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@thejevans
Last active February 16, 2022 19:02
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "PS1.ipynb",
"provenance": [],
"collapsed_sections": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"source": [
"PS 1, Group 2: Lee Sharma, Sandeep Damera, Shohini Banerjee, Nathan Zimmerberg, John Evans, Jared Ott"
],
"metadata": {
"id": "WDcs1oqWfq8M"
}
},
{
"cell_type": "code",
"source": [
"# Import the C.elegans dataset from the Github repository\n",
"\n",
"![ ! -f celegansneural.edges ] && \\\n",
"wget https://raw.githubusercontent.com/CambridgeUniversityPress/FirstCourseNetworkScience/master/datasets/celegansneural/celegansneural.edges"
],
"metadata": {
"id": "UJl6To98_2OW",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "99f08830-def8-4cf8-aef8-3542fb982e11"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--2022-02-16 18:51:31-- https://raw.githubusercontent.com/CambridgeUniversityPress/FirstCourseNetworkScience/master/datasets/celegansneural/celegansneural.edges\n",
"Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.109.133, 185.199.110.133, 185.199.108.133, ...\n",
"Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.109.133|:443... connected.\n",
"HTTP request sent, awaiting response... 200 OK\n",
"Length: 21371 (21K) [text/plain]\n",
"Saving to: ‘celegansneural.edges’\n",
"\n",
"celegansneural.edge 100%[===================>] 20.87K --.-KB/s in 0.001s \n",
"\n",
"2022-02-16 18:51:32 (14.3 MB/s) - ‘celegansneural.edges’ saved [21371/21371]\n",
"\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"from google.colab import drive\n",
"drive.mount('/content/drive')"
],
"metadata": {
"id": "4PTRsuRYvpn9"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"We first define the "
],
"metadata": {
"id": "jqdc63YB3t_L"
}
},
{
"cell_type": "code",
"source": [
"# Load NetworkX module, NumPy for linear algebra, and tools for drawing networks in the Jupyter notebook\n",
"import networkx as nx\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Access C. elegans dataset file\n",
"celeg_file = 'celegansneural.edges'\n",
"\n",
"# Define methods for betweenness centrality, node removal, network core access, and \n",
"\n",
"def betweenness_centrality(G):\n",
" \"\"\"Returns array of betweenness centrality for each node\n",
"\n",
" Betweenness centrality of a node v is the fraction of all pair shortest\n",
" paths that pass through v.\n",
"\n",
" For more details, refer to networkx.algorithms.centrality.betweenness_centrality\n",
" \"\"\"\n",
" bet_dict = nx.betweenness_centrality(G,normalized=False,endpoints=False)\n",
" bet = np.empty(nx.number_of_nodes(G))\n",
" # convert to a numpy array for efficient computation\n",
" for key, val in bet_dict.items():\n",
" bet[key - 1] = val\n",
" return bet\n",
"\n",
"def remove_nodes_get_core(G, nodes):\n",
" \"\"\"Removes list of nodes from network G iteratively\n",
"\n",
" This is a lazy method that yields the current state of G after each\n",
" removal. It can be used as an enumerable as follows:\n",
"\n",
" # print core size after each node removal\n",
" for core in remove_nodes_get_core(G, nodes):\n",
" print(len(core))\n",
"\n",
" Args:\n",
" G [NetworkX graph] An undirected graph\n",
" nodes [Enumerable] Ordered list of nodes to remove\n",
"\n",
" Yields:\n",
" The core of the network after each removal\n",
" \"\"\"\n",
" G = G.copy()\n",
" yield core(G)\n",
" for node in nodes:\n",
" G.remove_node(node)\n",
" yield core(G)\n",
"\n",
"def core(G):\n",
" \"\"\"Gets the core of an undirected network\n",
" \n",
" Args:\n",
" G [NetworkX graph] An undirected graph\n",
"\n",
" Returns:\n",
" either the core of the network or an empty set if no core exists\n",
" \"\"\"\n",
" try:\n",
" return next(nx.connected_components(G))\n",
" except StopIteration:\n",
" return set()\n",
"\n",
"def attacks_core_size(G, nodes):\n",
" \"\"\"Computes fraction of nodes in the core for the given node removal attack\n",
"\n",
" Args:\n",
" G [NetworkX graph] An undirected graph\n",
" nodes [Enumerable] Ordered list of nodes to remove during attack\n",
"\n",
" Returns:\n",
" list of fraction of nodes in the core component after each removal\n",
" \"\"\"\n",
" return [len(c) for c in remove_nodes_get_core(G, nodes)]"
],
"metadata": {
"id": "DFmVg7RO7-31"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
""
],
"metadata": {
"id": "hux3usNx3lv_"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"### Problem 1"
],
"metadata": {
"id": "_NZSircZ8yTb"
}
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "oY-1QkbMSTRc"
},
"outputs": [],
"source": [
"# Converting the C.elegans data from a directed network to an undirected network\n",
"G = nx.read_weighted_edgelist(\n",
" celeg_file, nodetype=int, create_using=nx.DiGraph).to_undirected()\n",
"\n",
"# Adjacency matrix of the undirected network\n",
"adj = nx.convert_matrix.to_numpy_array(\n",
" G, nodelist=np.arange(1, len(G.nodes) + 1))\n",
"\n",
"# Calculating the betweenes centrality\n",
"bet = betweenness_centrality(G)\n",
"\n",
"# Calculating the degree vector using k= A.1\n",
"k = adj.dot(np.ones(len(adj)))"
]
},
{
"cell_type": "markdown",
"source": [
"PLOTS"
],
"metadata": {
"id": "Tq4Z_0bbX1YM"
}
},
{
"cell_type": "code",
"source": [
"# Histogram of the degree distribution\n",
"plt.title('Histogram of the Degree Distribution')\n",
"plt.xlabel('Degree of node (k)')\n",
"plt.ylabel('Number of nodes (frequency)')\n",
"plt.hist(k, bins=40, log=True)\n",
"plt.savefig('1a_degree_distribution_histogram.pdf')\n",
"plt.show()\n",
"\n",
"# Histogram of the betweenness distribution of nodes\n",
"plt.title('Histogram of the Betweenness Distribution')\n",
"plt.xlabel('Betweenness of node (b)')\n",
"plt.ylabel('Number of nodes (frequency)')\n",
"plt.hist(bet, bins=40, log=True)\n",
"plt.savefig('1b_betweenness_distribution_histogram.pdf')\n",
"plt.show()\n",
"\n",
"# Scatter plot of the node degree vs node betweeneness\n",
"plt.title('Node Degree vs Node Betweenness')\n",
"plt.xlabel('Degree of node (k)')\n",
"plt.ylabel('Betweenness of node (b)')\n",
"plt.loglog(\n",
" k, bet,\n",
" linestyle='',\n",
" marker='.', markersize=10, markerfacecolor='skyblue',\n",
" markeredgewidth=1, markeredgecolor='k',\n",
")\n",
"plt.savefig('1c_degree_vs_betweenness_scatter.pdf')\n",
"plt.show()"
],
"metadata": {
"id": "fdlEYd-4-fH-",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 855
},
"outputId": "a66647e0-30b1-447c-f1d3-5a6e5bd00d43"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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zKRR3C1qtlj/SMxi3aHWZJ+XZU0p+n83lzJkzHDt7kU5DHufAht+5fu0aG7dspWb1arh5VOPy6T+ZFRNGq979SU2Ix6uqmwpTrYAU6qOQUi633hZC1BBCVLc6flpKWWyvsRBioRDitBDijzz7I4QQB4QQ6UKISaZzpEkpxwHDgKDinkuhuBcxGAy8/MorNO8e9rck5VlnioePf5PRC3Xs3LuPE2cv8sIPSUYfxHdrqVG3ARoXN06dOoWHRxUGv/YeDVu149KpkwiDnhnvvK0c2RUQh5zZQoguQoi9wB7gDyHEbiGEXe+4g3wFROQ5hwb4BIgEWgMxQojWpmODgeXAijs4p0Jxz6DT6bh8U0/61iSbpLz0jWvKJCnPXqZ41ToN8AseYLOvRc8wat7XmIYNG+LfrCkbv/yImvUbcvFoOp06tFO+iQqKo1FPXwDPSSl9pJTewD+BhSU9qZQyCTifZ3dXIF1KeURKmQ0sBqJN3/9NShkJPFbScyoU9xIpKSn4hw3Es959fDoynPjZ05gVE0ZVZ8rEtGMvU/za2b9I37jGZt+hTeu49OdRhg0bhnbpr8yZ8TZ9m9dlzoy3VbJgBcbRooAGKeV684aUcoMQIqeUZWkEHLPaPg50E0KEAg8BbhSyohBCjAXGAjRtWqZuE4WiwhMYGMjCuFiemq8lfVsSJ9J2I/W3mPHfGcWejB2JnIqMjKTV3M+ZPyrCkinesV0bpITZj4bgFxzO/vWruX7xHD27dbUk1kVFRalVRCWg0IQ7IYS5StYTQBXge0ACw4GbUsoXS3xiIXwArZSyrWl7KBAhpRxt2h4BdJNSPl+MMc09s8ccOnSopKIpFJWeokp8OBo2W5yWofYyxcHoVF+yZAkAQ4cOtSiG8g7bVdhS4sxsIcS6QsaVUso+dyCUD7aKogfwbylluGn7NdNJ/lPcsVVmtkJRcImP7OxsgoJDOHn+Ei2C+pG1PanAyV+r1TJ+UqxVOXM980dFMGfG2yVeCah+1RWTEvfMllKGlY1IdtkOtBBCNANOAI8C/yjOAFYrijIQT6GoWBS0Ksi7/7XXXrNMwAaDgR5BvTh29iIT4xJtJn97YbOFlTMvqaJQvTQqH4U6s4UQjwshRCHH7xdC9CruSYUQ3wObAT8hxHEhxNNSyhzgeWAlkAb8UNzMb1VmXFHRKKt2pea38vGTYlmbcZbxk2KJih5Cdna23f3m8+p0Oo5kHaN1aKTN5O/TNcRu2GxZlDNXvTQqH0U5s72AXUKIZCAZOIMxM9sXCAHOApOKe1IpZUwB+1egQmAVdwllmRld0Fv59OnTC31bT0lJoXGHLhzakkD/Z29nRB8qICPanpO6lU8TDAYD06ZNK5F/wexoN+hvnz9jawIBD719R/dEUXYUlXA3E+iI0YldF+hr2j4BjJBSPiylrDBeY9XhTlGRsJeElpZxtFSK3hX0Vr5x48ZC39YDAwO5cjKLGnXrG8NmZ01j5vBgGnrVtBs2q9FobMJYZ74zFYAX3phsd8WSF3srKtU4qPJRZB6FlNIgpVwtpfy3lPIZKeULUsrPpZRH/w4Bi4MyPSkqEmVpYinIJBQUFFSoqSgyMhL/Zk25fvYvajf2YdfyOJrUqcXGpMQCVwXmMNbY2Fg0Gg0Hso47pPwKMo8BKoeikuFoHkWlQDmzFRUJR00s1s7n9u3bA7Bnz55CzTr2TEL+zZry2muvsVwXz/tRgTTp0JXLJzJp3dzb8rZuXiFYoqEmji2W6ag4zu2inNYqh6LyoBoXKRRlhCPtSrOzs+kR1IsjWcdo3KELpw/v58bli3SMGk7WjvWFho3mDX8dMGAAgx98iJQ/UvHwqsflv07QrEkjNq1PwtXVtVSuqTjhstOmTWNtxlnCx79p2bdy9jT6Nq9LbGxsqcijKD1U4yKFohzIa9/Pa2IxGAwEBYdw7OxFOgwcxvnjWdRu7EM1r/p4B/Yo0qdhbRKKiopCp9Oxaes2nD2q4x3QDXfP2hw8fKRUGwEVx79QFhFTivLBoRWFEKI+8A7QUEoZaSrW10NK+UVZC1gcVGa2ojKh1Wp55sVXeO7bNZa3809HhlO7sQ/3tWxDn9EvFesN/PHHH+f3LcmM/26tZbxZMWEM6NmFb775ptTkdrRXtyMrKkXFocQJd1Z8BXwJvGHaPgjEYSwWWGGQUi4DlnXu3HlMecuiUFhjLzkuJSWFFkH9bKurdg9jpzaOjlGPFjtsNDc3F79etuO16t2fXH3e+pt3hqM1mvL5Qx56W5XqqKQ4anqqI6X8AcgFMCXHlU7mkEJxl1NQ9E/79u3J2m5bBnzfuhXk3LpBVsrmYoeNNm/enNSEeJvxUhN0NGvWzK5MZZEImJe85jGlJConjq4orgkhvDAWBEQI0R1QyQoKhRUFldQoKPoHsNj7fbqGcGjDarzre/H6f2eQmppKwNDivYG7uLggnARzHutHy159ObhhDcLJKZ8j++9ukaqo/DiqKF4EfgPuF0JsxJh8N7TMpCohKjxWUV4YDAYGDo42RRzV5/qCLwls25rlvy0lOTkZ7y7B+UJK9+7da2Oaefnh9y2K4aGHHrJ7jsIqrnbq1AmPH36m99MvcepwGv2efZWkBR/QsWNHm3FUrSVFcXHI9CSl3ImxZEdP4BmgjZRyT1kKVhJUwp2ivNBqtVYRR11x9qjOpq3bWLp0Kb9pl+czCZmjfxw1zRRkvrI2GZmT6dZ/8SH6G9dZ/8WHNjkUZlStJUVxKXRFIYTI/1pjpKUQAinlz2Ugk0JR6fjxxx/xqOnFc1/Ho3Fxof+4ScyKCWP27Nmcu34LryY+fDoynBbdw0hNWIF3/TqF+h7yrh4MBkORqwBHnceq1pKiuBRlehpk+m89jKuJtabtMGAToBSF4p7DngkIsBtxdG5nIt5dQgh/PpYDG9fw58G91Gvux8DenQsMKdVqtbz6+htcM4Bvz74sjIvFTebg3SUs3yogLi4unymqqIikgrK6Va0lRUE4mkexChgppfzTtH0f8JW5yVBFQ2VmK8qKgprujHlqFM/96zXGf59geUuf/WgIvg3rkbIvjYfe/Aj/4HBkbi4zhwczbkQMU6dOtRnXrCDOXrqCs7uHTT7E3BH9yb55nQk/brQZXxpyaN13EJnbEvHzbsyzY8cUWf7DfD5HciEU9w4l7nBnNUCalNLfatsJ2Ge9ryKgEu4UZY29EhZzR/SjeYM6HMk6isHFnZa9+nN40xpyrl1BuFfFt2cfdq/8hZzsbNyqVsVJ40LbZo1xcnKiXr16tGjRghXxKzl26gxOru607TuIHP0tIvKUvjixcSXZzm406xZK+sY1XDx7iujX3uev9DRysm+x6ft51PCqS9t+gzm8ZR1VNfDOtKloNBqHlIfi3qY0SnisEUKsFEI8KYR4ElgO/F5aApYWypmtKGvsOYKb9+hD1uVbZGvcuHjqJCc2rWTkIw/i5lmLZ79Zzdmsw1SrXZdOg4aTm2Pgypm/SM08gaFpW9ZuTea/cz7lUOYxrl2+RKve/WnUOoBDmxPyOb/ff2+GpRxI707tqeJZi3VffIT+5nVS162g5n2Nca3myemMQ4z9Mp4LN3N4+rnxjHh6DGsOny6yJLhCURCORj09D8wFOpg+86SU48tSMIWiItK+fXtS1yzj97nvkZa0Cv3Nm6RvSSTkyQlM+H4dtRp6c+lGNpmZmTTrFsqhLeu48Odxxi1czpnMdAw5elzcqxA+4U3Cn3+DiXFJeNSoSa4hB5+OPUhN0OHbNRjPevfx6RPh6GZOYU5MKHWrexAZGWmJkPL19QUJz30dT+TEyUyMS8TFzZ2+Y1/m0umTpG9Lwj8knE5DHqeaV300rm7cHzSA5D1/oNVqy/s2KioZxSkKuAmjM3sNsLFsxFEoKi4Gg4HP5s1HOLugv3WDlbOnMWNgADXq3YdfUF9jCY6eYVSt0wAhBBlbE9DNnELLnmEc3JLA8X0pVK1Zm06DY1g7/0O+fWkkwsmJ1mEDcdJoyM3JoXZjH2bFhFHH+36unj/Llh8WUsenBWeuXCcoOIQpU6ag1WpxcnLCPyTctvxHjzBOHU6jRY8wTqTt5tCmddzn144cfTb71i4nR38LJ1d3Xn39DbWqUBQLhxLuhBDDgPeBBEAAs4UQ/5JSLilD2RSKCoVOp+NA1nGLw3rAc6/z8bDedBocg5NGY2wpumkd+utXGDp0Eqn7D3Dh7BnStyZx6a+TVK3lZeOg/nRkOGlJK0nfmkD0a++xdt4H9H3mX+zUxrH+28+oWb8RsWsO4OLujkGvZ+awYJas38FXP/5C7SqunL+ejUGvv93OdPM6+ox5mVWfvMPNq5ep2aAR0pADUlrO23/cJOaO6K+S6xTFwtHM7DeALlLK0wBCiLoYfRRKUSjuGVJSUvJlWLcOjeSX6S9x7I9k9q9fzdXzZ6ju4WEp+rf2yBnOZh3m4OY1dHlwhM1vfbuFsvQ/r9C4dQD+weEc3bOd46m7OZOZjptHVdqHD0Hj4kJa0ipOHthLfV9/GrTwJ/Sdecx7Mpx6Naoyf1QE3l2CSU2IRzg5sfrTdxFOTjRuE8i1C+f49e2X6BT9D9vzBvW122hIoSgIR01PTmYlYeJcMX6rUNwVBAYGcmjj7zZO5vQtidTxbs6eVUsRGg1dHhyBa42arFq1itzcXPavX83wtz/Ht1to/oJ961bQKfofPP7h18jcXFIT4tm8eD5ejX0Y+u/ZpCbE882LI/h97gz0N65z6vB+Dm5ai3Byolm3UAY9EMmcGW/TWH8e/fUrtOs3mPDxsfxz0Soun8iid9sWvPDPZzmyZZ3qCaG4IxxdUcQLIVYC35u2hwMrykakkqNqPSnKCoPBgMFgQKO/yczhwbQOfYBDW9ZRo14DzmQdwUmjoVWvfhzavA79rVvs2LEDIQQSyQfRXfCoWRshBB8P603r0EhSE+K5fuUiBzasRuYaOLR5HcJJ4HlfYx7/8GsAln3wOueOZTAxLsloNnp2Ep8+YTRXHdywmpcffp+oqCgGDBhAUHAIaeu0GPS3SJw3g7YtmvHVV18BkLxrt0quU9wRDrdCFUI8DASZNtdLKX8pM6nuEJVwpyguhRXcs06ya9oxiO2/fouTxoVmnXty+vB+rl44x6QVuy2+hI+HBdO3eydatmzJzLkL8KhZi+e//R3h5ERa0kp+mf4St65fwbN+IyInTubU4TTq3++PbuYUqtepT/ATz9O8UxBv9/enx/CniZw42SKnbuZUdvz6Pxo3bEDqXmO5NXNzoOoNvTm+ZzvNmzZh88YNlqqxKrlO4Qil0bgIKeVPwE+lJpVCcQcUVUm1qN8lJycbVwgaDQEBAXw2bz4Hso7bLbudt9pqv2dfY/bw3gQ08GT3KXf8ej2Ki7s7YPQB+AcPIG33Bk6fPs2t61foEPGgxUfQJuwBju7ZDhl72LlnL/GzptE6NJL4mVO5cfkirUOMLUavnDlFleo1Sd+aZOOw3p+0kjrezYl5cKCxtpNWy/7MY4z5Mt6mh/WqVatsakA50mhIoSgIR6OeHgJmYKz5JEwfKaWsUYayKRQ2WE/yWl08Z6/eKFY/BevWnDdu3ERKSave/fnok2dwrVrdYuLJW3Avb5Kdi7s7bfoNxq95XZo1a8Zni77HO6Abf6WnUa+5H8nLFlOzTn1qdWxL9SNH2fbLNzRp34U2oZHI3FwOrF/F2MeGExwczKJlqzi4eS05er1lVRL+fCyzY0Lx8vZFGgzGYoI9wkhLXIlwcgL9LTp3Nr74FVYJVikGRWnhqEP6PWCwlNJTSllDSlldKQnF34l1me0lG5LJOnWO0Qt1hI9/k9ELdaRlHEWn0xU6hnll0Pvpl3B2c2f8d2s5m3WYXAn+IZFoXFzINRg4uHkdws2DuLg4DAYDgYGBZG5LxKDXk2swsG/dCnb8+j/i4uLw9/fnxsVzrJw9jezr19C+/zoenrV47n9riJjwFi/8sB7Peg3Rvm8Mpf3okd7kSsmC735kefxKbpw7hczNpVHr9rYFBYPDyUzZSsy7C+g3bhLOru7cunYV/fVrNqXDrWUD5axWlA2Omp5OSSnTylQShaIQrM0/CV/NwqtxM8vEKpycqN7Qm48++gigQDOU+e37r1J/cSsAACAASURBVPQ0WvQIJX1bEpdO/2nMYZj/IfqbN/l+0mgunf4T327BJGxZR1T0EJb+/BOt5n7OvCfDuXHzJkhJx8Ex7E9axajRY6lRr4FlNeLi5o7+1g2bSd8/JBxnV3d2x/9Eu/6D6T/uVQx6Pe8+0AEPz9r4BfUlLXEl37w4ghH//QaZm8v+pJU4u7oy96kHaNE9jAMbfifXYGBg3xAWLVpkub7IyEj8PpvLzKE9qVqnAdfO/kXHdm2Us1pRqji6otghhIgTQsQIIR4yf8pUMoXCCmsTS0O/dhzakmB5w//mxRGcSt+PoWmbQusZmd++G/j6c2hzAidSd9GiRyj+weF41ruPj4f14vyJLEtZjLFfxpO85w+eeuopxo0ZTbe2rZC5uUyMSyJy4mQmLE6get0G1G3W0qIYGrUO4MAG2xDaQ5vX0ci/A61DH8DFzQ0njYb0bUlU96rHCz8kWUpwnD2awXevPs2smDCuXTxPbo6e0KdfxNXDg37PvkqtunWJiYmxqwTdPKri3aELbh5Vy/ZBKO5JHFUUNYDrwACMPSoGAcoAqvjbsDax+AX1pUbd+swcHsz3k0Zz7lgmE+MSiZjwVqFmqMjISFr5NCFpwQfk3LrJ9l+/ZX/SKmRuLv94byE16jXEvbonBzevIyc7m+8njcbJ1Z3jLrV54Y3JJG7YiH9weJ6EuwjStySgv3kTAN+uwVw5d5qPhwWjmzmFT58Ix7NeQ3y7BpOaoKP+/caCyydSd+XrX9E6NIIbVy4RMeEtXtGmUNWzFqtnTcnXrc5cknzatGlMmTKFA1nHGbdoNRET3mLcotXszzxWpBnOegytVqtKeigKxeHw2PJCCDEEGIhRWX0hpVxV1G9UeOzdh7Ujulm3UI5sWUedqu54Vq9GrndbIia8ZfnuytnT6Nu8LrGxsXbH0el07Ny5k+zsbJb88itX9RJ9Tg5S5uIfEkH61iRj7SWDwdKxzqDX88ljfbh26RKvaJNvl+F4IpyrF88icCIg8iEObljNjWtXQTjh7OJCTnY27foN4sCmNdy4dJGqtevSskcoe1YtxdnVlRd+WG8Za1ZMGBET3sI/eIDlOhrrz+Pn52cJawUsobrenXuz45dvqdPcj5AnJ+AX1Bcnjcbm+gtqsmQ9Rtq65dRwd+GD994rtB2r4u6mNMqMlypCiIVCiNNCiD/y7I8QQhwQQqQLISYBSCl/lVKOAcZhTPRT3IOY23yay2x/8t47bNuymRdffJGs7UkOO3PNoaJvvfUW06dPZ9+e3Tz16MM4O2ssJqXnvo7nwsmj+HazLdfh13sAt65cZFZMGPGzp/HpyHA86zckIPxhbl27gsjcy1PDH0bq9XQYMIT/W7KRph26cmDjGhq2bEf0pBn0G/cqWbt3cP3Sea6dP8vMR0PQzZzCzEdDuHr+LL5dg22uY/jw4Tb9tM2+mqfmazmdcYjq9Rvi3aELv8+dwbcvjUR/8yYZWxNo164dS5cupVXr1jz9zwk2ZcbNIbXmMZw9qtOwxwCef/UNVYZcYZdyWVEIIYKBq8AiKWVb0z4NcBDoDxwHtgMxUspU0/EPgf9JKXcWNb5aUdw75F1pmDOPiwqVtWbatGmszThLuFWjoG9ffpIzmelM+H6dzYriyUceZN6i/xEQ9SiN/Dvg2zWYWTFh6G9ep6ZXHVr5NOH0qVMcO3uRAc+/ge7jf+Ps4mLK5E6gRt36nMk8zH2t2vHIv2dzcNMafpn2f3QJ7MDVGzc5e/VGoddhlrVph278PneGzYpnVkwYUn+Lju3aALDvcCbNu4eRvjUJz3r3EfPuAr4YPZCeHdpw0q0O3gHd840xf1QEc2a8rUJr70FKnHAnhJgopZwphAiSUpZaaXEpZZIQwifP7q5AupTyiOnci4FoIUQa8C6gc0RJKO4tzCsNS+bxQ28XO/M4MDCQhXGxGPSTLBPm6YxDVKlewzaH4cZV/v3vf5OyZy9p6+PJuXmDFf99CydnZ178eQsaZ2fmj4rggylvMu6f49G+/zpVqnvertz67CRmDg/GcO0yl48fYd2CD8jYmkBw715ol/4KUOR1mGXVuLjRokeobXRV8ACa5Fxg6NChvPDGZMYtWm1TqTZ9WxLNuoWSsPInclw9cHZ1zzeGysFQ2KPQFYUQYpeUMkAIsVNK2bFUT2xUFFqrFcVQIEJKOdq0PQLohnGVMRLjCmOXlHJuAeONBcYCNG3atFNWVlZpiquopDiSwZ13VXJg/SounT3NK8t2ciR5IyfSdrP950UMCOlF+/btadOmDdPf+Q/pmVk07dCN8yeyqFm/IY9/+DWrP32HxvrzbEjZy/1BA8jJvkXEhNsrlfhZUwnz8aJTp06WkhoDBgxg1apVDmWZm2VN3vMHTq7uNmXLzauBlJSUfCuk+NnT0Di7sksbx7VL56lSvRYIcKtaLV9v7jnvvU10dHTZPBBFhaXEPbOFEN8DnYGGwGHrQxgzs9vfgVA+OKAoTN31ioUyPSnAtkaTT9cQMrcl0sqniY05x6xItm/fzoEDBzh9+jReXl4sX72GWg0a06JnGIc2rePiqRN4VKtO2/7RpK5ZhnB2sfSlML+x9xnzMuu/+JBege044epFk3adWTl7OhMW3/7e7EdD+Pyj9y0TcV4Z0zetoaoGZrzztsUvkVfZDRgwAJ1Ox6uvv8G1HPAN6mtjqtLpdPn6es98NJRr589QxbM2DXxbkZmyFf3NG2hcXKlaqzatQyNJS1zJ9YtnCerRgxXLflNO7XuMEpuepJQxQogGwEpgcFkIZ8UJoInVdmPTPodR1WMV1uSt0WTQT+KTx/owZcoUYmNjLZPt1RyJXp+DlBL/kHA2bFhNtVp16PPMK5xK30e/ZyeRkbwRV49q9HvmX2hc3PIl1fl2C2XZu6/Qo2sXHnnkEV54YzINWwdy/dIFPn0i3KJwrl++WKiM/cZNYlZMGGMn/B8d5y9g6c8/Ef3QwxZFYl2uJCoqyq6pKm8S3pVTJ3FzknjWqY9nwyZcOHmMztH/IDVBx+Wzp7h85i9Slv+Id0BXzh3LZPO27Wi1WrWqUFgoMupJSvmXlLID8CdQ3fQ5KaUsbdvOdqCFEKKZEMIVeBT4rTgDSCmXSSnHenp6lrJoispA3tyA5OTkfHWQWgT1Z/bn8/Fu7suY8S9w8ZaBsGdexdnNnYlxiUROnMzz361DSgkylz6jX8K3azB7Vi3l3NEjpCWtomGrdvmS6tI3rmbCuLGWCbyVTxOWvzeJwIHD6PfsJFyreNDv2Ul0jBrO3r17LTLbq9XkHxJOu8hHSMs4yvTp0y2KpP9zr9PrqRfZvG07U6ZMAbD00LYX1mpOwqtSvTrVqtegtvf9XD5ziue+jidiwptMjEukeu26eNSoxavLU3jsvYX8c9FKqnjW5ocffvg7HpmikuBoUcAQYBGQidHs1EQIMVJKmVSSk5pMWqFAHSHEcWCylPILIcTzGFcvGmChlHJfMcdVK4pKzp1UhbU24SyMi6VOtSqcuXIdw7jbTupDW9YRMCiGbT99Tb3mfjRt14k/D+7LFwrbOjSCX9/5F1m7trJTG0eVGrXwrH8fK2dPw6WKB9cvnGXuiP4Ws097P18mT55skVW79FemTJnCF4uXEP78G/gHD8Cg17P203f4vwfftshtz5F+aPM6+o2bhCH7Jhs3bsSnawjCyYlvXxrJpdN/0uGBYXyxeAnbd6bYje4yt2y1OLOffY25I/pzbvt6uj78pO11hkWStXu7bZ2p3v1Zt/oXS3VdhcKh8FghRDLwDynlAdN2S+B7KWWnMpavRCgfReXEEZ9CQWi12nx2+fmjIvDycOPPi1doEdSfQ1vWcf3ieTQurlSvU5+Lfx4nJ/sWnYc8Ruq6FUyMS7xt0x8WTNXadTiTeQgXN3de/HmLTb8J/eULfPnFfPbt21dgjweDwcDAwdHsSjuIX3A4+9ev5sal8/Ts1pXlvy21+B+ioofwx6EMmvcII31LIp71G1pCWZ94OJpvfv6NXk+9yNr5HzoUymov3Hfl7GkcWLmEHFcPqyq5emYOD+bW9Wu8sizZyp8RAvpsFn42R0U/3UOURsKdi1lJAEgpDwIupSFcaSKEGCSEmHfp0qXyFkVRAqzt9cWpCgsFl9uOHhTF6JhH2KP7kZY9+2LQ63GvVgOfwG5UreWFRLLlxy9BwKcjw42JdE+Ec+3yBa5fukCnwTG4Va3O95NGk2swoHFxoU3YA+DsjIuLS4FmHzOdAwO4eu4MF/86QZuwB+jy0BPs3LvPUjZDp9PRvUtnRj4yhJObVqG/foV6zVrwxeiB+DdrSmxsLK18mrDs3Vfw7Wa/nHheCqoo+8mcOTSt58Ws4cbyInMe60ftxs1wr1bDmPg3aypzHuuHV+NmtO47yO7YinuT4hQFXCCECDV95gMV7pVd+SgqN4X1ViiKgibHjh07MnnyZLp36cz2n76mai0vo41+/Js893U81WrVwZB9i1yDgT5jXsa1igcte/XDo0ZNJny/jsiJkxn/3VounTrJgY1rLOarJh26FiiXwWCwZEV/tvBrAgfFcGT7BvatXY5Bnw3OLjw/8QUeGBTN+EmxJGSd53+/arm/RQvmz/6Yfr71mfnOVMaNGc2MGTMYN2Y0z48dTfqm3/Ndn70MdHNNq/mjjE2Q5o+KwL9ZUwYPHszWTRt5ZkQMe3RL6Pfsqzzx0Tf0e3YSt65dxcWtCgOef4N/zPiCzO1JqlS5woKjpic34J9AL9Ou9cCnUspbZShbiVGmp7KhpP4DRynIfORIpnBRGdoGg4G+ffsifdoROXEyuQYDBzauIfGrWVw/cYRregM16jSgZVBfkn/7jk6DY/K0IJ3C0T07yL5xjRp1G3Dx5FHG/GOYjV/CWo4/0jMsWdH26ka9N6gT7lWrMWHxbXPXJ4/1YXTMI8TGxtpEOmVuS8TPuzEA+zOPOZSBXlj7U3t1s7IvX8TNs1aJs9sVlZ8S51FUNqyc2WMOHTpU3uLcVdyJ/6C45yhpOY6iekMvXbqUZ158hX9+u8am70Rqgo7rly7gVrU6nvXu4+zRI1SpXsPGlj9reDBXz5+lWecgTh3ej5OThipV3C3ygdF0tnjxYhJ37LLJip4xMIDAgcOJnHi7cOHnTw+iafvO+fph79H9SPOmTTh/I5un5mtJ35bEidRd7NH9yNyPP8TV1bVUel/nvVfmpD/VV/ve5Z5RFGbUiqL0uZO3/eJQ1GR/p2MPHBzNjl17ca7iYZOR/PGwYCImvEmbsAfQ37zJuw90wLNOPfx6DyBjawJ1qlWhqrsbybv3EB37kaWt6fxREcx8Zypz5y9gf+YxcK2STwH875WnOHX4ABOtEu/++3APnF3dmGAnaW/Zu6/QIXIoZzLTuXT6T1r0CGV/0ipqumnYt2d3ke1e7VWLLcuVoOLuoMQJdwqFmeTkZJp27m3jP/DuEszOnTtLVVGYq7uWRbSNRqNh+W9LGTlyJMddaucJh43k1OE02oQ9gIu7O50GPUoTw0X8fLy4vNeNs1dvUK11V6qdOE3KssW0CY20+FCWLFliccIf3LyO3+fOwKDXWxTAX4fSuHL2FB8PC6ZN2AMc2rKOuj4tOJm6mzkxobTsHU761gQ86zXEPzicXbol/LF6Ke6etS3mqv7jJjF3RH9LH2972AsR9vvMWPHmQNbxYvUXVyisKXaZcSGEkxCiQvbLVlFPZYfBYCAtcaWNMzUtMZ6cnJxCf1PRmuNoNBoeffTRfKXJ0xJvNxUy6PUcTd5ATEwMHTt25PyNbJ5esBzvgO607TuIU4f3k7Z+tcWhLKW0OOH9gvriWe8+ZsWEGcuHDw9GOAlq39eInCsX2bU8jtqNfbhx7hQ9u3flaVNEVp8xL/P4h18jc3O5fCITdw35cjvu7xFGXFxcgffTXtTYvvRMUv5ILVEkmUJhxtGEu+8w9oMwYMygriGEmCmlfL8shSsuUsplwLLOnTuPKW9Z7jY0Gg1CCEs11UOb1yGEE87O9v8Xsvd2W1HeZCMjI2k193Pmj4rAu0swaYnxXL90gfhZU8natZX9CSvwrOKKwWBg165deHfubfFptOgRiot7FZa+8y+S6taldXNvS8kOc9JczLsLmDk0iORfv+XBt2biHxyOzM1l3pPhjBw6BFdXVwICxlrMQsm7drP+iw85/kcyGVsTaN3cm7FPT2HCa29ieO51NC4u6G/eZKc2jsN16nHcpbbd+2kvauz+nn3yJdSpCrGK4uKo6am1lPKyEOIxQAdMApKBCqUoFGVHp06dqPLDz/R++iVOHU6jz5iXSVrwAR072i8qbK/O0vxREWi1WjQaTbnay61Lk+/cuZOQpjEAHDhwgDXxP4JrFRr1GMALb0ymdhVXjp8+i7NHdRsz0JyYUEYOHWKpGeWsv8HMoT3xDxvIoU1r8HDV0Lb/47QJe4Bcg4GDm9fh5F6VjIwMvvrqK5trtlcmHWDeFwuZPyqCZt1C2ff7b1SpUdPKSW68nzqdjsjISGM29oEDpO/YRT+rTPTDm9aSffM6Br0e4eREWtJKUrRx9B43VmVeKxzG0fDYfUAA8B0wR0qZKITYbaoBVeFQzuzSp7gRSfayg+NnTuGv7eu4JZyLrOZa2oqksHHthbSaG/0sePoBcq5cwLfvEBsH9crZ0wjz8WLztu2kZRylekNvMnZsRH/rJr49wjhzaB9OLq6WCKuLp05Su1FTju3ehm8zHzZv3ICrq6tDMu/cuZO5n8+jRf8HC5TB3NZ0pzYOjxo18Q+NJGNrAq18jHU20zKOcvPmLUvhw6M71v9t915ROSgNZ/bnGOs87QaShBDewOXSEa/0ULWeyo7iNgiyV8Moda0WN4+qjFuky/dWHBUVVWbmqqLGNa9+7DX6ad49jAY3TrP6999wcatCo9YB+HYNJmNrAr0bR5OWcZQqXvU5fzyLzkMeJzVBx9Wzp/jndwl8OKQLM4cGoXGvQu1GTblw8hiBg2JITdDh69eK2R9/VGhWt9mxD2BwdiV9a5KNkzx94xqCGhoVnFn2vs+8yuzhvWmsP89LM26vTsx1p577do1N1NqUKVNwcXGhffv2fDZvvnJ6K+zikKKQUs4CZlntyhJChJWNSCVH+SjKluJEJFn7AcwrEM8qrjTu2bdAe3lB5irzZFbSt9yCxjUrKHu2/RY9wjiRtpsjW9ZxuVoVNK7G0uIrZ0/j5wtnua9ePRITE6l+X1POnzh62yz17CRm/aMPR5I30jFqOBdSksitm/87Hw/rzcgxz9C9S2dL3aeCSElJwT9sIKczDtl03Kvl7sziH36gec9wi+wu7u606TcYv+Z1bZ6Ti4sLLXv1zxe1Nvvz+QQMHMacBf+Xp8eG7T1S3Ns4FPUkhJgohKghjHwhhNgJ9Clj2RSVGPMKZM6Mt+nbvC5zZrzNB++9Z7fMhrlUhL0J2zyZrc04y/hJsURFD8FgMBQroqqo0iD2yn+kJa5kz4of8PJw48S5i0xYnGgp5+Fe3ROX+t5s372XAxt+p1bDJggnJ8vYrXr14/i+FDK3JxEdHc3xPTto0d225Wjr0EhyJWzaug2tVlvovQwMDCRrx3pi3l1Av3GTcHZ1R+pvMfTBIVy5lWNZaZhlT9+4Jl/5DfvXGE/UqzMIH/8m7SKG4td7QInKpyjufhwNj31KSnkZGADUAkZg7GOtUBSIeQViLpxn7tOQtwaR2TxS1GRmDu3UarVERQ9h/KTYfArEjLUi0ev1hSqovLWR5o7oTy13Z+bP/phWLVvkm0DbhA3kTOYhat3XhB6Pjub0kQN88+IIcg0Go4ktIZ4dvyyyFPVr7t2E1ASd7WS+JZHo196jimdtlixZUuh9NMv3xeiBHN29lfT18XRq3xYXFxf8wwbiWe8+S0HDWTFhVHXGck/zjmG+xk8e64MQTvgHhwPQqHVAvh4bGVsTaNeuXYULcVb8/TjqzN4jpWwvhJgJJEgpfxFCpEgpA8teRMdRJTwqPsWpQXRg/SoMhlwm/mCslwRGB665J3VBWeJ5fRIZWxO4delCobWMCpLr8ccf5/ctyTZZ3HMe60f2zeu8+NMmm3Ld9X39OX88E/2tm/Tv0YVFixah0WjIzs4mKDiEo6fO0iokwlJK/PEPv2blnOk0NVzkm2++KfZ9M7c8tZT6SNvNnhU/MH/2x3a701mPcfPmTeYt+h/tIx+hUesAmncK4sMhXfD0qmfpsWF2hJv9FmVRtkVRcbjjEh5CiC+BRkAzoAPGxkIJqh+ForSxnsyys7NZ9NNSxnxp24PB3JM6b7+Fvs3rEhsba7fciG0Og+OlQZYuXcqIp8dQvU4DWvQIJTVBh5OTM369+9lEIMXPmsrx1F30GD6apAUf8Ml779jY9g0GA5MnT+bjT+fyYOx/LbkVeXtoF/delaQ2lqVPxv5D+PUewIENv3P94jl6dO3Cc8+MZe/evQQEBGAwGHjhjcllXrZFUTEojainpzGGxx6RUl4XQngBo0pLQIXCjLXD3GAwsC15p6X387Wzf9GxXZt8CW4WU9JDxs5x9nwSzbuH4erqSmxsbLHkiYqKokfXLmzZvoPd8b9w/dI53Kt5cmDD7wwwJcMZ9Hr2rdPRwLcVaz77Dw1re6LX65k2bZqNA37KlCnsSNlFwufvcWzvDg5vWkuAf8sST7rFjUQzY+6AZ3ZcD3judeaO6M9zz4wlOjraorSmTZtWoG9HKYp7C0d9FBJoDUwwbVcF3MtEIkWZURFLajiCufezm0dVoOB+C4X5Ogrq3WCmsHsjhKCGV106RDxIvabNud+7CZdOneDjYcHoZk7l42HBXD79J0e2byDHkEvagYM8+/KkfP4Tc62pzz58l3731+OzD98tMuKpKPL6gRwZy54i9Q3qa9PLG0p2HxV3J46uKD4FcjFGOk0FrgA/AV3KSC5FKVORS2oUREG9n5966inGjRkNYDST5HmTtg7N9ekSTOparaUkh71s5MLujT0ZPnmsDy5VqhIx4U1jIcE+A9n+yzfUbNCY2o29OSVlgWGmGo3GotBSUlIs8v6dz8BejsuB9avo3fgRm/tjL8TZWiEr7h0cVRTdpJQdhRApAFLKC0KIwtNKFRWKonIJzFSk7Fy7JqQeYSxf9Sur128isG1ru2/kZpOMVqvl1dffwM2jKo179uWFNyYzd/6CfMqxsHtjN8ciqB9Zu3fQJuwB/IPDWTDuIUvnvISvZuHVuJnN9326hvDRRx8BMGDAAJumROWhsO3VuhLCiUU/LWX7zhSLLCU1bSnuPhw1PemFEBqMJiiEEHUxrjAUlQRH2oya36wLCzv9OykoXLZxm0CcPaoXmoNgnuhuCWfGLVpdaOXUwu6NPRkObfydCyez0N+8ybcvjeRMxiH8gyPQuLjQ0K8dh7Yk2Hw/NUHHaaeqjJ8US1BwCGkZR8u1mqtZATzxcDR7dEsIH/8mE39IYsyX8fxxKIORI0dazG8lMW0p7j4cVRSzgF+AekKIt4ENwDtlJlUJUWXGC8YRe7O9MtXlWZLa2hcRb/IFeDVpRsx/5vPc1/FF5iBYKwBzYT7h5kFcXJyN8ivs3tjzh7RrcT9VnDV8MKQr509kMeSND0jfavy9X1BfatStz8fDgomfNZWZw2/LPHqhjhPnLlK9oXe5J7ZpNBpcXFwIGDiMNmEP4KTRWFZsG1MPl/tLgqJi4ZCikFL+D3gF+A/wJzBESvljWQpWEqSUy6SUYz09PctblApHUQ5gcGzV8Xdind19ISWR+vf7MeK/31gmtVa9+xf6e7MCML/5/z53Bk3bdyZhe4rNJFjYvbGXYb5i2VKOZhwm0L8lfr364R8cbkl6Wznnbc4dy6BJnZo4Zf1BfV9/G5lb9urP8T3bK4SD2J6CTN+SSPDI8eX+kqCoWBSncdEhjKuK34BrQoimZSOSoiywN+HltYtXxCgXs+lj6tSpnM08hMzNtci2P3GlJVrJ3puvWQHMHt6b8yeyeO7reCInTmbcotU2k6BGo2Hpzz/xxMPROGX9wRMPR7P0558s98ae+cXV1ZWXX36ZozvWI3NzefzDr+kz5mWSf/ue7GtXqFe/PhMnTuTqn0dtZM7clkjzpoUr7L8LmxXbrKnMignDs35D/IL6lvtLgqJi4WjC3XhgMnAKY/MiAUgpZfuyFa9kqIS7klHSBK7inqMkznJzkti+9Ezu79mHtAQdN65comPUcLLslMy2/p259WnEhLcs+60T9PJGPTmagWwpT34og+Y9wiwZ1zHvLuCL0QMtvbSt72crnyY8M/ppfvrpJ4QQDB06tEjbf3Z2NtOnT2fjxo0EBQURGxtbZIlye7Lau+/m/XFxcaxK2sjzi5NwcXdXyXX3IKWRmZ2OMfLpXGkLVxYoRVFyCiuxURpjDxwcTcofqXh41ef6uVMFRi4VJltxJzV7mdrW3y/qeFEyjRw5ko2phwkeOR6/oL44aTQWRfTaa69Z7me7du1sSnk7opCys7Pxbu6LwcUd/5AI0hLj0ehvknUk3WFlUZAiXPrzT6xatYqUlBRLmfH9mcfK7CVBUbEpTFE4ano6BigPcSXHkYS7soxy0Wq1bNq6DWeP6ngHdC0ycqkg2Vq2bEnrvoNwcTfmfBZlJinMB2EwGFi8eDHeXYJL5Jsx9+Am+wYte4ThpNHYmOys76dGo+FA1vFiBQtMnz4dg4s7E+MSiZz4FhPjEjG4uDF9+vQiZTM/75EjR/JHeobNeVOPZBEUHGKJcHvhDWM5kpnvTC3QNKm4d3E0j+IIkCCEWA7cMu+UUv63TKRSlDoVIeHuxx9/xKOml01L0VkxYSxZsqRYtY7sJYxZl/DIS0H5AABR0UPYuXcfwsWN/s++5tB4eSkoMW3AgAFotVqLuSc5ObnYJTE2btyIf0iEzW/8QyLZtGlToTJZP29cq9C8e5jNGDUa+XAyK92qkZExd0Sj0RS7zIniAI4/iwAAFvdJREFU7sdRRXHU9HE1fRSVDEcT7soav179bCasVr37g+FiscZwJGPYnk0+b9MlrVbL/sxjPL84ie8njebTJ8Lx7R7Ckc3raNuimcMOZnuKyF5iXe0qrpy/ke2wggMICgpi7jeLGfDcbSWWlqhj3IiYQmWyft4HN6/j97kzbLrjHdu9jYCBw1QdJ4VDONrhbkpZC6IoWwoLff27JoZHHnmEZ158xaaY3oGklbz40fvFGqeojGFHV0/me+Li7s7jH37NgY1rSPp6NqFdA/nqq6+KtdLK2/3PrISsFfO8J8OpV6NqkSsP62uJjY1l/sKvmDk8GP+QSFITVpBz5RJOTk5otdoCfUjWz9svqC/bf17ErJgw/IMHkLktkfu9m5K13ba1anFWUYp7C4cUhRCiJfAy4GP9GyllmXe5E0I0B94APKWUQ8v6fHcrxTXXlAVRUVEEzJvP3BH9ub9nnzuqnlpYW9bCVk/mPg4pKSnoTffAMM54T1r2CCNx3gyGDx8OUODkbY+8Kxh7Zqbm3cMI8/GiY8eOha48rJWaq6srWUfSLVFPtT3cyK7aiMSjF/h6ScHmw7zPO+bdBcwe3psmORd4ecbt86o6TgpHcDTqaTcwF0jGGB4LgJQyuUQnFWIhEAWcllK2tdofAczE2O9igZTyXatjSxxVFCrqKT9/R+iro3KUVVSVmWnTprE242y+fhVhPl5s3rbdMimnb1rDlbOnqFa7Hi169bPck6U//2QzeRcVnWQvqshsZioqkqo4EVfF+a4jz/vveBaKykNp9KPIkVJ+VooyfQXMARaZd5hqSX0C9AeOA9uFEL9JKVNL8bz3LBWlwFthK4HSoqDVU+/G0TYrjX4mZ/rVi+c4sXElM9+bQVRUVLH9Ofa+X5CZKa8fpbCIq7znKo750JHn/Xc8C8XdgaOKYpkQ4jmMmdnWUU/nS3JSKWWSEMInz+6uQLqU8giAEGIxEA04pCiEEGOBsQBNm6qkcXtUxomhJAl6BTm7NRpNvonWPyQcZ1d30tfHWwoJFtefU1CjpLxmJnt+lOJEXJUk2ivv865I1YEVlQdH8yhGAv8CNmE0PyUDpW3baYQxX8PMcaCREMJLCDEXCBRCvFbQj6WU86SUnaWUnevWrVvKoinKg5JWs7UuVxLm48UTD0fTvUtnDAZD/kqwm9fRyL+DTd5EcUuZFPT9jh07FpiTYl6FPL84idqNvPn0iXB0M6cwd0T/An0FjtTrKov7qVA4GvXUrKwFKeTc54BxjnxXCDEIGOTr61u2Qin+Fu4kpNfcIOiTuZ9bfAcZWxO4dekCc0f0o3mPPpaSG75dg0mcN8PyZl7chj2Ffb+gN/iSRFzdqfmwooRIKyofDq0ohBAeQohYIcQ803YLIURp/591Amhitd3YtM9hVPXYu4s7rWabt2z6mC/jwd2DngFtObl5FfrrV6jXrAVfjB5oowgcKaBojfn7M9+ZSmP9eXoFtmPcmNGFvsFbr0L+v707j5KrLPM4/v3RJIBRohJwAUJAwhJGJCSAGGBYJAtGg8qIuBxFTQbUzMocGSeaYTgeD+Pg0YAQEhJwZhQZ0VEJRJZACDCIWRUwMkFAgVFZ1IgkEtI888e9rZWyurqq6966Vbd+n3Ny0nXr1q2n39NdT993ed6d+vo46NiTiOe3cOaZZ9b94G9l5XynVQe27tFo19NVwDbgTenjJ4Chawg0ZzUwXtL+6e557yapVNsw70dRLq1Ws631wXjQcVO5eeUqXnfgeBZf8gXefOCraiaC4XwgL1x8JXetv48nRu7B3/zTfI6dctyg+3u02o00HJ1YHdi6Q6OD2a+LiDMlnQUQEVskabhvKuka4ERgjKTHgfkRsUTSx4GbSKbHLo2IB5q5bkRcD1w/efLk2cONzbLT6sBpq3s21xr8fejelcz8xEXcueTiTMtV1OrW+dzMiXVXP7d7Fpr3wLbhajRRbJO0G3/cCvV1VMx+alZE1Kw/EBE3AjcO97oeo+gcWdSWarVPfuCD8UvvPZnxU07loXtXMnqv13LoCdN4/P61ma5Kr3X3su8bjmbT3bcOOqMp61loQyXmTpkibd2n0QV3pwLzgAnAzcAU4IMRsTLX6IbJC+6K10rp7iz19/dzwQUXcMkVi5n5iYs49IRpxIsvZh5Lre93YC3FU89uyX2R43D31DAb0PKCu4i4RdI64I0kmxb9dUQ8nWGMVjKdUFsKkr+i58+fz+p167lzycU8fv/aXLpcpk6dyu/P+egfajJtvGM5fS88z6q197JixYrc/4L3jCbLU6OzngTMACZFxDLgJZKOzjWyYfBgdufopIHTZmcxDcfNN9/MLqNfwbS5n2KXUaOYNvdTjNz95axYsSK3/T0qeUaT5anRMYrLgBeBk4F/AZ4FvgEclVNcw+LB7M7RaQOng40HZLVSef369ex/zIkcdtJpHHbSaQCZj4PU0wlFH628Gk0Ux0TEkZLWA0TEr9MprGY1dcPAaZabObX7g7o6wU2dOpWDL1+4Q2Xeww4c5xlNlolGE8ULadG+gVlPe5LcYXQUz3rqLMOZ1dPOWkRZ9uu38w6qVoI7+PKFRATbfr+Fn/5gNdt+vyXz97Xe1WiiWEBSEHAvSZ8BziCZBdVR3PXU3dq9XWuWA+7tvIOqleC+eMab2OUlo/irr9+9wywzD2ZbFhqd9fQVSWuBU0hmPZ0eERtzjcx6Trtn7mTdXdSu6ry1EtyoMa9mvzccVfgsMyunRmc9XUhSh+nqiLjUScLy0O6ZO0WU0ajU39/PsmXLuPDCC1m2bFnDVVxrzSh77ulf8JN7buuIWWZWPo0uuDsbOB44lmTG053Aqoj4dr7hNadijGL2pk2big7HmlTEIr2idnlrZYFcrd3rDhmX1NP88aOPFbqDoXWvegvuGkoUFRd6NfAukv2zXxERL8smxGx5ZXZ36pTtWtuh1aRYK8EB3trUhq3lRCHpSpLyHb8kuZu4C1gXEduzDDQrThTdq5P2cc5zBtZg+3qfcsCemRUqNGtGFntm70FS0fU3wK+Apzs1SVh365TtWvOegeUFctZNGp319HYASYcC04DbJfVFxD55BmfWjCzvAPKegdVpK9fN6mkoUaS72R0PnAC8HLiNpAuqo3jBXe/K+g4g76KG3bBy3WxAo11P00kSwxcj4v9yjKclXnDXu7K+A2hH11CndLOZDaXRrVCfi4hrK5OEpItyismsaVmvwejWNRZmeWg0UZxa45g7U61jZF3WvB2lyQcz0I029/x53PbI08w9fx4zZ53uZGGFqTs9VtK5wEeBA4CfVDz1MuDuiHhfvuENj6fHdo+sBqDLtAajU3YHtN7SyvTYrwLLgc8C51ccfzYifpVRfNZB8q7eWnn9ww8/nMsXLebBnz7e8gB0mQaHO2V3QLMBdRNFRGwGNgNnSToOGB8RV0kaI2n/iHikLVFaW+S9dqD6+pde+bdo5xHMvWZlJgPQZRkc9hoL6zSNTo+dD0wGDgauAkYC/wlMyS+05nl6bGvyXjtQff2+EbvwwvNb/ZdzFa+xsE7T6GD224G3Ac8BpLOfOq7OU0RcHxFzRo8eXXQoXSnv6q3V1997whE8eNetwxqALvOsoCIH0s1qaTRRbItk1Htgh7tR+YVkRcl65tBQ1z/w6BPY8ptnWPj+U5uagtoLs4IGutHmzZvHzJkznSSsUI0WBTwPGE8yTfazwIeAr0bEJfmGNzye9TQ8ec8cGqw89rlzZnPfffc1XATQs4LMstdyUcCI+DdJpwK/JRmn+HRE3JJhjNYB8p45VO/6s2bNavg6nhVk1l6NlvAgTQy3SBoDPJNfSFakvGcOZXF9zwoya6+6YxSS3ihppaRvSpoo6X7gfuCXkqa3J0SzHRVdXsOs1wx1R3Ep8ElgNEnF2BkR8T1JhwDXAN/NOT6zP9FKF1neCwrNymioEh4bIuKI9OuNEXFoxXPrI2Ji7gEmM6wuA7YBKyPiK0O9xoPZVksr+1SblV29weyhpse+WPH11qrnGt9s+08DWirpybQrq/L4dEkPSnpI0kDJkHcA10XEbJK1HGbDUrngb9rcT/GRpcvZ+MjPWL58edGhmXW0oRLFGyT9VtKzwOHp1wOPX9/C+15NssfFH0jqA75EUpV2AknZkAnAPsBj6WnlmSjfo4pcKJf3gkKzsqqbKCKiLyJ2j4iXRcTO6dcDj0cM900jYhXJ3tuVjgYeioiHI2Ib8DVgFvA4SbIYMl7rbEUvlMt7QaFZWTU8PbYN9uaPdw6QJIhjgAXApZLeAlw/2IslzQHmAIwdOzbHMG248q4lNRTXUDIbnk5KFDVFxHPA2Q2ct0jSz4G3jhw5clL+kVmzil4oV6ZS5Gbt1EldOU8A+1Y83ic91jAXBexsndD14xpKZs3rpDuK1cB4SfuTJIh3A+9p5gIuM97Z3PVj1p0aKgqY+ZtK1wAnAmOAXwLzI2KJpNOALwB9wNKIGFZNBq+j6FwDC942bNjQcBFAM8tfvXUUhSSKvDlRmJk1p5UFd11F0lslLdq8eXPRoZiZlUapEoUHs61IZd51z3pbqRKF7yisKEUvJjTLU6kShe8orCiuI2VlVqpEYVYU15GyMitVonDXkxWlExYTmuXF02PNMjAwRrHxkZ/tsJjQe11Yt6g3PbaTVmabdS3XkbIy8x2FmZl5wZ2ZmQ1fqRKFp8eamWWvVInCzMyy50RhZmZ1OVGYmVldpZoe642LrNMM7L+xfv16Jk6c6Cmz1pU8PdYsJwOL8H786GOMO/rPefT7d3DIuH29CM86khfcmRWgslBg34gR9L9wPovPns7y5cuZOXNm0eGZNcxjFGY5caFAKwsnCrOcuFCglYW7nsxyMmPGDA5ZeAWLz56+Q6HAGTNmFB2aWVOcKMxy4kKBVhalmvVUMT129qZNm4oOx8ysa/RMUUDXejIzy16pEoWZmWXPYxRmGfAKbCszJwqzFlWvwF567TwOWXiFV2BbaThRmLXIK7Ct7DxGYdaitWvXMnby8TuswN7vqBNYt25dwZGZZcOJwqxF/f39bLzjph1WYG+847ts37694MjMstHxXU+SDgD+CRgdEWcUHY9Ztb6+PiRx2QemMf7Yk9h0z+1IO7Hzzh3/62XWkFzvKCQtlfSkpPurjk+X9KCkhySdX+8aEfFwRHw4zzjNWjFp0iR2221XTp59HiN3ewknzz6PXXfdhSOPPLLo0MwykXfX09XA9MoDkvqALwEzgAnAWZImSHq9pGVV//bKOT6zls2YMYND9x/LnUsu5oWtW7hzycVMOGA/13Sy0sj13jgiVkkaV3X4aOChiHgYQNLXgFkR8VnAU0Ss67imk5VdEZ2oewOPVTx+HDhmsJMl7QF8Bpgo6R/ThFLrvDnAHICxY8dmF61ZA/r6+pg5c6anw1opdfxoW0Q8A5zTwHmLgEWQbIWad1xmZr2iiOmxTwD7VjzeJz3WMklvlbRo8+bNWVzOzMwoJlGsBsZL2l/SSODdwHeyuLCrx5qZZS/v6bHXAPcAB0t6XNKHI2I78HHgJmAj8F8R8UBG7+c7CjOzjJVq46IBkydPjjVr1hQdhplZ16i3cVEpE4WkzUCtLe5GA9W3G9XHxgBP5xRaLbViyvsajZxf75xmn3O7N35+2du9Vgx5v77Vdq/3/HDbHTrvZ36/iNiz5jMRUbp/wKJGj1cfA9Z0Qqx5XqOR8+ud0+xzbne3e5Zt3+52r/f8cNu9iLZvpd3LWhTw+iaOD3Zuu2Tx/s1eo5Hz653T7HNu98bPL3u7Q+sxtLvd6z3fE+1eyq6nVkhaE4P001l+3O7FcLsXp5vavqx3FK1YVHQAPcrtXgy3e3G6pu19R2FmZnX5jsLMzOpyojAzs7qcKMzMrC4nijokjZL0ZUmLJb236Hh6iaQDJC2RdF3RsfQSSaenP+/XSppadDy9QtKhkhZKuk7SuUXHU63nEkWT27O+A7guImYDb2t7sCXTTNuHt8DNTJPt/q305/0c4Mwi4i2LJtt9Y0ScA7wLmFJEvPX0XKKgie1ZSUqgD2yy1N/GGMvqahpve8vO1TTf7vPS5234rqaJdpf0NuAG4Mb2hjm0nksUEbEK+FXV4T9szxoR24CvAbNIdt/bJz2n59oqa022vWWkmXZX4iJgeUSsa3esZdLsz3tEfCciZgAd183tD79Ere1Z9wa+CbxT0uV0xhL8MqrZ9pL2kLSQdAvcYkIrtcF+5ucCbwbOkDTkzpLWtMF+3k+UtEDSFXTgHUXHb4VapIh4Dji76Dh6UTS4Ba5lKyIWAAuKjqPXRMRKYGXBYQzKdxSJ3LZntSG57Yvhdi9GV7a7E0Uit+1ZbUhu+2K43YvRle3ec4mi3duz2h+57Yvhdi9GmdrdRQHNzKyunrujMDOz5jhRmJlZXU4UZmZWlxOFmZnV5URhZmZ1OVGYmVldThTWlST1S9og6QFJP5D095I6+udZ0p6S7pW0XtLxGV/7UUljmnzNdZIOSL/+XY3n95T03axitO7lWk/WrbZGxBEAkvYCvgrsDsxv9cKS+iIij7LypwD3RcRHcrh2UyQdBvRFxMODnRMRT0n6uaQpEXF3G8OzDtPRf4GZNSIingTmAB9Py2T3SfqcpNWSfijpLwEk7STpMkk/lnSLpBslnZE+96ikiyStA/5C0lRJ90haJ+nrkl6anjdJ0h2S1kq6SdJrquORNE7Sbel7r5A0VtIRwL+SlPLeIGm3qtc8KumC9P3uk3RIevyVkr6VXut7kg5Pj+8h6eb0jupKQBXXep+k76fvc0W6B0K19wLfrhH7mPT7fkt66Ft0YNlray8nCiuF9C/jPmAv4MPA5og4CjgKmC1pf5IdC8eRbBjzfuDYqss8ExFHAreSbNzz5vTxGuDvJI0ALgHOiIhJwFLgMzXCuQT4ckQcDnwFWBARG4BPA9dGxBERsbXG655O3+9y4Lz02AXA+vRanwT+PT0+H7grIg4D/hsYC8mWmiQ7001J77j6qf1BPwVYW3lA0qtINs75dETckB5eA2TaTWbdx11PVkZTgcMH7haA0cB44Djg6xHxIvALSbdXve7a9P83kiSTuyUBjCSt2QP8GXBLerwP+HmN9z+WJCkB/AfJnUQjvpn+v7bi9ccB7wSIiNvSO4ndgRMGzomIGyT9Oj3/FGASsDqNcTfgyRrv9RrgqYrHI4AVwMci4o6K408Cr20wfispJworhXRQtp/kg03A3Ii4qeqc04a4zHMDpwK3RMRZVa9/PfBARFTfiWTl+fT/fob/uymSu5mhNnvaCuxa8Xg7SYKaBlQmil3Tc62HuevJup6kPYGFwKWRVLm8CTg37SpC0kGSRgF3k+xYuFPazXLiIJf8HjBF0oHp60dJOgh4ENhT0rHp8RHpoHC1/yEpHw1Jt8+dLXx7d6bXQNKJJN1TvwVWAe9Jj88AXpGev4Jkd7q90udeKWm/GtfdCBxY8TiADwGHSPpExfGDgPtbiN9KwHcU1q12k7SBpMtkO0kXz+fT564kGYtYp6T/5SngdOAbJF0zPyLZjnIdsLn6wulsnw8C10jaJT08LyL+N+3OWiBpNMnvzxeA6jLRc4GrJP1D+t6t7JL4z8BSST8EtgAfSI9fkMb3AEli+lka+48kzQNuTqcLvwB8DPhp1XVvIEmUt1Z83/2SzgK+I+nZiLgMOCk913qYy4xbT5H00oj4naQ9gO+TDPr+oui42i2ddXU7yfc/6FRgSauAWRHx68HOsfLzHYX1mmWSXk4yQH1hLyYJgIjYKmk+sDfp3Ui1tEvv804S5jsKMzOry4PZZmZWlxOFmZnV5URhZmZ1OVGYmVldThRmZlaXE4WZmdX1/+Uxvh2ok23bAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"### Problem 2"
],
"metadata": {
"id": "5-jURj8Q9Uug"
}
},
{
"cell_type": "code",
"source": [
"# Create an indexing vector of size N, (1,2,....N) \n",
"rand_idx = np.arange(1, len(k) + 1)\n",
"\n",
"# Shuffle the indices to create a randomly generated order of node removal\n",
"np.random.shuffle(rand_idx)\n",
"\n",
"# Random removal attack\n",
"rand_nic = attacks_core_size(G, rand_idx)\n",
"\n",
"# Removal attack by node degree\n",
"k_sorted_nic = attacks_core_size(G, np.argsort(k)[::-1] + 1)\n",
"\n",
"# Removal attack by node betweenness\n",
"bet_sorted_nic = attacks_core_size(G, np.argsort(bet)[::-1] + 1)"
],
"metadata": {
"id": "APcVeGrI9XMy"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"x = np.arange(len(adj) + 1)\n",
"# Using pyplot to plot the size of the Core as a function of the number of nodes \n",
"# being removed.\n",
"\n",
"#Plot info\n",
"plt.title('Robustness to Targetted Attack')\n",
"plt.xlabel(r'Number of nodes removed ($N_r$)')\n",
"plt.ylabel(r'Size of the Core ($N_c$)')\n",
"\n",
"#Plotting random removal attack\n",
"plt.plot(x, rand_nic, 'b-', label = 'Random')\n",
"\n",
"#Plotting removal attack by degree\n",
"plt.plot(x, k_sorted_nic, 'r-', label = 'By degree')\n",
"\n",
"#Plotting removal attack by distribution\n",
"plt.plot(x, bet_sorted_nic, 'c-', label = 'By betweenness')\n",
"plt.legend()\n",
"plt.savefig('2_robustness_to_targetted_attack.pdf')\n",
"plt.show()"
],
"metadata": {
"id": "s-h7Lfxt9adJ",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 299
},
"outputId": "057ab8b5-2b58-4a0a-c843-458c5007790f"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
}
]
}
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