{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Redes Complexas (continuação)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Erdös e Rényi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Continuando com o modelo de Erdös e Rényi, vamos agora analisar dois resultados importantes:\n", "\n", "- Existe uma transição brusca de percolação.\n", "- As distâncias no grafo são pequenas (efeito _small world_)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Percolação" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A percolação em grafos de Erdös e Rényi é definida pela formação de um chamado **componente gigante** na rede. Lembrando que um componente é um subconjunto (máximo) de vértices do grafo que têm caminhos de um para o outro, é de se esperar que, com a presença de maior número de arestas, o que acontece quando $p$ aumenta, surjam componentes maiores.\n", "\n", "Um componente gigante é definido como um componente cujo tamanho cresce com o número de vértices no grafo. O que acontece é que, para $p$ suficientemente baixo, os componentes presentes são pequenos, e o seu tamanho é independente do tamanho do grafo. A partir de um certo valor crítico $p_c$, surge um componente que cresce com o tamanho do grafo. De acordo com os resultados de Erdös e Rényi, isso acontece para\n", "$$p_c = \\frac{1}{n-1},$$\n", "o que indica que ele ocorre quando o grau médio é 1:\n", "$$\\langle k \\rangle_c = p_c(n-1) = 1.$$\n", "\n", "É importante notar que esse resultado é valido para o limite $n\\to\\infty$.\n", "\n", "Como os grafos de interesse prático têm em geral um alto valor de $n$, o valor de $p_c$ tende a ser muito baixo. Por isso é mais conveniente trabalhar com $\\langle k \\rangle_c$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos avaliar em primeiro lugar o que acontece quando aumentamos $\\langle k \\rangle$ com $n$ fixo." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def largest_component_size(g):\n", " return max(len(c) for c in nx.connected_components(g))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def evaluate_largest_components(n, k_avg, num_repetitions):\n", " p = k_avg / (n - 1)\n", " comp_sizes = np.zeros(num_repetitions)\n", " for rep in range(num_repetitions):\n", " g = nx.erdos_renyi_graph(n, p)\n", " comp_sizes[rep] = largest_component_size(g)\n", " return np.mean(comp_sizes), np.std(comp_sizes, ddof=1)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "N = 100\n", "REP = 100\n", "ks = np.linspace(0., 5., 50+1)\n", "avg_size = np.zeros_like(ks)\n", "std_size = np.zeros_like(ks)\n", "for i, k_med in enumerate(ks):\n", " avg_size[i], std_size[i] = evaluate_largest_components(N, k_med, REP)\n", "avg_size /= N\n", "std_size /= N" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.set_size_inches(8, 6)\n", "ax.errorbar(ks, avg_size, std_size)\n", "ax.set_xlabel(r'$\\langle k \\rangle$')\n", "ax.set_ylabel('Fraction of nodes in largest component');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note que como esperado, temos uma transição abrupta após $\\langle k \\rangle_c=1$.\n", "\n", "Agora vejamos o que acontece com o tamanho do maior componente antes e após a transição à medida que aumentamos o número de vértices no grafo." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "ns = np.arange(50, 550, 50, dtype=np.int)\n", "REP = 100\n", "K = 0.1\n", "avg_size = np.zeros(ns.shape)\n", "std_size = np.zeros(ns.shape)\n", "for i, n in enumerate(ns):\n", " avg_size[i], std_size[i] = evaluate_largest_components(n, K, REP)\n", "avg_size = avg_size\n", "std_size = std_size" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.set_size_inches(8, 6)\n", "ax.errorbar(ns, avg_size, std_size)\n", "ax.set_xlabel(r'$n$')\n", "ax.set_ylabel('Number of nodes in largest component');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note como o número é sempre pequeno, e não existe tendência clara de crescimento." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "ns = np.arange(50, 550, 50, dtype=np.int)\n", "REP = 100\n", "K = 2.0\n", "avg_size = np.zeros(ns.shape)\n", "std_size = np.zeros(ns.shape)\n", "for i, n in enumerate(ns):\n", " avg_size[i], std_size[i] = evaluate_largest_components(n, K, REP)\n", "avg_size = avg_size\n", "std_size = std_size" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.set_size_inches(8, 6)\n", "ax.errorbar(ns, avg_size, std_size)\n", "ax.set_xlabel(r'$n$')\n", "ax.set_ylabel('Number of nodes in largest component');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aqui o número de vértices no maior componente é grande, e cresce linearmente com o tamanho do grafo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Distâncias" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vejamos agora o que acontece com as distâncias num grafo, após o ponto de percolação.\n", "\n", "Os resultados de Erdös e Rényi indicam que as distâncias no maior componente do grafo devem crescer logaritmicamente com o número de vértices." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def evaluate_distances(n, k_avg, num_repetitions):\n", " p = k_avg / (n - 1)\n", " dists = np.zeros(num_repetitions)\n", " for rep in range(num_repetitions):\n", " g = nx.erdos_renyi_graph(n, p)\n", " # Extract the largest connected component\n", " largest_cc = max(nx.connected_components(g), key=len)\n", " gcc = g.subgraph(largest_cc)\n", " # Compute average distances\n", " dists[rep] = nx.average_shortest_path_length(gcc)\n", " return np.mean(dists), np.std(dists, ddof=1)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "ns = np.arange(50, 550, 50, dtype=np.int)\n", "REP = 10\n", "K = 2.0\n", "avg_dist = np.zeros(ns.shape)\n", "std_dist = np.zeros(ns.shape)\n", "for i, n in enumerate(ns):\n", " avg_dist[i], std_dist[i] = evaluate_distances(n, K, REP)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.set_size_inches(8, 6)\n", "ax.errorbar(ns, avg_dist, std_dist)\n", "ax.set_xlabel(r'$n$')\n", "ax.set_ylabel('Average distances');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "É clara uma tendência de crescimento sublinear. Vamos plotar as distâncias em função de $\\ln n$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.set_size_inches(8, 6)\n", "ax.errorbar(np.log(ns), avg_dist, std_dist)\n", "ax.set_xlabel(r'$\\ln n$')\n", "ax.set_ylabel('Average distances');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Como esperado, um crescimento aproximadamente linear." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Watts e Strogatz" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Na década de 1990, o interesse na área cresceu após um artigo de Duncan Watts e Steven Strogatz, descrevendo o uso de teoria dos grafos na modelagem de alguns sistemas reais de origem distinta, e como algumas características comuns aparecem nos diversos sistemas.\n", "\n", "O resultado principal consistiu em mostrar que os diversos sisteamas apresentam distâncias pequenas e coeficientes de aglomeração altos. Isto é interessante pois:\n", "\n", "- Grafos de Erdös e Rényi apresentam distâncias pequenas, mas o coeficiente de aglomeração é sempre baixo.\n", "- É fácil construir grafos regulares com alto coeficiente de aglomeração, mas eles têm distâncias médias relativamente altas.\n", "\n", "Para modelar o fenômeno, eles propuseram um grafo aleatório construído da seguinte forma:\n", "1. Começamos com um grafo regular, com $n$ vértices organizados em um círculo e cada vértice ligado com $k$ vizinhos.\n", "2. Em seguida, percorremos todos as arestas e, com probabilidade $p$, mudamos um dos vértices da aresta para um vértice escolhido aleatoriamente.\n", "\n", "Se $p\\approx 0$ o grafo preservará a estrutura regular original, com alto coeficiente de aglomeração mas também altas distâncias; já para $p\\approx 1$ ele terá uma estrutura aleatória, com baixas distâncias mas baixos coeficientes de aglomeração.\n", "\n", "No modelo como apresentado, como cada vértice tem inicialmente $k$ vizinhos, e como nenhuma aresta é retirada ou acrescentada no processo, o grau médio será sempre $\\langle k \\rangle = k$, independentemente de $p$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 3)\n", "fig.set_size_inches(12, 4)\n", "ax[0].set_aspect('equal')\n", "nx.draw_circular(nx.watts_strogatz_graph(12, 4, 0), ax=ax[0])\n", "ax[0].set_title(r'$p=0$')\n", "ax[1].set_aspect('equal')\n", "nx.draw_circular(nx.watts_strogatz_graph(12, 4, 0.1), ax=ax[1])\n", "ax[1].set_title(r'$p=0.1$')\n", "ax[2].set_aspect('equal')\n", "nx.draw_circular(nx.watts_strogatz_graph(12, 4, 0.95), ax=ax[2])\n", "ax[2].set_title(r'$p=0.95$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Watts e Strogatz mostraram que, para uma faixa de valores relativamente baixos de $p$, os grafos do modelo apresentam simultaneamente alto coeficiente de aglomeração e baixas distâncias.\n", "\n", "Vamos reproduzir esse resultado abaixo." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def evaluate_distance_clustering_ws(n, k, p, num_repetitions):\n", " dists = np.zeros(num_repetitions)\n", " clstr = np.zeros(num_repetitions)\n", " for rep in range(num_repetitions):\n", " g = nx.watts_strogatz_graph(n, k, p)\n", " clstr[rep] = nx.average_clustering(g)\n", " largest_cc = max(nx.connected_components(g), key=len)\n", " gcc = g.subgraph(largest_cc)\n", " dists[rep] = nx.average_shortest_path_length(gcc)\n", " return np.mean(dists), np.std(dists, ddof=1), np.mean(clstr), np.std(clstr, ddof=1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "N = 100\n", "K = 4\n", "REP = 20\n", "ps = np.logspace(-3, 0, 20)\n", "avg_dists = np.zeros_like(ps)\n", "std_dists = np.zeros_like(ps)\n", "avg_clstr = np.zeros_like(ps)\n", "std_clstr = np.zeros_like(ps)\n", "for i, p in enumerate(ps):\n", " avg_dists[i], std_dists[i], avg_clstr[i], std_clstr[i] = evaluate_distance_clustering_ws(N, K, p, REP)\n", "# Normaliza as distâncias e aglomeração em relação ao valor de p=0\n", "ws0 = nx.watts_strogatz_graph(N, K, 0)\n", "d0 = nx.average_shortest_path_length(ws0)\n", "c0 = nx.average_clustering(ws0)\n", "avg_dists /= d0\n", "std_dists /= d0\n", "avg_clstr /= c0\n", "std_clstr /= c0" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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r3WgxidxlF/MuW3ijNQg2bdpkW0UpODiYrVu3cttttxX6s+V+LijckpHXW+oxKiqqUJ8r72e70edycXEhMTHxiufyW35x//79N2wZBwQEcOLECdtzeZdeBPstv1jgNWOl1OdKqTNKqXznIFO6KUqpQ0qpXUqp5vntJ4QQ5cVtt91Geno6s2fPtj23efNm27J/oF9X3bFjB1arlePHj7Np0yYAzp49i9Vq5e677+bNN9+0LU2Yd2nFRo0akZCQYAvjzMxMYmJibrre9u3bs3DhQgD27NnD33/rXfsxMTEEBQVhNpsBmDBhAs8995ztGmh6ejpTpky55nh16tRh69atAHz//fe25wuzZOT1lnq8GUFBQRw5csTWA7BgwQLba40bN+bQoUNX7P/dd99htVo5fPgwR44coVGjRjRq1CjfpRd37NhBpUqVqF69Oh4eHmzcuBFN05g7dy79+/e3HdNeyy8WpmX8JTAVuN7Y+V5Ag5ytFTA956vIxyvnns159KehdRhFru+L8kApxY8//siTTz7Ju+++i7OzM3Xq1OHDDz+07dOuXTsCAwMJCQmhadOmtuuXcXFxPPjgg7aW5cSJE4F/Bxi5uLgQHR3NokWLGDduHImJiWRlZfHkk08SHBx8U/U+/vjjDB8+nNDQUJo1a0ZoaCheXl4sXrz4irWOe/fuzenTp+nWrRuapqGU4qGHHrrmeK+++ioPP/ww77zzDq1a/fvrvjBLRj7xxBP5LvV4M1xcXPjkk0/o2bMnPj4+REZG2l7r2LEjTz/9tO1zgP5HTqdOnTh9+jQzZszA2dm5UOeZPn06I0aMIDU1lV69etGrVy9A/yPp0KFDRETkuxBT0WiaVuAG1AF2X+e1mcCQPN/vB6oXdMwWLVpo9jJwxgZt4IwNdjtert1vt9N2v92u1B+zuD5/cShLtYrSac+ePUV/0+e99a2CysrK0lJTUzVN07RDhw5ptWvX1tLT07Vu3bpp8fHxBld3a5KTkzVN0zSr1ao99thj2gcffGB7bdy4cdqqVas0TdO04cOHa999951dz/3DDz9oL7/8cr6v5fffKbBFu04m2uOacQ3geJ7vT+Q8d9IOxy6UV84+g0ID6zpQJrjqukB5V5Za22WpVlGO2OlacVmVkpJCly5dyMzMRNM0pk+fjqOjI6tWrTK6tFs2e/Zs5syZQ0ZGBs2aNWPUqFG211588UX++uuvYjt3VlYWTz/9tF2OZY8wzi/58r2qrpQaCYwEqFWrlh1OratkvUCN7Dh4o7L+hMkBTJacr2YwW/I8Z9Yfm3Mf577mAGaHfx+bLARkHkVTCn58DBwcwXz1ZtG/Ojj9+/jqzeHKfR21NP1HdjoGsjMgOzPn63UeZ6XneT7/ff2zjuvHXP8RVAuF6mHgWtluP18hRNnm4eFR5tc1vp7x48czfvz4fF+rWrUq/fr1A/T7vu3t3nvvtdux7BHGJ4Caeb4PAPId561p2ixgFkBERMT1h8EVUapy4bS5KlU7PgLWLD2orFlXbtmZYM0Ga57XsvPZJyMl5/tsnEhHWTWIXXdtMFozb6rWBrkPpt/CNG9mpysC3s16We8ZWPXKv/t41YLqOcGcu3lUK9p57DwCVQghRP7sEcY/A2OUUt+iD9xK1DStxLqoAV7ynQrAgk72HRR0+J32AASPz6dL1WrVAzm3lZqVnqfFmn7d549//xIKjYC73r6yhX1N6/o6j00O13TDH8yt88mf4eROfTu1S/+6L88sM25+OcGcJ6Qr1bZ/t35WBlw6BUnxkBSX81V/HJh5CA0Ff/wPGtyu11CRLivIHzh2oeUZlCNEaaPd4Jar6ykwjJVS3wCdAR+l1AngVcCSc8IZwFKgN3AISAHsc/d4EWRZrWRk2a2hXTgmE5ic9BAtgqSf/gdAQPAAu5XyRhX9mAtcK0O9LvqWKz0ZTu2+MqAP/w6aPvcrzl7/dm3nblXq6134+clMg+T4KwL2mseXznDNlQqLG3jVwIoZE9mw5i19c6+mh3LDHlC3Mzh52O3nIsonZ2dnzp07R5UqVSSQRamjaRrnzp0r9EjtXAWGsaZpQwp4XQP+U6Sz2tm5SxnEnkuh10frGBDuT79wf6p73fpN2LaQu+UjGcjJA2q30bdcmWlwZs+VAb35U8jKuXnf4gpVm8LF44AGXw/+N2hTzuZzDi/w9Ne3qk3BswZ41ch5LuerkycoxdHcVvy4H+DQajiwAvYshu3z9Ov3ddpBgx56OFepV/jPWRwtTmnFlkq5kzAkJCQYXYoQ+XJ2ds539rEbKRczcFV2c0TTwNHBxMRl+3h3+T5aBVamf3gNejetjperxegSSxeLM9Rorm+5srPg7IEru7kvn9G7kBNP6IFao8W/4WoL2uo315p194Pw+/QtOxOObYSDK+DASlgxQd8q19NDucHtULtdkXshRPlksViuO2WiEGVVuQhji9lENS9nFoxqQ+zZyyzeEc/iHXFM+OFvXl0cQ+dGvvQPr0HXxn44W67T/VpCSm1r2+wAVZvoW3hOZ0hJtQzNFgjsoG/d34ILsXooH1wBmz+DjZ+Ao7vejd2gu755Vi/goEIIUXaUizDOq46PG090a8C4rvXZHZfETzvi+GVnPCv3nMbdyYGeTavRP9yftvV8MJvkelNJK9QfI951oNVIfctIgX/W/ttqzh2QVi00p9Xc48oWvhBClEHlLoxzKaUICfAiJMCLF3s3ZuORc/y0PY7lu0+xaOsJfD2cuCPUn/7h/oQGeMlAkNLK0RUa9dQ3TdOvdR9YAQdXwrr3Ye3/wLUKYNK7saM/ATdfcKsCrj76Y9cq+v3eQghRSpXbMM7LbFK0q+9Du/o+vDmgKb/vO8PiHXHM33iUz9f/Q10fN/qF+9M/vAaBPtdfNUQYTCmoGqxvHZ6ClPP6yPCDKyHmR0jJ0K8158fJSw9oN9+ckM4T1m4+emDbHvuUvfCWwWZClGkVIozzcraY6R1Snd4h1UlMyWTZ7pMs3hHPR78d5MPVBwkL8KJ/eA36hpW+a5IZWVZOJ6Vx4kIq8RdTibuof917MgmrBicTU+0yitymtP9id60MIffoW2Kc3nIePB8un9VHfef9mvfxhViI2wIp5/QJXvLj5KnfH252hIXD9QlT3KuCR3XwqKrfkuVRDVy8K9Z90kKIYlHhwjgvL1cLgyNrMTiyFicTU/llZzyLd8Tzxq97eGvJHtydHHB1NPPR6oN4ujjg6WzBw9kBTxcLns4WPF0c8HC24OHkgMkO15+T0zJtARt3IZW4i2nEXUwl7kIK8RfTOJ2cxtX3kvu4O5Jt1UjJzGbi0n1MGdLslusos5TSA9q1MtCw4P01DdIuXhXWCXD5nP7470X6SO/TMXoLPD3p2mOYnfKEc05Yu1fVg9qjWs7z1fWaJLSFENdRocM4r+peLozsWI+RHetx6EwyP22P59M/j3ApOYvJqw/c8L1KgbtT/mHt6WzBM89z5y9noGkaM/44nCd09S057cpWmsWs8K/kgr+XC+3q+1DD24UalZypUckV/0rO+FdywdliZtDMaE5cSOHnnfHc37o2kYEyL3WhKKW3bF28wafBta+fylnCO7eHIOMyJJ+CS6ch+SQkn9ZnGkvO2RIO6IPN0hKvPZbJood0WqJ+a1nMT/otW45yWUQIIWGcr/p+HjzToxGbY88DMP+RVlxKyyIpLZOk1CyS0zJtj5PSMklKyyIpVX8uOedx3MVU9p7MJDktk+T0rGtatO8u24enswM1vF0J8HahVWBl/Cu5UMPbBf9KLgRUcsHH3anQLe7qXi5oGrz2cwy/jG0vI8WLg6ObPhFJQZORZKZeP7T3L4PUi/DdcHBw0QO5SX99ZLjMPiZEhSVhXAgWswlvN0e83W5uUI/VqnEpI4vktCxGz9NXTvn60dZ4ONtvMhKzSTGhd2PGfrOdbzcfY2ir2nY7tigiiwtUDtS3q33RR+8e7zJBn3ls78/65uAM9bv9G8zOXiVftxDCMBLGJcBkUjnd1RZcHfUfuT2DOFff0OrM23iUSSv20zfE/5ZnHhs0MxqABaPsuwBHsSjtg83yUurfSU56/ReOb9KDec9i/T5qsyPUu00P5ka99G50IUS5Vi7CuEyERQlQSvHaHcH0/Xgdk1cf4LV+wUaXJApiMv87d3iPd/RR3rnBfGC5vkpX3c45wdxHvyWrpMjtUkKUmHIRxuJfTfw9ua9VLeZtPMrgyJoEVfM0uiRRWCYT1IzUt+5vQfw2PZRjfoKfx4J6Um9NNxkAQX3B3dfoioUQdmIyugBhf0/f3gh3Jwde/3nPTa2rKXI8uMS4VqFS+sIct78BT+yEUWuh/ZP6Slq/PgnvN4Qv+8Km2frAMCFEmSZhXA55uznyTPeGRB85x/Ld8ou6zFNKX2e66yswdiuMXg8dntFHay99Bt4P0lfZungMjm6ArHSjKxZCFJF0U5dTQyJr8dVfx3hryV46N/LDxdHY1aqEnSgF1Zrq220vwZl9elf2+o8g8Rh80UsfmV0zEmq3hzrtISBClp8UopSTMC6nHMwmXr0jmCGzNzJz7WGe7FaIGalE2eMXpG//rNVnC2v/BMT+CbHrIGoioOnhHNBSD+Y67aFGhD7xiBCi1JAwLsfa1KtCn9DqTI86zD0tAgjwdjW6JFGczBYI6qNvAKkX4Gh0nnB+F9D0KTxt4dxOf2yx45zmQogikzAu517s3Zjf9p5m4tJ9TBsq6/5WKC7eENRb30AP52Mbc8L5T1j7Hvxh1e9rDmgJtdvpAV0zUsJZiBImYVzO1ajkwmOd6jN59QGGHj5L23o+RpdUsRl5z66Ltz6JSKNe+vepF/VwPpoTzusm6QFtdtRHciee0JeTFEIUOxlNXQGM6lSXGpVceOOXPWRlW40uR5QWLpWgUU/9nuaRUfB8LNy3EFqN1kdkJx6Hk9th+QRITza4WCHKNwnjCsDZYub/+jZm36lkvt50zOhyRGnl7KXPi939TRi5BgJa6UtAbpwOU1tCzI9cs+JJUX3R59+ZvYQQNhLGFUSP4Gq0rVeF91ce4MLlDKPLEWWB2QJV6sPDq8DNB74bAfPvhnOHja5MiHJHwriCUErx6h3BXErP4v1V+40uR5QlNVvCo1HQ8119UYtP2kDUf2VyESHsSMK4AmlUzYMHWtfm67+OEROfaHQ5oiwxO0Drx2DMZn10dtQ7eigfXmN0ZUKUCxLG5cCCUW0KvXLV+G4N8XKxyLzV4uZ4Vod7v4T7fwA0mDcAFj0k82MLcYskjCsYL1cLz/YIYlPseX7dddLocuxm0Mxo2/rLFVJJL2pRvys8Fg2dJ8DeX/UBXn/NBGt2ydUgRDkiYVwBDWpZk2B/T95ZupeUjCyjyxFllcUZOr8Aj0fr818vew5mdYYTW42uTIgyR8K4AjKbFK/1C+ZkYhozokpuZKzVqnEmOZ24i6nSRV6eVKmnd1vf8wVcOgOfdoVfx+szfgkhCkXCuIJqWacy/cP9mbH2CMfPpxT7+Q6eTmbQrGj+OXuZExdSmbfxaLGfU9yionR9KwVN79IHeLUaDVu/1Luud3576/cmC1EBSBhXYBN6NcbBpHhryZ5iO0daZjaTVuyn95R1HDxzibo+blRysfDmr3vYefxisZ1XGMTZE3q9q8/oVak2/DgK5twBCXI7nRA3ImF8A0UZpVwWVfNy5j9d6rMi5jR/Hjxr9+P/efAsPT5cy9Q1h+gXVoPfnuqEr4cTdX3d8PNw5j9fbyMxJdPu5xWlQPUwfbKQvpPh1C6Y3g5Wvy4DvIS4DgnjCu7h9oHUquzK67/EkGmneavPXkpn/IId3P/ZX5iU4utHWvH+wDCquOsL3FvMJqbe14zTSWk8/d1OuX5cXplMEPEQjNkKIffAnx9A/DZIOW90ZUKUOhLGFZw+b3UTDp65xLzoW7uOq2kaCzcfp9sHf/DrrnjGdW3Asic60Lb+tSv/NKvlzYRejVm99zSfrvvnls4rSjl3X7hzBoxYogd0wh744z25lixEHhLGgm6N/ejQwIfJqw9w7tLNTXF46Ewyg2Zt5Lnvd9HQz4NlT3Tgqdsb4mwxX/c9D7arQ6+m1Xh3+T62xFaM1lKFvh+6Tnuo3gzc/GDN27B4DAhRh20AACAASURBVGTLZQohQMJYkDtvdRNSM7KZtLJoA23SMrP5YOV+en20jv2nkvnv3SF8O7I19f08CnXe/94TSoC3C2O+3n7TfwiIMkSZoEoD6PQ87JgPX90LaUlGVyWE4SSMBQD1/TwY0bYO324+zt8nCjdv9YZDZ+n10Tqm/H6IvqH+/PZ0Jwa1rIXJpAp9Xk9nC9Pua875lAzGL9yJ1Spdl+WeUtDlReg/DWLXwec9ITHO6KqEMJSEsbAZ160BVdwcee2XmBsOqjp/OYOnFu7gvk//wqppzH+4FZMHheOTM0CrqJrW8OK1O4JZeyCBT6IO3Wz5oqxpdj8MXQSJx/WJQk7uuvljyTrJooyTMBY2ns4WnusRxNajF1i8I/6a1zVN47stx+n6fhS/7IxnTJf6rHiyI+0bXDtAq6iGRNZkQLg/H6w6wIbD9r/NSpRS9brAQ8v17usvesGh1UZXJIQhJIzFFe5pEUBogBcTl+0lO0+X8eGESwyZvZFnF+2inq87S8Z14JkejW44QKsolFK8fWcIgT5ujPtmB2eS0+xyXFEGVA2GR1aDdyB8NRC2zjG6IiFKnISxuIIpZ97q00npxF9MxappfLj6AL0+XMee+CQm3hXCwlFtaFi14AFaReXm5MD0+1twKT2Tcd9sv+KPAVHOefrDQ8v0lvIv4+C3N+TWJ1GhSBiXsLIwq1fzWt7c1bwGJxPT+DsukQ9XH6RXSDV+e7ozQyKLNkCrqBpW9eCtASFsPHKeD1cfKLbziFLIyQOGfAvNh8O69+GHRyFLRtiLisHB6AJE6fRCzyAW74hH02DOQ5F0auhbYue+p0UAm/85z8e/H6JFbW86N/IrsXMLg5ktcMdH4F1bbx0nnYTB88HF2+jKhChW0jIW+fLzdCYswIvQAK8SDeJcr/cPJqiaB+MX7CD+YmqJn18YSCno8DTc9Smc2ASfdYcLsUZXJUSxkjAW12UxmzCp4uuSvhFni5lPhjYnI8vKmK+32W3ebFGGhN4LD/wIl07Dp90gbpvRFQlRbCSMRalV19edd+8OZduxi7y3fJ/R5Qgj1Gmvr/5kcYEv+8D+ZUZXJESxkDAWpdodYf4Ma1Ob2ev+YWXMKaPLEbfqwSX6VhS+jeCR3/Sv394Hm2YXT21CGEjCWJR6L/VpTEgNL57+bifHzqUYXY4wgrufvupTw56w9BlY8RJY5dKFKD8kjEWp5+SgXz8G+M/X20jPkgXqKyRHNxg0HyJHQvRUWDQCMmVwnygfChXGSqmeSqn9SqlDSqkX8nm9llJqjVJqu1Jql1Kqt/1LFRVZzcquvH9vGH/HJfL2kr1GlyOMYjJDr/eg+9uw52eY0w8unzO6KiFuWYFhrJQyA9OAXkATYIhSqslVu70MLNQ0rRkwGPjE3oUK0T24Go92CGRu9FF+2Xnt3NmiglAK2o6BgXPg1C74rJu0kEWZV5iWcSRwSNO0I5qmZQDfAv2v2kcDPHMeewHym1IUi+d6BtG8ViVe+H4XRxIuGV2OMFKT/jD8F0hLhFM7IT3Z6IqEuGmFCeMawPE835/IeS6v14D7lVIngKXAWLtUJ8RVLGYTU+9rjqODice/2kZaZvFdPx40M5pBM6OL7fjCDmpG6rc+mcxwZjfE7zC6IiFuSmHCOL9ZH66ewX0I8KWmaQFAb2CeUuqaYyulRiqltiiltiQkJBS9WiEA/0ouTB4Uzr5Tyby6OMbocoTRqtSDqiGgHGBufzj1t9EVCVFkhQnjE0DNPN8HcG039MPAQgBN06IBZ+CaRW41TZulaVqEpmkRvr4lP8WiKD86N/JjTJf6LNhynEVbTxhdjjCag7MeyI5ueiCf3mN0RUIUSWHCeDPQQCkVqJRyRB+g9fNV+xwDugIopRqjh7E0fUWxerJbA1rXrczLP/1NSkaW0eUIo1mc9WvIZkeY2w8S9htdkRCFVmAYa5qWBYwBVgB70UdNxyil3lBK9cvZ7WngUaXUTuAbYISmyWKkong5mE1MGdwMdycLB89ckvWPhd5lPfwXUCaYcwecPWR0RUIUSqHuM9Y0bammaQ01TaunadrbOc+9omnazzmP92ia1k7TtDBN08I1TVtZnEULkcvP05kpQ8JJy7RyKEECWQA+DWDYz2DN1gP5/BGjKxKiQDIDlyjz2tbzoXYVVy6mZPLuMpkQRAB+QTD8Z8hKgy/vkCUYRaknYSzKhWqezlT1dGL2un/4ZtMxo8sRpUHVYBi2GDIu6S3ki8cLfk9eX/TRNyFKgISxKDdqV3alY0Nf/u+n3Ww4fNbockRpUD0Uhv0EqYkwpy8kxhldkRD5kjAW5YZSiqn3NSPQx43H5m+TGbqEzr8ZPPCDPof1nDsgWZbiFKWPhLEoVzydLXw+oiVmk+LhOVu4mJJhdEmiNAiIgPu/h0un9UC+dMboioS4goSxKHdqVnZl1gMtiLuQymPzt5GRJeveCqBWK7hvISSeyFntSS5liNJDwliUSxF1KvPfe0KIPnKO//tpN3LbuwCgTjsY8i1c+EefqSvlvNEVCQFIGIty7M5mAbYpMz9d94/R5YjSom4nGPINnD2oB3LqBaMrEkLCWJSsBaPasGBUmxI731O3N6R3SDXeWbaXVXtOl9h5RSlX7zYY/BUk7IN5d+nLMAphIAljUa6ZTIr37w0npIYXT3y7nZh4+aVbLj24RN+KosHtMHAunNoF8++R9ZCFoSSMRbnn4mjm02EReLlYeHTOFs4kpRldkigtGvWCe76AuK3w1b2QLrfDCWNIGIsKwc/TmU+HR3AxNZNH524hLTPb6JJEadGkH9z9KRz/C74ZDBkpRlckKiAJY1FhBPt78eGgcHbFJfL0wp1YZVEJkavpXXDnLDi6Xg/kzFSjKxIVjISxqFC6B1fjhZ5BLPn7JB+uPmB0OaI0Cb0X+n8C/6yFb4eCJveni5LjYHQBQpS0kR3rcjjhElN+P0RdX3cGNKthdEmitAgfAtZM+HksuHiDb2OjKxIVhISxqHCUUrw1IISj51J4btEualZ2oUXtykaXJUqL5sMgOxOWPAXnDhpdjaggpJtaVEiODiZm3N8C/0rOjJy7lePnZdCOyKPlw+BVEy4nQOyfRlcjKgAJY3FdJT1BR0nzdnPksxEtycy28vCczSSnZRpdkihNPAPA7ATLJ4BVRt+L4iVhLCq0er7uTL+/BYcTLjP2m+1kZcugHZHDZAbv2vqkIDu/MboaUc5JGIsKr119H97s35So/Qm8tWSv0eXclEEzoxk0M9roMsofV18IaAm/vSETgohiJWEsBHBfq1o83D6QLzfEMi861uhyRGmhFPSYqK+D/Odko6sR5ZiEsRA5XuzdmNuC/Hjtlz2sPZBgdDmitKjZEkLuheipcPGY0dWIckrCWIgcZpNiypBmNPBz5z9fbSM1QwbtiBxdX9W/rn7N0DJE+SVhLEQe7k4OfDo8AieLmf2nk7mcnsU/Zy9z7FwKJy6kcDIxlTNJaZy9lM7FlAyS0jK5nJ5FWmY2GVlWsq0amibTbJY7lWpC23Gw+3s4vsnoakQ5JJN+CHGVAG9XZg1rwd3TN7A7Pokuk6KKfAyT0lvaJqUwm/7dLqVl4WwxE38xFf9KLvYvXhSfdk/Atrn6rU4PrwKTtGWE/UgYC5GP5rW8aervRUpGFmNuq0+2FaxWjWxNI9uqYdU0srL1r9k5z1utGtlW/n1se+7f9y3ffYpzlzK4d0Y0Xz3Sijo+bkZ/VFFYTu7Q9RVY/DjsXgShA42uSJQjEsZCXIeroxlXRzN3Nguw2zH3n0rGz8OJuIupDJypB3KDqh52O74oZmFDYNNM/dpxUF9wdDW6IlFOSD+LECXMzcnBNrPZwJnR7I5LNLgiUWgmE/R8F5LiYMPHRlcjyhEJYyEM0LCqBwtHtcHV0YEhszayJfa80SWJwqrdFpr0h/UfQlK80dWIckLCWAiD1PFx47vRbfD1cOKBzzbx58GzRpckCqvb62DN0mfmEsIOJIyFMJB/JRcWjGpD7SquPPTlZlbtOW10SaIwKgdC68f1OavjthldjSgHJIxFuVCWV5jy9XDi25GtaVzdg9Hzt/LzTun6LBUeXKJv19PhaXDzhRUvgtxbLm6RhLEQpUAlV0fmP9KKFrW9eeLb7SzYLNMulnrOntDlJTgWDXt+MroaUcZJGAtRSng4W5jzYCQdG/jy/Pd/8/mf/xhdkihI82FQtSmsegUy0wre/4s++ibEVSSMhShFXBzNzBrWgh7BVXnj1z1M/f2gTK9ZmpnM0ONtfQGJjZ8YXY0owySMhShlnBzMTLuvOXc2q8GklQf47/L9EsilWd3O0Kg3rPsAkmUAnrg5EsZClEIOZhPv3xvG0Fa1mPHHYV79OQarVQK51Lr9TchKhTVvGV2JKKMkjIUopUwmxVsDmjKyY13mRh/lue93kZVtNboskR+f+hA5CrbNg1N/G12NKIMkjIUoxZRSTOgVxPhuDVm09QTjvt1ORpYEcqnU6Vlw8dZXdZLLCqKIJIyFKOWUUjzRrQEv9W7M0r9PMWreFtIys40uS1zNxRs6T4DYdbB/qdHViDJGwliIMuLRjnV5584Qog4k8OAXm7mUnmV0SeJqEQ+CTyNY+TJkZRhdjShDJIyFKEPua1WLyQPD2RR7nvs//YvElEyjSxJ5mS36rU7nj8CmWUZXI8oQCWMhypgBzWow7b7m7IlPYvDsjZy9lG50SSKvBrdD/W7wx3tw+ZzR1YgyQsJYiDKoZ9NqzB4ewT9nLzFoZrQM6iptur8NGZcg6h2jKxFlhISxEGVUp4a+zHkwktNJ6ew5mUR6lgzqKjX8giDiIdjyBZzZZ3Q1ogyQMBaiDGtVtwpfPdKKLKvG/lOXZFBXadJ5Aji6w8qXjK5ElAESxkKUcWE1K1Hf153UzGye/HY72TJTV+ngVgU6PQeHVsPBVUZXI0o5CWMhyoFKrhZqV3Fl9d4zvLdcukVLjciRULkurHgJsmXku7g+CWMhyolqns480Lo2M9ceYeGW47d8vEEzoxk0M9oOlVVgDo7Q/S04u1+/fizEdRQqjJVSPZVS+5VSh5RSL1xnn4FKqT1KqRil1Nf2LVMIURiv3NGE9vV9eOnHv/nriNxWUyo06g2BHfWR1dlyTV/kr8AwVkqZgWlAL6AJMEQp1eSqfRoAE4B2mqYFA08WQ61CiAJYzCam3decmpVdGT1/K0fPXTa6JKEU9HgHUi9C4jGjqxGlVGFaxpHAIU3TjmialgF8C/S/ap9HgWmapl0A0DTtjH3LFEIUlperhc+Gt8SqwcNztpCUJtcqDVctBJoPg+STkJlqdDWiFCpMGNcA8l6AOpHzXF4NgYZKqfVKqY1KqZ75HUgpNVIptUUptSUhIeHmKhZCFCjQx43p9zcn9uxlxny9XZZeLA1uexmUCS78Y3QlohQqTBirfJ67+t4JB6AB0BkYAnyqlKp0zZs0bZamaRGapkX4+voWtVYhRBG0refDmwOasvZAAm8t2Wt0OcLdD7xqQup52LXQ6GpEKVOYMD4B1MzzfQAQn88+izVNy9Q07R9gP3o4CyEMNCSyFg+3D+TLDbHM23jU6HKEpz84ecLP4+B0jNHViFKkMGG8GWiglApUSjkCg4Gfr9rnJ6ALgFLKB73b+og9CxWipC0Y1YYFo9oYXcYte7F3Y7o08uW1n2P48+BZo8up2JQJfILA2RMW3A9piUZXJEqJAsNY07QsYAywAtgLLNQ0LUYp9YZSql/ObiuAc0qpPcAa4FlN0+S+CiFKAbNJMWVIM+r5uvH4V1s5nHDJ6JIqNgdHuHcOXDwGPz4GVrmeLwp5n7GmaUs1TWuoaVo9TdPeznnuFU3Tfs55rGma9pSmaU00TQvRNO3b4ixaCFE0Hs76CGsHs4lH5mzhYoosfG+o2m3g9jdh/xJY/6HR1YhSQGbgEqKCqFnZlZkPtCDuQiqPzd9GpoywNlbrxyD4Lvj9TTgSZXQ1wmASxkJUIC3rVGbiXSFEHznHK4tj0DRZVMIwSkG/j8GnISx6CBJPGF2RMJCEsRAVzN0tAniscz2+2XSML9bHGl1OxebkDgPnQVYGLBwGWelGVyQMImEsRAX0bPdGdG9SlbeW7GHNfpkwz1C+DWHAJxC3FZZPMLoaYRAJYyEqIJNJMXlQOEHVPBn79XYOnE42uqSKrUk/aDsOtnwGO74p+vu/6KNvosySMBaignJzcuDT4RG4OJp5eM5mzl2SLlJDdX0V6nSAX5+EU38bXY0oYRLGQlRg/pVcmD0sgjNJ6Yyev5X0rGyjS6q4zA5wz+fg4q1PCJJ6weiKRAmSMBaigguvWYlJ94axOfYCL/6wW0ZYG8ndDwbOhcQ4+HG0TAhSgUgYCyG4I8yfJ7o24PttJ5i5VmayNVTNSH394wPL4c/3ja5GlBAHowsQQpQOT3ZrwOGES/x3+T4CfdyMLqdii3wUTmyG398G/+ZQv6vRFYliJi1jIQQASikm3RtGaA0vxi/YweX0LKNLqriUgjs+BL/G8P0j+jzWolyTMBZC2DhbzMweFoGns4UDpy+RkSXXLA3j6AaD5oM1S58QJDPN6IpEMZIwFkJcwc/TmU+HR5BltbL3VBJHZJUn41SpB3fOgPjtsPx5o6sRxUjCWAhxjaY1vGhU1YOsbI3+U9fz297TRpdUcQX1gfZPwdYvYft8o6sRxUQGcAlRDiwY1cbux/R0sdDU35MsTePhOVsY360hY2+rj8mk7H4uUYDbXtany/z1KajaFPzDja5I2Jm0jIUoQQtGtSmW4CwuThYzi0a35a5mNZi8+gCj5m8lOS3zpo83aGY0g2ZG27HCCsJk1icEcfOBhQ9AynmjKxJ2JmEshLghZ4uZ9weG8eodTfh93xn6T1vPoTNyHfmmPLhE326Gm48+IUjSSfhhpEwIUs5IGAshCqSU4sF2gXz1SCsSUzIZMG09K2NOGV1WxRMQAb3+C4dWwdr3jK5G2JGEsRCi0FrXrcIvY9tT19eNkfO28sHK/VitMn1miYp4CMKGQNS7cHCV0dUIO5EwFkIUiX8lFxaOasO9LQKY8vshHpm7hcTUm7+OLIpIKejzgT6Q6/tH4EKs0RUJO5AwFkIUmbPFzHv3hPJm/2DWHkhgwLT1HJQ1kUuOoysMmguapk8IYpXVtso6CWMhxE1RSvFAmzp8M7I1yWlZDJi2nuW7TxpdVsVRuS7cNQtO7oTzsrhHWSdhLIS4JS3rVObXse1pUNWD0fO38b8V+8iW68glo1FP6PgsXD4Nl84YXY24BRLGQohbVs3LmQWjWjO4ZU2mrTnMQ19uJjFFriOXiM4TwNEdLh6FrAyjqxE3ScJYCGEXTg5m3r07lHfuDGHD4bP0m/Yn+0/JdeRiZzJDpdqQnQ7b5xpdjbhJEsZCCLu6r1Utvh3ZhtSMbO78ZD1Ldsl15GLnXAmcPGHt+7K6UxklYSyEsLsWtb35dWx7Glf35D9fb+PdZXIduVgpBZVqQXK8vqCEKHMkjIUQxcLP05lvHm3N/a1rMeOPw4z4YhOZ2TKFY7FxrgR1OsC69yEjxehqRBFJGAshio2jg4m3BoTw37tD+OvIeWLik7icnmV0WeVXl5fg8hnY/KnRlYgikjAWQhS7QS1rsWBUa6yaxp6TSSzYfAxNk25ru6vdBurdBus/hHRZzKMskTAWQpSIZrW8CanhhbuTA89//zdPLtjBJWkl21+XlyDlHGyaaXQloggkjIUQJcZiNhFUzYNnujfkl53x9J2yjt1xiUaXVb4ERECDHrB+CqTJz7askDAWQpQopRRjbmvAtyPbkJZp5a5PNjA3Ola6re2py4uQdhE2zjC6ElFIEsZCCENEBlZm6RMdaN/Ah1cWxzB6/laZtcte/MMhqC9ET4PUC0ZXIwpBwlgIYZjKbo58OiyCl3o35re9Z+g9ZR3bjkl42EXnCZCeCBumGl2JKAQJYyFEvhaMasOCUW2K/Twmk+LRjnX5bnQblIKBM6KZtfYw1iJMEjJoZjSDZkYXY5VlULWm0GQA/DUDLp8zuhpRAAljIUSp0KyWN0vGdeD2JlV5Z+k+HpqzmXOX0o0uq2zrPAEyLsOGj4yuRBRAwlgIUWp4uVj4ZGhz3uwfzIZD5+g9ZR0bj0ir7qb5BUHIvbBptiyxWMpJGAshShWlFA+0qcOP/2mLq6MD983eyJTfDsrc1jer0/OQlQZ/fmh0JeIGJIyFEKVSsL8Xv4xtT78wfz5YdYAHPvuLM0myIlGR+dSHsCGw5TNIkhW0SisJYyFEqeXu5MDkQeG8d08o245doNdH61h7IMHossqejs+CNUtfREKUShLGQohSTSnFwIia/DKmPVXcHRn2+SbeW76PLFkBqvAqB0L4UNg2By4eN7oakQ8JYyFEmdCgqgeL/9OewS1r8knUYQbN2kjcxVSjyyodHlyibzfS8Vn967pJxV+PKDIJYyFEmeHiaObdu0P5aHA4+04m0fujdazac9rossqGSjWh+XDYPh/O/2N0NeIqEsZCiBJjr4lE+ofX4NdxHQjwduHRuVs4eu4yVpnbumAdngJlhrXSOi5tJIyFEGVSoI8bPzzelhFt63AqKZ3dcUmyAlRBPP2h5cOw8xs4d9joakQeEsZCiDLLycHMa/2CaVjVnSyrlQHT1vPBqgNkZMngrutqPx7MjhD1rtGViDwkjIUQZZ63qyOhNby4I8yfKb8dpP+09eyJTzK6rNLJ3Q8iH4W/v4OE/UZXI3IUKoyVUj2VUvuVUoeUUi/cYL97lFKaUirCfiUKIUTBHMwmJg8KZ9YDLUhITqff1D+Z8ttBMuUWqGu1exIc3SBq4vX3+aKPvokSUWAYK6XMwDSgF9AEGKKUapLPfh7AOOAvexcphBCF1T24GqvGd6R3SHU+WHWAOz9Zz/5TyUaXVbq4VYFWoyDmRzi12+hqBIVrGUcChzRNO6JpWgbwLdA/n/3eBN4DZL46IYShvN0cmTKkGdOHNufkxTTu+PhPpq05JBOF5NVmDDh53rh1LEpMYcK4BpB3ypYTOc/ZKKWaATU1TfvVjrUJIcQt6RVSnZXjO3J7k6r8b8V+7p6+gYOnpZUMgGtlaPMf2PcrxO8wupoKrzBhrPJ5znZDn1LKBEwGni7wQEqNVEptUUptSUiQ+WWFEMWvirsT04Y2Z+p9zTh2PoU+H//JzD8OyypQAK0fA+dKsOYdoyup8AoTxieAmnm+DwDi83zvATQFopRSsUBr4Of8BnFpmjZL07QITdMifH19b75qIYQoor6h/qwc34kujXyZuGwf98zYwOGES9fdf9DMaAbNjC7BCg3g7AVtx8LBFXBii9HVVGiFCePNQAOlVKBSyhEYDPyc+6KmaYmapvlomlZH07Q6wEagn6Zp8i8rhChVfD2cmHF/Cz4aHM6RhMv0/mgdn647UrFbya1GgWsVWPO20ZVUaAWGsaZpWcAYYAWwF1ioaVqMUuoNpVS/4i5QCCHsSSlF//AarBrfkQ4NfHhryV4Gz4om9uxlo0szhpMHtHsCDv8OR8t5T0AppjSD5nONiIjQtmyRxrMQwjiapvHj9jhe+zmGjGwrz/cMYnibOphMytZFbY+5tEu9jBT4KAx8G8GInHG4ufcYF7QalCg0pdRWTdPynYdDZuASQlRYSinuah7AyvGdaFO3Cq//sofBszdy7FyK0aWVLEdXfRGJ2HXwz1qjq6mQJIyFEBVeNS9nPh/RkvfuCWVvfBI9P1rL6aQ0jOo5NESLB8GjOvz+NlSkz11KSBgLIQR6K3lgRE1WjO9Ii9rexJ5LIeZkEst3n6wYA7wsztDhaTi+Ub9+LEqUhLEQQuThX8mFuQ9FEujjRla2xuj52+g8aQ1frP+HS+lZRpdXvJoPA6+a+shqaR2XKAljIYS4ilIKPw8nwgK8mHF/c6p6OPP6L3toM/E3Ji7dS/zFVKNLLB4OTtDxGYjbCqkXjK6mQpEwFkKI61BK0bNpdRY91pYfH29Lx4a+zF53hA7vrWHcN9vZdeKi0SXaX/hQ8K4DiUeldVyCHIwuQAghyoJmtbyZdp83x8+nMGdDLN9uPs7PO+OJDKzMI+0D6dq4KmZTfrMHlzFmC3R6Hn56DFLPGV1NhSEtYyGEKIKalV15uW8Toifcxst9GhN3IZWR87bS9f0o5kbHkpJRDq4rhwwEBxe4eExaxyVEwlgIIW6Ch7OFRzrU5Y9nOzP1vmZ4uTryyuIY2kz8nf8u38epxDK8mqzZAbwCIDMFjqwxupoKQWbgEkIIO9A0jW3HLvDpun9YEXMKk1L0C/PnofaBNK3hBVC2ZvX6vBfEbYY6HeGBH4yuply40Qxccs1YCCHsQClFi9qVaVG7MsfOpfDFhn9YuPk4P2yPo03dKjzSIRBN01CqjFxXVibw8IfDv8HpPVC1idEVlWvSTS2EEHZWq4orr94RzIYJXXmxdxCx5y7z8Jwt7IpL5FRSGicTy8itUe7V9GvH0dOMrqTck25qIYQoZpnZVpb+fZIXf/ibyxnZADSs6k6HBr50bOhLq8DKOFvMBld5ldyFInwbwfZ58ORu8KhqbE1lnHRTCyGEgSxmE/3Da/DVxqOkZmbTN9SfdQfPMi/6KJ/9+Q+ODiZaBVamY044N6zqXnq6s9v8B7Z8DptmQdf/M7qackvCWAghSohSCldHB0Z1qseoTvVIzchm4z/nWHfgLGsPJvD20r28vXQvVT2dbK3mDvV98HZzNK7oKvWgUW/Y8pk+d7Wjq3G1lGMSxkIIYRAXRzNdGvnRpZEfAHEXU1l3IIF1B8+yas9pFm09gVIQWsPLFs7NalXCYi7h4T5tx8D+JbDza2j5SMmeu4KQa8ZCCFEKZVs1dp64aGs1bz92AasG7k4OtKlXhY4NfenUwJdaVVyL55ap3GvGDy7RJ/6YfRukJcKYLWCSsb83Q64ZCyFEGWM2KZrXWWlmewAAD+lJREFU8qZ5LW+e6NaAxNRMog+f5Y8DZ1l7IIFVe04DUKeKKykZ2Xi7WsjIsuLoUAxBqZTeOl70EBxYBkF97H+OCk7CWAghygAvFws9m1anZ9PqaJrGkbOXWXcggbUHzxK1/wxnktOJeGsV3ZpUpVfT6nRo4GPfEdqN++vLK26YKmFcDCSMhRCijFFKUc/XnXq+7oxoF8i90zeQmJZJSI1KrNpzih+2xeHmaKZLkB+9mlancyNf3Jxu8de92QFajYaVL+lLLNZoYZ8PIwAJYyGEKPNMJoW3qyPvDwwjMzuE6MPnWLb7FCtjTvHrrpM4OZjo1NCXXiHVuC2oKl4ulps7UfNh8Md/9dbxvV/Y90NUcBLGQghRxuUduGUxm+jYUB95/daApmyOPc/y3adYvvsUK/ecxmJWtKvvQ6+m1bi9STUqF+W2KWdPPZA3TtdXdKpUqxg+TcUko6mFEKICsP5/e3cfXFV953H8/c0TIQESCWAg4VFYEDCKRAE7rrqlCJVCtzqu7jJjHXZdrVg77Lbruk6n47hdXaZ1hGWsWC3O7lofGKcNAuosal07oEREHkQ0sGACRAKYIOEhJPz2j3MLMeThJpx7f+dePq+ZO7n3nN8595vMd+4nv3vvOee0Y1NNPa9trWXN1v1UHz5OZoYxZWR/Zk0s5sYJxQzql3t2g9bfpm6tvhqeuBym3gM3/mvyfoE00Nm3qRXGIiIXGOcc2/YdORPMO+saMYPJwy5i5sRiZk4spuHJGQBMePDdc3ewYj58+jos3Aa5BUmuPnUpjEVEpEOfffEVa7bWsmZrLdv3HwFgTMZ+rsqq4lt/vZCy0gKK+vQ6u8HejfD0DTDjEbjmPk9Vpx6FsYiIxGX3wUZe21bLkjc/o/Fky5nlJYW9KSst4LLSAi4vLWTKH+aR1VAN92+CzB5+IewCo5N+iIhIXEYMyOfu6y7hrU8O0HLa8Y83jmVLTQMf1dSzZW8Da7bWAjA94xp+nfMLlv/6CZrHf4+y0kImlvQjL0ex0hP6q4mIyDlaf0N76qiiM/frjzWxZW8Dm6vHULvuRabUPs+s/xsHGBkGowf1oay0kLLSAspKCxlX3Dd6l4eMIIWxiIjErTAvh2vHDOTaMQOh70KKVy3kwzvy2ch4Ntc0sLmmnrc+OcCKD2oAyM40xhb35bKSQtbvOkh+ThYv3T1NM+g29JmxiIj0TNMxeHwCDJsKt//2zGLnHPsbTrC5pj4W0EFIHznRfGbMoL69GFGUz/CiPEYMiP2MPe6bm56fQeszYxERCV9OXnBJxXcWwcEqGDAaCE7XOaSwN0MKezNz4mAgCOjvLv0jjU0t/OWkEvYcamT3oWO881kdL8dm0X9SlJ/TKpzzGTEgL/hZlEdhnsdrOyeQZsYiItJzRw8Es+NJ82D24z3axbGmZj4/fIzdB4+dCek9hxrZc+gY+xqO0zqmCnpnM6LobDgPbzWbNgMj+Gfga/eBjNgyCC5ClXFmjHW4XaYZBXnhzdI1MxYRkcToMwjKboVNz8MND0F+UdfbtJGXk8W44n6MK+53zroTp1qo+TII6t2xgN59qJFN1fW8unkfpxM4n8zMMHb+/NuJe4JWFMYiInJ+pi2AD/8LKp+B634S6q5zszMZPagvowf1PWddU/Np9tYfZ/ehRo6dbMHhcA4cwdviwf3YTwenncMBxJafji1vdzvnyE7EtaE7oDAWEZHzM+hSGD0d3l8G1/wQsnO73iYEOVkZjByQz8gB+Ul5vkRKXuyLiEj6mrYAGutgy8u+K0lJCmMRETl/o66HiyfCuqXg6YvBqUxhLCIi588smB3XbYeqtb6rSTkKYxERCcfEm6FPMaxb4ruSlKMwFhGRcGTlwJS7YNfbULvFdzUpRWEsIiLhmXwnZOcFnx1L3BTGIiISnrz+wdm4tqyAI/t9V5MyFMYiIhKuqffA6WZ4/6mvL//NTcFNzqEwFhGRcPUfBZfOhspn4eRR39WkBIWxiIiEb9p9cKIhOGe1dElhLCIi4Rs2BUqvgvVL4XSL72oiT2EsIiKJMe1e+HI3fLLKdyWRpzAWEZHEGPcdKBwG6/7DdyWRpzAWEZHEyMyCqT+A6vegeoPvaiItrjA2s5lmtsPMqszsgXbWLzSzj81ss5mtNbPh4ZcqIiIpZ9I86FWgU2R2ocswNrNMYCkwCxgP3G5m49sM+xAod86VASuAfw+7UBERSUG9+kL592H7Sjh1wnc1kRXPzPhqoMo5t8s51wS8AMxtPcA595Zz7ljs4XqgNNwyRUQkZV3992AZ8NU+35VEVjxhXAJUt3pcE1vWkfnAmvZWmNldZlZpZpV1dXXxVykiIqmroCS4otPRL4Izc8k54glja2dZu1eONrN5QDmwqL31zrllzrly51z5wIED469SRERS27R7wbXAV7W+K4mkrDjG1ABDWz0uBc55r8HMpgP/AlznnDsZTnkiIpIWBl8efJHrq33Q3BRcblHOiGdmvAEYY2YjzSwHuA2oaD3AzCYBTwFznHMHwi9TRERSXkEptDTBe0/6riRyugxj51wzsAB4HdgOvOSc22ZmD5vZnNiwRUAf4GUz22RmFR3sTkRELlS5hdC7P7z1czi003c1kRLP29Q451YDq9ss+2mr+9NDrktERNKNGfS/BA5+CivvhztWBstEZ+ASEZEkyuoFMx6G3f8LG5/zXU1kKIxFRCS5rrwDRlwLb/wUjuz3XU0kKIxFRCS5zOA7T0DLSVj1D+DaPVr2gqIwFhGR5Cu6BG54EHasgo9/57sa7xTGIiLix9R7YfAVsPrHcOyw72q8UhiLiIgfmVkwZ0kQxG885LsarxTGIiLiz+Ay+Mb9sOm/YeebvqvxRmEsIiJ+XfdPUDQ6OPa4qdF3NV4ojEVExK/s3ODt6vrP4c1HfFfjhcJYRET8G34NlM+H9U9CTaXvapJOYSwiIslx56rg1pHpP4N+Q6DivuDKThcQhbGIiERDbj+46Zdw4GN493Hf1SSVwlhERKJj7EyYeAu8swgOfOK7mqRRGIuISLTMegx69YWKBXC6xXc1SaEwFhGRaMkfADMfhZoN8P7TvqtJCoWxiIhET9mtMPpbsPbh4JCnNKcwFhGR6DGD2b8M7q/8Udpf2UlhLCIi0VQ4LDjcaeda2Pyi72oSSmEsIiLRddXfwtAp8NoDcLTOdzUJozAWEZHoysgITpXZ1AhrfuK7moRRGIuISLQNHAt//mPY9grsWOO7moRQGIuISPR940cwaAK8uhBONPiuJnQKYxERib6sHJi7BI7Wwv/87OvrfnNTcEthCmMREUkNJZNh6g+g8lnY/a7vakKlMBYRkdRxw4NQOBwqfginjvuuJjQKYxERSR05+TBnMRzeCX94zHc1oVEYi4hIahl1PUyaB39cDPs/8l1NKBTGIiKSemY8ElxQ4vcL0uJUmQpjERFJPb0vgm8vgtrNcGSv72rOm8JYRERS0/i5MG42NHweHHvc0hzevpN8uFRW0p5JREQkbDf9Aj59Db7YAo8OhcFXQOlkKCkPDoUqKA2uABVxCmMREUldfYthyJVwoh4u+QuoqYT3noKWJcH6PhcHoVwyGUrLYcgkyC3wW3M7FMYiIpLaMnMgfxDMih3q1NwUzJRrPoC9H8DeStixOjbYYMCfxcI5NoO+eAJkZnsrHxTGIiKSbrJyzs6G/+T4l7B3YyycP4DP3oCPno+Nz4XBl8fe2r4ymEE7l9S3txXGIiKS/npfBKO/GdwgCNv6PUEw18Rmz5XPwPqlwfqMbOjVJ/hSWGbio1JhLCIiFx4zuGhEcJt4c7Cs5RR8sS0I6LcfhdOnkhLEoDAWEREJZGbDkCuC29ZXkvrUOs5YRETEM4WxiIiIZ3qbWkREUtudq3xXcN40MxYREfFMM2MREZG2kjzb1sxYRETEM4WxiIiIZwpjERERzxTGIiIinimMRUREPFMYi4iIeBZXGJvZTDPbYWZVZvZAO+t7mdmLsfXvmdmIsAsVERFJV12GsZllAkuBWcB44HYzG99m2HzgS+fcaOBx4LGwCxUREUlX8cyMrwaqnHO7nHNNwAvA3DZj5gLPxe6vAL5plsSrMouIiKSweMK4BKhu9bgmtqzdMc65ZqABKAqjQBERkXQXTxi3N8N1PRiDmd1lZpVmVllXVxdPfSIiImkvnjCuAYa2elwK7OtojJllAQXA4bY7cs4tc86VO+fKBw4c2LOKRURE0kw8YbwBGGNmI80sB7gNqGgzpgK4I3b/FuBN59w5M2MRERE5V5dXbXLONZvZAuB1IBN41jm3zcweBiqdcxXAM8B/mlkVwYz4tkQWLSIikk7M1wTWzOqAPR2sLiD4Elh31g0ADoZQWiJ19ntFZf892Ud3tolnbFdjOlrf2XZR7w/1RmJ7o7N1Ue8NSGx/qDeS1xvDnXPtf0brnIvcDVjW3XUEs3Tvtff094rK/nuyj+5sE8/YrsZ00gOd9U2k+0O9kdje6Gxd1Hsj0f2h3ohGb0T1dJgre7gu6hJdexj778k+urNNPGO7GtPRevVGYvefyr3R3VqiJpG1qzci0Bve3qYOm5lVOufKfdch0aT+kI6oN6QjyeyNqM6Me2KZ7wIk0tQf0hH1hnQkab2RNjNjERGRVJVOM2MREZGUpDAWERHxTGEsIiLi2QURxmZ2qZn9ysxWmNk9vuuR6DCz75rZ02b2ezOb4bseiRYzG2Vmz5jZCt+1iH9mlm9mz8VeM/4mzH1HPozN7FkzO2BmW9ssn2lmO8ysyswe6Gwfzrntzrm7gVsBHcKQJkLqjd855/4O+D7wVwksV5IspP7Y5Zybn9hKxadu9sn3gBWx14w5YdYR+TAGlgMzWy8ws0xgKTALGA/cbmbjzewyM3u1zW1QbJs5wLvA2uSWLwm0nBB6I+ah2HaSPpYTXn9I+lpOnH1CcNXC6tiwljCL6PJCEb45594xsxFtFl8NVDnndgGY2QvAXOfcvwGzO9hPBVBhZquA5xNXsSRLGL1hZgY8Cqxxzm1MbMWSTGG9dkh6606fEFwuuBTYRMiT2VSYGbenhLP/nUDwByrpaLCZXW9mi83sKWB1oosTr7rVG8B9wHTgFjO7O5GFSSR097WjyMx+BUwys39OdHESGR31ySvAzWb2JCGfQjPyM+MOWDvLOjx7iXPubeDtRBUjkdLd3lgMLE5cORIx3e2PQ4D+SbvwtNsnzrlG4M5EPGGqzoxrgKGtHpcC+zzVItGi3pDOqD8kHknvk1QN4w3AGDMbaWY5wG1AheeaJBrUG9IZ9YfEI+l9EvkwNrPfAuuAsWZWY2bznXPNwALgdWA78JJzbpvPOiX51BvSGfWHxCMqfaILRYiIiHgW+ZmxiIhIulMYi4iIeKYwFhER8UxhLCIi4pnCWERExDOFsYiIiGcKYxEREc8UxiIiIp4pjEVERDz7f62wx0tq9tdzAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "fig.set_size_inches(8, 6)\n", "ax.errorbar(ps, avg_dists, std_dists, label='Distance/Distance(p=0)')\n", "ax.errorbar(ps, avg_clstr, std_clstr, label='Clustering/Clustering(p=0)')\n", "ax.set_xscale('log')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Barabási e Albert" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pouco depois do trabalho de Watts e Strogatz, uma nova descoberta foi feita sobre redes associadas a sistemas reais por Albert Lázló Barabási e Reka Albert. Eles perceberam que ao contrário de redes aleatórias ou de Watts e Strogatz, redes reais geralmente apresentam grande heterogeneidade nos valores dos graus.\n", "\n", "De fato, eles notaram que é frequente uma região de distribuição de lei de potência (ou livre de escala) na distribuição de probabilidades dos graus.\n", "\n", "Isso acarreta que a grande maioria dos vértices tenha graus menores do que a média, enquanto alguns poucos vértices têm graus muito maiores do que a média. Esses vértices de grau muito alto são denominados **hubs** e têm um papel extremamente immportante no funcionamento da rede.\n", "\n", "Para modelar esse fenômeno, eles introduziram um processo de geração de redes aleatórias que consiste no seguinte:\n", "\n", "1. Começa-se com uma quantidade pequena de vértices, ligados entre si (os detalhes desse subgrafo inicial não são importantes para grafos grandes).\n", "2. Depois acrescenta-se um vértice por vez, até atingir o número de vértices desejados $n$.\n", "3. A cada novo vértice acrescentado, acrescentamos $m$ arestas para vértices previamente existentes.\n", "4. Para escolher os vértices aos quais o novo vértice se conectará, usa-se a regra da **ligação preferencial** (_preferential attachment_): A probabilidade de ligar com um vértice é proporcional a seu grau.\n", "\n", "O resultado é que os grafos assim gerados, para $n$ suficientemente grande, têm uma distribuição em lei de potência para os graus altos. Mais precisamento, sabemos que a probabilidade de um grau escolhido aleatoriamente ter grau $k$ é dada por:\n", "$$P(k) = \\frac{2m(m+1)}{k(k+1)(k+2)}.$$\n", "\n", "Vamos verificar a distribuição de graus desses grafos.\n", "\n", "Como a cada novo vértice acrescentamos $m$ arestas, no caso de $n$ grande o grau médio será $\\langle k \\rangle = 2m$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "REP = 20\n", "N = 1000\n", "M = 2\n", "all_degs = []\n", "for rep in range(REP):\n", " g = nx.barabasi_albert_graph(N, M)\n", " all_degs = all_degs + list(dict(g.degree).values())\n", "max_deg = max(all_degs)\n", "h, b = np.histogram(all_degs, bins=range(2, max_deg+2), density=True)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "degs = b[:-1]\n", "fig, ax = plt.subplots()\n", "fig.set_size_inches(8, 6)\n", "ax.loglog(degs, h, '.', label='data')\n", "ax.loglog(degs, 2*M*(M+1)/(degs * (degs + 1) * (degs + 2)), label=r'$2m(m+1)/(k(k+1)(k+2))$')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dinâmicas em Redes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Um dos interesses principais da área de redes complexas é verificar como certas características topológicas da rede afetam dinâmicas que ocorrem nessa rede.\n", "\n", "Existem várias dinâmicas estudadas, influenciadas por diferentes características topológicas. Uma característica importante é a distribuição de grau: Para diversas dinâmicas, existe uma diferença significativa se o segundo momento da distribuição de grau diverge ou não.\n", "\n", "Um dos casos é a transmissão de doenças infecciosas, que estudamos abaixo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### O modelo SIR" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Epidemiologistas têm estudado modelos matemáticos para entender as características de propagação de diversas doenças infecciosas. Esse modelos em geral eram estudados sem considerar a estrutura da rede de contatos entre pessoas. Depois da introdução da área de redes complexas, se percebeu que a estrutura da rede tem uma influência importante em se uma epidemia vai se espalhar por uma fração significativa de toda a população ou não.\n", "\n", "Para doenças que conferem imunidade, um modelo simples consiste em considerar que cada indivíduo está em um de três possíveis estados:\n", "- Susceptível (S): Indica que o indivíduo está são, mas pode pegar a doença.\n", "- Infectado (I): Indica que o indivíduo tem a doença e pode transmiti-la para outro com que entre em contato.\n", "- Removido (R): Indica que o indivíduo já teve a doença e ou se recuperou, tendo agora imunidade, ou morreu. Em qualquer dos casos, ele não participa mais do processo de propagação da doença.\n", "\n", "Um indivíduo no estado S pode ir para o estado I se entrar em contato com um indivíduo no estado I. Um indivíduo no estado I pode se tornar saudável ou morrer, passando para o estado R, espontaneamente.\n", "\n", "É fácil notar que a dinâmica irá continuar enquanto existirem indivíduos no estado I. Isto significa que a dinâmica termina quando não há mais indivíduos no estado I.\n", "\n", "Para fechar o modelo, vamos considerar tempo discreto. Em cada instante de tempo, com probabilidade $\\gamma$ cada vértice I transiciona para R e contagia cada um de seus vizinhos com probabilidade $\\beta$.\n", "\n", "Desta forma, $\\beta$, $\\gamma$ e a estrutura da rede de contatos são os parâmetros do sistema.\n", "\n", "Vamos denotar por $s(t)$ a fração dos vértices que estão no estado S no instante $t$, $r(t)$ a fração dos vértices no estado R e $i(t)$ a fração dos vértices no estado I. Obviamente $s(t) + r(t) + i(t) = 1$. Começamos sempre com $r(0) = 0, i(0) = 1/n, s(0) = 1 - 1/n$.\n", "\n", "No final da epidemia, $r(t_\\mathrm{max})$ dá o número total de indivíduos afetados pela epidemia." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def propagate_sir(g, β, γ):\n", " # S = 0; I = 1; R = 2\n", " n = g.number_of_nodes()\n", " state = np.zeros(n)\n", " patient_zero = np.random.randint(n)\n", " state[patient_zero] = 1\n", " infected = {patient_zero} # All infected\n", " t = 0\n", " it = [1]\n", " rt = [0]\n", " while len(infected) > 0:\n", " new_it = it[t]\n", " new_rt = rt[t]\n", " for infected_individual in infected.copy():\n", " if np.random.random() < γ:\n", " state[infected_individual] = 2\n", " infected.remove(infected_individual)\n", " new_it -= 1\n", " new_rt += 1\n", " for j in g.neighbors(infected_individual):\n", " if state[j] == 0 and np.random.random() < β:\n", " state[j] = 1\n", " infected.add(j)\n", " new_it += 1\n", " it.append(new_it)\n", " rt.append(new_rt)\n", " t += 1\n", " return np.array(it)/n, np.array(rt)/n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def evaluate_sir(graph_generator, β, γ, num_repetitions):\n", " its = []\n", " rts = []\n", " tmax = 0\n", " for rep in range(num_repetitions):\n", " g = graph_generator()\n", " itr, rtr = propagate_sir(g, β, γ)\n", " its.append(itr)\n", " rts.append(rtr)\n", " if itr.size > tmax: tmax = len(itr)\n", " its_arr = np.zeros((num_repetitions, tmax))\n", " rts_arr = np.zeros((num_repetitions, tmax))\n", " for rep in range(num_repetitions):\n", " its_arr[rep, :its[rep].size] = its[rep]\n", " rts_arr[rep, :rts[rep].size] = rts[rep]\n", " rts_arr[rep, rts[rep].size:] = rts[rep][-1]\n", " return (np.mean(its_arr, axis=0), np.std(its_arr, axis=0, ddof=1),\n", " np.mean(rts_arr, axis=0), np.std(rts_arr, axis=0, ddof=1))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "N = 1000\n", "KMED =10\n", "REP = 20\n", "β = 0.01\n", "γ = 0.01\n", "avit_ba, sdit_ba, avrt_ba, sdit_ba = evaluate_sir(lambda : nx.barabasi_albert_graph(N, KMED//2), β, γ, REP)\n", "avit_er, sdit_er, avrt_er, sdit_er = evaluate_sir(lambda : nx.erdos_renyi_graph(N, KMED/N), β, γ, REP)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(3, 1)\n", "fig.set_size_inches(8, 18)\n", "ax[0].plot(avit_ba, label='I BA')\n", "ax[0].plot(avit_er, label='I ER')\n", "ax[0].legend()\n", "ax[1].plot(avrt_ba, label='R BA')\n", "ax[1].plot(avrt_er, label='R ER')\n", "ax[1].legend()\n", "ax[2].plot(1-avit_ba-avrt_ba, label='S BA')\n", "ax[2].plot(1-avit_er-avrt_er, label='S ER')\n", "ax[2].legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parece que a doença se propaga com mais facilidade na rede BA, levando a uma fração um pouco maior de pessoas afetadas do que na rede ER.\n", "\n", "Mas o interessante é o que acontece quando a taxa de transmissibilidade da doença é baixa:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "N = 1000\n", "KMED =10\n", "REP = 20\n", "β = 0.001\n", "γ = 0.01\n", "avit_ba, sdit_ba, avrt_ba, sdit_ba = evaluate_sir(lambda : nx.barabasi_albert_graph(N, KMED//2), β, γ, REP)\n", "avit_er, sdit_er, avrt_er, sdit_er = evaluate_sir(lambda : nx.erdos_renyi_graph(N, KMED/N), β, γ, REP)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(3, 1)\n", "fig.set_size_inches(8, 18)\n", "ax[0].plot(avit_ba, label='I BA')\n", "ax[0].plot(avit_er, label='I ER')\n", "ax[0].legend()\n", "ax[1].plot(avrt_ba, label='R BA')\n", "ax[1].plot(avrt_er, label='R ER')\n", "ax[1].legend()\n", "ax[2].plot(1-avit_ba-avrt_ba, label='S BA')\n", "ax[2].plot(1-avit_er-avrt_er, label='S ER')\n", "ax[2].legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vemos que, em redes BA, ainda existe transmissão da doença mesmo nesse caso, quanto nas redes ER a epidemia morre rapidamente!\n", "\n", "A conclusão tirada pelos pesquisadores que avaliaram o problema é que não existe limiar epidêmico em redes cujo segundo momento da distribuição de graus diverge. Uma taxa de transmissibilidade menor vai apenas diminuir o número de pessoas afetadas, mas numa população grande sempre haverá um número grande de pessoas afetadas. Já em redes com segundo momento não-divergente, existe uma limiar da relação entre $\\beta$ e $\\gamma$: até um certo valor de $\\beta/\\gamma$ não a epidemia morre sem se propagar, a partir de um valor crítico de $\\beta/\\gamma$ haverá uma epidemia. O valor de $\\beta/\\gamma$ é relacionado com o conhecido $R_0$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }