Project_SIR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MONTE CARLO SIMULATION OF SIR MODEL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "from numba import jit, prange\n",
    "import networkx as nx\n",
    "from matplotlib.lines import Line2D\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from scipy import optimize, stats\n",
    "from pylab import *\n",
    "from scipy.ndimage import measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython = True)\n",
    "def init_lattice(L, perc):\n",
    "    '''\n",
    "    Returns an initial configuration of size N with N*perc initial infected chosen randomly\n",
    "    \n",
    "    INPUTs:\n",
    "    -size of the lattice\n",
    "    -percentage of initial infected\n",
    "    OUTPUTs:\n",
    "    -lattice\n",
    "    '''\n",
    "    N = L**2\n",
    "    lattice = np.full(N, 0)\n",
    "    initial_infected = int(N*perc)\n",
    "    for i in range(initial_infected): lattice[i] = 1\n",
    "    np.random.shuffle(lattice)\n",
    "    return lattice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_lattice(lattice, nodesize = 100):\n",
    "    '''\n",
    "    Plot a configuration\n",
    "    '''\n",
    "    fig = plt.figure(figsize = (6, 6))\n",
    "    N = len(lattice)\n",
    "    L = int(np.sqrt(N))\n",
    "    #L = lattice.shape[0]\n",
    "    G = nx.grid_2d_graph(L, L)\n",
    "    pos = dict( (n, n) for n in G.nodes() )\n",
    "    colors = np.full(N, [\"blue\"])\n",
    "    #print(pos)\n",
    "    for i in range(N):\n",
    "        if lattice[i] == 1: colors[i] = \"red\"\n",
    "        elif lattice[i] == 2: colors[i] = \"grey\"\n",
    "    \n",
    "    colors = (colors.reshape(L, L).T).reshape(-1, N)[0]\n",
    "    legend_elements = [Line2D([0], [0], marker = \"o\", color=\"w\",label=\"Scatter\",\n",
    "                                 markerfacecolor = \"blue\", markersize = 14),\n",
    "                           Line2D([0], [0], marker=\"o\", color=\"w\", label=\"Scatter\",\n",
    "                                  markerfacecolor= \"red\", markersize=14),\n",
    "                      Line2D([0], [0], marker=\"o\", color=\"w\", label=\"Scatter\",\n",
    "                                  markerfacecolor= \"gray\", markersize=14)]\n",
    "    \n",
    "    nx.draw_networkx(G, pos = pos, with_labels = False, labels = None,\n",
    "                         node_color = colors, node_size = nodesize)\n",
    "    plt.title(\"Example of initial state\", weight = \"bold\", size = 16)\n",
    "    plt.axis('off')\n",
    "    plt.gca().invert_yaxis()\n",
    "    #plt.gca().invert_xaxis()\n",
    "    plt.legend(legend_elements, [\"Healthy\", \"Infected\", \"Recovered\"], bbox_to_anchor=(1, 1), loc=\"upper left\", fontsize = 14)\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = init_lattice(20, 1/400)\n",
    "plot_lattice(a, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython = True)\n",
    "def build_I(lattice):\n",
    "    '''\n",
    "    Returns a list with the positions of the infected nodes\n",
    "    \n",
    "    INPUT:\n",
    "    -lattice\n",
    "    OUTPUT:\n",
    "    -a list with positions\n",
    "    '''\n",
    "    N = len(lattice)\n",
    "    I = np.array([2*N], dtype = np.int64)\n",
    "    for n in prange(N):\n",
    "        if lattice[n] == 1: I = np.append(I, n)\n",
    "    return I\n",
    "\n",
    "\n",
    "@jit(nopython = True)\n",
    "def SIR(L, I, R, rec_rate):\n",
    "    '''\n",
    "    Performs N_infected trials of infections/recovery\n",
    "    \n",
    "    INPUTs:\n",
    "    -lattice linear size\n",
    "    -list of initial infected\n",
    "    -list of initial recovered\n",
    "    -recovery rate\n",
    "    \n",
    "    OUTPUTs:\n",
    "    -new list of infected\n",
    "    -new list of recovered\n",
    "    '''\n",
    "    N = L**2\n",
    "    c = rec_rate#/(rec_rate + inf_rate)\n",
    "    n_infected = len(I)-1 #get number of initial infected\n",
    "    n_recovered = len(R) - 1 #get number of initial recovered\n",
    "    \n",
    "    if (len(I)-1) > 0: #check if there is at least one infected\n",
    "        for j in prange(n_infected): #repeat n_infected times\n",
    "       \n",
    "            #get random infected\n",
    "            i = np.random.randint(1, len(I))\n",
    "            random_site = I[i]\n",
    "            \n",
    "            #recover with prob. c\n",
    "            if np.random.uniform(0., 1.) < c:\n",
    "                #idx = I.index(random_site)\n",
    "                I[i] = I[-1]\n",
    "                I = I[:-1]\n",
    "                R = np.append(R, random_site)\n",
    "                #n_infected -= 1\n",
    "            else:\n",
    "                #get a random neighbor\n",
    "                nbrs = [(random_site-1)%N, (random_site+1)%N, (random_site+L)%N, (random_site-L)%N]\n",
    "                j = np.random.randint(0, 4)\n",
    "                random_nbr = nbrs[j]\n",
    "                #try to infect it if it is susceptible\n",
    "                if np.any(R == random_nbr)==False and np.any(I == random_nbr)==False:\n",
    "                    \n",
    "                    I = np.append(I, random_nbr)\n",
    "                    \n",
    "\n",
    "    return I, R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython = True)\n",
    "def trajectory(L, perc, nsteps, rec_rate):\n",
    "    '''\n",
    "    Simulates a \"trajectory\": at each step the lattice is modified\n",
    "    \n",
    "    INPUTs:\n",
    "    -the linear size of the lattice\n",
    "    -the percentage of initial infected\n",
    "    -the number of steps to do\n",
    "    -recovery rate\n",
    "    \n",
    "    OUTPUTs:\n",
    "    -a vector with the number of the susceptible nodes at each step, including the initial value\n",
    "    -a vector with the number of the infected nodes at each step, including the initial value\n",
    "    -a vector with the number of the recovered nodes at each step, including the initial value\n",
    "    '''\n",
    "    N = L**2\n",
    "   \n",
    "    lattice = init_lattice(L, perc)\n",
    "    I = build_I(lattice)\n",
    "    R = np.array([2*N], dtype = np.int64)\n",
    "    infected = np.zeros(nsteps +1)\n",
    "    infected[0] = 1\n",
    "    sus = np.zeros(nsteps +1)\n",
    "    sus[0] = N-1\n",
    "    rec = np.zeros(nsteps +1)\n",
    "    rec[0] = 0\n",
    "\n",
    "\n",
    "    for i in prange(nsteps+1):\n",
    "        I, R = SIR(L, I, R, rec_rate)\n",
    "        rec[i+1] = len(R) - 1\n",
    "        infected[i+1] = len(I) - 1\n",
    "        rec[i+1] = len(R) - 1\n",
    "        sus[i+1] = N - rec[i+1] - infected[i+1]\n",
    "        if (len(I)-1) == 0:\n",
    "            sus[i+2:] = (N -(len(R)-1))\n",
    "            rec[i+2:] = (len(R)-1)\n",
    "            break   \n",
    "    return sus, infected, rec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n",
    "@jit(nopython = True)\n",
    "def simulate(L, perc, ntraj, nsteps, rec_rate):\n",
    "    \n",
    "    trajectories = np.zeros((ntraj, nsteps + 1))\n",
    "    for i in prange(ntraj):\n",
    "        #tr = trajectory(L, perc, nsteps, rec_rate, surv_prob, dist_sq)\n",
    "        #trajectories[i][:len(tr)] = tr\n",
    "        #trajectories[len(tr):] = tr[-1]\n",
    "        trajectories[i] = trajectory(L, perc, nsteps, rec_rate)\n",
    "    #trajectories = np.mean(trajectories, axis = 0)\n",
    "    return trajectories"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot one simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 20\n",
    "N = L**2\n",
    "s, i, r = trajectory(L, 1/N, 100, 0.05) #start with one infected node"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(s, c = \"blue\", marker = \".\", linestyle = \"None\", label = \"Susceptible\", markersize = 3)\n",
    "plt.plot(i, c = \"red\", marker = \".\", linestyle = \"None\", label = \"Infected\", markersize = 3)\n",
    "plt.plot(r, c = \"green\", marker = \".\", linestyle = \"None\", label = \"Recovered\", markersize = 3)\n",
    "plt.xlabel(\"t (MC steps)\", size = 12)\n",
    "plt.ylabel(\"counts\", size = 12)\n",
    "plt.legend(fontsize = 12, markerscale = 2)\n",
    "plt.grid(alpha = 0.5, linestyle = \"--\")\n",
    "fig.savefig(\"presentazione/Images/sir/example.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis of cluster size distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython = True)\n",
    "def cluster(L, perc, rec_rate):\n",
    "    '''\n",
    "    Returns the number of recovered nodes when the absorbing phase is reached\n",
    "    \n",
    "    INPUTs:\n",
    "    -linear size of the lattice\n",
    "    -percentage of initial infected\n",
    "    -recovery rate\n",
    "    \n",
    "    OUTPUTs:\n",
    "    -the number of recovered nodes once the absorbing phase is reached\n",
    "    '''\n",
    "    N = L**2\n",
    "    lattice = init_lattice(L, perc)\n",
    "    I = build_I(lattice)\n",
    "    R = np.array([2*N], dtype = np.int64) #put a dummy first element to be able to work with numba (numba has problems with empty lists)\n",
    "    \n",
    "    while (len(I) - 1)>0: #repeat till absorbing phase\n",
    "        I, R = SIR(L, I, R, rec_rate)\n",
    "    cluster_size = len(R)-1\n",
    "    return cluster_size\n",
    "\n",
    "@jit(nopython = True)\n",
    "def cluster_dist(L, perc, ntraj, rec_rate):\n",
    "    '''\n",
    "    Returns the distribution of the cluster size after simulating many times\n",
    "    \n",
    "    INPUTs:\n",
    "    -linear size of the lattice\n",
    "    -percentage of initial infected\n",
    "    -number of simulations to do\n",
    "    -recovery rate\n",
    "    '''\n",
    "    sizes = np.zeros(ntraj)\n",
    "    for i in prange(len(sizes)):\n",
    "        sizes[i] = cluster(L, perc, rec_rate)\n",
    "    return sizes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Critical point and $\\theta$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 40\n",
    "N = L**2\n",
    "sizes_smaller = cluster_dist(L, 1/N, 10**4, 0.16)\n",
    "sizes_mid = cluster_dist(L, 1/N, 10**4, 0.18)\n",
    "sizes_g = cluster_dist(L, 1/N, 10**4, 0.19)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = np.linspace(0, 500, 50)\n",
    "\n",
    "P_smaller = np.zeros(len(s))\n",
    "P_mid = np.zeros(len(s))\n",
    "P_g = np.zeros(len(s))\n",
    "\n",
    "for i in prange(len(s)):\n",
    "    size = s[i]\n",
    "    P_smaller[i] = len(sizes_smaller[sizes_smaller >= size])/len(sizes_smaller)\n",
    "    P_mid[i] = len(sizes_mid[sizes_mid >= size])/len(sizes_mid)\n",
    "    P_g[i] = len(sizes_g[sizes_g >= size])/len(sizes_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tau = 187/91\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(s, P_smaller, marker = \".\", linestyle = \"None\", markersize = 3,\n",
    "         c = \"black\", label = \"c = 0.16\")\n",
    "plt.plot(s, P_mid, marker = \".\", linestyle = \"None\", markersize = 3,\n",
    "         c = \"red\", label = \"c = 0.18\")\n",
    "plt.plot(s, P_g, marker = \".\", linestyle = \"None\", markersize = 3,\n",
    "         c = \"blue\", label = \"c = 0.19\")\n",
    "\n",
    "\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"s\", size = 12)\n",
    "plt.ylabel(r\"$P_{\\geq s}$\", size = 12)\n",
    "plt.legend(markerscale = 3, fontsize =12)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/sir/P.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#@jit(nopython = True)\n",
    "def find_critical_point(L, perc, ntraj, lower, upper, nintervals):\n",
    "    \n",
    "    rates = np.linspace(lower, upper, nintervals)\n",
    "    taus, r_sq = np.zeros(len(rates)), np.zeros(len(rates))\n",
    "    s = np.linspace(0, 100, 50)\n",
    "    P = np.zeros(len(s))\n",
    "    \n",
    "    for i in prange(len(rates)):\n",
    "        sizes = cluster_dist(L, perc, ntraj, rates[i])\n",
    "        for j in prange(len(s)):\n",
    "            size = s[j]\n",
    "            P[j] = len(sizes[sizes >= size])/len(sizes)\n",
    "        x_range = np.log(s[1:])\n",
    "        x_range = x_range.reshape(-1,1)\n",
    "        y_range = np.log(P[1:])\n",
    "        model = LinearRegression()\n",
    "        model.fit(x_range, y_range)\n",
    "        r_sq[i] = model.score(x_range, y_range)\n",
    "        taus[i] = 2 - model.coef_\n",
    "    return rates, r_sq, taus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 0.175\n",
      "Relative R_squared: 0.9995746379413813\n",
      "Estimated tau expontnet: 2.053032593211227\n",
      "[0.99415258 0.99891413 0.99957464 0.99940995 0.99804276]\n",
      "CPU times: user 1min 8s, sys: 1.17 s, total: 1min 9s\n",
      "Wall time: 1min 14s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "L = 20\n",
    "N = L**2\n",
    "a, b, c = find_critical_point(L, 1/N, 10000, 0.17, 0.18, 5)\n",
    "\n",
    "\n",
    "i_10 = np.argmax(b)\n",
    "print(\"Estimated critical point:\",  a[i_10])\n",
    "print(\"Relative R_squared:\", b[i_10])\n",
    "print(\"Estimated tau expontnet:\", c[i_10])\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.17  , 0.1725, 0.175 , 0.1775, 0.18  ])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(0.17, 0.18, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Restricted set of $c_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 0.1765\n",
      "Relative R_squared: 0.9996109431356418\n",
      "Estimated tau expontnet: 2.0538093654052614\n",
      "[0.99955075 0.99791148 0.99937274 0.99961094 0.99906362]\n",
      "CPU times: user 1min 4s, sys: 367 ms, total: 1min 5s\n",
      "Wall time: 1min 6s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "L = 20\n",
    "N = L**2\n",
    "a, b, c = find_critical_point(L, 1/N, 10000, 0.175, 0.177, 5)\n",
    "\n",
    "\n",
    "i_10 = np.argmax(b)\n",
    "print(\"Estimated critical point:\",  a[i_10])\n",
    "print(\"Relative R_squared:\", b[i_10])\n",
    "print(\"Estimated tau expontnet:\", c[i_10])\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.175 , 0.1755, 0.176 , 0.1765, 0.177 ])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(0.175, 0.177, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 0.175\n",
      "Relative R_squared: 0.9995529562644712\n",
      "Estimated tau expontnet: 2.053540820931104\n",
      "[0.99663997 0.99953313 0.99955296 0.99840256 0.99693779]\n",
      "CPU times: user 2min 40s, sys: 1.13 s, total: 2min 41s\n",
      "Wall time: 2min 43s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "L = 30\n",
    "N = L**2\n",
    "a, b, c = find_critical_point(L, 1/N, 10000, 0.17, 0.18, 5)\n",
    "\n",
    "\n",
    "i_10 = np.argmax(b)\n",
    "print(\"Estimated critical point:\",  a[i_10])\n",
    "print(\"Relative R_squared:\", b[i_10])\n",
    "print(\"Estimated tau expontnet:\", c[i_10])\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.17  , 0.1725, 0.175 , 0.1775, 0.18  ])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(0.17, 0.18, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 0.175\n",
      "Relative R_squared: 0.9985309797035988\n",
      "Estimated tau expontnet: 2.0529571391728005\n",
      "[0.9926917  0.99845196 0.99853098 0.99824852 0.9977888 ]\n",
      "CPU times: user 10min 33s, sys: 3.61 s, total: 10min 36s\n",
      "Wall time: 10min 46s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "L = 50\n",
    "N = L**2\n",
    "a, b, c = find_critical_point(L, 1/N, 10000, 0.17, 0.18, 5)\n",
    "\n",
    "i_10 = np.argmax(b)\n",
    "print(\"Estimated critical point:\",  a[i_10])\n",
    "print(\"Relative R_squared:\", b[i_10])\n",
    "print(\"Estimated tau expontnet:\", c[i_10])\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "sizes = cluster_dist(20, 1/400, 10**4, 0.1765)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = np.linspace(1, 100, 50)\n",
    "P = np.zeros(len(s))\n",
    "for i in prange(len(s)):\n",
    "    size = s[i]\n",
    "    P[i] = len(sizes[sizes >= size])/len(sizes)\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9997860460043879\n",
      "[2.0591334]\n"
     ]
    }
   ],
   "source": [
    "x_range = np.log(s[2:])\n",
    "x_range = x_range.reshape(-1,1)\n",
    "y_range = np.log(P_mid[2:])\n",
    "model = LinearRegression()\n",
    "model.fit(x_range, y_range)\n",
    "print(model.score(x_range, y_range))\n",
    "print(2 - model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(s, P, marker = \".\", linestyle = \"None\", markersize = 3,\n",
    "         c = \"blue\", label = \"c = 0.1765\")\n",
    "plt.plot(s[2:], s[2:]**(model.coef_)*np.exp(model.intercept_),\n",
    "         c = \"red\", linestyle = \"--\", linewidth = 1.5,\n",
    "         label = \"regression line: 2-τ (slope) = {}\".format(round(model.coef_[0],3)))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"s\", size = 12)\n",
    "plt.ylabel(r\"$P_{\\geq s}$\", size = 12)\n",
    "plt.legend(markerscale = 3, fontsize =12)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/sir/p_crit.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\gamma/\\nu_\\perp$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3min 1s, sys: 1.56 s, total: 3min 2s\n",
      "Wall time: 3min 8s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "ntraj = 10**3\n",
    "Ls = np.arange(10, 80, 5)\n",
    "S = np.zeros(len(Ls))\n",
    "\n",
    "for i in range(len(Ls)):\n",
    "    Ni = Ls[i]**2\n",
    "    s = cluster_dist(Ls[i], 1/Ni, ntraj, 0.1765)\n",
    "    s = np.mean(s)\n",
    "    S[i] = s\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9997801301274715\n",
      "[1.79657088]\n"
     ]
    }
   ],
   "source": [
    "x_range = np.log(Ls[:])\n",
    "x_range = x_range.reshape(-1,1)\n",
    "y_range = np.log(S[:])\n",
    "model = LinearRegression()\n",
    "model.fit(x_range, y_range)\n",
    "print(model.score(x_range, y_range))\n",
    "print(model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(Ls, S, marker = \"o\", linestyle = \"None\", c = \"blue\", mfc = \"None\")\n",
    "plt.plot(Ls, Ls**model.coef_*np.exp(model.intercept_), c = \"red\",\n",
    "         linestyle = \"--\", linewidth = 1,\n",
    "         label = r\"$\\gamma/\\nu_\\perp$ (slope) = {}\".format(round(model.coef_[0], 3)))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"L\", size = 12)\n",
    "plt.ylabel(r\"$\\langle S(L) \\rangle$\", size = 12)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(fontsize = 12)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/sir/S.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\nu_\\perp$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 18min 3s, sys: 7.04 s, total: 18min 10s\n",
      "Wall time: 18min 30s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "gam_nu = model.coef_\n",
    "rates = np.linspace(0.1, 0.3, 20)\n",
    "ntraj = 3*10**3\n",
    "\n",
    "L1, L2, L3 = 20, 30, 50\n",
    "y1, y2, y3 = np.zeros(len(rates)), np.zeros(len(rates)), np.zeros(len(rates))\n",
    "\n",
    "for i in prange(len(rates)):\n",
    "    c = rates[i]\n",
    "    S1 = cluster_dist(L1, 1/(L1**2), ntraj, c)\n",
    "    S1 = np.mean(S1)\n",
    "    y1[i] = S1*L1**(-gam_nu)\n",
    "    \n",
    "    S2 = cluster_dist(L2, 1/(L2**2), ntraj, c)\n",
    "    S2 = np.mean(S2)\n",
    "    y2[i] = S2*L2**(-gam_nu)\n",
    "    \n",
    "    S3 = cluster_dist(L3, 1/(L3**2), ntraj, c)\n",
    "    S3 = np.mean(S3)\n",
    "    y3[i] = S3*L3**(-gam_nu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v_perp = 1.33\n",
    "x1 = (rates - 0.1765)*(L1**(1/v_perp))\n",
    "x2 = (rates - 0.1765)*(L2**(1/v_perp))\n",
    "x3 = (rates - 0.1765)*(L3**(1/v_perp))\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x1, y1, c = \"blue\", marker = \"o\", linestyle = \"None\",\n",
    "         mfc = \"None\", markersize = 5, label = \"L = 20\")\n",
    "plt.plot(x2, y2, c = \"red\", marker = \"s\", linestyle = \"None\",\n",
    "         mfc = \"None\", markersize = 5, label = \"L = 30\")\n",
    "plt.plot(x3, y3, c = \"limegreen\", marker = \"^\", linestyle = \"None\",\n",
    "         mfc =\"None\", markersize = 5, label = \"L = 50\")\n",
    "plt.ylabel(r\"$SL^{\\gamma/\\nu_\\perp}$\", size = 12)\n",
    "plt.xlabel(r\"$(c-c_c)L^{1/\\nu_\\perp}$\", size = 12)\n",
    "plt.grid(alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(fontsize = 12)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/sir/nuperp_133.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v_perp = 0.7\n",
    "x1 = (rates - 0.1765)*(L1**(1/v_perp))\n",
    "x2 = (rates - 0.1765)*(L2**(1/v_perp))\n",
    "x3 = (rates - 0.1765)*(L3**(1/v_perp))\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x1, y1, c = \"blue\", marker = \"o\", linestyle = \"None\",\n",
    "         mfc = \"None\", markersize = 5, label = \"L = 20\")\n",
    "plt.plot(x2, y2, c = \"red\", marker = \"s\", linestyle = \"None\",\n",
    "         mfc = \"None\", markersize = 5, label = \"L = 30\")\n",
    "plt.plot(x3, y3, c = \"limegreen\", marker = \"^\", linestyle = \"None\",\n",
    "         mfc =\"None\", markersize = 5, label = \"L = 50\")\n",
    "plt.ylabel(r\"$SL^{\\gamma/\\nu_\\perp}$\", size = 12)\n",
    "plt.xlabel(r\"$(c-c_c)L^{1/\\nu_\\perp}$\", size = 12)\n",
    "plt.grid(alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(fontsize = 12)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/sir/nuperp_07.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PgIqKChobGzPGNba1tdHX18f4+DgAjY2NjI+PMzIyAkBNTQ39/f2UlZX5fp5KSko4ePAgg4ODRKNRqquricViABnnKTmoP/08AaxZs4aZmRkGBwcBp+pvVVVV3ucJnJECw8PDqbvic50ncPoek/Psy8rKmJmZSR2jtLSUkpKSVP9kSUkJZWVlqfZMvm8u73Hs2DFCoRAlJSWEQqGM5Nnl5eVMTk6mvGa/R3J2V7L9Zr+HiBAOhxf0HjMzM1RUVLi+RzgcJh6Ppz7b7PdIb594PE5PT88J58kVVfXlAbQBL2ZZVwVUJn6+GPht4uf3A3enbXcV8JX5jrVp0yZVVX399dfVJOb0iUZn97jqkfqobtum+vDDqvF4kX18xPq4M5/PSy+9VBwRVR0fHy/asXKh0D7Z2hJ4XrPEHSNHC6jqqKqOJX5+FCgTkTqcK9XWtE0jOFe2S4e0aYfTceU9lyrviHRw9CjccgtcdhkYlIDeYskbL8u8ANxzzz2UlpZmJHl58sknU+sDWeZFRBol0SMtIptxPAeBnwNvEpF1IhIGrgB+kOv7Rl0ST/jBfD67dkF3Nzz3HNx6q/MciznLF0ouCbYXW/sUG+uTHRP6ONNJ+rztbW/LSPJyflqC+iVZ5kVEvgP8F3CaiMRE5GMicq2IXJvY5H3Ai4k+1y8DVySuwuPA9cBjwMvAv6nTF5sTyb43U5jPp70dLrgAEt2OlJXBhRfCnj0LP1YuCbYXW/sUm6D5LKTixWJLarNky7yo6pWq2qSqZaoaUdV/UdU7VfXOxPp/UtU3q+rZqvpWVX02bd9HVfVUVT1FVbNnZZiD5A0YU5jPZ8MGePxxSI6HnpqCxx6D9euPbzM9DY88Atu3O89zdRloWxs7nvkCt12zm30v/pBntqyac2LCYmufYhM0n4VUvPAyWXY+ZV6SPu3t7dTV1XHqqaeyffv2VNC1ZV4Cztat0NIC554LN93kPEciznJwAulllzl9sW59su2rByk5/Qw2P3eIG86/i9vvehcTvfuL/4Esiwb1sOLFQsmnzAvAO9/5Tl588UX6+/vZsWMH3/nOd7j99tsBW+al4DQ0NPitkMF8PqWl8NBDsG0brFjhPD/0kLMccu+TffDyuhMTbF914rEXW/sUmyD5LLTiRXLInCmUlZXxhje8gXXr1lFSUsJZZ53FZz7zGb773e8CtsxLwUkfe2cCufiUlsIll8DNNzvP6cl+cu2T3b+2/MQE25tP/CVajO1TTILks9CKF152C+RT5mUuHxFJjXEtRpkXkycRFJzh4eETvgr4ycn6bNjgdAVs2+YE1mSf7LZtmdvd+5FXnOFd6WySxBSLwvkUGuvjjpc++yf2s2t4V0Z/6+Hpw1zddPWc209PT+dV6iVZ5iVJKBQ64X2SZV4WwvT0NE888QQbN26koaGBX//612zfvp33v//9QGaZl7vvvps9e/bw/e9/n2effXaed86dQAXXpcbWrXDXXU5f7IUXOoE1vU82RbLEzOxlFksWvKx4kc7FF1+c8frTn/40n/vc5wry3j/+8Y/5kz/5E8bGxmhoaOBDH/oQn/rUp1Lrv/a1r/HRj36U+vp6amtrC17mRXT2Fc0S5JxzztHnn3+ekZERqqur/dZJUQif6Wmnj3XPHmcUwdatmV0HxfYpJNbHnfl8Xn75Zc4444yiuMTj8byLFHpBoX2ytaWI7FbVc+bax5zWKAIVFRV+K2RQCJ9kn+wll5jhU0isjzsm+ZiQnDodE3z8NygiyUQiplAMn1zGwRbTZyFYH3dM8jEhOXU6JvgEKrgGjVzHwVoslsITqOBq0tco8N5nobkJ5vJZyBTIQhO087VQTPIx4Wt4Oib4+G9QRBobG/1WyMBrn4XmJpjLZyFTIAtN0M7XQsnFx8vxp+mYOImgUOR70z9QwTU9WbMJeO2TS24CNx+/p0AG7XwtlPl8VqxYQXd3d0aCaK9IT7BtAoXyUVUGBwfz+pYQqNECQSPncbBZmGsK5Dkrz6G8xJzaTZbsRCIRBgYG6Ozs9Dxr1VIeilVRUUEkElnwfua0hqXgJHMTJMfBbtu2sHGws6dAPjjwIPcduC/rLB2LWZSUlFBfX099fb3nx+ro6KBtrhLwPmGCT6AmEVgWxod//WH2Hs1MwbapchN3nXqXT0YWi1nYSQQJ+vr6jLopYZrPdGsrpYnCewD3gjNN1qe+RtPax/pkxyQXMMMnUDe00hNEmIApPsmJBqWxGI887NTuSpVHTFRb9QNT2ieJ9cmOSS5ghk+ggqvlRNInGoCdaGCxFIpABVe/vybMxgSf9IkGcHJFEAuNCe2TjvXJjkkuYIZPoIKrCV8V0jHBp5BFEAuNCe2TjvXJjkkuYIZPoILryMiI3woZmOCTPtEg3tICItx6m3Dz34qTA9bHvK8mtE861ic7JrmAGT6BCq6WE0kvgvg/3vMiGzco77k07aaWYbOSLJbFQqCGYtXU1PitkIEJPukTDZ57rmLBEw28xIT2Scf6ZMckFzDDJ1DBNRwO+62QgSk+yYTb7363smzZieuT1Q7a251uhGIFX1PaJ4n1yY5JLmCGT6C6BQ4cOOC3QgaLwcfPnLCLoX38xCQfk1zADJ9ABVfLwlloTliLxeLgS3AVkW+KSL+IvJhl/QdF5JeJx7Micnbaug4R+ZWI7BGRBSUMWDbXd14fWQw+fg7VWgzt4ycm+ZjkAmb4+JK4RUTeCYwB96rqW+ZY/3bgZVUdFpGtwGdV9dzEug7gHFUdyPV4ycQtqorMLjHtI4vB55FHnK6A555zAuvUFBysbKN5cta0WA9yECyG9vETk3xMcoHi+bglbvHlylVVfwIMuax/VlWHEy+fAxaeTHEOOn2cJz8Xi8EnfajWTTc5z82TnZn5BzzKQbAY2sdPTPIxyQXM8FkMfa4fA9J7+BR4XER2i8g1PjkFhuRQrW3bYMUK5zm53GKxZMfooVgi8i6c4Hpe2uItqtojIvXAEyLy68SV8Ox9rwGuAScje0dHB4ODg9TU1BAOh1N3E5ctW0Z9fX3qP52IEI1G6e3tTZWKaG5uZmxsjNHRUQBWr15NKBSiv78fgOXLl1NXV8f+/fsBKC0tpbW1lZ6eHiYnJwFoaWlhdHSUw4cPA1BbW8vk5GSqVEdlZSXV1dXEEin/QqEQkUiEWCyWyiIfiUQYGRlhbGwMgDVr1jAzM8Pg4CAAK1eupKqqiu7ubsAZjtLc3ExXVxfTidv7a9euZWBggKNHjwJQX19PPB5naGiIwcFBqqqqqKyspKfHKUhYXl5OU1MTZ53VyVvecrwL6cCBAxw7dgyAhoYGlnG87Eh1dTUVFRWp0s8VFRU0NjZmlCVpa2ujr68vNU2xsbGR8fHx1MyampoapqamUvv4eZ5KSko4ePAgg4ODRpwngKqqKqanp1PtkzxPnZ2dqZIu0WiU/v7+jPM0OTnJ8PBwQc9TOBxOfTYTzhPA2NgY8Xjc8/Pkhm/JskWkDXhkrj7XxPrfAR4Ctqrqb7Js81lgTFX/t9uxbLLsAiPidAXMt8xiWeIY1+c6HyKyFngQuCo9sIrIChFZmfwZuACYc8TBXPT29hZa9aRYtD7RqBNM0x8e5CBYtO1TJEzyMckFzPDxpVtARL4DnA/UiUgMuAUoA1DVO4HPALXA1xJ3/OKJ/w4NwEOJZSHg26r6w1yPu1QrVBaKnH2KlG9g0bZPkTDJxyQXMMPHl+CqqlfOs/5q4IQqeKr6GnD2iXtYTGIkPsLNHTfzqdZP0Vze7LeOxeILRnYLeEVzs1l/6EvVZ+fgTvYe2csdsTuM8CkU1ic7JrmAGT6BCq7Ju4KmsBR9VJUdAzu4bd1t7BvfxzOHnvHVp5BYn+yY5AJm+AQquCaHfpjCUvRpH2unRErYvHIzN0Ru4PbY7UzM5Nf/tRTbp5CY5GOSC5jhE6jgavGOZAXZ//Xkg5x24HJmZoQtq7ZwSsUp3HfgPr/1LJaiY/QkgkKzevVqvxUyWCo+ybSE3d1Q9cX9/HDVLn74wvH+1sPTh7m66YT7k575eIX1yY5JLmCGT6CCayhk1sddKj7paQnLyu5lasrJQbBtm5OEu9g+XmF9smOSC5jhE6hugeT0OlNYKj5epSVcKu3jFSb5mOQCZvgEKrhavCG9giw4z489BuvX++tlsfhJoILr8uXL/VbIYKn4zJWWMBJxlvvh4xXWJzsmuYAZPr4lbikmycQtMzMzlJSY8/9kKfkkixju2eNcsRaiiOFSah8vMMnHJBcons+iS9ziFckUZqawlHySFWRvvtl5LkS+16XUPl5gko9JLmCGT6CCq8VisRSLQAXXUsPS5wfCp63txPSEbW3++ZwE1ic7JrmAGT6B6nO1+IBNrG1Zwtg+1wTJ0iWmYH3csT7umORjkguY4ROo4Jqsv2MK1scd6+OOST4muYAZPoEKrhaLxVIs/J+AW0RaWlr8VsggED7Jeluzl/nlcxJYn+yY5AJm+ATqytWEHI/pBMKno8O5eZX+yLEGVyDa5yQwycckFzDDJ1DBNVnj3BSsjzvWxx2TfExyATN8AtUtYPGP5PTY9nYn0UshpsdaLCYTqCvX2tpavxUyCIpPMpn2LbfA0aPO82WXOcv98MkX65Mdk1zADJ9ABVeTEktAcHzSk2nfeqvzHIs5y/3wyRfrkx2TXMAMH/8NisjBgwf9VsggKD75JtMOSvvki0k+JrmAGT6BCq4Wf7DJtC1BJFDBtbKy0m+FDILik28y7aC0T76Y5GOSC5jhE6jELfF43IjCZUmC5JNPMu0gtU8+mORjkgsUz8e4xC0i8k0R6ReRF7OsFxH5sojsE5FfisjGtHUXicgriXU3LuS4sVjsZNULSpB88kmmHaT2yQeTfExyATN8/OoWuAe4yGX9VuBNicc1wNcBRKQU+Gpi/ZnAlSJypqemFovFkge+BFdV/Qkw5LLJe4F71eE5oFpEmoDNwD5VfU1VJ4EHEtvmhElfW8D6zIf1ccckH5NcwAwf/w3mpgXoSnsdSyyba/m5c72BiFyDc9VLJBKhIzGf/dChQ4TDYQ4cOADAsmXLqK+vp7OzM7kf0WiU3t5eJiYmAGhubmZsbCw1X3n16tWEQqFUbfTly5dTV1eXqttTWlpKa2srPT09qdRnLS0tjI6Opqbl1dbWUlNTk/KqrKykuro69XUmFAoRiUSIxWLE43GSn2NkZISxsTEA1qxZw8zMDIODgwCsXLmSqqoquru7AQiHwzQ3N9PV1cV0YsT+2rVrGRgY4OjRowDU19cTj8cZGnL+1w0NDVFZWZnKh1leXk5TUxOdnZ0k++ej0Sj9/f0cO3YMgIaGBiYnJxkeHgagurqaiooK+vr6AKioqKCxsTH1WQHa2tro6+tjfHwcgMbGRsbHxxkZGQGgpqaG2tra1D5+nqeSkpLU0J6BgQEjzlNVVRX19fWp9vHzPIXDYeLxOB0dHcacp8rKSuLxuOfnyQ3fbmiJSBvwiKq+ZY51O4FbVfXpxOsfAzcAbwAuVNWrE8uvAjar6sfdjpW8oRWLxYhEIoX9ICeB9XHH+rhjko9JLlA8H09uaInIJ/JXmpcY0Jr2OgL0uCzPieR/LFOwPu5YH3dM8jHJBczwyTm4ikiZiGxOPM4FzvPQ6wfAhxOjBt4KHFLVXuDnwJtEZJ2IhIErEttaLBaLUSykz3UGOJL2ev5OhyyIyHeA84E6EYkBtwBlAKp6J/AocDGwDzgK/GliXVxErgceA0qBb6rq3lyPa9LXFrA+82F93DHJxyQXMMMn5+CqqtNAKpCJyJP5HlRVr5xnvQLXZVn3KE7wXTAjIyPU1dXls6snWB93rI87JvmY5AJm+OTd56qq/1RIkWKQvCtoCtbHHevjjkk+JrmAGT7zXrmKyDuA04GnVfVl75UsFotl8ZPLlesWYAT4lIjc4rGPp6xZs8ZvhQysz3FG4iNcv+96eiaOD/6w7eOOST4muYAZPvMGV1W9TVX/n6peBXSLyB1F8PKEmZkZvxUysD7H2Tm4k71H9nJH7Pivl20fd0zyMckFzPCZN7iKyDdEZKeI/BznJtPbvNfyhuTMC1OwPg6qyo6BHXwhehu/HNzH9Xc+wyOPQH+/bR83TPIxyQXM8HP+60EAACAASURBVMna55oYLvVj4F7gN0C/BiE/oaXotI+1U7LvVd76lrfy2bdXcfsn9/EHf/QywyWtTI912kKGlkWJ25Xrx4A+4I+Bu4AvicjviUhZUcw8YOXKlX4rZGB9HB4ceJDL/28v52xUNj95iFPOuoh7XruLxvH989bZKib2fGXHJBcwwyfrlauqHgUeEZGfq+oBETkVJ03gn4vIDlV9oGiWBaKqqspvhQysj8P+if3s+utWYBNv/ZWz7PC0k5Bjzx4n/6sJ2POVHZNcwAyfXEYL3CUi24AeVf2yqr5/MQZWIJXdxhSsj8O9p9/L7k2/gD/bzXNn7Wb3xt18dd1dgFl1tuz5yo5JLmCGTy6jBd4LPA3sEJHrRcTUNIWWRc7sOlswf50ti8VUcg2UzwIDwN8CfyUi9wO/VNXvembmAeFw2G+FDKxPGtEoP3hYnJ/b4VYgHokQMuhmlj1f2THJBczwmTefq4g8hpOw5Tc4iVT24SRxebOqft1zwwKQzOdqsVgsheRk87l+TlUvV9UbVfVuVX1SVX+yWAJrOl1dXfNvVESsjzvWxx2TfExyATN8culzfaoYIsUgl9IMxcT6uGN93DHJxyQXMMPHr+qvFovFsqQ56RpaiYoAe1X1TYVRKjzJPteZmRlKSsz5f2J93LE+7pjkY5ILFM/Hkxpa6e8PnFKA9/GcgYEBvxUysD7uWB93TPIxyQXM8MkpuIpI0zybLIqcA8kyxaZgfdyxPu6Y5GOSC5jhk+s4124ROQjsSXu0A694JWaxWCyLmVyD6xpgA7A+8fhD4DRgAnjJG7XCU19f77dCBtbHHevjjkk+JrmAGT65BtcwTpmXHyUXiEg5cBZOsD3bA7eCY0It83SsjzvWxx2TfExyATN8cr2hdT/wgeQLEakDPgd8FHhBVT/ugVvBGRoa8lshA+vjjvVxxyQfk1zADJ9cg+vZwPfSXn8TeD/QCvxYROYcimCxWCxBJdfgWqKqQwAiUgtcDFymqpcC/wP4Xx75FRQTcjymY33csT7umORjkguY4ZNrcH1VRJKZNX8PiKlqe+L1t4GNBTfzgMrKSr8VMrA+7lgfd0zyMckFzPDJNbj+PfBvIvIJ4LPAg7PWryiklFf09PTMv1ERsT7uWB93TPIxyQXM8MlptICq3p+onfVRIAbclrb6HKB3IQcVkYuAfwRKgbtV9bZZ6z8JfDDN8QxgjaoOiUgHcBiYBuLZpp5Zlh7T07BrF7S3w4YNTiJtW7zQYio5T39V1XtU9Z2qeqGq9qetegeQc9JsESkFvgpsBc4ErhSRM2cd63ZVXa+q64GbgP9M9vkmeFdi/YICa3l5+UI29xzr4066z/Q0XHYZ3HILHD3qPF92mbPcDx8TMMnHJBcww+ekcwuo6hdV9dML2GUzsE9VX1PVSeAB4L0u218JfOdkHJM0Nc03i7e4WB930n127YLubnjuObj1Vuc5FqOo1WFNbh+/MckFzPDxox5WC5CeyTYGnDvXhiKyHKfi7PVpixV4XEQU+GdVvSvLvtcA1wBEIhE6OjoYHBzkjW98I+FwmAMHDgCwbNky6uvr6ezsTO5HNBqlt7eXiYkJAJqbmxkbG2N0dBSA1atXEwqF6O93LuCXL19OXV0d+/fvB6C0tJTW1lZ6enqYnJx0PnRLC6Ojoxw+7FQ1ra2tpbe3N1WOorKykurqamKxGAChUIhIJEIsFksNiI5EIoyMjDA2NgbAmjVrmJmZYXBwEHDKCVdVVaWKs4XDYZqbm+nq6krlt1y7di0DAwOpudf19fXE43GGhoYYHBxk3bp1VFZWpvqsysvLaWpqorOzk2QGtWg0Sn9/P8eOHQOgoaGByclJhoeHAaiurqaiooK+vj4AKioqaGxspKOjI3V+2tra6OvrY3x8HIDGxkbGx8cZGRkBoKamhv7+fsrKnEruTz1Vxx/8wQpkXSt0d1MG/ALgUoi3tBB7+mnPzlNJSQkHDx5kcHCQaDTq+3kC52748PAwpYl+ET/PUzgc5qWXXqK2ttbXv6fkeQIYGxvj9NNP9/w8uaKqRX3gjI+9O+31VcBXsmz7x8DDs5Y1J57rgReAd853zE2bNqmq6uuvv64mYX3cSfd5+GHVjRtVFVRVdXJSdcMGZ3lyWTF9TMAkH5NcVIvnAzyvWeKOHwkYYziTD5JEgGy39q5gVpeAqvYknvuBh3C6GSxLnK1bneqwcLw6bCRiq8NazOWkk2Uv+IBOae7fAO8GuoGfAx9Q1b2ztlsFvA60quqRxLIVOBMaDid+fgLYpqo/dDtmMlm2qiIihf9QeWJ93JntMz0NpSHhc9uV9evTRguIQBF+j01vHz8xyQWK5+N1suwFoapxnD7Ux4CXgX9T1b0icq2IXJu26WXA48nAmqABeFpEXgB+BuycL7Cmk+zTMQXr485sn+Swq5tvhksuKf4wLNPbx09McgEzfPy4oYWqPgo8OmvZnbNe3wPcM2vZa5xEBq5kx74pWB935vSJRp0r1dnL/PLxEZN8THIBM3x8Ca4WS96k3cm2WEzGnIpiRaChocFvhQysjzvWxx2TfExyATN8AhVck2PkTMH6uGN93DHJxyQXMMMnUME1OXjaFKyPO9bHHZN8THIBM3wCFVwtFoulWAQquFZXV/utkIH1ccf6uGOSj0kuYIZPoIJrRUWF3woZWB93rI87JvmY5AJm+AQquCYTVJiC9XHH+rhjko9JLmCGT6CCq8VisRSLQAVXE74qpGN93MnFZyQ+wvX7rqdnwvuyHouxfYqFSS5ghk+ggmtjY6PfChlYH3dy8dk5uJO9R/ZyR+wOI3yKiUk+JrmAGT6BCq4dhk2dtD7uzOejquwY2MFt625j3/g+njn0jK8+xcYkH5NcwAwfm1vAsmhpH2unRErYvHIzN0Ru4Pau2+l/6hxebC+3BQwtvhOoK1fL0uLBgQe5vO5yRIS3Vm7h4Aun8Lmf3edbAUOLJZ2iJ8v2g2SybMvS4sO//jB7j2bkWGfDik3cfdpdTE051Qq2bXNyv1osXmBUsmw/MWHsWzrWx535fO49/V52b9zN7o27+W87d3PB/9vN3ac59SrLyuDCC2HPnuL5FBuTfExyATN8AhVckxUsTcH6uLMQnw0b4PHHYWrKeT01BY89BuvX++NTDEzyMckFzPAJVHC1LF2SBQzPPdcWMLSYQaD6XMfHx40YXJzE+rizUJ/padi1y+kKyChg6JOP15jkY5ILFM/Hrc81UEOxgvoLkCuL3ae01Ll55dUNrMXePl5ikguY4ROoboGRkRG/FTKwPu5YH3dM8jHJBczwCVRwtVgslmIRqOBaU1Pjt0IG1scd6+OOST4muYAZPoEKruFw2G+FDKyPO9bHHZN8THIBM3wCFVwPHDjgt0IG1scd6+OOST4muYAZPoEKrhaLxVIsAhVcly1b5rdCBtbHnZP2aWsDkcxHW5t/PgXGJB+TXMAMH1+Cq4hcJCKviMg+EblxjvXni8ghEdmTeHwm133dqK+vL4R+wbA+7py0T2cnqGY+Ojv98ykwJvmY5AJm+BQ9uIpIKfBVYCtwJnCliJw5x6ZPqer6xGPbAvedk86T+MPyAuvjjvVxxyQfk1zADB8/rlw3A/tU9TVVnQQeAN5bhH0tFoulaPgx/bUF6Ep7HQPOnWO7t4nIC0AP8NequncB+yIi1wDXAEQiETo6OhgcHKSmpoZwOJy6m7hs2TLq6+tT/+lEhGg0Sm9vLxMTEwA0NzczNjbG6OgoAKtXryYUCtHf3w/A8uXLqaurY//+/QCUlpbS2tpKT08Pk5OTzoduaWF0dJTDhw8DUFtby+TkZKocRWVlJdXV1cRiMQBCoRCRSIRYLEY8Hif5OUZGRhgbGwNgzZo1zMzMMDg4CMDKlSupqqqiu7sbcIajNDc309XVxXQia/TatWsZGBjg6NGjgPP1KR6PMzQ0xODgIFVVVVRWVtLT4xT8Ky8vp6mpic7OTpJ5KKLRKP39/Rw7dgyAhoYGJicnGR4eBqC6upqKiopU2reKigoaGxszSm+0tbXR19eXyl7U2NjI+Ph4amZNTU0NU1NTqX3yOU9twNGjRzPOUz3HS4Dkep5KSko4ePAgg4ODRpwngKqqKqanp1Ofxc/zFA6HU5/Nz7+n5HkCGBsbIx6Pe36e3Ch64hYReT9woapenXh9FbBZVT+etk0VMKOqYyJyMfCPqvqmXPadC5ssO6C0tZ3YxxqNggH1lSxLA9OSZceA1rTXEZyr0xSqOqqqY4mfHwXKRKQul33d6O3tzdfZE6yPOyft09Fxwg2t6Vc7eOQR2L4dHnlkYWVgllz7FBCTXMAMHz+C68+BN4nIOhEJA1cAP0jfQEQaRUQSP2/G8RzMZV83kl9LTMH6uFNon+lpp67WLbeQV52tpd4+J4NJLmCGT9H7XFU1LiLXA48BpcA3VXWviFybWH8n8D7gz0UkDhwDrlCn/2LOfYv9GSyLk127oLsbnnvOKQOzbZuTVHvXLltny1J4ApUse3Jy0og5x0msjzuF9tm+3blivfXW48tuuglWrICbby6+z8liko9JLlA8H9P6XH0jeVfQFKyPO4X2Odk6W0u9fU4Gk1zADJ9ABdfk0A9TsD7uFNrnZOtsLfX2ORlMcgEzfAJV5sUSbEpL4aGHjtfZ2rat8HW2LJYkgQquq1ev9lshA+vjjhc+J1NnKwjtky8muYAZPoHqFgiFzPpfYn3csT7umORjkguY4ROo4JqcXmcK1scd6+OOST4muYAZPoEKrhaLxVIsAhVcly9f7rdCBtbHHevjjkk+JrmAGT6BCq51dXV+K2RgfdyxPu6Y5GOSC5jhE6jgmkxhZgrWxx3r445JPia5gBk+/t9Ss1gMYnraGQfb3u7M6LLjYC35Eqgr11LD/kqsjzvF9pkva1bQ28cNk1zADJ9AJW6xWNx45BEnoCazZk1NOVNkt22zWbMsc2MTtyRIli4xBevjjlc+I/ERrt93PT0TifdPlOC+5FJh9y+EsrBTgrusDC680Jkq66VPvpjkY5ILmOETqOCarL9jCtbHHa98dg7uZO+RvdwRu8NZkCjB/cjDyqaNytSkU4J7dtasoLRPPpjkAmb4BCq4Wiyqyo6BHdy27jb2je/jmUPPpNalZ82ChWfNsljSCVRwbWlp8VshA+vjjhc+7WPtlEgJm1du5obIDdweu52JsADHs2Zt2+Zsu22b8zp5byQI7ZMvJrmAGT6BCq4m5HhMx/q444XPgwMPcnnd5YgIW1Zt4ZSKU7jvqobU+mTWLHCe0286B6F98sUkFzDDJ1DBNVnj3BSsjzte+Oyf2M8dsTvY9ItNbPrFJp489CQ/e+caEMl8RKNF8TkZTPIxyQXM8LGTCCyB4t7T7z1x4Ubgw0VXsSxxAnXlWltb67dCBtbHHevjjkk+JrmAGT6BCq4lJWZ9XOvjjvVxxyQfk1zADB//DYrIwYMH/VbIwPq4Y33cMcnHJBcwwydQwdVisViKRaBuaFVWVvqtkIH1ccdUH1MyZ5nUPia5gBk+gbpyra6u9lshA+vjjok+82XOKraPKZjkAmb4+BJcReQiEXlFRPaJyI1zrP+giPwy8XhWRM5OW9chIr8SkT0isqBUV7FYrBD6BcP6uGOiz65d0N3tZM669VbnORZzrmT98DEFk1zADJ+iB1cRKQW+CmwFzgSuFJEzZ232OvC7qvo7wHbgrlnr36Wq67Ol+rJYvKK9HS64wElJCJyQOctiSeLHletmYJ+qvqaqk8ADwHvTN1DVZ1V1OPHyOSBSiAObUMs8Hevjjok+GzbA4487uV6BEzJnFdvHFExyATN8/DBoAbrSXseAc122/xiQ/qVLgcdFRIF/VtXZV7UAiMg1wDUAkUiEjo4OAA4dOkQ4HObAgQMALFu2jPr6ejo7O5P7EY1G6e3tZWJiAoDm5mbGxsZS85VXr15NKBRK1UZfvnw5dXV1qbo9paWltLa20tPTk0p91tLSwujoaGpaXm1tLTU1NSmvyspKqqurU19nQqEQkUiEWCxGPB4n+TlGRkYYGxsDYM2aNczMzDA4OAjAypUrqaqqoru7G4BwOExzczNdXV1MJzoF165dy8DAAEePHgWgvr6eeDzO0NAQAENDQ1RWVqbyYZaXl9PU1ERnZyfJxOrRaJT+/n6OHTsGQENDA5OTkwwPO/8Pq6urqaiooK+vD4CKigoaGxtTnxWgra2Nvr4+xsfHAWhsbGR8fJyRkREAampqqK2tTe3j53kqKSnh4MGDRM47j0u6u7kEIOx8jv6yKJGLOjjrrBgdHcU7T1VVVdTX16fax8/zFA6HicfjdHR0GHGewPl7isfjnv89uaKqRX0A7wfuTnt9FfCVLNu+C3gZqE1b1px4rgdeAN453zE3bdqkqqpdXV1qEtbHHdN8FFRVNR5Xffhh1e3bnWXxuD86JrWPSS6qxfMBntcsccePboEY0Jr2OgKckDZcRH4HuBt4r6oOJperak/iuR94CKebISeS/7FMwfq4Y5pPkmTmrJtvPv7aD0xqH5NcwAwfP4Lrz4E3icg6EQkDVwA/SN9ARNYCDwJXqepv0pavEJGVyZ+BC4AXi2ZuseTA9LRTj2v7dufZj2FaFv/xpUChiFwM/ANQCnxTVT8vItcCqOqdInI38EdAZ2KXuKqeIyJvwLlaBae/+Nuq+vn5jpcsUBiPx43o6E5ifdwxzQcRmP33MmtZchxsd7czquDxx53qBulJtwuFSe1jkgsUz8etQKEvraGqjwKPzlp2Z9rPVwNXz7Hfa8DZs5fnysjICHV1dfnuXnCsjzum+Uy3tlIqkrlwVt7X9HGwZWVONYNzz3WWF7qCrEntY5ILmOETqBlaybuCpmB93DHNp+snP3GuUtMfaXfWobjjYE1qH5NcwAyfQAVXiyVfRuIjbD+8/Xg57iyYNA7W4i+BCq5r1qzxWyED6+OOST47B3fy6vSrx8txZyG9guxNN3lbQdak9jHJBczwCVRwnZmZ8VshA+vjjik+mijHfUvTLSeU455NegXZFStOrCBbSExpHzDLBczwCVRwTc68MAXr444pPsly3G1H246X456ZyLp9+jjY2RVkkxRiuJYp7QNmuYAZPoEKrhZLPsxZjvvAfXm/n0lpCy3eEajgunLlSr8VMrA+7pjikyzH/UdDf3S8HPfhn7nv1NZ2YrnutjaAgqUtNKV9wCwXMMPHnFG/RaCqqspvhQysjzum+CTLcU9NTVGWHGM1H52dc084wH241kLGwprSPmCWC5jhE6gr12R2G1OwPu4sVZ9CDdcyqX1McgEzfAIVXC0WE8hluJbNT7D4CVRwDYfDfitkYH3cWao+8w3XyvWGl0ntY5ILmOHjS+KWYpNM3GKxFI22NqffNZ1o9ITpsnPxyCNOQE3mJ5iacq5ut20rfH4Cy8nhlrglUFeuXV1d829URKyPO4vap6MDVBmZGub6315Hz3j33IF1jlEF513VllN+go6OLmO6Dhb1ufKIQAXXnEozFBHr485S8Nk5uJO9R/ZmnzabHFWQ9qge6Zz3htf0NFx9da0xY2WXwrkqNIEKrhZLMUlOm71t3W3zTpudzXw3vHbtggMHSo0o8W2Zm0AF17Vr1/qtkIH1cWex+ySnzW5euTmnabPpzJefoL0d/vAPw65dB8UccbDYz5UXBCq4DgwM+K2QgfVxZ7H7nMy02RPyE5zSltEv+7efET7+d+uydh0Ue4rtYj9XXhCoGVrJMsWmYH3cWew++yf2s2t4V0Z/6+Hpw1zdlFZkIxpNzdzKWDabWTO+pqehJSRsPNe5Yn3sscyug1wqIkxPO6/b252JDVu35p+9a7GfKy8IVHC1WIpJctqsKzkMzZqLZBDcts3pCti2LTM4zjfFdnatr1tugbvuOrH7oZABOHBkq7m9lB6bNm1SVdUjR44srCi5x1gfd4LqMzw1rNf99jrtHu8+vhBO3HCuZaqq0ejsYjQ6E43qhg2qDz/sbPLww6obN6pOTjqvJyc1Y72qajyueumlznY33ug8X3qps3w2QT1XwPOaJe4Eqs/VhFrm6Vgfd4LqM+/wrfno7GQ6rrznUmXjBuWmGxXp7MzoNmhvhx/ta6Ms7PThloWFX7Q7Y2yTLCR7V1DPlRuBCq5DQ0N+K2RgfdwJoo9mG76V7JtNe8RbWlL7jcRHuH7f9akaX7On2ELmV/4NG6BmtJOpSefadmrSCcTVI8dnlS2k2GIQz9V8BCq4Wiymk3X4VmLGV/oj9vTTqf3mutpNH3GQfJ0keQU7eyxtOhnZuxIzyW69Tbj5bzPz01rmJlDB1YQcj+lYH3eC6LOQ4VtJnxOudt8+v2cy0N64fYQ951/PX32+h4ceytwmPXsXnZ1s3OB0NUzHEwE+LXdCqm1ckoQXExN+dwIVXCsrK/1WyMD6uBNEn2TVg02/2DRv1YOkzwlXuzetY6K8JDPAzTW8C5g6ZyfjjXvZc+odJ4wCSO9agOOTGQ5rogui6XjmqVTbzDGd94QENuB5EDbhdydQwbWnx73mfLGxPu4E0efe0+9l98bdGY+7Tr3L1eeEq90z3s19HXdlBrg5hnxpNMqOZ77AbdfsZt+LP+SZLatOCMLJrgU4Xmwx1QXxieP9CPO1zew+4VyD8An75YgJvzu+BFcRuUhEXhGRfSJy4xzrRUS+nFj/SxHZmOu+FkvQWMjVbjrtv3qQktPPYPNzh7jh/Lu4/a53MfHaK677ZHRBvLEi53wJ+Y6AyGe/kfgI2w9vX1BAzjeIu1H04CoipcBXga3AmcCVInLmrM22Am9KPK4Bvr6AfbNSXl5+0v6FxPq4Y33cSfos5Go3nQVNz02MVmjfVEXJy79m86q3csM9k6kbbm5to5BXApusIyfmYefgTvbF9y0oIJ/08Lc58OPKdTOwT1VfU9VJ4AHgvbO2eS9wb2Kc7nNAtYg05bhvVpqamgrzCQqE9XHH+rhzsj4LuuJNjFZ4cMdfcPk7b0ZU2fLQb1MBOeUyx5Cx9q2nnDgCIixzHyeNfBLfJAPyl075Us4BOd8gPh9+TH9tAdIz2caAc3PYpiXHfQEQkWtwrnqJRCJ0dHQwODjIG9/4RsLhMAcOHABg2bJl1NfX05no7xERotEovb29TEw4J7K5uZmxsTFGR0cBWL16NaFQiP7+fgCWL19OXV0d+/fvB6C0tJTW1lZ6enqYnJx0PlBLC6Ojoxw+fBiA2tpaent7U+UoKisrqa6uJhaLARAKhYhEIsRisdSA6EgkwsjICGNjYwCsWbOGmZkZBgcHAaeccFVVVao4Wzgcprm5ma6urlR+y7Vr1zIwMJCae11fX088HmdoaIjBwUHWrVtHZWVlqs+qvLycpqYmOjs70cTc9mg0Sn9/P8eOHQOgoaGByclJhoeHAaiurqaiooK+vj4AKioqaGxspCOt36+trY2+vj7Gx8cBaGxsZHx8nJGREQBqamro7+9PVVv18zyVlJRw8OBBBgcHiUajvp8ncO6GDw8PU5q4C5XPefpy45cXfJ46jnWckC9hZGqEDT0bqK2tZdlPf3rCeXpw5hv8/nSEzs5OWmhhXXgd37r+VK6ZlVMh3tJCrKMjdZ7u67yP80PnE4vF2NK6hW/Hvs1XXvkK71v2vqzn6cmeJ5memmZ553I+0fIJvvD6F/j7VX/P8rLlWc/TT4d/yvTUNG8ueTMfr/14ap/aqtp5z5MbRS/zIiLvBy5U1asTr68CNqvqx9O22QncqqpPJ17/GLgBeMN8+85FssxLR0cHbQaNzbM+7lgfd0zycXP58K8/zN6jezOWbarcNG/XRT773fz6zZy54kzefvTttLW18YlXP8EZy8/ITJaTZZ8P1H8AIKd9kriVefHjyjUGtKa9jgCze5GzbRPOYV+LxWIQOSWwKdB+qUxk3AGJSVonZCLLto9b9rI88OPKNQT8Bng30A38HPiAqu5N2+YPgeuBi3G+9n9ZVTfnsu9cJK9cVRWZnd7NR6yPO9bHHZN8THKB4vkYVaBQVeM4gfMx4GXg31R1r4hcKyLXJjZ7FHgN2Ad8A/jvbvvmeuxk35spWB93rI87JvmY5AJm+PiSz1VVH8UJoOnL7kz7WYHrct03V5Id+6ZgfdyxPu6Y5GOSC5jhE6gZWhaLxVIsAhVcGxoa/FbIwPq4Y33cMcnHJBcwwydQwTU5ltEUrI871scdk3xMcgEzfAIVXJODp03B+rhjfdwxycckFzDDJ1DB1WKxWIpF0ce5+oGIHAQ6gTrA/4Lmx7E+7lgfd0zyMckFiucTVdU1c60IRHBNIiLPZxvw6wfWxx3r445JPia5gBk+tlvAYrFYPMAGV4vFYvGAoAXX+TMIFxfr4471ccckH5NcwACfQPW5WiwWS7EI2pWrxWKxFAUbXC0Wi8UDlnRwFZHVIvKEiPw28VyTZbtqEfmuiPxaRF4Wkbf56ZPYtlRE2kXkES9ccvURkVYR+Y9Eu+wVkb8osEPelYC9IAefDyY8fikiz4rI2X76pG33/4nItIi8z28fETlfRPYkfl/+008fEVklIg+LyAsJnz/10icDVV2yD+BLwI2Jn28Evphlu28BVyd+DgPVfvok1v9P4NvAI362D9AEbEz8vBInWfmZBTp+KfAqTvmeMPDC7PfGSZi+CxDgrcBPPWyPXHzeDtQkft7qt0/adv+Ok4rzfT63TzXwErA28breZ59PJX+vgTU49QnCXjmlP5b0lStOZdhvJX7+FvDfZm8gIlXAO4F/AVDVSVUd8csn4RQB/hC42yOPnH1UtVdVf5H4+TBOkvKWAh3/ZCoBe8G8Pqr6rKomJ64/h1NqyCtyrXb8cWAH4HWG6Fx8PgA8qKr7AVTVS6dcfBRYKU5Zgkqc4Br30CnFUg+uDaraC06QAOrn2OYNwEHgXxNfw+8WkRU++gD8A05BxhmPPBbqA4CItAEbgJ8W2vb3twAABZlJREFU6PjZqvwudJtCsdBjfQznqtor5vURkRbgMuBOvCeX9jkVqBGRJ0Vkt4h82GeffwLOwKm19yvgL1TV678rwKdKBIVERH4ENM6x6tM5vkUI2Ah8XFV/KiL/iPMV+W/98BGRS4B+Vd0tIufn41BIn7T3qcS5OvpLVR09Wa/k286xbPbYwFy2KRQ5H0tE3oUTXM/zyCVXn38A/kZVp4tQMyoXnxCwCafO3TLgv0TkOVX9jU8+FwJ7gN8DTgGeEJGnCvg7nJVFH1xV9fezrRORAyLSpKq9ia+Sc31FiQExVU1ejX0XJ7j65bMFeI+IXAxUAFUi8n9U9UM++SAiZTiB9X5VfTAfjyycTCVgL8jpWCLyOzhdNltVddAjl1x9zgEeSATWOuBiEYmr6vd88okBA6p6BDgiIj8Bzsbpq/fD50+B29TpdN0nIq8DpwM/88Ang6XeLfAD4COJnz8CfH/2BqraB3SJyGmJRe/G6ZD3y+cmVY2oahtwBfDv+QbWQvgk+qr+BXhZVf+uwMf/OfAmEVknImGcz/uDORw/nBg18FbgULIrwwPm9RGRtcCDwFUeXY0tyEdV16lqW+L35bvAf/cosObkg/M79A4RCYnIcpzqzS/76LMf528aEWkATsMpfuo9xbhr5tcDqAV+DPw28bw6sbwZeDRtu/XA88Avge+RuBvsl0/a9ufj7WiBeX1wvvZqom32JB4XF9DhYpyrmleBTyeWXQtcm/hZgK8m1v8KOMfj35n5fO4GhtPa4nk/fWZtew8ejhbI1Qf4JM4Fyos43Uh+nq9m4PHE786LwIe89El/2OmvFovF4gFLvVvAYrFYfMEGV4vFYvEAG1wtFovFA2xwtVgsFg+wwdVisVg8wAZXi8Vi8QAbXC2WApJIcfczERkTkbfMWrdCRB7wy81SXGxwtVgKy1GcjGbfnWPd7+GkBrQEABtcLcYhIreKyF/67ZEkcSX65ly2VdUpVT2YZfVFwCsicnfifW8Skd8tlKfFLGxwtRiFiKwBPgz8s98uafxvYFv6AhGpExFNpPzLlbU4UzWT+7yKk0TEsgSxwdViGn+Ck9fgmN8iafwAeNesJN0bcLI/defyBonEQL8BDnA8b+57gKfTtgklEpBYlgA2uFpMYyuQUXdJRK5MJF4+JCKvFiLP7ULeV1XHgd3ABWmL1+MkbsmVi4Bd6iRqLhWRPwNeVdW9aducjpNb2LIEWPT5XC1LjrOAV5IvROQTwEeBq3CC2ZuBwyd7kDze92WcvKRJsgZXEXk0sf40EflnVb0Hp5RQslrAOE6tp786mc9gMRsbXC2mUU0iyCX6X28B3qGqLyTW/+pkD5Dn+x7GKdaYZD1OQcATUNWL51i8Q1UnEuvfujBjy2LEBleLaQzjVJkF+H3gV2kBcE5E5Ekg2133Z1R1dimWnN53FiuBkcTxKnCSLrfnurOqftttvYh8HCd/b0hEnlbV2xfgZjEQG1wtpvFLnCJ3PwdWkwhobqjq+Qs8Rtb3FZE/Bq7DKdv8j6r6b4lVZwD/J/HzWcAkad0XJ4uqfgX4SqHez+I/9oaWxTQe5fhVaDtwnoicnSjz8iYROaMAx5jzfUVkPc5ohXer6hbgIQARKccpuvdEYv/1OJn2y0SkIvEoL4CXZQlhg6vFNO7FKbK3TFWfBT4HPILT5/kQTkXRk8LlfS8B/k5VpxLbTSV2eQ/wpKomi9+djRNsj6U9vKq7Zlmk2DIvFuMQkS/glBf/hyIf9w7gcVV9TERCqhpPLP8p8DFVfbGYPpbFjQ2uFkuCRJfDvwITwM9U9ZM+K1kWMTa4WiwWiwfYPleLxWLxABtcLRaLxQNscLVYLBYPsMHVYrFYPMAGV4vFYvEAG1wtFovFA2xwtVgsFg+wwdVisVg8wAZXi8Vi8YD/HzpHfZkfgxq5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v_perp = 2\n",
    "x1 = (rates - 0.1765)*(L1**(1/v_perp))\n",
    "x2 = (rates - 0.1765)*(L2**(1/v_perp))\n",
    "x3 = (rates - 0.1765)*(L3**(1/v_perp))\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x1, y1, c = \"blue\", marker = \"o\", linestyle = \"None\",\n",
    "         mfc = \"None\", markersize = 5, label = \"L = 20\")\n",
    "plt.plot(x2, y2, c = \"red\", marker = \"s\", linestyle = \"None\",\n",
    "         mfc = \"None\", markersize = 5, label = \"L = 30\")\n",
    "plt.plot(x3, y3, c = \"limegreen\", marker = \"^\", linestyle = \"None\",\n",
    "         mfc =\"None\", markersize = 5, label = \"L = 50\")\n",
    "plt.ylabel(r\"$SL^{\\gamma/\\nu_\\perp}$\", size = 12)\n",
    "plt.xlabel(r\"$(c-c_c)L^{1/\\nu_\\perp}$\", size = 12)\n",
    "plt.grid(alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(fontsize = 12)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/sir/nuperp_20.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\beta$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2min 56s, sys: 1.56 s, total: 2min 58s\n",
      "Wall time: 3min 4s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "ntraj = 10**3\n",
    "Ls = np.arange(10, 80, 5)\n",
    "M = np.zeros(len(Ls))\n",
    "\n",
    "for i in range(len(Ls)):\n",
    "    Ni = Ls[i]**2\n",
    "    s = cluster_dist(Ls[i], 1/Ni, ntraj, 0.1765)\n",
    "    s = np.mean(s**2)\n",
    "    M[i] = s\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9998874814418303\n",
      "[3.69180458]\n"
     ]
    }
   ],
   "source": [
    "x_range = np.log(Ls[1:])\n",
    "x_range = x_range.reshape(-1,1)\n",
    "y_range = np.log(M[1:])\n",
    "model = LinearRegression()\n",
    "model.fit(x_range, y_range)\n",
    "print(model.score(x_range, y_range))\n",
    "print(model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(Ls, M, marker = \"o\", linestyle = \"None\", c = \"blue\", mfc = \"None\")\n",
    "plt.plot(Ls, Ls**model.coef_*np.exp(model.intercept_), c = \"red\",\n",
    "         linestyle = \"--\", linewidth = 1,\n",
    "         label = r\"$(\\beta + 2\\gamma)/\\nu_\\perp$ (slope) = {}\".format(round(model.coef_[0], 3)))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"L\", size = 12)\n",
    "plt.ylabel(r\"$\\langle M(L) \\rangle$\", size = 12)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(fontsize = 12)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/sir/beta.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}