Project_CP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MONTE CARLO SIMULATION OF CONTACT PROCESS"
   ]
  },
  {
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython = True)\n",
    "def init_lattice(N, 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",
    "    -linear lattice of length N and N*perc infected nodes\n",
    "    '''\n",
    "    #array full of \"healthy\" nodes\n",
    "    lattice = np.full(N, 0)\n",
    "    #get the number of initial infected\n",
    "    initial_infected = int(N*perc)\n",
    "    #infect the first nodes and shuffle the array in order to randomize the system\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):\n",
    "    '''\n",
    "    Plot a lattice\n",
    "    '''\n",
    "    fig = plt.figure(figsize = (8, 3))\n",
    "    N = len(lattice)\n",
    "    G = nx.grid_2d_graph(N, 1)\n",
    "    pos = dict( (n, n) for n in G.nodes() )\n",
    "    colors = np.full(N, [\"blue\"])\n",
    "\n",
    "    for i in range(N):\n",
    "        if lattice[i] == 1: colors[i] = \"red\"\n",
    "\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",
    "    nx.draw_networkx(G, pos = pos, with_labels = False, labels = None,\n",
    "                         node_color = colors, node_size = 100)\n",
    "    #plt.title(\"Example of initial state\", weight = \"bold\", size = 16)\n",
    "    plt.axis('off')\n",
    "    plt.gca().invert_yaxis()\n",
    "    plt.legend(legend_elements, [\"Healthy\", \"Infected\"], bbox_to_anchor=(1, 1), loc=\"upper right\", fontsize = 10)\n",
    "    plt.show()\n",
    "    fig.savefig(\"presentazione/Images/CP_init_loc.pdf\", transparent=True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_example = init_lattice(20, 1/20)\n",
    "print(initial_example)\n",
    "plot_lattice(initial_example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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",
    "    #get the size of the lattice\n",
    "    N = len(lattice)\n",
    "    #build a list with a dummy first element in order to have always a list with at least one element (Numba has some problems with empty lists)\n",
    "    I = np.array([2*N], dtype = np.int64)\n",
    "    #check infected nodes and add their position to the list\n",
    "    for n in prange(N):\n",
    "        if lattice[n] == 1:\n",
    "            I = np.append(I, n)\n",
    "    return I\n",
    "\n",
    "@jit(nopython = True)\n",
    "def contact(N, I, inf_rate, rec_rate):\n",
    "    '''\n",
    "    Performs N trials of infections/recovery\n",
    "    \n",
    "    INPUTs:\n",
    "    -lattice size\n",
    "    -initial list of infected\n",
    "    -infection rate\n",
    "    -recovery rate\n",
    "    \n",
    "    OUTPUTs:\n",
    "    -new list of infected\n",
    "    '''\n",
    "    \n",
    "    \n",
    "    #recovery probability\n",
    "    c = rec_rate/(rec_rate + inf_rate)\n",
    "    #number of initial infected (-1 is necessary because of the first dummy element)\n",
    "    n_infected = len(I)-1\n",
    "    \n",
    "    if n_infected > 0:\n",
    "        #monte carlo step\n",
    "        for s in prange(n_infected):\n",
    "            #get random infected\n",
    "            i = np.random.randint(1, len(I))\n",
    "            random_site = I[i]\n",
    "            \n",
    "            #we recover it with prob. c\n",
    "            if np.random.uniform(0., 1.) < c:\n",
    "                #swap the i-th element with the last and delete the last element of I\n",
    "                I[i] = I[-1]\n",
    "                I = I[:-1]\n",
    "            #otherwise we infect a random neighbor and we add it to the I list\n",
    "            else: \n",
    "                nbrs = [(random_site-1)%N, (random_site+1)%N]\n",
    "                j = np.random.randint(0, 2)\n",
    "                random_nbr = nbrs[j]\n",
    "                if np.any(I == random_nbr)==False:\n",
    "                        I = np.append(I, random_nbr)\n",
    "    \n",
    "    \n",
    "    return I\n",
    "\n",
    "@jit(nopython = True)\n",
    "def trajectory(N, perc, nsteps, inf_rate, rec_rate, surv_prob):\n",
    "    '''\n",
    "    Simulates a \"trajectory\": at each step the lattice is modified\n",
    "    \n",
    "    INPUTs:\n",
    "    -the size of the lattice\n",
    "    -the percentage of initial infected\n",
    "    -the number of steps to do\n",
    "    -infection rate\n",
    "    -recovery rate\n",
    "    \n",
    "    OUTPUTs:\n",
    "    -a vector with the values of the infected density at each step, including the initial value\n",
    "    '''\n",
    "    \n",
    "    if surv_prob == False:\n",
    "        #build an initial lattice\n",
    "        lattice = init_lattice(N, perc)\n",
    "        #build the list of initial infected\n",
    "        I = build_I(lattice)\n",
    "        #build an array to be filled with the infected density at each step\n",
    "        infected_density = np.zeros(nsteps +1)\n",
    "        infected_density[0] = perc\n",
    "        #simulate the contact process and update the infected_density list\n",
    "        for i in prange(nsteps):\n",
    "            I = contact(N, I, inf_rate, rec_rate)\n",
    "            infected_density[i+1] = (len(I)-1)/N\n",
    "            #stop the simulation if there are no more infected\n",
    "            if (len(I)-1) == 0: break     \n",
    "\n",
    "        return infected_density\n",
    "    \n",
    "    else:\n",
    "        #start with one infected node\n",
    "        perc_1 = 1/N\n",
    "        lattice = init_lattice(N, perc_1)\n",
    "        I = build_I(lattice)\n",
    "        #build an array to be filled with: 1 if there is at least one infected node and 0 otherwise\n",
    "        surv = np.zeros(nsteps +1)\n",
    "        surv[0] = 1\n",
    "        for i in prange(nsteps):\n",
    "            I = contact(N, I, inf_rate, rec_rate)\n",
    "            if (len(I)-1) == 0: break\n",
    "            else: surv[i+1] = 1\n",
    "        return surv\n",
    "  \n",
    " \n",
    "@jit(nopython = True)\n",
    "def simulate(N, perc, ntraj, nsteps, inf_rate, rec_rate= 1, surv_prob= False):\n",
    "    '''\n",
    "    Simulates many trajectories\n",
    "    INPUTs:\n",
    "    -size of the lattice\n",
    "    -percentage of initial infected\n",
    "    -number of trajectories to simulate\n",
    "    -number of steps per trajectory\n",
    "    -infection rate\n",
    "    -recovery rate\n",
    "    \n",
    "    OUTPUT:\n",
    "    matrix with trajectories\n",
    "    '''\n",
    "    #matrix with \"ntraj\" rows and \"nsteps + 1\" columns\n",
    "    trajectories = np.zeros((ntraj, nsteps + 1))\n",
    "    #fill the matrix by rows\n",
    "    for i in prange(ntraj):\n",
    "        trajectories[i] = trajectory(N, perc, nsteps, inf_rate, rec_rate, surv_prob)\n",
    "    \n",
    "    #trajectories = np.mean(trajectories, axis = 0)\n",
    "    return trajectories\n",
    "\n",
    "def find_critical_point1(N, perc, ntraj, nsteps, lower, upper, nintervals, rec_rate = 1, loc = False, surv_prob = False):\n",
    "    '''\n",
    "    Gives an estimate of the critical point\n",
    "    \n",
    "    INPUTs:\n",
    "    -size of the lattice\n",
    "    -percentage of initial infected\n",
    "    -number of trajectories to simulate\n",
    "    -number of steps for each trajectory\n",
    "    -lower bound for the critical point\n",
    "    -upper bound for the critical point\n",
    "    -number of points between lower and upper\n",
    "    -recovery rate\n",
    "    -bool that is TRUE if we want to simulate with localized i.c. and FALSE otherwise\n",
    "    -bool that is TRUE if we want to compute the survival probability\n",
    "    OUTPUTs:\n",
    "    -list of rates used for the computations\n",
    "    -list of r_sq for the various regressions\n",
    "    -list of thetas for the various regressions\n",
    "    '''\n",
    "    #build the list of rates to consider for the computation\n",
    "    rates = np.linspace(lower, upper, nintervals)\n",
    "    \n",
    "    if loc == False:\n",
    "        #build lists to be filled with: delta exponents and r_sq of the regressions\n",
    "        deltas, r_sq = np.zeros(len(rates)), np.zeros(len(rates))\n",
    "        for i in range(len(rates)):\n",
    "            #simulate some trajectories for each rate and get the mean\n",
    "            sim = simulate(N, perc, ntraj, nsteps, rates[i], 1, surv_prob)\n",
    "            sim = np.mean(sim, axis = 0)\n",
    "            if any(sim == 0): continue # skip iteration if absorbing phase is reached (it's not the critical point)\n",
    "            else: #otherwise perform a linear fit on a double log graph\n",
    "                x_range = np.log(np.arange(50, nsteps + 1, 1))\n",
    "                x_range = x_range.reshape(-1,1)\n",
    "                y_range = np.log(sim[50:])\n",
    "                model = LinearRegression()\n",
    "                model.fit(x_range, y_range)\n",
    "                r_sq[i] = model.score(x_range, y_range)\n",
    "                deltas[i] = model.coef_*(-1)\n",
    "        return rates, r_sq, deltas\n",
    "    else:\n",
    "        #build lists to be filled with: theta exponents and r_sq of the regressions\n",
    "        thetas, r_sq = np.zeros(len(rates)), np.zeros(len(rates))\n",
    "        for i in range(len(rates)):\n",
    "            #simulate some trajectories for each rate and get the mean\n",
    "            sim = simulate(N, perc, ntraj, nsteps, rates[i], 1, surv_prob)\n",
    "            sim = np.mean(sim*N, axis = 0)\n",
    "            if any(sim == 0): continue\n",
    "            else:\n",
    "                x_range = np.log(np.arange(50, nsteps + 1, 1))\n",
    "                x_range = x_range.reshape(-1,1)\n",
    "                y_range = np.log(sim[50:])\n",
    "                model = LinearRegression()\n",
    "                model.fit(x_range, y_range)\n",
    "                r_sq[i] = model.score(x_range, y_range)\n",
    "                thetas[i] = model.coef_\n",
    "        return rates, r_sq, thetas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "rate1 = 2.8\n",
    "rate2 = 3.2\n",
    "rate3 = 3.7\n",
    "\n",
    "N = 10**2\n",
    "\n",
    "sim1 = simulate(N, 1, 10**3, 10**2, rate1)\n",
    "sim1 = np.mean(sim1, axis = 0)\n",
    "\n",
    "sim2 = simulate(N, 1, 10**3, 10**2, rate2)\n",
    "sim2 = np.mean(sim2, axis = 0)\n",
    "\n",
    "sim3 = simulate(N, 1, 10**3, 10**2, rate3)\n",
    "sim3 = np.mean(sim3, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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b7WeWbS+qd9Kp+mXtQeNXXuP19UDmix7xOLB0qVB70VX9HnjgAVx77bUoLCzEVVddhSeeeCLrOPQFF1yQWvg/87jggguEzp1MJpFIJPDXv/41a84PPfQQ7rrrLrS3t6Ours7TFQp1R30c09raiqamJrS2tgadima2UFMDV3txCZC+FRcAoa24+vr6HLfiSufPf/4znn/+ecRiMYyNjeGnP/0pXnrpJZx77rmW+kceeQRf+tKX8OKLL+KEE07w5oOmoTtqBewWBK+qqhKyhYEogNfy8xH1IbbbzyzbXlTvpFP1y9qDxq+88vLy4GYvLpHF9tO34srLyxPaikt24wBmxle+8hVUVVWhsrISDz74IB5//HE0NTUBmLwVV15eHm6//Xb09fXhjDPOSN2tb9iwwfGcolC2Xxc02VmxYgW/8cYblr7BwcEpC95Y2ULBqlXAtm1AczOQ5W5EFbefWba9qN5Jp+qXtQeNSF67d+/GBz/4Qam44+PjrsZmZduL6kV0dhoVn12bbNeWiHYw85SpJfqOWgG7Oajm2glOtlDQ2oqRpibAh6EPt59Ztr2o3kmn6pe1B41feemNA+TOKYpelOl4JhpFz1NPYcmSJUFnotFobNB31ArYrTM7k9ajbm8HPvnJRfBhdp5ej1oyr+nGr7z0xgFy5xRFd9QK2BXAfMDgZAsDLS3A66/nw4fZea4/s2x7Ub2TTtUvaw8av/LSGwfInVMU3VErYLcguLmer5MtDLS2Ak1NI34MUbv+zLLtRfVOOlW/rD1o/MpLbxwgd05R9Bj1cUw0Cjz1VI8eo9ZoQo7uqCUwd3ipr6/PusNLLBYD8+QdXgoKCkK7w8vo6KgvO7yYO6Wo7vCSSCSkdngpKCgQ2uHFzCvbDi9Hjx613eEFgOUOL4cPH0ZnZ+eUOuXm5oZyhxcAvuzwkt5GZYcXZpba4WV8fDy1K4zdDi9E5LjDCzNn3eHFXHPDaoeX8fFxjI6OTrk+ADzb4UXPo1bg9NNP5+3btwedRmhpb29HS0sLWltbEY368TqNZjpQmUetEUPPo54G7BYhN+/QnGxhwY/cWlpasG3bNldriMjmJap30qn6Ze1B41de6XfPfra/5pprUFlZ6bjEqUxcO42Kz+21SEd31B5j9RtKmH9r8SM3L9YQkc1LVO+kU/XL2oMmrHmJIrsVlwqiW3EBxsJP6Ys9RSIRrFy50rNcdEet8ZxoNIqnnnpKD3tofOXqq69GX1+f0FZcKohuxQUYCz+lL/bU3NyMSy+91LNcdEetgN2mlQ0NDUK2sOBXbm7jyrYX1TvpVP2y9qDxKy/zu9HT04NXX3019QBYtr0IMltxqWxum74VVyQSyboVV2a7PXv24OWXX8Y111zjeE5RdEetgN38SHPmhpMtLPiVm9u4su1F9U46Vb+sPWj8yiuRSODHP/4xTjjhBKxZswYnnHACfiyxFZfM+hgyW3GVl5c7bsVldW5zK66zzz4761Zcme02b96M1atXY/HixcKfxQndUStgN75nTjFzsoUFX3Jrb8e8Cy+Em3fTZfMS1TvpVP2y9qDxK6/u7m7ccMMNiMViGBwcRCwWww033CB8Zy2z2P6DDz6Ir33taxgaGsIf/vCHrLqtW7fiwIEDGBgYmHJs3brV9txbt27F0NAQfvGLX+BjH/uY5duGme02b96Ma665Rm8coAk5LS0o3LkTvrybrgk1e/bsQX7GVlyRSATvCW7FJYq5FdfVV18ttBWXG/Lz8/Gxj30s61Zc6fzud79DT08PLr/8ck9z0B21AnaLkFdXVwvZwoIvubW2Yvyss5SXT21vb8dVV10ltZej6Odw0qn6Ze1B41deJ5988pShwXg8jqWCW3FldvLZMLfimjdvntBWXBUVFY5bcdmdOz8/P+tWXOntfvSjH+HSSy9FcXGx8GcRwmrHW33YH6eddprlDsLMzAMDA0K2sOBXbm7iNjc3MwBubm72/HxOOlW/rD1oRPJS2YV8bGyMN2/ezEVFRTxv3jwuKirizZs3S7V3or+/n4uLi/m///u/eWxsjMfHx3nhwoX88ssvu4qbrtm9ezc/99xzfPToUY7H4/zwww9zfn4+79ixI2u7o0eP8rx587i9vd3xnHoX8mnA7nXP/v5+IVtY8Cs3N3FV5mGLns9Jp+qXtQeNX3mNj49j/fr1ePfdd/H888/j3XffxXqJrbicXqUGJm/FNT4+LrQVl0jcdA1nbMX1rW99K+tWXGa7LVu2YN68efjoRz8qfE5R9FofmtBhzsPWi0XNXGpqalDj4Ya26dx000246aabJtnuu+8+T8/xwQ9+cNIDytHR0dT6JwCwevXq1NorJuvWrcO6des8zcNE31ErYLcedVlZmZAtLPiRW3s7cOWVda42JJDNS1TvpFP1y9qDxq+89MYBcucURXfUCtgtCF5YWChkCwt+5NbSArz2Wp6rSR8yebW3t+OCCy4QevjoFFfVL2sPGr/y0hsHyJ1TFN1RK2D3wovVfFHZt7OmEz9y82JDApm8Wlpa8Pvf/15oESinuKp+WXvQ+JWX3jhA7pyi6I5a4znmhgTKS320t6PmssuEX5jxYhEojSbM6I5aASLK6tNDHx7ElXxhJhqN4tlnnxVaBEoPfRiI5sWSq+zpoQ9nu+w1BXRHrYTdRHarJ91+Pf32Ar9ycxW3tRVobpZ6YUb0fE46Vb+sPWhE8srNzZX+9d3tSx6y7UX1IjqnF15kfdnssVhM+nPqjloBu40D0reHsrOFBb9ycxU3GsWeRx6BzNiJyPna29uxcuVK24eOTnGy+WXtQSOSV1lZGQ4cOCC1ZsV0bRwgqw/DxgHMjKNHj2Lfvn2oqqpyzCcdPY9aAnPPxMWLF2fdM3FwcHDKnokAQrtn4vDwsC97JpoxVPdMjMViUnsmAnDcM/G2227Dzp07cfPNN+O5556z3DPR3FMxW53i8bjlnol9fX2WdRofHw/lnonxeNxxz8Tq6mq8/fbbeOutt1K5jY+Pp+qWm5ub2uMQMH7VHx8fT/2bJyLk5uZOWl3OKQYzpzQiMZLJZGq/w/Q8gGOLJRHRlOEGqzwSiUQq98wY5nnSX2LJy8tL7ZGYk5OD3NxcJJPJVExmTtnMmJFIBMyM999/H8PDw8J7Jgb+OvZMPJYvX275+icz83vvvSdkCwt+5eY2rmx7EX1bWxs3NTVxW1ubcpxsfll70BxPdRfV2WlUfCrXAlleIdeb2yqgN7fVaDR+oDe39RA9j9r/uFLt29sRP+MMoel8dnHb29txxhln2I5h63nU/saVbS+qF9HZaVR8Xl5j3VErYPdbiDlG6mQLC37l5iZuezvw8Y+Xib+C3tKCyPbtQtP57PJqaWnB9u3bbV+cydZe1h40Yay7SntRvYjOTqPi8/Ia645aEzpaWoCdOwvFX0FvbcVIU5Py+tfHwugXZzQhxWrgWh/2R1NTU9aHAbFYTMgWFvzKzU3ctjbms88eZ5tnfsrnc9LZ+dva2vjss8+2fBiZrV1Yax/Guqu096ruThoVn8q1gF6P2jvs5pXqoQ/3caNR4PnnB6VeQffqV2CnoZFsa4rooQ9v4uqhD2t0R62A3ZxHc96uky0s+JWb27iy7UX1Tjo7f7ahkfb2dkSjUcuHkGGtva67nEbF5+U11h215vhBcrGnTMwNDTLXFGlpacHOnTuFVu/TaFTQHbUCdguCl5eXC9nCgl+5uY0r215IL7DYk1McK39rayvOPPNMyzvtK6+8UmqT3uniuKq7oM5Oo+Lz8hrrjloBu9XzIpGIkC0s+JWb27iy7YX0ArujO8Wx8kejUfz2t7+1vNN+7bXXJt1pt7e3Y9WqVYF33sdV3QV1dhoVn5fXWHfUCqSvO5CJueaHky0s+JWb27iy7YX00Sg6H3vMdrEnpzjZ/FZ2qzHtlpYWbNu2LfBhkuOq7oI6O42Kz8trrDtqjcYnrMa0W1tb0dzcPKnzDstdtia86I5aAbuhj6KiIiFbWPArN7dxZdq3twNXXFEr9IzQNm57O2qvuML2YWO29qL2aDSKV155ZVLnnXmXPR0d92you4xeRGenUfF5eo2tJlfrw/5YuXJl1gnryWRSyBYW/MrNbVyZ9s3NzIDxp6u4AoGytZe1p9PW1sbNzc2pF2mam5sZADdP5JHp94LZUHcZvYjOTqPiU7kWyPLCS+Cd3kw89DKn/seVad/WxtzUFBN6k9E2blsbx5qa2C7QdCxzOh0d92you4x+pi9zqoc+NDMe15vppgXqeeopqZ1l/CBzeCRzXDssDyQ104fuqD3Gavzabkw7aPzKzW1c2faieiedrd/mhZls7by4vk4dd/qYtuj4tq67nEbF5+k1trrNPh4PACcA+CGAnzlp7caoNbMYmcHwaSR9aCT9736MbWv8BWEbowZQBuBnAP4MYDeAcxTjPASgF8CbFr41AN4G8A6AWwTjOXbUp556atYL3d3dLWQLC37l5jaubHsRfVsb8+mnj9qOZdvGaWvj0dNPtxzDztZuOmqf3iGn/z1bp93W1sann366Lx14GOsuqrPTqPhUrkUYO+ofAfjMxN8jAMoy/FUASjJsJ1nE+RsATZkdNYBcAH+duFOOAPgvAI0AlgPYmnFUpbVz7Kj1w0T/4/rxUEnkhlhpz0Sbh5BB1j5bp+3nXXcY6y6qC/PDxEB2ISeiUhgd7DUAwMxxAPEM2bkAPktEFzLzCBFdD+ATAC5MFzHzS0S0xOI0ZwJ4h5nfnTjnYwAuZuavA7jIu0+jmSm0tgI33zyC1tZCbwOnryES8IPIdKLR6JT52ua49s0334zW1tbUg8kNGzagrKwMra2tU16F14QAq97b7wPAaQBeA/AwgDcA/ADAXAvdzQC2APh7AK8CKM4Sbwmm3lFfDuAHaT+vB3C/TU4VAL4D4y78Vrv87TYOGB0dFbKFBb9ycxtXtr2o3kmn5G9r4/Gzz7a8ow5r7c28zDvqxsZGT+6yZ2rdnTQqPpVrgTDdUQPIgzFc8U/M/Aci+iaAWwDckS5i5nsm7oS/DeBEZh6WOIfVI9esmx0ycx+AG20DEq0FsLahoQF79uwBYKyQFYlEUu/1JxIJnHjiiejo6DDboKSkBKOjoxgdHQUA1NbWYnh4GIODgwCA+fPnIy8vD729vQCAOXPmYMGCBdi7dy8AY7W+xYsXo7u7G/G48YvHokWLMDg4iKGhIQBARUUFcnJycPDgQQBAcXExysrK0NXVBQDIy8tDXV0durq6UmuVmD/n5BiTfyorK5FMJtHX1wcAKCkpQWlpKfbt2wfAWGSmtrYWnZ2dqTW56+vrcejQIRw9ehQAUFVVhUQigc7OTsydOxelpaUoLi5Gd3c3AKCgoAALFy5ER0eH+R8kGhoa0Nvbi1gsBgCorq7GwYMHUxs0lJWVobCwMLVZaGFhIWpqalI1AIDS0lLE4/HUYu01NTUYGRlJrQls1undd9/F3LlzUVRUhKqqqkl1MutqLqZjVafh4eFUDVJ1OvFEHPnBD1BaWorFQKpOha+8gvnf/CYO33or+lescFWngYEBDA8Pe1anSCSC4uJinHjiiXjkkUfwxhtv4J577sHnPvc53Hzzzdi5cyc2bNiAwsJCfPGLX8SqVass6xSPx9Hf35+q08jISKoGVnVasmQJenp6stYpJycHlZWVqe9Ttjrt378fo6OjOHLkCE4++WTH71NOTk7q+mX7Pu3bty81UyOzTslkEvX19ZZ1Onz4MObOnTulTvn5+SgtLZWqU1asem+/DwA1APak/bwawLMWutUA3oQxnm13N7wEU++ozwHwQtrPt8LhTln00GPU/scNaqxS1W9pD+ksEWb7z5l5l93Y2MjNzc18zz33ON5pz9S6O2mCHqMOZB41M/cA6CSiUyZMUQC70jVEtALA9wFcDOBaAPOJ6GsSp3kdwMlEtJSIIgCuAvBL18lrZi3t7cBll9Wo7iswFY823Z1uzHnbmzZtQnNzMwBg27ZtuPPOO1Mv2qjM3da4wKr3no4Dxjj1dgB/hDEOXZ7hXwVgedrP+QCut4jzKID9AMYAdAG4Ls13IYC/wBh3vs2r3E877bSs/yMePnxYyBYW/MrNbVzZ9qJ6O53IDXC29sL2tjbjBCN9OwQAACAASURBVAHPbZa5vuYddvodtTlzpLGxkUtKSlJ/P/PMM4XuvL3IS0YvorPTqPhUvgMI2/S8mXysWLEi64U+cuSIkC0s+JWb27iy7UX1drq2NuazzkrY9qHZ2gvbQzIc4rY+mcMjJSUlk/4OySET1by8qLuIRsWnco11R+3hoceo/Y87K8aorexWd9QB3GV7VffMF2mamppSHXNmx11SUsL33HMPNzY2cmNjo2XHrceowzXrQ6M5PolGp861bmkBtm0L3TxsETLnaj/11FNYsmQJNm7ciPb2drS0tOCSSy7BnXfeiaGhodSfALBhw4ZUu02bNun52zboRZkUMKezWTFnzhwhW1jwKze3cWXbi+qddKp+WfskWluB5uZjDx3b24FVq5R3SxdhOupuPpTcuHEjnn76aTQ3N+OOO+5AY2MjGhsbAQC7du3Crl27sGHDBqxatQrbt2+XejjpVd2dNCo+T6+x1W22PuwPu0WZxsfHhWxhwa/c3MaVbS+qd9LZ+dvamM85J2k5QpGtndJ1mIZx7DDUva2tLTUMYg6TFBcXTxoycRrX9qruThoVn8o1Rpim5810zEnyVpgvqTjZwoJfubmNK9teVO+ks/O3tACvvkqwWgY6Wzul65B5h+0DYah7NBrFW2+9hbfeegubNm1CSUlJ6mWRkpISDA0NYe3atVi2bBnuvfdeLFu2DA0NDalj2bJlePTRRz3Ly06j4vPyGuuOWqMRpLUVaGoa8X9adDQKvPLKsfHqaRgKCZpoNIqnn34aTU1N2LRpE55++mmUlJQgFoth165duPPOO7Fr1y7s3bs3dezatQuf+cxnLDty0zZb5nfrh4kek5ubK2QLC37l5jaubHtRvZPOzh+NAlu2HMTixYuF23lyfX142BjGukejUWzZsiV1fZ9++unUA8drrrkGDz/8cOqOGwAOHjw4qSM3H1Ka3HLLLUgmk7jwwgvBzCgvL0dh4bEFuUZGRjA0NISvfvWr2Lhxo23uKj5Pr7HVeIg+1MeoNccfvs+uyzxBSF6aCZr0MW5z2l99fT3X19dzUVERA+CcnByGscZP1oOIuL6+nquqqjgSiXBVVdWk6YPTuQED9Dxq7w67jQP27dsnZAsLfuXmNq5se1G9k07Fb/fsz5fr68HDxtle9/S3Kevr6zk/P5+rqqpSHbnZMRORbQdudt4AOBKJWM7/zpaDyrXI1lHrMWoFjOtpjdWDRruHj0HjV25u48q2F9U76VT8dmPXvlxfD6bzzfa6p08N7OjowF/+8hccOHAAHR0dqePAgQN48cUX0djYiPr6elRUVCASiaCqqgpEBGZGb29v6hzxeBy7du3CmjVrkJ+fj0gkgiVLluA3v/nNpHOb0wsz7W7QHbVG4xLPdkGXOWH6w8b0Mezj4MGjl5gzTzo6OrB9+3aMjo7iwIEDuPvuu1NLrNbX12PRokWp5W8TiQQSiQTGxsbQ0dGB9evXo7y8HPn5+cjLy8N5552Hbdu24eqrr8a9997rTaJWt9n6sD/sNg6Ix+NCtrDgV25u48q2F9U76VT9Vva2Nuazzx73fyg5fcxacFhE111OE4/HU2PiVVVVnJeXx/n5+bZDJ5iYCy4D9NCHd9gt8m0uXu5kCwt+5eY2rmx7Ub2TTtVvZW9pAX7/+xzLedeekn6HnT4sYnN3resupxkcHEzdfR84cABjY2OIx+O4++67UVhYiLKyMuTl5SE3NxcFBQW48MILUVxcjDvuuCNrTBl0R62AufOIFZlThLLZwoJfubmNK9teVO+kU/Vb2adt3nU66Z22zZCIrrucJptv48aN2L17N/r7+zE2NoZEIoGRkRE8++yz+NOf/oSNGzcK5eeE7qg1Gp+Y9rHrTNLvrtM7bc2MQ3fUCuTlZX9PqKKiQsgWFvzKzW1c2faieiedql/WPi3YDInUXXmlLw8cZ2rdnTQqPi9rrztqj7FaWc9utb2g8Ss3t3Fl24vqnXSqflF7YJMyMoZE8l57zZdZIjO17k4aFZ+X363w9iAhxtwd2gpz12InW1jwKze3cWXbi+qddKp+UXsoRiDS93L0OKGZWncnjYrPy++W7qg1mmlkGhbGcyYaRc9TT00eErnkEj3/OsTojloBu19piouLhWxhwa/c3MaVbS+qd9Kp+kXtme+qBEUqLzOhLVs8eWlmptbdSaPi8/K7pTtqBexWxSorKxOyhQW/cnMbV7a9qN5Jp+qXtacTxLj1lLw8miEyU+vupFHxefnd0h21AmNjY1l9XV1dQraw4FdubuPKthfVO+lU/bL2dIIYt56Sl9UMEYXhkJladyeNis/L75Zej1oCIloLYO3ixYuxZ88eAEB5eTkikQgOHDgAwHiDiZnR0dFhtgEA7N+/H6OjowCA2tpaDA8Pp96Emj9/PvLy8tDb2wvA2GttwYIFqR0icnNzsXjxYnR3d6cWiFm0aBEGBwdTE/ErKiqQk5OTeoBRXFyMsrKy1D+WvLw81NXVoaurK/UwtK6uDsPDw6nPUllZiWQyib6+PgDGLhulpaXYt28fACASiaC2thadnZ2ptzPr6+tx6NAhHD16FABQVVWFRCKRilFaWori4mJ0d3cDAAoKCrBw4UJ0dHSkFrdqaGhAb28vYrEYAKC6uhqxWCyVV1lZGQoLC9HT0wMAKCwsRE1NTcpv0tPTg5GREQBATU0NRkZGMDAwMKlOZl7mOg7pdWpoaMDhw4dTca3qFI/HU/70OvX19VnWaXx8HH19fbZ1+vKXy3HrrWP43OcG0NWVsKzTwMBAai1mL+oUj8cxODiI999/f2qdTjwRBT/7GRZefjmwbRviN96IZGkpCu6+G73Ll0+qUzweR39/f6pOY2NjqetjVaclS5bY1ikWiyEWi6W+T9nqZH6f+vr6hL5PyWQylUe279ORI0dSmsw6DQ8PI5FIWH6fzDpk1ml0dBRDQ0NSdcqK1Xvl+rA/li9fnvVd/c7OTiFbWPArN7dxZduL6p10qn5Zux3Tsdy0UF5mIo2NxvohjY2Oic3UujtpVHwq1wJZ1vog5uxLdmqsOf3003n79u1Bp6GZpaxaZQyFNDcboxGB095ujMsMDAC7dk0ey25tDf7J6CyCiHYw8+mZdj1GrYDdmrl6jNqbuMfTGHUm0zGFTyovc/x606apDxw3bJg0jj1T6+6kmXFj1ERUAuACAMsB/ArA71jflqewehnG7gWZoPErN7dxZduL6p10qn5Zux3RqP83qUr1yUzMvMvetg34xCeAp59G4sQTpzUvr+rupFHxefndErqjJqJaIrqRiF4A8N8ALgZwBMBXAewjon8noouJqMizzDQaDYCQ7gWQfpddUgIMDQEbNqDmsstClujsQGiMmojeBfBLAM8A+E9mTqT5ygB8HBOdNzNf61OuoWHlypW8Y8cOS18ikZiyaJOVLSz4lZvbuLLtRfVOOlW/rF0GP8asPa271Ri2YqJB1d1Jo+JTucauxqiZ+QRm/mdmbk/vpCd8A8z8CDN/8njopAH7jQPMaUZOtrDgV25u48q2F9U76VT9snYZ/Biz9rTuaXfXY2ec4ep19KDq7qRR8Xl5jfXDRAXsNg4w51A62cKCX7m5jSvbXlTvpFP1y9plyHzt3IuhEF/qHo1i3xNPHHsdPeNBox95eVV3J42Kz8trLNxRE1E1Ea0non8joh9M/LmeiGo8y0aj0TgSihX47DB/BQCUO2zNZBw7aiL6IBH9DMAuAOsB5APomfhzPYC3iOhnRNToa6Yhwm7cqbKyUsgWFvzKzW1c2faieiedql/W7gYvhkJ8rXvmdD7g2MwQh846qLo7aVR8Xl5jkTvqhwE8BqCWmc9n5puY+faJP88HsBDA4wB+6FlWMxirYRG7oZKg8Ss3t3Fl24vqnXSqflm7G7wYCpmWumeZGYJly4zDIuGg6u6kUfF5eY0dO2pmPouZf8bMo0Q0Rc/McWZ+kpnP8SyrkGM3P9J8r9/JFhb8ys1tXNn2ononnapf1u4lKkMh01r3aBR4+uljd9e7dhmHxZBIUHV30qj4vLzGsg8TD3h2Zo1G4wkZ2yGGczg4/e66sdE4AOEhkeMd0RdeTiWifACFWfx7Pc0q5NhtHFBSUiJkCwt+5eY2rmx7Ub2TTtUva/eSjO0Qhe6uA6t7NAq89ZZxZA6JrFqF8jfe8PZ8Ejo7jYrPy2ssekf9HIBhAIVE9CgR/QsRrSGiGiKqBTDPs4xmAHYbB5SWlgrZwoJfubmNK9teVO+kU/XL2v1C9EFjKOqeOSSybRtKr75a6u7aq7o7aVR8Xl5j0Rde6gAsAjAG4GUAJ8B4ffyvADoB/MSzjGYAdhsHmGvNOtnCgl+5uY0r215U76RT9cva/SL97tpuGCQ0dc944EjDw44PHFXOJ6Kz06j4vLzGwmPUzHwIwHJmfpCZb2DmswAUAyhh5v/lWUYajcYTQj/fOp2Ju+uRpibjZ/OBox6/BiA2j3oDERUAADP/Nd03sdb1USIqIKINfiUZNsxdW6yIRCJCtrDgV25u48q2F9U76VT9svbpwO4hYyjrHo3i/WeeOfbAsajIGL+26ay9qruTRsXn5TV2XJSJiP5fGC+2PAfgPwG8DWAIQAmADwD4CIxlTzcz8+2eZRZi9MYBmplG6DYjEKG93eikh4aMjrusbNZvVKC8KBMzfwnAChjLm14H4HkAb8LouP8BwJ8BrDheOmnAfuOAzs5OIVtY8Cs3t3Fl24vqnXSqfln7dJP5kHFG1N3iYSPWrp00du1V3Z00Kj4vr7How8RDzPxvzBxl5ipmjjBzNTOfx8z/m5nD+0bHNGO1sp7jxpUB4ldubuPKthfVO+lU/bL26SbzIeMll1T6MvTred0z326MxYyx64kOO/+llzzLy06j4vOy9tKr5xFRFRH9X0R0kmdZaDSaaaOlBdi5s3BmPGQ0Me+uzbHriQ676jOfMe6w771XeKbIjMRqx9tsB4B/BpAA0AFgAMZwyCdkYsyGY+XKlZyN8fFxIVtY8Cs3t3Fl24vqnXSqfll7kLS1MZ9zTpLb2rzf8Xxa6t7WZuyIXlRk7I4OMJeUTP57xgcSiWunUfGpXAtk2YVc9o76FgDnMXMDgHIAnwVwFxF9yrP/OWYAdmt9HDp0SMgWFvzKzW1c2faieiedql/WHiTRKLBly0GpNxlFmZa6m283PvMMxk45xbjLvuOOyTNFMj6QSFw7jYrPy9rLdtQRAL8DUlPz2gBcCuAOzzKaAditinX06FEhW1jwKze3cWXbi+qddKp+WXvQmHl5vXvMtNY9GsW+//gPo9PeuDHVeaOxEejqOjYksmoVki++6OrcKj4vay/bUT8J4KYM2zsAqr1JR6PRTCfmszogpIs5yRKNGtP49u41HjrecguwbRuqr77a6LRnKEKb26bERMUAtgBgAL8A0AfgcgBvMvOXfckwhDQ1NfHOnTstfUePHsWcOXMcbWHBr9zcxpVtL6p30qn6Ze1Bk5mXV/OsQ1H39nbjNfT33jMeOprk5AC/+lXWedh251bxqVwLV5vbmjDzMDP/HYD7ACwH8C8A1gC4jIieJKJWIvq/pTKbgdj952Y1fm03ph00fuXmNq5se1G9k07VL2sPmsy8vFoqNRR1TxvDRnMzcP314JwcIJmcMg9b9NwqPi9rr7S5LTM/y8Z6H6fBWDlvHYw77UIYbzHOauzmR77//vtCtrDgV25u48q2F9U76VT9svagycxLZalUkbh+t7fVmx/qe9/Dgc2bp87Drq4G5sxJDYnYxVLxeVl70fWo/z8i+pssO7wkAOyBMW3vPWa+wLPsphEiOoGIfjixP6RGc9xi3l1fcsksGbcGMLJq1dR52L29xp+33BL6Dyl6R70XwJcBdBHRvxPRJUR0IhF9loheAPAXAGthrAMiDBHlEtEbRLRVLu1JMR4iol4ietPCt4aI3iaid4joFrs4zPwuM18nck67jQP0etTexNXrUfuLXV7mjeiWLfJ31qGue/qQSGMjUFUFEBlDIp/4BObbbFowU9aj/iYzRwE0AngRxlDHL2EsynQ3gDpm/hQz/1ry/DcB2G3lmHgDsiTDZvU25MMwxskz2+cCeADGglGNANYRUSMRLSeirRlHlUzSdhsHFBcXC9nCgl+5uY0r215U76RT9cvag0YkL5U76xlRd7PDPnAAePHF1C4zJTabFtidZzpqL/swcYCZf8rMVzLzMmb+AjP/mpmlX2onojoAHwfwgyyScwH8gogKJ/TXA9hkkdNLAKwGg84E8M7EnXIcxk7qFzPzn5j5ooyjVyZ3u40Duru7hWxhwa/c3MaVbS+qd9Kp+mXtQSOSl8qd9Yyru/lqurlpwfnnW07jszvPdNQ+z7NI8twH4GYYy6VOgZmfJKKlAB4joidhrNR3nkT8RTB2nzHpAnBWNjERVQD4VwAriOhWZv66hWYtgLWLFy/Gnj17AADl5eWIRCI4cMDY93dwcBDMjI6ODrMNAGD//v0YHR0FANTW1mJ4eBiDg4MAgPnz5yMvLw+9vcb/F3PmzMGCBQuwd6+xFWVubi4WL16M7u7u1Mp9ixYtwuDgIIaGhgAAFRUVyMnJwcGDBwEY/5uXlZWhq6sLAJCXl4e6ujp0dXWlnkbX1dVheHg49VkqKyuRTCZTuyeXlJSgtLQ0tVNFJBJBbW0tOjs7Uw9U6+vrcejQodTk/qqqKiQSiVSM0tJSFBcXp/7RFhQUYOHChejo6EjNnmloaEBvby9iE1OpqqurEYvFUnmVlZWhsLAQPT09AIDCwkLU1NSk/CY9PT0YGRkBANTU1GBkZAQDAwOT6mTmVVRUhKqqqkl1amhowOHDh1NxreoUj8dT/vQ69fX1WdZpfHwcfX19rus0MDCA4eFhz+oUj8cxODiYeuBlV6fPfa4AIyNl+OpXC3DgwOQ6xeNx9Pf3p+o0NjaWuj5WdVqyZIltnWKxGGKxWOr7lK1O5vepr69P6PuUTCZTeUyp04knou7JJ5F74YWgZBL8L/+C5EMPIX7vvTjwoQ8BAIaHh5FIJCzrZNYhs06jo6MYGhqSqlNWrN4r9/sAcBGAByf+/hEAW220jwEYBFBpo1kCYy53uu0KAD9I+3k9gG95kf+pp5465R19k+7ubiFbWPArN7dxZduL6p10qn5Ze9Co5CWyLshMrTsz88DttzPn5BxbMyQnh/meexzbe1l7ZFnrI6iO+usw7nD3AOgBcBTATyx0q2Gsff0jAPfbxLPqqM8B8ELaz7cCuNWL/O0WZdJoZivNzUaPYXbWXi7mFBrMBZ+IjA9LZPw8TR80VB31pASy3FHD2KzgzwBOhDGW/lMAX8sSw6qjzgPwLoClMNYo+S8Ay7zIefny5Vkv9J49e4RsYcGv3NzGlW0vqnfSqfpl7UGjkld655zeabuN66a9V3Wfornnnkl31+Nz52btrL2sfbaOWumFl2liDoArmPmvzJwE8GkYy6tOgogeBfAqgFOIqIuIrgNS87s/D+AFGDNLnmDmt/xO2rjWzraw4FdubuPKthfVO+lU/bL2oFHJK/2lmGwzQmZq3adoNm40XjdvbAQiEeQcOQJceKHlW43TUfsgHyYCAJj5twB+a2F/JePnMQDft9Cts4n9HIwtwzQajYdEo8ZhrhHS0jILtzI0p/EtW2a8zRiPH3ur8ZlnpvUDSy3KpDGw29yWmafsUm5lCwt+5eY2rmx7Ub2TTtUvaw8ar/Jqbzc6aXPP2Zlad1tNezt4wwbQO+8YnTVgvN24dCmwaRP4b//Ws9p7siiTxsBuHrU5JcjJFhb8ys1tXNn2ononnapf1h40XuVlDoO0tBid9kytu60mGkXvr38NPPdcaigktWbIhg3TUnvdUStg91tILH1ZRRtbWPArN7dxZduL6p10qn5Ze9B4mZe5iNOGDcCFF85ztWxGUHV30sRisWNDISelvSD93nvgtjZXuYmgO2qNRuMK88EiMAM3zVVh06ZJiztVr18PLFni68JOuqNWIC8v+zPY6uqpm91Y2cKCX7m5jSvbXlTvpFP1y9qDxsu8zNkgmzYBZ5017mrVvaDq7qSZ5Etf3CknB8QMdHQA550HlJcDBQVAeTkaPvhBz3aV0R21AnZDH+arw062sOBXbm7jyrYX1TvpVP2y9qDxI69oFHjhhWGlVfdU8/Kq7k4aS180Ctx1F5KFhcYqfMzAwIDxwHFgADQyAtx5p1B+TuiOWgG79/LNdQ+cbGHBr9zcxpVtL6p30qn6Ze1B42fd3axnHVTdnTRZfRs3Yu/u3cDddxudtUlZmdGB3+HNvt+6o9ZoNJ7iZj3rGcvGjcaSqc3NQFsb0N9vdOAbN3oSXnfUCtitR11WViZkCwt+5eY2rmx7Ub2TTtUvaw+a6ah7+j6MKu291Ivo7DRCvvRXNyVyE0F31ArY7fBSWFgoZAsLfuXmNq5se1G9k07VL2sPmumou9lvAeJDIEHV3Umj4vPyGuuOWgG7F17MNZOdbGHBr9zcxpVtL6p30qn6Ze1BM511l9ksN6i6O2lUfF5eY91RazQaX2ltNaYdDwyEfg/Z0KI7agXs3t/XQx/exNVDH/4ynXWPRoGystQb17bDIHrowxq9KJMCdosyaTSaqZiLNw0MGB12c/Ox8WvNMfSiTB5iNzE+cx+/bLaw4FdubuPKthfVO+lU/bL2oJnuuqe/vWg3EySoujtpVHxeXuPA16PWaDTHD+YSzuaDxVm3hrVP6DtqjUYzrcjMAtEY6DFqBfQYtUajjjlefcklxtuL5qYDGj1G7Sl6HrX/cfU8an8Jsu6Zr5h/4hPHZoHoedTW6I5aAbvfQkZGRoRsYcGv3NzGlW0vqnfSqfpl7UEThrq3tgIlJcDQkPO0PbfnE9HZaVR8Xl5j3VFrNJpAiEaBp58+tunAtm3AN74RzrVRgkaPUSuwcuVK3rFjh6VvZGRkykR3K1tY8Cs3t3Fl24vqnXSqfll70ISt7ua49e23x3HBBRHPzyeis9Oo+FSuhR6j9pBkMpnVp4c+vImrhz78JWx1NzfJ/cpXcqSGP/TQhyYrdhsHDAwMCNnCgl+5uY0r215U76RT9cvagyaMdW9pAV57LU9q2p5XdXfSqPi8vMa6o9ZoNKGgtRVoahpxtefibEV31ArYbRxQXl4uZAsLfuXmNq5se1G9k07VL2sPmjDWPRoFfv3rUctpe27PJ6Kz06j4vLzGuqNWwG71vEhk6oMQK1tY8Cs3t3Fl24vqnXSqfll70IS57unT9pyGQbyqu5NGxeflNdYdtQKJRCKr78CBA0K2sOBXbm7jyrYX1TvpVP2y9qAJc93NaXsia1h7VXcnjYrPy2usO2qNRhM60tew1muC6I5aCbuhj6KiIiFbWPArN7dxZduL6p10qn5Ze9DMhLqL7AzjVd2dNCo+L6+xfuFFAbtFmZh5SkduZQsLfuXmNq5se1G9k07VL2sPmplS91WrjAeLjY3GHXbmAk5e1d1Jo+JTuRb6hRcPsds4oKOjQ8gWFvzKzW1c2faieiedql/WHjQzpe6trZNfMc+cCeJV3Z00Kj4vr7HuqDUaTWhJ3xnGnAkiMm1vtqE7ao+x+lUnjL/6mviVm9u4Cr8yeqJT9cvag2am1d2cCZLZWXtVdyeNis/La6zHqCcgohMA3AZgHjNfbqfVGwdoNMHQ3m500kNDs3OD3FCNURNRIRG9RkT/RURvEdFXXcR6iIh6iehNC98aInqbiN4holvs4jDzu8x8ncg57TYO2L9/v5AtLPiVm9u4su1F9U46Vb+sPWhmat0z51g/8USfZ3nZaVR8Xl7joIY+RgH8LTN/GMBpANYQ0dnpAiKqIqKSDNtJFrEeBrAm00hEuQAeAHABgEYA64iokYiWE9HWjKNKJnm730JGR0eFbGHBr9zcxpVtL6p30qn6Ze1BM5Prnj7H+u6753oW106j4vPyGgfSUbPB8MSP+RNHZu93LoBfEFEhABDR9QA2WcR6CcD7Fqc5E8A7E3fKcQCPAbiYmf/EzBdlHL0efTSNRjMNmHOsh4bklkWdqeQFdeKJO94dAE4C8AAz/yHdz8xPEtFSAI8R0ZMA/gHAeRKnWASgM+3nLgBn2eRTAeBfAawgoluZ+esWmrUA1i5duhR79uwBYCy8EolEUq+L5ufng5lTU3OICLW1tdi/f3/qf9ja2loMDw9jcHAQADB//nzk5eWht9f4/2LOnDlYsGAB9u7dC8BYBGrx4sXo7u5OTQ1ctGgRBgcHMTQ0BACoqKhATk4ODh48CAAoLi5GWVkZurq6AAB5eXmoq6tDV1dX6hX4uro6FBQUpD5LZWUlkskk+vqMXydLSkpQWlqKffv2ATDWLqitrUVnZ2dqqdf6+nocOnQIR48eBQBUVVUhkUggkUhgz549KC0tRXFxMbq7uwEABQUFWLhwITo6OlK/mTQ0NKC3txexWAwAUF1djeLi4lReZWVlKCwsTO1BV1hYiJqampTfvKY9PT2pNYBramowMjKSWmrSrJOZV1FREaqqqibVqaGhAbm5uam4VnUqLy9P+dPrlEgk0NnZOaVOlZWV6Ovrc12ngYEBDA8Pe1an8vJyDA4O4v33jXsc1TrF43H09/en6lRRUZG6PlZ1WrJkiW2diouLEYvFUt+nbHVqbNyPwsJy7NpViNtvT2LFigHb71N6Htm+T0VFRSlNZp0KCgqQSCSy1mnPnj1T6jRv3jwMDQ1J1SkrzBzoAaAMwG8AfCiL/zEAgwAqbWIsAfBmhu0KAD9I+3k9gG95kfOHP/xhzkZfX5+QLSz4lZvbuLLtRfVOOlW/rD1oZkPd29qYTzlljBsbjb+7jWunUfGpXAsA29mizwl8eh4zDwD4LazHmVcD+BCApwF8WTJ0F4DFaT/XAehWy3Iydju8mP+rO9nCgl+5uY0r215U76RT9cvag2Y21D0aBebOTQitByIS106jTHdYEgAAFX5JREFU4vPyGgc166OSiMom/l4E4O8A/DlDswLA9wFcDOBaAPOJ6GsSp3kdwMlEtJSIIgCuAvBLL/LXaDTh4ItfHEBzM2b9ZgNB3VEvBPAbIvojjA71RWbemqGZA+AKZv4rMycBfBrAlHcyiehRAK8COIWIuojoOgBg5gSAzwN4AcBuAE8w81teJG+3ccD8+fOFbGHBr9zcxpVtL6p30qn6Ze1BM1vqvnbtHLzyClKbDWS7sxaJa6dR8Xl5jQN5mMjMfwSwwkHzSsbPYzDusDN162xiPAfgOcU0s2L3xlFe3tRLamULC37l5jaubHtRvZNO1S9rD5rZVvfWVmDDhmMr7aUv3CQa106j4vPyGgc+Rj0Tsds4wHzS7GQLC37l5jaubHtRvZNO1S9rD5rZVnen9atF4tppVHxeXmPdUWs0mlmByPrVMxXdUSuQk5P9ss2ZM0fIFhb8ys1tXNn2ononnapf1h40s7HudnfVInHtNCo+L6+xXpRJAbtFmZLJ5JSO3MoWFvzKzW1c2faieiedql/WHjSzte7t7cZYNWAsjWqOVYvEtdOo+FSuRagWZZrp2G0cYL5N6GQLC37l5jaubHtRvZNO1S9rD5rZWvf0u+r0datF4tppVHxeXmPdUWs0mllFa+vs22RAd9QeYzXH2m7eddD4lZvbuLLtRfVOOlW/rD1oZnPdrTYZePVV5/Fiu3Or+Ly8xnqMWgG9cYBGE37SNxkoKTE678z51WFDj1F7iN3GAebqY062sOBXbm7jyrYX1TvpVP2y9qA5HuqeeWfttB6IXSwVn5fXWHfUCtj9FmL1oNHu4WPQ+JWb27iy7UX1TjpVv6w9aI6XukejwB13AHPnJnHJJeqxVHxeXmPdUWs0mlnNli3AkSM5+PKXgWXLZubDRT1GrcDKlSt5x44dlr6xsTHk5+c72sKCX7m5jSvbXlTvpFP1y9qD5niqe3s7cMkljOFhY42ebJvi2sVS8alcCz1G7SF2uzHo9ai9iavXo/aX46nu0SiwefMgGhuNV8xbW+VjHZfrUc907DYOMLdccrKFBb9ycxtXtr2o3kmn6pe1B83xVvcVK/rx1lvG24obNlgPgdjFUvF5eY11R63RaI4bWlqMtxYz31wMO7qjVsBundmKigohW1jwKze3cWXbi+qddKp+WXvQHK91N1fYKyqaOmXPLpaKz8trrDtqj7FahCWMi/KY+JWb27iy7UX1TjpVv6w9aI7XukejwFtvAc88M3VJVLtYKj4vr3E4/xWFHLuNA8zt5Z1sYcGv3NzGlW0vqnfSqfpl7UFzvNfdfENx165jq+3ZxVLxeXmNdUet0WiOa957L/xj1bqjVsDuV5ri4mIhW1jwKze3cWXbi+qddKp+WXvQ6LobM0BKSoBYzHiwuHNnudJ5pqP2+oUXBexeeEkkElMeNlrZwoJfubmNK9teVO+kU/XL2oNG190gfeGm4mLGli1kuXCT3Xm8rL1+4cVD7BZl6urqErKFBb9ycxtXtr2o3kmn6pe1B42uu0H6wk3Dw5R1yp7deaaj9rqj1mg0xzVmZz13blJolb0g0B21x1j9qhPGX31N/MrNbVzZ9qJ6J52qX9YeNLruk4lGgX/+50GUlMBylT279tNRez1GrYDeOECjmX2sWgVs22a8DLN06eTNcacLPUbtIXbrzOoxam/i6jFqf9F1n8o//dPB1CyQXbsmD4HoMepZhtXLMHYvyASNX7m5jSvbXlTvpFP1y9qDRtd9KmeffQRPPw3LVfbs2k9H7XVHrdFoNBOYr5hfc40xbe/ee4POyECPUSug51H7H1fPo/YXXXd7TWnpsU1xBwf1POoZid3GAQMDA0K2sOBXbm7jyrYX1TvpVP2y9qDRdbfX3HGH8VBx/nxjXrVd++move6oFbDbOGB4eFjIFhb8ys1tXNn2ononnapf1h40uu72mo0bgRUrgI4OYwjkhReyjzdPR+11R63RaDQWtLYaQx9DQ8ANN1QFunCT7qgVsBt3qqysFLKFBb9ycxtXtr2o3kmn6pe1B42uu7PGfGOxqMjYxdxcDlU0tpfXWHfUHmM1LGI3VBI0fuXmNq5se1G9k07VL2sPGl13MU00arz8AmRfDnU6aq87agXs5kf29fUJ2cKCX7m5jSvbXlTvpFP1y9qDRtddXLNpk7EOiLkcamZnPR211x21RqPR2BCNAt/9bm9qn8VsQyB+ojtqBew2DigpKRGyhQW/cnMbV7a9qN5Jp+qXtQeNrrucZs2a/KxDINNRe91RK5Cbm5vVV1paKmQLC37l5jaubHtRvZNO1S9rDxpddzlNaWnppB1h0tcBmY7a645aAbuNA/bt2ydkCwt+5eY2rmx7Ub2TTtUvaw8aXXc5zb59+1KzQOrrgTfeOPZ6+XTUXnfUGo1GI0g0CvT3G3fVd945fefVHbUCRJTVF4lEhGxhwa/c3MaVbS+qd9Kp+mXtQaPrLqdJ92W+Xj4dtdeLMimgNw7QaI5vli0z1qxubDRW2/MKvSiTh9htHNDZ2SlkCwt+5eY2rmx7Ub2TTtUvaw8aXXc5TTbfe+8Bjz7a6yo3EXRH7TFWK+vZrbYXNH7l5jaubHtRvZNO1S9rDxpddzlNpi99Bsj11y+wfGPRy2usO2qNRqORxJwBUlJirAPi987leoxaAbsx6mQyOeWFGCtbWPArN7dxZduL6p10qn5Ze9Doustpsvna24E77mDceSdN2QhX5VroMWoPsVvr49ChQ0K2sOBXbm7jyrYX1TvpVP2y9qDRdZfT2PkSCev3Kry8xrqjVsBuVayjR48K2cKCX7m5jSvbXlTvpFP1y9qDRtddTpPN19ICvP56xHKxJi+vse6oNRqNRpHWVmNlvaEh4Pzz/dsMV3fUCthtHFBVVSVkCwt+5eY2rmx7Ub2TTtUvaw8aXXc5TTZfNAo8/ngcOTlAMgnccsuxO2svr7HuqBWwewBrNX5tN6YdNH7l5jaubHtRvZNO1S9rDxpddzmNnW/16jjuugupztqcAeLlNdYdtQJ28yPff/99IVtY8Cs3t3Fl24vqnXSqfll70Oi6y2mcfBs3AnfdZUzXu+QSudxE0B31BER0AhH9kIh+FnQuGo1m5rFli7GxwJYt3scOpKMmosVE9Bsi2k1EbxHRTS5iPUREvUT0poVvDRG9TUTvENEtdnGY+V1mvk7knHZzI/V61N7E1etR+4uuu5xGxNfaOnkJ1NmwHnUCwP/DzB8EcDaA/0VEjekCIqoiopIM20kWsR4GsCbTSES5AB4AcAGARgDriKiRiJYT0daMQ2rU327jgOLiYiFbWPArN7dxZduL6p10qn5Ze9DoustpRHzpS6Decgvw2mszfIcXZt7PzDsn/j4EYDeARRmycwH8gogKAYCIrgewySLWSwCsBoPOBPDOxJ1yHMBjAC5m5j8x80UZh/WqKlmw2zigu7tbyBYW/MrNbVzZ9qJ6J52qX9YeNLruchpR3x13HHuoeNtt3q31kX2e2TRBREsArADwh3Q7Mz9JREsBPEZETwL4BwDnSYReBCB9+aouAGfZ5FEB4F8BrCCiW5n56xaatQDWLl68GHv27AEAlJeXIxKJ4MCBAwCAwcFBMDM6OjrMNgCA/fv3Y3R0FABQW1uL4eFhDA4OAgDmz5+PvLw89PYa/1/MmTMHCxYswN69ewEYd/CLFy9Gd3d3auW+RYsWYXBwEENDQwCAiooK5OTk4ODBgwCM/+XLysrQ1dUFwJhSWFdXh66urtTT6Lq6OgwPD6c+S2VlJZLJZGr35JKSEpSWlqZ2qohEIqitrUVnZ2fqgWp9fT0OHTqUmtxfVVWFRCKRilFaWori4uLUP+aCggIsXLgQHR0dqdkzDQ0N6O3tRSwWAwBUV1cjFoul8iorK0NhYSF6enoAAIWFhaipqUn5TXp6ejAyMgIAqKmpwcjICAYGBibVycyrqKgIVVVVk+rU0NCAw4cPp+Ja1Skej6f86XXq6+uzrNP4+Dj6+vpc12lgYADDw8Oe1Skej2NwcDD1wEu1TvF4HP39/ak6jY2Npa6PVZ2WLFliW6dYLIZYLJb6PmWrk/l96uvrE/o+JZPJVB7Zvk9HjhxJaTLrNDw8jEQiYVknsw51dXW49toB1NYm8JWvzMfgIOGZZ45i+fJe4TplhZkDOwAUA9gB4FIbzWMABgFU2miWAHgzw3YFgB+k/bwewLe8yPvUU0/lbHR3dwvZwoJfubmNK9teVO+kU/XL2oNG111OI+trbGQGjD9lALCdLfqcwBZlIqJ8AFsBvMDM38iiWQ3g2zA68yFm/nwW3RIAW5n5Q2m2cwB8hZk/NvHzrQDAFnfKsuiNAzQajR2qGwuEalEmMsYDfghgt00nvQLA9wFcDOBaAPOJ6GsSp3kdwMlEtJSIIgCuAvBLd5kb2G0cYP6K5mQLC37l5jaubHtRvZNO1S9rDxpddzmNrG/TJqCpaQSbpjxVUyOoWR+rYAxF/C0R/Z+J48IMzRwAVzDzX5k5CeDTAKZcESJ6FMCrAE4hoi4iug4AmDkB4PMAXoDxsPIJZvZw0xxrrH5DCeq3FhH8ys1tXNn2ononnapf1h40uu5yGllfNAo89VTPlKVPVQnkYSIz/w5A9h1iDc0rGT+PwbjDztSts4nxHIDnFNPUaDSaUKA3DlDAboyamafsUm5lCwt+5eY2rmx7Ub2TTtUvaw8aXXc5jYpP5VqEaox6pmM3j9qcEuRkCwt+5eY2rmx7Ub2TTtUvaw8aXXc5jYrPy2usO2oF7H4LMeeYOtnCgl+5uY0r215U76RT9cvag0bXXU6j4vPyGuuOWqPRaEKO7qgVsNs4oLq6WsgWFvzKzW1c2faieiedql/WHjS67nIaFZ+X11h31ArYDX1YzbG2m3cdNH7l5jaubHtRvZNO1S9rDxpddzmNis/La6w7agXs3ss31z1wsoUFv3JzG1e2vajeSafql7UHja67nEbF5+U11h21RqPRhBw9j1oBIjoM4L+zuOcBOJxhWwDgkK9JqWOVbxjiyrYX1TvpVP3Z7GGtva67nEbFp1L7BmaunGK1WqlJH46r/n1PxocsK2KF4bD7LEHGlW0vqnfSqfpt7KGsva67nEbF52Xt9dCHGs8o+sKIX/m6jSvbXlTvpFP167p7EzeoujtpAv3O66GPaYCItrPFa6Ga2Y+u/fGLl7XXd9TTw/eCTkATGLr2xy+e1V7fUWs0Gk3I0XfUGo1GE3J0R63RaDQhR3fUGo1GE3J0Rx0ARDSXiH5ERN8nor8POh/N9EFEJxDRD4noZ0Hnopk+iOiSie/7L4jofNn2uqP2CCJ6iIh6iejNDPsaInqbiN4holsmzJcC+BkzXw/gf057shpPkak9M7/LzNcFk6nGSyTrvmXi+34NgCtlz6U7au94GMCadAMR5QJ4AMAFABoBrCOiRgB1ADonZNlXeNLMFB6GeO01s4eHIV/32yf8UuiO2iOY+SUA72eYzwTwzsRdVBzAYwAuBtAFo7MGdA1mPJK118wSZOpOBncDeJ6Zd8qeS3cS/rIIx+6cAaODXgTg5wAuI6JvY+a9eqwRw7L2RFRBRN8BsIKIbg0mNY2PZPvO/xOAvwNwORHdKBs0+1YlGi+w2oKYmfkIgGunOxnNtJKt9n0ApL+omhlDtrpvArBJNai+o/aXLgCL036uA9AdUC6a6UXX/vjEl7rrjtpfXgdwMhEtJaIIgKsA/DLgnDTTg6798YkvddcdtUcQ0aMAXgVwChF1EdF1zJwA8HkALwDYDeAJZn4ryDw13qNrf3wynXXXizJpNBpNyNF31BqNRhNydEet0Wg0IUd31BqNRhNydEet0Wg0IUd31BqNRhNydEet0Wg0IUd31JrjEiIqIKJdRFQTdC5+Q0TfUFlfQhMedEetmXUQ0R4i+jsH2T8CeImZeybaPExETEST1gcnovsm7Nek2RZOLP6/n4iGiOjPRPRVIpormedviegzMm0UuRfAbRNvymlmILqj1hyv3ADgxxm2vwD4tPkDEeUBuALAX9Ns82G8jVYE4BxmLgFwHoAyACf6nLMSzLwfwJ+hN6mYseiOWjOrIKIfA6gH8AwRDRPRzRaaehid6h8yXM8AWEVE5RM/rwHwRwA9aZovAhgC8Clm3gMAzNzJzDcx8x8tzlVIRD8hoj4iGiCi14momoj+FcBqAPdP5Hn/hP5/ENGLRPT+xC4hn0yL9TARfWfCP0RE/0lEDRM+IqL/PbHjyGEi+iMRfSgtld8C+LjoddSEC91Ra2YVzLwewF4Aa5m5mJnvsZAtB/DuxLoM6YzAWEDnqomfrwawOUPzdwB+zsxJwZQ+DWAejBXVKmAscRpj5tsAvAzg8xN5fn5i6ORFAD8FUAVgHYAHiWhZWry/B3AngAUA/g+ARybs5wP4GwAfgHF3fyWAvrR2uwF8WDBnTcjQHbXmeKQMxl2xFZsBXE1E8wCcC2BLhr8CwH6Jc41NtDmJmceZeQczD2bRXgRgDzP/OzMnJnYCeQrA5WmaZ5n5JWYeBXAbgHOIaPHEeUoA/A8Ya/jsnhjyMBmC8bk1MxDdUWuOR/phdGpTYObfAaiEsbfdVmaOZUj6ACyUONePYayk9hgRdRPRPUSUn0XbAOCsiSGSASIagHEHnT4zJbV7CDMPw9gKqpaZfw3gfhj78f3/7d0/aBRBFMfx76+QNDGIlWCXQsiJNkEEEUTs7OxsYm8d7QIiFiKo4BWC2iiIlaVgY4rYpZLYWKiFJIVp4p9gleJnMasslz1MkJjx8vvAVju7PBbu3fBmmLcq6aGkidZz+4Gv24g7KpJEHaPoT0dCvgUmm8XCLk+BWTaXPQBeARckbem3Y3vD9nXbPeAUZdZ8aUicy8CC7QOta9z25daY34fSSxoHDtIcTG+7b3saOEopgVxtPTcFLG0l5qhPEnWMolVgcthN2yvAe0oj0i59yk6O1x337gITwJPWQt7hZq/y8cHBks5KOtZ0p/5OKVH86jw/GOcL4IikGUn7muuEpKnWmPOSTjdb7W4Ai7aXm3Enm9n6D0q9vd3h/gzwctg3ibolUccougnMNeWDK0PGPABmum7YXrM9747D2m2vUWbGG8CipHVgHvgGfOh43SHgOSVJvwMWKDN2gHuUZqdfJPVtr1MWBS9SZsmfgVvAWOt9z4BrlJLHNKU0AuXP4xGlrPOJUqK5DWXfN9Bjc709/hNpHBB7kqQx4A1wbmDRrVqSHgMrtue2+dwd4KPt+zsSWOy4dCGPPanZNdHb7Tj+Bduzux1D/J2UPiIiKpfSR0RE5TKjjoioXBJ1RETlkqgjIiqXRB0RUbkk6oiIyiVRR0RU7icy1vfKk95g+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time = np.arange(1, 102, 1)\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(time, sim1, marker = \".\", markersize = \"3\", linestyle = \"None\",\n",
    "         c = \"blue\", label = \"λ = {}\".format(rate1))\n",
    "plt.plot(time, sim2, marker = \".\", markersize = \"3\", linestyle = \"None\",\n",
    "         c = \"red\", label = \"λ = {}\".format(rate2))\n",
    "plt.plot(time, sim3, marker = \".\", markersize = \"3\", linestyle = \"None\",\n",
    "         c = \"black\", label = \"λ = {}\".format(rate3))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"t (MC steps)\", size = 12)\n",
    "plt.ylabel(r\"$\\langle ρ(t) \\rangle$\", size = 12)\n",
    "#plt.xticks(size = 12)\n",
    "#plt.yticks(size = 1)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(markerscale = 3, fontsize =12)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/rho_t.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Homogeneous initial conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 3.2975\n",
      "Relative R_squared: 0.9011813373224974\n",
      "Estimated delta expontnet: 0.8613968533116381\n",
      "CPU times: user 56 s, sys: 190 ms, total: 56.2 s\n",
      "Wall time: 55.4 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "N = 20\n",
    "perc = 1\n",
    "rates, r_sq_10, delta_10 = find_critical_point1(N, perc, 10**4, 10**3, 3.29, 3.32, 5)\n",
    "\n",
    "i_10 = np.argmax(r_sq_10)\n",
    "print(\"Estimated critical point:\",  rates[i_10])\n",
    "print(\"Relative R_squared:\", r_sq_10[i_10])\n",
    "print(\"Estimated delta expontnet:\", delta_10[i_10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 3.2975\n",
      "Relative R_squared: 0.962542260709981\n",
      "Estimated delta expontnet: 0.23531636357587202\n",
      "CPU times: user 3min, sys: 1.47 s, total: 3min 2s\n",
      "Wall time: 3min 4s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "N = 50\n",
    "perc = 1\n",
    "rates, r_sq_10, delta_10 = find_critical_point1(N, perc, 10**4, 10**3, 3.29, 3.32, 5)\n",
    "\n",
    "i_10 = np.argmax(r_sq_10)\n",
    "print(\"Estimated critical point:\",  rates[i_10])\n",
    "print(\"Relative R_squared:\", r_sq_10[i_10])\n",
    "print(\"Estimated delta expontnet:\", delta_10[i_10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 3.3049999999999997\n",
      "Relative R_squared: 0.999475010491045\n",
      "Estimated delta expontnet: 0.1541208806905507\n",
      "CPU times: user 4min 22s, sys: 1.33 s, total: 4min 23s\n",
      "Wall time: 4min 24s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "N = 100\n",
    "perc = 1\n",
    "rates, r_sq_10, delta_10 = find_critical_point1(N, perc, 10**4, 10**3, 3.29, 3.32, 5)\n",
    "\n",
    "i_10 = np.argmax(r_sq_10)\n",
    "print(\"Estimated critical point:\",  rates[i_10])\n",
    "print(\"Relative R_squared:\", r_sq_10[i_10])\n",
    "print(\"Estimated delta expontnet:\", delta_10[i_10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.29   3.2975 3.305  3.3125 3.32  ]\n"
     ]
    }
   ],
   "source": [
    "print(rates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\nu_\\parallel$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "exp_delta = 0.159\n",
    "pc = 3.29785\n",
    "ntraj = 1000\n",
    "nsteps = 1000\n",
    "time = np.arange(1, nsteps +1, 1)\n",
    "\n",
    "rho1 = simulate(100, 1, ntraj, nsteps, 2.8)\n",
    "rho1 = np.mean(rho1, axis = 0)\n",
    "\n",
    "rho2 = simulate(100, 1, ntraj, nsteps, 3)\n",
    "rho2 = np.mean(rho2, axis = 0)\n",
    "\n",
    "rho3 = simulate(100, 1, ntraj, nsteps, 3.7)\n",
    "rho3 = np.mean(rho3, axis = 0)\n",
    "\n",
    "rho4 = simulate(100, 1, ntraj, nsteps, 3.5)\n",
    "rho4 = np.mean(rho4, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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": [
    "timey = time**exp_delta\n",
    "\n",
    "y_axis1 = [a*b for a, b in zip(rho1, timey)]\n",
    "y_axis2 = [a*b for a, b in zip(rho2, timey)]\n",
    "y_axis3 = [a*b for a, b in zip(rho3, timey)]\n",
    "y_axis4 = [a*b for a, b in zip(rho4, timey)]\n",
    "\n",
    "v_par = 1.7\n",
    "\n",
    "x_axis1 = time*np.abs(2.8-pc)**v_par\n",
    "x_axis2 = time*np.abs(3-pc)**v_par\n",
    "x_axis3 = time*np.abs(3.7-pc)**v_par\n",
    "x_axis4 = time*np.abs(3.5-pc)**v_par\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x_axis1, y_axis1, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"blue\", label = \"λ = 2.8\")\n",
    "plt.plot(x_axis2, y_axis2, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"red\", label = \"λ = 3\")\n",
    "plt.plot(x_axis4, y_axis4, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"green\", label = \"λ = 3.5\")\n",
    "plt.xscale(\"log\")\n",
    "plt.plot(x_axis3, y_axis3, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"black\", label = \"λ = 3.7\")\n",
    "\n",
    "#plt.ylim([10**(-3), 10])\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(r\"$t|λ - λ_{c}|^{ν_\\parallel}$\", size = 14)\n",
    "plt.ylabel(r\"$ρ(t)t^{\\delta}$\", size = 14)\n",
    "#plt.title(\"$ν_\\parallel$ = {}\".format(v_par), size = 14)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(markerscale = 3, fontsize = 14)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/nu_par_1_7.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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": [
    "timey = time**exp_delta\n",
    "\n",
    "y_axis1 = [a*b for a, b in zip(rho1, timey)]\n",
    "y_axis2 = [a*b for a, b in zip(rho2, timey)]\n",
    "y_axis3 = [a*b for a, b in zip(rho3, timey)]\n",
    "y_axis4 = [a*b for a, b in zip(rho4, timey)]\n",
    "\n",
    "v_par = 1.2\n",
    "\n",
    "x_axis1 = time*np.abs(2.8-pc)**v_par\n",
    "x_axis2 = time*np.abs(3-pc)**v_par\n",
    "x_axis3 = time*np.abs(3.7-pc)**v_par\n",
    "x_axis4 = time*np.abs(3.5-pc)**v_par\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x_axis1, y_axis1, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"blue\", label = \"λ = 2.8\")\n",
    "plt.plot(x_axis2, y_axis2, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"red\", label = \"λ = 3\")\n",
    "plt.plot(x_axis4, y_axis4, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"green\", label = \"λ = 3.5\")\n",
    "plt.xscale(\"log\")\n",
    "plt.plot(x_axis3, y_axis3, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"black\", label = \"λ = 3.7\")\n",
    "\n",
    "#plt.ylim([10**(-3), 10])\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(r\"$t|λ - λ_{c}|^{ν_\\parallel}$\", size = 14)\n",
    "plt.ylabel(r\"$ρ(t)t^{\\delta}$\", size = 14)\n",
    "#plt.title(\"$ν_\\parallel$ = {}\".format(v_par), size = 14)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(markerscale = 3, fontsize = 14)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/nu_par_1_2.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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": [
    "timey = time**exp_delta\n",
    "\n",
    "y_axis1 = [a*b for a, b in zip(rho1, timey)]\n",
    "y_axis2 = [a*b for a, b in zip(rho2, timey)]\n",
    "y_axis3 = [a*b for a, b in zip(rho3, timey)]\n",
    "y_axis4 = [a*b for a, b in zip(rho4, timey)]\n",
    "\n",
    "v_par = 2.2\n",
    "\n",
    "x_axis1 = time*np.abs(2.8-pc)**v_par\n",
    "x_axis2 = time*np.abs(3-pc)**v_par\n",
    "x_axis3 = time*np.abs(3.7-pc)**v_par\n",
    "x_axis4 = time*np.abs(3.5-pc)**v_par\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x_axis1, y_axis1, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"blue\", label = \"λ = 2.8\")\n",
    "plt.plot(x_axis2, y_axis2, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"red\", label = \"λ = 3\")\n",
    "plt.plot(x_axis4, y_axis4, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"green\", label = \"λ = 3.5\")\n",
    "plt.xscale(\"log\")\n",
    "plt.plot(x_axis3, y_axis3, marker = \".\", linestyle = \"None\", markersize = 2,\n",
    "         c = \"black\", label = \"λ = 3.7\")\n",
    "\n",
    "#plt.ylim([10**(-3), 10])\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(r\"$t|λ - λ_{c}|^{ν_\\parallel}$\", size = 14)\n",
    "plt.ylabel(r\"$ρ(t)t^{\\delta}$\", size = 14)\n",
    "#plt.title(\"$ν_\\parallel$ = {}\".format(v_par), size = 14)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(markerscale = 3, fontsize = 14)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/nu_par_2_2.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $z$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ntraj = 10000\n",
    "nsteps = 2000\n",
    "time = np.arange(1, nsteps +1, 1)\n",
    "\n",
    "rho1 = simulate(10, 1, ntraj, nsteps, 3.28)\n",
    "rho1 = np.mean(rho1, axis = 0)\n",
    "\n",
    "rho2 = simulate(20, 1, ntraj, nsteps, 3.28)\n",
    "rho2 = np.mean(rho2, axis = 0)\n",
    "\n",
    "rho3 = simulate(30, 1, ntraj, nsteps, 3.28)\n",
    "rho3 = np.mean(rho3, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "exp_delta = 0.159\n",
    "pc = 3.29785\n",
    "timey = time**exp_delta\n",
    "time1 = np.arange(1, nsteps +1, 1)\n",
    "\n",
    "y_axis1 = [a*b for a, b in zip(rho1, timey)]\n",
    "y_axis2 = [a*b for a, b in zip(rho2, timey)]\n",
    "y_axis3 = [a*b for a, b in zip(rho3, timey)]\n",
    "\n",
    "z = 1.5\n",
    "\n",
    "x_axis1 = time/(10**z)\n",
    "x_axis2 = time/(20**z)\n",
    "x_axis3 = time/(30**z)\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x_axis1, y_axis1, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"blue\", label = \"N = 10\")\n",
    "plt.plot(x_axis2, y_axis2, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"red\", label = \"N = 20\")\n",
    "plt.plot(x_axis3, y_axis3, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"green\", label = \"N = 30\")\n",
    "plt.ylabel(r\"$ρ(t)t^{\\delta}$\", size = 14)\n",
    "plt.xlabel(r\"$t/N^z$\", size = 14)\n",
    "#plt.title(\"z = {}\".format(z))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(markerscale = 3, fontsize = 14)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/z_1_5.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)\n",
    "#plt.ylim([10**(-4), 10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "timey = time**exp_delta\n",
    "time1 = np.arange(1, nsteps +1, 1)\n",
    "\n",
    "y_axis1 = [a*b for a, b in zip(rho1, timey)]\n",
    "y_axis2 = [a*b for a, b in zip(rho2, timey)]\n",
    "y_axis3 = [a*b for a, b in zip(rho3, timey)]\n",
    "\n",
    "z = 1.1\n",
    "\n",
    "x_axis1 = time/(10**z)\n",
    "x_axis2 = time/(20**z)\n",
    "x_axis3 = time/(30**z)\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x_axis1, y_axis1, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"blue\", label = \"N = 10\")\n",
    "plt.plot(x_axis2, y_axis2, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"red\", label = \"N = 20\")\n",
    "plt.plot(x_axis3, y_axis3, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"green\", label = \"N = 30\")\n",
    "plt.ylabel(r\"$ρ(t)t^{\\delta}$\", size = 14)\n",
    "plt.xlabel(r\"$t/N^z$\", size = 14)\n",
    "#plt.title(\"z = {}\".format(z))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(markerscale = 3, fontsize = 14)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/z_1_1.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)\n",
    "#plt.ylim([10**(-4), 10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
    "timey = time**exp_delta\n",
    "time1 = np.arange(1, nsteps +1, 1)\n",
    "\n",
    "y_axis1 = [a*b for a, b in zip(rho1, timey)]\n",
    "y_axis2 = [a*b for a, b in zip(rho2, timey)]\n",
    "y_axis3 = [a*b for a, b in zip(rho3, timey)]\n",
    "\n",
    "z = 2.1\n",
    "\n",
    "x_axis1 = time/(10**z)\n",
    "x_axis2 = time/(20**z)\n",
    "x_axis3 = time/(30**z)\n",
    "\n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(x_axis1, y_axis1, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"blue\", label = \"N = 10\")\n",
    "plt.plot(x_axis2, y_axis2, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"red\", label = \"N = 20\")\n",
    "plt.plot(x_axis3, y_axis3, marker = \".\", linestyle = \"None\",\n",
    "         markersize = 2, c = \"green\", label = \"N = 30\")\n",
    "plt.ylabel(r\"$ρ(t)t^{\\delta}$\", size = 14)\n",
    "plt.xlabel(r\"$t/N^z$\", size = 14)\n",
    "#plt.title(\"z = {}\".format(z))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(markerscale = 3, fontsize = 14)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/z_2_1.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)\n",
    "#plt.ylim([10**(-4), 10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Localized initial conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 3.2975\n",
      "Relative R_squared: 0.9995100919440325\n",
      "Estimated theta exponent: 0.3057713431120477\n",
      "CPU times: user 5min 4s, sys: 2.53 s, total: 5min 6s\n",
      "Wall time: 5min 15s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "N = 1000\n",
    "perc = 1/N\n",
    "rates, r_sq_10, theta_10 = find_critical_point1(N, perc, 10**4, 10**3, 3.29, 3.32, 5, loc = True)\n",
    "\n",
    "i_10 = np.argmax(r_sq_10)\n",
    "print(\"Estimated critical point:\",  rates[i_10])\n",
    "print(\"Relative R_squared:\", r_sq_10[i_10])\n",
    "print(\"Estimated theta exponent:\", theta_10[i_10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 3.3125\n",
      "Relative R_squared: 0.9992911450855456\n",
      "Estimated delta expontnet: 0.33703493612126484\n",
      "CPU times: user 5min 20s, sys: 2.39 s, total: 5min 23s\n",
      "Wall time: 5min 30s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "N = 5000\n",
    "perc = 1/N\n",
    "rates, r_sq_10, delta_10 = find_critical_point1(N, perc, 10**4, 10**3, 3.29, 3.32, 5, loc = True)\n",
    "\n",
    "i_10 = np.argmax(r_sq_10)\n",
    "print(\"Estimated critical point:\",  rates[i_10])\n",
    "print(\"Relative R_squared:\", r_sq_10[i_10])\n",
    "print(\"Estimated delta expontnet:\", delta_10[i_10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated critical point: 3.2975\n",
      "Relative R_squared: 0.9994056406139156\n",
      "Estimated delta expontnet: 0.3100760570808842\n",
      "CPU times: user 5min 30s, sys: 2.35 s, total: 5min 32s\n",
      "Wall time: 5min 37s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "N = 10000\n",
    "perc = 1/N\n",
    "rates, r_sq_10, delta_10 = find_critical_point1(N, perc, 10**4, 10**3, 3.29, 3.32, 5, loc = True)\n",
    "\n",
    "i_10 = np.argmax(r_sq_10)\n",
    "print(\"Estimated critical point:\",  rates[i_10])\n",
    "print(\"Relative R_squared:\", r_sq_10[i_10])\n",
    "print(\"Estimated delta expontnet:\", delta_10[i_10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = simulate(10000, 1/10000, 20000, 1000, 3.29785, rec_rate = 1, surv_prob = False)\n",
    "a = np.mean(a*10000, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9994929756489521\n",
      "[0.3111207]\n"
     ]
    }
   ],
   "source": [
    "x_range = np.log(np.arange(80, 1000 + 1, 1))\n",
    "x_range = x_range.reshape(-1,1)\n",
    "y_range = np.log(a[80:])\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": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YcRKRMc/aJz/jnmqcBgYGAnnWPnmsdcfpm998n+uumwUo/pX/5Ht8k83M41e/2s7pp0+nrW3k96mvr8+KkWqcRMT2+9Ta2sr06dPHjFPyXgQFBQWIiOs4Je9nYJ6113jW3ryhUY83bxFNzzaybxF94w15edZJUkJn4rF5AZG8PJE1a9KPkas1isOz9pFYI5Xhs0/dtl9IN44XPzdbJ96O09ErDE0ziRGEpl76x12NPvEEPSeezuSBTv7ACZzMQwyRT00NuL0KabzWaOTXSBM/93TbQeXhh5+brRNvx+noFYammcQIQlMv/eOqRm+6idhxJzB5IL4k8iIfZwjF3nu7T6I6McZjjUZiIk2sG+m2g8rDDz83WyfejtPRKwxNM4kRhKZe+sdFjQ4Owle+Av/yLxQwSA/FnM5v+AGrOPLInhEbj6Qdw4XP1RqdMBebDAwMfER3N5x9Nvz+9wDsYBYn8XteYylLlsBtt+0ESsLNMUzYLZ6O179UF5t2797tqe0X0o3jxc/N1om343T0CkPTTGIEoamX/pyu0a1bZdeeB1lXk95kodSyUSC9/MZrjRL1jZ37R20z49YOKg8//NxsnXg7TkevMDTNJEYQmnrpz+ka3byZwnfeAuCP/BOH8RKN1LFmTXr5TcQajcREmvweI512UHn44edm68TbcTp6haFpJjGC0NRLf67WaH09TD5yKedzB//DxZzAI3SqqaxZA1/7Wnr5TcQaNWukBgYGY7FpE8yfz9lnQ28v/IYz+Q1nUlICXV1hJ5d7iMQZaUVFhad2UHn44edm68TbcTp6haFpJjGC0NRLf87UaFkZXHopPR/en4+oN0i+Q0gpeOghG7+I12gkJtLi4mJP7aDy8MPPzdaJt+N09ApD00xiBKGpl/6cqNHOTsrOOw/+8z+ZPNDJLawEPnhg58knsX0tSNRrNBITaeL5Yt12UHn44edm68TbcTp6haFpJjGC0NRLf+g1umULnQd+gvzHHgPg7yzidH4LKJSCNWvsJ1Gv+U3EGp0wa6ROm5YkNvpIbLKQaCc2w0jeqMHPTUsScdPZtCR5Mwyw32QheQE91aYlyRs1pNq0BBizGUbyhhpVVVUjjpHYDCORV2IzjEQb/Nu0pLu7O6NNS+zGafSmJYnPYjdOyZunjN60JNU4AWM2LUneUCPVOCVvypHtTUsK33iDWf/8z5QNa/cox3Mm99JFKeef38e3v71tuD7sx6m1tdVxc5nk71N/f7/jpiWA46YlqcZpcHBwxKYlgOs49fb2mk1L7P5S3Ue6bds2T22/kG4cL35utk68HaejVxiaZhIjCE299IdWo7/7nfRNmmLdI3oDX5Z8BgScNx4ZjSjUKFHftMTAwCAFfvtb5MwzUSIMksdl/IT/5FIKCuDxx51/ykcRkd+0JHnPRZ12UHn44edm68TbcTp6haFpJjGC0NRLfxg1etnDR/GOfJguSjiZh/hPLmXKlMG0JtGo1+iEWSM1MDDQw4UXwi23AFTyBx6hhG7+zgGsWAH/9V+bqaurCznD8YdInJEaGBgAjY38+vAbhyfRODawpzWJPvJIeKmNd5g1UgODKOC11+hefhIlXTv4PL/gdj4PQH4+fP/7Ix/3NEiNyK+Rhn6PXoZxon6Pnh3MfaSauO8++j62jJKu+G1L+7IOiN8bGouNnERNjaaHSEykifsXddtB5eGHn5utE2/H6egVhqaZxAhCUy/9vtSoCBtW/gBOP52ioV4GyeNf+G++zpoxm45kFMej30SsUXOxycBgImJggK0n/wsffuxWADoo4wx+w1P5x7HG/JTPPuxuMB2vf6luyO/p6fHU9gvpxvHi52brxNtxOnqFoWkmMYLQ1Et/Nmv02d+9L88WHGXdZN/IPNmf12XJEndfU6P2IOobO5uf9np8rv5ssoP5aT8W9fXw8KdvZ1nsaQD+zCEs5VU+tvIjvPqqu7+p0fQQiYk08Uy3bjuoPPzwc7N14u04Hb3C0DSTGEFo6qU/GzV6/fVw9NHw48FLuYczuZ/TWMZznLhyDjff7OquHSdTv4lYo2aN1MBgAuDpJwb4+tcnASDkcT538J3rJrH765E4VwodkVB52rRpntpB5eGHn5utE2/H6egVhqaZxAhCUy/9adeoCHznO5ScvJxJ0md1n7+yiK+lMYmaGk0PkZhIE1uX6baDysMPPzdbJ96O09ErDE0ziRGEpl7606rRvj7ePPQC+Na3WNr3Av/BvwHx+0N1f8rr5pxNv4lYoxPmp73TfqRr166lsrLS2j8x0U7sn/iPf/yDqVOnAv7uR7p+/XoqKyvT2o90n3320dqPdP369da/tKn2I21sbGTy5MlA6v1IFy9ePGafy3feeYfy8nIgvs9lQ0ODdYzEPpcJTRP7XCba4N9+pO+99x4lJSVpjVNrayuLFi3S2o808Vnsxundd9+ltLQUGLsfaV1d3Zhx6u/vJz8/f8R+pBs2bKCsrMx2nNra2qx9NouKiphTVMTGA05k/80vAbCROm7gX1m1qo3TT++gp0d/P9IE6urqRoy1l3FqbW1lxowZWvuRbt++3ZrEUo3T4OCgpROM3Y90r732GjNOu3btsvYyLSgoIBaLWf+1G6fNmzdbu+Sb/Ug1bn/auHGjp7ZfSDeOFz83WyfejtPRKwxNM4kRhKZe+j3V6D/+Id1z97Rub3qJj8pMdsjKlY5pasHUqD2I+u1PiX/ZddtB5eGHn5utE2/H6egVhqaZxAhCUy/92jX6wgt0feSjTNn6DgD3cgbLeZqvrZmV9s95nZyz6TcRazQSm5aICEop7bZfSDeOFz83WyfejtPRKwxNM4kRhKZe+nVq9K1v3cue3z2fIuI/eb/DlVzNNfzxqbysbcJsatQekd+0JLHWptsOKg8//NxsnXg7TkevMDTNJEYQmnrpd9Pv7rt38PUfTCefQfqZxAXcxr8XfIfr1mRvEnXKOZt+E7FGJ8zFJgODiYyvf72SrbFj+Gd+TgN17LXySAay8FPeIDuIxBnp6NN3t3ZQefjh52brxNtxOnqFoWkmMYLQ1Et/Sv1aWvjOaf+LUrB1a/yc5w4u4IQ1R2ZlPVQ3t2z7TcQajcQaqYHBeMOtX1vPJ394AmV0sJRX2cgeALbb3xn4j8ivkW7bts1TO6g8/PBzs3Xi7TgdvcLQNJMYQWjqpT+5756LnuG0H36MPXiPmbTwRW6loEACmURNjaaHSKyRJm4O1m0HlYcffm62Trwdp6NXGJpmEiMITb30J/oeO+M2Pv3bC5lE/Ebyb/NtSn6wmnfOaAzkpXSmRtNDJCZSA4Ocx9AQrxz1TY5/5vsA9FHIFZW/4KR7z2H5cgjojeEGaSISa6T9/f0jnqt1a/uFdON48XOzdeLtOB29wtA0kxhBaKrb/5Pv9VBz1QWcLr8BoIVKLp51P/ftWJZWvpnA1Kg9Ir9G2tXV5akdVB5++LnZOvF2nI5eYWiaSYwgNNXpv/56KLny36xJ9G324tPVr3DOTQemnW8mMDWaHiIxkSY2TNBtB5WHH35utk68HaejVxiaZhIjCE11+q++Gv6dq9nCXJ5Xy/jjt1/mua0f5sAD29LONxOYGk0PkZhIDQxyDddfD0VF0NMDTczljFlPcUTvH/nXq6eHnZpBGojExabp06d7ageVhx9+brZOvB2no1cYmmYSIwhN7fpff30mq1bB0FC8nZcHq26ZB0nrdaZGvXFh12gkzkgT+zjqtoPKww8/N1sn3o7T0SsMTTOJEYSmqfrr6+HMM6dYk2hREVx3HRx9tHL0NTXqzIVdo5GYSBOb/eq2g8rDDz83WyfejtPRKwxNM4kRhKbJ/fX1sN9+sGIF9PbGJ82FC6G3N36TvalRPT5Xa3TC/LR32iE/sat8YkfvRDux8/quXbssHz93yE/ETWeH/OSd18F+R+/EjuiQeof8np4e67Om2iEfGLNDfkdHh+VTVVU14hiJndcTeSV2Xk+0wb8d8ru7u6080tkh326cRu+Qn/gsduPU1dVl5TF6h/yysjL+8pepnHJKHr29H5y3FBcP8c1vNtPQ0Mv8+fPp7Oy0jpFqnGKxmNUuKipizpw5Y8apubmZnp4ea5zS2SE/eay97pBvN06jv0/9/f1WjFTjBNh+n1pbW1OO0+DgoHXMxJmm2zj19vZabbNDvsYO+Tt27PDU9gvpxvHi52brxNtxOnqFoWkmMYLQdMeOHbJmjYhS1mb2UlgostdeA/LUU87HMDXqjQuiRnHYIT8SN+QPDQ2Rl5en3fYL6cbx4udm68TbcTp6haFpJjGC0PTJJ4c47rg8az108mR4+GH45Ce962dq1JkLokYjf0N+4meDbjuoPPzwc7N14u04Hb3C0DSTGH5rev31cNxxiqEhUApqa+OT6PLl6elnatSZC7tGJ8waqYFBruD66+GKKwAUeXnwxz+S1V3sDXIPkZhIEwvYuu2g8vDDz83WibfjdPQKQ9NMYvihaX09XHoprFuXYITrrlNjJtF09DM16syFXaORWCM1MPAb9fVw4onxJ5UgfpP9ddeZTZgnEiK/Rpq4vUe3HVQefvi52TrxdpyOXmFomkmMbGp6770tnHrqB5Po5Mnxn/PnnKOnZ6o+U6PeuLBrNBITaeJ+NN12UHn44edm68TbcTp6haFpJjGypen118PZZ1fS2RmfQBcu/OCikq6eqfpMjXrjwq7RSKyRGhj4gfp6hp+Zj19USkygBtFDJNZIBwYGmDRpknbbL6Qbx4ufm60Tb8fp6BWGppnEyETT66+Pb383NAR9fZCXF7+oNHo9VFfPVH2mRnOvRiO/Rmr2I9Xjc3WvRzuEsR9p4iy0pyc+iZaVwX33daS8qORln1JTo3p8rtZoJCbSxLPUuu2g8vDDz83WibfjdPQKQ9NMYqSjaX09nHoqI26yf/BBOPDA9x39dPpNjerxuVqjZo3UwMAFf/pTMSecABs3xs9Ey8riE2hiPdS8mM4gEhNpZWWlp3ZQefjh52brxNtxOnqFoWkmMXR96+vh4otnkXi9z+hJ1OlYXvpNjerxuVqjkfhpP3pjArd2UHn44edm68TbcTp6haFpJjF0fS+9FLq68igsjN/aNHoSdTqWl35To3p8rtZoJCbSxL6Fuu2g8vDDz83WibfjdPQKQ9NMYuj41tfHf84DfPjD8NZbqW9v0tXNqd/UqB6fqzUaiYnUwMALErvZJx75LCkZ4oYbws7KIJcRiTXS0tJST+2g8vDDz83WibfjdPQKQ9NMYtj5Jq7MJy7olpXB7bd3snz5VM/H8tJvalSPz9UajcQN+bFYbMSLrtzafiHdOF783GydeDtOR68wNM0kRirf5El08mRYsABuuAGWLUtPUy/9pkb1+DBrNPI35CfejaTbDioPP/zcbJ14O05HrzA0zSTGaN/kSbSsLP64Z2JNNF1NvfSbGtXjc7VGI/HT3sDADvX1sHo1tLd/MImmujJvYOCESJyRmvfa6/G5+s5wO2T6XvvEWehLL8X7Djss9SSazffa2/WbGtXjc7VGJ8waadLrmFc+/fTTQPqv+fXrdcyjX/Or+zpmQPt1zMmvj031OuZYLEZbWxsw9nXMfr7m14/XMWcyTn/6UzEXX1xFV5eipGSIn/2smZNOKjHjlGPjBLnzfVqwYIHtGmnor0/O9l+q1zFv3rzZU9svpBvHi5+brRNvx+noFYam6cZ46imRkpJBAZGyMhnzamSvcXR1c+o3NarHh1mjOLyO2fO5rVKqDDge+AjwR+DF4SA5i8S/SrrtoPLww8/N1om343T0CkPTdGIkfs53d+dpr4emq6mXflOjenyu1qjWGqlSqlopdbFS6gngHeBkoBv4d2CrUuo2pdTJSqnJWcvMwMAHrF4dv6hUUjJkLioZZA1aa6RKqfeA3wMPA8+JSCyJqwBOYHhyFZHP+5SrFsx9pOPzHr104CVG4ur8KafA734HV189yDHH6L1FMl1NzX2k6dnmao1mfB+piOwhIv9PROqTJ9Fhrl1E7hKRM8KeRO2QWCzXbQeVhx9+brZOvB2no1cYmurGSL46/7vfwZ/+BAcdlHoP0XTi6Orm1G9qVI/P1RqNxO1PiSt1uu2g8vDDz83WibfjdPQKQ1OdGIzHD/MAACAASURBVKNvtL/mGn1f3Ti6ujn1mxrV43O1RrXPa5VSVcAxwGKgAmgH/g48KSLbs5aRgUEWYG60NwgSrmekSql9lVL3AWuB84BJwPbh/54HvKWUuk8ptdDXTDPAzJkzPbWDysMPPzdbJ96O09ErDE3tYujcaB+Epl76TY3q8blaozpnpLcD1wPniEjfaFIpVUj8QtOtwMeyllkWMTQ05KkdVB5++LnZOvF2nI5eYWg6Okaqs9Abbkh9FhqEpl76TY3q8blao65npCKyVETuE5E+pdQYexHpF5HfikhOTqKA9fSCbjuoPPzwc7N14u04Hb3C0HR0jNWr3R/3tPP1EkeX99JvalSPz9Ua9Xqfww4gmN8YBgYeUF8fPxNduND+LNTAwC/o3pC/SCk1CSi24TdlNasso6yszFM7qDz88HOzdeLtOB29wtC0rKyM+no4/PD4u5XWroWKCr1JNAhNvfSbGtXjc7VGdc9IHyV+JpqnlPo18DfiV+z/Rnwytt8+PAdQXl7uqR1UHn74udk68Xacjl5Ba1pfD1ddNY2OjvgEunBh/Od84vYmNwShqZd+U6N6fK7WqO4N+TXAXGAAeAHYg/jjoe8Cm4FfZS0jH5DY0UW3HVQefvi52TrxdpyOXkFruno1vPJKvHwPOyz+c/5Pf9L/SR+Epl76TY3q8blao9prpCLSopT6iIi8m+hTSilgsojszlpGBgYOSH7Us7e3lzVris16qEHocJ1IlVKXAj8Tkb7kSRRgeNen3UqpIuAiEcnJdy0WFhZ6ageVhx9+brZOvB2no1dQmiZfmX/44Taqq6vTOk4QmnrpNzWqx+dqjbpuWqKU+h7xG+8fBZ4D3gY6gTJgL+BI4tvq/VJErspaZmki1aYlBuMfozcdueYac2XeIFhktGmJiHwTOJD49nlfBB4D3iQ+sX4BWA8cmAuTqB02b97sqR1UHn74udk68Xacjl5+a5o4E01sOrJ8eWYxgtDUS7+pUT0+V2tUa41URFqAHw7/jTskXhWg2w4qDz/83GydeDtORy+/NE0+E4WRV+UziRGEpl76TY3q8blYo2DeImqQ40heE/3Tn8LNxcDADp5efqeUWg58fbi5lg/uJ31TRAayn553pFojHRoaIi8vT7vtF9KN48XPzdaJt+N09Mq2pjpropnECEJTL/2mRvX4MGs0442dk3AH8CJwM/Ft9E4FHgKC2SwxTbS0tHhqB5WHH35utk68HaejV7Y1TbUm6hbTC4LQ1Eu/qVE9PpdqNBlef9oXiUhileq+RKdSanrWMvIBidfc6raDysMPPzdbJ96O09ErW5o6rYm6xfSCIDT10m9qVI/PhRpNBa8T6b1KqaNF5KnkThFpy1pGBpGGWRM1GI/w+tO+DrhHKfVVpdTePuTjC2bNmuWpHVQefvi52TrxdpyOXplomth4pL4+fgaq+8x8JuMWhKZe+k2N6vFh1agbvJ6RPgw0AqcA31JK5QNvAH8TkUuyllWWYd4ZrseH9c7wxFno6tXenpfPZNyC0NS81z4921ysUTd4OiMVkZ+JyJdE5BMiUgF8BPgB0JS1jHxAW1ubp3ZQefjh52brxNtxOnp51TTds1AvMbLlm66mXvpNjerxQdaoF2idkSqlfkT86vyLImLtzy8iDUCDUupppdSZwHQR+Z+sZWcwYZHuWaiBQS5C96f9JuBqYF+l1BPEJ9U3iL9V9BRgEVAP/MKPJHWglDoROHHBggU0NDQAMG3aNAoLC+nu7qahoYHJkycza9Ysq62Uora2lv7+fsunurqarq4uOjo6AJg+fToFBQU0NzcDMGXKFGbMmMGmTfG9rPPz85k3bx5NTU309/cDMHfuXDo6Oujs7ASgsrKSvLw8K25paSkVFRVs2bIFgIKCAmpqatiyZYv1c6Ompob29na6urro7u6mu7uboaEh6/UIZWVllJeXW1uBFRYWUl1dTW9vr/VZ5s+fT0tLi3V1ctasWeTn51t8eXk5paWlNDXFf1Ak8m9sbCRxf3FtbS2xWMzyqaqqIi8vz2pXVFRQXFxsfbbi4mJmz55ttQHq6urYvn079fXw4x9X8J3v5HHFFf1cc00Bl1zSzq5dkyksLGTHjh0A1jg1NjYmxpba2lq2bdtGX1+fNU6AFcPrOHV3dzMwMJBynHbu3AlgjVPis9iN09DQkJXHzJkzrXHq7u6mtbV1zDiVl5ezefNm68ma+fPnMzg4aB0j1ThNnjzZahcVFTFnzpwx49Tc3ExPT481Tv39/bz//vsjxmn79vgLfxPjlDhmYpwGBgasvtmzZ9Pb22u9/z3xfUo1Tt3d3TQ2NqYcp9Hfp8LCQitGqnEqLy+3/T51d3fT2dk5ZpxKSkqsYxYUFFBeXu46TgUFBVbb7vuUPE5O8HpDfgWwgvjL7vYH/kh83fQ5EQnmGTYXpLohv7+/f8ROL25tv5BuHC9+brZOvB2no5eOzeGHx89CDzssO1fkMxm3IDT10m9qVI/3u0adkLUb8kWkXUTuFpEzRWQ/EblMRJ7OlUnUDokzLt12UHn44edm68TbcTp66dikuxZqh0zGLQhNvfSbGtXj/a7RdGGetTcIDMuXm7VQg4kJ/x/ezQEUFRV5ageVhx9+brZOvB2no5edTfLV+Wwjk3ELQlMv/aZG9Xg/ajQb8LRGOh5gNnbOLWR7XdTAICxkc9OScYnE1V/ddlB5+OHnZuvE23E6etnZZHtd1C0PP3zT1dRLv6lRPd6PGs0GIjGRjj7rdmsHlYcffm62Trwdp6NXcl99PZx2WhX19fE1Ub/uE81k3ILQ1Eu/qVE9Pls1qpOHF0RiIjUIFqtXw//+bzGrV4ediYFBMIjEGqmIEH9ztF7bL6Qbx4ufm60Tb8fp6JXcV18P3/qWcO21yter9JmMWxCaeuk3NarHZ6tGveYMZo3UetpFtx1UHn74udk68Xacjl7JfcuXw4MPNvt+q1Mm4xaEpl76TY3q8dmqUZ08vCASE2nisTnddlB5+OHnZuvE23FuetXXw4oVU0fc4hSEppnECEJTL/2mRvX4dGtU1yZdRGIiNfAXZk3UIOqIxERaVVXlqR1UHn74udk68Xacm17XXANLlw6OuMUpCE0ziRGEpl76TY3q8enWqK5NuojERJrYRUa3HVQefvi52TrxdpybXsuXwxNPdI1YEw1C00xiBKGpl35To3p8ujWqa5MuIjGRJrYS020HlYcffm62Trwdl9xfXw9HHVU05pHPMDTNJEYQmnrpNzWqx+tqmo7GmSASE6lB9mDWQw0MxiISE2lFRYWndlB5+OHnZuvE23HJ/ddcA0uWxMY88hmGppnECEJTL/2mRvV4XU3T0TgTRGIbveLiYk/toPLww8/N1om345L7ly+H556LUVxcYGujk0c2kEmMIDT10m9qVI/X1TQdjTNBJM5IE69X0G0HlYcffm62TnwqLtU2eKnswtA0kxhBaOql39SoHq+radA1GomJ1CB9mDVRAwN3RGIiNT+b9PhU3DXXwCGH9I9YEw36Z5MdzE/77GM81miq/qBrNBKblhgYGBhkishvWpL8ylmddlB5+OHnZuvE23E6eoWhaSYxgtDUS7+pUT0+V2s0EhOpgYGBgZ8wE6kBEL8q/+lPz/blJXUGBhMdZo3UADAvqTMwcEPk10jNPXrufKqr83Y+5j5SPd7cR5qe7Xi8jzQSTzb19vZ6ageVhx9+brZ2/PLl8NvfNlFXV+fqk+oYYWiaSYwgNPXSb2pUj9fVNOgajcQZqYGBgYGfiMQaaW9v74ibb93afiHdOF783GydeDtOR68wNM0kRhCaeuk3NarHh1mjkV8jNT+b4qivh2XLCmyvzOfqzyY7mJ/22UfYNerG52qNRmIibW9v99QOKg8//JxsV6+G114rsH1u3s5XR68wNM0kRrY0deK99Jsa1eNztUYjMZEaxHHNNXDQQb0pr8wbGBikj0hctZ82bZqndlB5+OHnZLt8OTz9dB9Tp6ZeF7Lz1dErDE0ziZEtTZ14L/2mRvX4XK3RSJyRFhYWemoHlYcffm62Trwdp6NXGJpmEiMITb30mxrV43O1RiMxke7YscNTO6g8/PBzs3Xi7TgdvcLQNJMYQWjqpd/UqB6fqzUaiYnUwMDAwE9EYiKdPHmyp3ZQefjh52brxNtxOnqFoWkmMYLQ1Eu/qVE9PldrNBI35IsISinttl9IN46uX309fOtbwrXXKpYv934sO05HrzA0zSSGF183W13dnPqjUqM6trlao5G/Ib+xsdFTO6g8su23ejW8/LJyfL+S07HsOB29wtA0kxhefN1sdXVz6o9KjerYjscanTC3PymlTgROXLBggbXz9bRp0ygsLKS1tRWIn8rPmjXLaiulqK2tZdeuXZZPdXU1XV1ddHR0ADB9+nQKCgpobm4GYMqUKcyYMYNNmzYBkJ+fz7x582hqaqK/vx+AuXPn0tHRQWdnJwCVlZXk5eVZcUtLS6moqGDLli0AFBQUUFNTw5YtW4jFYgDU1NTQ3t5OV1cXra2tzJw5k6GhIesYZWVllJeXs3XrViB+BfKaa6r5yle6uOSSLhoaepk/fz4tLS3s3r0bgFmzZtHT02N91vLyckpLS2lqagJg165dQLzAEr9Uamtr6ejosHyqqqpGHKOiooLi4mIrr+LiYmbPnm21Aerq6ti+fbv1JMns2bPp7e21bohOjFNi8T8xTolCT4zTtm3b6Ovrs8apu7vbysPrOLW2ttqO086dO0eMU+Kz2I1TV1eXlUfyOLW2tqYcJ4DNmzczODgIwPz58+ns7LSOkWqcYrGY1S4qKmLOnDljxqm5uZmenh5rnPr7+3n//fdHjFNix6PEOCXvEl9XVzdirL2MU2trq+04jf4+9ff3WzFSjRNg+31qbW1NOU6Dg4PWMQsK4tOa2zj19vZa7VTjVF1dPWKcHCEiE+rv4IMPltFoaGjw1PYL6cbx4udm68TbcTp6haFpJjGC0NRLv6lRPT7MGgX+IjbzTiTWSA0MDAwyReTXSLdt2+apHVQefvi52TrxdpyOXmFomkmMIDT10m9qVI/P1RqNxESaWK/RbQeVhx9+brZOvB2no1cYmmYSIwhNvfSbGtXjc7VGIzGRGhgYGPiJSKyR9vf3j3iu1q3tF9KN48XPzdaJt+N09ApD00xiBKGpl35To3p8mDUa+TXSrq4uT+2g8vDDz83WibfjdPQKQ9NMYgShqZd+U6N6fK7WaCQm0sQ9bLrtoPLww8/N1om343T0CkPTTGIEoamXflOjenyu1mgkJtLxjPp6+PSnZ9u+HsTAwCB8RGIinT59uqd2UHnoYPVq+N//LXZ87NNLDCfejtPRKwxNM4nhxTddTb30j+ca9eo3EWs0EhNp4pEx3XZQeejgmmtg6dJB7deDuMVw4u04Hb3C0DSTGF5809XUS/94rlGvfhOxRiMxkSaev9ZtB5WHDpYvh3vu2Wy7m5PXGE68HaejVxiaZhLDi2+6mnrpH8816tVvItZoJCZSAwMDAz8RiYl0ypQpntpB5eGHn5utE2/H6egVhqaZxAhCUy/9pkb1+Fyt0UjckD80NEReXp522y+kG8eLn5utE2/H6egVhqaZxAhCUy/9pkb1+DBrNPI35Cf2OtRtB5WHH35utk68HaejVxiaZhIjCE299Jsa1eNztUYjMZEaGBgY+IlITKSJXbd120Hl4Yefm60Tb8fp6BWGppnECEJTL/2mRvX4XK3RSKyRGhgYGGSKyK+RJt5JpNsOKg8//NxsnXg7TkevMDTNJEYQmnrpNzWqx+dqjUZiIk28REu3HVQefvi52TrxdpyOXmFomkmMIDT10m9qVI/P1RqNxERqYGBg4CcisUY6MDDApEmTtNt+Id04XvzcbJ14O05HrzA0zSRGEJp66Tc1qseHWaORXyM1ez3q8bm616MdzH6k2Yep0fQQiYm0s7PTU9sP1NfDMceUpLWvqJf83GydeDtOR68wNM0kRhCaeunPhRrNJE7UazQSE2kuwOu+ogYGBuMHkZhIKysrPbX9wDXXwJIlMe19RZPhJT83WyfejtPRKwxNM4kRhKZe+nOhRjOJE/UaDWa32JAxemMCt7YfWL4cnn66j5IS75J7yc/N1om343T0CkPTTGIEoamX/lyo0UziRL1GI3FGunPnTk/toPLww8/N1om343T0CkPTTGIEoamXflOjenyu1mgkJlIDAwMDPxGJibS0tNRTO6g8/PBzs3Xi7TgdvcLQNJMYQWjqpd/UqB6fqzUaiRvyY7HYiBddubX9QrpxvPi52TrxdpyOXmFomkmMIDT10m9qVI8Ps0Yjf0P+li1bPLWDysMPPzdbJ96O09ErDE0ziRGEpl76TY3q8blao5GYSA0MDAz8RCQmUvPOcD0+V98ZbgfzXvvsw9RoeojEGqmBgYFBpjBrpGb9SYvP1fUnO5g10uzD1Gh6iMREGovFPLWDysMPPzdbJ96O09ErDE0ziRGEpl76TY3q8blao5GYSA0MDAz8RCTWSM09enq8uY80PVtzH2k0ajTya6Tt7e2e2kHl4Yefm60Tb8fp6BWGppnECEJTL/2mRvX4XK3RSEykXV1dntpB5eGHn5utE2/H6egVhqaZxAhCUy/9pkb1+Fyt0UhMpAYGBgZ+IhIT6cyZMz21g8rDDz83WyfejtPRKwxNM4kRhKZe+k2N6vG5WqORmEiHhoY8tYPKww8/N1sn3o7T0SsMTTOJEYSmXvpNjerxuVqjkZhIW1tbPbWDysMPPzdbJ96O09ErDE0ziRGEpl76TY3q8blao5GYSA0MDAz8RCQm0rKyMk/toPLww8/N1om343T0CkPTTGIEoamXflOjenyu1mgkJtLy8nJP7aDy8MPPzdaJt+N09ApD00xiBKGpl35To3p8rtZoJCbSrVu3emoHlYcffm62Trwdp6NXGJpmEiMITb30mxrV43O1RiMxkRoYGBj4iUhMpIWFhZ7aQeXhh5+brRNvx+noFYammcQIQlMv/aZG9fhcrdFIbFoSBDo6OmhubmZgYCDw2AYGBtlBSUkJNTU15OWNPcd02rQkmPcXhIzNmzczb9487bZXdHR0sGPHDubOncvkyZNRSqW06+/vT+tfQS9+brZOvB03uj+VnY5NtpFJjCA09dLvpl8QemYSZyLU6NDQEFu3bqWlpYVZs2ZpfZYEIvHTfnBw0FPbK5qbm5k7dy5TpkyxnUQB0j379+LnZuvE23Gj+1PZ6dhkG5nECEJTL/1u+gX1yzHKNZqXl0dVVRW7du1yzC8VIjGR+o2BgQEmT54cdhoGBgYZYtKkSWntnB+JiXT+/Pme2unA6Uw0AbOQn12Yi03ZR9RrVOd7nAqRmEhbWlo8tf2CeR+OHl544QX23ntvVzuvMRoaGlBKEYvFiMViHH/88dxxxx0Zx9HR7Sc/+QlVVVVUVVXx4x//2NF2586d7L333vT29jrGuP322/n4xz/umr8XpIpz2mmn8fjjj3v2S9d2PNToaERiIt29e7entl8wO+vo4ROf+ARvv/22q12muz899thjnH/++RnHcdPt2WefZc2aNbz22mu8/PLLrFmzhueee872GNdddx2f+9znKC4u1s4hW0gVZ9WqVVx55ZWe/XRs7777bmpraykpKeGUU06hra3N9lif/OQnqa6upry8nMWLF/PQQw9Z3NatWznppJOorq5GKcV77703wvc3v/kNRxxxBFOmTOHII4/0nLMbIjGRGnyAbL+NMqi3W45n3HLLLaxcuZLa2lr22GMPVq5cyc0335zStq+vjzvuuIOzzjor4CztsWTJEjo6Osj2bYVvvfUWF110EXfeeSc7duxgypQpXHLJJbb2//Ef/0FDQwMdHR3cfPPNnHvuuWzbtg2IXyg67rjjuP/++1P6Tp8+nS9/+cusWrUqq58hgUhMpKNvZXBr+4V0X17mxS+VbV1dHT/4wQ9YtGgR06dPJxaL8corr3DYYYdRUVHB4sWLefbZZy3fjRs3csQRR1BWVsbRRx/NZZddxrnnngvEfx4XFxdz6623Mn/+fI466igA7rzzTvbdd1+mTZvGscceaz1+JyJcdtllzJo1i6lTp7Jo0SLefPNNAB599FEWLlxIWVkZc+fO5Yc//CEQP4Orqamx8l+3bh1HHnkkFRUV7Lfffvz+97+3PusFF1zAl770JU444QTKyspYunQp7777rpZORx55JD//+c+BD34mX3755UybNo0FCxbw2GOPWba7du3ii1/8InPmzGHu3LlcddVV1t0eduOT6H/11Vc5/PDDrf6lS5fy2muv2dpWVFRQV1dncbfffjv77rsvZWVlLFiwgLvuuitlvJdeeolDDz2UqVOncuihh/LSSy9Z3JFHHsk3vvENlixZwtSpUzn55JNpa2uz+EQ9VFVVWfWQjCOPPJJHHnnEUU9dJGzvuusuTjzxRI444ghKS0u59tpreeCBB+jp6Unpt2jRIussXSnFwMAAmzdvBmDu3LlccsklHHrooSnzOfroo/nsZz9LdXV1Wjm7QkQm1N/BBx8so7Fr1y5Pba9Yu3atll0sFkvr+F78UtnW1tbK4sWLZdOmTdLZ2SlbtmyR6dOnyyOPPCKDg4Pyxz/+UaZPny7btm0TEZGPfvSj8tWvflX6+vrkhRdekLKyMjnnnHNERGTjxo0CyHnnnSddXV2ye/duefDBB+VDH/qQrF27VgYGBuTaa6+Vj370oyIi8vjjj8tBBx0k77//vgwNDcnatWulqalJRERmz54tzz//vIiItLW1yV//+lcREXnmmWdk7ty5IiLS398vH/rQh+S73/2u9PX1SX19vZSWlsr69eslFovJ+eefL9OmTZNXX31VBgYG5Oyzz5YzzzwzpTaJ3AcGBiQWi8myZcvklltuERGR2267TQoKCuTmm2+WWCwm//3f/y1z5syRoaEhicVicvLJJ8uFF14oXV1dsmPHDjn00EPlpptuEhGR9957T6ZOnSqNjY0px6KkpGREjfztb3+T0tLSlLY33nijrFixwmp3dXVJWVmZvPXWWyIi0tTUJG+++aaV8+GHHy4iIq2trVJRUSG//OUvZWBgQO6++26pqKiQlpYWERFZtmyZVFdXyxtvvCFdXV1y2mmnWWOaXA/9/f1WPTQ3N1v5/ehHP5JTTz01pa6NjY0ydepU27+77ror5Wc96aST5LrrrhvBlZSUyKuvvpoyjojIihUrpKioSAA59thjZXBwcMQxBwYGBJANGzaM8Y3FYnLLLbfIsmXLRviMht33GfiL2Mw7kbghv62tbcROL27trOD22+N/SVBDQ5D8xMQBB8BPf/pB+29/g//3/8YcaozfqLOFZMRiMfLz88f0X3rppcybN4++vj5+9atfsWLFClasWAHAP/3TP3HIIYfwhz/8gWOOOYY///nP1NfXU1hYyMc//nFOOOGEMcf79re/TUlJCQA/+9nPuPzyy9l3330B+OY3v8n3vvc9GhsbmTRpEp2dnaxfv54lS5ZYNhC/1WTt2rUsXryYadOmMW3atDFxXnnlFbq6uli1ahV5eXkcddRRfOpTn+LXv/413/jGN4D4xZAlS5YAcM455/CVr3zFVp9knUajtraWlStXAnD++edzySWXsGPHDvr7+3nsscdob29n8uTJlJSUcNlll3HzzTdz0UUXUV1dnfKNlMljsXTpUutpmVRrcwnb9vZ2ysrKRvjm5eXx+uuvs2DBAubMmcOcOXPG+D/yyCPsueeenHfeeQCcddZZ3HDDDTz88MNccMEFAJx33nnsv//+AFx77bUccMAB3HHHHSPqoa+vz6qHRx991FpDLisrs33r5vz589mxYwdFRUX2gqf4rF1dXUydOnUEN3XqVMe3ez7wwAPk5eXx1FNPsX79ekvT0XWve7Ep1XclHUTip30oaGiA554b8Zf3wgsj+/72t5E+7e1jfFL6pYHkJ7caGxv57W9/S0VFhfX34osvsn37dpqampg+fTpTpkyx7JN/Ztsd7/LLL7eONX36dESErVu3ctRRR/HlL3+ZL33pS1RVVXHhhRfS0dEBwP3338+jjz5KbW0ty5Yt4+WXXx4Tp6mpiXnz5o14ZK+2tnbEzj2zZ8+2/n/KlClpvx1y9HEg/qbJTZs2MTAwwJw5c6zPeNFFF9Hc3Kx13Dlz5vDiiy/S3t5Oe3s79fX1KSdDgGnTptHZ2Wm1S0pKuPfee7nllluYM2cOJ5xwAuvXrx/j19TURG1t7Yi+0Tolj1ltbS0DAwO0tLSMqIeqqiqrHhLrjwCdnZ1UVFRofV5dlJaWWrWQQEdHh+s+oZMmTeL444/niSeesJZ5wkYkzkhD2euxrg6WLRvRJSIj71M74ICRPhUVY3xS+jnA7l/YhH9+fj7z5s3jvPPO45ZbbhlhE4vF2Lp1K21tbezevduaTLZu3Trm2ePkfObNm8eqVav43Oc+N+JYiTWoSy+9lEsvvZTm5mbOOOMMrr/+eq699loOPfRQHnroIQYGBrjxxhs544wzrDWvBKqrq9m8eTNDQ0NWDps2bWKvvfbK6GzCi29tbS1FRUW0tLSkXFezO1by2eiGDRtYtGgRABs2bLDOoEfbLlq0iJ/85CcjjnnssceyfPlyBgYGuOqqq1i5ciUvvPDCCP/q6moaGxtH9G3atInjjjvOaidru2nTJiZNmsSMGTNG1EPyuCVj3bp1LF68OOXn3LRpEwsXLkzJQfwXyznnnDPms+633378/e9/t/rfe+89+vr62GeffWyPNfqsM7EePnoMUo2Jjk3asPvNnyt/QAlwB3ALcI6bfao10r6+Pk9tr9BdI02s53iFF79UtrW1tfLkk09a/KZNm6Sqqkoef/xxicVi0tPTI88884y1xrd06VL52te+Jn19ffLSSy9JeXn5mDXSgYEB6/gPPPCA7LffftbaXXt7u9xzkNPkdgAAEF5JREFUzz0iIvLaa6/JK6+8Iv39/dLV1SXHHnusXH311dLX1ye/+tWvpL29XUREfv7zn0ttba2IjFwj7evrkz322EO+//3vS39/vzzzzDNSWloq69atk8HBQTn//PPlyiuvtHJJ9h2N5NwHBwfHrJEm1hsTAOSdd96RwcFBOemkk+TSSy+VXbt2yeDgoGzYsEGeffZZW82T+5999lk5+OCDZdu2bdLU1CQHHnig5Tvatq+vT2bMmCGbNm0SEZHt27fLQw89JB0dHTI4OCirV6+21viSc25pabHWIwcGBuSee+6RqVOnys6dO0UkvkY6d+5ceeutt6S7u1s+85nPyFlnnSUiMqIe+vv7rXrYvHmzld+ee+7puHaZTo2++eabUlZWJs8//7x0dXXJOeecI2eeeWbKY61bt04effRR6erqkv7+frnzzjtl0qRJ1rr64OCg9PT0SFdXlwCydu1a6enpsfxjsZh0d3fL//zP/8gnPvEJ6enpkd7e3pT5pbNGGtbk+AugGXhzVP9xwNvABmDVcN95wInD/3+v27FTTaQbN2701PYK3YnUbuCy6ZfKNnkiTfCvvPKKHHHEETJt2jSZMWOGrFixQv7xj3+IiMiGDRvk4x//uJSWlspRRx0lX/jCF+QLX/iCiKSeSEVEbr31Vtl///2lrKxMampq5HOf+5yIiDz11FPykY98REpKSqSyslLOPvts6ezslL6+Pjn22GOloqJCysrK5JBDDpEXXnhBRMZOhm+++aYcccQRUl5eLvvuu6888MAD1mdJdyLt7e3Vnkh7e3ulvb1dLr74Ypk7d66Ul5fLAQccIL/+9a9FROQf//iHlJSUjLnYlDwWP/rRj2TmzJkyc+ZMWbNmzZjckm0vv/xy+c53viMi8YtLic8+depUWbZsmXXhaXTOL7zwghx00EFSXl4uBx10kKWnSHwiXbVqlRx66KFSVlYmn/rUp6xJViR1PSQ+z2uvvSYHHHBASk1T5e+GZNu77rpL5s2bJ1OmTJGTTjpJWltbLf6iiy6Siy66SETi37ElS5ZIaWmpTJ06VQ455BCrDhLHBMb8JXDbbbeN4c4999yU+Y2nifQI4KDkiRTIB94F9gAKgb8DC4FvAAcM29ztdmwzkTrbOvF23Gc+8xlZvXq1o93ovnQ/qxdkEiMITb30J/c1NzfLXnvtJbt379bOwQ3J/2g4IVWc0047TR555BHPfunaplOjOvWnW6PpTKShXGwSkeeBtlHdS4ANIvKeiPQD9wAnA1uAxNWOtPIdfTUxuV1fD6efXk19fTpH9oZ0n+P14udm68QnuD//+c+8++67DA0N8fjjj/Pwww9zyimnOB5jdF+6n9ULMokRhKZe+pP7Zs6cyRtvvDFiI5wg9LSLc//991t3eHjxS9dWp0bd+oOu0Vy62DQXSL7SsAVYCtwA3KiUOgF4OJWjUupC4EKIX2FuaGgA4ldACwsL6evro6GhgcmTJzNr1iyrrZRi9epa/vKXQq64opf7799OdXU1XV1d1tXE6dOnU1BQYF2hnTJlCjNmzGDTpk3ABwvW/f39iTNrJk2axNDQ0JgbtkWEvr4+8vLyKCgooL+/P5E/hYWFI45RWFhILBazbpVJHCtxC0d+fj55eXnWRtKJY0D86ZhUxygoKCA/P9/iUx0D4hclTj31VNra2qipqeHGG29k4cKF9PX1MWnSJPLy8sYcI/mzTZo0yWpD/B+ugYEBK4/R+ozOY7Q+iWOM1jg5j4TGCX10NB4aGko5TqOPkfgsduOklLLNIxaLpRwnt2OMHqeCggKrnThGop1qrEdrLCIMDQ1ZPolxSj5GUVHRiDy8jlNfX1/KcRqtcfJn0xmn0ccY/V0Y/VnS1Tjx2WKxGE1NTdaFTq1tNu1OVf3+A+oY+dP+dODnSe3zgP/0etxUP+0bGhps2089JXLQQT3y1FMpz+a1MNF/2mfzZ1M2MVF/2uu0/YKp0fF/Q/4WIHmb+hqgKRsHFrHf0HX5crj//u0jHskzMDAw8IJcuiH/z8CeSqkFSqlC4LNAbtxta2BgYOCAUCZSpdSvgZeBvZVSW5RSXxSRGPBl4AlgHfAbEXkrG/FSPfHh1E4HOltyRX3T3GzDbOycfUS9Rkf/etVFWFftzxKROSIySURqROTW4f5HRWQvEfmQiHw3W/FGP8rn1vaKkpIStm7dOmJxOxXMxs7ZRSYxgtDUS7+bfkFtVxjlGhURWltbR+wDq4tcWiP1DaO35XJre0VNTY31zLJbEaSzdZcXPzdbJ96OG92fyk7HJtvIJEYQmnrpd9MvCD0ziTNRarS4uDjl3hKusLsKNV7/wrghXxfpxvHi52brxNtxOnqFoWkmMYLQ1Eu/qVE9PswaxeGqvZI01wRyFYcccoiM3sm7p6dnxM3Nbm2/kG4cL35utk68HaejVxiaZhIjCE299Jsa1ePDrFGl1F9F5JBUXC5dtfcNyTd267SDysMPPzdbJ96O09ErDE0ziRGEpl76TY3q8blaoxNmjVQpdSJw4oIFC8Y82bRhwwYqKyutJ5sSbaUUtbW1NDQ0WBvMpvNk07x582hqarIGZu7cuXR0dFj7SlZWVpKXl2fFLS0tpaKigi1btgDxpyxqamrYsmWLtcZaU1NDe3s7XV1dtLa2ss8++zA0NERraysQ32i3vLzc2m+ysLCQ6upq3nvvPWuD5Pnz59PS0mK93G/WrFk0NTXx/vvvA/HtA0tLS2lqit+uu2vXLhYvXkxjY6N10ay2tpbGxkZrq8GqqqoRx6ioqKC4uNj6bMXFxcyePdtqQ/xVJ9u3b7feijl79mx6e3utDXwT47Rjxw4Aa5wS28Ilxmnbtm3WkyjV1dVs2bLFysPrOLW2trJo0aKU47Rz504Aa5wSn8VunDZv3mzlMXPmTGucWltbqaurGzNO/f39dHR0WE/MzJ8/n02bNln7cKYap7a2NqtdVFTEnDlzxoxTc3Oztd5fVVVFf3//mHHavn07gDVOie9KYpySx9rLOLW2tjJjxoyU4zT6+7Rjxw4rr1TjNDg4SHd3d8rvU2trK3vttdeYcdq1a5d1zIKCAmKxGJ2dnY7jtG3bNqtt933K+Seb/Poza6TOtrm6/pQOzBpp9mFq1B5EaY1UKbUTaBzVPRXY5dCeAQTxcvvRcf3wc7N14u04N/1S9QWhabp6evVNV1Mv/aZG9fgwa7RWRGamZOxm2In0B9zs0rb9l8bPPPzwc7N14u04N/3C0jRdPYPS1Eu/qVE9PldrNBIXmxi7a1TKXaQCQLpxvfi52TrxdpyOfmFomknMIDT10m9qVI/PyRqdcD/t04FS6i9ic1uDQXowmmYXRs/sI5uaRuWM1A03h53ABITRNLswemYfWdPUnJEaGBgYZAhzRmpgYGCQIcxEamBgYJAhzERqYGBgkCHMRJoCSqkSpdQdSqlblFLnhJ3PeIdSag+l1K1KqfvCzmWiQCl1ynB9PqSUOibsfMY7lFL7KqVuUkrdp5T6F6/+kZlIlVK/UEo1K6XeHNV/nFLqbaXUBqXUquHu04D7RGQlcFLgyY4DeNFT4q/Y/mI4mY4feNT0d8P1eQFwZgjp5jw86rlORC4GzgA83xIVmYkUuB04LrlDKZUP/BdwPLAQOEsptZD4i/cSr4bW2LEgkrgdfT0N9HA73jW9apg3GIvb8aCnUuok4EWg3mugyEykIvI80DaqewmwYfiMqR+4BziZ+BtNE9tkR0YjL/Cop4EGvGiq4vgB8JiI/G/QuY4HeK1REfm9iBwGeF7Oi/okMZcPzjwhPoHOBR4APq2U+h/Ce1RvPCKlnkqpSqXUTcCBSqlvhJPauIVdjf4rcDTwGaXUxWEkNk5hV6NHKqVuUEr9DHjU60EnzH6kaUKl6BMR6QY+H3QyEwB2erYC5sueHuw0vQG4IehkJgDs9HwWeDbdg0b9jHQLMC+pXQM0hZTLRIDRM/swmmYXvugZ9Yn0z8CeSqkFSqlC4LPA70POaTzD6Jl9GE2zC1/0jMxEqpT6NfAysLdSaotS6osiEgO+DDwBrAN+IyJvhZnneIHRM/swmmYXQeppNi0xMDAwyBCROSM1MDAw8AtmIjUwMDDIEGYiNTAwMMgQZiI1MDAwyBBmIjUwMDDIEGYiNTAwMMgQZiI1yDkopYqUUmuVUrPDzsVvKKV+bJ6VH/8wE6lBoFBKNSiljnYxuxB4XkS2D/vcrpSS4W3Oko/10+H+C5L65gxvIr1NKdWplFqvlPp3pVSJxzyfVUr9sxefNHE9cOXwUzYG4xRmIjXIRVwE3Dmq7x/A+YmGUqoAOB14N6lvOvEnWSYDHxORMuCfgArgQz7nnBZEZBuwHrOB+LiGmUgNAoNS6k5gPvCwUqpLKXVFCpv5xCe9V0dRDwOHK6WmDbePA14HtifZfAXoBM4VkQYAEdksIv8mIq+niFWslPqVUqpVKdWulPqzUqpKKfVd4BPAjcN53jhsv49S6kmlVNvwDutnJB3r9uFXVTw5fCb8nFKqdphTSqmfDO/Wvksp9bpSav+kVJ4FTtDV0SD3YCZSg8AgIucBm4ATRaRURNakMPsI8N7wM9HJ6CW+ucRnh9ufA345yuZo4AERGdJM6XxgKvHdgCqJb/XXIyJXAi8AXx7O88vDSwNPAncDs4CzgP9WSu2XdLxzgGuBGcDfgLuG+48BjgD2In52fCbQmuS3DlismbNBDsJMpAa5hgriZ5Wp8Evgc0qpqcAy4Hej+Epgm4dYA8M+HxaRQRH5q4h02Nh+CmgQkdtEJDa8K/39wGeSbB4RkedFpA+4EviYUmrecJwyYB/i+1usG/5Jn0An8c9tME5hJlKDXMP7xCedMRCRF4GZxN9T9AcR6Rll0grM8RDrTuK7AN2jlGpSSq1RSk2ysa0Flg4vAbQrpdqJn4Em31lg7bwuIl3EX3NRLSJPAzcSf1fQDqXUzUqp8iS/MqDdQ94GOQYzkRoEDbftxl4H9hi+mJQKvwK+ytif9QBPAacqpbTqWkQGROTfRWQhcBjxs87P2eS5GXhORCqS/kpFJPnVvdaGwUqpUmA6w5sGi8gNInIwsB/xn/hfS/LbF/i7Ts4GuQkzkRoEjR3AHnakiGwB3iH+krJUuIH4lfjnU3A/BsqBO5Iu9Mwdvldz0WhjpdQnlVIfGX6zZAfxn+CJt8aOzvMPwF5KqfOUUpOG/w5VSu2bZLNCKfXx4VuZrgVeFZHNw3ZLh892u4mv9ya/nXYZ8JidJga5DzORGgSN7wNXDf88vtzG5mfAeakIEWkTkXpJsZGuiLQRP7McAF5VSnUSf7XuLmBDisPNBu4jPomuA54jfsYL8B/EXyz3vlLqBhHpJH7R6LPEzzK3Az8AipKOdzdwNfGf9Afzwdsoy4FbiC9bNBJfgvghxO97Jf5a4NHrvQbjCGZjZ4Ocg1KqCPg/YPmoizI5C6XU7cAWEbnKo9+PgHdF5L99ScwgEET9LaIGOYjhq94Lw84jCIjIV8POwSBzmJ/2BgYGBhnC/LQ3MDAwyBDmjNTAwMAgQ5iJ1MDAwCBDmInUwMDAIEOYidTAwMAgQ5iJ1MDAwCBDmInUwMDAIEP8f6nRzpoJR7CVAAAAAElFTkSuQmCC\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(range(1, 1002),a, marker = \".\", markersize = 3, linestyle = \"None\",\n",
    "         c= \"blue\")#, label = \"θ (slope) = {}\".format(round(model.coef_[0],3)))\n",
    "plt.plot(range(80, 1002), range(80, 1002)**(model.coef_)*np.exp(model.intercept_),\n",
    "         c = \"red\", linestyle = \"--\", linewidth = 2.5, label = \"regression line: θ (slope) = {}\".format(round(model.coef_[0],3)))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"t (MC steps)\", size = 12)\n",
    "plt.ylabel(r\"$\\langle n(t) \\rangle$\", size = 12)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(fontsize = 12)\n",
    "#plt.text(1, 10, \"ciao\")\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/theta.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.plot(range(1, 1002),a, marker = \".\", markersize = 3, linestyle = \"None\", c= \"blue\", markerfacecolor = \"white\")\n",
    "plt.plot(range(10, 1002), range(10, 1002)**(model.coef_)*np.exp(model.intercept_),\n",
    "         c = \"red\", linestyle = \"--\", linewidth = 1,\n",
    "         label = \"regression line: θ (slope) = {}\".format(round(model.coef_[0],3)))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"t (MC steps)\", size = 12)\n",
    "plt.ylabel(\"n(t)\", size = 12)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(fontsize = 12)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/theta_reg.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = simulate(10000, 1/10000, 20000, 1000, 3.29785, rec_rate = 1, surv_prob = True)\n",
    "a = np.mean(a, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9997175834118089\n",
      "[0.1587783]\n"
     ]
    }
   ],
   "source": [
    "x_range = np.log(np.arange(10, 1000 + 1, 1))\n",
    "x_range = x_range.reshape(-1,1)\n",
    "y_range = np.log(a[10:])\n",
    "model = LinearRegression()\n",
    "model.fit(x_range, y_range)\n",
    "print(model.score(x_range, y_range))\n",
    "print(model.coef_*(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TU1OxdetWFBZ+99CLyPFGjBiB0aNH48svv8SECRMA9P0DEhm7devWYcqUKTjhhBMwevRoJb+goABpaWmor6/H2LFjAfT5Fj3RbNu2LaZfW7duxWmnnab7ft1uNzZu3Ijq6mrNW5KnTZuGdevWqXKTJk3C888/PyB+44034sYbbwTwXe0ccsgh+OijjzBu3DgAwEcffYRDDjkkxiO1/onEGWMxdTx58mS89957yiWVo0ePxm9+8xvVY5nBsPjG7DTa29u5MTVeFxdeCLz2Gv91330xKcFDD9XPibsMSMnt/+VYD+eeey5WrlyJF198EaFQCD09PXjttdfQ2NiIqqoqHHPMMfj973+PQCCAd955BytXfncFoto5LrvsMtxxxx349NNPAQB79uzB0qVLEQwG8d5772H9+vXo7e1Feno6MjIy4HK5EAgE8Pjjj2PPnj1IS0uD1+tVfYTP+PHjMWLECNx1113o7e3Fa6+9hpUrVwpfRyvqCQ+lpaU45ZRTcPXVV6OjowPhcBjffPMNXo/6y0XvPNH82Wefjeeffx4vvfQSent7ceeddyrf4tT006dPx+uvv67Eli5dqlxXn52dDcYYXC5XTI7L5cKsWbNw0003obOzE/X19bj33ntj/vFsaWnB/Pnz0dvbi6VLl+Kzzz7D9OnTdd9vMBjE66+/jmnTpmm+3+effx4+n2/Aa/fu3aqTspZfP/nJT3Dvvfdi27ZtaGpqwj333IMLL7xwgEcR+P1+5S+mQCCAnp4eZZJ/5plnsHv3bhARNmzYgPnz52PGjBlK7ocffoju7m50dHTgmmuuQUVFBWpra3X7Kgy19Q35GoI1ZhMQXYMzkltVVUUvv/xyjO7dd9+lE044gXJzc6mgoICmT5+urBd++umn9L3vfY88Hg+ddNJJNHfuXLr44ouJ6Ls15sg6bQSLFi2iQw89lLKzs6miooIuuugi6unpoTVr1tBhhx1GI0aMoPz8fPrxj39MnZ2d5Pf7acqUKZSTk0PZ2dl07LHHKj9ixV+V8cknnyhXIRx88MH0zDPPKNwFF1xAN910k9KOzzWyxjxx4sSY94S4Kxwuu+wyKi8vJ6/XS0ceeSQ99dRTRNT349+IESO4663xY7Ns2TI6+OCDyev10oQJE+ijjz7S1G/atInGjh1L3d3dRER07bXXUllZGY0YMYJqamqUqxai15iJ+n5QPe+886igoIAqKiro1ltvHXBVxs9//nPyer10wAEH0Isvvqick/d+e3p66NBDD6X//ve/mu9X1Ac9XTgcpmuvvZZyc3MpNzeXrr32WmVdvKenh8aOHUtPPPGEkldVVUUAYl6Rz+7ZZ59NeXl5NGLECBozZgzdf//9Mf0599xzyev1ktfrpVmzZtGOHTu4/U3KH//sfiXTxGxUF8/PmjWLbr75Zm6uWjw+pte2A074KaLl8SLezZ49m55++mmuzkh/1f4hEsW///1vOvvss03lWlWjPI1TNWp0YpZrzCYQvb6nFlPj7UAi7EPw4YcforCwEDU1NXjppZewYsUKXH/99dxcuVeGvXtlPPnkk6o3MAzFXhmnn346zjzzTFO5w2WvDDOQE7MJRO6E0oqp8cMVzc3NOPvss9HW1oaKigo8+OCDOOqoo4a6WxIS+zTkj38m0NbWxo2p8XZgMD9Wiebq6aZNm4aGhgZ0dXXhyy+/xEUXfXe3u1auWjw+pte2A074KaLl8SLeicSM9PfCCy80vRdEItQoT5OoNSonZgkJCYkEg5yYTSA7O5sbU+Pj0bfuPzioXTJmda6ejsdrcWrx+Jhe2w444aeI1qinZmJO+DnY81hVozyNEzVq5rMuJ2YTULtQPjqm92wvl8tl+IkGakiEp0PIJ5gYz5VPMLE2N9GfYNLd3W34iUVyYjaB6FtV1WJqfDRycnKwY8eOQf9IOJjJXTRXT8fjtTi1eHxMr20HnPBTRGvUUzMxJ/wc7HmsqlGexs4aJSJ0dXVh27ZtKCoq0u1jNORVGUOAgoICNDY2DnqD98j+xnbm6ul4vBanFo+P6bXtgBN+imiNemom5oSfgz2PVTXK09hdo2lpaSguLjb0hGwA8gYTkVf8DSbbtm0bcKF4dEyNtwODOY9orp6Ox2txev6JtO2AE36KaI16aiaWTDXK0wx1jULjBhNGFvwINdxx7LHH0saNG4e6GxISEsMMjLH3iejY+LhcYzaB+F3N4mNqvFP9sDpXT8fjtTg9/0TadsAJP0W0Rj01E0umGuVpErVG5RozB4yxmQBm1tTUxDzzr6enZ8Az/1paWhAKhcAYAxFh+/btyrPP4p/5l5eXh9TUVGXP2qysLBQUFGDr1q0A+q7aqKysRFNTk/J8ufLycnR0dCh72+bn56Orq0vph8fjQU5OjrKTWGpqKioqKtDY2Khc+F5RUYH29nb4fD60tbUhLy8P4XBYuSEmOzsbXq9X+fHS7XYjFArFPKNs1KhRaG1tRVdXF4C+Xbk6Ojqwa1ffQ8q9Xi88Hg+amprQ1taG1NRUlJaWor6+XrlsiIiwY8cOdHd3AwCKi4vh8/mU95KTkxPjcUZGBkKhkNIGgOrqajQ3N6OnpwdA3/aWPT09ys5+ubm5cLvd2LFjR8w41dfXR8YWVVVVMeMUDAaxa9cuU+MUGX+1cUpJScHOnTuVcQoEAsp7URunUCiE1tZWZeezwsJCZZza2tqQlZUVM07t7e2orKyMGadwOIyWlhZlnIqKimI83rt3LwKBAJqa+p5LmZ6ePmCcqqqq0NLSEjNOgUBAeb5lTk4OMjIy0NzcrIxTSUlJzDgBMD1ObW1tCIfDA8Yp/vPU3d2Nrq4u7jiFQiHVz1Nk3OLHyefzobS0NObzFAqFuOPk9/vR2dnJ/Twl3TP/7HxZvYmRVRjMeURz9XQ8XovT80+kbQec8FNEa9RTM7FkqlGeZqhrFHKN2Tzi15ijN2JXi6nxdmAw5xHN1dPxeC1Ozz+Rth1wwk8RrVFPzcSSqUZ5mqGuUbnGbCFaW1u5MTXeqX5Ynaun4/FanJ5/Im074ISfIlqjnpqJJVON8jSJWqNyYjaByLqdVkyNd6ofVufq6Xi8Fqfnn0jbDjjhp4jWqKdmYslUozxNotaonJglJCQkEgxyYjYBtdsro2NGb7+0sh9W5+rpeLwWp+efSNsOOOGniNaop2ZiyVSjPE2i1qicmE3Ayr1ure6H1blW7x2sFZf7MYvxQ7Ef82CQCDXK0yRqjcqJ2QQi1+xqxdR4p/phda6ejsdrcXr+ibTtgBN+imiNemomlkw1ytMkao3KiVlCQkIiwSAnZhMY7H7MdvbD6lw9HY/X4vT8E2nbASf8FNEa9dRMLJlqlKdJ1BqVE7MJeDwebkyNd6ofVufq6Xi8Fqfnn0jbDjjhp4jWqKdmYslUozxNotaonJhNILK/gFZMjXeqH1bn6ul4vBan559I2w444aeI1qinZmLJVKM8TaLWqJyYJSQkJBIMcmI2gfT0dG5MjXeqH1bn6ul4vBan559I2w444aeI1qinZmLJVKM8TaLWqNzESAByo3wJCQk7IDcxshCRPX21Ymq8U/2wOldPx+O1OD3/RNp2wAk/RbRGPTUTS6Ya5WkStUblxGwCan9lRMec+itkMOcRzdXT8XgtTs8/kbYdcMJPEa1RT83EkqlGeZpErVE5MUtISEgkGOQaswDi15iJCIyxGE10TI23A4M5j2iuno7Ha3F6/om07YATfopojXpqJpZMNcrTDHWNyjVmCxF5tphWTI13qh9W5+rpeLwWp+efSNsOOOGniNaop2ZiyVSjPE2i1qicmE0g8nBKrZga71Q/rM7V0/F4LU7PP5G2HXDCTxGtUU/NxJKpRnmaRK1ROTFLSEhIJBjkGjMHjLGZAGbW1NTMfeWVVwD0PW49HA5jz549AL573PrXX3+NtLQ0MMZQVFSE9vZ2zcet5+XlITU1lfu49crKStXHrXd2dgIA8vPzEQgElLbH40FOTk7M49YrKipiHrdeUVGB9vZ2+Hw+9Pb2oqysDOFwmPu49dzcXLS2tiqPWx81ahRaW1uVx+h4vV6kpqYqWx56vV54PB40NTWht7cXHo8HpaWlqK+vV361LioqQmdnp/INo7i4GB0dHUo7JycHAJRH3GdkZGDkyJHKI+4BoLq6Gs3Nzejp6QEAlJSUoKenR8nJzc2F2+1WciLjFLmkiTGGqqoqbN++XRmn3NxchEIhU+O0d+9epKWlqY5TSkoKdu7cqYxTenq64rnaOOXn58Pv98Pn8wEACgsLlXHq7e1FXl5ezDgREWpqatDQ0KCMU2FhIfbu3auMU1FREXw+n9JOT09Hfn6+chtxenr6gHGqqqpCS0tLzDgFAgHs3r1bGaeMjAw0Nzcr41RSUoK6ujplnIqLi7Fnzx5T49Tb2wu32z1gnOI/T1lZWfB4PNxxKigowO7duwd8nnbt2oW0tLQB45SWlobi4uKYz1N+fj7a2to0xyk7Oxtut5v7eSorK4sZp5qaGtU15gGPzZavga9jjjmGotHe3k7xiI6p8XZgMOcRzdXT8XgtTs8/kbYdcMJPEa1RT83EkqlGeZqhrlEAG0llzpFLGSYQ+cagFVPjneqH1bl6Oh6vxen5J9K2A074KaI16qmZWDLVKE+TqDUqJ2YJCQmJBIOcmE0gsgaqFVPjneqH1bl6Oh6vxen5J9K2A074KaI16qmZWDLVKE+TqDUqJ2YTyMjI4MbUeKf6YXWuno7Ha3F6/om07YATfopojXpqJpZMNcrTJGqNyonZBCK/QmvF1HirsXYtMHFi33/NQLSPejoer8Xp+SfStgODOYeRXKs9NRNzws/BnseqGuVpErVG5cS8j+Lmm4EPPsjAzTcPdU8kJCSshpyYTSAR/ky87Tbg2GMDuO02c/lyKWMg5FKG9ZBLGeYgbzARgNwoX0JCwg7ITYwsRPSdTWoxNd6pflidq6fj8Vqcnn8ibTvghJ8iWqOemoklU43yNIlao3JilpCQkEgwyIlZQkJCIsEg15gFINeYJSQk7IBcY7YQ8hpRMT5RrxHVgryO2XokQo3yNIlao3JiNoHIFoZaMTXeqX5Ynaun4/FanJ5/Im074ISfIlqjnpqJJVON8jSJWqNyYpaQkJBIMMiJ2QRKSkq4MTXeqX6IYO1aYPbsUUK3c+udg8drcXr+ibTtwGDOYSTXak/NxBK9Ro3kiuiM1KJW3MkalROzCezrfybefDPw7rspQrdzy6UM63PlUoa1uXIpQwLAd4880oqp8U71QwS33QYcfXSP0O3ceufg8Vqcnn8ibTswmHMYybXaUzOxRK9RI7kiOiO1qBV3skZTLTuSxD6D2lrg3/9uRnV19VB3RUJCQgXyG7MJ5ObmcmNqvFP9sDpXT8fjtTg9/0TadsAJP0W0Rj01E0umGuVpErVG5cRsAm63mxtT453qh9W5ejoer8Xp+SfStgNO+CmiNeqpmVgy1ShPk6g1KidmE4g8al0rpsY71Q+rc/V0PF6L0/NPpG0HnPBTRGvUUzOxZKpRniZRa1ROzBISEhIJBjkxm0BmZiY3psY71Q+rc/V0PF6L0/NPpG0HnPBTRGvUUzOxZKpRniZRa1RuYsQBY2wmgJk1NTVzX3nlFQB9C/xpaWloaWkB0DcYRUVFqKurA2MMjDGMGjUKzc3N8Pv9AICysjL4fD50dHQAAPLy8pCamqocIysrCwUFBdi6dSsAwOVyobKyEk1NTQgEAgCA8vJydHR0oLOzEwCQn58PxhhaW1sBAB6PBzk5OWhsbAQApKamoqKiAo2NjQgGgwCAiooKtLe3w+fzgYhQVFSEcDiMtrY2AEB2dja8Xi+2bdsGoG/NrLS0FI2NjQiFQgCAUaNGobW1FV1dXQCAwsJChEIh7Nq1CwDg9Xrh8XjQ1NQEIkJGRgZKS0tRX1+PSK2NGjUKO3fuRHd3NwCguLgYfr9fudwoJycH6enpyp+GGRkZKC4uRn19vTI21dXVaG5uVq4dLSkpQU9Pj3KM3NxcuN1u5RiRcYocgzGGqqoqbN++XRmn0tJS7N2719Q4+f1+MMZUxyklJQU7d+5UxmnkyJGKx2rjVF5ejj179sDn8ykeR8aJiOD1emPGKS0tDXkYapkAACAASURBVOXl5WhoaFDGqbKyEm1tbco4FRUVobe3F7t37x4wTgCQnp4+YJyqqqrQ0tISM06BQEA5Rk5ODjIyMpQ9IjIyMlBSUhKzL3FVVRV27NhhapyICCkpKQPGKf7zFP+ZVBuniooKbN++fcDnqaOjA4yxAeM0YsQI5ObmxnyeysvLsW3bNs1xKigoABFxP09lZWUx41RTU6O6iRGISL50XscccwxFY8uWLRSP6JgabwcGcx6R3DVriI4+upvWrDF3HC1Ozz+Rth2w209RrVFPzcSGS42K6ozUolbcjhoFsJFU5hy5lCGhCfnAVwmJoYGcmE2AMcaNqfFO9cPKXJE7BHnH0eL0/BNp2wG7/RTVGvXUTGy41KiozkgtasWdrFG5xiwAuVG+hISEHZAb5VuI7du3c2NqvFP9sDpXT8fjtTg9/0TadsAJP0W0Rj01E0umGuVpErVG5cRsApFfh7ViarxT/bA6V0/H47U4Pf9E2nbACT9FtEY9NRNLphrlaRK1RuXELCEhIZFgkGvMAohfYw4EAgPui4+OqfF2YDDnEc3V0/F4LU7PP5G2HXDCTxGtUU/NxJKpRnmaoa5RucZsISIXlGvF1Hin+mF1Lk+3di3wve8xzSehaOXq+SfStgNO+Cmi5fEi3onEkqVG9TSJWqNyYjaByB1HWjE13ql+WJ3L0918M/Dee2ma1zlr5er5J9K2A074KaLl8SLeicSSpUb1NIlao3JiljANI09CkZCQEId8gokJ5OXlcWNqvFP9sDqXp6utBV59NQCvN8NQrp5/Im074ISfIloeL+KdSCxZalRPk6g1Kr8xm0Bq6sB/z6JjarxT/bA6V0/H47U4Pf9E2nbACT9FtEY9NRNLphrlaRK1RuXEbAKRXay0Ymq8U/2wOldPx+O1OD3/RNp2wAk/RbRGPTUTS6Ya5WkStUblxCxhC9auBc46q0Tzig0JCQltyInZBLKysrgxNd6pflidq6fT4nk70+n5J9K2A074KaLl8SLeicSSqUZ5GiNxJ2tU3mAigPgbTMLhMFJSYv9Ni46p8XZgMOcRzdXTafFr1wK/+x1h3jyG2lr9nPiYXtsOOOGniJbHi3gnEkumGuVpjMTtqFF5g4mFiDwZQSumxjvVD6tz9XRafG0t8OST9QMmZa2c+Jhe2w444aeIlseLeCcSS6Ya5WmMxJ2sUTkxSzgKufYsIaEPOTGbgMvl4sbUeKf6YXWuno7Hq3Faa8/xWr22HXDCTxGtUU/NxJKpRnkaI3Ena1SuMQtAbpRvHdau7Zucb7sNqsscEhLJBLnGbCEiTxbWiqnxTvXD6lw9HY9X42prgaVLmwZMyvFavbYdcMJPEa1RT83EkqlGeRojcSdrVE7MJhB5BLpWTI13qh9W5+rpeLwWp+efSNsOOOGniNaop2ZiyVSjPE2i1qicmCWGHPIHQQmJWMg1ZgHErzH39vYiLS0tRhMdU+PtwGDOI5qrp+PxWlx8fOJE4O23gQkTgLfeUtc44akTfopojXpqJpZMNcrTGInr1aSZ9yrXmOPAGNuPMbaIMbbMaK7c61aMF93r9rbbgOOO643ZPlTuxyzOyf2Y5X7MpsEYy2GMLWOMfc4Y+4wxdrzJ4zzCGGthjH2iwk1ljH3BGPuaMXY97zhE9C0RXWKmD52dndyYGm8HBnMe0Vw9HY/X4uLjtbXA009vi/lBMF7jhKdO+CmiNeqpmVgy1ShPYySuV5NWeurkN+b7AbxARAcBOALAZ9EkY6yIMZYdF9tf5TiPApgaH2SMuQD8HcA0AGMBzGaMjWWMHcYYey7uVWTNW5KwA3LNWSLZ4cjEzBjzAjgBwCIAIKIAEbXHySYDWMEYy+jPmQtgfvyxiOgNALtUTjMOwNf934QDAJYAOJ2INhHRqXGvQe3Pl5+fz42p8XZgMOcRzdXT8XgtTs8/tZtQnPDUCT9FtEY9NRNLphrlaczWqEh7MHDqCSb7AdgJYDFj7AgA7wP4JRHtjQiIaCljrAbAEsbYUgAXA5hi4BzlABqi2o0AxmuJGWP5AG4HcBRj7AYiukNFMxPAzJqaGtTV1QEAcnNzEQwGlXZmZiaKiorQ1NSE9PR0MMZQUFCA7du3w+/3AwDKysrg8/mUNai8vDykpqYq+7dmZWWhoKBAudfe5XKhsrISTU1NyiU45eXl6OjoUP5cys/PR09PD9ra2gAAHo8HOTk5aGxsBNC3aXdFRQUaGxsRDAYBABUVFWhvb4fP54Pf70dFRQXC4bByjOzsbHi9Xmzbtg0A4Ha7MXLkSDQ0NCAUCgEARo0ahdbWVnR1dSnnJSLs2tX3b6XX64XH40FTUxP8fj+8Xi9KS0tRX1+PyA/NBQUF2LFjB7q7uwEAxcXF2Lt3r9KP664rwO23p+OKK9pQV9eDjIwMZGdnK54DQHV1NZqbm9HT0wMAKCkpQU9PD9rb25Vxcrvd2LFjR8w41dfXR8YWVVVVMeM0cuRI7Nq1y9Q4dXZ2Ij09XXWcUlJSsHPnTsUvt9utvBe1ccrLy0Nra6vycM/CwkJlnPx+PwoKCmLGKRwOIzs7O2ac8vPz0dLSooxTUVERurq6FI/dbjfS09OVa2/T09MHjFNVVRVaWlpixikQCGD37t0AgJycHGRkZKC5uRkAkJGRgZKSkphxKiwsND1Ofr8fGRkZA8Yp/vOUmZkJl8vFHae8vDzVz1NrayvS09MHjJPL5UJmZmbM5yk3N5c7TiNGjAAA7ueprKwsZpw0QUS2vwAcCyAIYHx/+34A8zS0SwB0ACjkHK8awCdxsbMBPBzVngPgr1b0/5hjjqFobNmyheIRHVPj7cBgziOaq6fj8Vqcnn/x7TVriI4+upvWrOF2ZdBwwk8RrVFPzcSSqUZ5GqtqVLQf8QCwkVTmHKfWmBsBNBLR+v72MgBHx4sYY5MAHApgOYBbTJyjMqpdAcCZ25skbAVvb2cJieEIRyZmImoG0MAYG9MfqgWwOVrDGDsKwEIApwO4CEAeY+wPBk7zHoADGGM1jDE3gHMBPDvozqvA4/FwY2q8U/2wOldPx+O1OD3/4tu33QYcd2zA9qdxO+GniNaop2ZiyVSjPI1VNSraD1E4doMJY+xIAA8DcAP4FsBFRLQ7ip8IoIOINvW30wBcSEQL447zFIATARQA2AHgFiJa1M9NB3AfABeAR4jodiv6Hn+DSTAYHPDgxeiYGm8HBnMe0Vw9HY/X4vT8G9AOhRA+6yykTJ0KXHaZbp/Nwgk/RbRGPTUTS6Ya5Wksq1ED/Y3GkN9gQkT/JaJjiehwIvph9KTcz78VmZT7273xk3J/fDYRlRJRGhFVRCblfm41ER1IRKOtmpTVEPlBQCumxjvVD6tz9XQ8XovT829A+6abkLJiBXD55Wg44yqcMCFoy6V0TvgpojXqqZlYMtUoT2NZjQr2QxRJe+efxD6EM85AqKAAAFD5n7/ixndOxZ9u3DPEnZKQsA9yYjYBtT9XomNO/Ik42POI5urpeLwWp+ffgPb48Wh57jngiCMAAFPxIpY3Hw988w23b0bhhJ8iWqOemoklU43yNJbVqGA/RCE3MRKA3Cg/QeDzAeedBzzb/5tufj7ev+kZXLXsBLnxvsQ+iSFfYx5OkOt3Yrzl63ceD/DMM8C11/YF29pw+NUnY/+3H7PkUjq5xmw9EqFGeRq5xjyMELnzRyumxjvVD6tz9XQ8XovT84/bdrmAu+4CHnkESEtDGvWi6sAM3HZb3x4bEyfC9A+DTvgpojXqqZlYMtUoT2NLjVoAp27JlpCwFhddBIweDWzYgNuuOQfAd/s633yzXNaQ2Lch15gFIK9jHuLrmAX7u3Yt8Mg1mzFpejb+77VKw+vO8jpm65EINcrTJP11zMMJkQ1YtGJqvFP9sDpXT8fjtTg9/0Taaqg9rAX/3D0dP7p7HHrf3mB43dkJP0W0Rj01E0umGuVpnK5RUciJ2QQiu0lpxdR4p/phda6ejsdrcXr+ibRV8a9/AfX1KOhtxrqUyfjH95fo5xg9hwW5VntqJpZMNcrTOF6jgpATs8TwwS9+ATzwAOByIT3cg0Nvn41vf/J7TJxActN9iX0LalvOyRd/20+fz0fxiI6p8XZgMOcRzdXT8XgtTs8/kTYXL71ENHIkEUAE0FM4h04c36Wb5oSfIlqjnpqJJVON8jRDVqP9gBXbfjLGPIyxCsaYM1tTJSjC4TA3psY71Q+rc/V0PF6L0/NPpM3FlCnAu+8C++8PADgX/8KTTZNx2nHbud+cnfBTRGvUUzOxZKpRnmbIalQHuhMzY+xQxthfGWPfAtgDYCuAPYyxbxhjf2OMHWZZb/YRRJ5QoBVT453qh9W5ejoer8Xp+SfS1sVBB/VNzieeCAAobXgPv9x4Pq66SvtaZyf8FNEa9dRMLJlqlKcZ0hrlgDsx92+x+SSA7QDOR99Wm+7+/84BsA3APxljxn5lkZBwAvn5wIsvAj/9KXo9OVh41IMAvrvWWUIiUaH3jflJ6tum849E9DYR7SaiYP9/3yaiO4jocABPONHZREF2djY3psY71Q+rc/V0PF6L0/NPpC0MtxtYsABpn36EJR8ciPnzgQkT+jbfX7uGYr49O+GniNaop2ZiyVSjPE1C1KgKhG8wYYyNp+8eDRUdH0dEGyzrUQIi/gaT3t5epKWlxWiiY2q8HRjMeURz9XQ8XovT80+kPWgsXozVv30dZ+z8B46dkI633nLGTxGtUU/NxJKpRnmaoa5RK24weVkj/oKhngwDRJ56qxVT453qh9W5ejoer8Xp+SfSHhTefBP42c8wfedj2JB9MmafvBMTJwJPP21+jdBI/6z21EwsmWqUp0nUGhX58S+FMebq+1/G+tuR1wHoe/q1hMS+gwMPBI7t+5JyROebOONP49H+9qe4996cIe6YhEQfRL4xBwEEAGT1/39v1GszgAds612Cwu12c2NqvFP9sDpXT8fjtTg9/0Tag0JREfDKK317OwMo92/B+pTjcfSOl03fiGKkf1Z7aiaWTDXK0yRqjequMTPGqgAwAK8DOCGKIgA7iajbst4kKORG+cMURMAddwA33QQACCEFdxXfi+f2uwq3zWNyhzoJ22F6jZmI6omojoiq+v8/8tqaDJOyGhoaGrgxNd6pflidq6fj8Vqcnn8ibUvAGHDjjcCyZQilZ8KFMG7Y8SvMeedy3Po7Yyt0RvpntadmYslUozxNotao3nXM9zLGSnQ0JYyxey3r0T6AUCjEjanxTvXD6lw9HY/X4vT8E2lbirPOguutdQgWFwMADsjfhZmnpxjadN9I/6z21EwsmWqUp0nUGtXbPPQLABsYY5+hbynjCwCdALIBHAjgRABjAPzBsh5JSAwFjjkG2//zH1QuWoTa++/HzVNS5Kb7EkMGkTXmNACnA5gG4DAAOQB2A/gYwGoAK4loWF+ZEb/GHA6HkZIS+8dGdEyNtwODOY9orp6Ox2txev6JtO1A9DnWru2blM861Y/Pn/oQ5/zlf7gTtJH+We2pmVgy1ShPM9Q1OpjrmNMAHA2gEMDzAA4novFENJeIlg/3SVkNra2t3Jga71Q/rM7V0/F4LU7PP5G2HYg+R20t8NabhIP/Mhd/3zQJK2Ys4C5rGOmf1Z6aiSVTjfI0iVqjIhPz3wDMBPA5gLMA3G3Z2fdRdHV1cWNqvFP9sDpXT8fjtTg9/0TadmDAOTZvxintTyMNQcz3/wxNs36FSRNCqhO0kf5Z7amZWDLVKE+TqDUqMjFPA3AKEV3X//+nWnZ2CYlExiGHwPX6qwjkFAEA5uy6Hze8MxM/+WGH3Hhfwl6obdIc/QLQEdfepZcz3F7xG+Xv3buX4hEdU+PtwGDOI5qrp+PxWpyefyJtO6B5jro6osMOUzbe34RD6KyjvzXdP6s9NRNLphrlaYa6RjGIjfJTGWPfZ4ydxBg7Kb7dH0sqBIMDl9WjY2q8U/2wOldPx+O1OD3/RNp2QPMcVVXAW28Bp/b9sXgoPsWCj8Zh4/1vmeqf1Z6aiSVTjfI0iVqjIldl1KHvLj8tEBHtZ1mPEgiMsZkAZtbU1Mx95ZVXAAC5ubloaWlRdpHKzMxEUVERPvjgA+Tn54MxBiJCeno6/H4/AKCsrAw+nw8dHR0AgLy8PKSmpqKlpQUAkJWVhYKCAmzduhUA4HK5UFlZiaamJgQCAQBAeXk5Ojo60NnZCQDIz89HU1MT0tPTAQAejwc5OTlobGwEAKSmpqKiogKNjY1KwVRUVKC9vR0+nw9tbW046KCDEA6HlQ2+s7Oz4fV6lc1Y3G43AoEAXC6Xco3mqFGj0NraqqynBQIBlJSUYNeuXQAAr9cLj8eDpqYmtLW1oaysDKWlpaivr4/8xQUiQlZWFrq7++5PKi4uRl1dHTIzMwEAOTk52Llzp+JxRkYGenp6Ysamuroazc3NSrykpAQ9PT3Kk4pzc3PhdruxY8eOmHGqr6+PjC2qqqqwfft2ZZyCwSDy8vK0xyk9HYX33AN2zz0AgC6WhbOP2YKfXJOC/fevR35+vuo4paSkYOfOnco47dmzBy6XS3OcQqEQRo4cqTzcs7CwUBmntrY2VFdXx4xTe3s7jjzySDQ0NCjjFA6H4fF4lHGKvPeIx3v37sUBBxyApqYmAEB6evqAcaqqqkJLS0vMOAUCAezevVsZp4yMDDQ3NyvjVFJSgrq6upixih4/I+PU1taGgoKCAeMU/3nq7u5W+gqof55CoZBSz8B3n6e6ujrk5+cPGCefz4eDDjoo5vMUDAaV/6qNk9/vR1lZGffzVFZWFjNONTU1qldlDPkywb7wil/K2LJly4A/SaJjarwdGMx5RHP1dDxei9PzT6RtB0TP8enVD1OApdGtJQ8QQJSdTfTEE9stO49RT83EkqlGeZqhrlFY8cw/iT54vV5uTI13qh9W5+rpeLwWp+efSNsOiJ5j7J8vQdqXmzHxicuRnQ10dgKXXVYk/IOg1Z6aiSVTjfI0iVqjcmI2AY9n4LNoo2NqvFP9sDpXT8fjtTg9/0TadsDQOfbfH7W1wPLlQHY2UOirA/vBKXhzSeOgz2PUUzOxZKpRniZRa1ROzCYQWZfTiqnxTvXD6lw9HY/X4vT8E2nbATPnqK0Fnn2iA6vYTJwUehlj5hyHSw5/j/vt2WpPzcSSqUZ5mkStUTkxS0gMEidOz4KrdhwAoDDYjL9tOgGPn/q0vNZZwjTkxGwCkSshtGJqvFP9sDpXT8fjtTg9/0TadsD0OVJTkf34H4G//Q3hFBcy0YPHes7B+um3Yu2agRc0We2pmVgy1ShPk6g1Kvww1mSG3ChfQhgvvYTgGWcjtavvUq5lqecif8Uj+P70zCHumEQiwoqHsUr0I3ItrFZMjXeqH1bn6ul4vBan559I2w5Y4ucppyB147voKu27tP9HwSXwzPw+1i1tFj6PUU/NxJKpRnmaRK1ROTGbgNpfGdExp/4KGcx5RHP1dDxei9PzT6RtByzz8+CDkfXxeuw+vO9JbGXhBlz0kxAOOaRvO1GrPTUTS6Ya5WkStUblxCwhYQcKCpD73stonHk5Zmc9i296yrF5M3DGGcBbb2UMde8kEhxyjVkA8WvMRATGWIwmOqbG24HBnEc0V0/H47U4Pf9E2nbALj/XrgWuugrYsgXo7gYmud9F2+jxmP9X9Qe+GvXUTCyZapSnGeoalWvMFiJyT75WTI13qh9W5+rpeLwWp+efSNsO2OVnbS3w6afAypXAuRn/wWuBCbj6s0sw64cB1UvqjHpqJpZMNcrTJGqNyonZBCKbumjF1Hin+mF1rp6Ox2txev6JtO2A3X7WnhjCw0U3IgWEi7EYy30n4+YrBj71wqinZmLJVKM8TaLWqJyYJSScgsuFEetfQc9RRwEATsA6/N9X4/HuI5uHuGMSCQe1nY3ki7+7XFdXF8UjOqbG24HBnEc0V0/H47U4Pf9E2nbACT+JiLp27aLt359NkY332+GluaNeoDVr9I8l4p1ILJlqlKcZ6hqF3F3OOkT2dNWKqfFO9cPqXD0dj9fi9PwTadsBJ/wEgEBKCkrW/hPfXHgbAGAkOvDg1ul4YcZfsXYNGfbUTCyZapSnSdQalROzCUQ2CteKqfFO9cPqXD0dj9fi9PwTadsBJ/xUtIxh9OLfYdP//gs9LAMuhHG3/yosPGUp7rwzZOg8ZmLJVKM8TaLWqJyYJSSGEIfNm4WM9W/An1+Kl3AKltGZ+NOfcpWbUSSSE3JiNoGcnBxuTI13qh9W5+rpeLwWp+efSNsOOOGnqva445D+3w34/NZ/gVJSQcSweTMwc+bAyVnEO5FYMtUoT5OoNSonZhPIyBh451Z0TI13qh9W5+rpeLwWp+efSNsOOOGnpraiAlfdnIOXXgIyMwkpCOEf3XNwz8zXYiZnEe9EYslUozxNotaonJhNIPLwSa2YGu9UP6zO1dPxeC1Ozz+Rth1wwk89bW0tsHDhDizOuwZz8ARWdE/Bv6Y8jLvv1s41E0umGuVpErVG5cQsIZFgmDixBz+572iE09xIQxALaC5c112NtS9p/ygoMbwgJ2YTkH8mivGJ+meiFoZ0KSOenzMHKa++gr0jCgEAv8G96Jn6Q5w5xTtg3VkuZQy/pQy5iZEA5Eb5EkOGujp8ddCpOMD/KQDgYxyG3+y/Emu+qhrijklYAbmJkYWoq6vjxtR4p/phda6ejsdrcXr+ibTtgBN+imhj+OpqbHv6bbzumQ4AOByb8M+vx+G8mreVb84ifsbHkqlGeZpErVE5MUtIJDhOPM2Lye3PYuuZvwIAFKMFgbptmDIFyo+CEsMLqUPdAQkJCQG4XBj1779g/SVleO7xEJYFzwYIuP56oKwsA9XVQ91BCSsh15gFINeYJRIJa9cCF18MbN3a1z40/SvM/3c5vj8ja2g7JmEYco3ZQshrRMX4RL1GVAuJcB2zHt/c3IzaWqC+Hhg7FihGM1b5azFy5gl481/buMdI1hrlaRK1RuXEbAI9PT3cmBrvVD+sztXT8XgtTs8/kbYdcMJPEa2op/PnAze67sIoNOBoeh/7nTsOGx58X/MYyVqjPE2i1qicmCUk9lHU1gKHrvoTFrh+BgAoQxMOvWISVsxZNsQ9kxg01DZpli/+Rvnd3d0DNryOjqnxdmAw5xHN1dPxeC1Ozz+Rth1wwk8RrVFPV6/qoV+nzacgUpTN91+bcitROKyZm0w1ytMMdY1CbpRvHeSfiWJ8ov6ZqIV9bSkjguMndGPG87/ARYWrsAdeAMDkl2/BU6lzcO8f1esymWqUp0nUGpUTswm0t7dzY2q8U/2wOldPx+O1OD3/RNp2wAk/RbRGPW1vb0dtLfB4y1T8++p38C1qAACzw/9E/k0/U651TtYa5WkStUblxCwhMYxw8Z/HYvXN6/Em+x7akId5+B2uuw649NKh7pmEEciJ2QRyc3O5MTXeqX5Ynaun4/FanJ5/Im074ISfIlqjnsbHrry1EIc1/xvP/uZ1fIP9AQALFwInnFCp3MadTDXK0yRqjcqJ2QTcbjc3psY71Q+rc/V0PF6L0/NPpG0HnPBTRGvUU9VYdjYuuudQzJ37XeyUhsV46Qf3YO0aSqoa5WkStUblxGwCO3bs4MbUeKf6YXWuno7Ha3F6/om07YATfopojXrKiy1YANx1F3AiXsWDuBx/Cl2Duilzcfste4T7OxgkQo3yNIlao0k7MTPG9mOMLWKMyYs+JYY1rr0WuPBXuWhGCQDgEizCyXefi7/+vm2IeyahBUcnZsaYizH2IWPsuUEc4xHGWAtj7BMVbipj7AvG2NeMset5xyGib4noEjN9yMzM5MbUeDswmPOI5urpeLwWp+efSNsOOOGniNaopyKxC/5yJD5a8BI2sHEAgBPxOqbdOh615Z/b+jTuRKhRniZRa9TRTYwYY78BcCwALxGdGscVAegmos6o2P5E9HWc7gQAPgCPE9GhUXEXgC8BTAHQCOA9ALMBuADcEdeVi4mopT9vGRH9iNfv+E2MiAiMsRhNdEyNtwODOY9orp6Ox2txev6JtO2AE36KaI16aiT22vM92DnzIswK/wsA0I6R+HHqUlz9whTU1gp13xASoUZ5mqGu0SHfxIgxVgFgBoCHNSSTAaxgjGX06+cCmB8vIqI3AOxSyR8H4Ov+b8IBAEsAnE5Em4jo1LhXy2DeS319PTemxtuBwZxHNFdPx+O1OD3/RNp2wAk/RbRGPTUS+/70TOS/+BT+nP07AEAO9uDZ4DSs+MEDtnxzToQa5WkStUad3I/5PgDXAchWI4loKWOsBsASxthSABej79uvKMoBNES1GwGM1xIzxvIB3A7gKMbYDUQU/60ajLGZAGbW1NQoTyfIzc1Fb2+v0s7MzERRURHa2toiOQCA7du3w+/3AwDKysrg8/nQ0dEBAMjLy0NqaipaWvr+fcjKykJBQQG29u/j6HK5UFlZiaamJgQCgb43V16Ojo4OdHb2/UGRn58Pv9+v9MPj8SAnJweNjY0AgNTUVFRUVKCxsRHBYBAAUFFRgfb2dvh8PrS1taGwsBDhcFjpe3Z2NrxeL7Zt69ulLPIrc0NDA0KhvgeBjho1Cq2trejq6gIABAIBdHR0YNeuvn8rvV4vPB4Pmpqa0NbWhvT0dJSWlqK+vh6Rv86ICDt27EB3dzcAoLi4GN3d3cp7ycnJifE48iy16CdEVFdXo7m5WbnbqqSkBD09PcpF/rm5uXC73coPMpFxinx4GGOoqqqKGadgMIhdu3aZGqeIh2rjlJKSgp07dyrjFAqFlPeiNk6hUAitra3w+XwAEDNObW1tA8Yp8p6jxykcDqOlpUUZp6KiIsXj0fsDJe+cg//84SD8YMklyEQP/if0JqacfDmuv6Edl17a98NgVVUVWlpaYsYpEAhg9+7dyjhlZGQou6plZGSgpKRkwJM8zI5TW1ub6jjFIe/9TQAAHYhJREFUf566u7vR1dXFHScAqp+nyLjFj5PP50MwGIz5PAHgjpPf70dnZyf381RWVhYzTppQu0/b6heAUwE80P//JwJ4jqNdAqADQCFHUw3gk7jY2QAejmrPAfBXK/ofv1dGXV0dxSM6psbbgcGcRzRXT8fjtTg9/0TadsAJP0W0Rj01E4v8/+NXrqdn8EPKQFdkmw266y5u9wwhEWqUpxnqGoXGXhmOrDEzxu7onyiDADIAeAE8Q0Tnx+kmAXgQwPsAOonoSo3jVaNvco9eYz4ewO+J6Af97RsAgFS+CRuF3ChfYjjj7ruB3/62b1oGgHT04NfnNuOOp6qHtF/JgCFdYyaiG4iogoiqAZwL4BWVSfkoAAsBnA7gIgB5jLE/GDjNewAOYIzVMMbc/ed51pI3EIft27dzY2q8U/2wOldPx+O1OD3/RNp2wAk/RbRGPTUTi/7/a68FXn4Z6Fu5IizCJbh6ybG4e+Yb3H6KIBFqlKdJ1BpNpOuYswCcTUTfEFEYwAUABqymM8aeAvAOgDGMsUbG2CUAQERBAFcCeBHAZwCeJqJP7ehoZK1LK6bGO9UPq3P1dDxei9PzT6RtB5zwU0Rr1FMzsXi+thZYvRo4OeVVnIcnUYA2/PK5k/FT1+JBPfA1EWqUp0nUGnV8Yiai1yjuUrn++FtEtCmq3UtEC1V0s4molIjS+r+FL4riVhPRgUQ0mohut+9dSEgMP9TWAte/dBKuyl6MANLgRi8eDl8MXHct/vwnnR+rJCyFfBirAOLXmAOBwID74qNjarwdGMx5RHP1dDxei9PzT6RtB5zwU0Rr1FMzMb0+3DVzHS5+7gwUoO8KgxU4DVvm/RO/+l+P9hsz+F6syhXRGalFrbgdNTrk1zEPJ0Quj9GKqfFO9cPqXD0dj9fi9PwTadsBJ/wU0Rr11ExMrw/XrZyEZ367AZ9iLADgdDyL7/9uIq7/8VZunkg/rM4V0RmpRa24kzUqJ2YTiFw/qRVT453qh9W5ejoer8Xp+SfStgNO+CmiNeqpmZhIfy+9cz+sufVtPI+pAIAj8DF+/tREnDm1SzfXyHkGmyuiM1KLWnEna1ROzBISEpr45c0jkf7iSvyVXQUAuA03Y/mLWZgxY4g7NswhJ2YTyMvL48bUeKf6YXWuno7Ha3F6/om07YATfopojXpqJmakvyedkoqxL9+PqZ438TD6NnhevRrIzYXubdyJUKM8TaLWqJyYTSBye6ZWTI13qh9W5+rpeLwWp+efSNsOOOGniNaop2ZiRt9rbS3wQudETJ/+XSy//WtsmXIpXl2lvbSRCDXK0yRqjcqJ2QQi9+RrxdR4p/phda6ejsdrcXr+ibTtgBN+imiNemomZva9rloFTJ8OjEQ7VmImfkoL4Tn1RKx7Wv3mikSoUZ4mUWtUTswSEhKGsGoVcOGcMLajFABwHN5DzTnHYc6hHw5xz4YP5MRsAllZWdyYGu9UP6zO1dPxeC1Ozz+Rth1wwk8RrVFPzcQG6+d9j+fhvqkvYkH/mnMFtuGhT7+H3x7wjG4/RGFVjfI0iVqj8gYTAcTfYBIOh5GSEvtvWnRMjbcDgzmPaK6ejsdrcXr+ibTtgBN+imiNemomZpWfl84lZD18P+7B1XAhDAB49MA/4sLPrwcYS4ga5WmGukblDSYWIrLPq1ZMjXeqH1bn6ul4vBan559I2w444aeI1qinZmJW+blgIcN99Ctce+Cz6Ojfav3CL2/Ek+4L8crz/oSoUZ4mUWtUTswSEhKDxr1fzMDU7LdRhyoAwKTgK5hz6m689VbGEPds34ScmE0g8kQErZga71Q/rM7V0/F4LU7PP5G2HXDCTxGtUU/NxOzwc97yQ/H9rA14EadgJlaiKVyC888vxqWXmjueVTXK0yRqjco1ZgHIjfIlJMQxY0bfDSjRuP6cLbhjSc3QdCiBIdeYLURTUxM3psY71Q+rc/V0PF6L0/NPpG0HnPBTRGvUUzMxO/2MXOscwVlYhnn/OgB/qbrvu8ekCMCqGuVpErVG5cRsApEHOmrF1Hin+mF1rp6Ox2txev6JtO2AE36KaI16aiZmt5+rVgFz5wJZ8OFBXI5UhPDrrb/G8uLLgN5eoWNYVaM8TaLWqJyYJSQkbMGCBcBV1wfwA7yIRpQDAM7YuQBr3VPx11t3DXHvEhtyjVkA8WvMvb29SEtLi9FEx9R4OzCY84jm6ul4vBan559I2w444aeI1qinZmJO1ugbb6ThgilNWE6n4zj0fY6+xAG48bDnsOzjA7m5VtQoTzPUNSrXmC2E3I9ZjE/UvW61IPdjth4dHR2orQUee7kMP0h/HU/jbADAgfgKCzeNx88P0t6eTu7HLGEInZ2d3Jga71Q/rM7V0/F4LU7PP5G2HXDCTxGtUU/NxJyu0dpaYFdPFh6ftgS34mYAQC7acf8XP8DsUW9xc0XPYUaTqDUqJ2YJCQnH8NzqFGTddStm40n0IB0v4RQsbRgPxiA334+CnJhNID8/nxtT453qh9W5ejoer8Xp+SfStgNO+CmiNeqpmdhQ1ui11wI/XTMbk/AmZuMphNC3j/Hq1cD48fxc0XOIahK1RuXEbAJqG5VEx5zYwGiw5xHN1dPxeC1Ozz+Rth1wwk8RrVFPzcSGukZra4E71xyL7rSRSsyFIOZsuBITS7811EcRnZFa1Io7WaNyYjaBnTt3cmNqvFP9sDpXT8fjtTg9/0TadsAJP0W0Rj01E0uEGq2tBQKBvuudAeAv+DWuxN/xn+bxmMTWYeJEselJ5L0YqUWtuJM1KidmCQmJIcWCBcDcnxK6kQkAKEQr1qIWR3z0Lxx00BB3boggJ2YT8Hg83Jga71Q/rM7V0/F4LU7PP5G2HXDCTxGtUU/NxBKtRhcsZLiO7sIvPYsQQBrc6MVjuAgXfnE9Dh4THvQ5jNSiVtzJGpU3mAgg/gaTYDA44MGL0TE13g4M5jyiuXo6Hq/F6fkn0rYDTvgpojXqqZlYItfon2e+joueOxP56Ls7cDl+iHkH/B8++FJ94hM5h5Fa1IrbUaPyBhML0djYyI2p8U71w+pcPR2P1+L0/BNp2wEn/BTRGvXUTCyRa/SalZPxzG834DP0rWOcgf9g0VeTMDa7wfQ5jNSiVtzJGpUTs4SERMJh7p2j8eczX8SLOAUAcBT+i/19HyI1FVirfbPgsIH9f8sMQ6j9uRIdc+JPxMGeRzRXT8fjtTg9/0TadsAJP0W0Rj01E9sXavTW+1Ow5LhV+PKGX2MbyrESpwEh4OSTgTVr+q7qED2HkVrUijtZo3KNWQByo3wJiaHFSC+ho5Mp7TJsQ/aBZfj8C8bJSnzINWYLsS+v3xnNlWvM1ufKNWbjuXs6GLzevv8vRRM2YBxu+fLHqCzolmvMEn0IBoPcmBrvVD+sztXT8XgtTs8/kbYdcMJPEa1RT83E9sUa3bMHKCjouxGlHE2YjSVY1nYixlWm6K47G6lFrbiTNSonZgkJiX0GO3cCy09+AK9hMgBgPDZgPcbj6pP/O6w2QZJrzAKQ1zHL65itzJXXMQ8+9/JLAjjmkSvwUywCAPgwAufhn/hizOn4/HPxYw11jco1ZgvR3t7OjanxTvXD6lw9HY/X4vT8E2nbASf8FNEa9dRMbF+v0QcXufHT8ELckPZnhMHgwV4sxxk47Yu7UFkx8MumkVrUijtZo3JiNgGfz8eNqfFO9cPqXD0dj9fi9PwTadsBJ/wU0Rr11ExsWNQoY7gjcDUuyl2GTniQAsJd+C0u2XYrRowQO1ai1qicmCUkJPZp3PrB0bjs0LdQj1FoRT4ex0/Q1YV9evN9eYOJCRQWFnJjarxT/bA6V0/H47U4Pf9E2nbACT9FtEY9NRMbbjX6z03VmHb0BrR+uBVbsJ/CrV4NjBgBtLSI16JW3Mkald+YTSAcHrjbVXRMjXeqH1bn6ul4vBan559I2w444aeI1qinZmLDsUaf/6AYs+46Loa7GIswqesFeDxZqpfUJWqNyonZBNra2rgxNd6pflidq6fj8Vqcnn8ibTvghJ8iWqOemokN1xq99lqACPB6gVqswT/wM6zCDPwCf8XJJ9OA/Z0TtUblxCwhITHssGcPcObJnQjADRfCmI9f4gFcgW++6MWllw517/QhJ2YTyM7O5sbUeKf6YXWuno7Ha3F6/om07YATfopojXpqJpYMNXrFy2cg67030IRSAMDleAjPYxqWLtytPPQ1UWtUTswm4I3ctK8RU+Od6ofVuXo6Hq/F6fkn0rYDTvgpojXqqZlY0tTosceirGEDPko5CgBwMtbiXfwPdm34CjNmJG6NyonZBLZt28aNqfFO9cPqXD0dj9fi9PwTadsBJ/wU0Rr11EwsmWoUFRXI2fQElqecCQAYgy+xHuPRvfoV5Oer70431DUqJ2YJCYlhD8rKwhm9S3FX6o0AgDzsxvl4Ap2dLmRkDHHnVJC0EzNjbD/G2CLG2DKjuW63mxtT4+3AYM4jmqun4/FanJ5/Im074ISfIlqjnpqJJVONKpqUFFzXezsuSv0/rMVJuBwPAmDw+4GUFBW9znnsrFFHNjFijGUAeANAOvpuallGRLeYPNYjAE4F0EJEh8ZxUwHcD8AF4GEiulPgeMuI6Ec8jdwoX0JieKGygtC47btljAx0I531oj3szNp7BEO9iZEfwElEdASAIwFMZYz9T1wHixhj2XGx/VWO9SiAqfFBxpgLwN8BTAMwFsBsxthYxthhjLHn4l5Fg3kzDQ0DHwoZHVPj7cBgziOaq6fj8Vqcnn8ibTvghJ8iWqOemoklU42qaRoaGcaNAwACQHgUF2IdTUQ1q9M8ppM16sjETH2I7PCR1v+K/6o+GcCK/m/XYIzNBTBf5VhvAP3PNY/FOABfE9G3RBQAsATA6US0iYhOjXu1DOb9hEIhbkyNtwODOY9orp6Ox2txev6JtO2AE36KaI16aiaWTDWqpVm/Hrj++t34MZ7EOXgah+ETbMA4THK9PeQ16theGf3faN8HsD+AvxPR+mieiJYyxmoALGGMLQVwMYApBk5RDiD6n6xGAOM5/ckHcDuAoxhjNxDRHSqamQBm1tTUoK6uDgCQm5uL3t5epZ2ZmYmioiLlrh/G+v482r59O/x+PwCgrKwMPp8PHR0dAIC8vDykpqb+f3vnHxxXdd3xz0HGsrEsZPwD2ZYtm5ZfhjST8RQSUpoydhhKU3AaQ8jwK4yhTWfodFpK0xZmMpmk7UQJSeuSNMGTVAkpoQyhhB/JEDvFuOmkKukvN4mdBBjL1siSrJWMZFm2sHT6x3u7Wa3fb719+1Z7PjM7cM85972z33f3+Onu23sZGnL+fTjvvPNYsWIFhw8fBqCpqYl169bR39/P1NSU8+bWrmVsbIzx8XEAli9fzunTp0t5tLS00NbWVtreZsGCBXR0dNDX11faWaGjo4Pjx49z4sQJCoUCK1euZGZmppT70qVLaW1tLX27XJwzO3LkSGnQrV+/nuHhYU6ePAnA1NQUY2NjjIw4/1a2trbS0tJCf38/hUKB5uZmVq9eTW9vL8VpM1VlcHCQyclJAC688EImJydL76WtrW2Wxovcb2eKbYANGzYwMDDAqVOnAGhvb+fUqVOlpReXLVvGwoULGRwcnHWdent7S9eps7Nz1nU6c+YMIyMjia5TUUOv63TOOedw7Nix0nWanp4uvRev6zQ9Pc3w8HBptbLy61QoFM66TsX3XH6dZmZmGBoaKl2nVatWzdJ4YmKCqakp+vv7ATyvU2dnJ0NDQ7Ou09TUFKOjo6XrtGjRIgYGBkrXqb29fdZ1AhJfp0Kh4HmdKj9Pk5OTnDx5MvA6AZ6fp+3bD/HIGzfyyFN/xAN8jlUcY8/MdezYuIvutzpmfZ6AwOt0+vRpxsfHAz9Pa9asmXWdfFHVTF9AG/AycKWP/0lgDFgZcIwNwI8qbLfgzCsX23cCf5dGzps3b9ZypqentZJym5e/GszlPFH7hsUF+f18YfpFaVeDLPSMEhtX0yS2RhqjQTFF+549qjvYpVMsUHV+1a2f5C+0Sfw1S2OMAj9Uj5qT+VMZqnoc2Iv3PPG1wJXAPwNxvxzsA9aVtTuA/mRZBjM8PBxo8/JnlUfafcPigvx+vjD9orSrQRZ6RomNq2kSWyON0aCYon3LFvi/q+7ler7LCMsAeIi/4km9ldamCc9jVHOMZlKYRWSliLS5/78Y2AocrIh5B7ALuBm4B7hARD4Z4zSvAheLyEYRWQjcBjyXRv6VFP889LN5+bPKI+2+YXFBfj9fmH5R2tUgCz2jxMbVNImtkcZoUEy5vacHXtbruJoefsolAGznm7w0s5Ummc50jGZ1x7waeFlE9uMU0N2q+kJFzHnALar6uqrOAHcDvZUHEpFvAD8ALhWRPhHZAaCqZ4D7gZeAA8BTqvrjqr0jwzDmJT/Xi7n3ipfZzVYAdnEfMzSxceO6kJ4p4jW/Ya/gOeaJiYmz5orKbV7+ajCX80TtGxYX5PfzhekXpV0NstAzSmxcTZPYGmmMBsUE2duXT+k2nilOOSvMKKjed5933yTvlbzMMc8Hit/K+tm8/FnlkXbfsLggv58vTL8o7WqQhZ5RYuNqmsTWSGM0KCbIfnT4XKZufH+ZVbiYn9G2q4tPd2lVx6gV5gQUHw3zs3n5s8oj7b5hcUF+P1+YflHa1SALPaPExtU0ia2RxmhQTJj9xRehq8uxLaPAC7yPLj7Kmo/ewejRo4nyjYIVZsMwjACKu6Is5xhNOM8f384THL3sLnCf4U4bK8wJsLVuo/nzutatH7Yec/rkYYwGxcSx9xRWcTU97ONaAN7Jf3B49VWwf3+sfKNghTkBLS0tgTYvf1Z5pN03LC7I7+cL0y9KuxpkoWeU2LiaJrE10hgNiok7Rv9pzwrey26+wj0ArOcIJ95+Dc/c83yqmlphTkDxZ6x+Ni9/Vnmk3TcsLsjv5wvTL0q7GmShZ5TYuJomsTXSGA2KiTtGt2yBjZc2s4Mv8yBdzCC0MMG27pv52LLPR8o3ClaYDcMwYnDwIHR1CZ/hAbbxLCdYAsBPTm5kyZJ0zpHZIkbziebm5kCblz+rPNLuGxYX5PfzhekXpV0NstAzSmxcTZPYGmmMBsUkHaMPPgh33DHImjU38W7+jXfy7zzHNkjpx3+ZLJRf79hC+YZh+CEV2wbGKam1Xih/XlFcOtLP5uXPKo+0+4bFBfn9fGH6RWlXgyz0jBIbV9MktkYao0ExaYxRVUqL7jv/nTs2lZEAr78yym1Z/RUyl/NE7RsWF+T384XpF6VdDbLQM0psXE2T2BppjAbFpDVGe3rg0KFeNmzYEJpLFOyO2TAMI2fYHHMEKueYVbW0U4mXzctfDeZynqh9w+KC/H6+MP2itKtBFnpGiY2raRJbI43RoJhaj1GbY06R4hY2fjYvf1Z5pN03LC7I7+cL0y9KuxpkoWeU2LiaJrE10hgNisnrGLXCnIDiHmh+Ni9/Vnmk3TcsLsjv5wvTL0q7GmShZ5TYuJomsTXSGA2KyesYtcJsGIaRM2yOOQKVc8yTk5MsXrx4Vky5zctfDeZynqh9w+KC/H6+MP2itKtBFnpGiY2raRJbI43RoJhaj1GbY06R4hbofjYvf1Z5pN03LC7I7+cL0y9KuxpkoWeU2LiaJrE10hgNisnrGLXCnIDR0dFAm5c/qzzS7hsWF+T384XpF6VdDbLQM0psXE2T2BppjAbF5HWMWmE2DMPIGTbHHAEROcbsHbvPB96sCCu3rQCGM0jNK4+0+4bFBfn9fGH6ebWz0DQLPaPExtU0ia2RxmhQTK3HaKeqrjzL6rVDq72CX8BjQTZ8dr7NIo+0+4bFBfn9fGH6+bSrrmkWelZD0yS2RhqjQTF5HaM2lZGM5yPaqs1czhm1b1hckN/PF0W/+apnlNi4ms7FVm3yMEaDYnI5Rm0qowqIyA/V4xEYIzmmabqYnumTpqZ2x1wdHqt1AvMQ0zRdTM/0SU1Tu2M2DMPIGXbHbBiGkTOsMBuGYeQMK8yGYRg5wwpzBojIEhH5qojsEpHba53PfEBELhKRL4vI07XOZT4gItvc8fktEbm+1vnMB0TkchH5oog8LSK/H6evFeaEiMhXRGRIRH5UYb9BRH4qIq+JyJ+55t8BnlbV+4CbMk+2Toijqaq+oao7apNpfRBTz2fd8flh4IM1SLcuiKnpAVX9CHArEOsxOivMyekGbig3iEgT8HngN4FNwIdEZBPQARxxw6YzzLHe6Ca6pkY43cTX82HXb3jTTQxNReQm4PvA9+KcxApzQlR1HzBSYb4KeM29m5sCngRuBvpwijOY5r7E1NQIIY6e4vAp4Duq+l9Z51ovxB2jqvqcql4DxJrCtCKRLmv5xZ0xOAV5LfAM8AER+Xtq87PYesZTUxFZLiJfBN4hIn9em9TqEr8x+gfAVmC7iHykFonVMX5j9DdEZKeIfAn4dpwDLkgzOwOvLXJVVSeAe7JOZp7gp2kBsAISHz89dwI7s05mnuCn6V5gb5ID2h1zuvQB68raHUB/jXKZL5im6WJ6pk/qmlphTpdXgYtFZKOILARuA56rcU71jmmaLqZn+qSuqRXmhIjIN4AfAJeKSJ+I7FDVM8D9wEvAAeApVf1xLfOsJ0zTdDE90ycrTW0RI8MwjJxhd8yGYRg5wwqzYRhGzrDCbBiGkTOsMBuGYeQMK8yGYRg5wwqzYRhGzrDCbDQEItIsIj8RkfZa51JtROSztt5FfWOF2ah7ROSQiGwNCftdYJ+qDrh9ukVE3WUZy4/1N679w2W21e6i/EdFZFxEDorIx0VkScw894rIvXH6JOTTwEPur9CMOsQKs9Eo/B7weIXtZ8DdxYaILABuAV4vs12A80uvxcC7VHUp8F6gDfilKuecCFU9ChzENmWoW6wwG3WNiDwOrAeeF5ETIvKnHjHrcYpoT4XreeDdIrLMbd8A7AcGymL+GBgH7lDVQwCqekRV/1BV93uca5GIfF1ECiJyXEReFZELReQvgWuBR908H3XjLxOR3SIy4u6AcWvZsbrdrYl2u3fqr4hIp+sTEfmcu5vGmyKyX0SuLEtlL/BbUXU08oUVZqOuUdU7gcPAb6tqi6p2eYS9DXjDXdOgnFM4i83c5rbvAr5WEbMVeEZVZyKmdDdwPs5qY8txliadVNWHgH8F7nfzvN+dCtkNPAGsAj4EfEFErig73u3AJ4AVwP8A/+jarwd+HbgE5+79g0ChrN8B4O0RczZyhhVmoxFow7nr9eJrwF0icj7wHuDZCv9y4GiMc73l9vllVZ1W1f9U1TGf2PcBh1T1H1T1jLtzyDeB7WUxL6rqPlU9DTwEvEtE1rnnWQpchrPmzQF3CqPIOM77NuoQK8xGIzCKU8TOQlW/D6zE2evuBVWdrAgpAKtjnOtxnFXGnhSRfhHpEpFzfWI7gavdKY/jInIc5w65/MmR0s4YqnoCZ1ujNar6L8CjOHvNDYrIYyLSWtZvKXA8Rt5GjrDCbMwHwpZI3A9c5H6558XXgQc4exoDYA/wfhGJ9FlR1bdU9eOqugm4Bueu+C6fPI8Ar6hqW9mrRVXLt7ovLcAuIi3ABbiLsKvqTlXdDFyBM6XxYFm/y4H/jZKzkT+sMBvzgUHgIj+nqvYBP8fZNNOLnThPWuzz8H0WaAW+WvbF21r3WeFfqQwWketE5G3uzsljOFMOxZ3RK/N8AbhERO4UkXPd16+KyOVlMTeKyK+5j759AuhR1SNu3NXu3fgEznx5+Q7s7wG+46eJkW+sMBvzgb8GHnanA/7EJ+ZLwJ1eDlUdUdXvqcfi5Ko6gnPn+xbQIyLjOFvRvwm85nG4duBpnKJ8AHgF544c4G9xNjsdFZGdqjqO8yXebTh3wQPAp4DmsuM9AXwMZwpjM7/YbbkV2IUzTdOLM+XyGXCeuwY2cfZ8uVEn2EL5RkMgIs3AfwNbKr4kyy0i0g30qerDMfs9Aryuql+oSmJG1bFdso2GwH2qYVOt88gCVX2g1jkYc8OmMgzDMHKGTWUYhmHkDLtjNgzDyBlWmA3DMHKGFWbDMIycYYXZMAwjZ1hhNgzDyBlWmA3DMHLG/wMMqKNSnKZKPQAAAABJRU5ErkJggg==\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(range(1, 1002),a, marker = \".\", markersize = 3, linestyle = \"None\",\n",
    "         c= \"blue\")#, label = \"δ (slope) = {}\".format(round(model.coef_[0]*(-1),3)))\n",
    "plt.plot(range(10, 1002), range(10, 1002)**(model.coef_)*np.exp(model.intercept_),\n",
    "         c = \"red\", linewidth = 2.5, linestyle = \"--\", label = \"regression line: -δ (slope) = {}\".format(round(model.coef_[0],3)))\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"t (MC steps)\", size = 12)\n",
    "plt.ylabel(\"P(t)\", size = 12)\n",
    "plt.grid(which = \"both\", alpha = 0.5, linestyle = \"--\")\n",
    "plt.legend(fontsize = 12)\n",
    "plt.show()\n",
    "fig.savefig(\"presentazione/Images/cp/delta.pdf\", transparent = True, bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}