{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Overlapping communities and statistical inference of communities\n", "\n", "
\n", " \n", " \n", " Open this notebook in Google Colab\n", " \n", "
\n", "\n", "\n", "
\n", " \n", " \n", " Download this notebook (File -> Save As)\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What's wrong with modularity-maximization or similar methods?\n", "\n", "They are not necessarilly wrong! Those methods we tested last time may work perfectly fine for many networks and the community structure that you are interested in. However, there is an important implicit assumption shared by most community detection methods. That is, the communities are _disjoint_ or _non-overlapping_, which means that each node belongs to exactly one community.\n", "\n", "Imagine the social network around you. Do you belong to exactly one community? Probably not, because you have friends, family, and colleagues in many different contexts (a figure from [Palla et al., 2005](https://www.nature.com/articles/nature03607)). \n", "\n", "\n", "\n", "Moreover, this is not only true for yourself, but also for all other nodes in the network. If this is how the network is structured, then community detection methods that assume disjoint communities will not be able to capture the true community structure of the network.\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another way to think about this situation is to use a bipartite network of people and communities. There are many people and many communities and each person can belong to multiple communities. Then, the social network we see is a projection of this bipartite network. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at a simple example. Here, there are two communities. Most people belong to only one of them, but person \"D\" belongs to both. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import networkx as nx\n", "\n", "people = [\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"]\n", "communities = [\"C1\", \"C2\"]\n", "membership = {\n", " \"A\": [\"C1\"],\n", " \"B\": [\"C1\"],\n", " \"C\": [\"C1\"],\n", " \"D\": [\"C1\", \"C2\"],\n", " \"E\": [\"C2\"],\n", " \"F\": [\"C2\"],\n", " \"G\": [\"C2\"],\n", " \"H\": [\"C2\"],\n", "}\n", "\n", "B = nx.Graph()\n", "B.add_nodes_from(people, bipartite=0)\n", "B.add_nodes_from(communities, bipartite=1)\n", "B.add_edges_from(\n", " [(person, community) for person in people for community in membership[person]]\n", ")\n", "\n", "nx.draw(\n", " B,\n", " with_labels=True,\n", " node_color=[\"orange\" if B.nodes[n][\"bipartite\"] == 0 else \"blue\" for n in B.nodes],\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you project this bipartite network to the network of people, then you will see a network with two overlapping communities. They overlap at node \"D\". \n", "\n", "**Q: perform a bipartite projection of B to get the network of people P. And then draw the network**" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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f9fz5c2bMmMGiRYswNjZm6NCh9O/fH1NTU6WjCSGEUIgUlKnY7du3456LfPDgAQUKFIh7LrJ48eJKx1PMvn37aNSoEVOnTmXEiBFKx4kXXW3Q+Z6goCCmTp3KsmXLyJIlC8OHD6dPnz5p5nQAIYQQ8ScFZSrz4sWLuOciz5w5g5mZWdxzkdWrV0/zz0X+SFBQELa2tpQrV47du3enqt+Py5cvU758eaZOnapzDTrf8/jxYyZPnsyff/6Jubk5o0aNomfPnhgbGysdTQghRAqRgjIV+Pz5M9u3b0etVrNnzx4AGjduHPdcpHzjjvXlfvEbN25w6dKlVNmNrOsNOt9z//59Jk2axNq1a7GwsOC3336ja9euqWK1VQghRNJIQamjYmJiOHr0KGq1mk2bNvHu3TsqVaqEq6srbdu2TZfPRf7IpEmTmDBhAgcOHKB27dpKx0mU1NKg8z137txh4sSJrFu3jvz58zN27Fg6deqEoaGh0tGEEEIkEykodczNmzdRq9V4eXnx8OFDChYsGPdcpNyx/G1Hjhyhbt26jBs3jvHjxysdJ0nUajWdOnVKFQ0633P9+nUmTJjApk2bKFy4MOPHj6djx47o6+srHU0IIYSWSUEZGQZhgRAdDvpGYGINhiYpGuH58+ds2LABtVrNuXPnyJo1K23btsXV1ZVq1arp7PmJuuLFixfY2tpStGhR9u/fn+oLli8NOi9fviQgICDVbxkHBAQwfvx4tm3bRvHixZkwYQJt2rRJVc+3CiGE+L70WVCGXoc7S+HZbgi7B/zzt0AFJoXAygGK9AKzkskS4dOnT/96LlJPTw8HBwdcXV1p0qSJPBcZTzExMTRt2pRz585x6dIlrKyslI6kFam1Qed7zp07x7hx4/Dz86NMmTJMnDgRR0dH+YFJCCHSgPRVUIbdhzM9IdgfVAagifr2e7+8blEfKi4Dk4JJnj4mJoa//voLtVrN5s2beffuHZUrV8bV1ZV27drJzSOJMHPmTIYPH86ePXto2LCh0nG0auDAgaxcuTJVNuh8z4kTJxg3bhwHDhygfPnyuLu74+DgIIWlEEKkYumnoAxcCef7QUzU9wvJ/6UyAD0DqLAArLslaurr16/j6emJl5cXjx49olChQnHPRRYpUiRRYwo4efIkNWvWZOjQoUydOlXpOFoXGhpKsWLFqFWrFt7e3krH0brDhw8zduxYjh07RqVKlZg0aRI///yzFJZCCJEKpY+C8uoUuDwm6eOUnQylf4vXW0NCQli/fj1qtZoLFy6QLVs22rVrh6urK1WqVJFvmkn05s0bbG1tyZs3L4cPH06zHcRppUHnWzQaDfv372fs2LGcPn2aGjVqMGnSJGrVqqV0NCGEEAmQ9gvKwJVwprv2xqu0Egp3/epLHz9+ZNu2bajVavbt24eenh5NmzbF1dUVBwcHjIyMtJcjHdNoNLRs2ZIjR45w6dIl8ufPr3SkZJPWGnS+RaPRsHv3bsaOHcvFixepV68ekyZNokqVKkpHE0IIEQ9pu80y7H7sNvc33H8OfT2g6BDI1CX2V8lh0Gc1XH70jQ+d6xs77t9iYmI4ePAgXbp0wcLCgo4dOxIaGsrChQsJDg5m69atODk5STGpRQsWLMDX1xcPD480XUwCqFQqFi1axJ07d5g/f77ScZKNSqWiSZMmnD9/nq1btxISEkLVqlVxcHDg3Llz2p0sMgzeXIKXp2P/NzJMu+MLIUQ6lLZXKA82gJBDX31mcucFaLcQDPTAuRrY5Ac9Fdx8BlvPwcOXcH8uFPjf88NVBpC7Dtdyz407L/LJkycULlwYV1dXXFxcKFy4cMp8fenQuXPnqFq1Kn369GHu3LlKx0kxabVB51tiYmLYtGkTEyZM4ObNmzRv3hx3d3dsbGwSN6AOnOwghBBpWdotKEOvw65SX33pbgjYjIL85nBgNFhm+/frUdGw2B+c7CHfNxqvSwyD55+zxz0XWblyZXkuMpmFhoZSvnx5smfPzvHjx9Ps9u/XpPUGnW+Jjo5m3bp1TJw4kbt379KmTRsmTJhAyZLxLPoUPtlBCCHSi7RbUJ7rD3eWfPUbSM9VsPwgnJoIlawTPnR0jIoHGRzI57g1XRU1StJoNLRv3549e/Zw4cKFdLkKnNYbdL4nMjKStWvX4u7uzuPHj+nYsSPjxo37/u1RCp7sIIQQ6U3aLSi3W0PY3a++lKcvZMoAd+YkYXwTa2h+JwkDiIRYvnw5PXv2xNvbm7Zt2yodRxHppUHneyIiIli1ahVTpkwhODgYV1dXxo0bR8GC/7OaqMDJDkIIkZ6lzaacyPd/Pyf1X+8+wrM3UDrff197+wFevv//X58ivjNH2F15mD+FXL58mQEDBtCrV690W0zCvxt05s2bp3QcRWTIkIHevXsTGBjI7Nmz8fPzo2jRovTs2ZPHjx/HvilwpXaKSYgd5+4q7YwlhBBpWNpcoXxzCfzKffWlJ68gX39wqQbqX//9mu0oCPhHd/fMjjC0ybeneWazC7LZYmhoiKGhIRkyZMDQ0BADAwN5nlJLwsLCsLe3J0OGDJw6dYqMGTMqHUlx6a1B53s+fPjA4sWLmT59Ou/fv2dUv/aMt9uIKubzV9/vcQS6LP/6WCOawbT2X3lB3xiaXJdnKoUQ4jsMlA6QLKLDv/mS6d/1SNhX3rKsK7z/DCGh4LL4x9M4tWjCma/vqv+nyIzPX+vK6/r6+vH4TU4Zffv25fHjx5w7d06Kyb9NnDiRDRs2MGTIkHTVoPM1mTNnZtiwYfTq1Ys//viDKp8nEBUZheEP/gi7t4aC/3OCQ+lv1eYxUbGNPXX3aSWzEEKkRWmzoNT/9pmPZpnAMitcffzf17406Dx4Eb9p5i1YwhtNfiIiIoiMjCQyMvKrf52Q18PDwwkLC0vwWFFRCWg6+AGVSpUsBWtCxzp8+DBr1qzht99+IzQ0lAsXLvzw84aGhujppc0nOb4wMzNj1qxZuLq60r17d37++WelIynO1NSU3/o6wa74bXU3tgG7QvEcXBMV2yUeegPMSiQ+pBBCpGFps6A0sQZU/Pusuf/XxBZWHoYzd6FiopuFVVT52QUMTRI7gFbFxMQQFRX1w+I1sYVufN/78ePHRI0VExPzza9typQpTJkyJd6/F/r6+oqv9iZ2rPg+LuHs7Mzy5cvp169fum3Q+Y87S398NFBiqQxiT42w+0P7YwshRBqQNgtKQ5PYg4q/0eU9vBmsOwm/LI89hzK32b9fj9dTpSaFdaaYBNDT0yNDhgyptrCIjo6OKzJDQ0OpX78+UVFRbN26FUNDw2QvhL/89bt37xI1ljbFtyCNjIzk5s2blC5dmqJFi+pE8azo4xLPdse7mAz9GNt49085TL/zAU0UPPNLfDYhhEjj0mZBCbG3XnzjHMoiFrDuV+iwCIoNBeeqYFMgtpC8/wLWnYi9NSdv9m+MrTIAq8bJmz+d0dfXR19fH2NjY4YNG8aDBw84e/YspUuXVjraD2k0GqKjo5O10P3W658+fSIwMJCCBQui0WjiHpdIyFjafFxCT09PkZXhTBmiaad3l/i2wv089Sv/Hr1+8KEvJzvo0A+SQgihK9JuQVmkF9xe8M2XW9jBlWkwezfsuwJ/HgGVCgrkiN0S71Uvtsj8Kk0UFOmdLLHTO29vb5YtW8aKFStSRTEJsc+cGhgYYGCQ8v85fblBJ2vWrIlu0NFoNCleCH/trz9+/EhoaGiCx4qJicGmALT/Pf5f8yI3KGqZ4N8pCAuEbLYJ/aAQQqR5abegNCsZe4XaN+7yBiicGxZ3SdiwkdFw87UF2d6bktfsx+8X8Xf37l26d+9Ohw4d6Nq1q9JxUgVtNOh8acLKkCEDmTNnToaUySs6OpqokONwuFa8P1OxcAKacv412bdPkBBCiPQsbbfDVlwWe4WalmgAlZ4hvyyNpFixYri7u/Px40etjZ+ehYeH065dO3Lnzs3SpUvlHM8EcHZ2pkaNGvTt21frz3OmBvr6+hhlzJJCk337BAkhhEjP0nZBaVIw9j5eLVEBBpWXcOD0Pfr06cPkyZMpUaIE3t7epMXz4VPSiBEjuHLlCt7e3mTJkkLFQRrx5QadwMDAdHuDDibWaOL9BGViqf4+QUIIIcT/StsFJYB1t9j7eLXBZgoU7kqWLFmYMWMG169fp1y5crRv356aNWty/vx57cyTzvj6+jJ//nxmz55N+fLllY6TKpUpU4Z+/frh7u7+/1cQpgMajYZTp07RZ+AIHrxI5oJSx052EEIIXZL2C0qA0r9BxRWxV6ipErgFrjKI/VyllVBq9L9esra2xtfXl/379/P27Vvs7e3p2rUrwcHBWgyftj18+JAuXbrg5OREnz59lI6Tqk2YMAETExOGDBmidJRkd//+fSZNmkSxYsWoUqUK27Zt4xm2aEimY4vkZAchhPiu9FFQQuxKZZPrkLtO7N//oLCM0cT+1oQal4/9XOFvN4nUq1ePixcvsnDhQrZt20bRokWZPn064eHyAP/3REZG0qFDB8zMzFi1apU8N5lEXxp0Nm3axP79+5WOo3Vv375lxYoV1KhRg0KFCjF9+nSqVq3K/v37efjwIdXc1KiITp7J5WQHIYT4LpUmPT78F3o99laNZ35/H37+z98CFZgUJsayEY5D9/Apw0/4+/vHe+g3b94wceJEFi5cSIECBZg1axaOjo5SLH3FyJEjmT17NkePHqVy5cpKx0kTNBoNtWrV4vnz51y+fDnVHnT/RUREBHv27EGtVrNjxw4iIyOpX78+rq6uODo6/rcr/WCD757skCgqg9gfROUubyGE+Kb0WVD+U2RY7Nly0eGxHZwm1nHPSfn6+uLk5MSBAweoW7dugoa9ceMGgwcPZs+ePdSpU4d58+ZRtmzZ5PgKUiU/Pz8cHByYOXMmQ4cOVTpOmnLlyhXKlSvHlClTGDFihNJxEkyj0XD27FnUajXr16/n1atX2NjY4OrqSseOHbG0/M4BkmH3YVdJiP6svUD6xrG7FCYFtTemEEKkMVJQfodGo6FSpUro6elx8uTJRK0y7t69m8GDB3Pnzh169OiBu7s7OXPmTIa0qcfTp0+xtbWlYsWK7NixAz299PPkRUoZNGgQK1as4MaNG+TLl0/pOPHy4MEDPD09UavV3L59GysrK5ydnXF1daVMmTLxHyhwJZzprr1glVZ+95EXIYQQUlD+0P79+6lfvz7btm2jefPmiRojIiKCRYsWMXHiRCC2eaJPnz4YGhpqM2qqEBUVRb169QgMDCQgIIAcOXIoHSlNCg0NpXjx4tSoUYONGzcqHeebQkND2bRpE2q1mr/++ovMmTPTsmVLXF1dqVu3buLvBr86BS6PSXpAmyn/acYTQgjxX1JQxkO9evV4/vw5ly5dSvw3OODFixeMGzeO5cuXU6RIEebMmYODg4MWk+q+8ePHM3nyZA4dOkTNmjWVjpOmeXp64urqir+/f6Ju0EkukZGR7N27F7VazbZt24iMjKRevXp06tQJR0dHTEy0dDRP4Eo43w9iohL2TKXKIPZCBLuFsjIphBDxJAVlPJw6dYoqVarg6emJs7Nzkse7fPkygwYN4uDBgzRq1Ig5c+ZQokQJLSTVbQcPHuTnn3/G3d2dMWO0sHokvkuXGnQ0Gg3nzp1DrVazYcMGXrx4QdmyZeOei7SyskqeicPuw5meEOwfWyh+r7D88rpF/dhbtuSZSSGEiDcpKOOpRYsWXL16lZs3b2plq1qj0bBt2zaGDBnCo0eP6NOnD+PHjydbtmxaSKt7QkJCsLW1pVSpUuzduzdJK70i/pRu0Hn48CFeXl6o1Wpu3ryJpaUlHTt2xNXVFRsbm5QLEo+THbBqHHs0kFna/+FOCCG0TQrKeLpy5Qo2NjYsXryYXr16aW3c8PBw5s2bx+TJkzEyMsLd3Z0ePXpgYKC9O8iVFhMTQ6NGjQgICCAgIAALCwulI6UrgwYNYvny5dy8eTNFGnTevXvH5s2bWbt2LUeOHCFTpkxxz0XWq1dP+R8m/j7ZYeL40dx/+AyPzcfkBhwhhEgiaa+NpzJlytCxY0fc3d359OmT1sY1MjJixIgR3LlzhxYtWtC3b1/KlSuXpg6mnj59Ovv378fLy0uKSQVMmDCBLFmyJOsNOpGRkezatYv27duTO3duunXrhqGhIWvWrCEkJAS1Wk2DBg2ULyYhtnjMZkuoQXFO3w6XYlIIIbRACsoEmDhxIi9evGDRokVaH9vCwoJVq1Zx9uxZzMzMqF+/Po6OjgQGBmp9rpR07Ngxxo4dy+jRo3WqMSQ9+ecNOgk5pP9HNBoN58+fZ+DAgeTJk4emTZty7do1Jk6cyKNHj/D396dTp07aa7LRMnNzc16+fKl0DCGESBNkyzuBevfuzcaNG7l37x5mZmbJModGo2Hjxo0MGzaM4OBgBg4cyJgxY8iSJUuyzJdcXr16ha2tLQULFuTgwYNpahs/tdFoNNSuXZuQkJAkN+g8fvwYLy8v1q5dy40bN8idOzcdO3akU6dO2NjYpJpboZYuXUqfPn2IjIyUs1CFECKJ5P9FE2jMmDF8/PiROXPmJNscKpWKdu3acfPmTcaMGcPChQspUqQIq1atIjo6me4q1jKNRoObmxufPn1i3bp1UkwqTKVSsXDhQgIDA5k7d26CP//u3TtWr15N3bp1KVCgAO7u7pQrVw4/Pz+ePHnCnDlzsLW1TTXFJMSuUMbExBAaGqp0FCGESPWkoEygPHny0LdvX+bMmcOLFy+Sda5MmTIxbtw4bt++Tf369enWrRv29vYcPXo0WefVhnnz5rFz507WrFlD3rx5lY4jiH0OuH///ri7u/P48eMfvj8qKgo/Pz86duyIhYUFXbt2RaVS8eeffxISEoKXlxeNGjVKtT8smJubA7Er6UIIIZJGCspEGDlyJCqViqlTp6bIfHnz5sXT05MTJ05gYGBAzZo1adeuHQ8fPkyR+RPqzJkzjBgxgqFDh9KkSROl44h/+NKgM3jw4K++rtFouHjxIoMGDSJv3rw4ODgQEBDA+PHjefjwIQcOHMDNzQ1TU9MUTq59X25pkoJSCCGSTgrKRDA3N2fo0KEsXrw4Xis92lKlShVOnTrFmjVrOHr0KMWLF2fs2LF8+PAhxTL8yNu3b2nfvj3ly5dnypQpSscR/yNLlizMmjWLzZs3/6tB58mTJ0yfPp0yZcpQvnx51q1bR4cOHTh//jxXr15lxIgRqeZO8PiSFUohhNAeacpJpPfv31OoUCGcnJxYvnx5is8fFhbGtGnTmDVrFubm5kyfPp2OHTsq2lyg0Who27Yt/v7+XLp0iZ9++kmxLOLbvjToPHv2jBEjRrBhwwYOHjyIkZERjo6OdOrUifr166farez4+vz5MxkzZmTNmjV06tRJ6ThCCJGqyQplIpmamjJ69Gj+/PNPbt++neLzm5iYMHnyZG7cuEHVqlVxdXWlatWqnD59OsWzfLF06VI2b97Mn3/+KcWkjoqKimLv3r2YmJgQGBhI9+7diYmJYdWqVYSEhLB+/XoaN26c5otJAGNjYzJlyiQrlEIIoQVSUCZB7969sbS0ZPz48YplKFiwIJs2beLw4cOEh4dTuXJlXF1defr0aYrmuHTpEoMGDaJv3760bNkyRecW36fRaLh06RJDhgwhX758NG7cmPv371OtWjWMjY1Zs2YNXbp0SXXHUmmDubm5FJRCCKEFUlAmgbGxMePGjWPDhg0EBAQomqVWrVqcO3eO5cuXs3fvXooWLcqkSZO0eqvPt7x//5527dpRsmRJZs6cmezzifh5+vQpM2fOpGzZspQrVw61Wk27du04d+4c165dY/fu3WTNmvWbDTrpgRSUQgihHfIMZRJFRkZSqlQpihUrxo4dO5SOA0BoaCiTJ09m/vz5WFlZMWPGDNq0aZMsZwRqNBpcXV3Ztm0bFy5coEiRIlqfQ8RfWFgYW7duRa1Wc+DAAYyMjGjRogWurq40aNAAQ0PDf73fy8sLFxcX9u3bR/369RVKrZz69euTLVs2Nm7cqHQUIYRI1WSFMokMDQ1xd3dn586dHD9+XOk4QOxVezNnzuTatWuULVuWdu3aUatWLS5cuKD1uTw8PPDy8mL58uVSTCokOjqaffv24erqSu7cuencuTORkZGsWLGC4OBgNmzYQJMmTf5TTAJ07NiRmjVr0rdvX8LDwxVIryxZoRRCCO2QglIL2rZti42NDaNHj0aXFnyLFCnC9u3b2bdvH69evcLOzo5u3boREhKilfGvXbtGnz596NatGx06dNDKmCL+Ll++zNChQ8mXLx8NGzbk7Nmz/Pbbbzx48IDDhw/TtWvXH14PqlKpWLRoEXfv3k3UDTqpndznLYQQ2iFb3lqya9cumjZtyt69e2nQoIHScf4jKiqKZcuWMW7cOCIjIxkzZgwDBgzAyMgoUeN9/PgRe3t7VCoVZ86cIVOmTFpOLL7m2bNnrFu3DrVazeXLl8mRIwcdOnTA1dUVOzu7RD/WMHjwYJYtW8bNmzfT3HmT3zNu3Dj+/PNPnjx5onQUIYRI1aSg1BKNRkP16tUJDw/n7NmzOnun8evXr5k4cSKLFi3ip59+Yvbs2TRv3jzBebt168a6des4d+4cJUuWTKa0AuDDhw/4+PigVqvZv38/hoaGNG/eHFdXVxo1avTVreyEevfuHcWKFaN69eps2rRJC6lTh/nz5zNy5MgUaV4TQoi0TLa8tUSlUvH7779z/vx5tm7dqnScb8qePTvz58/n8uXLWFtb4+joSP369bl69Wq8x/Dy8mLVqlUsWrRIislkEh0dzf79++ncuTO5c+fG1dWVT58+sWzZMoKDg9m4cSPNmjXTSjEJsTfozJ49+z836KR15ubmfP78mY8fPyodRQghUjVZodSyhg0b8ujRI65evYq+vr7Scb5Lo9Gwe/duBg8eTGBgIL169WLixIlxdxx/ze3bt6lQoQKOjo6sXbtWZ1diU6srV66gVqvx8vLi2bNnFC1aFFdXV5ydnSlYsGCyzq3RaKhTpw5BQUFcvnw50Y9DpCZ79uyhcePGPHr0KF1t9QshhLbJCqWW/f7779y8eRO1Wq10lB9SqVQ0adKEK1euMHPmTLy8vChSpAjz588nMjLyP+///Pkz7dq1w8rKisWLF0sxqSXBwcHMmTOHcuXKUbZsWf7880+cnJw4deoUN2/eZMyYMcleTELsn4eFCxemqwYduc9bCCG0Q1Yok0Hr1q05d+4ct27dSlWrPC9evGDs2LGsWLGCokWLMmfOHBo3bhz3et++fVm5ciWnTp3C1tZWuaBpwMePH/H19WXt2rX4+/tjYGDwr+ciM2TIoFi2IUOGsHTpUm7cuEH+/PkVy5ES7t27R+HChfH39+fnn39WOo4QQqRaskKZDCZNmsTjx49ZsWKF0lESJGfOnCxdupQLFy5gYWGBg4MDDg4O3Lx5ky1btrBo0SLmzp0rxWQiRUdHc+DAAdzc3MidOzfOzs58+PCBJUuWEBwczKZNm2jevLmixSTA+PHjyZIlC0OGDFE0R0qQFUohhNAOWaFMJl26dMHPz4+7d++SOXNmpeMkmEajwcfHh6FDh/Lo0SP09fVp1KgRvr6+stWdQNeuXUOtVuPp6cnTp0+xtrbG1dUVFxcXChUqpHS8r1q3bh3Ozs46ewyWtmg0GjJkyMD8+fP59ddflY4jhBCplhSUyeTBgwcULVqUiRMnMmrUKKXjJNq7d+8oVaoUT58+JWvWrPz+++9069YNAwMDpaPptODgYNavX49arebixYtkz56d9u3b4+rqSqVKlXS+KE9PDTq5c+emb9++jB07VukoQgiRasmWdzL56aef6NmzJzNmzODNmzdKx0k0d3d3QkJC2LVrFy1atKB3796UL1+egwcPKh1N53z8+JH169fj4OBA3rx5GTlyJAULFsTHx4egoCAWLVpE5cqVdb6YhPTVoJMjRw7Z8hZCiCSSgjIZ/fbbb0RERDBz5kyloyTKzp07mT17NjNmzKBx48asXr2as2fPYmpqSr169XBycuLu3btKx1RUTEwMhw4dokuXLlhYWNCxY0dCQ0NZtGgRQUFBbNmyBUdHR8Wfi0yM0qVLM2DAACZNmsSjR4+UjpNs5D5vIYRIOtnyTmajR49m/vz53L17FwsLC6XjxNuTJ0+wsbGhevXq/3luUqPR4O3tzbBhw3j+/DmDBg3it99+w9TUVMHEKev69etx50U+fvyYwoULxz0XWbhwYaXjac27d+8oXrw4VatWZfPmzUrHSRZOTk58/vwZPz8/paMIIUSqJSuUyWzYsGFkyJCB33//Xeko8RYVFUWHDh3InDkzq1ev/s8WrUqlon379ty6dYvRo0fzxx9/UKRIEf78809iYmIUSp38nj9/zvz587Gzs6NUqVIsW7aMJk2acPz4ce7cucP48ePTVDEJsTfozJo1iy1btrBv3z6l4yQLWaEUQoikk4IymWXLlo3hw4ezdOlSHjx4oHSceJkwYQInT55k/fr1ZM+e/Zvvy5QpE+PHj+fWrVvUrVuXrl27Ym9vz7Fjx1IwbfL69OkT3t7eNG3aFCsrK4YNG0a+fPnYunUrQUFBLFmyhKpVq6aK5yITq0OHDtSqVYt+/foRHh6udBytk4JSCCGSTgrKFNC/f3+yZcvGxIkTlY7yQ/7+/vz+++9MnjyZatWqxesz+fLlY926dRw/fhw9PT1q1KhB+/btU+1zdzExMRw+fJiuXbtiYWFB+/btef36NQsWLCAoKAgfHx+cnJzSdOfzP/2zQWfOnDlKx9E6KSiFECLp5BnKFLJgwQIGDhzI1atXKVGihNJxvio4OBgbGxtsbW3x8/NDTy/hP2/ExMSgVqsZOXIkb9++ZdiwYYwYMSJVnMX55cpMT09PHj16RMGCBeOeiyxSpIjS8RSXVm/Q+fPPP+natSuRkZFyHJYQQiSSFJQpJDw8nGLFimFnZ6eTzQ3R0dE0aNCA69evExAQQK5cuZI03vv375k6dSpz5swhR44cTJ8+nY4dO+rc1vCLFy/YsGEDa9eu5dy5c2TNmpV27drh6uqa5reyEyqtNuhs27YNR0dHQkJCkvznXggh0ivZ8k4hRkZGTJgwgS1btnDu3Dml4/zH1KlTOXToEOvWrdPKN1VTU1N+//13bty4QeXKlXFxcaFq1aqcOXNGC2mT5vPnz2zcuJFmzZphZWXFkCFDyJMnD5s3byYoKIilS5dSrVo1KSb/R1pt0JHrF4UQIulkhTIFRUVFUaZMGQoUKMCePXuUjhPnr7/+ok6dOowdO5YJEyYkyxyHDx9m4MCBBAQE0KlTJ6ZOnYqVlVWyzPU1MTExHDt2DLVazcaNG3n37h2VKlXC1dWVdu3akSNHjhTLkpqlxRt0bty4QcmSJfnrr7+oUaOG0nGEECJVkhXKFGRgYMDkyZPZu3cvR44cUToOELvl26FDB2rWrJmsV8/Vrl2b8+fPs2zZMvz8/ChatChTpkzh06dPyTYnwK1btxgzZgyFChWiVq1a7N+/nwEDBnDr1i1OnTpFnz59pJhMAJVKxaJFi9JUg46sUAohRNLJCmUK02g02NvbY2RkxLFjxxTdVo2JiaFp06acPXuWgICAFFsxDA0NZdKkScyfP588efIwa9YsWrVqpbXfi5cvX7JhwwbUajVnzpzBzMyMtm3b4urqSrVq1RLVbCT+bciQISxZsoSbN2+m+gadqKgoDA0NWblyJV27dlU6jhBCpErynTWFqVQqpkyZwokTJ9i9e7eiWWbPno2fnx9qtTpFt5/NzMyYNWsW165do0yZMrRp04batWtz8eLFRI/5+fNnNm/eTPPmzbG0tGTQoEHkzp2bTZs2ERwczPLly6lRo4YUk1oyfvx4smbNyuDBg5WOkmQGBgZkzZpVViiFECIJ5LurAho0aECtWrX47bffFLtZ5uTJk4wePZoRI0bQqFEjRTIULVqUHTt2sHfvXl6+fEmFChXo3r07ISEh8fq8RqPh6NGj9OjRAwsLC9q0aUNISAhz587l2bNnbN++ndatW2NsbJzMX0n6kyVLFmbPns2WLVvYu3ev0nGSTM6iFEKIpJEtb4UcP36c6tWrs379etq3b5+ic7958wZbW1vy5MnDkSNHMDQ0TNH5vyYyMpKlS5cyfvx4oqKiGDduHP379ydDhgz/ee+dO3fizou8f/8+BQoUwMXFBVdXV4oVK6ZA+vTpS4POs2fPuHLlSqpu0KlUqRJlypRh5cqVSkcRQohUSQpKBTVt2pRbt25x/fr1FCvqNBoNLVu25MiRI1y8eJECBQqkyLzx9erVKyZMmMCSJUsoWLAgs2fPplmzZrx+/Rpvb2/Wrl3L6dOnyZIlC23atMHV1VW2shV07do1bGxsmDRpEqNGjVI6TqI5ODiQIUMGfH19lY4ihBCpknwXVtCUKVMIDAxkzZo1KTbnwoUL8fX1ZfXq1TpXTELs1uOCBQsICAigQIECtGjRgty5c2NhYUH//v3JmTMn3t7eBAcHs3LlSmrVqiXFpIJKlSrFwIEDmTRpUqq9ahNky1sIIZJKVigV1qFDB44dO8adO3eS/Vm/8+fPU7VqVXr37s28efOSda7E0mg0nDhxIu68yDdv3mBkZERERARubm7MnDkz7pgXoRvev39PsWLFqFKlClu2bFE6TqIMGjSIvXv3cv36daWjCCFEqiRLOwqbOHEiQUFBLFmyJFnneffuHe3ataNMmTJMnz49WedKjMDAQCZMmIC1tTXVq1dn9+7d9OrVi+vXr/Pu3TtmzpzJli1bKFKkCH/88QeRkZFKRxZ/MzU1Zfbs2WzdujXVNujICqUQQiSNrFDqgO7du+Pr68u9e/cwNTXV+vgajYYOHTrg5+fHhQsXKFy4sNbnSIwvz0Wq1WpOnjyJqalp3HORNWvW/M9W9vPnzxk7diwrVqygePHizJ07l4YNGyqUXvyTRqOhbt26PH36NFU26CxZsoT+/fsTEREhV24KIUQiyAqlDhg3bhzv379n7ty5yTL+ypUr8fb2ZsWKFYoXk+Hh4fj4+NCyZUssLCzo168f2bJlY/369QQHB7Nq1Spq16791ecic+XKxbJly7hw4QK5cuWiUaNGNG3alNu3byvwlYh/UqlULFy4kPv37zN79myl4ySYubk5UVFRvHv3TukoQgiRKklBqQPy5cvHr7/+yqxZs7S+7XblyhX69+9Pr169aNu2rVbHji+NRsPJkyfp3bs3lpaWtGzZkocPHzJz5kyePn3Krl27aN++PZkyZYrXeLa2thw6dIjNmzdz7do1SpUqxeDBg3n79m3yfiHiu0qVKsWAAQOYPHlyqmvQ+fJc7suXLxVOIoQQqZNseeuIFy9eUKhQIXr37s2MGTO0MuaHDx+ws7MjQ4YMnDp1iowZM2pl3Pi6e/cunp6eeHp6EhgYSN68eePOiyxZsqRW5vj8+TNz5szh999/J2PGjEyePJlu3bqhr6+vlfFFwrx//57ixYtTuXLlVNWgc+nSJcqVK8fp06epWLGi0nGEECLVkRVKHZEzZ04GDx7MggULePr0qVbG7Nu3L48fP8bb2zvFisk3b96wbNkyqlevjrW1NbNmzaJ69eocPHiQhw8fMnXqVK0VkwDGxsaMHj2a27dv06RJE3r16kX58uU5dOiQ1uYQ8WdqasqsWbNSXYNOjhw5AKQxRwghEkkKSh0yePBgMmXKxOTJk5M81tq1a/Hw8GDJkiUUL15cC+m+LSIiAl9fX1q1aoWFhQW//vorWbJkYd26dYSEhLB69Wrq1KmTrOdFWllZ4eHhwenTp8mcOTN169alVatW3Lt3L9nmFF/Xvn17ateuTb9+/QgPD1c6Trx82fKWglIIIRJHCkodYmZmxsiRI1m5ciV3795N9Dg3b97k119/xc3NDVdXVy0m/H8ajYZTp07Rp08frKyscHJy4v79+0ybNo2nT5+ye/duOnToEO/nIrWlYsWKHD9+HC8vL86cOUOJEiUYNWoU79+/T9Ec6VlqbNDJmDEjGTNmlIJSCCESSZ6h1DGfPn3C2tqaOnXq4Onp+e8XI8MgLBCiw0HfCEyswdDkP5+vXLkyERERnDt3jsyZM2s13/379/H09EStVnPnzh3y5MmDs7Mzrq6ulC5dWqtzJdWHDx+YOXMmM2bMwMzMjKlTp9KpUye5WSeFDB06lMWLF3Pz5k3y58+vdJwfypcvH126dMHd3V3pKEIIkepIQamDli5dyq+//kpAQABl8uvDnaXwbDeE3QP++a9LBSaFwMoBivQCs5L07t0bDw8Pzpw5Q5kyZbSS5+3bt2zatIm1a9dy7NgxMmfOTOvWrXF1daV27do63wDz6NEjRowYwYYNG7Czs2PevHlUq1ZN6VhpXmpr0LG1taVq1aosXrxY6ShCCJHqSEGpgyIiIqhfxZp5zp8pZ/ECVAagifr2B/5+PZiyVBl4mdFTltO9e/ckZ9izZw9qtZodO3YQGRlJ/fr1cXV1xdHRUesrnynh+PHjDBgwgPPnz9O+fXumT5+eKlbOUrMNGzbQoUMH9uzZo/OH0NerV48cOXLg7e2tdBQhhEh1pKDURYEriTr9K5qYSAwTsPgXFQ0x6GNYZQkq64QXlBqNhrNnz6JWq1m/fj2vXr3CxsYGV1dXOnbsiKWlZYLH1DUxMTGsWbOG0aNHExoayvDhwxk+fHiKP+uZXmg0GurVq8eTJ090/gaddu3a8erVK/bv3690FCGESHXkYTJdc3UKnOmOviphxSSAgT4Y6kejOtMjdpx4evDgAZMnT6Z48eJUqlSJrVu38ssvv3D58mUuXbrEkCFD0kQxCaCnp0eXLl24ffs2AwYMYOrUqRQrVox169YhP1tpn0qlYsGCBamiQUfu8xZCiMSTglKXBK6Ey2MASOxtwnGfuzwG7q765vtCQ0NZuXIltWrVomDBgkybNo1KlSqxb98+Hj16xIwZM7T2DKYuMjU1ZerUqdy4cQN7e3ucnZ2pVq0aZ8+eVTpamlOqVCkGDhzI5MmTefjwodJxvkkKSiGESDwpKHVF2H043++rL3kcAZXzt3+duvONMc/1jR33b5GRkezcuZN27dqRO3duevbsiZGREWq1muDgYNauXUv9+vV1vslGmwoVKsTWrVs5ePAgHz58oGLFiri5ufHs2TOlo6Up48aNI1u2bAwePFjpKN8kBaUQQiSegdIBxN/O9ISY7zTeAO6toWDO//5za4tvfCAmCs2ZnpwznYJarWbDhg28ePGCsmXLMnnyZDp27IiVlVXSs6cBderU4cKFC6xcuZIxY8awefNmRo8ezeDBgzE2NlY6XqpnamrK7Nmz4xp0GjVqpHSk/zA3N+fjx498+vQpxa8pFUKI1E6acnRB6HXYVeqbL3scgS7L4ewksCuU8OFLDINQjSUdO3bE1dUVGxubJIRN+96+fYu7uzsLFiwgb968zJo1i5YtW6JSJfZBBAH/36Dz+PFjrl69qnMNOrt376ZJkyY8fvyYvHnzKh1HCCFSFdny1gV3lsYe/ZMMomNU7FnQgsePHzNr1iwpJuMha9aszJkzh6tXr1KqVClat25NnTp1uHTpktLRUrUvN+g8ePBAJxt05D5vIYRIPCkodcGz3d8/Z/JvoR/h5ft//3r1gxsF9fU0FDC4lq6ei9SWYsWKsXPnTvbs2cPz588pX748PXv25Pnz50pHS7VKliypsw06cp+3EEIknhSUSot8//cNOD/281TI2evfv/J8vY/n38Luxl7bKBKlYcOGBAQEMG/ePDZu3EiRIkWYPXs2ERERSkdLlb406AwaNEjpKP8iBaUQQiSeFJRKC7vLv69T/LZFbuA/6t+//IbF55Oa2DvARaIZGhrSv39/AgMDcXV1Zfjw4ZQuXZodO3bI+ZUJ9KVBx8fHhz179igdJ46ZmRn6+vpSUAohRCJIQam06PB4v7ViYfi59L9/1fl2L0+i5xHfZm5uzsKFCwkICKBAgQI0b96chg0bcu3aNaWjpSrt2rWjTp069OvXj/Bw3fizqVKpyJ49Oy9fvlQ6ihBCpDpSUCpNP4U6XVNqnnSidOnS7Nu3j23btnH//n1sbGzo168fr1+/VjpaqvDPBp1Zs2YpHSeOnEUphBCJIwWl0kysSfy9OPGl+nseoU0qlYrmzZtz9epVpk6dypo1a7C2tmbhwoVERf24ySq9+9KgM2XKFJ1p0MmRI4cUlEIIkQhSUCrN0ARMEnG4ZAK80+Tk1Tvd2FZMi4yMjBg2bBh37tyhVatW9O/fHxsbG/bt26d0NJ2naw06skIphBCJIwWlLrByiNc5lH4B4Hnsv7/ufecUm6gYWLPvOblz56Zu3bosWLCAx48fazG8+CJ37tysWLGC8+fPkyNHDho2bEizZs24ffu20tF0lq416EhBKYQQiSM35eiCeN6U8y2re4BbrW+//qLSEbbuv4GPjw8HDx4kMjISe3t7nJyccHJyonjx4kkIL75Go9GwZcsWhg4dyrNnz+jfvz9jx47FzMxM6Wg6R5du0Bk+fDg+Pj7cuXNHsQxCCJEaSUGpKw42gJBD8TrgPN5UBpC7DtT9/63Xt2/fsnv3bnx8fPDz8+PDhw8UL148rri0s7OTKwa16NOnT8yZM4epU6eSKVMmJk+eTNeuXeWg+f9x/fp1bGxsmDBhAr/99ptiOaZPn860adN48+aNYhmEECI1koJSV4Tdh10lIfqz9sbUN4Ym18Gk4Fdf/vTpE/7+/vj4+LB9+3Zev35N3rx5cXR0xMnJiZo1a2JgkDxXQqY3T58+ZdSoUajVamxsbJg/fz61an1nWTkdGjZsGIsWLeLGjRsUKFBAkQwrV66ke/fuREZGyp99IYRIAHmGUleYFIQKC7Q7pt3CbxaTABkzZqR58+asXr2akJAQDh48iJOTE9u2baNevXrkzp0bNzc3tm3bxqdPn7SbLZ3JkycPa9eu5dSpU2TMmJHatWvTunVr7t+/r3Q0naELDTpf7vOWFUohhEgYKSh1iXU3KDtZO2PZTIHCXeP9dgMDA+rUqcMff/zBw4cPOXv2LL169eLMmTM4OjqSI0cOWrVqhZeXF2/fvtVOxnSoUqVKHD9+HE9PT06dOkWJEiUYPXo079//4FL2dMDU1JQ5c+bEPY6hBLl+UQghEke2vHVR4Eo43w9iohL2TKXKAPQMYlcmE1BM/sitW7fw8fHBx8eHM2fOYGBgQN26dXFycqJFixZYWlpqba705MOHD0yfPp2ZM2eSLVs2pk6diqurK3p66ffnPI1Gw88//8yjR48UadC5fv06pUqV4tixY1SrVi1F5xZCiNQs/X7n0mXW3WKffcxdJ/bvf3Sk0JfXc9eJ/ZwWi0mAYsWKMXLkSE6fPs3jx4+ZN28e0dHR9O3blzx58lC1alVmzpxJYKDcF54QmTNnxt3dnZs3b1KzZk3c3NyoXLkyJ06cUDqaYlQqFQsWLFDsBh1ZoRRCiMSRFUpdF3od7iyFZ34Qdhf4578uFZgUBqvGUKQ3mJVI0WivXr1i586d+Pj4sHfvXj5//kzp0qXjOsZtbW2lYzwBjh49ysCBA7lw4QIdO3Zk2rRp5MuXT+lYihg+fDgLFy7k+vXr/PTTTyk2b2RkJBkyZODPP/+kS5cuKTavEEKkdlJQpiaRYRAWCNHhsXdzm1jH3rSjAz58+MDevXvx8fFh586dvH37lp9++glHR0datmxJ1apV5aiceIiJicHDw4PRo0fz7t07RowYwbBhw8iUKZPS0VLU+/fvKV68OBUrVsTHxydF5zYzM2PMmDEMGzYsRecVQojUTApKoXWRkZEcPnwYHx8ffH19CQoKImfOnLRo0QInJyfq1aun6OHVqcG7d+/4/fffmTt3Lrlz52bGjBm0a9cuXa34ent70759e3bv3k3jxo1TbN7ChQvTpk0bpk2blmJzCiFEaicFpUhWMTExnDlzBh8fH7Zu3UpgYCCmpqY4ODjg5OSEg4MDpqamSsfUWXfv3mXo0KH4+vpSrVo15s2bh52dndKxUsSXBp2HDx9y9epVjI2NU2TeihUrYmNjw4oVK1JkPiGESAukKUckKz09PSpXrsz06dO5ffs2V65cYdiwYdy+fZv27duTI0cOmjRpwsqVK3n+/DuXkqdThQsXxsfHhwMHDvDu3TsqVqxIly5dCAoKUjpaslOpVCxcuJCHDx+maIOO3OcthBAJJyuUQjEPHjzA19cXHx8fjh07BkC1atXimnpSshkjNYiKimLFihWMHTuW8PBwRo8ezaBBg1Js5U4pKd2g4+LiwuPHjzly5EiyzyWEEGmFFJRCJ7x48YLt27fj4+ODv78/ERER2Nra0rJlS5ycnChVqlS6en7we968eYO7uzsLFy4kX758zJo1CycnpzT7+/P+/XtKlCiBvb19ijToDBgwgAMHDnD16tVkn0sIIdIK2fIWOiFnzpx07dqVnTt38vLlS7y9vSlevDgzZ86kTJkyFC1alOHDh3Py5EliYmKUjquobNmyMXfuXK5cuULx4sVp1aoVdevWJSAgQOloycLU1JTZs2fj6+ubIjfomJub8/Lly2SfRwgh0hJZoRQ6LTw8nIMHD7J161a2bdvGixcvsLS0jOsYr127NhkyZFA6pqL8/PwYNGgQd+7coXv37kyaNImcOXMqHUurUrJBZ/HixQwYMICIiIg0u+orhBDaJiuUQqcZGRnRuHFjVqxYQVBQEH/99Rft27dnz549NGzYkFy5cuHi4sKWLVv48OGD0nEV0bhxY65cucKcOXPw9vamSJEizJkzh4iICKWjaU1KNuiYm5sTFRUl96sLIUQCyAqlSJU0Gg0BAQFxd4xfuXIFY2NjGjRogJOTE82aNYu7Ri89efnyJePHj2fp0qVYW1szZ84cHBwc0sxK2/Dhw1mwYAE3btxItgad/fv3U79+fe7du0fBggWTZQ4hhEhrpKAUaUJgYGBcx/jJkyfR09OjVq1aODk54ejoSN68eZWOmKKuXLnCoEGDOHDgAA0bNmTu3LmUKJGyV3Mmh5Ro0Ll48SLly5fn7Nmz6ebMTyGESCrZ8hZpgrW1NUOHDuX48eM8e/aMRYsWYWhoyODBg8mXLx8VK1Zk6tSp3Lx5U+moKaJMmTL4+/vj6+tLYGAgZcqUYcCAAbx+/VrpaEliamrKnDlzkrVB58vKtpxFKYQQ8ScrlCJNe/v2Lbt27cLHxwc/Pz8+fvxI8eLF4866tLOzSzPbwd8SHh7O/PnzmTx5MoaGhri7u9OzZ08MDAyUjpYoyd2g8+HDB0xMTPD09MTZ2VmrYwshRFolK5QiTcuaNSvOzs5s3ryZly9fsm3bNipXrsyyZcuoWLEi+fPnp1+/fhw8eJCoqCil4yYLIyMjhg8fzu3bt3FycqJfv37Y2tri7++vdLRESe4GnUyZMmFsbCwrlEIIkQBSUIp0I2PGjDRv3pzVq1cTEhLCwYMHcXJywtfXl3r16mFhYUGXLl3Yvn07nz59Ujqu1llYWLBy5UrOnTtHtmzZaNCgAS1atODOnTtKR0uwEiVKMHjwYKZMmcKDBw+0OrZKpZLrF4UQIoFky1ukexqNhvPnz8d1jN+4cYPMmTPTqFEjnJycaNKkCVmzZlU6plZpNBo2bdrEsGHDCAoKYsCAAYwZMwYzMzOlo8VbWFgYxYsXT5YGHRsbG2rUqMHChQu1Oq4QQqRVUlAK8T9u3rwZV1yePXsWAwMD6tati5OTEy1atMDS0lLpiFrz6dMnZs2axbRp0zAxMWHKlCl06dIFfX19paPFy8aNG2nXrh27du3CwcFBa+PWrVuX3Llzs379eq2NKYQQaZkUlEJ8x5MnT+KOIzpy5AgxMTFUrlw5rqnH2tpa6Yha8eTJE0aNGoWnpye2trbMnz+fmjVrKh3rhzQaDfXr1+fBgwdabdBp06YNoaGh7Nu3TyvjCSFEWifPUArxHXnz5qVv374cOHCAkJAQVq9eTa5cuRg3bhxFihShTJkyjBs3jkuXLpGafzbLmzcvarWakydPYmRkRK1atWjTpo3Wn0/UNpVKxYIFC7TeoJMjRw65z1sIIRJACkoh4snc3JzOnTvj6+vLy5cv2bJlC7a2tixYsIBy5cpRqFAhBg8ezNGjR4mOjlY6bqJUrlyZEydOoFarOXHiBMWLF2fMmDGEhYUpHe2bkqNBR5pyhBAiYWTLW4gkioyM5PDhw/j4+ODr60tQUBC5cuWiefPmODk5Ua9ePYyMjJSOmWBhYWFMnz6dWbNmkT17dqZNm4azszN6err3c+iXBh07Ozt8fX2TPN7cuXMZO3asThfSQgihS3TvO4MQqYyhoSH169dn8eLFPHnyhBMnTtC5c2cOHz5MkyZNyJkzJ+3bt8fb25v3798rHTfeTExMmDRpEjdu3KBatWp06tSJKlWqcOrUKaWj/YeJiQlz5sxh27Zt7N69O8njmZub8+HDB8LDw7WQTggh0j5ZoRQimWg0Gq5duxbXMX7x4kUyZMjAzz//jJOTE82bNydXrlxKx4y3v/76i4EDB3Lx4kWcnZ2ZNm2aTt2Rrs0GnV27dtG0aVOePn2KlZWVFlMKIUTaJCuUQiQTlUpF6dKlGTt2LBcuXOD+/ftMnz6dsLAwevbsiaWlJTVr1mTevHk63/wCULNmTc6ePcvKlSvx9/enWLFiuLu78/HjR6WjAf9/g86jR4+YOXNmksaS+7yFECJhZIVSCAU8f/6cHTt24OPjg7+/PxEREZQrVy7uOKJSpUrp9B3j7969Y/LkycybNw9LS0tmzJhB27ZtdSLziBEj+OOPP7hx4wY//fRTosYIDAykSJEiHDx4kDp16mg3oBBCpEFSUAqhsPfv3+Pn58fWrVvZvXs379+/x9raOq64rFSpkk42wkBs4TV06FC2bdtG9erVmTdvHhUqVFA0kzYadN68eUP27NnZtGkTrVu31m5AIYRIg3Tzu5QQ6YipqSlt27Zlw4YNvHjxgl27dlG7dm08PDyoWrUqefPmpXfv3uzbt4+IiAil4/6LtbU1vr6+7N+/n7dv32Jvb0/Xrl0JDg5WLJOJiQlz585NUoOOmZkZenp6suUthBDxJCuUQuio6OhoTpw4EdfU8+DBA8zMzGjWrBlOTk40bNiQzJkzKx0zTlRUFMuXL2fcuHFERETw22+/MXDgQEWOTNJGg07OnDkZNGgQo0ePToaEQgiRtsgKpRA6Sl9fnxo1ajBnzhzu3bvHxYsXGTBgAAEBAbRq1YocOXLg6OjImjVreP36tdJxMTAw4Ndff+XOnTv88ssv/Pbbb5QsWRJfX98Uv0VIGw06cri5EELEn6xQCpEKBQYGxt0xfvLkSfT09KhVqxZOTk44OjrqxHE+N27cYPDgwezZs4e6desyb948ypQpk6IZvjToXL9+nYIFCybos9WqVaNIkSJ4eHgkTzghhEhDpKAUIpULCgpi27Zt+Pj4cPDgQaKiorC3t49r6ilevLii+Xbv3s3gwYO5c+cOPXr0wN3dnZw5c6bI3Elp0GnRogXR0dHs3LkzecIJIUQaIgWlEGnI27dv2bVrFz4+Pvj5+fHx40eKFy8eV1za2dkpcrRPREQEixYtYuLEiQBMmDCBPn36YGhomOxzb9q0ibZt27Jz506aNGkS78/98ssv3Lhxg5MnTyZjOiGESBukoBQijfr06RP+/v74+Piwfft2Xr9+Tb58+XB0dMTJyYkaNWpgYGCQoplevHjBuHHjWL58OUWKFGHOnDk4ODgk65xfGnTu37/PtWvX4t2gM2zYMLZt28bt27eTNZ8QQqQF0pQjRBqVMWNGmjdvzurVqwkJCeHgwYM4Ojri4+ND3bp1sbCwoEuXLmzfvp1Pnz6lSKacOXOyZMkSLl68iJWVFU2aNKFx48bcuHEj2eb80qDz+PHjBDXoSFOOEELEnxSUQqQDBgYG1KlThz/++INHjx5x5swZevTowalTp2jRogU5c+akdevWeHl58fbt22TPU7ZsWQ4cOMDWrVu5ffs2ZcuWZeDAgbx58yZZ5itevDiDBw/m999/5/79+/H6jLm5OW/evCE6OjpZMgkhRFoiW95CpHM3b96MO+vy7NmzGBoaUqdOHZycnGjRogWWlpbJOn94eDjz5s1j8uTJGBkZ4e7uTo8ePbS+HR8WFkaJEiUoX74827Zt++H7t27dSqtWrXj58mXc3d5CCCG+TlYohUjnihcvzqhRozhz5gyPHz9mzpw5REVF0bdvX/LkyUPVqlWZNWsWd+/eTZb5jYyMGDFiBHfu3KFFixb07duXcuXKceDAAa3OY2Jiwpw5c9i+fTu7du364ftz5MgBINveQggRD7JCKYT4qlevXrFz5058fHzYu3cvnz9/pkyZMnEd4zY2NsnSMX7+/HkGDBjA8ePHadGiBbNmzcLa2lorY2s0Gho0aMC9e/d+2KBz7do1SpcuzfHjx6latapW5hdCiLRKViiFEF9lbm5O586d8fX15eXLl2zZsgUbGxvmz59PuXLlKFSoEIMHD+bo0aNafc6wQoUKHD16lA0bNnDhwgVKlSrF8OHDeffuXZLHVqlULFiwgMePHzNjxozvvvfLNresUAohxI/JCqUQIkEiIiI4fPgwPj4++Pr6EhwcTK5cuWjevDlOTk7Uq1dPa/d3f/z4kVmzZjFt2jRMTU35/fffcXNzQ19fP0njjhw5kvnz53/3Bp2IiAiMjIxYvXo1bm5uSZpPCCHSOikohRCJFhMTw+nTp+OaegIDAzE1NcXBwYGWLVvSuHFjTE1NkzzPkydPGDlyJF5eXpQrV4758+dTo0aNRI8X3wadLFmyMH78eIYMGZLouYQQIj2QLW8hRKLp6elRpUoVZsyYwe3bt7ly5QrDhg3j9u3btGvXjpw5c9K0aVNWrVrFixcvEj1P3rx58fT05MSJExgYGFCzZk3atWvHw4cPEzVefBt05CxKIYSIH1mhFEIkiwcPHuDr64uPjw/Hjh0DoHr16nFNPQUKFEjUuDExMXh6ejJy5EjevHnD0KFDGTlyJJkzZ07QOPFp0LG3t6d8+fIsW7YsUVmFECK9kIJSCJHsnj9/zo4dO9i6dSv79+8nIiKCcuXKxRWXpUqVSnDHeFhYGNOmTWPWrFmYm5szffp0OnbsiJ5e/Ddebt68SdmyZRkzZgzjxo37z+uNGjUic+bMbNmyJUHZhBAivZGCUgiRot69e4efnx8+Pj7s3r2b9+/fY21tHVdcVqpUKUFF4f379xk+fDibN2+mUqVKzJ8/n0qVKsX7899r0PmlU1v0Ptxj5bJFoG8EJtZgaBLvsYUQIr2QglIIoZjw8HAOHDiAj48P27Zt48WLF1haWuLo6IiTkxO1a9fG0NAwXmMdOXKEgQMHcunSJVxcXJg2bRp58uT54ef+06ATeh3uLIVnu9G8v8u/F05VYFIIrBygSC8wK5m4L1wIIdIYKSiFEDohOjqaEydOxHWMP3jwgKxZs9K0aVOcnJxo2LDhD5+TjI6O5s8//+S3337jw4cPjBo1iiFDhpAxY8bvfm7z5s0M+7UNpxfYkiv6EqgMQBP17Q98ed2iPlRcBiZfP3pICCHSCykohRA6R6PREBAQEFdcXrlyBWNjYxo2bIiTkxPNmjUje/bs3/x8aGgokydPZv78+VhZWTFjxgzatGnzzec0NYEriDjRC31VDAYJOeJSZQB6BlBhAVh3S+BXKYQQaYcUlEIInRcYGBhXXJ48eRJ9fX1q1aqFk5MTjo6O5M2b96ufu3PnDkOGDGHHjh3UqFGDefPmUb58+X+/6eoUuDwGDZCkiyTLTobSvyVlBCGESLWkoBRCpCpBQUFs27YNHx8fDh48SFRUFPb29nFNPcWLF//PZ/z9/Rk4cCA3btzgl19+YcqUKeTOnRsCV8KZ7toLV2klFO6qvfGEECKVkIJSCJFqvX37ll27duHj44Ofnx8fP36kRIkSccVlhQoV4ra5o6KiWLZsGePGjSMyMpKZ43+lR575qGI+/2tMjyPQZfn//72RIWTPDGXyQRNb6FILTL/1SKa+MTS5Ls9UCiHSHSkohRBpwqdPn/D398fHx4ft27fz+vVr8uXLF9cxXqNGDQwMDHj9+jUTJkygaeYF1C3Jf56Z/FJQureGgjkhMhqC38LhG+B/FfKbw/YhUDb/V0KoDCB3Hai7LyW+ZCGE0BlSUAoh0pyoqCj++usvfHx88PX15cmTJ5ibm9OsWTOcnJxoUCkvxgcqfPWzXwrKs5PArtC/Xzt4DZrOglxZ4MZMyJjhGwGaXAezEtr9ooQQQofJXd5CiDTHwMCAunXrsmDBAh49esSZM2fo0aMHp06dokWLFqweXYnomIS34NQtBWMd4eFL8Dz2jTepDODOkiTlF0KI1EYKSiFEmqZSqbC3t+f333/nxo0b3Lhxg/Y1s6Cvl7jNGdfqsf+778o33qCJgmd+iQsrhBCplBSUQoh0pXjhPGQzfJPoz+c1B7NMcPf5d94UdhciwxI9hxBCpDZSUAoh0pewu0DSHh03MYL3n773Dg2EBSZpDiGESE2koBRCpC/R4UkeIiz8O0cHaXEeIYRILaSgFEKkL/pGSfr4k1cQ+hGscyfvPEIIkZpIQSmESF9MrEnKJYvqv7u7G5b93rtUf88jhBDpgxSUQoj0xdAETAr9+H1fcfAaTPKNPfDcuep33mhSOHYeIYRIJwyUDiCEECnOyiH2rEhN1Dff4hcAN59BVDSEvIstJv2vQoEcsTflGH/jUPPIaNh3MYZottO4cWMMDQ2T6YsQQgjdITflCCHSn9DrsKvUV1/637u8MxhAdhMokxealvvBXd5/a/VnCbYeuEHOnDlxcXGhc+fO2NjYaPELEEII3SIFpRAifTrYAEIOfXeVMsH+cZd3QEAAa9aswdPTkxcvXmBra4ubmxsdO3YkZ86c2ptTCCF0gBSUQoj0Kew+7CoJ0Z+1MpwGUOkbx97jbVIw7p9HRkayZ88ePDw82LFjBxqNhqZNm+Lm5oaDg4NsiQsh0gQpKIUQ6VfgSjjTXWvDfbZZiHGpPt98/eXLl6xfvx4PDw8uXLhAzpw56dixI25ubtja2mothxBCpDQpKIUQ6dvVKXB5TJKHcd9mxK4HNuzevRtzc/Mfvv/KlSusWbMGtVrN8+fPsbGxidsSz5UrV5LzCCFESpKCUgghAlfC+X4QE5WwZypVBqBnAHYLuRBajkaNGpEzZ0727dtHnjx54jVEZGQke/fuxcPDg+3bt6PRaGjSpAmdO3emSZMmZMjwjXZyIYTQIVJQCiEExD5TeaYnBPvHForfKyy/vG5RHyoui3tm8vbt29SvXx+VSoW/vz9FihRJUIRXr17FbYmfP38ec3NznJ2d47bEVarEH8guhBDJSQpKIYT4p9DrcGcpPPODsLvEttvEitFARIa8GBd0giK9wazEfz7++PFjGjRowOvXr9m7d2+in428evVq3JZ4SEgIZcuWxc3NDWdnZ9kSF0LoHCkohRDiWyLDICwQosMJj4Lc1tWYNmshvXr1+u7HXr58SePGjblz5w47d+6kevXqiY4QFRX1ry3xmJgYGjdujJubG02bNpUtcSGETpCCUggh4ql8+fKUK1eOVatW/fC979+/p0WLFpw6dYrNmzfj4OCQ5Plfv37Nhg0b8PDw4OzZs5ibm8d1iZcrV062xIUQipGCUggh4qlHjx6cPn2agICAeL3/8+fPtG/fnl27drF27Vo6dOigtSzXrl2L2xIPDg6mdOnScVviFhYWWptHCCHiQ0/pAEIIkVrY2dlx7do1Pn78GK/3Gxsbs3nzZlxcXHB2dmbx4sVay1KqVClmzJjB48eP2bVrFyVKlGD06NHkzZuXZs2asWXLFsLDw7U2nxBCfI8UlEIIEU/29vZER0dz6dKleH/GwMCAVatWMXDgQPr06cPkyZPR5saQgYEBDg4ObNy4kaCgIBYsWMDz589p3bo1VlZW9OvXj/Pnz2t1TiGE+F9SUAohRDyVLl0aIyMjzp07l6DP6enpMXv2bCZPnszYsWMZPHgwMTExWs+XPXt2evfuzenTp7l27RrdunVjy5Yt2NnZUaZMGWbNmkVwcLDW5xVCCHmGUgghEqBy5coUKVIEtVqdqM8vWbKEPn360KlTJ1auXImBgYGWE/5bVFQU+/fvx8PDA19fX6KiomjUqBFubm40a9YMIyOjZJ1fCJE+yAqlEEIkgJ2dXYJXKP+pd+/eeHl54eXlRevWrfn8+bMW0/2XgYEBjRo1YsOGDQQFBbFw4UJevnxJmzZtsLS0pE+fPpw9e1a2xIUQSSIrlEIIkQAeHh788ssvvH37lixZsiR6nN27d9O6dWsqV66Mr69vksZKjJs3b7JmzRrWrl3Ls2fPKFmyJG5ubri4uGBpaZmiWYQQqZ8UlEIIkQDXrl2jdOnSHDp0iNq1aydprGPHjtG0aVOsra3x8/MjZ86c2gmZANHR0XFb4j4+PkRGRtKwYUPc3Nxo3rw5xsbGKZ5JCJH6yJa3EEIkQPHixcmUKVOStr2/qF69OkeOHOHJkyfUrFmTx48fayFhwujr69OwYUPWr19PcHAwixcv5u3bt7Rr1w5LS0t+/fVXzpw5I1viQojvkhVKIYRIoBo1amBlZYW3t7dWxgsMDKR+/fpER0fj7+9PsWLFtDJuUty6dStuS/zp06eUKFEibkvcyspK6XhCCB0jK5RCCJFA9vb2Wlmh/MLa2ppjx45hampKjRo1uHDhgtbGTqxixYrx+++/8/DhQ/bu3YutrS3jx48nX758NG7cGG9v72RvKBJCpB5SUAohRALZ2dlx7949Xr9+rbUx8+TJw19//UXBggWpXbs2R44c0drYSaGvr0+DBg1Yt24dwcHBLF26lHfv3tG+fXssLS3p3bs3p06dki1xIdI5KSiFECKB7O3tAbS6Sglgbm7OgQMHqFixIo0aNWLHjh1aHT+pzMzM6N69O8ePH+fWrVv8+uuv7Ny5kypVqlCiRAmmTZvG06dPlY4phFCAFJRCCJFAhQsXxszMTOsFJYCJiQm7du3CwcEBJycnPD09tT6HNhQtWpQpU6bw4MED/P39sbOzY+LEieTPnz/u3MtPnz4pHVMIkUKkoBRCiATS09OjQoUKyVJQAhgZGeHt7Y2bmxuurq788ccfyTKPNujr6/Pzzz/j6elJcHAwy5YtIywsjA4dOmBpaUnPnj05efKkbIkLkcZJQSmEEIlgb2/P2bNnk218AwMDVqxYwbBhwxgwYAATJkzQ+aLMzMyMbt26cezYMW7fvk2/fv3w8/OjatWqFC9enKlTp/LkyROlYwohkoEcGySEEImwefNm2rRpQ1BQEBYWFsk61/Tp0xk5ciT9+vVj3rx56OmlnrWAmJgYDh06hIeHB1u2bOHz58/Ur1+fzp074+joSKZMmZSOKITQgtTz/0pCCKFD7OzsAO035nzNiBEjWLZsGQsXLqRz585ERkYm+5zaoqenR7169VCr1QQHB7NixQo+fvyIs7MzlpaW9OjRgxMnTuj86qsQ4vukoBRCiEQoUKAAOXLkSJGCEqBHjx5s2LABb29vWrZsmSobXrJkyULXrl05evQod+7cYcCAAezdu5dq1arFnXupxG1BQoikky1vIYRIpMaNG6Ovr8/OnTtTbM69e/fSsmVL7Ozs2L59O2ZmZik2d3KIiYnh8OHDcVvinz59ol69eri5ueHk5CRb4kKkErJCKYQQifSlMSclfy5v2LAh+/fv5/Lly9SpU4fnz5+n2NzJQU9Pj7p167J27VqCg4NZtWoVERERuLi4YGFhEXfupax9CKHbZIVSCCESafv27bRo0YJHjx6RL1++FJ37ypUrNGjQgCxZsrBv3z4KFCiQovMnt7t377J27VrWrFnDw4cPsba2pnPnznTq1In8+fMrHU8I8T+koBRCiER69uwZefLkYevWrTg5OaX4/Pfu3aN+/fpERESwb98+SpQokeIZkltMTAxHjhzBw8ODzZs38+nTJ+rWrRu3JZ45c2alIwohkC1vIYRINCsrK6ysrJL1PMrvKVSoEMeOHSNr1qzUqFEjxRqEUpKenh516tRhzZo1BAcH8+effxIVFYWrqyuWlpZx517K2ogQypIVSiGESIIWLVrw6dMn9u3bp1iGN2/e0KRJE65cucL27dupU6eOYllSyr179+K2xB88eEDhwoXjtsTT2va/EKmBrFAKIUQS2NnZce7cOUVXyLJly4a/vz9Vq1alcePG+Pr6KpYlpRQqVIgJEyZw9+5dDh8+TI0aNZg+fTo//fRT3LmXHz58UDqmEOmGFJRCCJEE9vb2vHnzhnv37imaI3PmzOzYsYMWLVrQqlUrPDw8FM2TUvT09KhVqxarV68mODgYDw8PYmJi6NSpExYWFvzyyy/89ddfsiUuRDKTglIIIZIgJW/M+ZEMGTKwbt06unXrRpcuXZg7d67SkVKUiYkJnTt35tChQ9y7d49hw4Zx+PBhatWqhbW1Ne7u7jx48EDpmEKkSVJQCiFEEuTIkYOffvpJscac/6Wvr8/SpUsZNWoUgwcPZsyYMelyda5gwYKMGzeOwMBAjhw5Qq1atZgxYwYFCxaMa/IJCwtTOqYQaYY05QghRBK1adOGFy9ecPjwYaWj/MusWbMYNmwYvXv3ZuHChejppe81hLCwMLZu3cqaNWs4ePAgmTNnpk2bNri5uVGjRo10//sjRFJIQSmEEEk0ffp0Jk+eTGhoqM4VJatWraJHjx60bduWNWvWkCFDBqUj6YQHDx6gVqvx8PDg3r17FCxYMK5LvGDBgkrHEyLVkYJSCCGS6ODBg9SrV4/r16/r5OHiW7dupUOHDtSrV4/NmzfL/dj/oNFoOHbsGB4eHmzcuJGwsDBq1aqFm5sbrVu3xsTEROmIQqQKuvWjtBBCpELly5cHdKMx52tatmzJrl27+Ouvv2jQoAFv375VOpLOUKlU1KhRg1WrVhEcHIxarcbAwIBffvkFCwsL3NzcOHToEDExMUpHFUKnyQqlEEJoQdGiRWnUqBF//PGH0lG+6fTp0zg4OJA3b1727t2LhYWF0pF01sOHD+O2xO/evUuBAgXo3LkznTt3plChQkrHE0LnSEEphBBa4OzszP379zlx4oTSUb7r2rVrNGjQgIwZM+Lv7y/PC/6ARqPhxIkTeHh44O3tzfv376lZs2bclripqanSEYXQCbLlLYQQWmBnZ8fFixeJiopSOsp3lSpViuPHj6NSqahWrRpXr15VOpJO+/L7tGLFCoKDg/H09CRDhgx07doVCwsLOnXqxMGDB2VLXKR7UlAKIYQW2Nvb8/nzZ65du6Z0lB/66aefOHbsGLly5aJmzZqcOnVK6UipQqZMmXB2dsbf35+HDx/y22+/cerUKerVqxd37uXdu3eVjimEIqSgFEIILbC1tUVPT09nG3P+V+7cuTl8+DAlS5bk559/xt/fX+lIqUq+fPkYPXo0t27d4vjx4zRs2JD58+djbW1NzZo1WbVqFe/evVM6phApRgpKIYTQAhMTE0qUKJFqCkqArFmzsm/fPmrWrEmTJk3YvHmz0pFSHZVKRdWqVVm+fDlBQUF4eXlhbGxM9+7dsbCwwNXVlQMHDsiWuEjzpClHCCG0pEuXLly5ciVVFZUAERERuLm54e3tzbJly+jWrZvSkVK9x48f4+npiYeHB7dv3yZ//vx06tSJzp07Y21trXQ8IbROViiFEEJL7OzsuHz5MuHh4UpHSZAMGTLg6elJr1696N69OzNmzFA6UqqXL18+Ro0axc2bNzlx4gSNGjViwYIFFClShOrVq7Ny5UrZEhdpihSUQgihJXZ2dkRGRnL58mWloySYnp4eCxcuZMyYMYwYMYKRI0ciG1hJp1KpqFKlCsuWLSMoKIj169djYmJCjx49sLCwwMXFhf379xMdHa10VCGSRLa8hRBCSz5//oypqSl//PEHvXv3VjpOos2bN49BgwbRvXt3lixZgr6+vtKR0pwnT57EbYnfunWLvHnzxm2JFy1aVOl4QiSYFJRCCKFF5cuXp1y5cqxatUrpKEmyZs0aunbtSsuWLVGr1RgZGSkdKU3SaDScPn0aDw8PNmzYQGhoKFWrVsXNzY22bdtiZmamdEQh4kW2vIUQQovs7e05e/as0jGSrHPnzmzZsoXt27fTrFkzwsLClI6UJqlUKipXrszSpUsJCgpiw4YNZMmShV69emFhYRF37qVsiQtdJyuUQgihRStWrKBXr168f/+eTJkyKR0nyQ4dOkTz5s0pXbo0u3btInv27EpHSheePn0atyV+8+ZN8uTJE7clXqxYMaXjCfEfUlAKIYQWXbx4kfLly3P8+HGqVq2qdBytOHfuHI0aNcLS0pK9e/diZWWldKR0Q6PRcPbsWTw8PFi/fj1v376lSpUqcVviWbNmVTqiEIBseQshhFaVLl0aIyOjNLHt/YWdnR1Hjx7l7du3VK9eXa4XTEEqlYqKFSuyePFigoKC8Pb2JmvWrPTu3RsLCws6dOjA3r17ZUtcKE5WKIUQQssqV65MkSJFUKvVSkfRqkePHlG/fn3evXvH3r17KVu2rNKR0q1nz57h5eXF6tWruXHjBlZWVnFb4sWLF1c6nkiHZIVSCCG0zM7OLk2tUH6RP39+jh49iqWlJbVq1eLEiRNKR0q3rKysGDZsGNeuXePMmTM4OjqybNkySpQoEdfk8+bNG6VjinRECkohhNAye3t7bt26lSZvQsmVKxeHDh2ibNmy/Pzzz+zZs0fpSOmaSqXC3t6eRYsW8ezZMzZu3EiOHDno06cPlpaWtG/fnj179siWuEh2UlAKIYSW2dnZAXDhwgWFkyQPMzMz9uzZQ7169WjevDne3t5KRxKAsbExbdq0YefOnTx58oTJkydz5coVGjduTP78+Rk5ciQ3btxQOqZIo6SgFEIILStevDiZM2dOk9veX2TMmJGtW7fSrl07OnTowLJly5SOJP7B0tKSoUOHcvXqVc6ePYuTkxPLly+nZMmSVKpUiSVLlsiWuNAqKSiFEELL9PX1KV++POfOnVM6SrIyNDRkzZo19O3bl169ejF16lS5/1vHqFQq7OzsWLhwIUFBQWzevJlcuXLRr18/LCwsaNeuHbt37yYqKkrpqCKVk4JSCCGSgZ2dXZovKAH09PSYP38+EydOZPTo0QwbNkyKSh1lZGREq1at2LFjB0+ePOH333/n+vXrNGnShHz58jF8+HCuX7+udEyRSsmxQUIIkQzWr19Px44defnyJebm5krHSRELFy6kX79+/PLLLyxbtgwDAwOlI4kf0Gg0XLx4EQ8PD7y8vHj9+jX29va4ubnRvn17uRlJxJsUlEIIkQzu3LlD0aJF2bt3Lw0aNFA6Torx8vKic+fONG/enHXr1mFsbKx0JBFP4eHh7Nq1Cw8PD3bv3o2+vj7NmzfHzc2Nhg0byg8I4rtky1sIIZJB4cKFMTMzS9ONOV/j7OyMr68vfn5+NGnShPfv3ysdScSTkZERLVu2ZPv27Tx9+pSpU6dy69YtmjZtSr58+Rg2bBhXr15VOqbQUbJCKYQQyeTnn3/G1NQUHx8fpaOkuL/++otmzZpRrFgx/Pz80s22f1qj0Wi4dOlS3Jb4q1evsLOzo3PnznTo0EH+vYo4skIphBDJJL005nxNzZo1OXz4MA8ePKBGjRo8efJE6UgiEVQqFeXKlWP+/Pk8e/aMrVu3YmVlxaBBg7C0tKR169bs3LlTusSFFJRCCJFc7O3tefLkCcHBwUpHUUS5cuU4duwYHz58oHr16ty5c0fpSCIJMmTIgJOTE9u2bePp06fMmDGDO3fu0KxZM/LmzcvQoUO5cuWK0jGFQqSgFEKIZPLlxpz0ukoJULRoUY4fP07GjBmpXr06ly5dUjqS0IJcuXIxcOBAAgICuHjxIu3bt2fNmjWULVuWChUqsGDBAl6+fKl0TJGCpKAUQohkkj9/fnLkyJGuC0qAvHnzcvToUfLnz0+tWrU4evSo0pGEFtna2jJv3jyePn2Kr68v+fPnZ/DgwVhZWcWdexkZGal0TJHMpClHCCGSkYODAyqVil27dikdRXHv37/H0dGREydOsHnzZpo0aaJ0JJFMXrx4wbp16/Dw8ODSpUvkypULZ2dn3NzcKFu2rNLxRDKQFUohhEhGXxpz5Gd3MDU1ZdeuXTRq1AhHR0fWrVundCSRTHLmzMmAAQO4ePEiFy9epGPHjnh6emJjY0P58uX5448/ZEs8jZGCUgghkpGdnR3Pnz/n8ePHSkfRCcbGxmzatAkXFxdcXFxYtGiR0pFEMrO1tWXu3Lk8ffqUbdu28dNPPzFkyBCsrKzizr2ULfHUTwpKIYRIRtKY818GBgasWrWKQYMG0bdvXyZNmiQruOmAoaEhzZs3Z+vWrTx79oxZs2bx8OFDWrRoQZ48eRg0aBABAQFKxxSJJAWlEEIkIysrK6ysrKSg/B96enrMmjWLKVOmMG7cOAYNGkRMTIzSsUQKyZkzJ/379+f8+fMEBATg6urKunXrsLW1jTv38sWLF0rHFAkgTTlCCJHMHB0d+fDhA/7+/kpH0UlLliyhT58+uLq6smrVKrkzOp2KjIxkz549eHh4sGPHDjQaDU2aNMHNzQ0HBwcyZMigdETxHbJCKYQQyUwac76vd+/erFu3jnXr1tGqVSs+f/6sdCShAENDQ5o1a8aWLVt49uwZc+bM4cmTJzg5OZEnTx4GDhwo55jqMFmhFEKIZLZnzx4aN25MYGAghQsXVjqOzvLz86NVq1ZUqlSJbdu2kSVLFqUjCR1w5coV1qxZg6enJyEhIdjY2ODm5kbHjh3JlSuX0vHE36SgFEKIZPby5Uty5szJ+vXrad++vdJxdNrx48dp0qQJ1tbW+Pn5kTNnTqUjCR0RGRnJ3r17WbNmDdu3bycmJgYHBwfc3Nxo0qRJym+JR4ZBWCBEh4O+EZhYg6FJymbQIVJQCiFECihYsCCtWrVi1qxZSkfReQEBATRs2JCsWbPi7+9Pvnz5lI4kdMyrV6/YsGEDHh4enDt3DnNzc5ydnencuTPlypVDpVIlz8Sh1+HOUni2G8LuAf8soVRgUgisHKBILzArmTwZdJQUlEIIkQLatGnD8+fPOXLkiNJRUoXAwEDq169PdHQ0/v7+FCtWTOlIQkddvXqVNWvWoFarCQkJoUyZMri5ueHs7Ezu3Lm1M0nYfTjTE4L9QWUAmqhvv/fL6xb1oeIyMCmonQw6TppyhBAiBdjb23PhwgWio6OVjpIqWFtbc+zYMbJkyUL16tW5cOGC0pGEjipdujQzZ87kyZMn7Nq1i+LFizNq1Cjy5MlD8+bN2bJlC+Hh4YmfIHAl7CoJIYdi//57xeQ/Xw85FPu5wJWJnzsVkYJSCCFSgJ2dHWFhYdy+fVvpKKlGnjx5+OuvvyhcuDC1a9eW1V3xXQYGBjg4OLBx40aCgoL4448/CA4OpnXr1lhZWdGvXz/Onz+fsNMWrk6BM90h+vOPC8n/pYmK/dyZ7rHjpHFSUAohRAqoUKECAGfPnlU4SeqSPXt29u/fT6VKlWjYsCHbt29XOpJIBbJnz86vv/7KmTNnuHbtGt26dWPLli3Y2dlRtmxZZs+eTXBw8PcHCVwJl8doJ9DlMXB3lXbG0lFSUAohRAowMzOjaNGicmNOIpiYmLBz506aNm1Ky5YtUavVSkcSqUjJkiWZPn06jx49Yvfu3ZQsWZLRo0eTN29emjVrxubNm/+7JR52H873++HYi/1B5QyVxsUjyLm+seOmUVJQCiFECvlywLlIOCMjI7y9vXFzc6NTp07Mnz9f6UgilTEwMKBx48Z4e3sTFBTEggULeP78OW3atMHS0pK+ffv+/wUEZ3pCzI+3uL2Ow0854cxdCPzBgicxUbHjplFSUAohRAqxt7fn4sWLREZGKh0lVdLX12fFihUMHz6cgQMHMn78eLl9SCRK9uzZ6d27N6dPn+b69ev06NGDrVu3Ym9vT4s6RWK7uX/wzOT953DiDsxxhpxZYovL79JExY4bekN7X4gOkYJSCCFSiJ2dHZ8/f+b69etKR0m1VCoV06dPZ9q0abi7u9O/f39iYmKUjiVSsRIlSjBt2jQePXqEn58fvX/WIzIehzF4HYdsmaFJOWhdEbxOxGMylQHcWZLkzLpICkohhEgh5cqVQ09PT7a9tWDEiBEsX76cRYsW0alTJ1n1FUlmYGBAo0aNaFw2BkP9H7/f6wS0tIcMBtChCtwJhrN3f/AhTRQ889NKXl0jBaUQQqSQzJkzU7JkSen01pLu3bvj7e3Nxo0bcXJy4tOnT0pHEqld5Pu/b8D5vvP34eYzaF8l9u+rF4O82eO5Shl2N/baxjRGCkohhEhB0pijXW3atGHnzp0cOnSIhg0bEhoaqnQkkZqF3eXf1yl+nddxyG0Gdf6+XVGlgnaVYcNJiP7hExia2DvA0xgpKIUQIgXZ29tz+fLlpN3cIf6lQYMG7N+/n6tXr1K7dm1CQkKUjiRSq+gf/3cZHRNbONYpGduYExgc+6uSNYSEwoGr2pkntZGCUgghUpCdnR2RkZFcvnxZ6ShpSpUqVfjrr78ICQmhRo0aPHz4UOlIIjXSN/rhWw5eg6C3sUVlkSH//6vtH7Gvx2vbOx7zpDYGSgcQQoj0pGzZshgYGHDu3Dns7e2VjpOmlC5dmmPHjlG/fn2qVavGvn37KFmypNKxRGpiYg2o+N62t9dxyJUFFrn997WtZ8HnLCz9BTJm+NYIqr/nSVtkhVIIIVKQsbExZcuWlcacZFKoUCGOHTtG9uzZqVmzpvw+i4QxNCE6Y4FvvvwpIrZobFoOWlf676++DeD9Z9h+/jtzmBQGQxPtZ1eYFJRCCJHCpDEneVlaWnLkyBGKFi1K3bp1OXjwoNKRhI77/PkzmzdvxtHRkSXbH33zHMrt52MLxublv/56Zeu/Dzn/1ra3ygCsGmsls66RglIIIVKYnZ0d165d4+PHj0pHSbOyZcuGv78/1apVo3Hjxvj6+iodSeiYmJgYDh8+TLdu3cidOzdt2rQhKCiIrPYjvnkOpdcJMDaE+mW+/rqeHjSxhT0B8Or9V96giYIivbX1JegUlUburRJCiBR16dIlypUrx7Fjx6hWrZrScdK0iIgIOnXqxKZNm1i5ciVdunRROpJQ2NWrV/H09MTLy4snT55QqFAhXFxccHZ2pmjRorFvOtgAQg798PrFBFEZQO46UHef9sbUIdKUI4QQKaxUqVIYGxtz7tw5KSiTWYYMGfDy8iJr1qz88ssvvHnzhsGDBysdS6SwJ0+esH79ery8vAgICMDc3Jx27drh4uJC5cqVUalU//5AxWWwqyREa7Gg1DOIHTeNkoJSCCFSmKGhIba2ttIwkkL09fVZsmQJ5ubmDBkyhNevXzNp0qT/FhEiTXn37h1btmzB09OTQ4cOYWRkRPPmzZk0aRINGzYkQ4ZvtmGDSUGosADOdNdeILuFseOmUVJQCiGEAuzs7PD391c6RrqhUqmYMmUK2bNnZ+jQobx69YqFCxeirx+PS5tFqhEREcHevXvx9PRk+/bthIeHU6dOHVatWkXLli0xMzOL/2DW3eBzCFweg4bYw4QSzWYKFO6alBF0nhSUQgihADs7OxYuXMi7d+/IkiWL0nHSjSFDhpAtWza6d+/OmzdvWLt27fdXqoTO02g0nDp1Ck9PT7y9vXn16hVly5bF3d2dDh06kDdv3sQPXvo3MM5N9Olf0cREfrNZ56tUBrHb3HYL03wxCdKUI4QQirh+/TqlSpXi4MGD1KlTR+k46c7WrVvp0KEDdevWZcuWLWTKlEnpSCKBbt++jZeXF56enty7d488efLg7OyMs7MzZcuW1do8z58/p34Va9YNykKp7E9jC8XvNet8ed2ifuwzk2l4m/ufZIVSCCEUUKxYMTJnzsy5c+ekoFRAy5Yt2b17Ny1atKB+/frs3LmTbNmyKR1L/MDz58/x9vbG09OTM2fOkCVLFlq3bs3KlSupVasWenraPw1x5MiRPHlrSO72l8DwOdxZCs/8IOwu/75RRxV7aLlV49ijgcxKaD2LLpMVSiGEUEjNmjWxtLTE29tb6Sjp1pkzZ2jcuDF58+Zl7969WFhYKB1J/I+PHz+ybds2PD092bt3L3p6ejRu3BgXFxeaNm1KxowZk23uEydOUK1aNZYuXUrPnj3//WJkGIQFQnR47N3cJtZp8gac+JKCUgghFDJkyBB8fHy4d++e0lHStevXr9OgQQOMjY3x9/enYMH0sUWpy6Kjozl48CCenp5s3bqVsLAwqlWrhouLC23atMHc3DzZM0RFRWFvb4+BgQGnTp2SBq4fkJtyhBBCIXZ2dty/f59Xr14pHSVdK1myJMeOHUOlUlGtWjWuXr2qdKR0SaPRcPHiRYYMGUK+fPlo0KABp06dYsSIEdy9e5djx47Rq1evFCkmAZYuXUpAQACLFi2SYjIeZIVSCCEUEhgYSJEiRdizZw8NGzZUOk66FxISQqNGjXj48CG7d++mcuXKSkdKFx4+fMi6devw9PTk+vXr5MqViw4dOuDi4kKFChUUOS/0+fPnFC1alLZt27J8+fIUnz81khVKIYRQSOHChTEzM+PcuXNKRxFA7ty5OXToEKVKlaJevXpyTmgyevPmDStWrKBWrVr89NNPTJ48mXLlyuHn58fTp0+ZN28ednZ2ih0+P2LECPT19fn9998VmT81koJSCCEUolKpsLOzk4JSh2TNmpW9e/dSu3ZtmjRpwubNm5WOlGaEh4fj4+NDq1atsLCwoFevXmTMmBG1Wk1ISAienp40atQIAwNlD6A5ceIEHh4e/P777+TIkUPRLKmJbHkLIYSCRo0ahVqt5smTJ0pHEf8QGRmJm5sbGzZsYOnSpXTvrsUr+NKRmJgYjh07hpeXFxs3buTt27dUqFABFxcX2rdvr3Nd9dKIk3hyDqUQQijIzs6OadOmERQUhKWlpdJxxN8MDQ1Rq9Vky5aNHj168Pr1a0aMGKF0rFTj+vXreHp64uXlxaNHjyhQoAB9+vTB2dmZEiV093zGL404p0+flmIygaSgFEIIBdnZ2QFw/vx5mjZtqnAa8U96enosWLCA7NmzM3LkSF6/fs20adMUe65P1wUFBbF+/Xo8PT25ePEi2bJlo23btri4uFC1atVkOXRcm0JCQhgzZgzdunXD3t5e6TipjhSUQgihoPz585MzZ07Onj0rBaUOUqlUuLu7kz17dgYNGsTr169ZunSprF797f379/j4+ODp6cmBAwcwMDCgWbNmjBs3jsaNG2NkZKR0xHgbOXKkNOIkgRSUQgihIGnMSR0GDhxI9uzZ+eWXX3j79i2enp6pqljSpsjISPz9/fH09MTX15dPnz5Rq1Ytli1bRuvWrcmaNavSERPs+PHjeHh4sGzZMmnESSRpyhFCCIWNGzeOpUuXEhISItupOm779u20bduWmjVrsnXrVkxM0sdVexqNhrNnz+Lp6cmGDRt48eIFpUqVwtXVlQ4dOpA/f36lIyZaVFQUdnZ2ZMiQgZMnT8rqcyJJQSmEEArbsWMHzZs35+HDh6n6G3N6cfjwYZo3b07JkiXZvXs32bNnVzpSsrl79y5eXl54enpy584drKys6NixIy4uLpQtWzZN/AC0cOFC+vfvz+nTp+XZySSQglIIIRQWFBSElZUVW7ZsoWXLlkrHEfFw/vx5GjVqRO7cudm3bx9WVlZKR9Kaly9fsnHjRjw9PTl58iQmJia0bt0aFxcXateunaZW8EJCQihWrBjt2rVj2bJlSsdJ1XS75UoIIdIBS0tL8uTJw9mzZ5WOIuKpQoUKHD16lNDQUKpVq0ZgYKDSkZLk06dPbNy4kebNm2NpacmAAQMwNzdnw4YNhISEsHr1aurVq5emikmQG3G0SQpKIYTQAdKYk/oUL16c48ePkyFDBqpXr87ly5eVjpQg0dHRHDx4kF9++YXcuXPTrl07Xrx4wbx583j27Bk7duygXbt2ZMqUSemoyeL48eOsWbOGqVOnYm5urnScVE+2vIUQQgdMnjyZ2bNn8/r16zTxXFp68vz5cxo3bszdu3fZtWsX1apVUzrSd12+fBlPT0/WrVvH06dPsba2xsXFBWdnZ6ytrZWOlyKkEUf75NggIYTQAfb29rx9+5a7d++mm2/qaUWuXLk4dOgQzZs3p379+mzdupVGjRopHetfHj9+zLp16/D09OTq1avkyJGD9u3b4+LiQsWKFdPdDzFLlizh8uXLciOOFskKpRBC6ICXL1+SM2dO1q9fT/v27ZWOIxLh06dPtGvXDj8/P9RqteL/Ht++fcuWLVvw9PTkyJEjGBkZ4ejoiIuLCw0aNMDQ0FDRfEoJCQmhaNGitG/fXhpxtEieoRRCCB2QI0cOfvrpJ2nMScUyZszIli1b6NChAx07dmTp0qUpniEiIoJt27bRpk0bLCws6N69OwYGBqxevZqQkBDWr19PkyZN0m0xCbGNOAYGBtKIo2Wy5S2EEDrC3t5eGnNSOUNDQzw8PMiWLRu9e/fm9evXjBo1Klm3lDUaDSdOnMDT05ONGzfy+vVrbG1tmTJlCu3btydPnjzJNndqc+zYMdasWcPy5culEUfLpKAUQggdYWdnx6RJk4iOjpbnulIxPT095s2bh7m5Ob/99huvXr1i1qxZWi8qb968iZeXF15eXty/f5/8+fPTo0cPnJ2dKV26tFbnSguioqLo06cPFStWpGvXrkrHSXOkoBRCCB1hb29PWFgYt27domTJkkrHEUmgUqkYN24c2bNnp1+/frx584bly5djYJC0b7shISFs2LABT09Pzp07h5mZGW3btsXFxYXq1aujpydPsn3LkiVLuHLlCmfOnJHfp2QgBaUQQuiI8uXLA3Du3DkpKNOIvn37ki1bNtzc3Hjz5g3r16/H2Ng4QWN8+PABX19fPD098ff3R09Pj6ZNmzJq1CgcHBwSPF56FBISwpgxY+jRowd2dnZKx0mTpMtbCCF0SLFixWjYsCF//PGH0lGEFu3atYvWrVtTtWpVfH19MTU1/e77o6KiOHDgAJ6envj4+PDhwwdq1KiBi4sLrVu3TtP3hyeHzp07s2vXLm7duiXPTiYTKSiFEEKHuLi4cPfuXU6ePKl0FKFlR48epWnTphQrVozdu3eTI0eOf72u0Wi4cOECnp6erF+/npCQEIoXL46rqysdO3bkp59+UiZ4Knfs2DFq1KjB8uXL6d69u9Jx0iwpKIUQQofMmzePUaNG8e7du3R9tEtadfHiRRo1aoS5uTn79u0jb9683L9/P+7Q8Zs3b5I7d246duyIi4sL5cqVS3eHjmtTVFQUFSpUwNjYmJMnT8qzk8lInqEUQggdYmdnx+fPn7l27Rq2trZKxxFaVq5cOY4dO0a9evWwsbGhYMGCnD9/nsyZM9OyZUvmz59P3bp1k9y8I2ItXrxYGnFSiPyJFUIIHVKuXDn09PQ4d+6cFJRpzOfPn9m1axeenp4EBQURFRVFWFgYU6ZMYcCAAWTOnFnpiGlKcHAwY8eOlUacFCLluhBC6JDMmTNTsmRJOeA8jYiJieHw4cN069YNCwsLWrduzdOnT5k9ezbXrl3DxsaG6dOnc+HCBaWjpjkjRozA0NCQKVOmKB0lXZAVSiGE0DH29vZyBWMqd/XqVTw9PVm3bh2PHz+mYMGC9O/fH2dnZ4oVKxb3vgMHDuDo6EiDBg3YvHkzTZo0UTB12nH06FHWrl3LihUrpKs7hUhTjhBC6JjFixczcOBA3r17J2cMpiJPnz5l/fr1eHp6EhAQQPbs2WnXrh0uLi5UqVLlm801nz9/pmPHjuzYsQMPDw+cnZ1TOHnaEhUVRfny5cmYMaM04qQgWaEUQggdY2dnR2RkJFeuXMHe3l7pOOI73r17x9atW/H09OTgwYNkyJCB5s2b4+7uTqNGjciQIcMPxzA2Nmbjxo306NEDFxcX3rx5Q9++fVMgfdq0ePFirl69Ko04KUwKSiGE0DE2NjYYGhpy9uxZKSh1UGRkJHv37sXT05Nt27YRHh5OnTp1WLlyJa1atcLMzCzBYxoYGLBq1aq4qxpfv37N2LFj5cigBPrSiNOzZ09pxElhUlAKIYSOMTIyokyZMtKYo0M0Gg2nT5/G09MTb29vXr58SZkyZXB3d6dDhw7kzZs3yXOoVCpmzpyJubk5o0eP5tWrV8ydO1dW2RJg+PDh0oijECkohRBCB9nZ2XHixAmlY6R7d+7cwcvLC09PT+7evUuePHn45ZdfcHZ2pmzZslqfT6VSMWrUKLJly8avv/7KmzdvWLVqlRxyHw9Hjx5FrVazYsUKuZpSAdKUI4QQOmjlypX07NmTd+/eyfmEKezFixd4e3vj6enJ6dOnyZIlC61bt8bFxYWaNWuir6+fIjm8vb1xcXGhcePGeHt7kzFjxhSZNzWSRhzlyQqlEELoIDs7O2JiYrh06RLVqlVTOk6a9/HjR7Zv346npyd79uxBpVLh4ODAxo0badq0qSLFXLt27TAzM6Nly5Y0btyY7du3kyVLlhTPkRosWrSIq//X3r3HVV3neRx/c1EQSPCYC1rJI6EwcrQMU9Pq4V3zUqR446jVWuLWbvN4OGnOTOO4o1vuzGN7jEKXyWFa/R1CN6O8IoymNNhM0GXN8JqXWQKx4WZoKpezfxwxNe4H+P0Ovp7/cOSc3+98wPPQ9+N7+xw4oJycHMKkSRihBAALqqysVNeuXfXyyy/rpz/9qdnldEjV1dX68MMPZRiGNm3apIqKCj3wwAOy2+2Ki4vTzTffbHaJkqTs7GxNmjRJffr0UXp6unr06GF2SZZy+vRpRUVFafbs2Xr99dfNLueGRaAEAIsaOnSoIiIiZBiG2aV0GE6nU1988YUMw9A777yjwsJC3XnnnbLb7Zo9e7YiIiLMLrFO+/fv19ixYxUSEqKMjAz17t3b7JIsY+7cudq+fbuOHDnC2kkTMeUNABYVExOjzMxMs8voEE6dOqWUlBQZhqG8vDz16NFDs2bNkt1uV0xMjOWP5+nfv7+ys7M1ZswYDRs2TJmZmerbt6/ZZZkuKytL69ev19q1awmTJmOEEgAsat26dZo3b57KyspadLbhja60tFTvvvuuDMNQVlaWunTpotjYWNntdo0ePdojd04XFBRo7NixKioqUnp6uu677z6zSzJN7UacgIAA7du3j7WTJuO3DwAWVXsw82effWZyJZ7j4sWLSktL09SpUxUWFqaEhAT5+/tr3bp1KioqksPh0IQJEzwyTEpSr169lJWVpcjISI0YMUJ79uwxuyTT1G7ESUpKIkxaAH8DAGBRUVFRCgwMVE5OjtmlWFpNTY0++ugjLViwQGFhYXr88cd18uRJvfLKK8rPz9fOnTs1Z84c3XTTTWaX2ipsNpsyMzM1ZMgQjR8/Xps3bza7pHZXWFioX/3qV0pISLihR2mthClvALCwhx9+WKGhodq4caPZpVjOwYMHZRiGHA6HTp06pfDwcMXHxys+Pl7R0dFml9fmLl68KLvdrrS0NCUnJ2vu3Llml9Ru5syZox07drARx0LYlAMAFhYTE6O0tDSzy7CMwsJCpaamyjAMffbZZ+rWrZumT5+u+Ph4DRs27Iaa+vTz81NqaqoSEhI0b948lZaW6vnnnze7rDaXlZUlwzDYiGMxjFACgIWlpqZq1qxZ+vbbby1zLmJ7q6ioUFpamgzD0J///Gf5+vpq8uTJV7rI+Pn5mV2iqZxOp5YuXapVq1bppZde0vLlyy2/a72lKisrNXDgQAUGBrIRx2IYoQQAC6vdmPPpp59q3LhxJlfTfqqqqpSZmSnDMPT+++/r/Pnzevjhh/Xmm29q6tSp6tatm9klWoaXl5deeeUV2Ww2LVmyRCUlJVq9enWHDFtJSUn66quvlJub2yF/Pk9GoAQAC4uIiFBISIhyc3M7fKB0Op3Kzc2VYRhKTU3VmTNnFB0drZdeekmzZs1SeHi42SVa2uLFi2Wz2bRgwQKVlpbq7bff9tjd7HUpLCzUsmXLlJCQoIEDB5pdDq5DoAQAC/Py8lJMTEyH3ul9/PhxORwOGYahI0eOqGfPnpozZ47sdrsGDBjQYadv28L8+fMVEhKi2bNnq7y8XBs3blRAQIDZZbWKxYsXq3PnzlqxYoXZpaAOBEoAsLiYmBitX7/e7DJaVXFxsTZu3CjDMLRv3z4FBQVp6tSpSkpK0ogRI+Tj42N2iR5r2rRpCg4OVmxsrMaNG6ctW7YoJCTE7LLcUrsR549//CMbcSyKTTkAYHGbNm3StGnTVFBQoJ49e5pdTot9//332rJliwzD0I4dO+R0OjV+/HjZ7XZNmTKlw4ykWcVf//pXPfLIIwoPD1d6erpCQ0PNLqlF2IjjGfhbAQCLGzRokCQpNzfX5Eqar7q6Wrt379ZTTz2l0NBQzZgxQ2fOnNGrr76qwsJCbd26VTNnziRMtoEhQ4YoKytLRUVFGj58uE6ePGl2SS1SuxHntddeI0xaGCOUAGBxTqdToaGhWrhwoZYvX252OU2yf/9+GYahlJQUffPNN4qIiJDdbld8fLzuuOMOs8u7oZw4cUJjxozRhQsXlJGR4VGHvhcWFioqKkpz5sxRUlKS2eWgAQRKAPAAEydOlNPp1Pbt280upV75+flKSUmRYRj68ssv1b17d82cOVN2u12DBw9mc42JTp8+rXHjxik/P187duzQ/fffb3ZJTWK327Vz504dOXKEo6IsjrFjAPAAMTExys3NldXGAMrLy5WcnKyRI0eqd+/eWrZsmaKjo7VlyxYVFhYqMTFRQ4YMIUyaLCwsTHv27FHfvn01cuRI7dq1y+ySGpWVlSWHw6FVq1YRJj0AI5QA4AG2bNmiKVOm6O/H83RbyEWp+qLk4ycFRUqdgtq1lkuXLik9PV2GYWjz5s26dOmSRo0aJbvdrtjYWHXt2rVd60HTnTt3TtOmTdPu3buVmpqq2NhYs0uqU+1GnKCgIGVnZ7N20gNwbBAAWF15nkZ2fV9H/0u69ePr1795SUF9pF6PSHckSMFtsz7O6XTq448/lmEY2rBhg0pKSnTPPfdo5cqVmjlzpm655ZY2eV+0rsDAQH3wwQeaO3eupk2bprfeektPPfWU2WX9SGJiIh1xPAwjlABgVRUnpE8WSKczJS9fyVlV/2trnw8bI93/phR0e6uUcPjwYTkcDjkcDh0/fly33Xab4uPjFR8fr379+rXKe6D9VVdX67nnntMbb7yh3/3ud1q0aJHZJV3BRhzPxAglAFjRsbXSp/8q1VwOkQ2FyaufL/pQ2hYt3bdGipzforcuKirShg0bZBiGcnJyFBwcrLi4OCUnJ+vBBx9kxKgD8PHx0Wuvvabu3bvrZz/7mUpKSrRixQpLrHV94YUX5OfnR0ccD0OgBACrObBS2v/Lll3rrJKqq6RPnpYuFEn9ftGky86dO6cPPvhAhmEoIyND3t7emjhxopYsWaKJEyfK39+/ZfXAsry8vLRixQrZbDYtWrRIxcXFSkpKMrVL0d69e+VwOJScnMxGHA/DlDcAWMmxta4w2FoGr5Ui/rnOp6qqqrR7924ZhqH33ntP586d0/Dhw2W32xUXF0eLuxvIn/70J82fP19xcXFat26dOnfu3O41sBHHszFCCQBWUXHCNc1dh7f3Sk/+4drv9egq3X2LtHiSNOGeeu6Z+5wUOvLKmkqn06nPP/9chmHonXfe0enTpxUVFaWlS5dq9uzZuv321ll7Cc/y5JNPKiQkRDNnztSjjz6qd999V4GBge1aQ2JiovLy8pSTk0OY9ECMUAKAVewe61oDWcd6ydpA+e/TpNt7SE6nVHRWejtL+ipf2rJImjSwjnt6+UqhI3Syzx/kcDhkGIYOHTqk0NBQzZo1S3a7XQMHDrTE2jmYb9euXXrsscfUv39/bd26td2mnQsKCtS3b1/NnTtXiYmJ7fKeaF0ESgCwgvI8advd9T5dGyhzfiPF9Pnh+6XnpNCFUtxgyfFs/be/6wXp/8oDFRsbK7vdrlGjRsnXl0kq/FhOTo4mTJigXr16aefOnerZs2ebv2d8fLwyMzN1+PBh1k56KP41AQArOPpG40cD1SEkQOrSWfJtYB9FVY2X3v/tGN366HvtPo0JzzNo0CBlZWVp7NixGj58uDIzM9WnT5/GL2yhvXv3KiUlhY04Ho5FCgBgBQXbmxQmy89L//hO+vasa6p7YbJUcUGyD6v/Gl9vp6KCjhMm0WTR0dHKzs6Wj4+Phg8frgMHDrTJ+1RWVurZZ5/V0KFDNW/evDZ5D7QPRigBwGyV30kVx5v00tEvX/tnv05S8jPSmJ80cmHF11JlRbu3aYTnCg8P10cffaTx48froYce0rZt2zR06NBWfY81a9bo4MGDdMTpAAiUAGC2iq8lNW05e9IT0p2Xl7QVlUvGX6T5a6WbukiPD2roSqdUcUzqdo97teKGEhoaqj179mjy5MkaPXq00tLSNHbs2KZdXFnh+szV03e+oKBAv/71r7Vw4ULde++9bfQToL2wKQcAzPaPv0kZQxp8SX2bcmpqpHt/4ZoCP/l7qXMDwwQrPpmkMt8o2Ww2de/eXTab7UePAwMD2fGNHzl//rymT5+ujIwMORwOxcXF1f3C8jzXeuCC7ZdH3a+OGNf2nY//l5VsxOlAGKEEALP5+LX4Um9vaUS09Pt06ehp6e5b63/t0eN/19+OHFVxcbFKSkpUU1Pzo9d07ty5zqDZUAjt3r27AgICCKIdWEBAgNLS0vTEE09oxowZKisr09NPX3UAf5P6zjtdo/FHX5eOrNG826THVq0iTHYQBEoAMFtQpCQvNXXa+3pV1a6vFRcaepWX/ntT9pUpx5qaGn333XcqKSm5EjDre3zo0KFrvt9QEG1OCLXZbARRD9KpUyetX79eNptNzzzzjEpKSrRkyZIW950f2U/y6bRMOmZrcd95WAeBEgDM1inINRVY8XWzL62skjK+dE1139WrgRcGRVyzfs3b21vBwcEKDg5uVnec2iDaWAgtKSnRwYMHrzxuKIjWFzobCqQEUXN4e3tr9erVstlsevHFFzXAd6vG9/xLi+7l6y2p+kKz+87DmgiUAGAFvR5xTQU2Mrqz43+lQwWux2fOSin7XFPdL06WugbUc5GXr9RrQquUeXUQbc7ZhDU1NTp79myjIbS4uFh5eXmNBlE/P78WTc136dKFIOomLy8vLV++XA/2OqzRN21onZvu/6XUJazevvOwPjblAIAVNLFTztX8O0l9e0kLRkoLRkkN5qSJeVLwXa1Tazu6Oog2ZVS09nFpaWmDQbS5U/ME0etUnJC2RctZdaHez93XRdJ/bpUyv5QKyqTOPtJPbpOmD5GeGek6kP8aPv6uz2kQ/eQ9EYESAKyigV7eLXa5l7dGZrTePT1AbRBtTghtLIg2N4TWTs13SI18Vrd9LsWtlvx8pbkPSv1ulS5VSX85Im36RHriIekP1y+bvEE/qx0FgRIArOLyqI+qG9xd0zyM+jRLTU2NysvLmxVCGwqi/v7+zQ6htVPzltXIaPqJM1L/pdKtNmn3z6We123iPnZa2vaF9Pz4em7goaPpNzoCJQBYybG1rk0KrWXwWtaltYOrg2hTQ2hxcbFKS0tV13/DVwfRpobQ2qn5Npf7bw2u912YLL2xS8peJj1wZzPv7eUr3bFQilntfp1oVwRKALCaAytdmxTcNWCldPfP3b8P2kxtEG3J1Hx9QbQlU/PNCqKbIxs8keDW51wtQb9+tSW/EbmO0ZpytIUXwyzs8gYAq+n3C8k/9Iez/ZqzptLLV/L2lWISGZn0AN7e3urWrVuzD/euqalRWVlZk0Lo/v37Gw2iXbp0aVII/aduXTSs4rjq25509rz0Tan06H0t+GXUou+8RyJQAoAVRc6XwkY1ofvIZbXPh46Q7n+TNZMdnLe395WQ1xzV1dVNnprPz8+/8ueysjI5nU4NCJe++I/673/2e9fXm/zd+OHoO++RCJQAYFVBt7t2vF7pj7zj8lTj9f2RI1znTN6xkM0MaJCPj8+VIBoZGdnk62qDaMWp3dLBevp4S+p6eeb8O3f3lVVfdPMGaG8ESgCwuuDoHzYpVFa4Rm+qL7p6gAdFMjWINncliHpFSgfrf13XAKlXN+lAvrtv2PL+9jCHt9kFAACaoVOQayrw5sGur4RJtKcrfefrN+le16HmH7d4X43X5feBJyFQAgCApqntO9+AxZOkQD9p/ltSUfmPn/+6SPp9egM3uK7vPDwDU94AAKDpGuk7HxEqpTwrzVgj3fXCtZ1y9h2V/udvrk45dWrFvvNoX5xDCQAAmq6RTjm1jp6WfrtVyjwgFZS62jD27y3NHCo9PcJ1VmWd6JTjkQiUAACgeeg7j+uwhhIAADTP/W+6DtBvTd6+rvvCIxEoAQBA8wTdLt23pnXvGZPIgfwejEAJAACaL3K+1H9F69xrwEpahXo41lACAICWO7aWvvMgUAIAADdVnGh+3/mwMfSd70AIlAAAoHXQd/6GRaAEAACtj77zNxQCJQAAANzCLm8AAAC4hUAJAAAAtxAoAQAA4BYCJQAAANxCoAQAAIBbCJQAAABwC4ESAAAAbiFQAgAAwC0ESgAAALiFQAkAAAC3ECgBAADgFgIlAAAA3EKgBAAAgFsIlAAAAHALgRIAAABuIVACAADALQRKAAAAuIVACQAAALcQKAEAAOAWAiUAAADcQqAEAACAWwiUAAAAcAuBEgAAAG4hUAIAAMAtBEoAAAC4hUAJAAAAtxAoAQAA4BYCJQAAANxCoAQAAIBbCJQAAABwC4ESAAAAbiFQAgAAwC0ESgAAALiFQAkAAAC3ECgBAADgFgIlAAAA3EKgBAAAgFv+HxYqMURFEUz2AAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR SOLUTION HERE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## So, how can we identify strongly overlapping communities?\n", "\n", "If you apply Louvain method or any other method that assumes disjoint communities to this network, they will have to put node \"D\" into either one of the communities, which is not ideal. A common approach to overlapping community detection is to _allow_ \"fuzzy\" boundaries between communities. There are many ways to do this, and in this simple example, this type of fuzzy overlapping community detection method will work perfectly fine. \n", "\n", "But, while keeping the example very simple, let's think about more complex cases where where the overlap is pervasive and each node can belong to multiple communities. Then the \"fuzzy\" community detection approach may not work well, again due to the limiting assumption that the communities are _almost_ disjoint. \n", "\n", "Going beyond this \"fuzzy\" assumption, we can think about \"pervasive overlapping communities\" where each and every node can belong to multiple communities. This is the most challenging case, and it can also be the most realistic case for many real-world networks. There are, again, many ways to do this, but let's try a conceptually simple and illustrative method based on the concept of \"link communities\" ([Paper](https://www.nature.com/articles/nature09182)), where we think about the communities of _links_ (edges) rather than nodes. It also happened to be my method as well. 🙈 \n", "\n", "The key idea is that 'disjoint link communities' is a better approximation than 'disjoint node communities'. Even when every node belongs to multiple communities, the links between nodes can be partitioned into disjoint communities very well. Instead of trying to put nodes into communities, we put links into communities. \n", "\n", "The method first constructs a weighted \"line graph\" where each edge in the original network becomes a node and two nodes are connected if the corresponding edges share a node. The weights of the edges in the line graph are calculated based on the shared neighbors of the corresponding edges. Then, it applies a hierarchical clustering to the nodes of this line graph. \n", "\n", "Let's try. First, activate your virtual environment and install the package to your virtual environment by running the following command. \n", "\n", "```bash\n", "pip install git+https://github.com/Nathaniel-Rodriguez/linkcom.git\n", "```\n", "\n", "If you use [`uv`](https://github.com/astral-sh/uv), you can install it by running the following command. \n", "\n", "```bash\n", "uv pip install \"linkcom @ git+https://github.com/Nathaniel-Rodriguez/linkcom.git\"\n", "```\n", "\n", "Then we can import and run the method as following. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "clustering...\n", "computing similarities...\n", "# D_max = 1.000000\n", "# S_max = 0.125000\n" ] } ], "source": [ "import linkcom\n", "\n", "e2c, S, D, Dlist = linkcom.cluster(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `e2c` stores the edge-to-community mapping. It is a dictionary where the keys are the edges and the values are the community IDs. \n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{('D', 'H'): 13,\n", " ('F', 'G'): 13,\n", " ('B', 'D'): 10,\n", " ('G', 'H'): 13,\n", " ('A', 'C'): 10,\n", " ('D', 'G'): 13,\n", " ('D', 'E'): 13,\n", " ('E', 'H'): 13,\n", " ('E', 'G'): 13,\n", " ('B', 'C'): 10,\n", " ('A', 'B'): 10,\n", " ('D', 'F'): 13,\n", " ('C', 'D'): 10,\n", " ('E', 'F'): 13,\n", " ('F', 'H'): 13,\n", " ('A', 'D'): 10}" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e2c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that there are two communities 3 and 15. Now we can set edge attributes based on the community IDs. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "nx.set_edge_attributes(P, e2c, \"linkcom\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Q: Can you draw the network again with the edge colors based on the community IDs?**" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR SOLUTION HERE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can you see now why link community approach can detect highly overlapping communities? \n", "\n", "**Q: Now, download a small network where you expect to see pervasively overlapping community strcuture and try the link community detection method. Visualize the network by coloring the edges using the found community ID.**" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# YOUR SOLUTION HERE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Statistical inference approach to community detection\n", "\n", "Pretty much all methods that we have discussed in the class so far are based on some heuristics and/or optimization algorithms. Although they may work perfectly fine for many cases, there is another powerful approach that we want to know about. That is the statistical inference approach to community detection. In this approach, we can be more explicit and flexible about the exact nature of the community structure that we are looking for. We can also quantify the uncertainty of the community structure that we infer and compare different community structures in a principled way." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Stochastic block models\n", "\n", "The key idea is that we can think of the community structure as a _generative model_ of the network. That is, we assume that the network is generated by some underlying community structure and we want to infer this community structure from the network. If we have a probabilistic model of the network, we can use the observed network to infer the parameters of the model (Bayesian inference). \n", "\n", "The most fundamental model is the stochastic block model (SBM). In this model, the network is generated by the following process.\n", "\n", "1. Each node belongs to one of the $K$ communities.\n", "2. The probability of an edge between two nodes depends only on the community assignments of the two nodes.\n", "\n", "Let's try an example. Let's have a network with 20 nodes and 2 communities. Nodes 0-9 belong to community 0 and nodes 10-19 belong to community 1. The probability of an edge between two nodes is 0.7 if they belong to the same community and 0.05 if they belong to different communities." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random\n", "\n", "G = nx.Graph()\n", "G.add_nodes_from(range(20))\n", "\n", "# add community id as node attribute\n", "for i in range(10):\n", " G.nodes[i][\"community\"] = 0\n", "for i in range(10, 20):\n", " G.nodes[i][\"community\"] = 1\n", "\n", "# Add edges between nodes with probability 0.7 if they are in the same community, and 0.05 otherwise\n", "# YOUR SOLUTION HERE\n", "\n", "nx.draw(G, with_labels=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Congratulations! Now you implemented a simple stochastic block model. This model generated a network given a set of parameters. Assuming that we fix the total number of nodes, what are the parameters that we set? \n", "\n", "1. The number of communities $K$\n", "2. The community assignments of the nodes $z_i$ ($ 1 \\times N$ vector)\n", "3. The edge probabilities $p_{ij}$ ($K \\times K$ matrix)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayes' theorem\n", "\n", "So how does this help us to detect communities? To understand this, let's look at the Bayes theorem:\n", "\n", "$$ P(\\theta | D) = \\frac{P(D | \\theta) P(\\theta)}{P(D)} $$\n", "\n", "Here, $\\theta$ is the set of parameters of the model and $D$ is the observed data. If we ignore $P(D)$ and $P(\\theta)$ for a moment, we get the following. \n", "\n", "$$ P(\\theta | D) \\propto P(D | \\theta) $$\n", "\n", "What this means is that the probability of any set of parameter given what the data tells us ($P(\\theta | D)$) is proportional to the probability that the data is _generated_ by the model with the parameters ($P(D | \\theta)$). This is the key idea of the Bayesian inference. If we have a generative model that can generate data from a set of parameters, then we can evaluate $P(D | \\theta)$, and this can in turn tell us how good the parameters are given the data $P(\\theta | D)$. \n", "\n", "Here $P(D | \\theta)$ is called the _likelihood_ of the parameters given the data and $P(\\theta | D)$ is called the _posterior probability_ of the parameters given the data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Maximum likelihood Coin flips \n", "\n", "To understand this better, let's take a super quick detore to the coin flips. Here, \n", "\n", "1. Our data $D$ is the sequence of 10 coin flips: \"H\", \"T\", \"H\", \"H\", \"T\", \"T\", \"H\", \"T\", \"H\", \"H\". \n", "2. Our model is the Bernoulli distribution with the parameter $\\theta$ which is the probability of getting \"H\".\n", "\n", "Then, the likelihood ($P(D | \\theta)$) is the probability of getting the observed sequence of coin flips given the parameter $\\theta$. We can calculate this directly. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.561000000000003e-07" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coin_flip_data = [\"H\", \"T\", \"H\", \"H\", \"T\", \"T\", \"H\", \"T\", \"H\", \"H\"]\n", "theta = 0.1 # parameter\n", "\n", "# likelihood\n", "likelihood = 1.0\n", "for x in coin_flip_data:\n", " if x == \"H\":\n", " likelihood *= theta\n", " else:\n", " likelihood *= 1 - theta\n", "\n", "likelihood" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can make it as a function. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "\n", "def coin_flip_likelihood(theta, data):\n", " return np.prod([theta if x == \"H\" else 1 - theta for x in data])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can evaluate the likelihood for several values of $\\theta$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0 0.0\n", "0.1111111111111111 1.1747213274285833e-06\n", "0.2222222222222222 4.4070404799312956e-05\n", "0.3333333333333333 0.0002709614049348847\n", "0.4444444444444444 0.0007342008296428648\n", "0.5555555555555556 0.0011471887963169767\n", "0.6666666666666666 0.0010838456197395387\n", "0.7777777777777777 0.0005398624587915844\n", "0.8888888888888888 7.518216495542947e-05\n", "1.0 0.0\n" ] } ], "source": [ "for theta in np.linspace(0, 1, 10):\n", " print(theta, coin_flip_likelihood(theta, coin_flip_data))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or, plot a likelihood curve." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot a likelihood curve\n", "import matplotlib.pyplot as plt\n", "\n", "thetas = np.linspace(0, 1, 100)\n", "\n", "# YOUR SOLUTION HERE\n", "\n", "plt.xlabel(\"$\\\\theta$\")\n", "plt.ylabel(\"Likelihood\")\n", "plt.title(\"Likelihood of theta given coin flip data\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can you find the best parameter now? How? " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yes, when the likelihood is maximized, we get the best parameter according to this reasoning. This is called the _maximum likelihood estimation_ (MLE) and it is one of the most common statistical inference method. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Back to SBM\n", "\n", "Although the community detection problem with SBM is more complex, involving many more parameters, the basic idea is the same. Let's go back to the graph that we generated. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nx.draw(G, with_labels=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To simplify things, let's assume that we fix the number of communities $K=2$ and the community assignments $z_i$ are known. Let's also assume that $p_{00} = p_{11}$ and $p_{01} = p_{10}$. Then, the only parameters that we need to infer are the edge probabilities $p_{ij}$, namely the two numbers $p_{00}$ and $p_{01}$.\n", "\n", "Note that given the data (the observed network) and parameters, we can calculate the likelihood. This is the probability of observing the network given the parameters. For instance, given a node pair $(i, j)$, the probability of observing an edge between them is $p_{z_i z_j}$ and the probability of **not** observing an edge between them is $1 - p_{z_i z_j}$.\n", "\n", "Then, the probability of observing the entire network is the product of these probabilities for all node pairs." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.227338810184705e-26" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from itertools import combinations\n", "\n", "p00 = 0.7\n", "p01 = 0.05\n", "\n", "# likelihood\n", "likelihood = 1.0\n", "for i, j in combinations(G.nodes, 2):\n", " # YOUR SOLUTION HERE\n", "\n", "likelihood" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Btw, do you note that the likelihood is extremely small? As we multiply many small numbers (probabilities), the result becomes extremely small. This can lead to all kinds of numerics problems and we often use the log-likelihood instead. Using log-likelihood makes the multiplication into addition and the numbers are much more manageable.\n", "\n", "Let's write a super simple function to calculate the log-likelihood of the SBM." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-59.66236416131314" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def sbm_likelihood(G, p00, p01):\n", " log_likelihood = 0.0\n", " for i, j in combinations(G.nodes, 2):\n", " # YOUR SOLUTION HERE\n", " return log_likelihood\n", "\n", "\n", "sbm_likelihood(G, 0.7, 0.05)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can vary a parameter to see how the log-likelihood changes." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p00 = np.linspace(0.001, 0.9, 100)\n", "p01 = 0.05\n", "likelihoods = [sbm_likelihood(G, p00, p01) for p00 in p00]\n", "plt.plot(p00, likelihoods)\n", "plt.xlabel(\"$p_{00}$\")\n", "plt.ylabel(\"Log likelihood\")\n", "plt.title(\"Log likelihood of $p_{00}$ given graph G\")\n", "# draw a vertical line at 0.7\n", "plt.axvline(0.7, color=\"red\", linestyle=\"--\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Q: try with p01.**" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p00 = 0.7\n", "p01_list = np.linspace(0.001, 0.9, 100)\n", "\n", "# YOUR SOLUTION HERE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's cool to see that the log-likelihood is maximized roughly around the true value of the parameter!" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We can vary both. \n", "p00_list = np.linspace(0.001, 0.9, 100)\n", "p01_list = np.linspace(0.001, 0.9, 100)\n", "X, Y = np.meshgrid(p00_list, p01_list)\n", "likelihoods = [[sbm_likelihood(G, p00, p01) for p00 in p00_list] for p01 in p01_list]\n", "\n", "# colormap\n", "plt.pcolor(X, Y, likelihoods)\n", "plt.colorbar(label=\"Log likelihood\")\n", "plt.xlabel(\"$p_{00}$\")\n", "plt.ylabel(\"$p_{01}$\")\n", "plt.title(\"Log likelihood of $p_{00}$ and $p_{01}$ given graph G\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the true parameter value is close to the maximum likelihood estimate, as it should be! \n", "\n", "This is the basic idea of the inference from a generative model. If your model is good, then the best parameters may be those that explain the data best. Although there are much more complexity beyond this simple maximum likelihood estimation, this is the basic idea that you want to really understand. Being able to generate a data from a set of parameters allows us to evaluate how good the parameters are given the data, which in turn allows us to identiy good parameter values given data. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Q: Can you identify the best parameters ($p_{00}$ and $p_{01}$) for the network that we generated, by finding the parameters that maximize the log likelihood?**" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p00_max: 0.746\n", "p01_max: 0.010\n", "max_log_likelihood: -56.752615142652324\n" ] } ], "source": [ "p00_list = np.linspace(0.001, 0.9, 100)\n", "p01_list = np.linspace(0.001, 0.9, 100)\n", "X, Y = np.meshgrid(p00_list, p01_list)\n", "likelihoods = [[sbm_likelihood(G, p00, p01) for p00 in p00_list] for p01 in p01_list]\n", "likelihoods = np.array(likelihoods)\n", "\n", "# YOUR SOLUTION HERE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's generate a network with these paraemters and compare the true network and the inferred network side by side. Note that we can generate as many networks as we want from the same MLE parameters. That means we can do all kinds of measurements on the generated networks and estimate the uncertainty of the measurements! This is one of the cool powers of the statistical inference approach!" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G_MLE = nx.Graph()\n", "G_MLE.add_nodes_from(range(20))\n", "\n", "# add community id as node attribute\n", "for i in range(10):\n", " G_MLE.nodes[i][\"community\"] = 0\n", "for i in range(10, 20):\n", " G_MLE.nodes[i][\"community\"] = 1\n", "\n", "# Create G_MLE and then draw both G and G_MLE\n", "\n", "# YOUR SOLUTION HERE" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 1 }