{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "375efb56-36f0-4af0-92f3-4e4663ad9b91",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Estimate Neural Topology"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ff5d6ed",
   "metadata": {},
   "source": [
    "## Set Up + Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a46009c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working directory:  /home/facosta/neurometry/neurometry\n",
      "Directory added to path:  /home/facosta/neurometry\n",
      "Directory added to path:  /home/facosta/neurometry/neurometry\n",
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n",
      "The jupyter_black extension is already loaded. To reload it, use:\n",
      "  %reload_ext jupyter_black\n"
     ]
    },
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'neurometry.curvature'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[2], line 17\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mplotly\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01msubplots\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m make_subplots\n\u001b[1;32m     16\u001b[0m \u001b[38;5;66;03m# import neurometry.curvature.datasets.experimental as experimental\u001b[39;00m\n\u001b[0;32m---> 17\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mneurometry\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcurvature\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mdatasets\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mgridcells\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mgridcells\u001b[39;00m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mneurometry\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mtopology\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpersistent_homology\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mpersistent_homology\u001b[39;00m\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mneurometry\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcurvature\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mviz\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mviz\u001b[39;00m\n",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'neurometry.curvature'"
     ]
    }
   ],
   "source": [
    "import setup\n",
    "\n",
    "setup.main()\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%load_ext jupyter_black\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import plotly.graph_objects as go\n",
    "from gtda.diagrams import PairwiseDistance\n",
    "from gtda.homology import WeakAlphaPersistence\n",
    "from gtda.plotting import plot_diagram, plot_heatmap\n",
    "from plotly.subplots import make_subplots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8b9adea6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working directory:  /home/facosta/neurometry/neurometry\n",
      "Directory added to path:  /home/facosta/neurometry\n",
      "Directory added to path:  /home/facosta/neurometry/neurometry\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "                <script type=\"application/javascript\" id=\"jupyter_black\">\n",
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       "                    if (window.IPython === undefined) {\n",
       "                        return\n",
       "                    }\n",
       "                    var msg = \"WARNING: it looks like you might have loaded \" +\n",
       "                        \"jupyter_black in a non-lab notebook with \" +\n",
       "                        \"`is_lab=True`. Please double check, and if \" +\n",
       "                        \"loading with `%load_ext` please review the README!\"\n",
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       "                    alert(msg)\n",
       "                })()\n",
       "                </script>\n",
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "import setup\n",
    "\n",
    "setup.main()\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%load_ext jupyter_black\n",
    "\n",
    "import os\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "os.environ[\"GEOMSTATS_BACKEND\"] = \"pytorch\"\n",
    "import geomstats.backend as gs\n",
    "import neurometry.datasets.synthetic as synthetic\n",
    "\n",
    "from neurometry.estimators.topology.topology_classifier import TopologyClassifier"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd9148db",
   "metadata": {},
   "source": [
    "## Classify neural manifold as circle, sphere, torus, or none"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d837dd0",
   "metadata": {},
   "source": [
    "### Create example torus point cloud"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "65817c15",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_points = 500\n",
    "encoding_dim = 10\n",
    "fano_factor = 0.1\n",
    "\n",
    "\n",
    "test_task_points = synthetic.hypertorus(2, num_points)\n",
    "test_noisy_points, _ = synthetic.synthetic_neural_manifold(\n",
    "    points=test_task_points,\n",
    "    encoding_dim=encoding_dim,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=5 * gs.random.rand(encoding_dim),\n",
    "    fano_factor=fano_factor,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48ced06c",
   "metadata": {},
   "source": [
    "### Fit `TopologyClassifier`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7da97bf0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier score: 1.0\n"
     ]
    },
    {
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       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
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       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
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       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
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       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
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       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
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       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
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       "\n",
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       "\n",
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       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>TopologyClassifier(fano_factor=0.1, homology_dimensions=(0, 1, 2, 3),\n",
       "                   num_samples=100, reduce_dim=True)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator  sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label  sk-toggleable__label-arrow \">&nbsp;TopologyClassifier<span class=\"sk-estimator-doc-link \">i<span>Not fitted</span></span></label><div class=\"sk-toggleable__content \"><pre>TopologyClassifier(fano_factor=0.1, homology_dimensions=(0, 1, 2, 3),\n",
       "                   num_samples=100, reduce_dim=True)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "TopologyClassifier(fano_factor=0.1, homology_dimensions=(0, 1, 2, 3),\n",
       "                   num_samples=100, reduce_dim=True)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_samples = 100\n",
    "homology_dimensions = (0, 1, 2, 3)\n",
    "\n",
    "TC = TopologyClassifier(\n",
    "    num_samples=num_samples,\n",
    "    fano_factor=fano_factor,\n",
    "    homology_dimensions=homology_dimensions,\n",
    "    reduce_dim=True,\n",
    ")\n",
    "TC.fit(test_noisy_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "151ebc31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted topology: torus\n"
     ]
    }
   ],
   "source": [
    "prediction = TC.predict(test_noisy_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "aa0bb016",
   "metadata": {},
   "outputs": [
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    "def plot_topo_feature_space(self):\n",
    "    \"\"\"Plot the topological feature space of the reference data.\"\"\"\n",
    "    import plotly.graph_objects as go\n",
    "\n",
    "    color_map = {\n",
    "        0: \"black\",\n",
    "        1: \"red\",\n",
    "        2: \"blue\",\n",
    "        3: \"green\",\n",
    "    }\n",
    "    names = {0: \"null\", 1: \"circle\", 2: \"sphere\", 3: \"torus\"}\n",
    "\n",
    "    fig = go.Figure()\n",
    "\n",
    "    for label in np.unique(self.ref_labels):\n",
    "        mask = self.ref_labels == label\n",
    "        fig.add_trace(\n",
    "            go.Scatter3d(\n",
    "                x=self.ref_features[mask, 1],\n",
    "                y=self.ref_features[mask, 2],\n",
    "                z=self.ref_features[mask, 3],\n",
    "                mode=\"markers\",\n",
    "                name=names[label],\n",
    "                marker=dict(size=3, color=color_map[label]),\n",
    "            )\n",
    "        )\n",
    "\n",
    "    fig.add_trace(\n",
    "        go.Scatter3d(\n",
    "            x=self.features[:, 1],\n",
    "            y=self.features[:, 2],\n",
    "            z=self.features[:, 3],\n",
    "            mode=\"markers\",\n",
    "            name=\"Input data\",\n",
    "            marker=dict(size=5, color=\"orange\"),\n",
    "        )\n",
    "    )\n",
    "    fig.show()\n",
    "\n",
    "\n",
    "plot_topo_feature_space(TC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "2fabf3b3",
   "metadata": {},
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       "                            \n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TC.plot_topo_feature_space()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc0955ec-59c8-4030-8286-6cf165a02973",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Persistence homology for synthetic sphere, torus point clouds"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8c7fb83",
   "metadata": {},
   "source": [
    "### Plot point clouds"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef72fe47",
   "metadata": {},
   "source": [
    "## Compute Topological Distance between Persistence Diagrams"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e45d85c9",
   "metadata": {},
   "source": [
    "Create torus point clouds with varying levels of noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "0b7c3b25",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_points = 500\n",
    "encoding_dim = 10\n",
    "fano_factors = np.linspace(0.1, 2, 20)\n",
    "\n",
    "tori = []\n",
    "\n",
    "scales = 5 * gs.random.rand(encoding_dim)\n",
    "\n",
    "for fano_factor in fano_factors:\n",
    "    test_task_points = synthetic.hypertorus(2, num_points)\n",
    "    test_noisy_points, _ = synthetic.synthetic_neural_manifold(\n",
    "        points=test_task_points,\n",
    "        encoding_dim=encoding_dim,\n",
    "        nonlinearity=\"sigmoid\",\n",
    "        scales=scales,\n",
    "        fano_factor=fano_factor,\n",
    "    )\n",
    "    tori.append(test_noisy_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e53abf5",
   "metadata": {},
   "source": [
    "Compute persistence diagrams for tori and compute pairwise landscape distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "e5c425f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from gtda.diagrams import PairwiseDistance\n",
    "from neurometry.estimators.topology.topology_classifier import (\n",
    "    compute_persistence_diagrams,\n",
    ")\n",
    "\n",
    "diagrams = compute_persistence_diagrams(tori)\n",
    "PD = PairwiseDistance(metric=\"landscape\")\n",
    "distances = PD.fit_transform(diagrams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "dab50d59",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [nan, nan,  0., nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
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       "         0., nan, nan, nan, nan, nan, nan],\n",
       "       [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "        nan,  0., nan, nan, nan, nan, nan],\n",
       "       [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "        nan, nan,  0., nan, nan, nan, nan],\n",
       "       [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
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       "       [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
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       "       [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "        nan, nan, nan, nan, nan,  0., nan],\n",
       "       [nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "        nan, nan, nan, nan, nan, nan,  0.]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "1a1bc59b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(fano_factors, distances[0, :], label=\"0D\")\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"Noise Variance\")\n",
    "plt.ylabel(\"Bottleneck Distance to Original Torus\")\n",
    "\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "efbd5ab1",
   "metadata": {},
   "outputs": [
    {
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       "config": {
        "plotlyServerURL": "https://plot.ly"
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     "metadata": {},
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   ],
   "source": [
    "plot_heatmap(distance, colorscale=\"blues\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "823a0d87",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'compute_persistence_diagrams' executed in 46.4076s\n",
      "'compute_persistence_diagrams' executed in 31.8140s\n"
     ]
    }
   ],
   "source": [
    "# diagram_0 = persistent_homology.compute_persistence_diagrams(\n",
    "#     torus_0, maxdim=2, n_threads=-1\n",
    "# )\n",
    "\n",
    "# diagram_1 = persistent_homology.compute_persistence_diagrams(\n",
    "#     torus_1, maxdim=2, n_threads=-1\n",
    "# )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fee00317-7da7-4698-a689-e17f92755716",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Persistence homology for place cell data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bd5cd03-70c5-48f9-9711-393f06e3c224",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Load place cell data \n",
    "\n",
    "From Ravikrishnan P Jayakumar, Manu S Madhav, Francesco Savelli, Hugh T Blair, Noah J Cowan, and James J Knierim. Recalibration of path integration in hippocampal place cells. Nature, 566(7745):533–537, 2019."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "174e9a78-80d3-4440-bb91-6d2d5f5addc9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: # - Found file at /home/facosta/neurometry/neurometry/data/binned/expt34_times_timestep1000000.txt! Loading...\n",
      "INFO: # - Found file at /home/facosta/neurometry/neurometry/data/binned/expt34_place_cells_timestep1000000.npy! Loading...\n",
      "INFO: # - Found file at /home/facosta/neurometry/neurometry/data/binned/expt34_labels_timestep1000000.txt! Loading...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(934, 40)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expt_id = 34\n",
    "timestep = int(1e6)\n",
    "\n",
    "dataset, labels = experimental.load_neural_activity(\n",
    "    expt_id=expt_id, timestep_microsec=timestep\n",
    ")\n",
    "dataset = dataset[labels[\"velocities\"] > 5]\n",
    "labels = labels[labels[\"velocities\"] > 5]\n",
    "dataset = np.log(dataset.astype(np.float32) + 1)\n",
    "dataset.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "795171be-bb1a-46aa-95f0-89bb7f0c3d4f",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Persistence diagrams for place cell data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e89a5fa0-1816-44ee-8f28-8719ce7b646a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Function 'compute_persistence_diagrams' executed in 1.6295s\n"
     ]
    },
    {
     "data": {
      "image/png": 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1Mbt27WL+/PmB7ppIuaWgIiJSQvr06cO7777L/PnzsVqttGnThoULF/Lggw8Gumsi5ZamfkRERCRoqY6KiIiIBC0FFREREQla5XqNSl5eHseOHaNatWolUtZbRERESp9hGJw/f54GDRrYD231pFwHlWPHjrkchiYiIiLlw5EjR2jUqJHXa8p1UMk/mv3IkSNez+oQERGRwLFarXz66af84Q9/wGw2k56eTnx8vP3nuDflOqjkT/fExMQoqIiIiAShw4cP88EHH5CXl8eHH37IU089ZX/Pl2Ub5TqoiIiISPD65ptv2LBhg/111apV/b6HgoqIiIiUKKvVyvTp00lNTbW39e7dmxtvvNHveymoiIiISIk5dOgQH374IXl5eQCEhYUxevRoatSoUaT7KaiIiIhIiUlOTraHlPj4eIYPH47ZbC7y/RRUREREpMTcfPPNJCUl0aJFC66//vpi309BRURERIps//79LFiwgJtvvpkePXoAMGTIkBK7v0roi4iISJF8/vnnzJs3j7y8PNauXYvVai3xZ2hERURERPySk5PD9OnTSU9Pt7f179+/WGtRPFFQEREREZ/t2bOHhQsXYhgGAFWqVGH06NHExsaWyvMUVERERMQniYmJLF682P66WbNmDB06tFSfqTUqIiIi4pO2bdvaTzu+++67Sz2kgEZURERExIPElES2/bqN5vHNubH5jZjNZh5//HGioqKIjo4ukz4oqIiIiIiLqZum8tuq32h0sRF7THvYcMcGJnSeQN26dcu0H5r6EREREQebDm/i1LJTxF+Mx4SJUCOUj7Z+RGJKYpn3RUFFRERE7Hbs2MFX731FlbwqAGSFZLEkfgmZ4ZkkpSeVeX809SMiIiIALFy4kN27dwNgYJBcNZkNdTbY30+ISSjzPimoiIiICKdPn7aHFJPJRJVrq7Dh7JWQMqrdKCy1LWXeLwUVERERoVatWnTo0IF9+/YxduxYIiMj6ZfSj6T0JBJiEgISUgBMRn5puXIoPT2d2NhY0tLSiImJCXR3REREypV58+YRGhrKoEGDyvS5/vz81oiKiIhIJZOWlsasWbPIysoC4Pfff6dNmzYB7pV7CioiIiKVyKZNm/jqq6/sr2NiYmjevHkAe+SdgoqIiEgl8f7775OUdGWLcYcOHbj77rsD2KPCKaiIiIhUcFarlddee42cnBwAQkJCeOihh2jWrFmAe1Y4BRUREZEKzmw2ExoaSk5ODrGxsYwdO5bw8PBAd8snCioiIiIVkNVqJT09nbi4OACefPJJ1q9fT69evQLcM/+ohL6IiEgFc/bsWV599VXeeust+3RPZGRkuQspoKAiIiJSofz444+89dZb5ObmYhgG3333XaC7VCya+hEREakArFYr7733HkePHrW3denShb59+wawV8WnoCIiIlLOpaSkMGfOHHJzcwHbrp4RI0YQHx9f6GcTUxIDXibfGwUVERGRcm727NlYrVYAatasyZgxYzCbzYV+buqmqcz9ba799ci2I5nQeUKp9bMotEZFRESknLv99tsBuOmmm3jyySd9CimJKYkOIQVg7m9zSUxJLJU+FpVGVERERMqZkydPsmrVKvthgtdffz2dOnXyKaDkS0pP8tgeTFNACioiIiLlyKpVq1i7di0A33zzjX2xrD8hBSAhJsGv9kDR1I+IiEg5YLVamTFjhj2kAFSpUqXI97PUtjCy7UiHtlHtRgXVaApoREVERCToHTt2jLlz59oXzIaGhvLoo49St25dh+v83cEzofMEeib01K4fERERKZrvvvuO9evX21/Xq1ePRx991GWqp6g7eCy1LUEZUPJp6kdERCSIHThwwP7nHj168MQTT7iElPKyg6coFFRERESC2KhRo6hTpw5jx46lW7dubq/xtoOnvFNQERERCSLffPMNL774IqdOnQJsu3nGjBlD7dq1PX6mvOzgKQoFFRERkSBgtVr517/+xYYNGzAMgw8++MDnz5aXHTxFocW0IiIiAXbo0CE+/PBD8vLyAAgLC2PUqFF+3aM87OApCgUVERGRAPrqq6/YtGmT/XV8fDzDhw/3u4AbBP8OnqJQUBEREQmQefPmsX//fvvrvn370qVLlwD2KPgoqIiIiARI9+7d2b9/P+Hh4YwePZq4uLhAdynoKKiIiIiUoZ9//pkbbrgBsE3zPPLIIzRu3LjQz/lbdbaiUFAREREpAzk5OUyfPp309HR27drFiBEjAHwKKUWtOlsRaHuyiIhIKduzZw9TpkwhPT0dgJSUFJ8/W5GrzvpCIyoiIiKlaNGiRezYscP+ulmzZgwdOtTnz3urOlsZpoAUVEREREpBZmYmM2bMICMjw9521113ce211/p1n4pcddYXmvoREREpBWvXrrWHlMjISJ599lm/QwpU7KqzvtCIioiISCno06cPu3fvpnbt2gwePLhY96qoVWd9YTIMwwh0J4oqPT2d2NhY0tLSiImJCXR3RESkEsuf6rn99tu55ppr7O2VdVuxN/78/A6aqZ8pU6ZgMpkYP358oLsiIiLis8SURD5Y+QGvvfYaGRkZLF68GKvVCti2FQ/5egjPr3ueIV8PYeqmqQHubfkTFFM/GzduZPbs2VgsSpoiIlJ+TN00ld+//52GmQ0xYQKgdevWmM1mj9uKeyb01MiKHwI+opKRkcGQIUOYM2eOSgeLiEi5seHwBlKWpdAosxEmTOSRx4+1f6TlrS0B79uKxXcBDyrjxo3jzjvvpFevXoVem52dTXp6usMvERERnyVvgu0Lbb8Xw/79+/nmvW+IyIsAIDMkk8/jP+dY1DF7EKns24pLSkCnfhYuXMiWLVvYuHGjT9e/8sorTJ48uZR7JSIiFdKKF2D9tCuvbxoPvYv2M6Vu3boAGBgcrnqYjXWu/BzLDyKW7BxG1u7K3JSf7O9Vpm3FJSVgQeXIkSM8/fTTrFixgipVqvj0mUmTJvHMM8/YX6enpxMfH19aXRQRkYoieZNjSAHb69YDoFFnn26RlpZGZGQk4eHhREdHc++99/J10tdsPHMlpNiDyOVQNAHoGRFOUpv+JNw4QSGlCAK2PXnJkiXcc889mM1me5vVasVkMhESEkJ2drbDe+5oe7KIiPhk+0JY/IRr+z2zof2gQj++efNmli5dSkxMDBMmOB4G6LL9OHkTvNvT9SaPrvQ5FFV0/vz8DtiISs+ePR3OPgB45JFHaNWqFX/5y18KDSkiIiI+q9ncv/YCPvjgAw4dOgTYfsCeOnWKOnXq2N+31LY4jpSc2ef+Rmf2KagUQcCCSrVq1WjXrp1DW1RUFDVr1nRpFxERKZZGnW1rUhzWqEzwGhzS0tKYMWMGOTk5AISEhDB48GCHkOJWMUKRuAqKOioiIiKlrvdk25qUM/tsocFLSPnll19YtmyZ/XVsbCxjx44lPDy88OcUIRSJZyqhLyIiUkBaWhrTpk2zv+7UqRP9+/d3ua7Q0vjJm3wKRZVRuVijIiIiEjBeQkRsbCyNGzcmOTmZoUOH0qRJE5ePT9001aHq7Mi2I5nQ2XGRLY06K6CUAI2oiIhI5eKmnspP0X25ePEiPXvaduvkn9XjbmNHYkoiQ74e4tI+/4752n7sI42oiIiIuONUT8UKvLf+BEdN3wLQsmVLGjVq5HXnqbfS+AoqJU9BRUREKo8CW4dTqM4cHibXFAbYdvX4Msmg0vhlK+Bn/YiIiJSZy1uEf6AzM3jEFlIMg5qxUTz//PM+VTu31LYwsu1IhzaVxi89GlEREZHyo5g7aaz1r+Xf0eM5nmECkwkMg64N4fbH/uTXfSZ0nkDPhJ7ed/1IiVBQERGR8qGEDhVMyQ4H0yXMITBywM006NCrSN1xqUgrpUJTPyIiEvw8HSqYvMmnjxfcxfPoo4/SoEEDJj3//4ocUqTsKKiIiEjw83Z+jhdWq5WZM2fy6quv2sNK3bp1eeyxxzAf32o7rNDHsCOBoakfEREJfkU4P+fYsWPMnTvXHlCWLFnCfffdZ3uzhKaRpPRpREVEpLxJ3uT7SIA/1waz/PNzCvJyfs7KlSuZM2eOPaTUq1ePgQMH2t4s5jSSlC2NqIiIlCf+jARUtFEDHw4VtFqtzJo1i9OnT9vbWl3Xiqotq/Lb2d9si1/3rnB//70rVPI+CCmoiIiUF55GAloPcP0B68+15Ukh5+e8/vrrZGdnAxAaGkrEjRH87+H/hRTb+yPbjmSCx09LMNLUj4hIeeHPgtIiLj4trxJTEvly/5c0vLohAA0aNOCOUXfwweEPHK6b+9tcEus0dX+TFr1Lu5tSBBpREREpL/xZUFqExaflkdVq5fX/vs78zPn2tmE3DuOx3o/x5f4v3X4mqUpVLDeNd5oW87zeRQJLQUVEpLzIX1Dqyw9Yf64tpw4dOsR/PvwPeXl5NIlrwsHYgwD859h/6JPSx/uZPL0HFLreRYKDgoqISHniw4LSIl0bZBJTEr2Wp//666/ZuHGj/XXdrLr2oAK2k4wHNBvAyLYjmfvbXHu7w5k8hax3keBgMnw5KjJIpaenExsbS1paGjExMYHujoiIlICpm6Y6hIuRbUcyobNtCWxOTg4zZ87k3Llz9ve3xW1jX6zj2pv5d8y3B5LCQo+UPX9+fmtERUREgkJiSiI/HP3BIaSAbQFsz4SeVMuoxrx588jLywMgPDyc0aNH8/7+99n325Wg4nySsc7kKd8UVEREJOCcR1GcJaUncWDpAXtISUhIYMSIEQBMSD1Hz2MnSAoLJSH3EpYGqWXRZSkj2p4sIiKBk7yJxB//6TWkgG0B7JgxY4iIiODOO++0h5T8ejGW7BwGZFzEkp2jKrMVjEZUREQkMC5Xzk2Krgq1a7m8XfdiXa4/fT01e9W0T91MnDjR8SI3dWESI8JJ2ruYhIhwTflUAAoqIiJS9gpUzk3IveTydudTnbnq4lW2Fz8CXT3cx6kuzNS4WOZWj4XDX8DhLxhZuysTLI9rd085pqkfEREpewVGQizZOYw8lwaA2WrmzsN3XgkpwG233eb5PgUOK0yMCLeFlALmpvxE4of9bKM3Ui5pREVERMqe00jIhNQ0Wp2vyy/W/va2yMhIxo4dS3R0tNdbJXa4j6TqNTlyZhec/MHl/aSwUCwV4ZyjSkpBRUREyp5T5dyvuI1N1vb2t6+++moGDx5c6G0K2y0EBaaWzuxTUCmHFFQ82Ho4lYOnL9CkVhTXNo4LdHdERCqeApVzG56NYNPaREwmE/fccw/XXHNNoR9PTEksNKSMOpdm2wkEFe6co8pCQcWNKct2MmvNAfvr0d2bMrFf6wD2SEQkSCVvKrxEv4drTp8+Ta3Lrzuwj7SOV9OpxwCiz+2C7QtJDDWRVKWqx4qySelJbh83uv1oGidtIuH3pVdCSgU756gyUVBxsvVwqkNIAZi15gB92tbTyIqICFwJHvu/h8SPr7TfNN42SlLQ5S3IztcsXLiQ3bt3c22dPO46aXu/O8CJOXB085XdO5cVLKOfz9Ohg7c0vAVLh3HQyYcQJUFPQcXJwdMXPLYrqIhIhVfYCIlz8CjIecFqgS3I+TLWz2LG5ggys3MBSDyZx10FLzi62f3unctl9J1L4+vQwYpPQcVJk1pRfrWLiFQYHkY/7NwEDxcFF6w6FWNLpCVL6IdxOaRERZgZl/W2yy2Swtz/aEr6cSqWu99zaJvQeQI9E3rq0MEKTHVUnFzbOI7R3Zs6tI3p3lSjKSLim+RNsH1h+Svh7i6EOJeid1MF1kXBBasF/jyfgSzmDgyT7cdO27Zt+dPQvkSS43ILdwXgABJ+X+r2+2qpbWFAswEKKRWURlTcmNivNX3a1tOuHxHxT2EjEsHMUwgpOEJS2K4Z5wWrl7cgf7t+E/tMtn8AmjB44MFBtGrV6vJnxjt+zxp2xnJ0EyPPpTlM/9h372iLcaVjMgzDCHQniio9PZ3Y2FjS0tKIiYkJdHdEpDJL3gTv9nRtf3Rl+fjB6mv/ncOYZRA06+F1wao1aQOvfbiciIhwnnz6GcLDw12fXXBdTPIm2LuCxJ/fuHIicv7uHcuDcO87xftaJeD8+fmtoCIiUhK2L4TFT7i23zMb2g8q+/4UhcuI0ATo/XfX63zYkrxgwQK6detGo0aNALBarZjNZv/6s+hxx11F+cpL+BOP/Pn5rakfEZGS4Gla5OxB2w/28vCDtUABNq9bet3spklMSSQpPYlaplqs+WQN2dnZHDhwgEmTJmE2m/0PKQDNbnMfVDT9U6koqIiIlASnkvB2a6bYfpWX9SpF2NKbX8a+SVoTOqZ2xIQJgKioqEJHUhJTEkk6tJqE3Fwsjbs7PttT+FOF2UpFUz8eqIS+iBTJ5fUVrJni+l4FnLJITElkyNdD6Ha8G7Wza2PChIFBkzZNGP6H4R4/k5SexI9Hf2TpwaX29pHn0pjQ5hHHQOfrdJSUK5r6KSaV0BeRImvU2bcdNMHG31L4AGf2sTv1OHcn3U2YEQZAHnmsqbuGTh07ub2Ft0ME51aPpeemGVgKFo3zdTpKKiwFFScqoS8ixVbepix82VbtoSJt3dD6hBqDMDC4EHqBb+p/A2b35e19OUQwKSwUi3OgU4XZSk0F35x4K6EvIuKT/PUqBQXroXi+FHpzusZ6+RdAt0vHiYjYyr5q+/imkS2kDGg6gKT0JBJTEh1u6+kQwYISci8Fb6CTgNCIipNca55f7SIibjlPWYBtC3OwTV/4Mk1V4JrTxPIOD1Ob0zzGQgAmZa0m0QgnKSWUH+Ov5csDX/LlgS8Bx8MEPR0imG/UuTQsnccF1/dHAk5BxUmY2f0gk6d2ERGP8qcsgrlirafRC2vulWB1+Zp1dGYlt4DJxDHqs8bcgO6XjgHYC7I9n3XE4TZzf5tLz8gGWNo+aDtE0FSDucZZ+/sDzmfQNSuLhGZ9sfRUSBFXCipONKIiIiXK09RKwQWjgeRuW3XDzvDFk/aX1hvG8+/o8RzPMIHJtqtnT7U9fFYzlJHnYpmQmgZ4OUxw2Xgsx36H1gOYcGAbPSPCXSvOXqeQIu4pqDjRiIqIlKji7ADyZSdOSSg4TWXNdQgpp4hjzs9WLpnCwARWrKyqt4pzVc4Bl3fqXMzEkp3j8TDBI6GhJG6agSW0CmAbfbEHFIAWfRRSxCP99HXSpFaUX+0iIl4VdQfQihdsZ+8sfsL2+4oXSr5vBTXqbCv1bw6zN2UQyUxG2EIKEBETweL4xfaQki9/JMWSncPIqKtdbj0zrjpDGtRjaupW98/u/lzJfA1SISmoOLm2cRyjuzd1aBvTvam2JotI0RRlB5AvO3FKS4EAFU0m1UkDw+Dm9s24Y+gd4KbIbEK/abYzjR5dyYT7/8v8zv+P0annXK6be34nidcNc2wM1t1QEjQ09ePGxH6t6dO2nirTikjJ8LdoWQALxh03N+T01eO5Zs80AMbwAec6PEWdgUMB2y6egrVQRrUbhaXtg/ZqswkpiVjaPkjSvm/gnGuwSmp1O5b2w1XATXymoOLBtY3jFFBEpOT4U7QsQAXjVq5cybp164AQGg9aSmz2UcJrNqdOgX5P6DyBngk9baEkJgFLbYtLtdmRbUfS88YJ8PUQl2ckxCRAbYsCivhMUz8iIoGSvMm2Bdh5SqeMC8ZZrVamT59+OaTYJOXE2tasuHmmpbaFAc0GYKltcVttNv/1yLYjHdpHtRuFpbalFL4Cqcg0oiIi5VdZ7YopDYXVVnE3XVQKX29ycjLvvfceeXm2EgyhoaE89thj1KlTB7hygGD+6IkzT9Vmk9KT3I6+iPhLQUVEyqdgLqKWz1Ow8LW2SsHKsL+8A4kfX3mvBL7e5cuX8/PPP9tfN2jQgJEjR2I221bMupvSya8ym89Ttdn8dkttiwKKFIumfkSk/Ankrhhfedte7G2xrKd7FAwpUOyv12q1smHDBvvrnj178thjj9lDiqcpHefzeyy1LZrikVKlERURKX8CuCvGJ4WNmPiyWNbdPZwV4+s1m8384Q9/4IsvvmDUqFHUqlXL4X1vUzrOIURTPFKaFFREpPwJ0K4YnxUWpNyVrXdeLOvpHgX5+fV+/fXX7Nu3j6eeegqA1q1b07p1a7fXFjal40xTPFJaNPUjIuVPGe+K8ZsvQar3ZHh0pb1QGr3/7ts98vnx9ebk5PDmm2+yceNGUlNTWbJkidfr8xfQ9m/S36FdUzoSCCbDMIxAd6Ko0tPTiY2NJS0tjZiYmEB3R0TKWjDv+nFZ7DvBNYz4ew/LIGjWw6+v9+CGZcxb/gt5l/9LHx4ezuib6xB3bgc07AQdH3a43nkBbf+m/bmxwY2a0pES5c/PbwUVD7YeTlVlWhEpnpIIUsW4x5czX2DLSduJxxgGCTEGI6r9AEc3269JbGQhqcdz9imdIW6KtM2/Y75CipQof35+a42KG1OW7WTWmgP216O7N2ViP/fzuCIipcqfirYFvDX1dc6mXQkp/VjJ9emJkH7lmqlxscwNOwfrngegW8Nubu/lbgGtSFlRUHGy9XCqQ0gBmLXmAH3a1tPIioj4LsB1XuLMFzlrMhFhZDGG94nlosP7iRHhzK0e69C29uhat/fytIBWpCxoMa2Tg6cv+NUuIuLCzzoviSmJfLn/S5caJf46deqU7Q8rXmDo2Te4xfiZicxwCSkASWH6d6qUD/pfqpMmtaL8ahcRceFHnRdfqr86cy5rn5OTw1tvvUVGRgbD+nWhyeWQdBs/erxHQu4l374WNPUjgaWg4uTaxnF0iI9l25E0e1uH+FhN+4iUZ2W9O8jHOi+eqr/2jGyApe2Dbm/hHGyGRvYne2cV8ndFrPhxG48X0r3EiHCSGl/HTdknWG/OLeRqTf1IYGnqx8nWw6kOIQVg25E0th5ODVCPRKRYvJWyz+fpFOOi8rHOi8fqr8vGu+2nc7C5/tT1ZO6MsIUUw6B59Twev78XiRHhfBldlcSIcJd7TKpVgyEN6vH8pSMOIaX/+QxGnktzuV61UyTQNKLixNsaFY2qiJQzvhz+V1qLXt2dfuzEY/XX3EtuDynMDzZmq5m+R/sSmRd5+Z087mEZltTdTP1lJ3Mb1LN/pv/5DG7MyiIh9xIfVYtmabVot89cWi2a+cdO0PO6p/mhahVMmLi54c0KKRJwCipOtEZFpAIpbK2Ir6cYF1UhW4vzD/QrOEoy6lwaluwc24s1r8GQT+zv5Qeb3sd720NKVkgWA03/wXIpw7aT5/xOh2cs9RJOnM2OjWF64+5Ygq14nlRqCipO9pw877FdIyoi5Uxha0V8WfRayutbJnSeQM/IBiQtG09C7qUrIQVg73LY8iGYw2zPvzyV80OdH+hzrA/HIo/xc92fGXwsBy4VfyfP2ijbdJHGUCSYKKg42X7knMf2B69rXLadEZHiKezwv8KCTBnVQrG0fRDLtv/agomzL54kgyosZCC1LLYQcyH8AoviF4HZdklSWCiW7By/dvJ4oh0+EmwCuph25syZWCwWYmJiiImJoWvXrixbtiyQXSIuynXxmbd2EQly3g7/87bo1c9aKMXW/Tm3zYm05A1Gc9TUgIM7CkzhmK/8MaHdQwBYsnPcLoj1h3b4SLAJaFBp1KgRU6ZMYfPmzWzatInbbruNu+++m99++y1gfWpW2/1crqd2ESkHGnWG9oPcT914CjLepoVKq49OoWkBd7OYOzBMIWAYxBspLkFk1Lk0LBG1oLotYExITWP+sROMTj1Hh8wsr4/U6chSHgR06mfAgAEOr1966SVmzpzJzz//TNu2bQPSJy2mFamE3C169bEWit+8rXm5vFMoI/l3pq9MIutSHgAmI48H+JxWHIRU6Hkxk6Sw0CtrWtZMcbiN8+6elnEt2Z2626UrNza8kcGtBzsUjxMJNkGzRsVqtfLpp59y4cIFunbt6vaa7OxssrOz7a/T09PdXlccWkwrIqXGhzUvW1PMfLH8oP11NeM8Y/iASK4ssrVk5zguui1gUq0aLrt83IUUwB5OFFAkmAW84NuOHTuIjo4mIiKC0aNHs3jxYtq0aeP22ldeeYXY2Fj7r/j4+BLvj7fFtCJSiZTw1E/ibx/z5fZ3HIuwuVnzcvbsWfufLRYLzzw6iMh73rJNSzmvp3F+RkS4x63Izicja5pHyouAj6i0bNmSbdu2kZaWxmeffcbw4cNZs2aN27AyadIknnnmGfvr9PT0Eg8r7eOrs+CXI27bRaSC8TYNU4JTP1NXPcfcw8ugdi0ARp5LY0Lq5bUmZ/ZhrX8tZrNtdWzPnj05efIk1113HS1atLCd6xMdRUJEOJb8InKbP4Ct/3F5jrftyU/U78YT7Z/QNI+UOwEPKuHh4TRvbvs/fqdOndi4cSNvvvkms2fPdrk2IiKCiIiIUu3Pg9c15v++3U3K+SvDqnWqhWtrskhFU9g0TGFbm32U+NUfmXt6tUPb3Oqx9LyYiSU7h19OhvLN5y/Rq1cvbrzxRgAeesi2i8fjgYVn9rkElcSIcA6Huv9P+oDzGVguGaBpHimHAh5UnOXl5TmsQylrWw+nOoQUgFPnc9h6OFVrVETKs4KjJ1DEirSGl/fcPzNp52f2kZSCksJC2Rz6GId/su1y/O677+xBBWxTRW4PLEzoieXy17AoOopfI8I5ZjazPqqq2y4MOJ/By6fPFn8RsEiABDSoTJo0iX79+tG4cWPOnz/PggULWL16NcuXuyl6VEZW7z7lsV1BRaScch49adHH/XXOFWmLW17/zD63RdgicyJJvDCSS9jWq4SEhDB06FCH/iZtf8d9wDm0Gkt4HR5q0oIdeP5H3ZjUc9ycmWVbdFuEkSCRYBHQoHLq1CmGDRvG8ePHiY2NxWKxsHz5cnr37h3IbolIReIucLirAAuOow6+lNcvTM3m9iJsc6vHAtA8rTkdUttzCRMYBtVJY8yQQYQ3aWLr694VsH4aCW5OPgZI+O4fLAoLY0ftml4fHX/Tn7GE1ym10v8iZSWgQeXf//53IB/v1q0t6/DmStf/QN3ask4AeiMixeYpcLTo4xhYnEcdSmIx7eV1LhPWT6PnxUx+zruO45faAybA4Dq2cQer4HwXWPG1a6ByY19YGF9Fu5/mKSjhqltB61GkAgj49uRgc23jOEZ3b+rQNqZ7U037iJRXnoJF9+c8l9YH7+X1/XG58q2lcQ/SI3eSh0Eeeays+z2747bYrrHmuoQUTzt4Xqhdk18iI70+UluPpSIJusW0wWBiv9Y0qRXF9iPnaB9fXTt+RMqzwnbveAse+duB966A9GMQGmGbnvEjrPz8zae0M+3mwOFVfNCgHtHVviXDnAFmmBsZS8/mA7GkJbt8zt8DBpvFNmPUNaO09VgqHAUVN6Ys28msNQcAWPDLEQ6evsDEfq0D3CsRKbL8wOGpZoo3O790DDlrpvh0irLVauXfU1/keIaJNWRxuG4MABnhGQ7XJbXqjWX1Ww5tiRHhJIWF0v98hscCbgU9ltCfp259xacvR6S8UVBxsvVwqj2k5Ju15gB92tbT9I9IeebuPB9nzluYLy9sdVHI7p9Tp04x553ZXLKGgAmyCWd9RDXA6nLtkeQNJJ7aSv4YyNS4WPvCW4D+5zOINAw+janmsdtN4m/0+J5Ieaeg4uTg6Qse2xVURCow5y3Mhdk6z/a7U1hZ8+VHrN6yx/bCMKjFGRpGfsanZtetxgAzD33OzAb1GHkujZ4XMx1CCsDSatFMTjnDp166khCT4Hu/RcoZLaZ1otOTRSohd1uYC7P5PXi3py3gYJvqmfX6C6zefPkAQMPgZn5hHP+haV7h603mVo9lXWQVt++FdXqEkWEN3L6nhbNS0WlERUSkiAcNAvZpoMPHTnPygglMJszGJUaxgPqc9utWnureJtSxMKDHS/T87WOSTiWSW7UmYbVaaOGsVAoKKk409SNSCVlzC7/m6n5w/hgc3+763pl9NImANuzhtBHH48zDXOBtb4cFFnRLZhY5pjSH6Z9R59Js5/QAlrYPYmn7oE/3EqkoFFSc5Frz/GoXkXLOl7UpDTvDnmUOTVtDw1meN5janGZUzebwyzv8ga9cPprY9g4OH11XaDeuybKVu7dk59DzYiZJYaEk5F6ylcDXOT1SiSmoOAkzu1+246ldRIJIwV07vmxBLmxtSkQsXP8Y/PB/Ds3/V60J6Rl3YcbMEWrw+sZP+HPixy4fn3r1Dcy9+CvEVS+0KzuqVCExItweVizZlw9HtQxSCXyp1BRUnGhERaSccnfwYPfnvP+Q97Q2JboeNOsJ0bVdQsp8c3cyMjpixoSBQWpYKv9N/Z4+l0NGvsSIcObmHvPrS0gKC3W4B/Fd4N7Zft1DpKJRUHHy/vpDHttVoVYkSHk6eHDvcvfF2fIP/0v3ECQyTsD2+Q5NVmAGIzibF4fpckhJrJ7I3up7AdeQ4eu6lIJcqtH2ednve4hUNAoqTpJTL/rVLiJBwNuuHefibP7WSwEyCef/GEOeybZE9pLpEivqr+BC+JXF9wkRtSEjyf76xyrutxo/lppGk0u5/FilikPV2VFRV2PJPnzlwqKcKyRSASmoOKkZFc757Ey37SISpApbbHpmn+2Hvrc1Ka36w66lbt+KJIcwcsk2QmjIMc5V+4YL4U47c1LT7K8TI8I9lr6fExfLyHNpvHL6LIN7TCGpStUr24xv8HONjUgloKDipEq4+2+Jp3YRKYQvC1z9XQTrzN3BgwXlBxlvIy912zkElRzMpFGN2pwDYAzvs6vJE3Tp+Thsrcrtv8533JkDEHcVpB4qdNpnbvVYel7MxHLJwNJsgOPXoYAi4kA/fZ2cycj2q11EvHCeZnG3XsSXa3yRf/Dgmtdsa1Pytehz5c/eRl5a9IZLWbB+GgdpyDzuh5AQnh/eD/O5g8TWbE6XAiHCsvk9x4WvAKmH4K63yT33Gxxx3apcUFJYKBZtOxYplPbcOokKN/vVLiIeuJtmWT/N1u7PNf5o1BmGfAKPrrwSUPYut5W6n/+A7bXFS8G03pP5stVU/mN6kDyTmTzDxIajVhIbtOHL7OMkpiQW2oWpJ37ghUJCCkBuoy4aPRHxgUZUnNSJqcKhs65rVOrEuF8YJyIeeJpmyV8v4us1+TxND3lqLziqkv9673LHEZYCck7tZvqnP5Cenm5v69evH4uzFrP06ytTQiMb92NCjY5u75EYEc7clJ/cf01Owuq29ek6kcpOQcVJTBX33xJP7SLigadpjYLtvlwDnqeHPLV7W4viHGCAfTTmo6X7yTNspeojIiIYM2YMUxKnsPSg4wLbuYeX0fPALzifsJMYEc6SaN8PL02oozN6RHyhqR8nNaMj/GoXEQ/yF7gW5Lzl1pdrPE0PbfnQ87SRn2s/Fpjus4eUpk2bMnHiRJJ2zGLpAfe7gJJSdzu8nhoXy5AG9fg0pprb6/ufz3B4PSrqap3ZI+IjDRM40WJakRKUv8DV246ewq7xNDpydLP79jP7oP0g21qUAmXtEyPCXXfpdJ8ILXpz26Esvv/+e/r370/Hjh1heheSMg9D7VpuH5GLiS+jq9oLtBU8RNDZqHNpjE9NY3DdriTVakJCHYtCiogfFFScpGdd8qtdRArhy5Zbb9d4Gh1p2Ak2v+f5+ma32YPK1LhYhzAx9FQ0jS+0YHCNJtCoMzc3gq5du2I2m2HefZCyi4QI97WTmmVn80LtmvbXHbKy3F73hwa3MrDBzbaTj2s2x9Kos8t0kYgUTlM/TrRGRSTIeJoe6viw92mjy4ElMSLcIaRcd+o6Mi/2YY+pKasOWe3tZrPZNm207zsALNk5jDx3pYgbwM0XM9kf4TgNvM1DBdqBHR6zjZy016GCIsVRpJ++J0+e5E9/+hMrV67k1KlTGJfndvNZrVYPnwx++05d8KtdRIrA3wJvnqaHvE0bXQ44SdvfAcBsNdP3aF8i8yIvX2BQMyTDttbFHGb7/JrXvHYjBMPr+/lGtRtlqzQrIsVWpKAyYsQIDh8+zF//+lfq16+PyWQq6X4FTFpWjl/tIuKnohZ48zQ95G3aqPdkEiKr0iDxe25IuYGQy4PIWSFZDDT9B8vmDPCw1MV5JAZgbdWqhXZzdPvRjOswrtDrRMQ3RQoq69at44cffqBDhw4l3J3Aq1OtCqkXM9y2i0gxedrBU/DQQG+fLThy4suozIoX2LV+HzeausLlE4+PRh6lbcRyuqS6/v+8IE9l8LtduMjaKM+B5ZaGt3j/OkTEL0UKKvHx8S7TPRVFqNn96JCndhHxg6cdPHtXeA8qzqMw1a+Cc4euvL5pvOsU0OVQdIrhgAnIo0n4d9xr3YMltfAR0vwdPc6eSEvnibR0ksJCXU9A1pSPSIkrUlCZNm0aEydOZPbs2Vx11VUl3KXAOprqWpXWW7uI+MHTDp41U2zn7LibAnI3ClMwpIDt/QLXWG8Yj/nACgDG8AHvGYMYwiIinc/m8cKSncPIqKuZe2GPvW3UuTT71mZLdg4DMi4y+HwGSdfcQ0KXJxVSREqBz0ElLi7OYS3KhQsXaNasGVWrViUsLMzh2rNnz5ZcD8tYaIiHERUP7SLiB2+nHHuaAvJWZdaNj7ibvT/DkxyhBmAGHmWhbx+O7wJ9XraPzExo1JmeKYkkpSeRkHURy6kDtlBVgCU7B0uHx0EhRaRU+BxUpk2bVordCB6hZvc7tj21i4ifek+G0CouP/AB92f8+FhlNoNIpjOCLJNtV8884z6ewk2dlbvehrRk988/sgF2fukwsmOpbbkyUtIW+wnLds6VdEWkRPkcVIYPH16a/Qga1jz3a288tYtIEbTo7T4ouAsl3kZhLttKG76gD1we9Y02zvMY891ffOgHuPcdSD3oULnWbv00W5CKbXRl23LBIOJLtV0RKTFFWqNiNps5fvw4derUcWg/c+YMderUKdd1VK6qWZWUDNd57KtqFr4tUaTC8bfeia/chQ8PpxoDV8LBmtdcDhX8kHs5QIItpBgGFn7nHlwPHrRL/BiOb4eUXbaX7krrO4co5y3UvlTbFZESUaT5DE87frKzswkPd192ury4v3O8X+0iFdaKF+DdnrD4CdvvK14o3v2SN8H2hbbfwfaD/9GVVwLK3uXen9OoMwz5xHaGz2UzGcoB01VgMmEy8niIRbaQ0ryX975cDin5hwk+X7sWQxrUY2qchzN78g87FJEy59eIyr/+9S8ATCYT7777LtHRV7blWa1W1q5dS6tWrUq2h2Vsxe8nPbY/eF3jMu6NSIAUp96JO96KvDmNkNifA66jOVs+dJiu6c1a5hv3EcN5xvEe4Vwezb1cBt8bdwXd5laPpefFzCsjKwW5Wz8jIqXOr6AydepUwDaiMmvWLNvZGJeFh4dz1VVXMWvWrJLtYRnbfuScX+0iFZKnnTZF+WHtLfR4es7y520LW/Pln+mzfhrfcyO38SMAzTnMGN6nDqn+9QnPBd2SwkLdBxUfF/WKSMnyK6gcPHgQgB49erBo0SLi4uJKpVOB5Glaq6IWuBNxy9MP5aL8sPYWejzdr2BIAVg/jVSimcU4ckwRnDRqM5jPAYoUUqjehITMo27fclvoTTt7RAKmSItpV61aVdL9CBqe8ohyilQq7ha7Ov+w9nWhrbfQ48OOHoANdOAbetgXzJ7Fw1oSLxIjwklq1JGEjiOxxDbD8m5PRp5Lc5j+GXUuDcsNz0CNJmDNdb/rR0TKVJGCCkBycjJffPEFhw8fJifHcZj0jTfeKHbHAiU9O9evdpEKy9s2XG9rTpwDTGGhp+Bzzh502HFjBT7gAY7Q0B5SrmMbd3D5H0t3vQ11Wts+u/9799uNsS2anVs9FvKOwab/pX/T/rxieZAJiR/T82Km466fFr0VTESCSJGCysqVK7nrrrto2rQpu3btol27dhw6dAjDMOjYsWNJ97FseRo50YiKVEbutuF6W3Oy80v3Aaaw2iP5z0neZA8qp4nlHR4m12TbSRhiMnjY+JirOGb7jGWQbcQDoP0g26+rboEvnnS4tbtFs0sPLIUmtrBiSfz4ypoUTfGIBJ0iBZVJkybxpz/9icmTJ1OtWjX++9//UqdOHYYMGULfvn1Luo9lKjLcTG6Wax2YyHCzm6tFKiFvBwu6CzChVa6MUhQWAgqMvqzlhsshxaBGjZqMHTsW8/H+BUZPFtp+wZVA1PFh2/sF+uFp0ezSg0sZfMd8LNc/ruJtIkGsSHVUdu7cybBhwwAIDQ0lMzOT6OhoXnzxRV599dUS7WBZi45w/x81T+0ilY6nNSfpx9y3r5niXx2Wy/VV7r3nXuKqRXLDDV354x//aNtl2Kiz7fnOUzwF65zk12e5ZzY078WPVap4fFRSepLtnu0HKaSIBKkiBZWoqCj7upT69euzf/9++3unT58umZ4FiKdK+aqgL3JZo84ORdcA25RJTAPvn3NXNK1AEbiUlBSmTJnCnj177OHhqWeeo08fp4q13nYRFexj+0EkksPSatHurwcSYhK891lEAq5IwwQ33HAD69ato3Xr1txxxx08++yz7Nixg0WLFnHDDTeUdB/LlM76ESnEihccRzQsD0LvvzusL/EoP0zsXQEHVtm3Ia/lelaZbgJMfPzxxzz//PMOdZoc+LB1OjElkaRDqzlyehvEVXd7+ah2o64cNigiQatIQeWNN94gIyMDgMmTJ5ORkcHHH39MixYtyvWOH1BQEfHK3ULaxI/h+sevjLR42HkD2NaWLH7C/tIKvMsQTlAHsB0oeGO7Jp5DCrjfRWQZBGf2kZi2n9nH17L26Fpbu4eQMvnGydzb4l7PzxCRoFGkoNK0aVP7n6Oiosp9NdqCLmS7P1DRU7tIpVJYxdpmt3kOKpZBVxa/AiepybsM4ZLJ9p8hs3GJUSyg/vbTEL3X+y6hgruILi+snXpkmcvuHndGJdyhkCJSjhR5hei5c+f47LPP2L9/P3/+85+pUaMGW7ZsoW7dujRs2LAk+1imcvPy/GoXCTr+nnjsz/WFTbt4ev+ut21biS8Hla204Qv62Guj1CGFx5mHfRxl/TSnEZMHIa6J7c8FdhAlpu0n6cCX5EZHeQ0po1PP0fjSJRJa/wHLreV7wb9IZVOkoJKYmEivXr2IjY3l0KFDPPbYY9SoUYNFixZx+PBh/vOf/5R0P8tMuNlE1iXXaZ5wsykAvRHxk7dCbL5cb3nQNiriKbQUVrzN0/sdH3ZYSNuUw7Y/GAbd+ZFbcSqZ76zgKM2aKdCiD1MbXMXcw8ugdi3vnwVuuX48lsbdtbNHpBwqUlB55plnGDFiBK+99hrVqlWzt99xxx089NBDJda5QAg3h5B1yXWaJ9xcpA1SImXH3xOPPa03yQ8FnkJOwWmX/DLzyZu8hABb8D8ZFk+ttg9i/u1jYsngXpZSl9PUqdMATvn+ZQIkHl7F3Ev1fLp2VLtRWDqN9+8BIhI0ihRUNm7cyOzZs13aGzZsyIkTJ4rdqUC6kOthjYqHdpGg4e+Jx56uz+ct5DTq7L4KbesBbsPSt+nN+enX/cQZkTx1ufka9tr+cCoVoutCxknv/SnAUxG3gro17MYT7Z/Qzh6Rcq5IQSUiIoL09HSX9j179lC7du1idyqQrB6WonhqFwka/p547MtJyJ5CjqfRm5TdDk1WYCbDOfPrfsBEKnFkUIVoshw/60dIAQ8nHAOTWz1CWK0WJMQkKKCIVBBFms+46667ePHFF8nNtR3UZzKZOHz4MH/5y1+47777SrSDIuKjRp2hYSfHtoZeytbnryfxpmZzh6Jsdp5GY84ft//xMPV4mac5Y6oJmAgzchjHXNeQ4kk1z4vyLdk5jDyX5tA2qk5X7u3yDAOaDVBIEalAijSi8s9//pP777+f2rVrk5mZSffu3Tlx4gRdu3blpZdeKuk+lqmIUBPZbhbTRoRqMa0EueRNcHSzY9vRTd7Xj7hs8y2waPWmCZ4PGfQ0GtO8FxzfxjJu5Reute/qaRieziM5/8avE7POH/X69oTUNMeTj3s+7s/dRaScKFJQiY2NZcWKFaxfv57t27eTkZFBx44d6dWrV0n3r8xFhpnJvuQ6rBwZpkMJJcj5u0YlX/5hge0H2Qq35W9VBtsZPQUVXLfivLsHIO8SR2K78EvalZByO6vpmrO18GJw/oiIgex0LNk5tpOPdeqxSIXld1DJy8vj/fffZ9GiRRw6dAiTyUSTJk2oV68ehmFgMpXvkYfMHPeLZj21iwSN4qxFyVfwhOPtC91fkx983N13/TTiu0+k/prDnDFq8AT/ITkiiy/DqpJQryWWuImFl9n3RXb6ldosOvVYpELzK6gYhsFdd93F119/Tfv27bnmmmswDIOdO3cyYsQIFi1axJIlS0qpq2Ujx+q+VL6ndpGgUViNE395Cz5O9Ve+4jaiyaA7vwAwigWYgalxscytfnkb8d73GVmtNROK1htX5jDbKJCIVGh+BZX333+ftWvXsnLlSnr06OHw3vfff8/AgQP5z3/+w7Bhw0q0k2XJUxxRTJFyoeCak+KONHgKPmBvy8HMDEaQRgwArdlLnRa9MV/KInHTDJdqsXPP76RnRLhtuqa4/BkpEpFyy6+g8tFHH/H888+7hBSA2267jYkTJzJ//vxyHVTMJnA3eKLCtFJuFJy+KS53wefylNA+GvMR95Bnsq3fijCyiOg4wv78pOo14fc5LrdMCgu1BZXuE23l8AEWPQZnD/jeL8sgTfeIVBJ+bU9OTEykb9++Ht/v168f27dvL3anAik81P23xFO7SIWXv9C2UWfbDqKzB1lCb+Zzny2kGAZNjUNMbL6H2Lv+bv9YwlW3ur2dvQZKjSZXwoa/IeVe14KTIlIx+TWicvbsWerWrevx/bp165KamlrsTgWS4WGOx1O7SMD5ewhhUa14gZz1b/E2IzlPO/uungEspyO/wz6ubIVO3oRlzWuMPJfmMP0z6lzalWmf/Kmbwirkgm30pUYTLZwVqYT8CipWq5XQUM8fMZvNXHKztbc8MTwkEk/tIgHl7yGERXW5Eq0ZuEBVMJmoYmQyjveJJvPKdWf2wS/v2LchTwDHWif5IcUy6EpA8WWtSf6JySJS6fi962fEiBFERES4fT87O7tEOhVIWkwr5Ya/hxAWg/XUbsyAGRjBQtYZXRjMF64X7vgU9n3n0GSvdQLQ6RHIvQiJC22/wBau3NVkyacaKSKVml9BZfjw4YVeU54X0oKCipQjRS3w5ofMzEymvzWN3JwcJl1ui+ek+5BiGXQlfHjSsBN88aRj2/pp8OhKx0W7UDbTWSIS9PwKKu+9915p9SNo5OW5jySe2kUCpiQKvHnx+++/89mnn2Bg2/L2PTdyGz96/kBmKokR4a7TPPksg1xL/Oc7s+/Kgt18CigiQhFL6FdkoSEmrG72J4eGaH+yBJmSKvDmZjHuJ598ws6dOwHbgtmW7PceUoCpp39mboN69tcjz6UxITUN4rtA3FXeR1tUE0VEPFBQESnPilvgzWkxbuZ143n792guXrwIgMnI4x6+4hr2er1NYkS4a3G36rH0rHENlraDXKd7CtIaFBHxQkHFSa6HUvme2kUCrqgF3twsxv2/jXnkmWwhJapKOOMy3yCSwqvIJoW5/09JEpeweAopnR6Ba4cqpIiIV6pi5iTPz3aRcsvNYtx27ALDoI2xiz91zCKy4TWOF9Ru5fZW9iJuzu3JWzw/XyFFRHygERWRymr/92QQyRauodvlwwTv4VtuYQO1SIP1X7t+JmUXNO/ldgty//MZLK0WbW8blRfl+UwfTfeIiI8COqLyyiuvcN1111GtWjXq1KnDwIED2b17dyC75PFMH531IxVK8ia2JW7nn4xmFTexg5b2t2qR5v2zsfEuTVPjYh1CSv/zGYxP2un+83e9Db3/XpRei0glFNCgsmbNGsaNG8fPP//MihUryM3N5fbbb+fChQsB65NK6EtlMO/LVXxOP1sZfOAo9Qr5RAFVazq8dLeQdmm1aBIjwl0/e9ME6Piw3/0VkcoroFM/33zzjcPr999/nzp16rB582a6desWkD5pjYoEnRI8yyctLY1Zs2aRlZUFJhMmI4/BLKYFSe4/4Gaahx/+z+Glx4W0BU9J1jk9IlJEQbVGJS3NNuRco0YNt+9nZ2c7lOlPT08vk36JBExxz/IpEHI2nYCvvvrK/lZM6CXG5U4nHKv7z9Zu5RpSnCRGhHPYw/lf9gW2OqdHRIohaIJKXl4e48eP56abbqJdu3Zur3nllVeYPLkUDlwrIMJsItvNVuQILVKRslbcs3ycQs7qsKexndYD1157LXd1bADLN8CRDa6fbd4b9q3wevupcbEuUz757Kcka9GsiBRT0ASVcePG8euvv7Ju3TqP10yaNIlnnnnG/jo9PZ34eNeFfcURFhpCttX1X5hhodrJLWWsOGf5uAk5o3NnM4MR3MfXNDu5Bt71UM7e8iA0u81rUHG3LgVgTPsx3BxWE8slQ1M9IlIigiKoPPnkkyxdupS1a9fSqFEjj9dFRER4PLm5pGjXjwQNX8/y2fKh7Qydhp2uLFQ9s48NdGAVN/IMswnHSjRZPMcs2/tHD3t+buLHcNUtHt9eFB3FV9FV3b4Xn3sJS4cHPd9bRMRPAQ0qhmHwxz/+kcWLF7N69WqaNGkSyO4AkJHtfr7eU7tIqfHlLJ85t1056G/ze7D5PawjV/DBj6c4Qg8wmZhlDOMp/DxQ9MgvbpsfapzADrPnLXAJubn+PUdEpBABDSrjxo1jwYIFfP7551SrVo0TJ04AEBsbS2RkZED65KlSviroS0B4O8snfySlgLNH9zLr5RfJzQsBk4kQw8pdLPf/uVv/49K0KDrKa0gZdS4NS+Pu/j9LRMSLgAaVmTNnAnDrrbc6tL/33nuMGDGi7DskEow8neXjFFJ+pCMr6A55thOP46oYjBt8J+ZzbWD/97YpnXwNO8PRTX5141d3dVGA6zMzeTo1DUvncVqTIiIlLuBTP8HGBLjrlZaoSNBp2Mk23QN8xN3soamtgJthcAOb6JP1A5gHQPtBtl/XP+44MpO8Cb56Fo5v8+lx7bJz+NRN+50Nu2PpP0YhRURKhbayOPEUnYIvUkml1/FhW1gBmnEQgBDjEiNZQB9+sF2z9/LOHXdF43Z+6TGkJEaE82V0VYfqsvdmXOCarCyH6yyhcdw74N8KKSJSaoJi14+I+C85OZlG/V6DzR9w/eGfyDuziuvYdrlSSgHOReMsD9pGV5xrtFzmXB9l5Lk0JqTaijEuOH6KRdFR/NrwGto17cO9XZ5xew8RkZKioCJSzlitVt59911OnDjODcYm++jJDe4ujm0EXzzp2Jb4MZz41e293dVHmVs9lp4XM+0nId+bcYF7b3lJoygiUiY09SNS1pI3wfaFtt/9dPLkSaZMmXJ5h5yJbbiv4gzYtjKbw9y/d+o3t83ezu1xuK9CioiUEY2oOAnB/QGESnRSIopxds+qVatYu3at/XUdI4XH+dD9xXe9bVvDcjkMJUaEkxQWSkLuJfvIiDv283mc2xN6wNV3qdqsiJQ5BRWRslLEs3usViuzZ88mJSXF3tatQ3N6bH3D87PyR1IadWbq1TcwN/eY/a2Ca06cWbJzGBl1NXMv7LG3jUq4A8utr3p+lohIKVJQceJuNMVbu4jPPJ3ds3eF16CyaNEie0gJDQ3l0UcfpW7iDO/PulxmPzEl0SGkgOuaE7vuE6FFbyY06kzPlESS0pNIiEnAUtvi/VkiIqVIQUWkrHg6u2fNFLiUdWUKyGkr8b333svevXupVasWo0aNwnx8q8cdOwBYBtnrpCTtXez2kqSwUMegctME6DHpyi1qWxRQRCQoKKiIlBV3Z/fky58C2vkl1vXT+DeDGchE6tw0HHPvyfzlL3/BbL688Xiv51ONAUhcaKuPkrKLhIhwaFDP5RKHtSj561lERIKQ1oiKlKXek21TLO7sXcGR9R/xMk9z3FSfOQzFun4aJG+6ElIA0o+5/3xBKbuAy2tOzjmuRxl1Ls1xNMXTziARkSCgERWRstait226x8k3mw+ygYfsZfDrcnnx7Jl9jmtYLqS4fNabCalp9LyY6XnXj6cpKRGRIKCgIlLWnKaArMD0iD+SmhFqDym9WcONbLFdXzBIrHgB9izz+5GW7Bz325JVE0VEgpyCikgg9J4MrQdweHciH6xPJi/HABOEGTmM5j/UIN12XYs+V4KEu+3NxaG1KSJSDmiNioivilFR1q1GnaFFL/IunyLe2DjC87x9JaQANLj2yvMKW0TrTe1Wjq9vmqCQIiLlgkZURHxRjIqyzqxJGzCfOwg1m9O4cWduvvlmqlWrxvVpX8F6p4vXTLH9umk8hFYpYueBmyfYppCcT1AWEQlyCipOzCawGu7bpZIqYkVZd/Z/8gILfjeI5ygjeAJuGk/P1gNsAaL1ANuvvStcF9uun2abqvGm7jVQrS7s+871vfxwooAiIuWMgooTdyHFW7tUAp4qyjrvxinE5wv+zbY9JjCFkGTEk0ZVYtdPcx2pqdPa/Q3MYdCwExzd7P79AdNs/Vn0uO2EZPs9tWBWRMovBRWRwnjavuvjtt6cnBymT59Oenq6fVdPf74llouuF3sbObHmeg4pADu/tAWSe9+B6x/XNI+IVAgKKiKFcVdR1sdRij179rBw4UKMywtmqxiZjOYD9yEl384vXdssg9y3F1RwOkrTPCJSQSioiPji8nZif0Ypjh8/zkcffWR/3axZM4bW3QvrvYQUgL3LXdsSF/rWTz+no0REgp2Cioiv/BylqG89SnQVMxlZVu6++246dOhQ8rVQnKnKrIhUMAoqIiVo586dGIZBm6Mfw/pp/BEzOYQTnZIHdIDPRpXew7VoVkQqIAUVkRLy6aef8vvvv2MC/mzMIBIIx0o4mbZRlJBQOHeodB7efSL0mFQ69xYRCSAFFZFiyszM5O233+bixfy1JwYnqE0TjjpeeGRD6XWiRe/Su7eISAApqDgxAe5Kpqjem7izY8cOFi9ebN/VU7VKOE9mvkEkbg4AjO8Ch35wbW8/BLbPd22/dpjt97P7Icm5ZG0BlkGa8hGRCktBRaSIFi5cyO7du+2v27Rpwx+utsJiNyGlRR/o+Vc4sMqxFkrDznDPDDAuORZpA9j6H9vvlgc9d8IyCO6dXYyvQkQkuCmoOPFUgFaFaaWgnJwce0gxmUz84Q9/oHXr1p4PLOz+nO33x76Hlf+wTQPFd7GFlxUvuIaUghI/toWVgte06GO7p0ZSRKSCU1ARKYLw8HDuvvtuVq1axei7uxB5fjskXyi8OFzBww0P/QBpR7yHlHzNblO1WRGplBRURHw0790ZpJ47xx8H3Q6NOtOhQwc6pCyG//S7cpHlQVsJe+ficMmbbIcNOtdQ8SWkgA4VFJFKS0FFpBBpaWnMemsqWVbbOT0r3/0bPW+6zhZGPAWPe99xP4pSFKqPIiKVmIKKiBebN29m6dKlgC2kxHCeW/gZ1q+Hi2fdfyjxY9s0Tf5Iir8h5aYJ0Lq/pnlERFBQEfHogw8+4NChQ7YXhkEHdnA33125INNDUIErZ+6c2ef7A6+6BXr9/UowUUAREVFQEXHntddeIzMzE4AQDB7ivzTjsONFV/eFXUvd38Caa/vdn7N3LA8qnIiIOAkJdAdEglGtWrUAqB4dyV+Mf7mGFMsg6PiwbZuwO+Yw2+/5u4AK07Cz7X4iIuJAQUUEsFqtV6Z5gOHDh9O3b1+e7tWYcKyuH2jWw/Z7fn0UlxvmwvaFtjUqvSfDoytt5/G4c8uf4LGVxfsCREQqKE39SKV39uxZZs2aRW5uLqNGjaJRo0aYzWa6dOkCyWb3H8qf0nFXN6VhZ/jiySuvbxpvCyue1qvUalECX4WISMWkERWp1H788UfeeustcnNta0p++MHpLB53UzfO24XzR0zumQ13vQ1HnarTrp9mG1nxtF7Fn3UsIiKVjEZUpFKyWq3MnTuXY8eO2du6dOlC3759XS/uPdm1gJuz/GJs2xe6f+CZfdB+kPeqtSIi4kJBRSqdlJQU3nnnHS5dugRASEgII0aMID4+3vOHfK0KW9ioiS+hR0RE7DT148TkZ7uUP++99549pNSsWZPnn3+eeNPJK4tfPUneVPg1vkwVNepsG11RSBERKZRGVJyEmMDq5qjkECWVCuPhhx9mzpw53HjjjfTq1cu1xH3+4teCfLkmn0ZNRERKjEZUnHgKJAoq5dfJkyeZOXMmVqttm3H9+vX529/+Zgsp7krc5y9+zefLNc40aiIiUiIUVJzk5vnXLsFt1apVzJo1i1OnTjF37lzXCzxtGd4670oQ8XSNP+XxRUSkSDT1IxWS1Wpl9uzZpKSk2NuaN3ez0NXT4tfN79l+3TTe8zX5ZfJFRKTUaERFKpxjx47xyiuv2ENKaGgoo0ePpkePHq4XF1bifv00SEt2/15+mXwRESk1GlGRCmXlypWsW7fO/rpevXo8+uijmM0eKszClcWvW+fZRlF8pUJtIiKlTkFFKpTs7Gz7n3v06EG3bt18+2D+old3QaVFb7iU5bqgdueXWiwrIlLKNPUj5V7+bh6AO+64g5YtWzJ27FjfQ0o+bzVQWg9wvb6wnT8iIlJsGlFxEgK42+CjRBecvvnmGzZs2ED//v3p1KkTAIMGDSr6DT3VQPG280ejKiIipUZBxYmnXcjanRxcrFYr06dPJzU1FbAFlvygUmzuyuXrQEERkYDQQIGUOwcPHuTll1+2h5SwsDDGjBlTug/1pTS+iIiUOI2oSLny1VdfsWnTlXUh8fHxDB8+3PuunpKi0vgiImVOQUXKjS+++IKtW7faX/ft25cuXbpcuSB5U+mHCF9PURYRkRKhoCLlRu/evdm2bRthYWGMHj2auLi4K2/6c2igiIiUGwoqUrqKOcqxfPlyunXrRmRkJJFnfuPp3lcRG98GCoYUT4cGZqRA2mGI7wI9/1qsL0NERAJDQUVKTzFGOXJycpg+fTrp6ens2LGDP7U/D+unEevuXp62Dm+fb/v90A+w9UP40x7/vwYREQko7fqR0uFplMOHAml79uxhypQppKenA2DNzcbq7V6+bBHOOAkr/1H4dSIiElQUVJx4+oboG+UnbwXSvFi0aBEfffQRhmEA0KxZM/5yRzPc7unJv1dhBwvmO7Kh8GtERCSoaOrHSVzVMM5czHXbLn7ws0BaZmYmM2bMICMjw9521113ce2113oehSl4r4Jbhw+svTLtU1B8F9c2EREJahoocFK/eqRf7eKBnwXS9u3bZw8pkZGRPPvss7aQ4s+9GnWG9oPgnhkQXdfxveh6WlArIlIOaUTFSa7VfbF8T+3ihR8F0q655hp+/fVXAAYPHlysewG2hbMr/2Gb7tGuHxGRcstk5C8GKIfS09OJjY0lLS2NmJiYErlni//5mlyr67ckzGxi70t3lMgzxDbVM336dFq2bMmAAW5OJhYRkQrLn5/fmvpx4i6keGsX/+3YsYPXX3+dCxcusGXLFvuZPSIiIs409eMkwmwi200oiTCbAtCbimfhwoXs3r3b/rp169aOFWZFREQKUFBxYg4NAavVfbsUWUZGBjNmzCAzMxMAk8nE/fffT5s2bQLcMxERCWYKKk4uZruGFG/tUriUlBRmzJhhfx0dHc3YsWOJjNROKhER8U5BRUpdjRo1CAsLIzc3l3bt2nHfffcFuksiIlJOKKhIqcjIyODixYvUqVMHs9nM448/ztmzZ7n66qsD3TURESlHArrwYu3atQwYMIAGDRpgMplYsmRJILsjJWTz5s3885//5J133sF6eb1PrVq1FFJERMRvAQ0qFy5coH379kyfPj2Q3ZAS9MEHH7B06VIArFYru3btCnCPRESkPAvo1E+/fv3o169fILvgomXdaHafzHDbLp6lpaUxY8YMcnJyAAgJCeGhhx6iWbNmAe6ZiEjJs1qt5Oa6ngsnNmFhYZjNbo+T9ZvWqDg5ei7Tr/ZKKXmTQyn7X375hWXLltnfjo2NZezYsYSHhwewkyIiJc8wDE6cOMG5c+cC3ZWgV716derVq4fJVLw6ZOUqqGRnZ5OdnW1/nZ6eHsDeVFIrXoD10+wvrTeMZ9mGKzOInTp1on///gHomIhI6csPKXXq1KFq1arF/iFcERmGwcWLFzl16hQA9evXL9b9ylVQeeWVV5g8eXKpPiPDQ70UT+2VSvImh5ACYP55Gjd3mM6POw4ydOhQmjRpEpi+iYiUMqvVag8pNWvWDHR3glp+naxTp07Zd38WVbkqtzpp0iTS0tLsv44cORLoLlUuZ/YB8BPXsoC77c09m4Ty17/+VSFFRCq0/DUpVatWDXBPyof871Nx1/KUqxGViIgIIiIiAt2NSstavQnvMYij2IbxfqQjN7LFtlZFRKSS0HSPb0rq+xTQoJKRkcG+ffvsrw8ePMi2bduoUaMGjRs3Dkifrkuozsakc27bK7OUlBTmzF9JrqkBACGGlUYcg5smQKPOAe6diIhUVAENKps2baJHjx7218888wwAw4cP5/333w9MpzwlwEqcoH/44Qe+//57++uasVGM6VYfc535CikiIlKqArpG5dZbb8UwDJdfAQspwKHTF/xqr+jmzJnjEFK6du3Kk+P/hLnjEIUUEZFyYsSIEQwcONClffXq1ZhMJp+2WycmJnLLLbdQpUoV4uPjee2110q+o26UqzUqZeF89iW/2iu6ixcvAmA2mxk5ciQNGjQIcI9ERKSspaenc/vtt9OrVy9mzZrFjh07GDlyJNWrV+fxxx8v1WcrqDipEhpCVm6e2/bKIicnx16sbcyYMXzyyScMHjy4xKoMiohI+TJ//nxycnKYO3cu4eHhtG3blm3btvHGG2+UelCpPD99fdSzdV2/2isSq9XKjBkzmDJlChkZtmMEwsPDGTp0qPuQkrwJti+0/S4iIj7bejiVRVuS2Xo4NdBd8clPP/1Et27dHCqO9+nTh927d5OaWrpfg0ZUnAy9IYH/bjnqtr0iO3bsGHPnzrWfdrxw4UIeffRRzx9wqlDLTeOhd+kW4xMRqQimLNvJrDUH7K9Hd2/KxH6tS/25S5cuJTra8dy6/P/mF+bEiRMutbLq1q1rfy8uLq5kOumGRlScLPzlsF/tFcHKlSuZM2eO/X+w9erV45FHHvH8ATcValk/TSMrIiKF2Ho41SGkAMxac6BMRlZ69OjBtm3bHH69++67pf7c4tKIipPUizl+tZdnVquVmTNncubMGXvbrbfeSvfu3b1/8Mw+z+3aCSQi4tFBDztID56+wLWNS29UAiAqKormzR0LdCYnJ/v02Xr16nHy5EmHtvzX9erVK5kOeqARFSct6lbzq708e/PNN+0hJTQ0lLFjxxYeUsBzJVpVqBUR8apJrSi/2oNF165dWbt2rUM5/BUrVtCyZctSnfYBBRUXp89n+9VenvXt2xeABg0aMHHiRGrXru3bBxt1tq1JKUgVakVECnVt4zhGd2/q0Dame9NSH00proceeojw8HBGjRrFb7/9xscff8ybb75pL9RamjT14+SXQ2f9ai9PrFYry5Yto3///gC0adOG8ePHExsb6//Nek+G1gNs0z01myukiIj4aGK/1vRpW4+Dpy/QpFZU0IcUgNjYWL799lvGjRtHp06dqFWrFn/7299KfWsyKKi48FQov7wX0D906BAffvgheXl5ZGVlcf/99wMULaTka9RZAUVEpAiubRxXpgHFU8X3/ArxvrBYLPzwww8l2CvfKKg4ubZxHAdOX3TbXl59/fXXbNy40f46v9qsiIhIsNMaFSc3Na/lV3swy8nJYdq0aQ4hpW/fvgwbNiyAvRIRkWDTr18/oqOj3f56+eWXA9o3jag4mfdzksf2ezs2KuPeFN3BgweZN28eeXm24wDCw8MZPXp0qa/OFhGR8ufdd98lMzPT7Xs1atQo4944UlBxsvfkeb/ag9WPP/5oDykJCQmMGDEisB0SEZGg1bBhw0B3wSNN/TiJjnCf3Ty1B6shQ4YQFxfHnXfeqZAiIiLlloKKkxs9rEXx1B4s9u7dy0svvcTBgwftbU899RSdO2tXjoiIlF8KKk4iQt1/Szy1B4PFixezYMECLl26xPz58wPdHRERkRITvD99A2TBL0f8ag+kzMxM/vnPf5KYmGhvu/POOwPYIxERkZJVvhZeiN2uXbv45JNP7IV6qlSpwrhx41yO8BYRESnPFFTKoVWrVrF27Vr766uvvprBgwcHsEciIiKlQ1M/Tg5NcT914qk9EK655hoATCYT9957r0KKiIh4NWLECAYOHOjSvnr1akwmE+fOnfP6+aysLEaMGME111xDaGio23uVFgUVN5xDSTCElP3792O1WgGoVasW999/P88884w9tIiIiJQWq9VKZGQkTz31FL169SrTZ2vqx4PFY2+0n2wZaAsXLmT37t3UqVOHMWPGANC2bdsA90pERCqLqKgoZs6cCcD69esLHYEpSQoqbkxZtpNZaw7YX4/u3pSJ/VqXeT8yMjKYMWOGvaxxSkoKVqsVs9lc5n0REZESlLwJzuyDms11Cn0hFFScbD2c6hBSAGatOUCftvXK9ATlxMRElixZYt/VExUVxbhx4xRSRETKuxUvwPppV17fNB56Ty71xy5dutRlZ2j+koJgpqDi5ODpCx7byyqozJ8/n3379tlft23blvvvv79Mni0iIqUoeZNjSAHb69YDSn1kpUePHvbpm3wbNmxg6NChpfrc4lJQcZJrzfOrvaTt2LHDHlJMJhODBg3i6quvLpNni4hIKTuzz3N7KQeVqKgomjdv7tCWnJxcqs8sCQoqTsLM7jdCeWovaddccw1r164lOzubJ598kvDw8DJ5roiIlIGazf1rFwUVZ552+ZTm7p8PP/yQ5s2b07VrVwDGjRtXas8SEZEAatTZtibFYY3KhHKxoPb3338nJyeHs2fPcv78ebZt2wZAhw4dSvW5CipOrm0cx+juTR0W1I7p3rRU1qekpaUxc+ZMsrOzOXDgAK1atSIuruwW7IqISAD0nmxbk1LOdv3ccccdJCUl2V9fe+21APZNH6VFQcWN/25xnLP7bEsyfynh7cm//PILy5Yts7+OiYkhKirwNVtERKQMNOpcpgHl/fffd9t+6623+hw0Dh06VHId8oOCipPXl+8i5XyOQ1vK+RxeX76LP/dpVSLPeO+99zh8+LD9dceOHRkwYECJ3FtERKQiUQl9J1uSUv1q90daWhqvvPKKPaSEhIQwbNgwhRQREQmofv36ER0d7fbXyy+/HNC+aUTFSceEOH46cNZte3FFRkZy6dIlAKpXr86YMWO0q0dERALu3XfftVdBd1ajRo0y7o0jBRUnf+7TirnrDpKZe6VuSmRYSJGnfaxWK1arlfDwcMLDwxk8eDB79+6lX79+JdVlERGRYmnYsGGgu+CRgoqTrYdTHUIKQGZuHlsPp/q98+f06dO88847hIaG8txzzwHQvHlzl4I7IiIi4p7WqDjxVkLfHz/88APTp08nNzeXzMxMtm7dWhLdExERqVQ0ouKkuAXfrFYr//73vzl+/Li97YYbbrDvNxcRERHfKag4KU7Bt1OnTjFnzhz7glmz2cyIESNo1KhRqfVXRESkItPUjxsFQwrATKfX7litVmbNmmUPKbVr12bSpEkKKSIiIsWgoOKk22vf+9Wez2w207JlSwBuvvlmxo4di9lsLvH+iYiIVCYKKk6Op7nfR+6u/fjx43z//ZUA8+CDD/Lss8/Ss2fPUuufiIiIv0aMGMHAgQNd2levXo3JZOLcuXNeP7969Wruvvtu6tevT1RUFB06dGD+/Pml01knWqPipH5sJIfPuoaS+rGRDq9XrlzJunXrAGjUqBFXX301ANHR0aXfSRERkTL0448/YrFY+Mtf/kLdunVZunQpw4YNIzY2lv79+5fqsxVUnKx97jaumviV23a4shbl9OnT9vfOnDlTZv0TEREpa88//7zD66effppvv/2WRYsWlXpQ0dSPG4em3EnjGpGEmaFxjUgOTbkTgOTkZF555RV7SAkNDWXMmDF07do1kN0VEZFyJjElkS/3f0liSmKgu1JkaWlpZVJeXyMqHuSPoORbvnw5P//8s/11gwYNGDlypBbMioiIX6Zumsrc3+baX49sO5IJnSeU+nOXLl3qsjzBarUW6V6ffPIJGzduZPbs2SXRNa8UVHy0bds2+5979uzJzTffHLjOiIhIuZSYkugQUgDm/jaXngk9sdS2lOqze/TowcyZMx3aNmzYwNChQ/26z6pVq3jkkUeYM2cObdu2LckuuqWg4sHry3exJSmVjglx/LlPK0aPHs27777L8OHDqVWrVqC7JyIi5VBSepLH9tIOKlFRUS5nzSUnJ/t1jzVr1jBgwACmTp3KsGHDSrJ7HimouHHdSytokrmXFqFnmH6gPZ9sOsLG/+nNs88+G+iuiYhIOZYQk+BXezBZvXo1/fv359VXX+Xxxx8vs+dqMa2TKV//SrecTbQJTSHclEf/8N2knM/h9eW7At01EREp5yy1LYxsO9KhbVS7UaU+mlJcq1at4s477+Spp57ivvvu48SJE5w4cYKzZ8+W+rM1olLAwYMHydq4iJgQA4AcI4RVOU0B2JKUGsiuiYhIBTGh8wR6JvQkKT2JhJiEoA8pAB988AEXL17klVde4ZVXXrG3d+/endWrV5fqs02GYRil+oRSlJ6eTmxsLGlpacTExBTrXl9++SVbtmwBwDDgRF403+S0sr8/rkcz/tynlaePi4hIBZeVlcXBgwdp0qQJVapUCXR3gp6375c/P781ogLMnj2bEydO2F/vCGnC5qya9td1qoUrpIiIiASA1qgAbdq0ASAiIoLx48fz378NY1yPZnRtWoNxPZrxy//0DnAPRURESk+/fv2Ijo52++vll18OaN8q7YjK3r17adGiBQC33HIL1apVo0OHDvb3NYIiIiKVxbvvvktmpvtDecui+qw3lS6o5OTk8NZbb5GRkUH37t259dZbARxCioiISGXSsGHDQHfBo0o19bNr1y6mTJlCRkYGANu3bw9wj0RERMSbSjOi8tlnn/Hbb7/ZX7do0YKHHnoogD0SEZHyqBxvli1TJfV9qvBBJTMzk+nTp3PhwgUATCYTAwcOxGIJ/n3rIiISPMLCwgC4ePEikZGRAe5N8Lt48SJw5ftWVBU+qCxcuNAeUiIjIxk7dqzL6ZEiIiKFMZvNVK9enVOnTgFQtWpVTCZTgHsVfAzD4OLFi5w6dYrq1atjNpuLdb8KH1SGDRvGq6++StOmTRk0aFCguyMiIuVYvXr1AOxhRTyrXr26/ftVHBWuMm1GRgZz587l4YcfJi4uLsA9FBGRishqtZKbmxvobgStsLAwryMplbYybWJiIkuWLMEwDGbNmsWkSZMC3SUREamAzGZzsac0xDcVJqgsWLCAvXv32l/nF3MTERGR8qtCBJWpU6fa/2wymXjggQdo1UqVZUVERMq7ChFUsrKyqFKlCtWqVWPMmDHaNiYiIlJBlOugkr8OODs7m3bt2jFgwAByc3O1wElERCSIpaenA74VhSvXu36Sk5OJj48PdDdERESkCI4cOUKjRo28XlOug0peXh7Hjh2jWrVqJV50Jz09nfj4eI4cOVLo1ikpW/q7CU76ewle+rsJXpX178YwDM6fP0+DBg0ICfF+7GC5nvoJCQkpNIkVV0xMTKX6H095or+b4KS/l+Clv5vgVRn/bmJjY326rlKdniwiIiLli4KKiIiIBC0FFQ8iIiJ44YUXiIiICHRXxIn+boKT/l6Cl/5ugpf+bgpXrhfTioiISMWmERUREREJWgoqIiIiErQUVERERCRoKaiIiIhI0FJQcWP69OlcddVVVKlShS5duvDLL78EuksCrF27lgEDBtCgQQNMJhNLliwJdJcEeOWVV7juuuuoVq0aderUYeDAgezevTvQ3RJg5syZWCwWezGxrl27smzZskB3S5xMmTIFk8nE+PHjA92VoKSg4uTjjz/mmWee4YUXXmDLli20b9+ePn36cOrUqUB3rdK7cOEC7du3Z/r06YHuihSwZs0axo0bx88//8yKFSvIzc3l9ttv58KFC4HuWqXXqFEjpkyZwubNm9m0aRO33XYbd999N7/99luguyaXbdy4kdmzZ2OxWALdlaCl7clOunTpwnXXXcfbb78N2M4Tio+P549//CMTJ04McO8kn8lkYvHixQwcODDQXREnKSkp1KlThzVr1tCtW7dAd0ec1KhRg9dff51Ro0YFuiuVXkZGBh07dmTGjBn87//+Lx06dGDatGmB7lbQ0YhKATk5OWzevJlevXrZ20JCQujVqxc//fRTAHsmUn6kpaUBth+IEjysVisLFy7kwoULdO3aNdDdEWDcuHHceeedDj9zxFW5PpSwpJ0+fRqr1UrdunUd2uvWrcuuXbsC1CuR8iMvL4/x48dz00030a5du0B3R4AdO3bQtWtXsrKyiI6OZvHixbRp0ybQ3ar0Fi5cyJYtW9i4cWOguxL0FFREpMSMGzeOX3/9lXXr1gW6K3JZy5Yt2bZtG2lpaXz22WcMHz6cNWvWKKwE0JEjR3j66adZsWIFVapUCXR3gp6CSgG1atXCbDZz8uRJh/aTJ09Sr169APVKpHx48sknWbp0KWvXrqVRo0aB7o5cFh4eTvPmzQHo1KkTGzdu5M0332T27NkB7lnltXnzZk6dOkXHjh3tbVarlbVr1/L222+TnZ2N2WwOYA+Di9aoFBAeHk6nTp1YuXKlvS0vL4+VK1dqTlfEA8MwePLJJ1m8eDHff/89TZo0CXSXxIu8vDyys7MD3Y1KrWfPnuzYsYNt27bZf3Xu3JkhQ4awbds2hRQnGlFx8swzzzB8+HA6d+7M9ddfz7Rp07hw4QKPPPJIoLtW6WVkZLBv3z7764MHD7Jt2zZq1KhB48aNA9izym3cuHEsWLCAzz//nGrVqnHixAkAYmNjiYyMDHDvKrdJkybRr18/GjduzPnz51mwYAGrV69m+fLlge5apVatWjWXNVxRUVHUrFlTa7vcUFBx8uCDD5KSksLf/vY3Tpw4QYcOHfjmm29cFthK2du0aRM9evSwv37mmWcAGD58OO+//36AeiUzZ84E4NZbb3Vof++99xgxYkTZd0jsTp06xbBhwzh+/DixsbFYLBaWL19O7969A901EZ+pjoqIiIgELa1RERERkaCloCIiIiJBS0FFREREgpaCioiIiAQtBRUREREJWgoqIiIiErQUVERERCRoKaiISEAdOnQIk8nEtm3bivR5k8nEkiVLSrRPIhI8FFREpFSNGDECk8lk/1WzZk369u1LYmIiAPHx8Rw/frzQ0uF///vf6dChQxn0WESCiYKKiJS6vn37cvz4cY4fP87KlSsJDQ2lf//+AJjNZurVq0doqPsTPQzD4NKlS2XZXREJIgoqIlLqIiIiqFevHvXq1aNDhw5MnDiRI0eOkJKS4jL1s3r1akwmE8uWLaNTp05EREQwb948Jk+ezPbt2+0jMwXPdzp9+jT33HMPVatWpUWLFnzxxReB+UJFpMQpqIhImcrIyGDevHk0b96cmjVrerxu4sSJTJkyhZ07d9K7d2+effZZ2rZtax+ZefDBB+3XTp48mQceeIDExETuuOMOhgwZwtmzZ8viyxGRUqbTk0Wk1C1dupTo6GgALly4QP369Vm6dCkhIZ7/rfTiiy86nPIbHR1NaGgo9erVc7l2xIgRDB48GICXX36Zf/3rX/zyyy/07du3hL8SESlrGlERkVLXo0cPtm3bxrZt2/jll1/o06cP/fr1IykpyeNnOnfu7PP9LRaL/c9RUVHExMRw6tSpYvVZRIKDgoqIlLqoqCiaN29O8+bNue6663j33Xe5cOECc+bM8foZX4WFhTm8NplM5OXlFbm/IhI8FFREpMyZTCZCQkLIzMz0+TPh4eFYrdZS7JWIBCOtURGRUpednc2JEycASE1N5e233yYjI4MBAwb4fI+rrrqKgwcPsm3bNho1akS1atWIiIgorS6LSJDQiIqIlLpvvvmG+vXrU79+fbp06cLGjRv59NNPufXWW32+x3333Uffvn3p0aMHtWvX5qOPPiq9DotI0DAZhmEEuhMiIiIi7mhERURERIKWgoqIiIgELQUVERERCVoKKiIiIhK0FFREREQkaCmoiIiISNBSUBEREZGgpaAiIiIiQUtBRURERIKWgoqIiIgELQUVERERCVoKKiIiIhK0/j/XeaCDuoeOIQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "place_cell_diagrams = compute_persistence_diagrams(dataset, maxdim=2, n_threads=-1)\n",
    "plot_persistence_diagrams(place_cell_diagrams)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb5725a2-750d-4663-bfa8-cf2687966234",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Synthetic Grid cell data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a84a86eb-0293-4900-a413-7696abf97dbe",
   "metadata": {},
   "source": [
    "### Generate synthetic grid cell data + compute persistence diagrams"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ebef170-6ea7-4c68-bb4e-6afc8d6d10f4",
   "metadata": {},
   "source": [
    "Orientation variability = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e7084c77-6d8a-48b4-b555-e034577df970",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of neural activity matrix: (2500, 256)\n"
     ]
    }
   ],
   "source": [
    "grid_scale = 1\n",
    "arena_dims = np.array([4, 4])\n",
    "n_cells = 256\n",
    "grid_orientation_mean = 0\n",
    "grid_orientation_std = 0\n",
    "\n",
    "field_width = 0.05\n",
    "resolution = 50\n",
    "\n",
    "neural_activity, _ = gridcells.load_grid_cells_synthetic(\n",
    "    grid_scale,\n",
    "    arena_dims,\n",
    "    n_cells,\n",
    "    grid_orientation_mean,\n",
    "    grid_orientation_std,\n",
    "    field_width,\n",
    "    resolution,\n",
    ")\n",
    "print(\"shape of neural activity matrix: \" + str(neural_activity.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b6394d55-4e61-4f01-b0a8-a2f54957f529",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Function 'compute_persistence_diagrams' executed in 4809.5422s\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diagrams = compute_persistence_diagrams(neural_activity, maxdim=2, n_threads=-1)\n",
    "plot_persistence_diagrams(diagrams)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40d713d8-0275-4900-8701-82941e8710e9",
   "metadata": {},
   "source": [
    "#### Orientation variability > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "005b056d-683b-4ca9-8b57-ae67c6f70944",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of neural activity matrix: (2500, 256)\n"
     ]
    }
   ],
   "source": [
    "grid_scale = 1\n",
    "arena_dims = np.array([4, 4])\n",
    "n_cells = 256\n",
    "grid_orientation_mean = 0\n",
    "grid_orientation_std = 3\n",
    "\n",
    "field_width = 0.05\n",
    "resolution = 50\n",
    "\n",
    "neural_activity, _ = gridcells.load_grid_cells_synthetic(\n",
    "    grid_scale,\n",
    "    arena_dims,\n",
    "    n_cells,\n",
    "    grid_orientation_mean,\n",
    "    grid_orientation_std,\n",
    "    field_width,\n",
    "    resolution,\n",
    ")\n",
    "print(\"shape of neural activity matrix: \" + str(neural_activity.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88866a97",
   "metadata": {},
   "source": [
    "## Shuffle Data and plot diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "dd16d020",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "noise level: 0.71%\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "\n",
    "os.environ[\"GEOMSTATS_BACKEND\"] = \"pytorch\"\n",
    "import geomstats.backend as gs\n",
    "\n",
    "import neurometry.datasets.synthetic as synthetic\n",
    "\n",
    "task_points = synthetic.hypersphere(1, 1000)\n",
    "noisy_points, manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=task_points,\n",
    "    encoding_dim=3,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.array([1, 1, 1]),\n",
    "    poisson_multiplier=100,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "874bd10a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting dreimac\n",
      "  Downloading dreimac-0.3.1-py3-none-any.whl.metadata (6.2 kB)\n",
      "Requirement already satisfied: matplotlib>=3.6 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from dreimac) (3.8.4)\n",
      "Requirement already satisfied: numba>=0.56 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from dreimac) (0.59.1)\n",
      "Requirement already satisfied: numpy>=1.23 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from dreimac) (1.26.4)\n",
      "Requirement already satisfied: persim>=0.3 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from dreimac) (0.3.5)\n",
      "Requirement already satisfied: ripser>=0.6 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from dreimac) (0.6.8)\n",
      "Requirement already satisfied: scipy>=1.10 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from dreimac) (1.13.0)\n",
      "Requirement already satisfied: contourpy>=1.0.1 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from matplotlib>=3.6->dreimac) (1.2.1)\n",
      "Requirement already satisfied: cycler>=0.10 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from matplotlib>=3.6->dreimac) (0.12.1)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from matplotlib>=3.6->dreimac) (4.51.0)\n",
      "Requirement already satisfied: kiwisolver>=1.3.1 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from matplotlib>=3.6->dreimac) (1.4.5)\n",
      "Requirement already satisfied: packaging>=20.0 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from matplotlib>=3.6->dreimac) (24.0)\n",
      "Requirement already satisfied: pillow>=8 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from matplotlib>=3.6->dreimac) (10.3.0)\n",
      "Requirement already satisfied: pyparsing>=2.3.1 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from matplotlib>=3.6->dreimac) (3.1.2)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from matplotlib>=3.6->dreimac) (2.9.0.post0)\n",
      "Requirement already satisfied: llvmlite<0.43,>=0.42.0dev0 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from numba>=0.56->dreimac) (0.42.0)\n",
      "Requirement already satisfied: scikit-learn in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from persim>=0.3->dreimac) (1.4.2)\n",
      "Requirement already satisfied: hopcroftkarp in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from persim>=0.3->dreimac) (1.2.5)\n",
      "Requirement already satisfied: deprecated in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from persim>=0.3->dreimac) (1.2.14)\n",
      "Requirement already satisfied: joblib in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from persim>=0.3->dreimac) (1.4.0)\n",
      "Requirement already satisfied: Cython in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from ripser>=0.6->dreimac) (0.29.37)\n",
      "Requirement already satisfied: six>=1.5 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from python-dateutil>=2.7->matplotlib>=3.6->dreimac) (1.16.0)\n",
      "Requirement already satisfied: wrapt<2,>=1.10 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from deprecated->persim>=0.3->dreimac) (1.16.0)\n",
      "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/facosta/miniconda3/envs/neurometry/lib/python3.11/site-packages (from scikit-learn->persim>=0.3->dreimac) (3.4.0)\n",
      "Downloading dreimac-0.3.1-py3-none-any.whl (36 kB)\n",
      "Installing collected packages: dreimac\n",
      "Successfully installed dreimac-0.3.1\n"
     ]
    }
   ],
   "source": [
    "!pip install dreimac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "2ecb451f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from dreimac import CircularCoords\n",
    "from persim import plot_diagrams\n",
    "\n",
    "# prepare plot with 4 subplots\n",
    "f, (a0, a1, a2, a3) = plt.subplots(1, 4, width_ratios=[1, 1, 1, 0.2], figsize=(14, 3))\n",
    "\n",
    "\n",
    "# plot the persistence diagram, showing a single prominent class\n",
    "cc = CircularCoords(X, n_landmarks=200)\n",
    "plot_diagrams(cc._dgms, title=\"Persistence diagram\", ax=a1)\n",
    "\n",
    "# plot the data colored by the circle-valued map constructed by DREiMac\n",
    "circular_coordinates = cc.get_coordinates()\n",
    "a2.scatter(X[:, 0], X[:, 1], c=circular_coordinates, s=10, cmap=\"viridis\")\n",
    "a2.set_title(\"Input colored by circular coordinate\")\n",
    "a2.axis(\"off\")\n",
    "a2.set_aspect(\"equal\")\n",
    "\n",
    "# plot colorbar\n",
    "img = a3.imshow([[0, 1]], cmap=\"viridis\")\n",
    "a3.set_visible(False)\n",
    "cb = plt.colorbar(mappable=img, ticks=[0, 0.5, 1])\n",
    "_ = cb.ax.set_yticklabels([\"0\", \"180\", \"360\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "38ebb291",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "marker": {
          "size": 3
         },
         "mode": "markers",
         "type": "scatter3d",
         "x": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot in 3d\n",
    "fig = go.Figure()\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=task_points[:, 0],\n",
    "        y=task_points[:, 1],\n",
    "        z=noisy_points[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "c8210194",
   "metadata": {},
   "outputs": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = noisy_points\n",
    "\n",
    "\n",
    "def shuffle_entries(data):\n",
    "    # Shuffle each row's entries independently\n",
    "    shuffled_data = np.apply_along_axis(np.random.permutation, 1, data)\n",
    "    return shuffled_data\n",
    "\n",
    "\n",
    "X_shuffled_1 = shuffle_entries(X)\n",
    "X_shuffled_2 = shuffle_entries(X)\n",
    "\n",
    "fig = go.Figure()\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=X_shuffled_1[:, 0],\n",
    "        y=X_shuffled_1[:, 1],\n",
    "        z=X_shuffled_1[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=X_shuffled_2[:, 0],\n",
    "        y=X_shuffled_2[:, 1],\n",
    "        z=X_shuffled_2[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "c64bdf1a",
   "metadata": {},
   "outputs": [
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   "source": [
    "rng = np.random.default_rng()\n",
    "\n",
    "# n_permutations = 10\n",
    "\n",
    "X_shuff_1 = rng.permutation(X, axis=0)\n",
    "X_shuff_2 = rng.permutation(X, axis=0)\n",
    "\n",
    "fig = go.Figure()\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=X_shuff_1[:, 0],\n",
    "        y=X_shuff_1[:, 1],\n",
    "        z=X_shuff_1[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=X_shuff_2[:, 0],\n",
    "        y=X_shuff_2[:, 1],\n",
    "        z=X_shuff_2[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "596234bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING! Poisson spikes not generated: mean must be non-negative\n",
      "noise level: 7.07%\n"
     ]
    }
   ],
   "source": [
    "from neurometry.datasets.synthetic import hypertorus, synthetic_neural_manifold\n",
    "\n",
    "num_points = 1000\n",
    "intrinsic_dim = 2\n",
    "encoding_dim = 1000\n",
    "\n",
    "torus_points = hypertorus(intrinsic_dim, num_points)\n",
    "\n",
    "noisy, manifold = synthetic_neural_manifold(torus_points, encoding_dim, \"linear\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "b32ab473",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1000, 1000])\n"
     ]
    },
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     "metadata": {},
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   ],
   "source": [
    "print(manifold.shape)\n",
    "\n",
    "from neurometry.topology.persistent_homology import compute_persistence_diagrams\n",
    "\n",
    "diagrams = compute_persistence_diagrams([manifold])\n",
    "\n",
    "plot_diagram(diagrams[0], homology_dimensions=(0, 1, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "165700d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1000, 1000])\n"
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   "source": [
    "transposed_manifold = manifold.T\n",
    "print(transposed_manifold.shape)\n",
    "transposed_diagrams = compute_persistence_diagrams([transposed_manifold])\n",
    "\n",
    "plot_diagram(transposed_diagrams[0], homology_dimensions=(0, 1, 2))"
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  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "ae84fc1a",
   "metadata": {},
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   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=10)\n",
    "pca_manifold = pca.fit_transform(manifold)\n",
    "\n",
    "pca_diagrams = compute_persistence_diagrams([pca_manifold])\n",
    "\n",
    "plot_diagram(pca_diagrams[0], homology_dimensions=(0, 1, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "4fb5eb01",
   "metadata": {},
   "outputs": [
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   "source": [
    "pca_transposed_manifold = pca.fit_transform(transposed_manifold)\n",
    "\n",
    "pca_transposed_diagrams = compute_persistence_diagrams([pca_transposed_manifold])\n",
    "\n",
    "plot_diagram(pca_transposed_diagrams[0], homology_dimensions=(0, 1, 2))"
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   "execution_count": null,
   "id": "2f1ca640",
   "metadata": {},
   "outputs": [],
   "source": []
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