is an interactive widget for comparing models of diffusion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import linalg as LA\n",
      "\n",
      "def compare(number_of_iterations=(10000, 1000000),\n",
      "            model=ALL_MODELS):\n",
      "    t_per_walker = number_of_iterations\n",
      "    markov_matrix = model[\"numerical\"](HG)\n",
      "    engine = DiffusionEngine(markov_matrix)\n",
      "    \n",
      "    frequencies, states = engine.simulate(t_per_walker)\n",
      "    connected_elements = [freq[0] + 1 for freq in frequencies]\n",
      "    \n",
      "    if model['name'] == \"node\":\n",
      "        missing_nodes = set(HG.nodes()) - set(connected_elements)\n",
      "        for missing_node in missing_nodes:\n",
      "            frequencies.append((missing_node, 0))\n",
      "\n",
      "    \n",
      "    frequencies = [(node, frequency) for node, frequency in frequencies]\n",
      "    frequencies.sort(key=lambda x: x[0])\n",
      "    xs, ys = zip(*frequencies)\n",
      "    \n",
      "    ys = np.array(ys, dtype='float')\n",
      "    ys /= sum(ys)\n",
      "    width = 0.2  \n",
      "\n",
      "    ys_prediction = model[\"analytical\"](HG)\n",
      "    \n",
      "    plt.figure(figsize=(10, 8))\n",
      "    plt.bar(xs, ys, width=width, color='crimson', label='Simulated')\n",
      "    \n",
      "    freqs_matrix = LA.matrix_power(markov_matrix, 20)[0]\n",
      "    plt.bar(np.array(xs) + width, freqs_matrix, width=width, color='gray', label='Transition matrix to N')\n",
      "    \n",
      "    plt.bar(np.array(xs) + 2 * width, ys_prediction, width=width, color='purple', label='Analytical')\n",
      "    plt.legend(loc=0)\n",
      "    plt.title(\"Comparison after %s iterations for hypergraph with %s nodes and %s hyperedges\" % (t_per_walker, 22, 23))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HG = generators.generic_hypergraph(22, ((3, 6), (4, 4), (5, 5), (6, 8)))\n",
      "print(HG.hyper_edges())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[{1, 9, 19}, {16, 3, 19}, {8, 17, 4}, {11, 20, 7}, {1, 2, 10}, {8, 19, 5}, {10, 12, 20, 22}, {1, 4, 12, 15}, {8, 13, 22, 7}, {9, 18, 14, 7}, {8, 3, 20, 13, 22}, {1, 10, 11, 5, 21}, {18, 11, 5, 13, 22}, {8, 9, 16, 4, 13}, {7, 2, 10, 18, 15}, {21, 22, 8, 9, 12, 13}, {16, 3, 4, 7, 8, 15}, {16, 18, 20, 22, 7, 10}, {16, 2, 20, 8, 13, 15}, {16, 19, 4, 6, 7, 12}, {1, 17, 5, 22, 11, 15}, {2, 18, 7, 8, 10, 11}, {1, 2, 21, 8, 12, 13}]\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(compare);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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z5s2LPQ/f+c53GDRoEI0aNaJp06Zcf/31/P3vf68yJvlw7owZM+jQoQPDhw+n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\nGtp/ACFckjqGNYreAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faa9a19e6a0>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It's random and interactive, however sample is small and it's not very scientific.\n",
      "\n",
      "Time to gather bigger statistic and serialize my results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from collections import Counter\n",
      "from collections import defaultdict\n",
      "import random \n",
      "from hypergraph.generators import generic_hypergraph\n",
      "\n",
      "\n",
      "HG = generic_hypergraph(6, ((2, 3), (3, 4), (4, 2)))\n",
      "HG.hyper_edges()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "[{1, 5},\n",
        " {1, 3},\n",
        " {3, 4},\n",
        " {2, 3, 5},\n",
        " {1, 4, 6},\n",
        " {2, 5, 6},\n",
        " {2, 4, 5},\n",
        " {1, 2, 5, 6},\n",
        " {2, 3, 5, 6}]"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from hypergraph.markov_diffusion import count_nodes\n",
      "from itertools import chain\n",
      "from collections import Counter\n",
      "import numpy as np\n",
      "from matplotlib import pyplot as plt\n",
      "\n",
      "from collections import Counter\n",
      "from itertools import chain\n",
      "from hypergraph import utils\n",
      "from hypergraph.markov_diffusion import (create_markov_matrix,\n",
      "                                         count_nodes)\n",
      "\n",
      "def entropy(pis):\n",
      "    \"\"\"Compute entropy based on probabilities of states\"\"\"\n",
      "    return -np.dot(np.log(pis), pis)\n",
      "    \n",
      "\n",
      "def compare_entropy(t_max=(9900, 10000), number_of_walkers=(1, 10), window_size=(5, 200)):\n",
      "    markov_matrix = create_markov_matrix_model_nodes(HG)\n",
      "    \n",
      "    engine = DiffusionEngine(markov_matrix, t_per_walker=int(t_max / number_of_walkers))\n",
      "\n",
      "    nodes = HG.nodes()\n",
      "    edges = HG.hyper_edges()\n",
      "    most_common, states = engine.simulate(t_max)\n",
      "\n",
      "    states_per_time = list(zip(*states))\n",
      "    \n",
      "    \n",
      "    xs = list(range(0, len(states_per_time), window_size))\n",
      "    ys = []\n",
      "    for i in xs:\n",
      "        try:\n",
      "            cum_states = chain(*states_per_time[i-window_size:i])\n",
      "            most_common = Counter(cum_states).most_common()\n",
      "\n",
      "            most_common_nodes = count_nodes(nodes, edges, most_common)\n",
      "            frequencies = (utils.get_names_and_occurrences(most_common_nodes)[1])\n",
      "            entropy_value = entropy(frequencies)\n",
      "            if entropy_value is not float(\"nan\"):\n",
      "                ys.append(entropy_value)\n",
      "            else:\n",
      "                ys.append(-1)\n",
      "        except ZeroDivisionError:\n",
      "            ys.append(0)\n",
      "        except:\n",
      "            import traceback\n",
      "            traceback.print_exc()\n",
      "            ys.append(0)\n",
      "    \n",
      "    plt.figure(figsize=(14, 6))\n",
      "    fig = plt.plot(xs, ys)\n",
      "    plt.title(\"Entropy with t_max=%s, walkers=%s, window_size=%s\" % (t_max, number_of_walkers, window_size))\n",
      "    plt.show()\n",
      "    return fig"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(compare_entropy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zwgJ1gHXaUs54kBJjQSpf25K2dbgMGAkhfAzYBbwxxvinJWx3SxyZqbHHER5J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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f0d3229cef0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "<function __main__.compare_entropy>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def compare_entropy_from_beginning(t_max=(100, 1000), number_of_walkers=(1, 4)):\n",
      "    markov_matrix = create_markov_matrix_model_nodes(HG)\n",
      "    \n",
      "    engine = DiffusionEngine(markov_matrix, t_per_walker=int(t_max / number_of_walkers))\n",
      "\n",
      "    nodes = HG.nodes()\n",
      "    edges = HG.hyper_edges()\n",
      "    most_common, states = engine.simulate(t_max)\n",
      "\n",
      "    states_per_time = list(zip(*states))\n",
      "    \n",
      "    \n",
      "    xs = list(range(0, len(states_per_time)))\n",
      "    print(len(states_per_time))\n",
      "    ys = []\n",
      "    for i in xs:\n",
      "        try:\n",
      "            cum_states = chain(*states_per_time[:i])\n",
      "            most_common = Counter(cum_states).most_common()\n",
      "\n",
      "            most_common_nodes = count_nodes(nodes, edges, most_common)\n",
      "            frequencies = (utils.get_names_and_occurrences(most_common_nodes)[1])\n",
      "            entropy_value = entropy(frequencies)\n",
      "            if entropy_value is not float(\"nan\"):\n",
      "                ys.append(entropy_value)\n",
      "            else:\n",
      "                ys.append(-1)\n",
      "        except ZeroDivisionError:\n",
      "            ys.append(0)\n",
      "        except:\n",
      "            import traceback\n",
      "            traceback.print_exc()\n",
      "            ys.append(0)\n",
      "    \n",
      "    print(xs[:10])\n",
      "    plt.figure(figsize=(14, 6))\n",
      "    fig = plt.plot(xs, ys)\n",
      "    plt.title(\"Entropy with t_max=%s, walkers=%s\" % (t_max, number_of_walkers))\n",
      "    plt.show()\n",
      "    return fig"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(compare_entropy_from_beginning)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "275\n",
        "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pK/q5bGP68EvX2EiSJEmPtGRGcnYdHOeDtz5AA3jFk0876v1kWcb7br6flz7p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\nJEmSJEmSJEmSJB0j/z/2Rf7XE8DykQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f0d328224a8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "<function __main__.compare_entropy_from_beginning>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}