{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Point Processes\n",
    "\n",
    "**Author: Serge Rey <sjsrey@gmail.com> and Wei Kang <weikang9009@gmail.com>**\n",
    "\n",
    "## Introduction\n",
    "\n",
    "One philosophy of applying inferential statistics to spatial data is to think in terms of spatial processes and their possible realizations. In this view, an observed map pattern is one of the possible patterns that might have been generated by a hypothesized process. In this notebook, we are going to regard point patterns as the outcome of point processes. There are three major types of point process, which will result in three types of point patterns:\n",
    "\n",
    "* [Random Patterns](#Random-Patterns)\n",
    "* [Clustered Patterns](#Clustered-Patterns)\n",
    "* [Regular Patterns](#Regular-Patterns)\n",
    "\n",
    "We will investigate how to generate these point patterns via simulation (Data Generating Processes (DGP) is the correponding point process), and inspect how these resulting point patterns differ from each other visually. In [Quadrat statistics notebook](Quadrat_statistics.ipynb) and [distance statistics notebook](distance_statistics.ipynb), we will adpot some statistics to infer whether it is a [Complete Spaital Randomness](https://en.wikipedia.org/wiki/Complete_spatial_randomness) (CSR) process.\n",
    "\n",
    "A python file named \"process.py\" contains several point process classes with which we can generate point patterns of different types."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pointpats import PoissonPointProcess, PoissonClusterPointProcess, Window, poly_from_bbox, PointPattern\n",
    "import libpysal as ps\n",
    "from libpysal.cg import shapely_ext\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "#import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Patterns\n",
    "\n",
    "Random point patterns are the outcome of CSR. CSR has two major characteristics:\n",
    "1. Uniform: each location has equal probability of getting a point (where an event happens)\n",
    "2. Independent: location of event points are independent\n",
    "\n",
    "It usually serves as the null hypothesis in testing whether a point pattern is the outcome of a random process.\n",
    "\n",
    "There are two types of CSR:\n",
    "* $N$-conditioned CSR: $N$  is fixed\n",
    "    * Given the total number of events $N$ occurring within an area $A$, the locations of the $N$ events represent an independent random sample of $N$ locations where each location is equally likely to be chosen as an event.\n",
    "* $\\lambda$-conditioned CSR: $N$ is randomly generated from a Poisson process.\n",
    "    * The number of events occurring within a finite region $A$ is a random variable $\\dot{N}$ following a Poisson distribution with mean $\\lambda|A|$, with $|A|$ denoting area of $A$ and $\\lambda$ denoting the intensity of the point pattern.\n",
    "    * Given the total number of events $\\dot{N}$ occurring within an area $A$, the locations of the $\\dot{N}$ events represent an independent random sample of $\\dot{N}$ locations where each location is equally likely to be chosen as an event."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating CSR\n",
    "We are going to generate several point patterns (200 events) from CSR within Virginia state boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# open the virginia polygon shapefile\n",
    "va = ps.io.open(ps.examples.get_path(\"virginia.shp\"))\n",
    "polys = [shp for shp in va]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the exterior polygons for VA from the union of the county shapes\n",
    "state = shapely_ext.cascaded_union(polys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create window from virginia state boundary\n",
    "window = Window(state.parts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Generate a point series from N-conditioned CSR "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonPointProcess at 0x1b122d7b70>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulate a csr process in the same window (200 points, 1 realization)\n",
    "# by specifying \"asPP\" false, we can generate a point series\n",
    "# by specifying \"conditioning\" false, we can simulate a N-conditioned CSR\n",
    "np.random.seed(5)\n",
    "samples = PoissonPointProcess(window, 200, 1, conditioning=False, asPP=False)\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples.realizations[0] # simulated event points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x1b1231dcc0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# build a point pattern from the simulated point series\n",
    "pp_csr = PointPattern(samples.realizations[0])\n",
    "pp_csr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_csr.plot(window=True, hull=True, title='Random Point Pattern')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr.n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Generate a point series from $\\lambda$-conditioned CSR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonPointProcess at 0x1b1aaf25c0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulate a csr process in the same window (200 points, 1 realization)\n",
    "# by specifying \"asPP\" false, we can generate a point series\n",
    "# by specifying \"conditioning\" True, we can simulate a lamda-conditioned CSR\n",
    "np.random.seed(5)\n",
    "samples = PoissonPointProcess(window, 200, 1, conditioning=True, asPP=False)\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-79.55664806,  38.25720619],\n",
       "       [-78.5166233 ,  38.30532302],\n",
       "       [-77.21660795,  37.57582983],\n",
       "       [-77.44823305,  36.74925133],\n",
       "       [-79.95384378,  37.55525777],\n",
       "       [-81.36397951,  36.71747455],\n",
       "       [-80.18215183,  37.35242254],\n",
       "       [-78.37289635,  38.26514268],\n",
       "       [-78.78567678,  38.80097021],\n",
       "       [-78.61625258,  38.36290302],\n",
       "       [-81.43369537,  37.00701809],\n",
       "       [-81.95031135,  37.07057506],\n",
       "       [-77.77370645,  36.89065808],\n",
       "       [-78.80401745,  38.72566936],\n",
       "       [-79.32844778,  36.95802405],\n",
       "       [-78.2800756 ,  38.90863979],\n",
       "       [-81.49037579,  36.99262809],\n",
       "       [-76.90806444,  37.72828737],\n",
       "       [-77.17489798,  37.64869473],\n",
       "       [-79.58599474,  37.9904752 ],\n",
       "       [-78.34778262,  37.22853963],\n",
       "       [-76.78862975,  37.8189276 ],\n",
       "       [-78.90167513,  36.90895769],\n",
       "       [-78.31750801,  37.13340462],\n",
       "       [-75.86084614,  37.62727824],\n",
       "       [-75.97937462,  37.17903022],\n",
       "       [-79.0679983 ,  38.62297192],\n",
       "       [-76.96164707,  37.31439593],\n",
       "       [-76.97054563,  37.09732441],\n",
       "       [-78.28781253,  39.27775751],\n",
       "       [-79.51445209,  37.2942029 ],\n",
       "       [-78.75479687,  37.39418456],\n",
       "       [-75.75445326,  37.78241231],\n",
       "       [-79.37160467,  37.43228348],\n",
       "       [-79.64158321,  38.491645  ],\n",
       "       [-79.33464281,  37.14352317],\n",
       "       [-79.90916235,  37.50562343],\n",
       "       [-76.92510237,  36.77946552],\n",
       "       [-76.91730122,  36.62173807],\n",
       "       [-82.06902468,  36.76063464],\n",
       "       [-79.8601599 ,  36.68065846],\n",
       "       [-77.74757811,  39.05919615],\n",
       "       [-79.23362271,  36.56074643],\n",
       "       [-78.10257435,  37.80365574],\n",
       "       [-77.18266793,  37.63777248],\n",
       "       [-77.27402385,  37.57885055],\n",
       "       [-77.68764731,  37.21503901],\n",
       "       [-77.75929316,  36.61739054],\n",
       "       [-77.20460382,  38.67318986],\n",
       "       [-80.52384818,  36.65326387],\n",
       "       [-80.60914236,  36.74210979],\n",
       "       [-76.84214327,  38.07338722],\n",
       "       [-79.88271974,  37.404438  ],\n",
       "       [-76.81805705,  37.34273888],\n",
       "       [-82.02798408,  36.94054096],\n",
       "       [-76.84238532,  37.82794034],\n",
       "       [-78.70526218,  38.83337292],\n",
       "       [-76.71235091,  37.95435389],\n",
       "       [-78.11460871,  36.82540288],\n",
       "       [-78.77656343,  37.18366661],\n",
       "       [-78.1748728 ,  38.89314571],\n",
       "       [-81.63574287,  37.11455891],\n",
       "       [-79.08592614,  38.45792181],\n",
       "       [-78.33817368,  37.64663718],\n",
       "       [-79.22973299,  37.19362583],\n",
       "       [-79.48678905,  37.29187339],\n",
       "       [-78.58205854,  37.40208832],\n",
       "       [-77.36276352,  38.76896337],\n",
       "       [-77.30130598,  37.47745852],\n",
       "       [-79.64493717,  36.72052872],\n",
       "       [-79.10398846,  38.05681891],\n",
       "       [-81.12955413,  37.04549049],\n",
       "       [-77.94793345,  37.59843086],\n",
       "       [-78.60434598,  38.89933921],\n",
       "       [-79.048031  ,  37.77049293],\n",
       "       [-78.25853547,  39.16083334],\n",
       "       [-78.72462602,  37.17396404],\n",
       "       [-77.29314545,  37.9220836 ],\n",
       "       [-77.28147432,  38.79060528],\n",
       "       [-76.66696623,  36.58417386],\n",
       "       [-80.46513532,  36.64153932],\n",
       "       [-78.65541452,  38.74225794],\n",
       "       [-76.805115  ,  36.78532921],\n",
       "       [-79.93532984,  37.08143783],\n",
       "       [-78.29407639,  39.34140688],\n",
       "       [-78.14216323,  38.3665535 ],\n",
       "       [-78.00505977,  36.7069097 ],\n",
       "       [-81.18975884,  36.62150498],\n",
       "       [-80.79290321,  37.05030562],\n",
       "       [-79.5153296 ,  37.75664579],\n",
       "       [-77.87487209,  37.40994143],\n",
       "       [-76.78504902,  38.11807362],\n",
       "       [-80.09560083,  37.35129105],\n",
       "       [-75.85714598,  37.57460507],\n",
       "       [-77.86127482,  38.34868698],\n",
       "       [-82.27493376,  36.99263064],\n",
       "       [-80.83633012,  37.16191786],\n",
       "       [-77.93737278,  36.57794908],\n",
       "       [-78.55997549,  37.60246875],\n",
       "       [-80.74982401,  36.93038256],\n",
       "       [-81.89152421,  37.32986349],\n",
       "       [-76.60039544,  37.49087981],\n",
       "       [-79.89144123,  38.026734  ],\n",
       "       [-77.53568375,  37.64300141],\n",
       "       [-79.36034573,  36.77163754],\n",
       "       [-77.32624847,  36.9372054 ],\n",
       "       [-82.34166665,  36.69837703],\n",
       "       [-77.14780326,  37.60598513],\n",
       "       [-80.24638938,  37.27287164],\n",
       "       [-77.41027396,  37.9199658 ],\n",
       "       [-78.73229552,  37.32763411],\n",
       "       [-79.50446982,  37.98941026],\n",
       "       [-77.34484259,  37.24072148],\n",
       "       [-80.34358018,  36.97299833],\n",
       "       [-78.28959166,  38.70289952],\n",
       "       [-79.23938464,  37.60233533],\n",
       "       [-77.10310375,  38.04796476],\n",
       "       [-78.11943302,  37.5521639 ],\n",
       "       [-82.63246378,  37.05615369],\n",
       "       [-76.6777552 ,  36.99804193],\n",
       "       [-79.31751436,  37.29870784],\n",
       "       [-77.02234401,  37.83495451],\n",
       "       [-77.54221373,  37.3812618 ],\n",
       "       [-75.71630753,  37.92836454],\n",
       "       [-80.21661887,  36.75870423],\n",
       "       [-78.75115924,  38.06910198],\n",
       "       [-76.86872936,  37.50425399],\n",
       "       [-79.21340288,  37.25364651],\n",
       "       [-77.77941742,  39.02429976],\n",
       "       [-77.3124049 ,  38.7084587 ],\n",
       "       [-77.9591418 ,  38.05055288],\n",
       "       [-77.9213301 ,  38.71767437],\n",
       "       [-77.66093307,  36.59501015],\n",
       "       [-77.21170491,  37.13898883],\n",
       "       [-81.91956901,  36.81108808],\n",
       "       [-76.68169985,  36.66281858],\n",
       "       [-77.30664489,  36.92944526],\n",
       "       [-81.85918569,  36.80543902],\n",
       "       [-76.86645645,  37.57131542],\n",
       "       [-80.68521276,  37.18782022],\n",
       "       [-81.41932788,  36.70007358],\n",
       "       [-78.8063798 ,  38.30071805],\n",
       "       [-77.14952496,  37.89347582],\n",
       "       [-79.07890941,  37.5601488 ],\n",
       "       [-83.00313472,  36.75272866],\n",
       "       [-78.68101007,  38.87234553],\n",
       "       [-77.63204774,  37.61550741],\n",
       "       [-78.88306754,  38.05667036],\n",
       "       [-77.45255789,  37.3391586 ],\n",
       "       [-78.47299022,  37.4129918 ],\n",
       "       [-79.02176971,  37.37256883],\n",
       "       [-78.28147935,  37.91147075],\n",
       "       [-79.58518375,  37.78361184],\n",
       "       [-77.77610921,  37.97641435],\n",
       "       [-80.99224637,  36.61994736],\n",
       "       [-80.58914692,  36.8579181 ],\n",
       "       [-77.80923356,  37.58006348],\n",
       "       [-78.86249696,  36.73878708],\n",
       "       [-82.21675753,  36.74153288],\n",
       "       [-83.24670184,  36.69004968],\n",
       "       [-81.28732939,  36.87113389],\n",
       "       [-75.84594392,  37.54487864],\n",
       "       [-79.22235094,  36.87297199],\n",
       "       [-78.48547431,  38.52479965],\n",
       "       [-78.20476584,  38.54799414],\n",
       "       [-77.89852106,  38.1201838 ],\n",
       "       [-81.37405706,  37.04456699],\n",
       "       [-78.02587914,  37.64685616],\n",
       "       [-78.42418842,  36.88536942],\n",
       "       [-76.68842544,  36.74893391],\n",
       "       [-80.81565379,  36.84864385],\n",
       "       [-77.83641513,  37.17473795],\n",
       "       [-77.50393746,  38.0087299 ],\n",
       "       [-82.66226354,  37.12507361],\n",
       "       [-81.50584616,  36.91097209],\n",
       "       [-78.50980015,  38.35200834],\n",
       "       [-77.99991705,  39.2235099 ],\n",
       "       [-77.75281574,  38.65985656],\n",
       "       [-79.18848841,  37.81637356],\n",
       "       [-75.99527387,  36.67900083],\n",
       "       [-78.10679754,  38.48234391],\n",
       "       [-77.72774175,  37.44640927],\n",
       "       [-79.16298721,  38.41845743],\n",
       "       [-80.79353455,  36.6361113 ],\n",
       "       [-79.09248227,  38.09955844],\n",
       "       [-79.43627162,  37.75365148],\n",
       "       [-82.44550608,  36.66466322],\n",
       "       [-78.88007206,  38.4383976 ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples.realizations[0] # simulated points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x1b1ab022e8>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# build a point pattern from the simulated point series\n",
    "pp_csr = PointPattern(samples.realizations[0])\n",
    "pp_csr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RUJC6aGlkOmVP3xCffcvylF3fK4QPDotcevHlthNUVVaPeQ0jMUz0DSMJ+vv7aWxsZO7cuaxevTrl8+CH8urdSKfMFNFaMyP3XFjALH83nZ2dKUl5Nd7ERN8wEuT69es0NTWxbNkyli5dmpYyYqVTujl/TqqJ1poJv+dVs0pGRu6a8KcOE33DSIDLly/T2trK+vXrqaioSFs50cQ9mekXvEy01kxkCmn4lA0m/KnBRN8w4uTs2bN0dHRQXV3NzJnpC7fEEvdo0yZkSvTT0cKIbM0APP7r47eUMWnSpFsmaVu8eHFKys5nTPQNIw5OnDjB66+/Tl1dHVOmTElrWbHEfbxx/mSFO50tjJBnP1oZkQO4TPjHh4m+YYyCqnLw4EEuXbpEfX09EyZMSHuZscR9PNMmjEe4M9HCGKuMiRMnmvCnCBN9w4hBIBBgz549DA4OUl9fT3FxcUbKHU3ck502YTzCnYlMomhlRLZMTPhTg4m+YUTB5/Oxe/duSkpKqKmpSWkOfjykek6c8Qj3WC2MVMT7o8X3o7VMTPjHj4m+YUQwMDBAU1MTM2fOZO3atSnPwXeD8c6oGasSSmW8P7yMx399PGbLxIR/fJjoG0YYN27coKmpicWLF7N8eepHwLqZZ5+OGTXTFe8fq2USLvyqypIlS8ZdZr5gom8YDt3d3bS0tLBmzRoWLEj9pGa5lmcP6Yv3x9MyCQl/KI/fhD8+TPQNA3jjjTdob29ny5YtzJ49Oy1luJlnny7SuRBLPC2TiRMn3jKAy4R/bEz0jbzn1KlTHDt2jJqaGqZNm5a2cnJ1Ph23F2Ix4U8ME30jrzl8+DDnzp2jvr6eiRMnprUst5cnzGUiO3dN+GNjom/kJYFAgH379nHz5k0aGhooKSnJSLlue8W5zIQJE27p3E3XZHjZji2XaOQdw8PDNDc34/P5qK2tzZjge4nWzh4e//VxWjt73DYlpYSE//XXX+fkyZNum+NJzNM38orBwUGampqYNm0aGzZsyIkc/BDxpoPmYhZROOEeP2AefwRjevoiUiYizSKyT0QOiMiXne1vFZE2EdkrIjtE5LakZhFZLCL9zjF7ReSf0nEThhEPN2/eZMeOHcybN4+NGzfmnOB//MlG/u5nR/j4k42jevDRsohyDfP4YxNPeGcQuFdVNwKbgPtFpAb4R+DjqroJeAb4YozzT6jqJufvMymx2jASpKenh507d3LnnXeyYsUKt81JOYkIeSiLqFDIqSyiSEz4ozNmeEdVFeh13hY7f+r8TXW2TwPOpcNAwxgvFy5cYO/evWzatIm5c+eOemy2rkyVSDpotCyibL3vsbBQz+3EFdMXkUKgFVgOPK6qTSLyMPCiiPQD14GaGKcvEZE9zjFfVNXfRbn+I8AjAIsWLUr8LgwjBqdPn+bw4cNs27aN8vLRxSybY92JpoOGZxFl833HQ0j4QwuxLFu2zG2TXCWu7B1V9TthnAXANhFZB/wJ8C5VXQB8C/halFPfABap6mbgT4FnRGRq5EGq+oSqVqtqdbpGQxr5x9GjRzl27Bj19fVjCj6kP9ad7oyZqspyPvuW5QkLdr7E+Gtra+ns7OTEiRNum+MqCWXvqOpVEXkVeCewUVWbnF3fA16OcvwgwT4BVLVVRE4AK4CW8RhtGKOhqrS3t3Pt2jUaGhooLS2N67x0jpiNx5t2K8SSqyOFIwkJf2jkbr56/GOKvojMBnyO4E8A7gP+GpgmIitU9SjwNuBQjHO7VdUvIkuBOwHrUTHSht/vp7W1lUAgQF1dHUVF8fs16RwxO9a8O26GWPJppHBkjD8fhT+eX8R84Gknrl8AfF9VXxCRTwPPikgA6AH+A4CIvBeoVtVHgbuBx0RkGPADn1HV7nTciGEMDQ3R3NzMpEmT2LhxY1ILn6R6xGzIey+fWDKqN+32ZGz5NFK4rKzslpG76ZhC28vEk73TDmyOsv054Lko238K/NR5/Szw7PjNNIzR6evro7GxkYqKClatWuW2OcDt3vuj71lLT99QVG86X0IsXiFc+IG8En4bkWtkPdeuXaO5uZnly5d7aqKtSO+9p2+Iz74lurjkU4jFK+Sr8JvoG1nNpUuXaGtrY8OGDcyfP99tc24hUe89n0IsXiEfhd9E38haurq6OHjwIFu3bmXGjBlum3Mb6fTeU5npk6sDs+Il34TfRN/ISo4fP86pU6eora1lypQpbpsTk3R479EyfYCkhDvRrKFcrSAiO3fvvPNOt01KGyb6Rlahqhw4cIDLly/T0NBAWVmZ2yZlnMi+gmfbuvhRW1dS6Z6JZA3l+sjdSI8/V4Xf5tM3soZAIEBrayvXr1+nvr4+LwUfbp8wTSDpEbWJTL6WDyN3Q8J/5swZjh075rY5acE8fSMr8Pl8NDc3U1ZWRk1NTVI5+NnEaGGUyL4CgB+0duEbDlBYmFi6ZyL9DvmSVhoS/tDI3Vzz+E30Dc/T399PU1MTs2fPZs2aNTk1D3404gmjRE6YhmpwR+h/AsTb75BPaaVlZWW3TNmQS8Kf2+6SkfXcuHGDnTt3snDhQtauXZvzgg+Jh1EaT15hOKAo4A9oWsMuyU7qlo2EhL+rqyunQj0m+oZnuXLlCrt27WL16tWuzZHixlqyiS5yMtrxuboWbqYIF/6jR4+6bU5KsPCO4UnOnTvH/v37qaqqYtasWa7Y4Fa2SjJz40c7PtezbTJFZKgn21deM9E3PMfrr7/O8ePHqa2tZerU25ZfyBhuToKWaH5/tOPdnsQtl4hM58xm4bfwjuEZVJWDBw9y6tQp6uvrXRV8yP61ZLPdfq9RWlpKXV0dZ8+ezepQj3n6hicIBALs3buX/v5+6uvrKSkpcdukrM9WyXb7vUhI+LPZ4zfRN1xneHiY3bt3U1RURE1NDYWFhW6bNEK2T4KW7fZ7kXDhV1VWrlzptkkJYeEdw1UGBgbYuXMnkyZNorq62lOCbxixCAn/uXPnOHLkiNvmJISJvuEavb297Ny5k4qKCjZs2JAXOfhG7hAS/jfeeCOrhN9E33CFnp4eXnvtNVasWJFTox2N/KK0tJTa2tqsEn4TfSPjnD9/nubmZjZt2sTChQvdNscwxkW2Cb+JvpFROjs7aW9vZ/v27cyZM8dtc4wEyMbRvZmyOZuE37J3jIxx5MgRzp49S319PZMmTXLbHCMBsnF0b6ZtDgn/rl27UFVWrVqVtrLGg3n6RtoJBALs27ePixcv5rXgZ6OnHCIb59J3w+aQ8J8/f57Dhw+nvbxkME/fSCt+v5+WlhYAamtrKSrKz69cNnrK4WTbXPqtnT2cvdpPUWEBfn9mbY4cwOU1jz8/f4FGRhgcHKS5uZkpU6awYcOGnF/4ZDSSnQfHK2vSZtPo3vAKtqhAeGjbIj6wZUFGbS4pKfGs8JvoG2nh5s2bNDU1UVFR4akvvFuUTyyhQATQmF5npMB7oXUQaZObYh9vBRhewfoDSsX0Ca7YHRL+0OycXvkdmOgbKefq1avs3r2bFStWUFlZ6bY5rtPa2cNjLxzAH1AKC4RH37P2NhGKJvBuz5LphUonGVu8FIoqKSm5ZVpmLwj/mO1tESkTkWYR2SciB0Tky872t4pIm4jsFZEdIrI8xvlfEJHjInJERN6R6hswvMXFixdpampi/fr1nhJ8NztRQ+KtBGcS7ekbinlMuMC7PUumlzpvE7ElFIr607ev9ETfSUj4L1y44InO3Xg8/UHgXlXtFZFiYIeIvAT8I/Cgqh4Skf8EfBH4VPiJIrIGeAhYC1QAvxCRFarqT+VNGN7gzJkzHDp0iK1btzJjxgy3zRnBbY81Hs8z2jFux9FT7TGPp38iUVvcDkVFEu7xqyqrV692zZYxRV9VFeh13hY7f+r8hSY8nwaci3L6g8B3VXUQeF1EjgPbgF3jtNvwGMeOHaOzs5O6ujomT57stjm3kIpO1NB1khGseMQ71jFuilcqK53xVrxuV4CpIDLU45bwxxXTF5FCoBVYDjyuqk0i8jDwooj0A9eBmiin3gE0hr3vcrYZOYKq0tHRQXd3Nw0NDZSVlblt0m0k47FGZoAgwrA/+ZZCPOLtNe8UxrYpmc7VZPsnvPh8EsULwh+X6DvhmE0iMh14TkTWAX8CvMupAD4PfA14OOLUaNMmauQGEXkEeARg0aJFCZhvuInf76etrY3h4WHq6uooLi5226SoJOMl3iJS/mDDVrFlB8PJ1s5Vt3Fb+BPK3lHVqyLyKvBOYKOqNjm7vge8HOWULiB8Rq0FRAkDqeoTwBMA1dXVt1UKhvfw+Xw0NzczYcIEqqqqPJ+Dn6iXGC5ShY6nn+lBPl4nEe/dC+EZr4x5gNtj/GvWrMlY2WOKvojMBnyO4E8A7gP+GpjmdMoeBd4GHIpy+k+BZ0TkawQ7cu8EmlNmveEK/f39NDY2MnfuXFavXp2T8+BHihQkH9PPVbKpc9XtzvxohAv/wYMHMyb88Xj684Gnnbh+AfB9VX1BRD4NPCsiAaAH+A8AIvJeoFpVH1XVAyLyfeAgMAx81jJ3spvr16/T1NTEsmXLWLp0qdvmpJVIkXJbJLzGeL33aIPR0lWxuj3mIRYh4W9sbOTZ37TxahdUdPak1bZ4snfagc1Rtj8HPBdl+08Jevih938F/NX4zDS8wOXLl2ltbWX9+vVUVFS4bY6RIOkQ1WS990jP+9H3rOWxFw6kzRP3cp9CSUkJZXes5gvfaMYXEH7+ZGNaWyI2IteIi7Nnz9LR0UFVVRWzZs1y2xwjQbwW3oj0vF/qeCOmJ56KysoLfQqjsfv0NYYVFEl7S8RE3xiTkydPcuLECWpra5k6derYJxiew2vhjUjP+53r5rP7VPdtnngqKysvp3zWLJ1JSWEBg8N+iosK09oSMdE3YqKqHDx4kEuXLtHQ0MCECRPcNslIEq+FN6J53ivnTbnNE/daZZUuqirLefxDK/nG87/lv/zBg+7G9I38JBAIsGfPHgYGBqivr/dsDr4RH14Mb0TrKI+0y2uVVTq5s7yI2mk30v7ZmOgbt+Hz+WhpaaG4uJja2lrP5+Ab8eHl8EYsYlVWXsq5TxV9fX0Zca5M9I1bGBgYoKmpiRkzZrBu3bqczME3sovIyiqeOH+oUiifWEJP31BWVA59fX2UlpamvRwTfWOE3t5eGhsbWbx4McuXR50p20iAXPRGvcBYcf7wSiGgwblgSovdz1gaCxN9I6N0d3fT0tLCmjVrWLBggdvmZD1eS5GMh2yppMaK84dXCkDWzJlkom9kjPPnz7Nv3z62bNnC7Nmz3TbHM4xHBLMt6ySbKqmxOqVDlULo+RfgziI08dLa2cOuE5fQKz4qJ1lM30gzp06d4tixY9TU1DBt2jS3zfEM4xXBWN6oV73pbKukRuuUDq8UvB7TD/+eFQr88dr096GZ6Ocxhw8f5ty5c9TX1zNx4kS3zfEU4SI4NBzg6784yufuWxH3HDHRvFEve9O5lhqZLZlKt4SiFI5dT3+ZJvp5SCAQYN++ffT29tLQ0EBJSYnbJnmOyBDBjmOX2X2qO6E5YiKFx8vetBfz+POB8O9ZUYFwZwYGvJvo5xnDw8O0tLRQUFBAXV0dhYWFbpvkSUIi+PVfHGXHscsjnYGjzREzFl73prPFO46FV0NnoxH6nv208RBb7phMQU9n2ss00c8jBgcHaWpqYtq0aWzYsMFy8MegqrKcz9234pY5YWLNERPv9cybTg9eDp2NRVVlOVwuZd68mbSZ6Bup4ubNmzQ2NrJgwQJWrlzptjlZQ7xzxCRyvWwRo2zCy6GzeOjr68tYv5qJfh5w9epVmpubWbVqla1BnATxzBFjuIvXQ2djYaJvpIwLFy6wd+9eNm3axNy5c902xzDSQjaHzoaHh/H7/RkZmAUm+jnN6dOnOXz4MNu2baO8PHt+BIaRDNnaAuvv78/otOU2fWKOcvToUY4dO0ZdXZ0Jfp7T2tnD478+TmtnT1rPSce1nmk6zR98o4lnmk6P2w6vksnQDpinn3OoKvv37+fq1as0NDRkrMloeJNkslpSmQkznms903Sa//7cfgB+d+wyAB/bnv19UpGppSb6RtL4/X7a2trw+/3U1dVRVGQfb76TTFZLKjJhQsJ29mp/0tdVwXxBAAAc60lEQVR6qeON295nu+hHqwTLTPSNZBgaGqK5uZlJkyZRVVVlC5+4SCYHCY1VVjJZLZHnlE8s4fFfH4/7fsKFraiwgKICwR/QhLNq3rlu/oiHD7B2fvavzxytQt02uS+jIVgT/Rygr6+PpqYm5s2bx6pVq2zQlYtkcpBQPGUlk9USOWFZtGknRqtswoXN7w/w0LZFVEyfkHAl+LHtizh95SZP/O4kqvDUrlO8be28rOysDRGtEu49ddY8fSN+rl27RnNzM8uXL2fJkiVum5P3ZHKQULxlJZPVEjrn8V8fv60MYNTKJlLYPrBlQdzlR654dWNwGEhsTnwvT8dQVVnOo+9Zy0sdb/DOdfOpqizn5UP9JvpGfFy6dIm2tjY2bNjA/Pnz3TbHk2RaAEYLp6TallQOSIplW7Qyxqpsks2Zj7biVXGhUFRYgN8f3z16fTqG1s6ekZbT7lPdLJ81AVXN6KSHJvpZytmzZzlw4ADV1dXMnJldow8zhRsCMNpC3qm2JVUDkkazLVYZY1U2ybQuoq145Q8oH9m2kDviDA95fTqGcPsGfQF+0HKad8/NXI4+mOhnJcePH+fUqVPU1tYyZcoUt83xLG4JQDTBS5ctqRiQFI/nngpPfixirXj1wQTCQ16fjqFm6UyKCoQhv6LAj9svsLEhs4sXjSn6IlIG/BYodY7/oap+SUR+B4QUZw7QrKrvi3K+H9jvvD2tqu9NieV5iKpy4MABLl++TENDA2VlZW6b5Gm8JABesiWSZGxLx+jXVKx45fXpGKoqy/lQ9UKeaTo90pI5ei2zNsTj6Q8C96pqr4gUAztE5CVVvSt0gIg8C/wkxvn9qropBbbmNYFAgLa2NoaGhqivr6e4OP1raWY7kSIS6oR0Qwi8LEZesm28lYmXO3FDfGDLAp5t68I3HKCwQNha6TFPX1UV6HXeFjt/GtovIlOAe4E/TIeBBvh8Pnbv3k1paSk1NTWWg58AoR++Fzr3vDw3jJdti5dE+03cqiDCK9lpAxfYumRWxsqGOOfeEZFCEdkLXAR+rqpNYbvfD/xSVWOt7lgmIi0i0igit4V/nOs/4hzTcunSpYRuINcZGBhg586dTJ06lS1btpjgJ0G0mLXhPcY7308in3Oogvi7nx3h4082pmSOoUSoqizns29ZzoIJvoyvTx1XR66q+oFNIjIdeE5E1qlqh7P7o8CTo5y+SFXPichS4Fcisl9VT0Rc/wngCYDq6mqNdpF85MaNGzQ1NbFkyRKWLVvmtjlZi5fj6UaQVGQ3JfI5eyXLJ9MzbEKC2TuqelVEXgXuBzpEZCawjaC3H+ucc87/k865m4ETsY43gly5coXW1lbWrl3LHXfc4bY5WY2XYta5ynhDJakQ4UQ+Zy84AkNDQ4hIxvvn4snemQ34HMGfANwH/LWz+0PAC6o6EOPccqBPVQdFZBZQD/xNakzPXd544w3a29vZsmULs2fPdtucnCAdMets6DTMBJn20kcj3s/ZC45AX19fxr18iM/Tnw88LSKFBPsAvq+qLzj7HgK+Gn6wiFQDn1HVh4HVwD+LSMA596uqejBl1ucgr7/+OsePH6e2tpapU7N/gqlcxasjP92oiDLtpacKtzuvMz2lcoh4snfaCYZkou27J8q2FuBh5/VrwPrxmZgfqCqHDx/m/Pnz1NfXu/JlyHVSKYheiAlH3k8mKqJozzDTXnqu0N+f2Tl3QtiIXA8QCATYt28fN2/epL6+PqPzcOQLqRbETMWEY1VU0e4n3RVRrGfohVBJNtLX18fkyZMzXq6JvssMDw/T0tJCYWEhtbW1FBYWum1STpJqQRyP0MXb4hitoop2P+muiEZ7hqN56db3EZ2+vj7mzJmT8XJN9F1kcHCQpqYmpk+fzvr1620e/DSSDkFMJhyRSItjNJGNdj/p9riTeYZe7fvwAp6N6Rvpobe3l6amJhYuXMiKFSvcNicrCfcggVHFzishiERaHKOJbKz7SWdcPJln6Gbfh9dbGG7k6IOJviv09PSwe/duVq1axaJFY6/56fUvrxvcsiRfgYAIw/7RvUkvdBQm4i2HRPbZti6itQHduJ9Ey4x2v5n4Pnu9hTE4OEhhYaEr61ib6GeY8+fPs2/fPjZv3hxXPM/rX163uMWD9CugCa2u5BbJeMs/autiaDjAs21dWff5R94vpH4epGiViBeyq0bDrdAOmOhnlM7OTo4cOcL27duZPn16XOd4/cvrFuEeZKHj6ce7ulKqSdRzTcRbzoXPP/x+oy2/ON5ZNaNVIl4YcTsaJvp5wJEjR+jq6qK+vp5JkybFfZ7Xv7xuEc2DTGfIoLWzZyTMEr7ma7pbYrn2+af6fmJVil7pw4mFW6NxwUQ/7agq7e3tXLt2jYaGBkpLSxM63+tf3kwT6VWHP490xoc/+sQuhvzBuQB/0NrFdz4dFPd0e+K59vmn+n7G6uz26vPq6+tj2rTMzqMfwkQ/jfj9flpbWwkEAtTV1SXdaePlL28mcat/o/HkFaffIEi4uGfCE8+1zz+V95OtlWJ/fz/z5893pWwT/TQxNDREU1MTU6ZMYcOGDTYPfgpwK75ds3QmxYUy4umHi3ss0bGMq8yRjZWixfRzjL6+PhobG6moqGDVqlVum5MzuBXfrqos5zuP1EaN6Yf2jzVFgpui5PUKyOv2pRpVdS1HH0z0U861a9dobm7mzjvvZPHixW6bk1O42ZTP1oybTFZAyYi31yrITDA4OEhxcbFrU66Y6KeQS5cu0dbWxsaNG5k3b57b5uQk2dCU91LGTaYqoGTF20sVZKZwM7QDJvopo6uri4MHD7J161ZmzJjhtjmeI9+a8B/YsiBqKCjTZKoCSla8vVRBZgoT/Rzg2LFjdHZ2UldX58pUqV4nn5rwkff6gS0LxnWtxpNXKJ9YQk/fUFIVZjpCYqmcUz9bs2/iJdqzMtHPYlSVjo4Ouru7aWhooKyszG2TXCcbh8SnklTda6jyGPQFUKBASLrCTGVILB1z6mdDyC4ZYj2rvr4+V6MBJvpJ4vf72bNnDz6fj7q6uowvbuxFsnVI/HgJr+hSda+hyiM0OsArFWayc+rnI7GelZuZO2CinxQ+n4/m5mYmTJjA9u3bLQffIVuHxI+HaBVdKu41VHkM+QIECHr646lEUtWnkskKPNv7gWI9KwvvZAmhL+DmOyYzePYQc+bMYc2aNbbwSRjZOiR+PESr6D77luXjvtfwinI8MX1IbZ9KpirwXOgHivasVJWBgQHz9L1O+BewUOBrD1TylrVr3TYrKm56R7ns0ccinZ5vqirKdCwVme7PNlf6gSKf1cDAACUlJa5GB0z04yD8CwhwesCbHbZe8I5y1aOPRTZUdNnYpxKvzdkWAnI7tAMm+nFRs2QGRQLDBDMovPqjyRXvKNWkWxi8XtFlQ8UUSTw2e8HJSRQT/Sxh0sBFvtgwlRsT5lGzdFbGvliJilU2enTpJhuFIR14vWKKxlg2Z6OTY6KfBVy4cIEzZ87wkbfeTcf5PhpPXgHSN3d7iGTEKlMDcdJ5XqrJRmEw4iMbnZy+vj5mzZrlqg0m+qPQ19fHvn37qK6upuN8X0Y9xmTFKl6PLh5RTtZL9pJ3nY3CYMRHNoat3FwxK4SJfgwCgQCtra0sX76cGTNm8J19qV3bcyzSKVbxinKyFY+XvOtsFAYjfrItbNXf3+/98I6IlAG/BUqd43+oql8Skd8BU5zD5gDNqvq+KOd/Evii8/YvVfXplFieZg4cOEBZWRlLly4FMu8xpkusWjt7+PovjsYlysnes9e862wTBiM3CQQCDA4OZoWnPwjcq6q9IlIM7BCRl1T1rtABIvIs8JPIE0VkBvAloBpQoFVEfqqqPakxPz2cPXuWS5cucdddI7c4bhFOJsad6jlTftTWxQ9azuDz68h8LqOJcrL3bN614VXc7Gvq7++nrKzM9QGdY4q+qirQ67wtdv5GFgwVkSnAvcAfRjn9HcDPVbXbOfbnwP3Ad8Zndvro7e2lo6OD2tra2+bTSVaE3Y5xR07eBVAA1C+fxefuWzGqLcnes3nXhtdw+3fohXg+BH/7YyIihSKyF7hIUMSbwna/H/ilql6PcuodwJmw913OtsjrPyIiLSLScunSpfitTzF+v5+WlhZWr17N1KlTU3bdaDHuTBI5eZcAJcUFYwq+F2jt7OHxXx+ntdPTjUMjC3D7d+iFeD7E2ZGrqn5gk4hMB54TkXWq2uHs/ijwZIxTo7Vj9LYNqk8ATwBUV1fftj9TtLe3M23aNBYtWpTS67od4w4vv7CwgN+vWsAHXV7cIx7c9szixSvpqcbouP079EKOPiSYvaOqV0XkVYIhmg4RmQlsI+jtR6MLuCfs/QLg1YStzACnT5/m2rVrt8TxU0UiMe50CEi2xti9lAUUi2ypmLxOJipOt38HfX19zJkzJ6NlRiOe7J3ZgM8R/AnAfcBfO7s/BLygqgMxTn8F+F8iEnq6bwe+ME6bU861a9c4dOgQ9fX1aVusOJ4YdzoFxK0Y+3h+zG57ZvGQDRWT1wnvcyosEB57cB0f257a1nYIN/uassnTnw88LSKFBPsAvq+qLzj7HgK+Gn6wiFQDn1HVh1W1W0S+Aux2dj8W6tT1Cj6fj5aWFtavX+/6UofpEhC3wg/jrcTc9sziIVUVUz6HiBpPXhlJMhgOKI/+pIOV86bk3HPImpi+qrYDm2PsuyfKthbg4bD33wS+mbyJ6WXv3r3MnTuXiooKt01Ji2frZvghFZWY17OAUlExZXOIKBWVVc3SmRQWCMPONLYB1ZxrMfn9foaGhigtLXXblPwekXvixAkGBgaoqqpy2xQgPZ6tm+GHbAjPpILxVkzp+Iwy0XJIVWVVVVnOYw+u49GfdBBQ9fRMtskSWiLR7Rx9yGPR7+7u5sSJE9x1112eWu4w1Z6tm/OSZ0N4Jh24PTtqploOqaysPrZ9ESvnTcnZ74pX4vmQp6I/ODhIa2srmzZt8sRgiXTixrzkkaIXq8xc/IF7YXbUTLXuUl1ZeT2UNx7cXgw9nLwTfVWlra2NhQsXeiJ9KhNkcl7yeEQvm2PYY5Hu2VHjIVNhtXxtySWDefoucvToUQBWrlzpsiXeIZUiEY/o5XKaoxf6MZIR42RbXrnsnaeSvr4+5s2b57YZQJ6J/sWLFzl9+jR33323JzpU4iHbBq3EI3peEMZ04RXvNxExzuWWl1cwT98F+vv72bt3L1VVVZ5Im4qHyB/jo+9ZS0/fUFrEJFUeWzyi5xVhTBfZ5v3mcsvLK5joZ5jQgihLly5l5szs8SrDf4xDvsAtKW1e9sbiEb1sE8ZcJhdaXtFaxF5JFhgeHsbv93vG2cwL0T906BAlJSUsW7bMbVMSIvzHKCIEVM0b8xheEZbxkO0tr2jhKcAzISsvZe5AHoj+uXPnOH/+/C1xfC/+UKPZFP5jLJ9YwmMvHMhqbyxVeOXzy6VYeDa3vGJNmeyVkJWXQjuQ46J/8+ZN9u/fT01NzciCKG7/UGM1Q2PZFP5jzJXBK+MRbbc/v3CydSSt26T6HmOFp6Jtc+P5muhniNCCKKtWrWLatGkj293stIolWPHalM3eWIjxiraXOh2zdSStm6TjHmOFpyK3ufV8vbJiVoicFf39+/czZcoUKisrb9nuZqdVLMFyyyY3vJ7xina6n1UizyRbR9K6SbruMZpDFLnNrefb399Pebl3PsecFP3Tp0/T09MTdUGUTHZaRQpILMHKdEda+CLpw4HMZgONV7TT+aySnUIh20bSxks6nAI379Gtsi28k0ZaO3v495M+zvQf5BPvaqCoKPrtZSJMEktAYglWpkI30RZJz6TXkwrRHs+zGk3I3Pa0vZRFk65QiJv36FbZJvpp4k0xK+FXFwNs3Hid6sXFFBcXuzKLZiwBcTsuH22R9Ex7XG49g7GEzAuettvfjxDprADdvMdMl9184hIvnvIz+42bVFWWZKzc0cgZ0X9TzIRhv/Kj3+2n91RwYARAcXExRUVFCf0Pfx1PxRHuRXpBQKLhxUXSM9W3MJaQecnTdhuvfn/HSyb7sZqOX+QT32phyA8/e7LRMx3zOSP6oS/pkM9PSXEhH3vbtpEH7Pf78fl8DA8Px/zf19c36n5g1MrhaLeP//byOXwBpbhQ+IcPreKfH1pLW1cvtctmsnnhtNHMzxheE7Zw77uoQPhQ9UI+kKZKKB4h84qn7TZe+56kgnRn7wwODtLd3c3ly5e5cuUKzx3pw+dXFG91zOeM6Ie+pE+9uINPvevWD7OwsHDcC577/f5RK4X289fx+ZUA4BtWfrb3FO9eUsTG4mGunTjDS0fGrjjiaYGkYuH2TPVpxCMYt0w14VeeaTrNs21dafGKclHI0kmuVYCpDlkNDg5y5cqVkb+BgQHKy8uZNWsWCxcuZMriAK98o8lzraWcEX0IfknPLSAtX9RQxRFr/oz3FJbznfbGkQ/4w/dsvs2OQCBwS2URrQLp7+8ftVUCsSuOeP/HU3GMJdqj7U/Eowp536GO5XR7RbkmZG7jlcFk8dgx3pDVwMDALSI/ODjIjBkzmDlzJgsXLmTatGm3zN5bNf32sQJeIKdE303i8SILCgooLS0d18RLkRVHtP8DAwP09vbGrGBUdaQSiNbSONo9zBdeeTNU9fjvr2LLoukj+/ef6+UTT7XEFPVEPKrQc3u2rYsftnbh93vLKzJiE2vOm0yLXLxORqItvXCRv3z5MkNDQ8ycOZOZM2dSWVnJ1KlTx5yi3YtOhol+CsnEB5yqiiNWpeHz+dh/6OItoapftHdS1nuO4eFhhoeHeeHEkOOZC0O+AM/8vJm+lRNHKpEZTnx+OKAUFQiLJwxx9uzZkf3hlU1RUdHIc/vglgWe84qM2ERW7s+2dfGjtq6Mj3hN1MkInRP+Ht4U+VBMPlzkFy9ezJQpU7JmHY7RMNHPQwoKCigpKaGkJHoKWWSo6kO/t+mWH0f5nT28/KSzv7CA9zesY928SSOVwrx5Pr42eTJtZ3tZN7uEhROHuXDhwsj+UCUT+gNGKoJ1RUUMnr1I84XbK4dY7xMJWxmJEyt0EhkuEdyZ5CyRsM0trYLCAr7+4FLmlwTF3ufzjYj8kiVLckbkIzHRN25jrGZwPM3khQvhPXGWF9nyCP8L3zY4OHjbMeHvA4HAbZVBIpVG+Pvx/Ni9EudOBWNNBvhvf7SNxpNX2LZ4BqjybGsXPn/QGdhcMYmbN28SCARQ1ZG/sd5Hbhtrf1kgwFfuncP+8/2sm1NK0dXT7Ok+FfXY5470MeQLECBYQf32yHk+Xb+IpUuXMnny5JwU+UhM9I2ojBWqSmUoa6yWR7yoaszWRPi2/v7+qMeE3vv9fgoKCuKqHCLfH7zQz6ef2c+QP+hJfvMTm9m0YGrKhW68++N9/++vD490sg/5Ajz90mucX8jIMSLCEhGuHClARPjPG4RjVwtYOaOA/q6DNJ0VRISCguD+8L/wbcnsLywsHHldVTmBrUtmxjw/9P5tZb08d/QIw07f0Qfv2sCSLK+YEyXnRL+4uJjnn3/ebTOMLCZUefT39+P3+0f9C4lj6HVzbzmDw7NRhMFhP//nOy9SNeEywIj4hL8O9yxHex/tf+Q1IrelYv+CkgKKCkoYDkBhASyZ5Gd4+M1jwysIgIUTgn8AfX1Dafl8xstnV8Ox63Dn1ADn2ndwrt1ti94kNAV8OhlT9EWkDPgtUOoc/0NV/ZIEvyl/CXwI8AP/qKp/H+V8P7DfeXtaVd+bKuOjcf/996fz8oYxKqFwSDC+XMiffer9WR/iuSeHwlVGfJ7+IHCvqvaKSDGwQ0ReAlYDC4FVqhoQkTkxzu9X1U0pstcwPE0uDgDzYtqhkTxjir6qKtDrvC12/hT4j8DHVDXgHHcxXUYaRjZhIml4mbimnxSRQhHZC1wEfq6qTcAy4CMi0iIiL4nInTFOL3OOaRSR98W4/iPOMS2XLl1K6kYMwzCMsYlL9FXV74RoFgDbRGQdwRj/gKpWA/8X+GaM0xc5x3wM+LqILIty/SdUtVpVq2fPnp3UjRiGYRhjk9BE86p6FXgVuB/oAp51dj0HbIhxzjnn/0nn3M3JmWoYhmGMlzFFX0Rmi8h05/UE4D7gMPBj4F7nsN8DjkY5t1xESp3Xs4B64GBqTDcMwzASJZ7snfnA0yJSSLCS+L6qviAiO4Bvi8ifEOzofRhARKqBz6jqwwQzfP5ZRALOuV9VVRN9wzAMl5Bgco53qK6u1paWFrfNMAzDyCpEpNXpPx39OK+JvohcAjozUNQs4HIGykkWs2/8eN1Gr9sH3rfR6/ZB5mysVNUxM2E8J/qZQkRa4qkV3cLsGz9et9Hr9oH3bfS6feA9GxPK3jEMwzCyGxN9wzCMPCKfRf8Jtw0YA7Nv/HjdRq/bB9630ev2gcdszNuYvmEYRj6Sz56+YRhG3mGibxiGkUfkleiLyCZnts+9zqye25ztD4pIe9j2Bg/a+HHHxnYReU1ENnrMvlUisktEBkXkv7phWxw2ioj8vYgcd57jFpfs+55j214ROeXMYIuIlIjIt0Rkv4jsE5F7PGZfsYg87dh3SES+4IZ9Y9j48bDte0UkICIZX88jln3Ovg3Ob+WA8yzLMmpc5DqaufwH/Ax4p/P6XcCrzuvJvNm/sQE47EEb64By5/U7gSaP2TcH2Ar8FfBfPfo5vwt4CRCgxq1nGGHr3wGPOq8/C3wr7Hm2AgUesu9jwHed1xOBU8BiLz3DiO3rgZNeso/g1DftwEbn/UygMJP25JWnT3Dxl6nO62lAaAbQXnU+AWCSc5xbxLLxNVXtcbY3Epzm2g1i2XdRVXcDPpfsCieqjcCDwL9okEZguojMd8NACLY8gA8D33E2rQF+CSOLEl0FXBvUE8U+BSaJSBEwARgCrrtkHhDVxnA+GmN7xohi39uBdlXdB6CqV1TVn0mbcm5h9DH4HPCKiPwtwdBWXWiHiLwf+H8Jeljvdsc8YBQbw/gjgh6rG8Rjn9vEsvEO4EzYcV3Otjcya94IdwEXVPWY834f8KCIfJfgUqRVzv9mj9j3Q4IV5xsEPf0/UdVul2wLEWljOB8haK+bRNq3AlAReQWYTbDl9DeZNCjnRF9EfgHMi7LrfwBvJfhFfVZEPgx8g+BU0ajqc8BzInI38JXQdi/Z6Jz7FoKin7Z+h/HYlymStFGiHJ+WVt1o9qnqT5zXkZ7oNwnOTNtCcP6p14BhD9m3DfADFUA58DsR+YUG18rwio2hc7cDfarakQ7bxmFfEcHf7lagD/ilM1HaL9Nl5224He/KcGztGm/G7gW4HuO414FZXrORYH/DCWCFV58h8Be4H9OPaiPwz8BHw447Asx3ycYi4AKwYJRjXgPWeMU+4HHgD8LefxP4sIufc8xnCPxv4L+7Zdsoz/Ah4Kmw9/8T+Hwm7cq3mP45ggu+QHABmGMAIrLcib3hZHSUAFdcsTC2jYuAHxH80d22YE0GiWqfx4hl40+BTzhZPDXANVV1K7RzH8GEga7QBhGZKCKTnNdvA4bVvfUnbrMPOA3c6zy/SQQ7ww+7Yl2QaDYiIgXAh4DvumLVm0Sz7xVgg/NZFxH8nmb0M8658M4YfBr4P87DHgAecbZ/kKAY+IB+4CPqVMMesvFRgj39/+DUT8Pqzsx9Ue0TkXkEwxJTgYCIfI6gl+pGR1+sZ/giwQye4wSb1n/ogm0hHuL2sMQcgn0RAeAs8AcZt+pNotn3OPAtoINgC+pbqtqeacPCiGYjwN1Al6Yp7JQAt9mnqj0i8jVgN8HQ4ouq+u+ZNMqmYTAMw8gj8i28YxiGkdeY6BuGYeQRJvqGYRh5hIm+YRhGHmGibxiGkUeY6BuGYeQRJvqGYRh5xP8PqMaRmCuN33EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_csr.plot(window=True, hull=True, title='Random Point Pattern')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "188"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr.n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulated point pattern has $194$ events rather than the Possion mean $200$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Generate a point pattern from N-conditioned CSR "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonPointProcess at 0x1b1abceeb8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulate a csr process in the same window (200 points, 1 realization)\n",
    "# by specifying \"asPP\" True, we can generate a point pattern\n",
    "# by specifying \"conditioning\" false, we can simulate a N-conditioned CSR\n",
    "np.random.seed(5)\n",
    "samples = PoissonPointProcess(window, 200, 1, conditioning=False, asPP=True)\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x1b1abc6550>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr = samples.realizations[0] # simulated point pattern\n",
    "pp_csr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_csr.plot(window=True, hull=True, title='Random Point Pattern')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr.n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Generate a point pattern of size 200 from a $\\lambda$-conditioned CSR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonPointProcess at 0x1b1acb4dd8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulate a csr process in the same window (200 points, 1 realization)\n",
    "# by specifying \"asPP\" True, we can generate a point pattern\n",
    "# by specifying \"conditioning\" True, we can simulate a lamda-conditioned CSR\n",
    "np.random.seed(5)\n",
    "samples = PoissonPointProcess(window, 200, 1, conditioning=True, asPP=True)\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x1b11e26ac8>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr = samples.realizations[0] # simulated point pattern\n",
    "pp_csr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_csr.plot(window=True, hull=True, title='Random Point Pattern')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "188"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_csr.n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustered Patterns\n",
    "\n",
    "Clustered Patterns are more grouped than random patterns. Visually, we can observe more points at short distances. There are two sources of clustering:\n",
    "\n",
    "* Contagion: presence of events at one location affects probability of events at another location (correlated point process)\n",
    "* Heterogeneity: intensity $\\lambda$ varies with location (heterogeneous Poisson point process)\n",
    "\n",
    "We are going to focus on simulating correlated point process in this notebook. One example of correlated point process is Poisson cluster process. Two stages are involved in simulating a Poisson cluster process. First, parent events are simulted from a $\\lambda$-conditioned or $N$-conditioned CSR. Second, $n$ offspring events for each parent event are simulated within a circle of radius $r$ centered on the parent. Offspring events are independently and identically distributed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Simulate a Poisson cluster process of size 200 with 10 parents and 20 children within 0.5 units of each parent (parent events:  $N$-conditioned CSR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonClusterPointProcess at 0x1b1ad8af28>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(5)\n",
    "csamples = PoissonClusterPointProcess(window, 200, 10, 0.5, 1, asPP=True, conditioning=False)\n",
    "csamples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: {'n': 200}}"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples.parameters #number of total events for each realization "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 10}"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples.num_parents #number of parent events for each realization "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples.children # number of children events centered on each parent event"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x1b1ad5e080>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_pcp = csamples.realizations[0]\n",
    "pp_pcp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_pcp.plot(window=True, hull=True, title='Clustered Point Pattern') #plot the first realization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is obvious that there are several clusters in the above point pattern."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Simulate a Poisson cluster process of size 200 with 10 parents and 20 children within 0.5 units of each parent (parent events:  $\\lambda$-conditioned CSR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.process.PoissonClusterPointProcess at 0x1b1ae4c6a0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.random.seed(10)\n",
    "csamples = PoissonClusterPointProcess(window, 200, 10, 0.5, 1, asPP=True, conditioning=True)\n",
    "csamples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: {'n': 260}}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples.parameters #number of events for the realization might not be equal to 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 13}"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples.num_parents #number of parent events for the realization, not equal to 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csamples.children # number of children events centered on each parent event"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_pcp = csamples.realizations[0]\n",
    "pp_pcp.plot(window=True, hull=True, title='Clustered Point Pattern')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Simulate a Poisson cluster process of size 200 with 5 parents and 40 children within 0.5 units of each parent (parent events:  $N$-conditioned CSR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(10)\n",
    "csamples = PoissonClusterPointProcess(window, 200, 5, 0.5, 1, asPP=True)\n",
    "pp_pcp = csamples.realizations[0]\n",
    "pp_pcp.plot(window=True, hull=True, title='Clustered Point Pattern')"
   ]
  },
  {
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}