PHATE_COMPARISON.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_yYG_wtgjy9r"
      },
      "source": [
        "### Mounting Google Drive"
      ],
      "id": "_yYG_wtgjy9r"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "K6Ek3B4sj6by"
      },
      "outputs": [],
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "id": "K6Ek3B4sj6by"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lPFyLmXUj3ZF",
        "outputId": "5b102c25-b876-462a-a3e0-e50d6abccfd5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "/content/drive/Othercomputers/My Laptop (1)/MY COLLEGE/ISI KOLKATA/PROJECTS/IIT J Summer Internship 2022/Code/Neural-Uncertainty-Representation\n"
          ]
        }
      ],
      "source": [
        "cd 'drive/Othercomputers/My Laptop (1)/MY COLLEGE/ISI KOLKATA/PROJECTS/IIT J Summer Internship 2022/Code/Neural-Uncertainty-Representation/'"
      ],
      "id": "lPFyLmXUj3ZF"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Rw-EyKzPkViE",
        "outputId": "4fb26f74-c0c3-4e58-dc5f-ae2b218f2a7e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Data-Prep.R                              old_data.npy           T-PHATE.ipynb\n",
            "Helper-Functions.R                       PHATE.ipynb            VC_voxel.xlsx\n",
            "l_OFC_voxel.xlsx                         \u001b[0m\u001b[01;34mPlots\u001b[0m/                 Whole_BOLD.xlsx\n",
            "m_OFC_voxel.xlsx                         README.md              \u001b[01;34mYOUNG\u001b[0m/\n",
            "Neural-Uncertainty-Representation.Rproj  SLR-Comp-ROIs.R        young_data.npy\n",
            "\u001b[01;34mOLD\u001b[0m/                                     Temporal_ratings.xlsx\n"
          ]
        }
      ],
      "source": [
        "ls"
      ],
      "id": "Rw-EyKzPkViE"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f2a2530a"
      },
      "source": [
        "### Importing necessary libraries"
      ],
      "id": "f2a2530a"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GRBjr6nzlQGL"
      },
      "outputs": [],
      "source": [
        "!pip install phate\n",
        "!pip install scprep"
      ],
      "id": "GRBjr6nzlQGL"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3d611e24"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import phate as ph\n",
        "import pandas as pd\n",
        "import scprep as scp\n",
        "import matplotlib.pyplot as plt"
      ],
      "id": "3d611e24"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ce7d26b2"
      },
      "outputs": [],
      "source": [
        "np.random.seed(1)"
      ],
      "id": "ce7d26b2"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d8f4f0ea"
      },
      "source": [
        "### Importing the data"
      ],
      "id": "d8f4f0ea"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b73c2281"
      },
      "source": [
        "We import the lOFC BOLD data for the young subjects"
      ],
      "id": "b73c2281"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "567d90b1"
      },
      "outputs": [],
      "source": [
        "data = pd.read_excel(r\"YOUNG/lOFC.xlsx\", header=None, engine='openpyxl', sheet_name=1)"
      ],
      "id": "567d90b1"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5d7981f2"
      },
      "source": [
        "Below we see the Voxel-Wise lOFC data for the $1^{st}$ young subject."
      ],
      "id": "5d7981f2"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "fc672962",
        "outputId": "cb6af789-72bd-433c-a727-fd308bd6a918"
      },
      "outputs": [
        {
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              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b6c6ea6d-cf4b-4426-a44b-7baf77d540a1');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "             0           1           2           3           4           5    \\\n",
              "0     107.251020  107.251020  106.781308  106.311595  106.155024  106.937878   \n",
              "1      76.406566   76.093425   75.936854   75.467141   75.310570   76.563137   \n",
              "2      76.876279   76.563137   76.719708   76.249995   76.093425   77.189420   \n",
              "3      75.936854   75.467141   75.780283   75.310570   74.684287   76.093425   \n",
              "4      80.320837   80.164266   80.164266   79.537983   79.224841   80.477408   \n",
              "...          ...         ...         ...         ...         ...         ...   \n",
              "1695  170.975349  170.975349  170.349066  170.662207  170.975349  169.409641   \n",
              "1696  165.025657  165.025657  164.399374  164.712516  164.712516  163.773091   \n",
              "1697  158.762824  158.762824  158.136541  158.136541  158.449682  157.823399   \n",
              "1698  164.712516  165.025657  164.399374  164.712516  164.712516  163.773091   \n",
              "1699  160.954816  160.954816  160.641674  160.641674  160.641674  160.015391   \n",
              "\n",
              "             6           7           8           9    ...         179  \\\n",
              "0     105.528741  105.372170  105.215599  105.372170  ...  102.867037   \n",
              "1      75.310570   75.310570   75.154000   75.780283  ...   71.866012   \n",
              "2      76.249995   75.936854   75.780283   76.406566  ...   72.492295   \n",
              "3      75.310570   74.997429   74.527716   75.467141  ...   70.926587   \n",
              "4      79.694554   79.537983   79.068270   79.851124  ...   76.249995   \n",
              "...          ...         ...         ...         ...  ...         ...   \n",
              "1695  169.409641  169.096499  169.722782  170.035924  ...  170.975349   \n",
              "1696  163.459949  163.459949  164.086232  164.086232  ...  165.025657   \n",
              "1697  157.510257  157.197116  157.823399  158.136541  ...  158.762824   \n",
              "1698  163.459949  164.086232  164.399374  164.399374  ...  165.965082   \n",
              "1699  159.702249  159.702249  160.328532  160.328532  ...  161.581099   \n",
              "\n",
              "             180         181         182         183         184         185  \\\n",
              "0     103.963033  104.119603  105.059028  104.432745  104.745887  105.059028   \n",
              "1      74.058004   73.588291   74.527716   74.214575   74.527716   74.840858   \n",
              "2      74.840858   74.058004   75.154000   74.840858   75.310570   75.780283   \n",
              "3      73.431720   72.648866   73.744862   73.118579   73.901433   74.214575   \n",
              "4      78.755129   77.972274   78.911699   78.441987   79.068270   79.381412   \n",
              "...          ...         ...         ...         ...         ...         ...   \n",
              "1695  171.288491  171.288491  171.914774  171.288491  170.975349  170.035924   \n",
              "1696  165.338799  165.338799  165.965082  165.338799  165.025657  164.399374   \n",
              "1697  159.075966  159.075966  159.389107  158.762824  159.075966  158.762824   \n",
              "1698  165.965082  166.278224  165.965082  165.965082  165.338799  164.712516   \n",
              "1699  161.581099  161.894241  161.581099  161.581099  161.267957  160.954816   \n",
              "\n",
              "             186         187         188  \n",
              "0     104.119603  104.119603  105.685312  \n",
              "1      74.371145   73.901433   75.154000  \n",
              "2      75.154000   74.527716   75.936854  \n",
              "3      73.744862   73.275150   74.214575  \n",
              "4      79.068270   78.285416   79.537983  \n",
              "...          ...         ...         ...  \n",
              "1695  170.662207  170.975349  170.662207  \n",
              "1696  164.712516  165.338799  165.338799  \n",
              "1697  158.762824  158.762824  159.075966  \n",
              "1698  165.338799  165.651941  165.338799  \n",
              "1699  160.954816  161.267957  161.267957  \n",
              "\n",
              "[1700 rows x 189 columns]"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data.T"
      ],
      "id": "fc672962"
    },
    {
      "cell_type": "markdown",
      "source": [
        "### One vs One comparison of a young and old subject"
      ],
      "metadata": {
        "id": "g2KRwvpJt5fT"
      },
      "id": "g2KRwvpJt5fT"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ddaae18a"
      },
      "outputs": [],
      "source": [
        "# We now instantiate the PHATE operator(matrix)/object of the PHATE class\n",
        "phate_op = ph.PHATE()"
      ],
      "id": "ddaae18a"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "39c5165f",
        "outputId": "2206db68-9fa6-4cee-f0d8-81268ea0f59e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Calculating PHATE...\n",
            "  Running PHATE on 1700 observations and 189 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.18 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.14 seconds.\n",
            "    Calculating affinities...\n",
            "    Calculated affinities in 0.02 seconds.\n",
            "  Calculated graph and diffusion operator in 0.38 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 23\n",
            "  Calculated optimal t in 2.86 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 2.08 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 4.70 seconds.\n",
            "Calculated PHATE in 10.06 seconds.\n"
          ]
        }
      ],
      "source": [
        "# PHATE requires Voxel x TR Data\n",
        "phate_embd =  phate_op.fit_transform(data.T)"
      ],
      "id": "39c5165f"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 315
        },
        "id": "c6b2f2f5",
        "outputId": "33b7b5ca-92e4-4c97-9b91-79974a717a06"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f2980aae450>"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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LFeJb52RacO2JbXNNmLD1J+kSPnuy16FY8JEPlvDuzyes2998PMi9NQEefa2b3nhIZ3JOdyg6mDvujv4wQgjGZxfpGYqkHTWRC6SbBWUPIZa68yzx1bpKH6GhqBWKqjvYSn2lD5cmHKXuJ3c3xsvDG9MqOuTS5zfxFRfQvCnxPfiKC+iMq0kI4K3n7k8b3rN/d1V3eOPfXeJzm83I4/H+qN/4QCmdAxGrUEQIYVU8FhcIpuaNM6k5ab7WtVohFGsHZaDWIfYcSvKiUeZxOZpgD3z8w7T3h9NW5vUMRamv8tM9FMFb6HIYJ4CPfqiciTndIe9TX+mjIE/jYjyvVOp2MTUXc4SwbiS/tNpkymeZ8kEPH+2wZH+6Bp0ViBIckkSQqEq0bwrWwkKavkIv8bulK92/1ndnGuHx2UWm5oxNy+RsjK89UsvnTvYSiheKHN9Vj6YJNAGb7/LzYlzN3cwFRqfm0aVuPGc4Sok7n/GZBeqr/JyOC+6q3qq1gzJQ64x0vSX2RcPuUV3sC7Pt8AVKbIUPAghW+rg0HCVY6efN3Q1cicyw7SvnrffQREJjDhILl6nKLYSwRkmk6+FZzoKGlSCTVzM6veAYC7IUmmoCSZuCtaNLl/w9LOV3u55HmK53KnUooyGO2zEQZnR6nj/73ntxY+RyFG1Aolm8azDCJ19u5+hjW/j86bct9fi18l2vV5SBWmdkmmKb3FxpygJJjI7/LRvLuXxllOZNG3jj8SA7Xu2iezDCZ74R4viueivck64/Jd3CZd9hJy9YuRrWuh7lRfk0bzKaXOsqfeTnCTr6jbEf4zMLltJ3c43R6Go2C98uY9iX43e7nmdmDmXs6B/B63Y5FEqSjVMyl66MEjz0lnV7LX/X6wVloNYZ6XIoyRxp2YyUkj2nL1s7zeO76i1PZ3R6wZEnGpuJXXP3vFYNzo2SqZn1ejOSlvKbrCeu55mdeKKBoZEpHrB57YClwrGk98DwXtf7d53rKAO1jjBj73ZjY18o04X/7I/LJGGT/Pf1TPL3YP5/8r/Jz8n1sGY2Sf5OhRBUbiimKV4sAakq7mf/5F5+568uptUOLIuHrFVVeu6jDNQ6IZ3xSRbklFI6Qk32KbLJiWW1oC4vysDfOGaxRLDCaOA2tQKbajagaZrDON3zoRIOf3ozIHjwhQtIjAIVU/cvGVVIkRsoA7VOyJTnsBuuxmr7xNVEqCmTcUueIaQuaMVqYZzPRrFEz3CUsZkYR+IVfb7iAsKTs47H57vy+O2v/ojG6gB331nK5ffH0YFnT13i5O6m60YS1DmdHZSBug1JZyzsYbmgTXzUPoU208TVpfRKqQtasZo4w8wBnj3V66jM04SzB6tneBQJjunNAG39kRQv6nYpWrkdUEoStxnplCFMg/XG40HqKo1RFo+93o2u6+w5nZhC21Dltyr60iXxTaUEsyzafA/7tFTzglYoVhK7ysaRllo6B8IpGyhzE1bqdtFU5cv4WqPT8+i67hBETj7fM0mBKVYW5UHdZiTv/swRBe3xCaumSGd7n9FT0m4bfbCoS2tsRrKsUKZeqY7+EaSU1FX6CcXHiqvKKMVqYIaZpZQpRTvRqXmr7Hx8NsbMwqJDwcSkzONi2+ELlJrTn5N6A8s8LmuWWHI1a3KUQIW5lx/lQd1mJO/+ACuEd+nKKHnx66bEk89Gv4dgVWJ0RtdQlODB1rSafGbYz7xo7WKonz9zmZ6hSHzya726OBWrylI0Cy+/P07txvKU+8dmYtb050VpXCtDI1OAkcuyz6Rq7xthx7HOtLqVRuSik7qDZ5Vw7TKiDNRtgl2R/EjLZrr3buf4rnoA6ioT4Q2zT2RydoGxmRgvPVJLQ6UPLX5N2zXw7Oi6TsvRDoIHz1qSM6F9D/K1HbXWWO/uoYgK7ymyQrJ4sK+4gK01ic3X1poA3366iXrbtdBc7UsMgozfV+Jxse3wecvI2Dd8wbisV7pQdnRqnot9YUt3cfCXk8pILQMqxHcbYI1h7xuhJB6qaKwOIIRRSttY7aeh0mdpk03MGH/fc7o3/vcA3Xu3seeUMb57S4UPXdeRUloaZy3HOi2Nufa45EzlhmIgMSVVl/DHb17izSeblBelyCpCCE7ubrIktUzj9a2nm637JJK6g+cAY2N294fKeCc+gt40MlV3eB1CwFsOnmNsZoGiQhel7uTxMQm2Hb7A1k2qYOhWUR7UGiLT3CZrjAGJUEVHf5j2uGfTORDh5Z119Ox7kN792+nZ7/R8zDHoJ55oIFjpo3soSt2hczz6aqcVV7drzHkLXWz7ynl2vtrJ4C8n+eqn77b+1j4QsRYAhSKbCCFSRrU47kua1/zez53ToLcdvsDO17oAw8CNzy4yHtf2m5iN8ciriSIkgOZqv/WKEmN+mjlSRXFzKAO1Rsg0t8m8QBID//Lj+acAzTUBKxdlVueZY7zTDcMbm4kRGk6obZuNjFJKmjcZr1+7sZyJ2Rg6xhTdBw5f4Le+csF5rGQegKhQ5Aq+4gKaqxNhwKbqAN6CxJJoNPMmQnnlRfnU23K23UMRIlNz7Hyti/pDrWiaILR3m1UxKIEHDp9H19PpWSiWgliNRSQYDMpQKLTi73M7E52aJ3jwLIvS2FWc++L9bPR72PFqF6HBCM2bAhxpqXWogwPXrCqyVx2Z77HnVK81CmNrtR+EoHPACAMe2bEZqUu2vXAhRZhzy8ZyLl8dJVjhI08TdA5ECNpGHCgUuYgZlTCpO9jqqPRrrDIU+M1rSkpJy9EOa2xKfVzZf1EaWoChfQ8SnZrjgcOJTdsPv3g/VXd4V+sjrUmEED1SymDy/WrlWCPYR4OXePLZdvg8tQda6Ro0RFvb+4yBf6aHJIS47tRZuxqEuQvUpaS+shwBxHTpCAN+9mQv9c+/lWKcyjz5fOupRoKVfrqHorQPGMfUNRhhxzFV0aTIXewhv/KifMco+oZKH2/ubuCx17utyIUQgpd31lkLZ8+QMXbGHomo3FBMqTvRg1URKHJMUVbXw9JRRRJrBLuK8/bD59FlYhotGBVGN9t/ZO9r6hyIgDDCEz3DUYJVfnqGIgQr/dbEVJPmaj//7+/8OnffWWZNwk2+9ELxyj7Via/IdcZmYkza5p69vLOO8dnFtKoS9mnC6XqjPvqhMtoHwmy6w0ssFqPl1W6rBzFYUc63nm5WkYUloL6hNYQQgopAEcFKP5owPBcNIwxxOj4I8Gawe2d1lT6aqhM7wtNPNhLa9yAnn6jHW5ioWtIEzC4s8tBL7XzmGyFHb9S9NQEaKn2OXaVCkeuY87zyBGzdZORtk/sK7WLJZt+VPWoBxoavfcCoar10dZT//c/PWsYJIDQ8SsvRDuVJLQGVg1pD2MvJg1V+Tu1uYHx2cVk61xcXF/nUKx1cvjpKc02AFx/e7OjUf+jldnptF1mJ28VEfLepAT37H0zR51Nd9Yq1hpmXtc/ughs7l6WUPPRSm8MopeOHX7yfyg3F6vogcw5KhfjWEPZy8p6hCOOzi8sSOpNSsuPVroQMUn+Yz77ZS89QhMbqALFF3WGc7v5QKe/+bNy6bYYXM81CUijWCqZiSrL48Y2ey4WuaxudPAEPfOW86pW6DirEt4ZIF25YDpL7nDbfVU73YMTqp7KXntduLOd7n9vK1ngo5FbDiwpFrpFOzfxGn981aFwzma6KRZlaxq5IRXlQOUgm0cmVGhRoxt6N0KGROzIDv43VfjRN0NEfJlhplNxqmqYGFipuW9JNjL7Z59dV+KySdDByt7otq3L3nWWUeVxWld/YzAKVG4pVAUUclYPKMZY6LG25lZPtU3XrD7Ua/VYCuvduw19cqIyRYl1xq9eXPZdl75sCqL2zlN73EyHyrdV+JJL2AeMxZR4XvfsfXFdGSvVBrRGWEl7IpCpxK5j5I0NhIgAYO709py4DXLOfSqG43bheD+FSn69pGqefcorUulxODb+2gYhlnMAodzcV1dc7ykDlGEvJM91qjPxaCCE40lJrnRidA2EVI1cobgFN03hlZ501MaDb5k1lYu/33yUyOecYpLgeUTmoHMOeZyrzuNKGGW41Rn49khsRVR+TQnFr+IoLaKoOpIycz0T7QJS6g62UuF1MzsZoqglwcvf6K0ZSOagc5Xq5qJWe3qmmgyoUy0tkco7goVZHkQQYYSwdrN6rTLz13H1U3eG9La9HlYNaY1wvjHerMfLrsdKvr1CsN3zFBTTXbEATWJOtiws0/ueB3+aHX7zfklnKxAPx8R/rKdynDFSOkDzrySk/5LcmfyoUirWJGb4/99z9mDZmdkFncl5SuaGYxurAdV+jrW9kXc1bUwYqB0hXlSeE4PiueurjYq2Pvd69pJ1TpqGGCoUi+wghqNxQbGn+2fX9vraj1iqkAKivLKfBVv0HRn/is6d61831rbblOUC6cJ6vuIDR6QW6hyLoSfdnIjlvlU5lWaFQZJdMDfdGCDDAxT6jkMIVb4jf8WoX3YOJSQEd/WEik3OO592u17fyoHKAdKXlUkqePXXJSqg21QSuW01nN3TtfSM8fLRjWXulFArF8pAux5va4hHhSmSG00820rNvuzX9V8fQ8dtysJUtB1vZ+ertO3NNGagcIFm+XwhBdGqetv6EPp6pLn4tyovyrTi2jtFvsRK9UgqFYmUwWzzMwaTbD5/nsde78RUX8LVHaq3HjdkKKi72hxn85eRtaaSUgcoRljL9dimvkRzH1lAzmRSKtYJVSPHF+5mcXbCiIUMjU6RMA7Wx/YULtBztQNf11TvYVUAZqBzFV1zA1poAGrC1JrBkuX+zlNUcHNj63H0c31V/28aoFYrbDbOQwqziNT2pz5+5TLCiPO1zdAmdgxFajt1e4T7VqLsK3GzT6608Lzo1z7OneukcCF9TdFahUOQmUkqGRqbYfvg8i9Loner80gM88JULjMdDfMGNZWiaZonRmsND19osNtWomyVuRdj1ZpplTaMGho6emYMaGpla97peCsVawu5JmQVUmtCYmotPshZw9DP1nH6qiYYqPxrQvOn2CuerMvMVJlMJ+UpICdnLzBurAzTVBOjoD+N157PtK+cp8eQzMbNAs5riqVCsCZJL0gGHDqe5gT3zVFPa9WStS5YpA7WCSCmRUtJYHYiH2gJIKdF1ncde777uzKcbxW4MOwfCdH1pG1ejM3zi623owNiM4VktpadKoVBkj2TDYr9W0/VQJT/GfI1szJZbTlSIb4UwT476Q60IAV1f2oaUUH+olZZjnQ6vamhk6obCbunUIuzGME9AU3WAz568xCe+3kaJJx9NQJknX1X1KRQ5znLNe8vWbLnlRHlQK8To9ALt/SPoEtr7w4zPxqycUGgwQn2Vn9BQxAq/LTXslm5XBNjuC9D1pW08c/KSNXdmYmaB1ufuo6woH4ESgVUocplrpQVupPhpKWN5Mr1XrqAM1ApR6s5DEwJdSjQhuLO8kNqN5YSGR2ms9nNydyPD4Wm2feU8Oks/OaJT87T3jTieQ/z/jZPMMIY9tqFowUof+3/wEzr6ww6jplAoco90hsXcmJqbXrh+TjuTpNL13iuXUAZqhbgSmSEWP5NiuuRTr3Rw+f1xAH7y83GklJZo5FJPDikle073YrbiNVYH0iZOKwJFNG/aQHvfCMEqPy89WkvDoXM5u0tSKBQJTKHo4fA0G/0eRqcXkFLSYTNO9lB9Og1Oc+PqKy645rW+FCOWTVQf1DKQbvei6zq1B1oZm1mg1O2y+hZMajeW8befvRdgySdHdGqe4MGzLEqjxDS0dzt+b2HaYzDDAWDsklaiKEOhUCw/hsHppL0/jLfQmKjbvCmAjBc/NVUHOPB7H2aj38PV6CylHpe1AdUE1N5VRs+VMQDu3RTgxBO5P4k3Ux+U8qCWiN0AQMKoSCnZcayT0FDEsfgLIXjrufsYm1ngLp+bX9//99hFSHqvjBGZmkMTWlrjlM7opXPHo1PzjkofKSXhyVlGp+bZ/4Of0DkQUcrmCsUaIjo1bymamxvb9v4wob3bAWPcxvYXLqAJQUyXeAs0igrymJhbRJdYxsl8XnLEJJer9pJRBmoJOF1o206mJsB8TLeKEczwWZnHRcuxTkKDEZo3beDAx3+DdNP7rsMAACAASURBVApZz5y4xKXhaIpXk/x+R1pqrcIG0x0vdec5DKPp1j97qpe2/rDjfTr6RxibiamwnkKxRvEWuigvymdsxii20iXo8ejX5Hxm/b3mpCkISy09zxWUgVoCjjEW/WGQhlp4e3/YigkDBOOTb3cc66Rr0FAib+sbocyTT5knn7GZBfIELEpoqPQRGoqmLZCwv9/FvjDBg62OKr/yonwePtphvUd7/wgPvdzO5SujKXqSAlVWrlCsJXzFBTRX+2kfSEwzmJyNWRGQxuoA7f1htPhakg4BnHvuPqru8DoM0Oj0glVk1d6X+/loZaAyYHeDyzwugpV+ugcjBCt95AlB12CE2rvKuPz+GDHd0Mk6+YQRRuseTJxYJW4XvuICevdvt5Ke47OLlHlcjryQ3YCYoTyzYsduxMqL8hkambKME0BxoYveK6Mpn6HUnccPv/ib+L2FOb1LUigUCYQQvPlkE5HJOT578hI98SiLuUYIYfzXWB3g6Y9V8od/02M91+OCuUVortmQYpwAyjwuSuKb5RKPsbblMrl9dFkiXUivazBCidtFaChKc3WALRU+K7QHxk7manSWyg3FBKv8lgGZnItZ4bWqO7wA+IrzgPQd4ZCorEnueSjzuIxS074RXFo8/ux2MZFUgBGsKOM/fOJuqu7wommqF1uhWGsIIQiUuDnzdLNjjYhOzdMRj9x0DoQ50rKZMo+LsZkYpW4Xl/ZtY2JOz5hfGpuJMTlrVPhNzi7kfOhfGag0pAvpSWwJy4FwymyWMk8+FYEihBCcfrLRkR/KFF5LJ09i/5vfW8jJ3Y3WCWoelw7o8dji9FyMhnjTrxlu7L0yht/rVsZJobjNSC6U8nsLubRvO+/+bJyPfqiUvLw8fK6E2oy9qtfMj6frscrVoglloNLgPAkC6LpO+0DUyh+VuF38xgdK6RqM0FDl59Dvf4TKDcWWQdA0jdMZxBtvFLsRM44rYFX4gJEEPb6rwSqQML0tlXNSKNY2mQoaksVjP/ON0DWUZYwCKjOd0Fgd4MiOzZaiTPJjc61oQhkoUssu7SE2XdfZ9sIFIJGQHJ+J8dePbLGen0466Fre0c0ihOBISy3Bg63oGM16R1pq0TQtxdvKpZNMoVBcn+R1KJMMkX1tMUJ+qXp79vuGw9PW7bb+MPWHztEcN0a5LnW07mNATrHETiKTc5Zg4rOnegk+/xZjM84cT2k8ubjn9GVD/HUVRy37igto3mTMh2netMFxMt3M/CiFQpF90om2mpEccxZUuqhIusck31cRKLKm8wJxfdARIlPGWtdUE3A8P50YdbZY90oSdnUGwBr69eLD91B36Fza52hA63P38eALF6znNVT5OfNU06oYh1yOGSsUihsnPDlL/aFz6PHJuaF9Dy55bly6x2RSltlzqpeL8T7JUrehUtFUE+BrO2qtze6jr3bS0R+msdrPXz+yZVU2vWqibhrM2UxedyLSmSzCavLdpxqp21hqPWbf371HXYXP+ntoMJJWzn4lUJ6SQnH7oOs6v/Xl81aRU2N1wBqfs5RrPd1jku8zi66O7Ki1Fv3x2Rg6RjWgmdqITs3T1h82+qQGIgQPtWZ1DMe6NVDWvKbnzzlCeFoGd/rQf/2f9FwZt2539Ed46dEtt+2oZYVCsToMh6cdWp0z8zHqkwzDcoXd7CmCpcyH068xS2o1WLdFElbJtkMd2OnqNlf76RiIUFSgcemqsxE2WOXH7y3MOGpZoVAolkJFoMhSmil1u3j76lhKc36mSrsbDfc7CsCkzvhMjMoNxdZzfcUF3LspQFtfmFKPGQLM3uZ73Rqo8qJ8mqoDtMfVgU3DZP/hNU0gBEwlaV3lCXjziXrHj6pQKBQ3g6ZpDqUZe9m4vf8xudJO1/W0QtUm1zJee073Wu0qW2sCnHiiwZJSOvFEo9UzlW2B6XVnoExXWdd13v3ZKLqE9342ltLQZsxfcWrtmZiqEaYyhEKhUNwKmqZZ60mywkymAYYtNs3Pjv4RolPz1uMhc3+TMe070UvZ3h9OMXTmpjvbm+91ZaDMOSv2RlcwkoXD4WkqNxQ7JI4aqwPW/JXZhZglY1/mcVERKMrGR1AoFLc5yT2U6YYKRqfmCdn0OOsqfI5G/SMtm21qOIbxMmfHlRfl02xr+A9W+ggNRSwPzW7osp22WFcGKjo179g5mJR5XJS6XUlNb2G64/NXRqfn2X7YaNYVwFvP3a9khBQKxaqRbLTKi/KdU7MfqaXh+cTUbMBSndGl0dN5cncjUkqGw9O88Xi9VRzmHGgacBi6bCtLrBsDJaXk2VO9KSG7v32miS+f/V80PH+Oxmo/3kIXY7MxigtdlLrz+MO/6aGjf4QSj4vxmRjNNQFrJ6JQKBTZIJ3kkT0M6CsucKjOdPSHGfjnCT7xcjtjMzHKPPn07t9ubbTN15JSUn+oNWeUJdaNgRqdXqBzwOk9NVf7KPMU0DEQiXdXRywN2PHZGJ96pYN33h9jURoqwAJD5l6hUCiyTbJXZRqZMo+LyOQcozMLNFb76RyIUOLJZ/sLP7LWt7GZBd55f4x77iq3eqDMxuDkfFc2ue2VJKz+ASR7Tl2mcyCM1x2Xpy/MY3xu0Xpsqdvl6EeA+GDB4aijHL1n/4NZTx4qFApFMlJKWl5po3PIaIspKczje59t5rf/6seO6JEpfL21xs/J3U2O6uXo1DyQXmN0pViXShJSSh59tZMtB1upO2jIFn376SYr9mo3TmDMbrLTVOXDlScs+REAr9sI/SkUCkWuEZmcs4wTwMTcIv/yTC/eQmewzJRoa+uPEJmcA2ziBYda2XP6csprZ0Oj77Y2UEb/QCKs19Yf5qGXO9I+tr6inOaaAJrA+jHNsB/YlMxnY+x4NXvSHwqFQpGJsZlUxYf3fjGVEhmyE52at/5Lp4wO6cVsV4Pb2kCZ85PspPtaa+8q48zTzRzf1cA9d5VZnlRoOEpxYepXtJq6e4rcJJcUnxUKk8oNxTcc4fmz779L8OBZnj3Vm6JsbpKuWXg1WHKRhBCiGfgEMAUclVL+3Pa3UuCrUspdy3+IN48QgpO7Gy1Zj2dOXCI0bLi/pW4Xk3MxNt9VzrefbkLTNCKTc/TGe50A7rmzjN6rY87XROnurXcyDZJTKLKNpmlc/vPfZmhkihJ3Hn/85mV6hqM01QR48eHN6LrOk8d7uPy+oSsa3FhGaGgUiVHpF9q33dHsa07lLfO4CFb6rzslfLlZkoESQvwO8J+BnwKlwOeFEA9JKX8Yf4gH+EMgpwwUJCpddr7WZRknMEJ1mz9UQu+VUR57vZuTuxtTnvsfH7qb7V/9kXU7WFHO0ceCSkn8NiSdLIyu6wyNTFHmycdXXODYNdp3k8kd/GZRjjm1VJ0ritVE0zSqf6UEgDNPN6eM3Sh256MJCFb4eHN3A3WH3mJsZoESjzFLStM0xyassTqAENA9GCFY5ef4rvpVO6eX6kHtAw5LKf+NMI5sL/CfhBD/j81I5QTpFprR6QXa+0ZSHnv5ZxOAkZuKTM4hhKA5XpbZVBOg+le83LspQHt/mGCFj9NPNakG3TVMJm0yXddpOdZJaDBC8ybDI5JSUnvgrFVQ4y3MYzJeVBOsKLd0HO+5q5zd3+yi9+o4TdV+QNI+ELVeu7nax6Hf/yiVG4rVuaNYdZJL0c28vC6hZzjKez+fYGLW2HhNzi5Y2ntDI1O0941YPVQIY8xQz1CEsZnYqlUxL9VAfQR4HEAaQfeDQogI8AMhxO8C/7hCx3dDJFt9UwC2vCifYJXf0q1KxzMnL3Ep7gqH9m23dr6mcGIuyH4obh5d13n4aAehoSjNNQFO7m5ECIGu6zz0UpsVym3rMzyisZkFxxiWSVvFZ2h4lM0fKjFU7q8kvPL2gdTzq30gygOHL6Q0RioU2cCu6+d15/MHX2+j1JPP5OwCTTUbKPO4rDW0xJPPxMwCTTWGB9XRH1713qilGigJOMTnpJRfF0IUAf8FeGy5D+xmsCfy2vrD1B1spb7Kz6ndDbz0SC3PnOih2xbmK3XnMTG7SH2lj9BQ1NotmI1rkLoDUaw9pJQ8/Eq79du39YeJTs3jKy6g5WiHI88oMWRhju+qt9Sc02F630tlbGaB4fC0EhhWZBVTgWJoZIoHvnIeCYzPLPDWF++nckOxIQcX95wmZhZofe4+65zNxkZ9qQbqfwD1wDv2O6WUX44XSJxe7gO7GczdgfkFS6BrMELtgVam5mI0Vvs594WPURqXLSorykcTWpIWlSqAuN2ITs07NibGfXNIJF1D0ZTHdw6EGZ9dpHf/gwyOTPFvvvsOPcOjBCvLWYjpVoL5enjyYF43WhRcGngLjEIclZdSZBMhBBWBIkrNGVSefEv8es/pXszhQjqw/wc/4fiuhqyN3ViSkoQQ4l8Dvyml/L8z/P2rwOellGnjF6upJGGW/z5zsoeuwdTFRwDFhRqTc8bPcO+mACeeMAokVChv7WPmmUrdeQyHpykrykfqkuDzb6U8NrixjJCtarOkMI+puUUrD5VuKJyUMjGaoDrAX3z8N9B1yYN/9eOU1zfPouQrzDzn1HmmyBbRqXmCB8+yKI0p4ueeu58yT76lw2eiAfVV/owzp5aLTEoSt5XUkbmQmFpUDxy+wPhsjDxhNN2m+6SagJ59SrrodsDMQbb3jSBEorm6vqI8xYNKJlhRzpmnmhifXbzuJiW52ELXdWr/4ixjSc2QzdU+fvqLiZQwoTrnFNnGnq8vLnQxMRujqdqPpgk6+sN43Ub+KVjlpyc+iiNPQPfeRBn6chqqTAZq2cRihRB+KWXmKoQVwm6UzDCd153P+MyCZZAWJXgLNX79V730XHGGZ4IVPhXSu00wqzV1cOxGQsOjNFT60obzwDAYRx8LkpeXh6/4+k2OyXnJsZkYEzbjdO4LH6O8uICx6QW2xce02GmuCahzTpFVzFzU4C8neSB+jrYPROjZuw1N06z8q31dzcYojqX2QY0D1VLKkfjtvwOellL+U/z2rwI/B1ZVpM6+C6irTFj6dHIfk3M6yRHI+spyTj/VpEItaxj7BkWXOt40gr9bawK82LKZ4KFzlt3ShDGorWcoao0nuFnM2TxmDrPqDi+Pvd5NW98IxbbydIDWL3yMml8pUeecIusYnlDqeW+qmpuPyeYojqV6UF6cskgPkFTVRyLkvmrYq/a6ByPUbizn8pXRtIuUN19w+X0jzKMJaP2CUZ2iFoq1i67r7DjWSfdghBKPEaawVOcFfPeZZjYGivAXG/O7mmsCtMW1GZtrAsuW/DUvYlMFenR6gba+ESRGebrZQ9VQ6aNanXOKHMJXXMDWaj9t8RaJz5+5zBuP17Pj1S5HX2C2RnEs5zyoVRcls1ftlXjyuXx1lM0by3n50c00/eV/d8jLSyHQ47uCYIWPMo8Ksaw17N7S6PQCTx0PWeog9jyPwDBAFYFiyovyrXyRKXsFiVECy7kD3HP6snHxVgccntPk3CJ331lGaDjKY693K2kkRU6xYFso2/vDfOqVDqu/72JfYlx8utHzK81Sq/h04NeklP8cvz0B3COlHIjf/lXg51LKtCG+lSySkFIyNDLFtsPnLYPkTQqrZGKrrWFTkdvYw7led37aMK7Jd59u5Mtn/9Ea1GY2IS6nYbAXSgAM/nKSbYcvIDG8N/vmyH4+5gkIqQIJRY4QnZqn7sBZq7R8y8Zyeq+MOryNe2sCnIivk5nUWG6VWy2SkKR6SDkh4yyEoHJDMfWVfjrjShHpjJNG6ofo6A9nfaSxYmnYw7nXMk4AD73Saf2/+djljJmn6JQBF21jXfR4Uc7knG6FnU2ClX5VIKHIGcyJD+39YYKVPk7tbuDTRzuTFFLCllFabZHkpequCODbQoi/F0L8PeAG3rDdPrNiR7iUgxOCU0820lDlRwNK3Kl2VwdqN5bTXO2z7mtS1VQ5S/I4izKPC6/b+K1cmkAAJdcZKyCAMk9+2vEBt4Jz9ECY9oFwymMm53S2bCznO083sXWTYcQaqnycelJ57IrcQgjjv4I8jc98I8SlK6MUFyaurebqgHU9rvbIjaV6UG/gdD5OpHnM4K0fzs2jaRpnnmpidHqBkkKNTx/t5PLVUYoKEuGVt6+O0r13u/Uc1dGfmxgeSift/WGaa4ym1rGZGBNxb2hRl7z1xfvZ6PfwyKtddA9F2HxXOa/srOVPzrwTL4MNcKSllvKi/GXvgrfrmaXzoEwuXx1lbCaGlIaxdGmaOt8UOYVdPLZ9IIyZ8ZmaW+SjHyzh1c9s4emTl6k72MrWTQEaqwNWmXnOFElIKf9ohY9jWTAbyHa+1sXlK6PUVfpwCWiPK0o01QSUUVoDRKfmudhnLPgX+8JEpubwFxdapdyN1QHKPMZYgNPxTYlpgE7uThX3Xe4QbnKyWEppCdEWF2hMzhsR/eb4sMzOgTB6/N/lDDMq5RPFrWLfbDXVBJiP6XTH+wXf/fkEzX953spPXewLc2nfyjTqZmKpfVCLwAfMIolcxgy/GNLwUav4XQOOtNSqi3kN8syJS3zr6WarlHvP6V7qD7VacXD7gr9a4r7294lOzdMzFEUCMws6bz13H+VFBdbfl7s0N93ARMCqcDQbLLOln6ZYOwghOL6rnuHwNBv9HkanF3jyjR4uXTVyULrtsV63y5oXtVosNcS3Zs7wlPCLTSZeFUOsDXzFBQ7lh56hqOV5CGFIsaxms+C1kFKy51SvowoqefbTcpfm2hUzLvaN0PdP43zp++/RPTyKtyCP6YVFStwuJmZiKbqCCoUdKWWKAo89t6uRMFLTc7FVnQUFy9sHlRMkh19AicCuJXRdZzg8zZu7G3jktW5rimeZxzhVnSGJ7CvPR6fmHfmn7uFRWo51cPrJxHDLW/HqksvZo1Pz6FKnuFBjIi54bBeqnZw38q1mX1h7X/aNuCJ3iU7N094/gm6rjh2fNc4hAXzkg8W88/MpIDsSXTdioOqFEOnFzOJIKdtu8XiWheQFwd6sqYxU7rK4uMjmA2eZmF2kzOOiZ+82Hn2tm9BQxNHgutrNgjdK12CUHcc6b1lGK7mcHSRt/Tcmd6lpgtLrVDsq1idSSp491Wv17JW68xifXaSkMI+JuUUkWMYJ4MWHN6/69XYjwcQfAD++xn8/WvajuwXMskhd19n5Whd1B8/y0EttLC5ev4FXsfrous4ffL2NidmEB/Djf/wl3YORlLJWcwOSC8bJV1zA1hp/yv2hochNleHay+tTytlv0DgBxHTJuz8bJxaLcflKlFgs5ijfV6xfRqcX6Iy3SAjgX/xaKZqAf/EB499kPn/m8qqfNzfiQTUCv1ypA1lOkkVkQ0MRdAmXroyy+UArb//5g2r0dg4hpaTlWCfv/MypNP9H37xEidvF5GwsJ8J56TAqB5uszdDn3uylZzh63eNNrsIzDZNdLfr4rnpbPtXPu++PWmG9MreL7zzTxO/81Y8dqhXJuDTB7389NbBxr8pNrXvs4XJTbFuXWFV8yWRD2OBGDNSVtVDFB85GytBghI/cWcY77xuD6SZmY/zoH3/Jx/63OywjZeY9KgJFynBlgdHpBUKD6b2DidkYWzaWc3xXfc4upkII/F5DkPbM083XDT/a51YFq3x8fUctf/Ktt2mP96OA4TGOzcQcStJ1B1ut1xifjRHwumm2aVFOzC5Q4k6Mqf/oB0t47+fpR9O3940wNDJF5YbinP1eFSuLPVxujNXosto7Uh7L8ja7L5XbrkgCUhPp3/yjOmoPtlrhoz/8Rogyj4ve/Q8CUHuglbGZBco8+fTu366M1CpTXpRPY7Wf9oFIWh3F3iujq149dLMspSDCXoXXNRhNO+3XVDkxX09K6VBj37rJ6OmzLzBjMzF0Xaf+0Dl04Cc/n6ChKiEBZsfrdrHt8HmaV0myRpGb2M/XIy21BA+2OkrLNQEdf/qbTM1LKgJFq36eLNVADQNpkzdCiA8ATwBPSCmrluvAboV0ifT//sXfpO7QOesxYzMx3nl/jFK3y6peGZtZYGhkiupfKcnWoa9LpJT89BdGeM80TgLw5AumFySlnnxK3XlEp+ZztjDiRigvyidY5acrg9coSO3ZM5uQk9XYzf83/5VSOmZTHd9VT3Rqnt/88n9nYm4Rb6FGVaCYd+OeVS6U6ityA19xAc2bAg4vqqk6EFdnidCUBXHtJbkKUsoqKaXD9xNC/K4Q4nsYxutp4HsrcHw3TXIi3e8tdCSz8wT8wdfb2Pf99yix6U7t/7ufqATyKjMcnnaMy9CEoac4vWD8DuMzC+x4tYvgwbPsfK0rq79PskbgzSCE4PSTjTRUJnQhSwoTl2JzXPEk3fP83kJr9EEmjrRspnvvdodn9C9+LbHpetcW9lPitQoTIYSxMbLdNzMfo30ggg609YetDdJqcUMhPru3BJQDpcAOKeW3VuDYlgV7Mvrk7iYik3MMh6f4xMsdALQNRGj9wsf47a/+CF1CxzLK0SiWRkWgiDKPMUIjLz6qwj5wsnZjOaFB4yLJ5o7/WgoON+rZaZrGmaebiU7NMzo9z/b42G1NwNd23JziSfLxvfF4kB3HOh2j7ifnEgGcLRvLlXitAnCuk/U27/7teO4+WyzJg4p7S98HBoCtwJ8CH8BoMn5v5Q7v1jAv2ODBszz8SjuRybm0C0l5UT7NNQE0oRTOs4GmafTu3873P7fVMRJFAxqr/Hz76SaaN21YdlXyGyU6NU97n1F80943Qu9whE+/3EbtgbN84usXb7iFwfSIqu7wWp+v+RYUT+zFQe19I3zqlQ6HcYKEJEyp28W3n25S+VYFuq7z8NEO6g6c5bHXuzm1u4HGKn/8fAywtcaPJuDeTU7PfjmiCddjqQMLY8B/BF6UUv7Cdv8CxuDCn17r+Ss5sPBaRKfmCR48y6LtI7o0iOnOx9VXlOPKE3QORLMSZ13P2CsowV6w4uKt5+63wlnZFkc1FdbN+LwgdSBaidt10y0My/H57B7Ulgofobg+YDo0AT1qcOK6R0pJy9EOq5BGA3r2P0h5Ub4VzivzuLgSmXFUOaeLJtzKdXmrAwvPAn8CbBJCfAP4r3INJGrKi/Kpq/A5dpHJxgkMeRoTs9ZfqU+sDLquMzQyRZknn/KifLYcPMfYzAKlbhdvPXcf46bcykwMzTaeYrVEYDNhjiUwSXfyT8zGGA5PU3WH94Zffzk+n1kcFJ2aZ8+pXusY01VGBit8KlKgMFo8hhLFOqasmCnK3NEfxuvOZ2JmwaHr6GwiX7mw+1LHbfyuEKIC2A0cA4QQ4qT552U/qvTHcMMGQwjBS49ucVTvXY+SeMXYak+OXA/ouk7tgbNWQcRHPuC16X/F+KNvdFESl1sp9eRb+nu5gNm6YOqWpaPU7bI8wWwyNrNAu82YppswnZdOKkBx25Jp/bS35AQr/by5u4HHXu+22iAg/VTq1dLEXPIKIKUcBvYLIf4/4OPAkxiRjjNCiNPAt6WU/7gSB3k9d/JaxsvvLeTepNJJO8m7y8nZBa5EZlZld7DeSK7We+8Xk+QJrBDse7+YtP42MWuU/JcXFazI0MEbxe6dPHvqUoom3uY7S/nuZ7dmNadjbwAudruYsBWagDMs2TUYUef1OiFZ0/FrO5yDPO0tOfZxRSYuTaDr0mGIVksT84a3qFLKRYyS8u/FvaongT8GDgArokp5LXfyesbL+CKN/pHPnQzRMTjqeO3JuUU231lKcWE+HXGJmYpAUU4pZt8uGNV6LoeR0iX8H7/m5R/+adLx2BK3iwfilW2lcbmjbI+OMIsaTGkjGR+VK8gNbUB7A7CpwFHo0ugciFDiMQxWaXwMhzqv1w/29bOtP0zdwVZK4+eDObHaXE/TRQrMCdbJqiOrEXa/pe2elHJYSrkPqAAeWp5DSsX80tJVcaUzXsmYC8vzf3B32te//P44L7ZsJrTvQU480YCmaZx4osG6ne2F53bBqNZ7kHNfuI/6inI0oL7Kzw/+eCt331nmeKzdiI3Pxhwl5tnGPJ8CJW4CXvd1+5JWC7MB2OTtq6P89SNbOPfF+5mcjaFLmJyNce6L96vzeh1hrp/mYi8xri9dGlNy7b1N5gDDoK1Hr7kmkDVJrGWJR0gpY1LK7y/Ha6XDdCfTGYxrGa9kKjcUU+Yx/l7qdjqPuaSQfTujaRo1v1rCmaebqa8yhHyDz/+Qd94fo7ggcTra80+lbhca2S0xXwuYDcCNVUZZsNmEW7mh2HGNKP299YW5fnbv3bakvO7YTMyYRs6t9eUtB0sd+b7AEoohpJQr5u9lciftuYEMx+SQh+ndv90ab/yZb3TT3h9O6dxf7hJKRSpjMzFLZd5Mwk7NJyLfk7Mxa3R6LuSg1gqapnHqyUZajnXSNRih5Vgnp59szPkZWoqVRQiBpmlM2CITgvSqJWUeF3UVPrqHolmv9lxqDupJEgZKAC8Bfw7khLq5lJKnT/QQGorSHO9jAqMP6tk3L9E2YCS0791kxFur7vCi6zoHPv5hyjz5KSGa1SqhXM+UeVx43Qn1iMWk7U9jdYCqO7wpenOK6zM2EyM0GEFiFEO0HO3g5Z11KkKwzikvyrd0Gs1iieRzwtycm605XUNRHnqpje8800xe3uoPvlxqmfnf2G8LIY4A35VSDqzEQd0IZqOZOcOkrT9MZHKOz595m7a+EYfb1x7XkpJS8sDh84zNxCwF80yllyqstDKMzcSYiHtOuoS7P1RqzYMSZDessJaRUqLrOvdsLKP3iiFT0zUUJXioVSmXr3OWUnkXnZq3FPNNeq+OUXuglctZmKOXO40mN4nRaOaUcxmbMTyg5JhksMLHs6d6HT/A2MyCo7nSLFk/vqtehZVukeTwavImwK66/cbjQXa82kVoMELzppuX+1nPmJI15matNF5qLjE2ASoaoLCnSuztOYDVQpGO8VtoQr8V1ryBMrydxJychkqfKP0gvQAAIABJREFUVSbe3jdCcWEeE3OLBCvKeenRLdQnNe3amytV7mn5kFLy6Kud1u9ihlftyhDJu7kzTzWpPMlNIqVkx7FOxzTUybkY33mmif/w3/7nkqb8Km5vkg1SojfKz8KiTDtJ1+wTLfPkZ6UJfc0bKHNOTmRyjmdOXiI0FOUz3whxfFc9o9ML7DnVS/tAmML8PHzFBY45PJqAH/6r+y23VeWelo9kaaC2eDmrOXkWUgtfsi1ntFaRUjI0MkV30nwpXcJDcdX++kpfTk8lVqwMplEyJuZ2W5vvFx++x+qZS246t/PDL97H5JyetWnjS1Uzf8T+H0ZD7sfT3J8VzAqVS8NRR7/M6PQ87QPheHgjzNhMzCrDNZWj/cXGgimlREpJY3Ug66rZtwOmZ2sigT2ne9WsrWXG9Pq3HT6PN9468dEPpg7cDA1Fc6KHTLF62FXKW451Wkr8bX0jfPbkJdLIkqbwJ2feoXJDcdYUUpaqZr6UzyKllGnLPFZDzTxZzkMAF207+Hs3BTi+qyFeGOFy5Jecob0AR1pSq1sUS8fctZUUatzz7/6eqfjgQaWgvbyYntO2w+etrn9vYR7T84t4C12OmVoA99YEOKGU+tcFuq7zyZfbuXQloZxT4k6oiUzGm9/TYVd2yRMQWoVr9pbUzKWUWvxF3IBLSjl5naesOvZ+qNHpeba/cMHx969++m6Hi2vPLzlDe2GEEOoivgnMoohnT/XSORDmIx8qtYwTwOa7ypVXukzYdfe87oQxMnUlx2djFBdojt6yi/2pYVbF7YdZ2Ww3TsUFmqXNODkXIxhvkrcLH5e485AS/uGfJnFpgsUk/b1ssNRGXR/wBvB/AZoQogN4JC4gm1PsOX2Z9r4RigpdTM4ldpDvR2cz5pdUWfmtYy2YNg2vt98fdzzm6GNbcmK20+2AXdRzfDbGRz9Y4hjlDs7GZ8X6ITo17xgxlCec50J9pZ9TTzYSnZ5n9zdD9F412hEmZhOi2TFd8v3PbeWeu8qzeo0utUjieaAR+LfALPA54BUMg5UzRKfmjQUSY5fgLdCYnNcpdbu4+86yjEZotZR5b2esBTNDxLih0kfA61aVkstEeVE+jdWJ6tUrkRnrbxrGqOvkBuj6Sp8Kr65D7OdA7cZyTj1phHk/f/ptLl8doyQe8gtWlvO//mmSsVkjDXKXz5O9g46zVAP1u8ATUsr/BCCE+G/AO0IIl5Qydu2nrgzJu3ApJc+e6rUWyHs3BXjj8XprEqQQgiMtm4HUnhxQFWS3it0Lbaz2E1uU1i6uodLH6aeaABgambKqh1Sl5M0jhOBrO2oJHmo15KJs+SZzryyB2rvKePv9MWvXrDYDtz++4gK21vit6jxzinip28W3n2pkbCaGlNLqFZ2cjVG7sZxLw6M0Vvs58PGPsP8H79Hw/LmsbyKXaqA+BPSYN6SUPxVCzAMfBK6sxIFdi3S78NHpBToHjN2kBhxpqSUvL8+SNWo52kH3YIRglZ/T6kJdduxeqJSS+kOtgFEY8e//4KNAou+ixONifCZGU01AhVNvAV9xAc01G7jYN5L277oET34eob3bVdHPOsJovWlKycdPzsV45LVueoYiNNUEaKwO0DkQpq7ST89QhEUJnQMRNE3QORDJiXabpdYO5gHJNaqLrND8p+uR3K9kyhc11Rgl4nYlAl3XeejldjoHI+gY2mQ7jnWqcucVwPRCyzwuiguNvY8uYdsLF2g51mH9ZuYoDfUT3BhmEYr93D3SsplvPp5S/GTRMRhRRT/rEHMkTOWGYkrcxibQW+giNBixisEO/t6H6frSNl56pNZaO+3z8HKh3eZGGnW/HfeaTNzAG0IIK/gtpfztZTuya+AMJwXYc7qXjv4wjdUBum27RbO7vveKc0hhaEhNE10ppJTseLUrpcS5ezBKQ5Wf7njlkAQ6B8Lqd1giyVGD47vqrarUhiqfFcZJzjtlW41akV3smpcTszEa4tV7Xnc+2w5fsErPm2uMtdOcHJArUm9LNVDfTHPfieU8kBshXTjJcE+dJeKGTl+iS9pb6GJ6XoWWboalVN6ZfTmhwdTO9K3xPrTR6QWrDD3bu7O1gpSSwV9OWuLHHf0jjlxe12CUzj97gPdHZ/nwB7w8+no3XYNRGqp8nH6ySXlP6xin5mWAFx/ezNjMAtsPX0CCtZFs7w8jpczYipMtltoH9fhKH8iNYoaTdF2nrtJPaDCSsuDZPa26Ch8uTdAxEFGhpRtkKZV3mfpyau8q59hnthDwum0j0xtVxWQG0hX/2DUNARqq/Oz7u59YxRDFhS5rwu+jr3YSGowahSlPNmVNAUCRG5gTcodGptj7/feoP3SOukofdRXldA8nIksSeOZkD5eGR3Mi92Syps9e0+L3DEWor/KnaI3ZJ/G+vLPOykOZoSXF0rDn/NrjOb90jzF39OOzMcxfoffqKJ892Ut0ah5d1zOqm69HknNKpjHacuAsn3q5jfDELNGpeYemoSbg0O9/hI6BxH0TszHGZmLWqAQdY8SGOscV5hq5/YULtA8Y61/3UBQhBPW2se4A3UOj1FX4ciL3ZLKmxWLtC2doKMLYTCyjxVfNuDePqat3sc/QNXz2VC8nbZI5Ukp0qVNcqDExZ+zrNVsupHsoypaDrZR58pmcXciZ8EE2SeeV2mfxhIZHqTt0jq01fhqr/bTHh242Vwco8+TTXB2wpLya4yHrTFOlFeuXTP2JoeEoob3biUzNsf2FH1n3v7RzC5rQcia6saYN1PWMTrrE8vUSf0rlIBWjh6yW4MFWhwdqLorPnuqlIy7Ka7Io4SMf8PLeLxKqWOZo91wJH2STdMr56Wjrj9D9pd9iYnaRUo+Lz59+m4bnz9FYHaBn3zYEwvJGfcUF3LspQHt/OO0ob8X6w75GNsQnOSxKYyiot0Dwm19usx5b6nbhKzLOpVxZA9e0gQKu2XxrKUvYFoFrfeFK5SAzvuICx4DBMo+Lna910t4fzqge8cKnN/M7L/7Y+nuJ28X0XEx5sKTfXOm6Tu1dZZb0jEnzX/6QRd3IPXXbwtSa0FLGlZx4QuX3FAnsBWXRqTkeOGz0RC1K+P2XOhi3yRuNz8aMEUWnL6ddA7OxeV+zBiqdMUkeyGVXlmiqDjiqx9IZHzUPKjPJclDRqXku9jlHQ5d5XFT53Vz+meE1/dv//FOaawJ09IcJVvp5c3cD47OLavHEKW4MsLi4SO3Bc0zMxvAW5vE3f1jHJ492AUb5OED3UIRglY+eoczDB5UiiiIZe39iqa2A6ae/mMBbqDEZD8s3V/sB0q6B2dq8r1kDla5Z1275j7RsdihLHPi9D/PgCxeMRH/fCIO/nKS8qMDheak81bVJHhedzPhMDKElerc7ByJ0792OEMIySr7irPR25yRSSp4+0UP3UNShPD45t8iB//IPKY/XJeQJ4ej1UyiWiqZp9O7fzqde6aD3yiilnnwmZhfYsrGcozu3EChxA6RdA7O1eV+zBirZmIDT8oPzi67cUGyNgS/xuCxXd2tNwJHw/6uH7+ZqZIa77yxTC0AaTC81nYGqr/I7eqCClX61kNpI9vBbjnZYY7btatPewjze/tlE2tfoUsoQiptESsn47CLfeaaZ4fA02+NzxN6+OkpeXp51TqUTzs7W5n3NGqjkEEnyF+grLkj5ok880WANeDPp6E8k/He+2mlVRpW6XVz+8wdVH4kNe69Ticd56mzZWM6bT9Tzh3/TQ3vfCMEqJU5qJzlEcqRls2Wc7Hz0gyX87WebqT14zprtBIYS+aXhzKE9heJapCsYu9Z0h2TvKFsTH9asgTKxh/XSVeklJ5ErNxQ7SnS9bhdlHpfRx2PrLRmfjTEcnqbqDu/qfqAcxVSJMHudTD09k0tXRnnktW5OP9mYExIpuUZyiERKSanb5VAhB/ibXQ1MzkumbMbJVINX36viZnH0MvYZITr7Bn8pZCO/uabdg+SL3uyDutYFLITgyI5aq5F0Mt7kWF5k9JaYlLpdVASKVvgT5D5SSiKTc+x8rZPth89T4jF2WiVuFwLjezIJDUaW9BusR0wP32yCRJBinBoqffiKCigvymfrpg1oGJV7p58yFCHU96q4Wcz5YWCMY9lzqpfI5BzPnuql/lArO1/rykkB7TXtQd1sXNRXXMDWTc7nCSE4/kQDA7+cZHxmgXvuKl/34T17SM/MkIzPLFgzhhqq/Jx8op5HXusmNBiheZMKP2UiXRWknc13lREaivLY692ceKJBDdBULCvJ88Mu9ocJHjqHaZJytWp5TRuoTHHRTPX65v1lHldK/5QhCdJllU4nF0+sR+xjxU0kWH06oaEIE3M6Z55qUotpBiw5I2RKU+1WqwTfR2gomjLEMdcWC0Vukk6/Md31aM4PM3tDTeOkkTvSRsmsaQMFqXHRTOoRZR4Xj73eTXv/CN5CQ2J+6yajnh/Mpt5EDqqjP8zQyBQVgSLGZmKUuvOs6bzrxbNKHitux35Sq96b9JiDMrtsxRD2jY8pmmuem6q9QXEt0hkeU7+xoz9MQ5WPQ3/wUfZ9/z264uLZyXl5M++U6AkNcKSlNmfDx2I14o7BYFCGQqEVfx8wDE3w4FkWpbGI1sfnnwQrDZkP+6fVgJ79D1LmcaUsJKXuvLi8jNEroAlBTJeUefLp3b993RipyOScFRYAQ2OvOcdP6mxjek1PHQ8RGnbOItOA0D5nb5j5HOWFKjKRqVE2PDFL3aFzaZ9jrn/2SeLmupVr55sQokdKmTJ5c817UMk4Rmz8/+2deXAb153nv68BigRJECCgzMaxJVIkayflxBZFggQpTZxD8iRTW9lkk8xItJVLh4/Y8mycqqlNZNdWxZJrUhU7E0sZO5YdZ6zTm1SOTe1MTUly1s6aJ0hKcZxUUjwl2zOZEADBCzyAfvvH6/fQ3QB4iZIA8PepYklqNLsb0MP7vfc7vr9qYZySXFThlxU7LKm7DVVeRKbncPDlnrSJREqASP043TDksfhCwWb3ZRq00i0gm0MebyPDtBi6rqPtRJdqzGinscqLh870qRWunGhoF0pkwlx3aO4oEJmeAwPDA6d7s/7u1s1etSiXncTP3deSV+Ot4HZQgDXWJF0ngWofukxFpNs2eTA0Np2WLr0U2XZQubYiWSmLSZnk+3u7UXDOsfv5TnRnaNgo0RiU4XIwIPTY3XkxURA3HvGdFHqXLTU+MDBVHuMudmB6PmlZBMluyhUlDtRuLMOltydQbnTMla/n6njLtoMqSD+VXB1omqb6QZ09GMQOU+rutz+3dcXG6Xv3bEPfYzszGqe9L3YjcOR8zqZrLoXs52Suk5DIz5OM0+KMzyxYlDQqjFR8j8upyhrME0qwhjo7E9mRepc6F6r23/yvt6txNDmXMk4MYk77/RMfx6uP3oX3v7cC/W9PgEP0CmvY7M2pHk8roeBcfHbMW9mT+5owGp5R9U0el1MlQLz/vRXoHY2ipcaP+aRuCHL68Na7E4jFE3BqDIfO9qMlg5urEERmPS4n3K4ixOILKC9xQuc6OOdklFaAaK/tR/tAGPWbPPjR/S2YnNNVIfgDp3pVnJMBON62jT5fYtl4SotQv9mL/iupcERzdSWe29uo5hvGGEKjqVi6u8SJH93fYhFpziePSMEbKInsLGnO7vvA+yrQMRjBB2/14NT+lAICAOUijM7M40p4Bp95tgMcQPtgGIGjFyyJAh6XEwEj3pWPqxRAKENMGvG2idkEAkcuoqm6Es/ubYCvrDjnB/LNRiZG6LquUvG/8FIIpw8EAYiJ4+zBINpe6FY1Y/m2iCFuLOZShJZaHx45dxmXrowrV567xImzB4NwOByWmsVyk2K5FCLwlRerovulujrkEuvGQNl3OaPhGXQNiQBi11AEo+EZVG8ss4gjyphMsMaHCmO3BQg3zRsDYTQcuYDttX4wBpUpY287ny+IHVTqPXKItuGNRy5iR50fp/av75qwxVCTg61zaedgOE1ln6SgiOViLkXgnKPp6AVwpDpVz8wlMDGbRGWZw1KzOGFSKOEADp3rx8l9zarMRo7RfPD2FGQMKhN2qZkqf6n6d3lJEXY+9ZolfmTRrhqMqECjnfbBsGjaB6DXaDufj8TiiazvscMQ1CUyk62tdkutkJZZqRwXQUhkiKKybANaakUM3eMqSospyflNyzCsOgfDGA3PWMZoLhfnmlk3Oyi76gQguvGOz8xj19Ovqyr+6PQ8GGPwuJxoqfXjjYEwOLJb8q23ulFWUoTOwUjeBb3NvmjhpqxE97DwX2uAUpBoqfHl1fu60Vglt/x4Zne9JfZJPcaIa8U8f8nYuT2m9PKXAxgNz+DwT99Ex3AqDhWs8asFuRyj+VLHWJBp5kthTqkO1ggXXedg2PL3ltqNeGb3VjQdvWiR+rFTUeLEB97nRtdwFK21+eEKk77oB8/0ITQcRUutHwxAx1AYgapK/I9P/Dk+9/1O6FykRYcO74KvvPhmP3ZOs1jgOZ+C0kR+YZ7LykuKMBFfsNR7mr+/uTwO102h7nIwu++6hsKq66v080p3DGMMrXVCu4oh5fs1MzGbQOdQFByp3lK57NOV0ihm+SLz37tHovjsc52ocBVhanZB9dYi0rF/4bN9TvlSFEnkHksZFfNcJkUFrH3EfJYMv3wbh+smBmXGHI+SEvTe0iLl55X+Xdn08Px//1BG4yQJVHmhAWis9sHjyl2br3o62bT1yjbY6roATMYXcOHRD+d8ls+NQAm+cm7J1sv32jcit1mqvlLXdYxNxOHa4Mj4++4SJ84cyO/vb+7OptcRs2jioXOiH4pMubSro3PO8fWf/SbtGmVFDNMLHC1bKnH6QBD3vNCN0EhEtUvItUFhzjRzm9JQAWu7cUDq7W20ZDWuVzK5gzsGwti62YvLV8eh53HtG5HbLFZfqes6tn3zfFpPMTPmLL98ZV3uoAAoParOwbBlANhVE4Q6QHpr7g/c6oXGAIdDQyyeUJp/8jqZMK/EbzRCrV1k8UzMJmDf6NVvqgAD0FrjQ+jwrpw0sjcD6yQRRvuAyNjsvzKO8mJn3lboE7mPPfPY43Kq+WNkbDrNOGkQi0uPqwgahHdI7vrzlXW5g5Isp+GhUAfYiI6BMZSVODE1mxAK6cMR6BCraQCWDBk5KOy9qLJp3V1vOOd4+Gy/JQ3anA2vAbh8dUI0IDwQXDdK7cvBPEaCNT68+XYMk4aPf3I2gVe/9mHaaRLXBbOnR+eidUvvqEhqSiaTaefrAF796l2o3liG8ZmFNO9QPo7RdW2gltvw8OUvB/Drt2O4zVsCh8MBj8uJhiMXEYsvwO0SKdrP7N6K6Mw8vv6TNzMOCmtdlUhnv1GZceMzC+gaSu/pJJEOvtBIqmU7ITCPEV3XLa0NmqoryTgRa0qmpIhD5/pVI1VA1CVm2xR5S4UGaSbvUD5+r9e1gQKWbnj48pcDaDhyQRXgttb48L17GjA5K9x4k7ML2HOiCz0jVjdgh21QeFxONFZVonskCp0DD5/tw/G2hhtSi+AtLUpTczdTUeLA1GySXFU2zJNFZdkGRKbmLK8/e28DGSdizcjkZRmfWUhLagpUVcKhMXQMie+zxyUUy1tr/Wq+WY53KB9Y9wbKjj0w+eY7ExZ1iM6hCDjncJcYwqrFzjTjBABlxU6hy2YsdT7/gx7Lee2DETQeuaC6+i410V1LDYPUgdv9/Q70GH2vKkoc+MkD21WV+nqX35HxQQDqS26fLCrLNmBHnR8dg2G01vqpNoxYUyxeloEx1dG7tcav2myUb9Bw5kAzHA6HGq/e0qK0728271C+QQbKhn3lccetFapyGxCqCowxJaw6NZtA/SYPLl2NWa4zOZtA05MX0Vq7Ecf21KNzcAz2XTkH0D6wtLtvqfhVNuNlPg4AMF7btsmDHz/QCocjld2Tj9v/tcJeG7ajTqhBdAyMKYUR+Tke27MNAPKiCp/IL+Tc0zEwBrerCLuefk0IBuypR+DoRXAAU/M67nmxB6/c16LmjGxJEPlY92SHDJSNTCuPvsd24fLVGCpKHKj5M7cq4DW7AdsMN195sUMF0WUKMiB02ToGw2l6bVLMcTEFisXSTbMZLznpCoUMH5I6Vzu4y1djeZ9+uhZYu5VaffwPnO5VsblgjR8elzPtcyaItUKORdkSaNfTr6l4NZjo9yRd9KHhiJoDbmby1Y2ADFQGzCsP2abDvLo+tT+YZsReub9V6WTJDBopmeQtLQLnyBrYXEyBQmYEBmv8SiJfppt6XE6MhmfSVvoyXiKfuWMoYhGRDGwhbT3rF9uPYI1P+fQDRqxQcmxPPWLxRN73/CJyE7uRObmvSemA6hx4+Ewfjn7qg/j6z95E78g4WutSMaVC6EW3GGSglkAMAOvqWg4C80AwGzVfeTFO7Q8qAyaz6KR9YhDqE3/44xRiswmUlxSlKVDImMihc/2iAd5mD7q+/jH4youFbL7hBpicXYCmMeg6V9fhnOP+U1btw7JiEUitKHHibJ5Xl68F9vqmnsO7AAAcHOPT89j5nV+pcxljBRN0Jq4fq40T241MLJ7AsT3bEDhyQZSyDEWx6x9+BY/LiZ7DO1FZtsESfyrkcUkGagnEAPCr3Uhr7fIUy6XB4pxD5zoaNnvROzqOoJEFCACBIxcACFkhc3q3ufmYdDP1X4nho0+9hh9+qQntAyKeJbW3dGNrJq+j6zpCo6mYWP1tFbj89gQAETMj9x5sTSZTclef/0EP2gfG4DYyG7fX+VW8qRCCzsT14VpcbWYjE6j2oaLEgVg8obozy4VtLJ5ALL6AR85dUkkT22v9OLW/uWCTnMhALYFsGmbO8FruIBCDtstSw5DUuRpIwRofOociCNraWZibj5mZnEvis9/vzPycAFrrRJHweNyqZPHtv96K//mL3xXsKmslmHemoslkJXRdiAQ3VosCbA5gcjaJhs1enNzXbMmMKiT3CbF2XIurjTGGk/uaRLnKcAQNRy5iMr6Allo/eg5/DDuffh2xeAIeVxEqXE5lnADh0Snk2kUyUMuAMbaslGL7Fj9TDUP3SBS7n+/EuYNB/PbfJsAB8adJecLjcqrJsnmLFz0j44uK1QLAD78UwHOvD6Hp6AU0b/GpzEOPy4ma95Sv+9W/NEwPnekTpQLG8dBIVMQHIboi12/yoN/IyLx0dbygv/zE2nGtrrZYPIHeEaFOIz0jXUNhODQH+h+/GyNj06gocabJqDVWeQt6wUkGao3ItMW3NwGU9IxE8eu3Yyp1PRZPYDQ8gy3vKYeuC0mT0GgUgepKfO+eBgRM6gVmnAxIGDPtF3+Yijl1D0fQ/Y2dmJhNoMpfqqSL1ttEKxcMHpdTue7Mdp5BKD6b29w7mOjxNTGbgDtDbJAgMiF3QaPhGVT5S5e1CJTjs6LEgej0HII1PnQNRVRfJ9kdgTGGx37+lqUtjuT7exsLesFJ3741QIo3mrf4wo10Cb0jUTRXV+Lop27H3d99Q/3OpkqXZZdT5S+Fruv47HPt6L8iVvDdI1GAAdvrNuKNgTHLPc//7V+gsmwDAk++ajkuWzn7yovhd5dc9/eeq5gXDIFqH3qGI2l1aD95sBWffbbDcix0JRW7s8cGCcKOfRFkL0NYrImljDNrGkNC5/C4nOj+xk54S4vQdqLL6I7QjWN7tlkStQDDpb8OisXJQF0j5oHmNjX5A6AMVu9oFD53iTJI7hIHvKVFuP2WCnQORXD7LRUAgLYTXco4pW4AnNrfjNf/8B/44kupXdLUfBK1/6nYUkS8vcaH4/fcGPmkXMccEwiNRNBYXYnQSFQkP8wl0Vrrx9ZNXiUEXG5rQSJbjhSy+4S4NjItgmS5h1ygZkuaMMeZdaM4MhZP4Go0DjCoMoc3BsLg4JZErR21fhxry4+W7dcKGahrxDzQJuMLuGioWwOw+KQZGCYMQzI5m8TfPN+FS1fGwSFccqPhGYRG0rXyZFuQv6jbCKcGJHTAqQF33uZBLJ7AlDGpagw4fk9Dwa+olotdhTxhBPHe/94KPHuv+JzMmXkVJQ60vdCN0LDI6ju+TiYAYvXYF0GBLT70jkTSFqiZkibk+LS7nT/9j+2o3+Sx3Idh9Yla+Q4ZqGvEHhw1q1ubExMAoGmLD91GNfilq+OWAV3lLxUyJ4NjKDdqlmSKMwA4HA78/olP4M13JnDHrRVwOBzwlmqWe5MrKoW5VcH9p3qVikb3SBQHX+7Fjx9sVcZffm6v3NeyrhNJiJVhliZqrPbh7IFmTMwmjcJ8rhKd7EkTMmHnmT1bEZtZwM6nX7cYqUtXY3AXy52+Txmk9bj4ZDeimVUgEOChUGjpE/OU5Rbo6bqufMuyYtxcv2D2Zy+3ruFaRGQLHRkb/NhTr6XFnxo3e/DjB3fQZ0ZcE/bvtIw9mV1/Zw+meqzZdR+31/qxkEii98q4KqaXyDjT6QPZZdAKBcZYL+c8YD9OO6g1YLn1MZqm4ZxtlZ5NjWIlNRS0c0rHrEVob3EPAL1XYje0JxdRWJh1HDN10za7/syJNnZlGnNm3gdvcYvfGRUteThEqnmhyRetBGqdeoOxt5Qnrg/R6Xm0D4r27BOzCfz4vuDNfiSiQJDJEYEj5/Hw2X4Ea3yqxbq3tCitVbt076V0NX0Zr9s1EsVzexsROrwL22t90JgQmV7PiTq0gyIKhrT2Iib+/l9/b/n3dsO3TxArxa7jGKiuBBiQSIr+b5qmpRXGm3f0LbU+9B7eCTDg4TP9SqTY3HAQYMAiAtPrBTJQREFgT/k9c6BZNRcMVIkUc0D49S8+ehe2vKecdrHEqjAnRjUaeo46Fwk4e0504ZX7WtJc73JHD4hmpTLp4czBlrTsvOj0PLqGxO5/vbv4yEARBYF5Vds1HEHbC904dzCoCqHNRZRknIhrwVye4HE50XaiK2OvpuVeyx4HLXSF8pVABoooCDwuJ7Zu8qLgNMRSAAATTklEQVTvimhpHxq2BqfXuxYhsbaYd0hnDwax50QXQsMR1avJnl1bWbZB7eitrrzM16bxKiADReQ9sqlk/5VxlMv6kTrrypOyHYnrhaZplho6ABlbb5h7xC1ldGi8CiiLj8grZJGjruuITs+rlWrnoKjIn5pL4s5bK/BPX2pUacAEcb0xZ+dmar1hP4dYHrSDIvIGu+7h5OwCmoyEiEC1T8UBfv3OBBqOXMT0XGLFzeMIYjWYXXpWmS2/Si83j0EqsF8etIMi8obo9LzqMhyLL0A3JUScOdCMhs1ede7EbCJtBUsQiyF35yvddcvGpI1HzmPvi10ARMyz5/AuMAY0Hb2AvS92q+ua66jsx1dz/0KGDBSRF3DOcehcv+oy7C5OtazvMRIifvxAK5q3iCJId4lTtR5Zz1lQxPLIZjTka4sZjuj0PN4YCEPnQn08Mj1nUpQIpy2UMrkAF7v/eoYMFJEX2CVi/vOflaF8g6FvBuDhs30AgGfv3Ybm6kpMzyXQtMWHk/uayIVCZIVzjvDkLC5diaJ9ID1uJA1H4xPnsfv5DoxNxBGZmrMYkGQyabnmA6f6lMpES60/TVEik9JEtrjVeodiUERe4C0tQmNVpeqT03t1wvJ6+2AEbSe60GMUTQLpOmgEYUaoO3SifVDELh0MSPKUZBFgFNgaLTG6h6OqQeiOOj9O7Q9C13W0fuuX6poNt7kRGokqHT3h5mOWWFOmNHKqfcoMGSgib1jM7VFerFmME7n3iKUYn1lAx2CqB1uSC6URxlJuvYfO9KUp4QNAx6BQeBgNTyOhp44nuKbOD9b4s2btZRKKptqndMhAEXnB+MwCQqPjWV+fmkvNEh6XE68++mHVlJAgMuEtLUJrrU/toADhLu4YCIvCW9OCx05LjQ/e0iJUlFTAabRsdzDgN++KjtgaA463bVvR+KPap3QoBkXkBR6XE+UljqVPBDART0DTNDJOxKLI4tlAlcj+dBjDpbzEie5hq3FqrfGh5xsfRcMmLzQGNbZEI9GP46cPtqKp2qt+Zym1CGJ5kIEi8oJYPIHJ2eTSJwLYXre+WxSsZ8wZd9n+biYWT6DfkMdKGi/Ze4cxAMfv2YaHzl5G39Vx6IaKuUxkcDgcqN5Yjp4RcR0NwLE9K9s9EZkhFx+RF3hcTjRXp5IksvEqKZXnLastXjV3ov78D7qF3l2NXyUqBGv8YAxGqwtr4ba5bbss/ra79bbX+cHAEBpOuQID1T7LIsie5EC7p7WBDBSRs1gnnh6ERq3G6djf3IHn/98I3nx3EoBon03GKT8xt0tZifqHrutKqLWhyqvilG8MhsFgxJSM8gQRXxqzqI3blcmj0/M48HII/Vdj6h7P7K4HIJoHdgyGUb/ZizMHrM9HSQ7XB3LxETmJuXBxz4kudA6OWTL0Wmt8+Mb//q0yTqsJShO5w2J1QJxzRKbm0uqPOOdoO9El4kVAWhJNY5VHnAfAYcx0bpcTyWTSci2zRt4jr1zG5bdjKh7lLnHi0Nl+NB29AICjqboSv746ji+8FEpzF5LW3tpDBorIScwTVmg4gkC1Dw4m6k9Cj+3CkU9/0BKTqt/khbe0KE1IlsgPpItMA9BY7UNFiUP9X977QhcajlxAw5EL2Ptil/p/HZ9ZQM9IJOs1v/WZO9UEJ1PBY/EEAk++mnYteT25EJLxqMnZBNqHIobhjCA0GqVi2hsIufiInMTu0z+5rwmxeEK5T+zV+3//6Q9g74vd6BoKo7ykCJPxBbTWkVBsLmN24Y7PLOC7u+/Eg6f60DMcwbYnzmNyNoltm70qiQEA2gfCuHx1HHfe5oHH5YS7pAix+ALKijTc/r4K9Bi7qMbNHnhKi9BS60fnYDhjfEnWMkl3n3nMlRU7LckSGgNabLEsSsS5/rAbscoMBAI8FApd9/sQhUW2oDnnHLu/32FJmJDxBjMOBoQeu5sC1jmIOeZUusGBybnsGZrlxZqqc3NqYjfkcRXh4lc/pJQdJA2bKqAxhtAVEUPaUevHsbZtSk7ooTO96BgS48bjcqL/8buhaSlHkhxzFSUOtL3QjdBwBC21fhxv26bGEcWZ1h7GWC/nPGA/TjsoImfJVLjIOcfI2HRawoQ0TgwibjA5m0Cwxq8C38udUBYziutxYroe71v+H0pl+sWMEyCKsC9+9UOIxRP4zHMdAISa/cGTvWnn9tkksDqGwmCMqZ/jbQ0IHL0IDmAynkiTwjKPOXMTQvN7pwXPjYMMFJE3ZOoHFaiqhEODWhU3bPbAoWkIjUbBAOX2WyozTNbJHDrXn5aOLDTbuozjfpw+EFwXRipbZp3ZNWd2u8rfWcygma/pdhVhIr5g2fnKxYWdx37+FsxXKy924pIp0y4b9Zu8qChxqHsGa/zYXudflpuOlB1uPmSgiLxBBbEBTMYX8JOvbMedt3kwPrOAwJEL0AH0XklNWh1DYYADOkR68cjYNKo3lqVNnGbDJwWTOgfHEJ2eB2MMuq6j3UhVbh8MIzo9D1958Q15zzeTTJl13tIiNdnLWJ90gXlLi/D5H/QsmipuvubU7AIuPnoXHv/5W+gYCiNQVYm5+QVcfncq7Vk6hyIWQzY9l4C7xJlWVGtGA9B/ZRz3vNCNHiPTL5uAK5GbUBYfkTeY2xS4XUX4zD+2i9454AjWVKadH6iqREutHxrE+buefg17X+xCZGoOuq6r1OXo9LwyfIAIiDdWVeKhM6Jtwn0nrfHTTA3mrkezOXnNZDKJ4T9NIZlMpt0j031X8iyLnbtUW4hYfAE6hNEOHL2gygEWy3LzlhYhWCP+T4I1om7t1IEgQod3gYNnNE4A4LbJXHEAU7MJaIvYF904LzQSQWCLT72PyrINlA6eJ9AOisgbZDHkyNg0dj71WmpyPHIR5cXWCeyO97lx9mAQmqZh+E9T2PWd11VDuYYjF+AuTgXmd9T6Eazxo2sojOYtPiQ5R89wVK3Yzbsy8SB295cfnGNZrsRsSEMBpGIce1/sRsfgGDSWEiPVObDdyE6UdUChkYi6r/y95RS8LlUcu1hbiI6BMZSZ3HG6UQ7QtMWnnie7+4wbn60w7LG4uEZoJLMY8E8eaMHnnuu0HBNq9SKrrmMwnKqRY0CguhKh4SjcriJMzS5kzAIl8gMyUERewRhD9cYytNZtVC45jvRA+2/encQXXgrh5L4mHP7Zb9Lka8zndwyFETLcPpxzNB29YEm6sO8tDp29hONt29T92weyKxUsJ+kCAPa+2IU3jOtsr/XheFuDqsnRjd2NrM1pHxDux/tOhlRxasfgGCJTc5iYTahdTIfhpszmjszkwrPHXMxxGPnML385INxmIxE0bPai2MnQPRxVhsBeZGt+/9HpeaUe3j4Ywe7nO9E3GhWxoVo/3jA1pZRUbSxDS61fuVmbqyvx7L0N6n1Fp+fx8Nl+tUCQxsgeI6N4Uv5BBorIO+TKXiY1dAyEUW6LR3CISXc0PIPOoezFnADgLnbCW1oETdOg6zrKjdoaj8uJ2o2laZlhnUNh6FyH2yXOq3A5oesck3NJuEuciEzNwuNygjGWNclAHg9U+3C8bauS4wHExM05FzuVwTEwpIwTIHYJiUTCopygc+CjT/1fTM4mUWFMzDoHHjrdi7/7xPtx520eOBzWXWamJnl2g2KXm+ocHMPWTV5cMkRT+66Mo3lLJXoO70Jl2QZwzvHA6T6Vnm3XwLNjb+4HCKN26NwldA4JTT1fWTFOHwgiMjWHB8/0ITQcxSOvXFafp69cvG5+bmmMyCjlN2SgiLxETkyn9gctxZ4cHIfOXlKr6Sp/KQLVlegx1Uzd8T63kkgChHq1TDeOxROYjIsdwEQ8gX6bcQKEMXjwdD8mZ8V5k7MJyBBObDaBnd/5FTyuIrz6tbsy7lDMO5eu4QiCT/4Suu0esfiC2gm4izV88vgb+N2/i/hMkgO/+2N6rGbCUNaQLjMA6BiO4r892wGnxvD7Jz6eZqSO7akX8ScGhKdm8ZXT/egdTe2GpFFqrPahZ1gkKvRdGbdk2/UMR9XuUEoPAcL9qhluSfP731HnTxN0lbEhaRQBANxUPsAYNE1D70gUOtJ3fLRDKkzIQBF5jXliki6f0weCKp7DGMMr97Vgz/OdCI1G0VLjA2CNQbTWptpzeEuL0Fq3UcWWdJ2jw9iBNVV5lVJB70hUxVuCNT689e6ExTDE4guIzSyYdih+lUzhLS1CoNqHLmMitxun8g0adj79uoo1Mcbwi4d34M8f/1ckOeDUGLbX+JQLKxNN1ZVqdwIACZ3jzXcmUL9ZJJNYU/bTr9NuZD1KQ9ozHEG5yShNziZQtkHD9LyOClcRKkocGBmbtkgPuUscuONWD7qGUjEp2YPJ7N60u0DHZxbQNRRWWXfSEFFb9PUHKUkQBUem4D8gJj4ZY0py4Sq78NX09hz2+JDMcnvk3CUVI9le68fJfU24EonDXeJA4KhV0cDjKkL/4yKuFZmewwOn+tA7ElXyS7quY+s3z2PKFAtzFztEdppxTAPQ+7hQwohOz6PhifPgEOa17/G7kdSTlvs2VVeidzSK1lo/Tu5rRmR6DsEnX1VGzbyDik7PI3DkvMV1aKe1xoeEztE7EkXAMMaZOsxqgNqlmo2YBiD02MpTuhdL3livBdOFDilJEOuGbMF/GSMxr8Izteewu4t85cUiFX1IGCeNAcfa6vGFl0LC/VVlTXH/6YOt2LrJC03TwDnHV073KxejTKIAgBmTcbrz1go8/ddbsesffqWO1W/2KiPpcTlRYYl56WC2neBz9zao98IYw0a3C3848gm8+c4E7ri1wuLes2TjFWeWGuoYikAD0LTFhzMHmvGFl0LoMKnKA8IINVR5lezU5GwC2zZ5cPlqDK11G1eVzp0pe9BsmMiVt34gA0UUHIu5glbbt8d+TQamjGDvaFTsXkaiaKn1o35zpcVdFTK5vQJbUo3uZCZiYIsP5w4GAYidVyy+gIoSJ350f4u6TiyewJQR84rFE2g6ehGtdX601vgMF5poMW4vlHU4HMqtZ8acaGLWp6uwJZvoEHVEE7NJdX4qY86PZ3bX48HTfZZrn/h8IxwOR0bjstzP2549uJpeUUT+QwaKKDiWMkKrCajbrwlgUbV1idmwBap9OHswJZMkJ3x5fcYY+h/fhdHwDKr8pRYRU7XjkannENlxZlUE885xMeUM83tiTKSIA2I39MuvfVgZlUPnUskm8n2ZM+Y8LidGwzNpuoiapq2pcVlOOjxRmJCBIgqS65HVZb+m3Qhmut9SxvLQuUuWyVvTNGx5T3nW69hrfswuNHv78l1Pv7akUbDvDGWiyfjMAk7tb85a3JoyPGFLksX2Wp/lc1gL40LJEesXSpIgiJuEOVFhJa1BFnOZSaXwXU+/tuzrphcNZ9/xqOw/UyyKAbj46F3wlqZLCK2Ve46SIwobSpIgiBxjtTuDxXaHUmljJdc1X0/qEmbb8Zi7zkoqXEWo3lhmcUmar72amN9iz0isH8hAEcRNYq0m77W87lJG0x4LA4Qqub2vkv15yLgQq4EMFEHcRK7X5L3a6y4nwSRTLIziQsT1gAwUQRAWljJu2fTvCGKtIQNFEMSqINcdcb2hhoUEQRBETkIGiiAIgshJyEARBEEQOQkZKIIgCCInIQNFEARB5CRkoAiCIIichAwUQRAEkZPcELFYxtifAIxe9xsRBEEQ+UgV5/w99oM3xEARBEEQxEohFx9BEASRk5CBIgiCIHISMlAEQRBETkIGiiAIgshJyEARhAFj7IeMMW78JBhjo4yx5xhjfuN1zhjbm+H3vsQYS2S55r8wxpKMsf9iOjZiuk/GnwzPY/6ZMl3rLsbYz41n5Yyxx9b+kyGImwMZKIKw8isAtwCoBvAIgM8CeHk1F2KMVQP4CIBvA7jP9FKTcY9bADQbxz5lOnZLhucx/9SYXi8H8FsAfwfg31fznASRq1A/KIKwMs85lxP924yxDwL4JmPMtYprHQDwzwC+C2CIMXYr5/wdzvmf5AmMsRLjrxHTfbM9Txqc83827gHG2LdW8YwEkbPQDoogFicO8T1Z0WKOMeYEsA/ADznn7wL4JYD9a/94BFG4kIEiiCwwxm4H8BCALs75pHH4BcbYlPkHwHMZfv2TEN+vfzH+/U8A9jPGVvqd+4j9foyxX6zm/RBEvkEuPoKw8hHD6DgAFAO4COB+0+uHAfzc9jufAfCk7dh9AE5zzmXyxM8gDNlfAfg/K3ieLgBftB2bWcHvE0TeQgaKIKxIg5AA8C7nfN72+h855wPmA4yx/7D9uxrAXwL4S8bY35peckAYrpUYqLj9fgSxXiADRRBW1sIgHADwOwB7bMc/AOC0TJa4xnsQRMFDBoog1hBTcsSznPPf2F57C8BTEMkS31zmJTcwxt6b4fgfOeecMVYOoE6eC+C9jLF6AFO08yLyHUqSIIi15ZMQtUr/y/4CF60DfoSVJUt8CMC/ZfjxG68HAPQbP7dAJHX0A3hh9W+BIHIDardBEARB5CS0gyIIgiByEjJQBEEQRE5CBoogCILISchAEQRBEDkJGSiCIAgiJyEDRRAEQeQkZKAIgiCInIQMFEEQBJGT/H93BGiZ9r/e9gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "scp.plot.scatter2d(phate_embd, ticks=None, label_prefix='PHATE')"
      ],
      "id": "c6b2f2f5"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dde50b92"
      },
      "source": [
        "We take a quick look at an old subject's data below"
      ],
      "id": "dde50b92"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "a56afd31"
      },
      "outputs": [],
      "source": [
        "data1 = pd.read_excel(r\"OLD/l_OFC_voxel.xlsx\", header=None, engine='openpyxl', sheet_name=1)"
      ],
      "id": "a56afd31"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "82e2f518",
        "outputId": "b594ba1a-bccd-4284-f245-61699c76e7eb"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-aadf9f61-baea-4d61-8387-b9a509630532\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>...</th>\n",
              "      <th>527</th>\n",
              "      <th>528</th>\n",
              "      <th>529</th>\n",
              "      <th>530</th>\n",
              "      <th>531</th>\n",
              "      <th>532</th>\n",
              "      <th>533</th>\n",
              "      <th>534</th>\n",
              "      <th>535</th>\n",
              "      <th>536</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>58.557491</td>\n",
              "      <td>66.542604</td>\n",
              "      <td>63.411187</td>\n",
              "      <td>65.916320</td>\n",
              "      <td>67.638600</td>\n",
              "      <td>69.987162</td>\n",
              "      <td>71.866012</td>\n",
              "      <td>66.699175</td>\n",
              "      <td>68.264883</td>\n",
              "      <td>70.143733</td>\n",
              "      <td>...</td>\n",
              "      <td>152.813132</td>\n",
              "      <td>156.883974</td>\n",
              "      <td>138.721757</td>\n",
              "      <td>141.853174</td>\n",
              "      <td>145.610874</td>\n",
              "      <td>149.368574</td>\n",
              "      <td>152.813132</td>\n",
              "      <td>139.348041</td>\n",
              "      <td>142.792599</td>\n",
              "      <td>146.550299</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>58.244350</td>\n",
              "      <td>66.229462</td>\n",
              "      <td>62.941475</td>\n",
              "      <td>65.446608</td>\n",
              "      <td>67.325458</td>\n",
              "      <td>69.674020</td>\n",
              "      <td>71.396300</td>\n",
              "      <td>66.229462</td>\n",
              "      <td>67.951741</td>\n",
              "      <td>69.987162</td>\n",
              "      <td>...</td>\n",
              "      <td>151.873707</td>\n",
              "      <td>155.944549</td>\n",
              "      <td>137.782332</td>\n",
              "      <td>140.600607</td>\n",
              "      <td>144.358307</td>\n",
              "      <td>148.429149</td>\n",
              "      <td>152.186849</td>\n",
              "      <td>138.408616</td>\n",
              "      <td>141.853174</td>\n",
              "      <td>145.924016</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>57.618066</td>\n",
              "      <td>65.759750</td>\n",
              "      <td>62.158620</td>\n",
              "      <td>65.133466</td>\n",
              "      <td>67.012316</td>\n",
              "      <td>69.204308</td>\n",
              "      <td>70.613445</td>\n",
              "      <td>65.290037</td>\n",
              "      <td>67.638600</td>\n",
              "      <td>69.674020</td>\n",
              "      <td>...</td>\n",
              "      <td>151.873707</td>\n",
              "      <td>155.631407</td>\n",
              "      <td>136.529766</td>\n",
              "      <td>139.974324</td>\n",
              "      <td>144.045166</td>\n",
              "      <td>148.116007</td>\n",
              "      <td>151.560566</td>\n",
              "      <td>137.469191</td>\n",
              "      <td>141.226891</td>\n",
              "      <td>144.984591</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>57.618066</td>\n",
              "      <td>65.759750</td>\n",
              "      <td>62.002050</td>\n",
              "      <td>64.663754</td>\n",
              "      <td>66.855745</td>\n",
              "      <td>69.047737</td>\n",
              "      <td>70.613445</td>\n",
              "      <td>65.290037</td>\n",
              "      <td>67.168887</td>\n",
              "      <td>69.517450</td>\n",
              "      <td>...</td>\n",
              "      <td>152.499991</td>\n",
              "      <td>156.570832</td>\n",
              "      <td>137.156049</td>\n",
              "      <td>140.287466</td>\n",
              "      <td>144.671449</td>\n",
              "      <td>149.055432</td>\n",
              "      <td>152.813132</td>\n",
              "      <td>138.095474</td>\n",
              "      <td>142.166316</td>\n",
              "      <td>146.237157</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>57.618066</td>\n",
              "      <td>65.603179</td>\n",
              "      <td>62.315191</td>\n",
              "      <td>64.976895</td>\n",
              "      <td>67.012316</td>\n",
              "      <td>69.360879</td>\n",
              "      <td>70.770016</td>\n",
              "      <td>65.603179</td>\n",
              "      <td>67.482029</td>\n",
              "      <td>69.517450</td>\n",
              "      <td>...</td>\n",
              "      <td>153.126274</td>\n",
              "      <td>156.883974</td>\n",
              "      <td>136.842907</td>\n",
              "      <td>140.287466</td>\n",
              "      <td>144.984591</td>\n",
              "      <td>149.681716</td>\n",
              "      <td>153.126274</td>\n",
              "      <td>138.095474</td>\n",
              "      <td>142.166316</td>\n",
              "      <td>146.550299</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>184</th>\n",
              "      <td>57.461495</td>\n",
              "      <td>66.229462</td>\n",
              "      <td>62.784904</td>\n",
              "      <td>65.446608</td>\n",
              "      <td>67.012316</td>\n",
              "      <td>69.204308</td>\n",
              "      <td>70.613445</td>\n",
              "      <td>65.759750</td>\n",
              "      <td>67.795170</td>\n",
              "      <td>69.674020</td>\n",
              "      <td>...</td>\n",
              "      <td>148.116007</td>\n",
              "      <td>151.873707</td>\n",
              "      <td>130.893216</td>\n",
              "      <td>135.277199</td>\n",
              "      <td>140.287466</td>\n",
              "      <td>144.671449</td>\n",
              "      <td>148.116007</td>\n",
              "      <td>133.398349</td>\n",
              "      <td>138.095474</td>\n",
              "      <td>142.479457</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>185</th>\n",
              "      <td>57.931208</td>\n",
              "      <td>66.386033</td>\n",
              "      <td>63.254616</td>\n",
              "      <td>65.446608</td>\n",
              "      <td>67.012316</td>\n",
              "      <td>69.360879</td>\n",
              "      <td>71.083158</td>\n",
              "      <td>66.542604</td>\n",
              "      <td>67.795170</td>\n",
              "      <td>69.674020</td>\n",
              "      <td>...</td>\n",
              "      <td>148.429149</td>\n",
              "      <td>152.186849</td>\n",
              "      <td>132.458924</td>\n",
              "      <td>136.529766</td>\n",
              "      <td>141.226891</td>\n",
              "      <td>145.297732</td>\n",
              "      <td>148.742291</td>\n",
              "      <td>134.650916</td>\n",
              "      <td>138.721757</td>\n",
              "      <td>142.792599</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>186</th>\n",
              "      <td>57.774637</td>\n",
              "      <td>65.916320</td>\n",
              "      <td>62.784904</td>\n",
              "      <td>65.133466</td>\n",
              "      <td>66.855745</td>\n",
              "      <td>69.204308</td>\n",
              "      <td>71.083158</td>\n",
              "      <td>66.229462</td>\n",
              "      <td>67.638600</td>\n",
              "      <td>69.830591</td>\n",
              "      <td>...</td>\n",
              "      <td>148.429149</td>\n",
              "      <td>152.499991</td>\n",
              "      <td>131.832641</td>\n",
              "      <td>135.903482</td>\n",
              "      <td>140.600607</td>\n",
              "      <td>144.984591</td>\n",
              "      <td>148.742291</td>\n",
              "      <td>134.024632</td>\n",
              "      <td>138.408616</td>\n",
              "      <td>142.479457</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>187</th>\n",
              "      <td>56.678641</td>\n",
              "      <td>65.133466</td>\n",
              "      <td>62.002050</td>\n",
              "      <td>64.976895</td>\n",
              "      <td>66.072891</td>\n",
              "      <td>67.951741</td>\n",
              "      <td>69.360879</td>\n",
              "      <td>64.820325</td>\n",
              "      <td>67.168887</td>\n",
              "      <td>68.891166</td>\n",
              "      <td>...</td>\n",
              "      <td>149.368574</td>\n",
              "      <td>153.126274</td>\n",
              "      <td>132.145782</td>\n",
              "      <td>136.216624</td>\n",
              "      <td>141.226891</td>\n",
              "      <td>145.610874</td>\n",
              "      <td>149.055432</td>\n",
              "      <td>134.337774</td>\n",
              "      <td>138.721757</td>\n",
              "      <td>143.105741</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>188</th>\n",
              "      <td>57.931208</td>\n",
              "      <td>66.699175</td>\n",
              "      <td>63.098045</td>\n",
              "      <td>66.072891</td>\n",
              "      <td>67.325458</td>\n",
              "      <td>69.517450</td>\n",
              "      <td>70.926587</td>\n",
              "      <td>66.229462</td>\n",
              "      <td>68.108312</td>\n",
              "      <td>70.143733</td>\n",
              "      <td>...</td>\n",
              "      <td>150.307999</td>\n",
              "      <td>153.752557</td>\n",
              "      <td>133.398349</td>\n",
              "      <td>137.782332</td>\n",
              "      <td>142.479457</td>\n",
              "      <td>146.863441</td>\n",
              "      <td>149.994857</td>\n",
              "      <td>135.590341</td>\n",
              "      <td>139.661182</td>\n",
              "      <td>143.732024</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>189 rows × 537 columns</p>\n",
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            "text/plain": [
              "           0          1          2          3          4          5    \\\n",
              "0    58.557491  66.542604  63.411187  65.916320  67.638600  69.987162   \n",
              "1    58.244350  66.229462  62.941475  65.446608  67.325458  69.674020   \n",
              "2    57.618066  65.759750  62.158620  65.133466  67.012316  69.204308   \n",
              "3    57.618066  65.759750  62.002050  64.663754  66.855745  69.047737   \n",
              "4    57.618066  65.603179  62.315191  64.976895  67.012316  69.360879   \n",
              "..         ...        ...        ...        ...        ...        ...   \n",
              "184  57.461495  66.229462  62.784904  65.446608  67.012316  69.204308   \n",
              "185  57.931208  66.386033  63.254616  65.446608  67.012316  69.360879   \n",
              "186  57.774637  65.916320  62.784904  65.133466  66.855745  69.204308   \n",
              "187  56.678641  65.133466  62.002050  64.976895  66.072891  67.951741   \n",
              "188  57.931208  66.699175  63.098045  66.072891  67.325458  69.517450   \n",
              "\n",
              "           6          7          8          9    ...         527         528  \\\n",
              "0    71.866012  66.699175  68.264883  70.143733  ...  152.813132  156.883974   \n",
              "1    71.396300  66.229462  67.951741  69.987162  ...  151.873707  155.944549   \n",
              "2    70.613445  65.290037  67.638600  69.674020  ...  151.873707  155.631407   \n",
              "3    70.613445  65.290037  67.168887  69.517450  ...  152.499991  156.570832   \n",
              "4    70.770016  65.603179  67.482029  69.517450  ...  153.126274  156.883974   \n",
              "..         ...        ...        ...        ...  ...         ...         ...   \n",
              "184  70.613445  65.759750  67.795170  69.674020  ...  148.116007  151.873707   \n",
              "185  71.083158  66.542604  67.795170  69.674020  ...  148.429149  152.186849   \n",
              "186  71.083158  66.229462  67.638600  69.830591  ...  148.429149  152.499991   \n",
              "187  69.360879  64.820325  67.168887  68.891166  ...  149.368574  153.126274   \n",
              "188  70.926587  66.229462  68.108312  70.143733  ...  150.307999  153.752557   \n",
              "\n",
              "            529         530         531         532         533         534  \\\n",
              "0    138.721757  141.853174  145.610874  149.368574  152.813132  139.348041   \n",
              "1    137.782332  140.600607  144.358307  148.429149  152.186849  138.408616   \n",
              "2    136.529766  139.974324  144.045166  148.116007  151.560566  137.469191   \n",
              "3    137.156049  140.287466  144.671449  149.055432  152.813132  138.095474   \n",
              "4    136.842907  140.287466  144.984591  149.681716  153.126274  138.095474   \n",
              "..          ...         ...         ...         ...         ...         ...   \n",
              "184  130.893216  135.277199  140.287466  144.671449  148.116007  133.398349   \n",
              "185  132.458924  136.529766  141.226891  145.297732  148.742291  134.650916   \n",
              "186  131.832641  135.903482  140.600607  144.984591  148.742291  134.024632   \n",
              "187  132.145782  136.216624  141.226891  145.610874  149.055432  134.337774   \n",
              "188  133.398349  137.782332  142.479457  146.863441  149.994857  135.590341   \n",
              "\n",
              "            535         536  \n",
              "0    142.792599  146.550299  \n",
              "1    141.853174  145.924016  \n",
              "2    141.226891  144.984591  \n",
              "3    142.166316  146.237157  \n",
              "4    142.166316  146.550299  \n",
              "..          ...         ...  \n",
              "184  138.095474  142.479457  \n",
              "185  138.721757  142.792599  \n",
              "186  138.408616  142.479457  \n",
              "187  138.721757  143.105741  \n",
              "188  139.661182  143.732024  \n",
              "\n",
              "[189 rows x 537 columns]"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data1"
      ],
      "id": "82e2f518"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8abc3feb",
        "outputId": "f0343390-d330-4abf-ea9b-cc74c65418f1"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Calculating PHATE...\n",
            "  Running PHATE on 537 observations and 189 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.08 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.03 seconds.\n",
            "    Calculating affinities...\n",
            "  Calculated graph and diffusion operator in 0.14 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 19\n",
            "  Calculated optimal t in 0.16 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 0.11 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.33 seconds.\n",
            "Calculated PHATE in 0.77 seconds.\n"
          ]
        }
      ],
      "source": [
        "phate_op = ph.PHATE()\n",
        "phate_embd =  phate_op.fit_transform(data1.T)"
      ],
      "id": "8abc3feb"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 315
        },
        "id": "62cf9712",
        "outputId": "b47f392b-a3d8-45f1-a86d-183209f97b03"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f2980c57650>"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "scp.plot.scatter2d(phate_embd, ticks=None, label_prefix='PHATE')"
      ],
      "id": "62cf9712"
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Average Young vs Average Old Subject Comparison"
      ],
      "metadata": {
        "id": "SpHYMeFOuDfi"
      },
      "id": "SpHYMeFOuDfi"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ac497e9a"
      },
      "source": [
        "After a brief one-to-one comparison of one old and one young subject, we turn our attention to the entire data for each group.\\\n",
        "Loading the entire young subjects data "
      ],
      "id": "ac497e9a"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7bda5b70"
      },
      "outputs": [],
      "source": [
        "data = pd.ExcelFile(r\"YOUNG/lOFC.xlsx\", engine=\"openpyxl\")"
      ],
      "id": "7bda5b70"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "25d7dcd4"
      },
      "source": [
        "We see that there are in total 111 young subjects in our data"
      ],
      "id": "25d7dcd4"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c917405b",
        "outputId": "11e38a7a-5701-4fd9-a12b-90b19bf38036"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "111"
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          },
          "metadata": {},
          "execution_count": 53
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      ],
      "source": [
        "len(data.sheet_names)"
      ],
      "id": "c917405b"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "00ace7b4"
      },
      "source": [
        "Let's look at the first young subject's data"
      ],
      "id": "00ace7b4"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
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          "height": 483
        },
        "id": "2f1396aa",
        "outputId": "04d15c96-da20-4d5f-b213-bacee4bb2969"
      },
      "outputs": [
        {
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              "          document.querySelector('#df-ddf379f9-a5d4-41b0-8617-3820f2c6ed10 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-ddf379f9-a5d4-41b0-8617-3820f2c6ed10');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "y1_data = data.parse(\"Sheet1\", header=None)\n",
        "y1_data"
      ],
      "id": "2f1396aa"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9fd7588c"
      },
      "source": [
        "Constructing a 3D Tensor of all the young subject's data\n",
        "- The Dimension of the Tensor is (TR, Voxel, Number of Subjects) "
      ],
      "id": "9fd7588c"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "38644bdf"
      },
      "outputs": [],
      "source": [
        "young_data = np.zeros((y1_data.shape[0], y1_data.shape[1], len(data.sheet_names)))"
      ],
      "id": "38644bdf"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0b0dc409"
      },
      "outputs": [],
      "source": [
        "# Run only once and save the .npy file\n",
        "# for i in range(len(data.sheet_names)): # Takes long duration to complete, prefer saving the output tensor\n",
        "#    young_data[:,:,i] = data.parse(\"Sheet\"+str(i+1), header=None).to_numpy()"
      ],
      "id": "0b0dc409"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "08bfdec4"
      },
      "outputs": [],
      "source": [
        "# np.save('young_data.npy', young_data) \n",
        "young_data = np.load('young_data.npy')"
      ],
      "id": "08bfdec4"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "03ac3174"
      },
      "source": [
        "Averaging the young subject's data over subjects"
      ],
      "id": "03ac3174"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "34772e1a"
      },
      "outputs": [],
      "source": [
        "avg_young_data = np.mean(young_data, axis=2)"
      ],
      "id": "34772e1a"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "598854b7",
        "outputId": "b82f7def-398a-4d57-af44-3a49369b3d89",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(189, 1700)"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ],
      "source": [
        "avg_young_data.shape"
      ],
      "id": "598854b7"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f3bd8bac"
      },
      "source": [
        "Loading all the old subject's data"
      ],
      "id": "f3bd8bac"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6fd53eb7"
      },
      "outputs": [],
      "source": [
        "data = pd.ExcelFile(r\"OLD/l_OFC_voxel.xlsx\", engine=\"openpyxl\")"
      ],
      "id": "6fd53eb7"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5748465c"
      },
      "source": [
        "We have 25 old subjects in our dataset"
      ],
      "id": "5748465c"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "e3ebb9c5",
        "outputId": "3d3997e1-55b6-425b-87e1-3e5a149212bd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "25"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ],
      "source": [
        "len(data.sheet_names)"
      ],
      "id": "e3ebb9c5"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "46529d42"
      },
      "source": [
        "Let's look at the first old subject's data"
      ],
      "id": "46529d42"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "00d68343",
        "outputId": "a479be59-e242-4704-e6d6-0aefd1d3a08f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           0          1          2          3          4          5    \\\n",
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              "..         ...        ...        ...        ...  ...         ...         ...   \n",
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              "186  67.393452  61.929118  70.672052  71.582775  ...  178.501576  183.965910   \n",
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              "\n",
              "            529         530         531         532         533         534  \\\n",
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              "2    146.444150  154.094217  163.565730  171.580086  176.315842  156.279951   \n",
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              "4    147.901306  155.551373  165.387174  173.401531  177.772998  157.737107   \n",
              "..          ...         ...         ...         ...         ...         ...   \n",
              "184  156.279951  165.751463  176.315842  183.965910  187.973088  168.301486   \n",
              "185  154.822795  163.930019  174.130109  182.508754  186.880221  166.480041   \n",
              "186  154.458506  163.930019  174.858686  183.237332  187.608799  166.480041   \n",
              "187  154.822795  163.930019  174.494398  182.508754  186.880221  166.480041   \n",
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              "\n",
              "            535         536  \n",
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              "4    166.115752  172.672953  \n",
              "..          ...         ...  \n",
              "184  176.680131  182.508754  \n",
              "185  174.858686  181.415887  \n",
              "186  175.951553  182.508754  \n",
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              "188  175.951553  182.508754  \n",
              "\n",
              "[189 rows x 537 columns]"
            ],
            "text/html": [
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              "    <div class=\"colab-df-container\">\n",
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              "      <th>0</th>\n",
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              "      <th>2</th>\n",
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              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>...</th>\n",
              "      <th>527</th>\n",
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              "      <td>168.665775</td>\n",
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              "      <td>172.308664</td>\n",
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              "      <th>1</th>\n",
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              "      <td>66.664874</td>\n",
              "      <td>68.668463</td>\n",
              "      <td>69.943475</td>\n",
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              "      <td>75.043520</td>\n",
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              "      <td>155.551373</td>\n",
              "      <td>164.658596</td>\n",
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              "      <td>66.300585</td>\n",
              "      <td>69.397041</td>\n",
              "      <td>70.307764</td>\n",
              "      <td>71.036341</td>\n",
              "      <td>72.675642</td>\n",
              "      <td>70.125619</td>\n",
              "      <td>74.132797</td>\n",
              "      <td>75.589953</td>\n",
              "      <td>...</td>\n",
              "      <td>167.937197</td>\n",
              "      <td>172.672953</td>\n",
              "      <td>146.444150</td>\n",
              "      <td>154.094217</td>\n",
              "      <td>163.565730</td>\n",
              "      <td>171.580086</td>\n",
              "      <td>176.315842</td>\n",
              "      <td>156.279951</td>\n",
              "      <td>164.658596</td>\n",
              "      <td>171.215797</td>\n",
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              "    <tr>\n",
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              "      <td>66.300585</td>\n",
              "      <td>69.214897</td>\n",
              "      <td>69.943475</td>\n",
              "      <td>70.854197</td>\n",
              "      <td>72.493497</td>\n",
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              "      <td>75.043520</td>\n",
              "      <td>...</td>\n",
              "      <td>169.394352</td>\n",
              "      <td>174.130109</td>\n",
              "      <td>147.901306</td>\n",
              "      <td>155.551373</td>\n",
              "      <td>165.022885</td>\n",
              "      <td>172.672953</td>\n",
              "      <td>177.044420</td>\n",
              "      <td>157.372818</td>\n",
              "      <td>165.387174</td>\n",
              "      <td>171.944375</td>\n",
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              "      <th>4</th>\n",
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              "      <td>65.025574</td>\n",
              "      <td>65.936296</td>\n",
              "      <td>68.486319</td>\n",
              "      <td>69.761330</td>\n",
              "      <td>70.672052</td>\n",
              "      <td>72.311353</td>\n",
              "      <td>70.125619</td>\n",
              "      <td>73.586364</td>\n",
              "      <td>75.225664</td>\n",
              "      <td>...</td>\n",
              "      <td>169.758641</td>\n",
              "      <td>174.494398</td>\n",
              "      <td>147.901306</td>\n",
              "      <td>155.551373</td>\n",
              "      <td>165.387174</td>\n",
              "      <td>173.401531</td>\n",
              "      <td>177.772998</td>\n",
              "      <td>157.737107</td>\n",
              "      <td>166.115752</td>\n",
              "      <td>172.672953</td>\n",
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              "    <tr>\n",
              "      <th>...</th>\n",
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              "      <td>...</td>\n",
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              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
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              "    <tr>\n",
              "      <th>184</th>\n",
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              "      <td>62.657696</td>\n",
              "      <td>62.293407</td>\n",
              "      <td>67.757741</td>\n",
              "      <td>67.393452</td>\n",
              "      <td>67.211308</td>\n",
              "      <td>67.939885</td>\n",
              "      <td>63.204129</td>\n",
              "      <td>71.400630</td>\n",
              "      <td>72.311353</td>\n",
              "      <td>...</td>\n",
              "      <td>180.323020</td>\n",
              "      <td>185.787354</td>\n",
              "      <td>156.279951</td>\n",
              "      <td>165.751463</td>\n",
              "      <td>176.315842</td>\n",
              "      <td>183.965910</td>\n",
              "      <td>187.973088</td>\n",
              "      <td>168.301486</td>\n",
              "      <td>176.680131</td>\n",
              "      <td>182.508754</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>185</th>\n",
              "      <td>55.371917</td>\n",
              "      <td>62.475552</td>\n",
              "      <td>61.929118</td>\n",
              "      <td>67.393452</td>\n",
              "      <td>67.393452</td>\n",
              "      <td>67.029163</td>\n",
              "      <td>67.757741</td>\n",
              "      <td>62.839840</td>\n",
              "      <td>71.036341</td>\n",
              "      <td>71.764919</td>\n",
              "      <td>...</td>\n",
              "      <td>178.137287</td>\n",
              "      <td>183.601621</td>\n",
              "      <td>154.822795</td>\n",
              "      <td>163.930019</td>\n",
              "      <td>174.130109</td>\n",
              "      <td>182.508754</td>\n",
              "      <td>186.880221</td>\n",
              "      <td>166.480041</td>\n",
              "      <td>174.858686</td>\n",
              "      <td>181.415887</td>\n",
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              "    <tr>\n",
              "      <th>186</th>\n",
              "      <td>55.007628</td>\n",
              "      <td>62.111263</td>\n",
              "      <td>61.200540</td>\n",
              "      <td>67.211308</td>\n",
              "      <td>67.029163</td>\n",
              "      <td>66.847019</td>\n",
              "      <td>67.393452</td>\n",
              "      <td>61.929118</td>\n",
              "      <td>70.672052</td>\n",
              "      <td>71.582775</td>\n",
              "      <td>...</td>\n",
              "      <td>178.501576</td>\n",
              "      <td>183.965910</td>\n",
              "      <td>154.458506</td>\n",
              "      <td>163.930019</td>\n",
              "      <td>174.858686</td>\n",
              "      <td>183.237332</td>\n",
              "      <td>187.608799</td>\n",
              "      <td>166.480041</td>\n",
              "      <td>175.951553</td>\n",
              "      <td>182.508754</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>187</th>\n",
              "      <td>55.371917</td>\n",
              "      <td>62.657696</td>\n",
              "      <td>61.746974</td>\n",
              "      <td>67.757741</td>\n",
              "      <td>67.393452</td>\n",
              "      <td>67.211308</td>\n",
              "      <td>67.757741</td>\n",
              "      <td>62.657696</td>\n",
              "      <td>71.400630</td>\n",
              "      <td>72.311353</td>\n",
              "      <td>...</td>\n",
              "      <td>178.137287</td>\n",
              "      <td>183.601621</td>\n",
              "      <td>154.822795</td>\n",
              "      <td>163.930019</td>\n",
              "      <td>174.494398</td>\n",
              "      <td>182.508754</td>\n",
              "      <td>186.880221</td>\n",
              "      <td>166.480041</td>\n",
              "      <td>175.222975</td>\n",
              "      <td>181.780176</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>188</th>\n",
              "      <td>55.189773</td>\n",
              "      <td>62.293407</td>\n",
              "      <td>61.564829</td>\n",
              "      <td>67.575597</td>\n",
              "      <td>67.211308</td>\n",
              "      <td>67.029163</td>\n",
              "      <td>67.575597</td>\n",
              "      <td>62.657696</td>\n",
              "      <td>71.036341</td>\n",
              "      <td>71.947064</td>\n",
              "      <td>...</td>\n",
              "      <td>179.230154</td>\n",
              "      <td>185.058776</td>\n",
              "      <td>155.187084</td>\n",
              "      <td>164.294307</td>\n",
              "      <td>175.222975</td>\n",
              "      <td>183.601621</td>\n",
              "      <td>188.337377</td>\n",
              "      <td>167.208619</td>\n",
              "      <td>175.951553</td>\n",
              "      <td>182.508754</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>189 rows × 537 columns</p>\n",
              "</div>\n",
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            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ],
      "source": [
        "o1_data = data.parse(\"Sheet1\", header=None)\n",
        "o1_data"
      ],
      "id": "00d68343"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f9393fce"
      },
      "source": [
        "Constructing a 3D Tensor of all the old subject's data\n",
        "- The Dimension of the Tensor is (TR, Voxel, Number of Subjects) "
      ],
      "id": "f9393fce"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7fc96615"
      },
      "outputs": [],
      "source": [
        "old_data = np.zeros((o1_data.shape[0], o1_data.shape[1], len(data.sheet_names)))"
      ],
      "id": "7fc96615"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ecc30f27"
      },
      "outputs": [],
      "source": [
        "# Run only once\n",
        "# for i in range(len(data.sheet_names)): # Takes long duration to complete, prefer saving the output tensor\n",
        "#     old_data[:,:,i] = data.parse(\"Sheet\"+str(i+1), header=None).to_numpy()"
      ],
      "id": "ecc30f27"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "c6427d48"
      },
      "outputs": [],
      "source": [
        "# np.save('old_data.npy', old_data) \n",
        "old_data = np.load(\"old_data.npy\")"
      ],
      "id": "c6427d48"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3f9273f8"
      },
      "source": [
        "Averaging the old subject's data over subjects"
      ],
      "id": "3f9273f8"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "753dbd99"
      },
      "outputs": [],
      "source": [
        "avg_old_data = np.mean(old_data, axis=2)"
      ],
      "id": "753dbd99"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "540e360a",
        "outputId": "6e3ab7b1-fc24-41eb-fdf5-969bd528324a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(189, 537)"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ],
      "source": [
        "avg_old_data.shape"
      ],
      "id": "540e360a"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9c1300a6"
      },
      "source": [
        "Running the PHATE Dimension Reduction on both average young and old subject's data and visualization with the averaged data below."
      ],
      "id": "9c1300a6"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4c996e81",
        "outputId": "2063cc1e-e0ad-4441-a885-2f92110f5089",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Calculating PHATE...\n",
            "  Running PHATE on 1700 observations and 189 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.15 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.08 seconds.\n",
            "    Calculating affinities...\n",
            "    Calculated affinities in 0.02 seconds.\n",
            "  Calculated graph and diffusion operator in 0.28 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 20\n",
            "  Calculated optimal t in 3.43 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 1.53 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 5.30 seconds.\n",
            "Calculated PHATE in 10.58 seconds.\n",
            "Calculating PHATE...\n",
            "  Running PHATE on 537 observations and 189 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.07 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.04 seconds.\n",
            "    Calculating affinities...\n",
            "    Calculated affinities in 0.02 seconds.\n",
            "  Calculated graph and diffusion operator in 0.15 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 22\n",
            "  Calculated optimal t in 0.15 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 0.10 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.30 seconds.\n",
            "Calculated PHATE in 0.75 seconds.\n"
          ]
        }
      ],
      "source": [
        "phate_op = ph.PHATE()\n",
        "phate_embd_young =  phate_op.fit_transform(avg_young_data.T)\n",
        "phate_op = ph.PHATE()\n",
        "phate_embd_old =  phate_op.fit_transform(avg_old_data.T)"
      ],
      "id": "4c996e81"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3d9f843c",
        "outputId": "8d28e8ec-dbdf-4342-beb6-71376203c3f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 595
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f298098c890>"
            ]
          },
          "metadata": {},
          "execution_count": 70
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "scp.plot.scatter2d(phate_embd_young, ticks=None, label_prefix='PHATE ', title=\"Average Young\")\n",
        "scp.plot.scatter2d(phate_embd_old, ticks=None, label_prefix='PHATE ', title=\"Average Old\")"
      ],
      "id": "3d9f843c"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4deb3497"
      },
      "source": [
        "We have lot less number of voxels in old subjects compared to young subjects(i.e. 537 vs 1700 voxels).\\\n",
        "So, I suspect that some part of the under represented structure in the old subject PHATE is attributed due to this less number of voxels.\\\n",
        "Some suggestions:\n",
        "- Filtering the same/similar 537 voxels from the young subject's data on which data is present for old subjects and then comparing the PHATE visualizations.\n",
        "\n",
        "Quick Fix:\n",
        "- For a heurestic/rough comparison of the above mentioned issue. I randomly selected 537 voxels from the young subject's data and applied PHATE on it. The visualization shows that the visualization for the young and old subjects are more or less the same."
      ],
      "id": "4deb3497"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "96cadf31"
      },
      "outputs": [],
      "source": [
        "rand_voxs = np.random.randint(1700, size=537) # Random Voxels picked from young subjects"
      ],
      "id": "96cadf31"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5b357dee",
        "outputId": "f3c2c2af-7270-4a98-d47c-3b6782442dae",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 695
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Calculating PHATE...\n",
            "  Running PHATE on 537 observations and 189 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.05 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.02 seconds.\n",
            "    Calculating affinities...\n",
            "    Calculated affinities in 0.01 seconds.\n",
            "  Calculated graph and diffusion operator in 0.13 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 26\n",
            "  Calculated optimal t in 0.15 seconds.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/graphtools/graphs.py:293: RuntimeWarning: Detected zero distance between 66 pairs of samples. Consider removing duplicates to avoid errors in downstream processing.\n",
            "  RuntimeWarning,\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 0.10 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.35 seconds.\n",
            "Calculated PHATE in 0.77 seconds.\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f29808933d0>"
            ]
          },
          "metadata": {},
          "execution_count": 72
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "phate_op = ph.PHATE()\n",
        "phate_embd_young =  phate_op.fit_transform(avg_young_data[:,rand_voxs].T)\n",
        "scp.plot.scatter2d(phate_embd_young, ticks=None, label_prefix='PHATE ', title=\"Average Young\")"
      ],
      "id": "5b357dee"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8524480b"
      },
      "source": [
        "A major drawback to the above quick fix is as shown below,\n",
        "- We see that the distribution of the voxel and their values across the TRs are differently distributed in randomly selected voxels of young compared to that of old are quite different(with very low number of higher and lower BOLD value voxels in young on average), which can be fixed by following the suggestions given before about extracting the same voxels.\n",
        "- The randomly chosen voxels when averaged across TRs of young subjects show approx. symmetric distribution compared to negatively skewed distribution for old subjects."
      ],
      "id": "8524480b"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "429af182",
        "outputId": "bef04868-0037-47ef-b831-ba4fcee7dcb4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 266
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.colorbar.Colorbar at 0x7f2980904050>"
            ]
          },
          "metadata": {},
          "execution_count": 73
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "p1 = plt.imshow(avg_young_data[:,rand_voxs])\n",
        "plt.title(\"Average Young Subject\")\n",
        "plt.colorbar(p1)"
      ],
      "id": "429af182"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6574d817",
        "outputId": "adfb3166-7530-4ebc-8eff-38d8910c3a0b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 266
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.colorbar.Colorbar at 0x7f29808f3950>"
            ]
          },
          "metadata": {},
          "execution_count": 74
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "p1 = plt.imshow(avg_old_data)\n",
        "plt.title(\"Average Old Subject\")\n",
        "plt.colorbar(p1)"
      ],
      "id": "6574d817"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "02640c32",
        "outputId": "f0247db5-8e65-49d0-fec6-4275c1bd0be7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.hist(np.mean(avg_young_data[:,rand_voxs], axis=0))\n",
        "plt.title(\"Young subject's voxel-wise average BOLD histogram\")\n",
        "plt.show()"
      ],
      "id": "02640c32"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5409cda6",
        "outputId": "1fe6d404-bb84-453a-e4f9-6e7b6a5159e4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAa8UlEQVR4nO3debxdVX338c+XhAABIUCuMSQpCRBU4GULDQgPCilgDWOoUgpFCYONWEWrtIytqJUKDk3RPgKxDGEQiBQlqKiIhOGxAQOCjIEAIYMJuQxhtEDg9/yx1jU7J+fc6dybc7Pyfb9e53X3dPZae5+9v2fttc85VxGBmZmVZYNWV8DMzPqew93MrEAOdzOzAjnczcwK5HA3MyuQw93MrEDrZbhL+pKkKzuZv0DSAX1c5mWSvtrJ/FckbdeXZa4rJB0n6c4+WM9Nkqb0RZ1s7ZI0UdLiTuZfKOlf1mad1nVFhnsOiwckvSZpmaQLJA1rdb06ExGbRcSTzaxD0mxJn6iZtt58kSEiDoyIGa2ux0CXz4+3coPiFUlPSvpUzTKjJV0l6TlJr0q6W9IhNcuEpB26sf6nJF0qacfe1jkiToqIf+3GtvV5w2xdVVy4SzoFOA/4J2ALYE9gW+BmSUNaWTezepSs7XPxf3KDYjPgo8DXJe2a67MVcCfwBrAzMByYBnxf0hE9WT/pHDwA+ANwj6Rd+ng71hpJg1tdh54oKtwlbQ58GTg5In4WEW9GxALgSGAs8LEGz/u4pKdzK+WsLso4SNLDkl6WtETSP+bpa3Qt1GnZDJd0c37ubZK2rbespI0kfVPSQknP5EvSTSrLTpZ0n6SXJD0haZKkc4APAv+ZW0v/Wafux+VW2su5NXVMnWW2kfSHfIJ3TNtV0rOSNpS0gaR/zvtruaTLJW2Rl/uppG9VnneNpEvy8BaSLpa0NO+3r0oa1Nm+zs8bJ2lFR/hJ+p6k5ZX5V0j6hzz8xysXSTvkffxirvu1lee8J78Oz0uaJ+nITso/XtIjeZ89KemTlXmPVFuzkgZLape0Wx7fU9Kvc/3vlzSxsuxsSedI+n/Aa8B2nZWVn3Nq3n+/l/SJnhwznYmI3wKPAO/Nkz4PvAKcGBHLIuIPEXE1cA7wLUnqznrzut+KiCci4u+B24Avdba8pFPycbVU0vGV6X/s1pQ0XNKP8359XtId+bi8AvgT4MZ8Dpyalz9M0kN5+dmS3ltZ726Sfpv3+Q8kXVspZ6KkxZJOk7QMuFTSlrnsdkkv5OHRlfXNzsf2r3MdbpS0tdJV0EuSfiNpbHf3X1MiopgHMAlYCQyuM28GcHUe/hJwZR7eiXQg7wNsBPx7XscBDcpYCnwwD28J7JaHjwPurFk2gB3y8GXAy5Vyzq8uX7PsNGAWsBXwDuBG4Gt53h7Ai8CHSG/Oo4D35HmzgU80qPemwEvAu/P4SGDnBsv+Cvi7yvg3gAvz8AnAfGA7YDPgeuCKPO9dwHJgP+AY4EngHXneD4GLcj3eCdwNfLLRvqupz0Lgz/PwvLze91bm7Vq7/cDVwFl5H20MfKCyHxYBxwODgV2BZ4GdGpR9MLA9IGBfUhB3vOZfBK6qWfaRPDwKeA44KNfhQ3m8rVLXhaSW8WBgwy7KmgQsy8sPBa7s7jFTZ5tW29/A7sAKYMc8Pgf4cp3njctldhxDfyy/s/VXpp8APNOgThNJ591X8r44KG//lpXz56t5+GvAhXm5DUmNGuV5C6icu8COwKt5/28InEo6fofkx9PA5/K8j5CuVr5aU6fzSOfsJsDWpCudoXk//wD4UaW82Xn925OuWh4GHiNdvQwGLgcuXSt5uDYKWVsPUst8WYN55wI35+EvsSrcvwhcU1lu0/wCNwr3hcAngc27OqBZM9yr5WwGvAWMqS5LOrFfBbavLLsX8FQevgiY1qBus+k83FfkA3OTLvbjJ4Bf5WGRwnCfPH4L8PeVZd8NvEl+Q83rX0QKzI5AHQG8Xi0XOBq4tdG+q6nPFcAXSG8e84CvAyeRwmYFsEHt9ueTaDowumZdfwPcUTPtIuDsbh5jPwI+l4d3IL1hD83jVwFfzMOnkd/0Ks/9OTClUtev9KCsS6iEdS67W8dMnfUeRwqtFbn+AXyHVQE5HzipzvM2zsvuXXt8d3Uu5OmTgDcb1GkiqetmcGXacmDPyvnTEbpfAW5oUPYCVg/3fwFmVsY3AJbk8vbJw6rMv5PVw/0NYONOXqM/A16oOQfPqox/C7ipMn4ocF93jrVmH0V1y5ACZbjq942NzPNrbUMKIwAi4lVSC6uRj5JaFU/ny/69elC/ajmvAM/n8qvaSK2Ce/Jl5ArgZ3k6wBjgiR6U2VHeq6RgOwlYKuknkt7TYPH/BvaSNJJ0ArwN3JHnbUNq7XR4mtQiGZHHbwQGAfMioqObaltSy2hpZZsuIrXgVyPpTK26EXdhnnwbq07G20kn0L75cUdEvF1nG04lhd7d+ZL8hEpd3t9Rj1yXY0hvHGuQdKCkOfnyfwXptR8OEBHzSd0Zh0oaChwGfL9Szl/XlPMB0nHYYVFluNOyqDlOa4a7OmbqmRMRwyLiHXnbdwb+Lc97tqaeHUZW5vfGKNIx38hzEbGyMv4aqRFU6xukN6Bf5O6r0ztZ52rHaz5WFuW6bAMsiZy62aLVn057RPxvx4ikoZIuUuqWfIl0PA7T6l2Mz1SG/1BnvN429bnSwv1/SC3Ej1QnStoMOJDU6qy1lBSYHcsOJV161RURv4mIyaRg+hEwM896lXSCdaynXlhUy9mMdAn9+5plniUdADvnk29YRGwR6eYUpINv+0bVa1TvXPefR8SHSCfpo8D3Giz3AvAL0pvB35KuODrW/XtScHX4E1IrsOMAPocUeCMlHV2p8+vA8Mo2bR4RO9cp+98i3+iLiJPy5NtIl94T8/CdwN6kcL+twTYsi4i/i4htSFda383904uA2yr1GJbL+lTtOiRtRHqj+yYwIiKGAT8lvWl0uJp0FTIZeDgHfsc2X1FTzqYRcW61mj0oaykwuvLcMZXhro6ZTkXEM7nsQ/OkXwIf0Zo3eY/M2/VYd9Zbx1+xqpHQaxHxckScEhHbkd5QvyBp/47ZNYuvdrzm+wVjSC32pcComnsIY1Z/+hrrO4V0tfr+iNic1OCA1Y+JAaGocI+IF0k3VL+jdJNxw3zzYiawmHR5X+s64BBJH1D6NM1XaLBfJA2RdIykLSLiTVIfdker8X5gZ0l/Jmlj6t84OqhSzr+SWk+rtRRyy+J7wDRJ78zljpL04bzIxcDxkvbPN5FGVVrgz5D6wuvVfYTSjdhNSUH7SqXu9XwfOBY4glWtUUhh9nmlG52bkVp710bESkn7kPqyjwWmkF6HURGxlPRm8S1Jm+d6by9p307Kr+6Tx0nh9TFSML+Ut/WjNAh3SX9dudH1AukkfRv4MbCj0k30DfNj9+pNtoohpL7WdmClpAOBv6xZ5po87VM1++lKUov+w5IGSdo436AbTX1dlTWT9Lq/NzdA/viZ724cM52StDUpeB/Kk6aR+osvlvSuXPejSfcw/qmmpTskz+94DKpZ96B8rHyH9Ob85e7UqYv6HqJ0w1yk+09vsepYrj0HZgIH5/NlQ1I4vw78mtQYfAv4jNLN8Mmke1qdeQfpWFyh9KGDs5vdnv5SVLgDRMTXgTNJLaCXgLtIrY39I+L1Oss/BHyadGIuJQVBwy9TAB8HFuRLspNIl/RExGOkN4ZfAo+TWpe1vk86GJ4H/pwGn94h9dfOB+bkcn5Jai0QEXeTAnQa6cC+jVUtk/OBI5Tu4n+7Zp0bkPqtf5/L35cUSI3MAsaT7mHcX5l+CelN8nbgKeB/gZOVPql0OfCZiFgSEXeQ3oguzSfhsaQAe5i0j6+j/qV/I7eRLtsXVcYF3Ntg+d2BuyS9krflcxHxZES8TArNo0j7YhmrbpitJi/7WVJAvEC6iplVs8xSUkj8H+DayvRFpNb8maTAXkT6eG7dc66rsiLiJuDbwK3kYyPP6jimGx4zDezV0f1FutJqB07OZT1H6kLamPR6PUc6dj4eEdfWrOchUth1PDo+4bJXXvdLpG60zYHdI+KBTurUXeNJ2/cKad9/NyJuzfO+Bvxz7p76x4iYRzrPvkO6wjkUODQi3oiIN0hX+SeS7j98jPTmv0ZOVPwH6cbqs6TX4Gd9sD39Qqu/CVsr5Mvft4BtI2Jhq+tjA1++0ngQ2Kimn9qaIOku0ifDLm11XZpVXMt9HbULqQW8rNUVsYFL0l8pfZ59S9LVxo0O9uZI2jd3PQ1W+umK9zGAW+M94XBvMUkfJV1qn5YvE80a+STp44FPkK70OutWs+55N+l+2QpSf/wRuattneduGTOzArnlbmZWoAHxQzjDhw+PsWPHtroaZmbrlHvuuefZiKj7ZbUBEe5jx45l7ty5ra6Gmdk6RdLTjea5W8bMrEAOdzOzAjnczcwK5HA3MyuQw93MrEAOdzOzAjnczcwK5HA3MyuQw93MrEAD4huqZmYAY0//SUvKXXDuwS0ptz+55W5mViCHu5lZgRzuZmYFcribmRXI4W5mViCHu5lZgRzuZmYFcribmRXI4W5mViCHu5lZgRzuZmYF6jLcJV0iabmkByvTviHpUUm/k/RDScMq886QNF/SPEkf7q+Km5lZY91puV8GTKqZdjOwS0S8D3gMOANA0k7AUcDO+TnflTSoz2prZmbd0mW4R8TtwPM1034RESvz6BxgdB6eDFwTEa9HxFPAfGCPPqyvmZl1Q1/0uZ8A3JSHRwGLKvMW52lmZrYWNRXuks4CVgJX9eK5UyXNlTS3vb29mWqYmVmNXoe7pOOAQ4BjIiLy5CXAmMpio/O0NUTE9IiYEBET2traelsNMzOro1fhLmkScCpwWES8Vpk1CzhK0kaSxgHjgbubr6aZmfVEl/9mT9LVwERguKTFwNmkT8dsBNwsCWBORJwUEQ9Jmgk8TOqu+XREvNVflTczs/q6DPeIOLrO5Is7Wf4c4JxmKmVmZs3xN1TNzArkcDczK5DD3cysQA53M7MCOdzNzArkcDczK5DD3cysQA53M7MCOdzNzArkcDczK5DD3cysQF3+toyZrV/Gnv6TVlfB+oBb7mZmBXK4m5kVyOFuZlYgh7uZWYEc7mZmBXK4m5kVyOFuZlYgh7uZWYEc7mZmBXK4m5kVyOFuZlagLsNd0iWSlkt6sDJtK0k3S3o8/90yT5ekb0uaL+l3knbrz8qbmVl93Wm5XwZMqpl2OnBLRIwHbsnjAAcC4/NjKnBB31TTzMx6ostwj4jbgedrJk8GZuThGcDhlemXRzIHGCZpZF9V1szMuqe3fe4jImJpHl4GjMjDo4BFleUW52lmZrYWNX1DNSICiJ4+T9JUSXMlzW1vb2+2GmZmVtHbcH+mo7sl/12epy8BxlSWG52nrSEipkfEhIiY0NbW1stqmJlZPb0N91nAlDw8BbihMv3Y/KmZPYEXK903Zma2lnT5b/YkXQ1MBIZLWgycDZwLzJR0IvA0cGRe/KfAQcB84DXg+H6os5mZdaHLcI+IoxvM2r/OsgF8utlKmZlZc/wNVTOzAjnczcwK5HA3MyuQw93MrEAOdzOzAjnczcwK5HA3MyuQw93MrEAOdzOzAjnczcwK5HA3MyuQw93MrEAOdzOzAjnczcwK5HA3MyuQw93MrEAOdzOzAjnczcwK5HA3MyuQw93MrEAOdzOzAjnczcwK5HA3MytQU+Eu6fOSHpL0oKSrJW0saZykuyTNl3StpCF9VVkzM+ueXoe7pFHAZ4EJEbELMAg4CjgPmBYROwAvACf2RUXNzKz7mu2WGQxsImkwMBRYCuwHXJfnzwAOb7IMMzProV6He0QsAb4JLCSF+ovAPcCKiFiZF1sMjKr3fElTJc2VNLe9vb231TAzszqa6ZbZEpgMjAO2ATYFJnX3+RExPSImRMSEtra23lbDzMzqaKZb5gDgqYhoj4g3geuBvYFhuZsGYDSwpMk6mplZDzUT7guBPSUNlSRgf+Bh4FbgiLzMFOCG5qpoZmY91Uyf+12kG6f3Ag/kdU0HTgO+IGk+sDVwcR/U08zMemBw14s0FhFnA2fXTH4S2KOZ9ZqZWXP8DVUzswI53M3MCuRwNzMrkMPdzKxADnczswI53M3MCuRwNzMrkMPdzKxADnczswI53M3MCuRwNzMrkMPdzKxADnczswI53M3MCuRwNzMrkMPdzKxADnczswI53M3MCuRwNzMrkMPdzKxADnczswI53M3MCuRwNzMrUFPhLmmYpOskPSrpEUl7SdpK0s2SHs9/t+yrypqZWfc023I/H/hZRLwH+FPgEeB04JaIGA/cksfNzGwtGtzbJ0raAtgHOA4gIt4A3pA0GZiYF5sBzAZOa6aSZmb9aezpP2lZ2QvOPbhf1ttMy30c0A5cKum3kv5L0qbAiIhYmpdZBoyo92RJUyXNlTS3vb29iWqYmVmtZsJ9MLAbcEFE7Aq8Sk0XTEQEEPWeHBHTI2JCRExoa2trohpmZlarmXBfDCyOiLvy+HWksH9G0kiA/Hd5c1U0M7Oe6nWfe0Qsk7RI0rsjYh6wP/BwfkwBzs1/b+iTmpqtZ1rZD2zrvl6He3YycJWkIcCTwPGkq4GZkk4EngaObLIMMzProabCPSLuAybUmbV/M+s1M7Pm+BuqZmYFcribmRXI4W5mViCHu5lZgRzuZmYFcribmRXI4W5mViCHu5lZgRzuZmYFcribmRXI4W5mViCHu5lZgRzuZmYFcribmRXI4W5mVqBm/1mHWfH8H5FsXeSWu5lZgRzuZmYFcribmRXI4W5mViCHu5lZgRzuZmYFcribmRWo6XCXNEjSbyX9OI+Pk3SXpPmSrpU0pPlqmplZT/TFl5g+BzwCbJ7HzwOmRcQ1ki4ETgQu6INybD3mLxKZ9UxTLXdJo4GDgf/K4wL2A67Li8wADm+mDDMz67lmu2X+AzgVeDuPbw2siIiVeXwxMKreEyVNlTRX0tz29vYmq2FmZlW9DndJhwDLI+Ke3jw/IqZHxISImNDW1tbbapiZWR3N9LnvDRwm6SBgY1Kf+/nAMEmDc+t9NLCk+WqamVlP9LrlHhFnRMToiBgLHAX8KiKOAW4FjsiLTQFuaLqWZmbWI/3xOffTgC9Imk/qg7+4H8owM7NO9MnvuUfEbGB2Hn4S2KMv1mtmZr3jb6iamRXI4W5mViCHu5lZgRzuZmYF8j/Ith7xb7yYrRvccjczK5DD3cysQA53M7MCOdzNzArkcDczK5DD3cysQA53M7MCOdzNzArkcDczK5DD3cysQA53M7MCOdzNzArkcDczK5B/FXId5F9mNLOuuOVuZlYgh7uZWYEc7mZmBXK4m5kVqNc3VCWNAS4HRgABTI+I8yVtBVwLjAUWAEdGxAvNV3Xg8Y1NMxuommm5rwROiYidgD2BT0vaCTgduCUixgO35HEzM1uLeh3uEbE0Iu7Nwy8DjwCjgMnAjLzYDODwZitpZmY90yd97pLGArsCdwEjImJpnrWM1G1T7zlTJc2VNLe9vb0vqmFmZlnT4S5pM+C/gX+IiJeq8yIiSP3xa4iI6RExISImtLW1NVsNMzOraCrcJW1ICvarIuL6PPkZSSPz/JHA8uaqaGZmPdXrcJck4GLgkYj498qsWcCUPDwFuKH31TMzs95o5rdl9gY+Djwg6b487UzgXGCmpBOBp4Ejm6uimZn1VK/DPSLuBNRg9v69Xa+ZmTXP31A1MyuQw93MrEAOdzOzAjnczcwK5HA3MyuQw93MrEAOdzOzAjnczcwK5HA3MyuQw93MrEAOdzOzAjXzw2EDgv+PqZnZmtxyNzMrkMPdzKxADnczswI53M3MCuRwNzMrkMPdzKxADnczswI53M3MCuRwNzMrkMPdzKxADnczswL1W7hLmiRpnqT5kk7vr3LMzGxN/RLukgYB/xc4ENgJOFrSTv1RlpmZram/Wu57APMj4smIeAO4BpjcT2WZmVmN/vrJ31HAosr4YuD91QUkTQWm5tFXJM3rp7q0wnDg2VZXokW87esnb3sv6bymyt620YyW/Z57REwHpreq/P4kaW5ETGh1PVrB2+5tX98M1G3vr26ZJcCYyvjoPM3MzNaC/gr33wDjJY2TNAQ4CpjVT2WZmVmNfumWiYiVkj4D/BwYBFwSEQ/1R1kDVJHdTd3kbV8/edsHGEVEq+tgZmZ9zN9QNTMrkMPdzKxADvcmSfq8pIckPSjpakkb5xvJd+WfXrg231Re50m6RNJySQ9Wpm0l6WZJj+e/W+bpkvTtvA9+J2m31tW8eQ22/RuSHs3b90NJwyrzzsjbPk/Sh1tT675Tb/sr806RFJKG5/HiX/s8/eT8+j8k6euV6QPitXe4N0HSKOCzwISI2IV08/go4DxgWkTsALwAnNi6Wvapy4BJNdNOB26JiPHALXkc0k9PjM+PqcAFa6mO/eUy1tz2m4FdIuJ9wGPAGQD5pzaOAnbOz/lu/kmOddllrLn9SBoD/CWwsDK5+Nde0l+QvnX/pxGxM/DNPH3AvPYO9+YNBjaRNBgYCiwF9gOuy/NnAIe3qG59KiJuB56vmTyZtI2w+rZOBi6PZA4wTNLItVPTvldv2yPiFxGxMo/OIX2fA9K2XxMRr0fEU8B80k9yrLMavPYA04BTgeonM4p/7YFPAedGxOt5meV5+oB57R3uTYiIJaR37IWkUH8RuAdYUTnpF5N+jqFUIyJiaR5eBozIw/V+gqLk/XACcFMeXi+2XdJkYElE3F8za33Y/h2BD+bu19sk7Z6nD5htb9nPD5Qg9y9PBsYBK4AfUOfSdX0RESFpvftsraSzgJXAVa2uy9oiaShwJqlLZn00GNgK2BPYHZgpabvWVml1brk35wDgqYhoj4g3geuBvUmXoR1vnKX/9MIzHZfc+W/H5el68RMUko4DDgGOiVVfGlkftn17UqPmfkkLSNt4r6R3sX5s/2Lg+tz1dDfwNukHxAbMtjvcm7MQ2FPSUEkC9gceBm4FjsjLTAFuaFH91oZZpG2E1bd1FnBs/uTEnsCLle6bIkiaROpvPiwiXqvMmgUcJWkjSeNINxbvbkUd+0tEPBAR74yIsRExlhR2u0XEMtaD1x74EfAXAJJ2BIaQfhly4Lz2EeFHEw/gy8CjwIPAFcBGwHb5BZ1P6qrZqNX17KNtvZp0b+FN0sl8IrA16VMyjwO/BLbKy4r0D1ueAB4gfaKo5dvQx9s+n9S/el9+XFhZ/qy87fOAA1td//7Y/pr5C4Dh69FrPwS4Mp/39wL7DbTX3j8/YGZWIHfLmJkVyOFuZlYgh7uZWYEc7mZmBXK4m5kVyOFuZlYgh7uZWYH+P7xrANrygobRAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.hist(np.mean(avg_old_data, axis=0))\n",
        "plt.title(\"Old subject's voxel-wise average BOLD histogram\")\n",
        "plt.show()"
      ],
      "id": "5409cda6"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, we have the same 537 voxel data available for the young subjects about which we mentioned in the suggestion above. So, let's proceed with the vanilla PHATE representation difference."
      ],
      "metadata": {
        "id": "4aVpj4_nuRZQ"
      },
      "id": "4aVpj4_nuRZQ"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f6739a56"
      },
      "outputs": [],
      "source": [
        "data = pd.ExcelFile(r\"YOUNG/l_OFC_537.xlsx\", engine=\"openpyxl\")"
      ],
      "id": "f6739a56"
    },
    {
      "cell_type": "code",
      "source": [
        "len(data.sheet_names)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ILTikGkXu7Sx",
        "outputId": "48372579-e8fe-4f13-d4aa-b2af5cbf0231"
      },
      "id": "ILTikGkXu7Sx",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "111"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we can see below the data of the young subjects is now comprising of the same 537 voxels of which we got the old subject's data on."
      ],
      "metadata": {
        "id": "3NKH5U7WvIx6"
      },
      "id": "3NKH5U7WvIx6"
    },
    {
      "cell_type": "code",
      "source": [
        "y1_data = data.parse(\"Sheet1\", header=None)\n",
        "y1_data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "kw_DgMk7u_Pp",
        "outputId": "171b2db5-ad95-4bbe-b005-f6cea82e823b"
      },
      "id": "kw_DgMk7u_Pp",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           0          1          2          3          4          5    \\\n",
              "0    58.468373  65.389863  66.482730  69.032752  70.307764  71.400630   \n",
              "1    57.921940  65.207718  66.664874  68.668463  69.943475  71.036341   \n",
              "2    58.286229  65.389863  66.300585  69.397041  70.307764  71.036341   \n",
              "3    57.921940  65.025574  66.300585  69.214897  69.943475  70.854197   \n",
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          "metadata": {},
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    {
      "cell_type": "code",
      "source": [
        "young_data = np.zeros((y1_data.shape[0], y1_data.shape[1], len(data.sheet_names)))"
      ],
      "metadata": {
        "id": "1GBwmW0gvGfy"
      },
      "id": "1GBwmW0gvGfy",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Constructing the 3D Tensor for the young data sample.\n",
        "- The dimension of the tensor is (TRs, Voxels, number of subjects)"
      ],
      "metadata": {
        "id": "axCaX4RdvbZA"
      },
      "id": "axCaX4RdvbZA"
    },
    {
      "cell_type": "code",
      "source": [
        "# Run only once and save the .npy file\n",
        "# for i in range(len(data.sheet_names)): # Takes long duration to complete, prefer saving the output tensor\n",
        "#    young_data[:,:,i] = data.parse(\"Sheet\"+str(i+1), header=None).to_numpy()\n",
        "# np.save(\"young_data_537.npy\", young_data)"
      ],
      "metadata": {
        "id": "h4R0pof0vadw"
      },
      "id": "h4R0pof0vadw",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "young_data = np.load(\"young_data_537.npy\")"
      ],
      "metadata": {
        "id": "ifo-ilP-wBLR"
      },
      "id": "ifo-ilP-wBLR",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "avg_young_data = np.mean(young_data, axis=2)"
      ],
      "metadata": {
        "id": "U1_2fS8iw1Sj"
      },
      "id": "U1_2fS8iw1Sj",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "phate_op = ph.PHATE()\n",
        "phate_embd_young =  phate_op.fit_transform(avg_young_data.T)\n",
        "phate_op = ph.PHATE()\n",
        "phate_embd_old =  phate_op.fit_transform(avg_old_data.T)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zU_X6zXXxJWm",
        "outputId": "727af054-0b1a-4599-b5ca-8bb895b0600a"
      },
      "id": "zU_X6zXXxJWm",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Calculating PHATE...\n",
            "  Running PHATE on 537 observations and 189 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.07 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.02 seconds.\n",
            "    Calculating affinities...\n",
            "  Calculated graph and diffusion operator in 0.11 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 23\n",
            "  Calculated optimal t in 0.21 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 0.20 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.64 seconds.\n",
            "Calculated PHATE in 1.21 seconds.\n",
            "Calculating PHATE...\n",
            "  Running PHATE on 537 observations and 189 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.10 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.05 seconds.\n",
            "    Calculating affinities...\n",
            "    Calculated affinities in 0.02 seconds.\n",
            "  Calculated graph and diffusion operator in 0.20 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 22\n",
            "  Calculated optimal t in 0.34 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 0.11 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.52 seconds.\n",
            "Calculated PHATE in 1.20 seconds.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "scp.plot.scatter2d(phate_embd_young, ticks=None, label_prefix='PHATE ', title=\"Average Young\")\n",
        "scp.plot.scatter2d(phate_embd_old, ticks=None, label_prefix='PHATE ', title=\"Average Old\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 595
        },
        "id": "xHYGpWDVxa7Y",
        "outputId": "9e74ad0b-e1dc-4848-b8e4-750f09d9b41b"
      },
      "id": "xHYGpWDVxa7Y",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f2980279c90>"
            ]
          },
          "metadata": {},
          "execution_count": 86
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The old subject's data seems to be more fragmented forming multiple breaking points and gaps compared to lesser number of discontinuations in younger subjects, on an average."
      ],
      "metadata": {
        "id": "R-f95fBaxnk6"
      },
      "id": "R-f95fBaxnk6"
    },
    {
      "cell_type": "markdown",
      "source": [
        "The above application of PHATE was done taking the BOLD values for each voxel along the row and the columns as the TRs, which is natural in the sense that we want to reduce the time dimension i.e. TR dimension to come up with a overall low-dimensional representation of the states of Voxels throughout the movie watching."
      ],
      "metadata": {
        "id": "0d_DmajByAkG"
      },
      "id": "0d_DmajByAkG"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Below, just for the sake of exploring, we look at the dimensionality reduction of the number of voxels to see how the data is represented in a lower voxel dimensional space."
      ],
      "metadata": {
        "id": "2TGqehzey13h"
      },
      "id": "2TGqehzey13h"
    },
    {
      "cell_type": "code",
      "source": [
        "phate_op = ph.PHATE()\n",
        "phate_embd_young =  phate_op.fit_transform(avg_young_data)\n",
        "phate_op = ph.PHATE()\n",
        "phate_embd_old =  phate_op.fit_transform(avg_old_data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xvO9jaxmxd-b",
        "outputId": "e903940d-8885-4294-f6b0-3066775ebdc2"
      },
      "id": "xvO9jaxmxd-b",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Calculating PHATE...\n",
            "  Running PHATE on 189 observations and 537 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.08 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.02 seconds.\n",
            "    Calculating affinities...\n",
            "  Calculated graph and diffusion operator in 0.13 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 17\n",
            "  Calculated optimal t in 0.05 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.11 seconds.\n",
            "Calculated PHATE in 0.32 seconds.\n",
            "Calculating PHATE...\n",
            "  Running PHATE on 189 observations and 537 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating PCA...\n",
            "    Calculated PCA in 0.11 seconds.\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.01 seconds.\n",
            "    Calculating affinities...\n",
            "  Calculated graph and diffusion operator in 0.17 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 26\n",
            "  Calculated optimal t in 0.07 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.04 seconds.\n",
            "Calculated PHATE in 0.34 seconds.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "scp.plot.scatter2d(phate_embd_young, ticks=None, label_prefix='PHATE ', title=\"Average Young\")\n",
        "scp.plot.scatter2d(phate_embd_old, ticks=None, label_prefix='PHATE ', title=\"Average Old\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 595
        },
        "id": "2fus4szqzQk5",
        "outputId": "88e35b1e-e137-40a5-ecfc-2f516beab7dc"
      },
      "id": "2fus4szqzQk5",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f297add3b10>"
            ]
          },
          "metadata": {},
          "execution_count": 88
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The above representation we saw was carried out for entire movie watching duration, let's do PHATE on only the ascent and descent data corresponding to the 5th of it's kind i.e. \n",
        "- Ascent 5(A5): From TR 175 to 181\n",
        "- Descent 5(D5): From TR 182 to 189"
      ],
      "metadata": {
        "id": "R8TeWGoC23-G"
      },
      "id": "R8TeWGoC23-G"
    },
    {
      "cell_type": "code",
      "source": [
        "young_data = np.load(\"young_data_537.npy\")\n",
        "old_data = np.load(\"old_data.npy\")"
      ],
      "metadata": {
        "id": "q1QEdmfn3VJl"
      },
      "id": "q1QEdmfn3VJl",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "avg_young_data = np.mean(young_data[175:,:,:], axis=2)\n",
        "avg_old_data = np.mean(young_data[175:,:,:], axis=2)"
      ],
      "metadata": {
        "id": "w-gZZJnB3xen"
      },
      "id": "w-gZZJnB3xen",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "phate_op = ph.PHATE()\n",
        "phate_embd_young =  phate_op.fit_transform(avg_young_data.T)\n",
        "phate_op = ph.PHATE()\n",
        "phate_embd_old =  phate_op.fit_transform(avg_old_data.T)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7dYV3eyi3pez",
        "outputId": "6d9a7d08-40c9-4cb1-bdb9-81aad4962aab"
      },
      "id": "7dYV3eyi3pez",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Calculating PHATE...\n",
            "  Running PHATE on 537 observations and 14 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating KNN search...\n",
            "    Calculated KNN search in 0.01 seconds.\n",
            "    Calculating affinities...\n",
            "    Calculated affinities in 0.01 seconds.\n",
            "  Calculated graph and diffusion operator in 0.04 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 24\n",
            "  Calculated optimal t in 0.28 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 0.13 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.55 seconds.\n",
            "Calculated PHATE in 1.05 seconds.\n",
            "Calculating PHATE...\n",
            "  Running PHATE on 537 observations and 14 variables.\n",
            "  Calculating graph and diffusion operator...\n",
            "    Calculating KNN search...\n",
            "    Calculating affinities...\n",
            "    Calculated affinities in 0.02 seconds.\n",
            "  Calculated graph and diffusion operator in 0.04 seconds.\n",
            "  Calculating optimal t...\n",
            "    Automatically selected t = 24\n",
            "  Calculated optimal t in 0.27 seconds.\n",
            "  Calculating diffusion potential...\n",
            "  Calculated diffusion potential in 0.11 seconds.\n",
            "  Calculating metric MDS...\n",
            "  Calculated metric MDS in 0.51 seconds.\n",
            "Calculated PHATE in 0.98 seconds.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "scp.plot.scatter2d(phate_embd_young, ticks=None, label_prefix='PHATE ', title=\"Average Young(A5 & D5)\")\n",
        "scp.plot.scatter2d(phate_embd_old, ticks=None, label_prefix='PHATE ', title=\"Average Old(A5 & D5)\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 595
        },
        "id": "IpxF35yI4KNi",
        "outputId": "76d14039-9275-4a4f-f823-96f95901cc1a"
      },
      "id": "IpxF35yI4KNi",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f2978f53890>"
            ]
          },
          "metadata": {},
          "execution_count": 100
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Even though PHATE is usually done on very high dimensional datasets, we see remarkly similar PHATE representation for average old and average young subject's data on the 5th Ascent and Descent concatenated. Even the number of lobes that appear and discontinuities appear to be very similar."
      ],
      "metadata": {
        "id": "6yxT8Yy_4YFB"
      },
      "id": "6yxT8Yy_4YFB"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, lateral OFC being an important region of interest for movie watching type task, we analyzed so far the PHATE carried out on this ROI. We, now shift our attention to the other ROIs data present with us."
      ],
      "metadata": {
        "id": "G-bJwdyNzX18"
      },
      "id": "G-bJwdyNzX18"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Below, we will look at the mOFC comparison. Let's start with young subjects data."
      ],
      "metadata": {
        "id": "yo9SydOQz7bk"
      },
      "id": "yo9SydOQz7bk"
    },
    {
      "cell_type": "code",
      "source": [
        "data = pd.ExcelFile(r\"YOUNG/mOFC.xlsx\", engine=\"openpyxl\")"
      ],
      "metadata": {
        "id": "PfrqG6EjzTtr"
      },
      "id": "PfrqG6EjzTtr",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "len(data.sheet_names)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OpPjDb7C0F_B",
        "outputId": "552b70cb-14ea-4493-b8e9-d4d8c2e57416"
      },
      "id": "OpPjDb7C0F_B",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "111"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y1_data = data.parse(\"Sheet1\", header=None)\n",
        "y1_data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "Lj_SrkMf0LrX",
        "outputId": "eca5f4e2-2699-42c1-bf3f-bae51ae5a290"
      },
      "id": "Lj_SrkMf0LrX",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "          0          1          2           3           4          5     \\\n",
              "0    88.886499  58.286229  85.607899   97.265144  108.922390  62.657696   \n",
              "1    87.793632  57.921940  84.515032   96.536566  108.193812  62.657696   \n",
              "2    88.886499  60.471962  85.972187   97.629433  109.286679  64.843430   \n",
              "3    88.886499  58.650518  85.607899   97.629433  108.922390  63.021985   \n",
              "4    88.522210  59.014807  85.607899   97.265144  108.922390  63.021985   \n",
              "..         ...        ...        ...         ...         ...        ...   \n",
              "184  92.165099  64.479141  89.979366  102.000900  113.293857  68.486319   \n",
              "185  92.893677  64.114852  91.072233  102.729478  113.658146  68.486319   \n",
              "186  92.529388  64.114852  90.707944  102.729478  114.022435  68.122030   \n",
              "187  93.257966  64.843430  91.436521  103.458056  114.386724  68.850608   \n",
              "188  92.893677  64.479141  91.436521  103.093767  114.022435  68.486319   \n",
              "\n",
              "           6           7           8          9     ...        1690  \\\n",
              "0     93.257966  103.822345  114.022435  73.950653  ...  168.665775   \n",
              "1     92.165099  102.729478  113.293857  73.950653  ...  168.665775   \n",
              "2     93.622255  104.186634  114.751013  75.407809  ...  169.758641   \n",
              "3     93.622255  104.186634  114.751013  74.314942  ...  169.030064   \n",
              "4     93.622255  104.186634  114.751013  75.043520  ...  169.030064   \n",
              "..          ...         ...         ...        ...  ...         ...   \n",
              "184   99.086589  110.379546  120.943925  79.779276  ...  169.758641   \n",
              "185   99.815167  110.743835  120.943925  79.414987  ...  169.030064   \n",
              "186  100.179456  111.108124  121.672503  79.050698  ...  167.208619   \n",
              "187  100.543745  111.836702  122.036792  79.414987  ...  169.394352   \n",
              "188  100.543745  111.472413  121.308214  79.414987  ...  169.030064   \n",
              "\n",
              "           1691        1692        1693        1694        1695        1696  \\\n",
              "0    163.201441  161.015707  155.187084  151.544195  171.580086  206.187534   \n",
              "1    164.294307  160.651418  154.094217  150.815617  170.851508  205.458957   \n",
              "2    163.930019  161.744285  155.915662  152.637062  170.851508  205.823245   \n",
              "3    163.201441  161.015707  154.822795  151.544195  171.580086  205.094668   \n",
              "4    163.201441  161.015707  155.187084  151.908484  170.851508  205.094668   \n",
              "..          ...         ...         ...         ...         ...         ...   \n",
              "184  167.937197  162.472863  158.101396  157.008529  174.130109  204.730379   \n",
              "185  166.115752  161.744285  157.372818  155.915662  173.765820  203.637512   \n",
              "186  166.480041  160.287129  156.279951  155.187084  173.765820  203.637512   \n",
              "187  167.572908  162.472863  158.465685  157.372818  173.765820  204.366090   \n",
              "188  167.208619  161.744285  157.008529  155.551373  174.130109  203.637512   \n",
              "\n",
              "           1697        1698        1699  \n",
              "0    197.080311  187.608799  184.694488  \n",
              "1    196.716022  187.608799  185.423065  \n",
              "2    196.716022  187.608799  185.058776  \n",
              "3    195.987444  186.515932  183.601621  \n",
              "4    195.987444  186.515932  183.965910  \n",
              "..          ...         ...         ...  \n",
              "184  196.716022  189.065955  186.151643  \n",
              "185  195.623155  187.244510  184.694488  \n",
              "186  195.258867  186.880221  185.058776  \n",
              "187  196.716022  189.065955  186.515932  \n",
              "188  195.987444  187.973088  186.151643  \n",
              "\n",
              "[189 rows x 1700 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-d4bcbee2-e9a4-4682-bd2e-f955d4323216\">\n",
              "    <div class=\"colab-df-container\">\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>...</th>\n",
              "      <th>1690</th>\n",
              "      <th>1691</th>\n",
              "      <th>1692</th>\n",
              "      <th>1693</th>\n",
              "      <th>1694</th>\n",
              "      <th>1695</th>\n",
              "      <th>1696</th>\n",
              "      <th>1697</th>\n",
              "      <th>1698</th>\n",
              "      <th>1699</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>88.886499</td>\n",
              "      <td>58.286229</td>\n",
              "      <td>85.607899</td>\n",
              "      <td>97.265144</td>\n",
              "      <td>108.922390</td>\n",
              "      <td>62.657696</td>\n",
              "      <td>93.257966</td>\n",
              "      <td>103.822345</td>\n",
              "      <td>114.022435</td>\n",
              "      <td>73.950653</td>\n",
              "      <td>...</td>\n",
              "      <td>168.665775</td>\n",
              "      <td>163.201441</td>\n",
              "      <td>161.015707</td>\n",
              "      <td>155.187084</td>\n",
              "      <td>151.544195</td>\n",
              "      <td>171.580086</td>\n",
              "      <td>206.187534</td>\n",
              "      <td>197.080311</td>\n",
              "      <td>187.608799</td>\n",
              "      <td>184.694488</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>87.793632</td>\n",
              "      <td>57.921940</td>\n",
              "      <td>84.515032</td>\n",
              "      <td>96.536566</td>\n",
              "      <td>108.193812</td>\n",
              "      <td>62.657696</td>\n",
              "      <td>92.165099</td>\n",
              "      <td>102.729478</td>\n",
              "      <td>113.293857</td>\n",
              "      <td>73.950653</td>\n",
              "      <td>...</td>\n",
              "      <td>168.665775</td>\n",
              "      <td>164.294307</td>\n",
              "      <td>160.651418</td>\n",
              "      <td>154.094217</td>\n",
              "      <td>150.815617</td>\n",
              "      <td>170.851508</td>\n",
              "      <td>205.458957</td>\n",
              "      <td>196.716022</td>\n",
              "      <td>187.608799</td>\n",
              "      <td>185.423065</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>88.886499</td>\n",
              "      <td>60.471962</td>\n",
              "      <td>85.972187</td>\n",
              "      <td>97.629433</td>\n",
              "      <td>109.286679</td>\n",
              "      <td>64.843430</td>\n",
              "      <td>93.622255</td>\n",
              "      <td>104.186634</td>\n",
              "      <td>114.751013</td>\n",
              "      <td>75.407809</td>\n",
              "      <td>...</td>\n",
              "      <td>169.758641</td>\n",
              "      <td>163.930019</td>\n",
              "      <td>161.744285</td>\n",
              "      <td>155.915662</td>\n",
              "      <td>152.637062</td>\n",
              "      <td>170.851508</td>\n",
              "      <td>205.823245</td>\n",
              "      <td>196.716022</td>\n",
              "      <td>187.608799</td>\n",
              "      <td>185.058776</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>88.886499</td>\n",
              "      <td>58.650518</td>\n",
              "      <td>85.607899</td>\n",
              "      <td>97.629433</td>\n",
              "      <td>108.922390</td>\n",
              "      <td>63.021985</td>\n",
              "      <td>93.622255</td>\n",
              "      <td>104.186634</td>\n",
              "      <td>114.751013</td>\n",
              "      <td>74.314942</td>\n",
              "      <td>...</td>\n",
              "      <td>169.030064</td>\n",
              "      <td>163.201441</td>\n",
              "      <td>161.015707</td>\n",
              "      <td>154.822795</td>\n",
              "      <td>151.544195</td>\n",
              "      <td>171.580086</td>\n",
              "      <td>205.094668</td>\n",
              "      <td>195.987444</td>\n",
              "      <td>186.515932</td>\n",
              "      <td>183.601621</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>88.522210</td>\n",
              "      <td>59.014807</td>\n",
              "      <td>85.607899</td>\n",
              "      <td>97.265144</td>\n",
              "      <td>108.922390</td>\n",
              "      <td>63.021985</td>\n",
              "      <td>93.622255</td>\n",
              "      <td>104.186634</td>\n",
              "      <td>114.751013</td>\n",
              "      <td>75.043520</td>\n",
              "      <td>...</td>\n",
              "      <td>169.030064</td>\n",
              "      <td>163.201441</td>\n",
              "      <td>161.015707</td>\n",
              "      <td>155.187084</td>\n",
              "      <td>151.908484</td>\n",
              "      <td>170.851508</td>\n",
              "      <td>205.094668</td>\n",
              "      <td>195.987444</td>\n",
              "      <td>186.515932</td>\n",
              "      <td>183.965910</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>184</th>\n",
              "      <td>92.165099</td>\n",
              "      <td>64.479141</td>\n",
              "      <td>89.979366</td>\n",
              "      <td>102.000900</td>\n",
              "      <td>113.293857</td>\n",
              "      <td>68.486319</td>\n",
              "      <td>99.086589</td>\n",
              "      <td>110.379546</td>\n",
              "      <td>120.943925</td>\n",
              "      <td>79.779276</td>\n",
              "      <td>...</td>\n",
              "      <td>169.758641</td>\n",
              "      <td>167.937197</td>\n",
              "      <td>162.472863</td>\n",
              "      <td>158.101396</td>\n",
              "      <td>157.008529</td>\n",
              "      <td>174.130109</td>\n",
              "      <td>204.730379</td>\n",
              "      <td>196.716022</td>\n",
              "      <td>189.065955</td>\n",
              "      <td>186.151643</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>185</th>\n",
              "      <td>92.893677</td>\n",
              "      <td>64.114852</td>\n",
              "      <td>91.072233</td>\n",
              "      <td>102.729478</td>\n",
              "      <td>113.658146</td>\n",
              "      <td>68.486319</td>\n",
              "      <td>99.815167</td>\n",
              "      <td>110.743835</td>\n",
              "      <td>120.943925</td>\n",
              "      <td>79.414987</td>\n",
              "      <td>...</td>\n",
              "      <td>169.030064</td>\n",
              "      <td>166.115752</td>\n",
              "      <td>161.744285</td>\n",
              "      <td>157.372818</td>\n",
              "      <td>155.915662</td>\n",
              "      <td>173.765820</td>\n",
              "      <td>203.637512</td>\n",
              "      <td>195.623155</td>\n",
              "      <td>187.244510</td>\n",
              "      <td>184.694488</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>186</th>\n",
              "      <td>92.529388</td>\n",
              "      <td>64.114852</td>\n",
              "      <td>90.707944</td>\n",
              "      <td>102.729478</td>\n",
              "      <td>114.022435</td>\n",
              "      <td>68.122030</td>\n",
              "      <td>100.179456</td>\n",
              "      <td>111.108124</td>\n",
              "      <td>121.672503</td>\n",
              "      <td>79.050698</td>\n",
              "      <td>...</td>\n",
              "      <td>167.208619</td>\n",
              "      <td>166.480041</td>\n",
              "      <td>160.287129</td>\n",
              "      <td>156.279951</td>\n",
              "      <td>155.187084</td>\n",
              "      <td>173.765820</td>\n",
              "      <td>203.637512</td>\n",
              "      <td>195.258867</td>\n",
              "      <td>186.880221</td>\n",
              "      <td>185.058776</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>187</th>\n",
              "      <td>93.257966</td>\n",
              "      <td>64.843430</td>\n",
              "      <td>91.436521</td>\n",
              "      <td>103.458056</td>\n",
              "      <td>114.386724</td>\n",
              "      <td>68.850608</td>\n",
              "      <td>100.543745</td>\n",
              "      <td>111.836702</td>\n",
              "      <td>122.036792</td>\n",
              "      <td>79.414987</td>\n",
              "      <td>...</td>\n",
              "      <td>169.394352</td>\n",
              "      <td>167.572908</td>\n",
              "      <td>162.472863</td>\n",
              "      <td>158.465685</td>\n",
              "      <td>157.372818</td>\n",
              "      <td>173.765820</td>\n",
              "      <td>204.366090</td>\n",
              "      <td>196.716022</td>\n",
              "      <td>189.065955</td>\n",
              "      <td>186.515932</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>188</th>\n",
              "      <td>92.893677</td>\n",
              "      <td>64.479141</td>\n",
              "      <td>91.436521</td>\n",
              "      <td>103.093767</td>\n",
              "      <td>114.022435</td>\n",
              "      <td>68.486319</td>\n",
              "      <td>100.543745</td>\n",
              "      <td>111.472413</td>\n",
              "      <td>121.308214</td>\n",
              "      <td>79.414987</td>\n",
              "      <td>...</td>\n",
              "      <td>169.030064</td>\n",
              "      <td>167.208619</td>\n",
              "      <td>161.744285</td>\n",
              "      <td>157.008529</td>\n",
              "      <td>155.551373</td>\n",
              "      <td>174.130109</td>\n",
              "      <td>203.637512</td>\n",
              "      <td>195.987444</td>\n",
              "      <td>187.973088</td>\n",
              "      <td>186.151643</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>189 rows × 1700 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-d4bcbee2-e9a4-4682-bd2e-f955d4323216')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-d4bcbee2-e9a4-4682-bd2e-f955d4323216 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-d4bcbee2-e9a4-4682-bd2e-f955d4323216');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "          element.appendChild(docLink);\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = pd.ExcelFile(\"OLD/m_OFC_voxel.xlsx\", engine=\"openpyxl\")"
      ],
      "metadata": {
        "id": "57ovyyM00RFx"
      },
      "id": "57ovyyM00RFx",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "len(data.sheet_names)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Jlwyj4941Kpw",
        "outputId": "8182f7c7-5b52-401c-e98b-9301800c014a"
      },
      "id": "Jlwyj4941Kpw",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "25"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "o1 = data.parse(sheet_name=\"Sheet1\", header=None)\n",
        "o1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "4JFnsRUU1U96",
        "outputId": "c09706a2-0f38-49e3-a81a-a7165991c11e"
      },
      "id": "4JFnsRUU1U96",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "            0           1           2           3           4           5    \\\n",
              "0    105.279501  124.222525  105.279501  116.208169  128.593992  132.965459   \n",
              "1    104.550923  122.765369  103.822345  114.751013  126.772548  131.144015   \n",
              "2    105.643790  124.951103  106.008079  116.936747  128.958281  133.694037   \n",
              "3    106.008079  124.951103  106.372368  117.301035  128.958281  132.965459   \n",
              "4    105.279501  124.222525  105.279501  116.572458  128.229703  132.601171   \n",
              "..          ...         ...         ...         ...         ...         ...   \n",
              "184  102.365189  128.958281  108.558101  118.758191  129.686859  134.058326   \n",
              "185  103.093767  129.322570  108.558101  119.122480  130.051148  134.058326   \n",
              "186  102.000900  129.686859  109.286679  119.486769  130.051148  134.058326   \n",
              "187  103.093767  130.051148  108.922390  119.486769  130.415437  134.422615   \n",
              "188  102.729478  128.958281  108.193812  118.758191  129.322570  133.694037   \n",
              "\n",
              "            6           7           8           9    ...         505  \\\n",
              "0    126.772548  105.279501  117.665324  130.051148  ...  179.230154   \n",
              "1    124.951103  104.186634  116.572458  128.593992  ...  179.594443   \n",
              "2    127.501126  106.008079  118.029613  130.051148  ...  179.230154   \n",
              "3    126.408259  106.008079  118.393902  130.415437  ...  179.594443   \n",
              "4    126.043970  105.279501  117.665324  130.051148  ...  180.323020   \n",
              "..          ...         ...         ...         ...  ...         ...   \n",
              "184  129.322570  107.465234  117.665324  128.229703  ...  183.237332   \n",
              "185  129.322570  107.465234  118.393902  128.958281  ...  184.330199   \n",
              "186  128.958281  107.829523  118.393902  128.593992  ...  184.330199   \n",
              "187  129.322570  107.829523  118.758191  129.322570  ...  185.058776   \n",
              "188  128.958281  107.465234  118.029613  128.229703  ...  183.965910   \n",
              "\n",
              "            506         507         508         509         510         511  \\\n",
              "0    179.958731  179.594443  174.858686  177.408709  178.865865  179.230154   \n",
              "1    180.687309  180.323020  174.858686  177.408709  178.865865  179.958731   \n",
              "2    180.323020  179.958731  174.858686  177.408709  178.501576  179.230154   \n",
              "3    180.323020  180.323020  175.222975  177.772998  178.865865  179.594443   \n",
              "4    181.051598  180.323020  175.587264  178.501576  179.958731  179.958731   \n",
              "..          ...         ...         ...         ...         ...         ...   \n",
              "184  184.694488  185.058776  178.501576  181.780176  183.601621  185.423065   \n",
              "185  185.787354  185.787354  178.501576  182.144465  184.330199  186.151643   \n",
              "186  185.787354  185.787354  179.230154  182.873043  185.058776  186.151643   \n",
              "187  186.151643  185.787354  179.594443  183.601621  185.787354  186.515932   \n",
              "188  185.058776  184.694488  178.501576  181.780176  183.965910  185.058776   \n",
              "\n",
              "            512         513         514  \n",
              "0    178.865865  177.044420  180.323020  \n",
              "1    179.594443  177.044420  181.051598  \n",
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        "Again, we observe there is a mismatch in the number of voxels in case of young and old subjects for mOFC i.e. there are 1700 Voxels for youngs whereas merely 515 Voxels for older people which was recorded. Hence, we will proceed with this part later when we have extracted the same 515 voxels for young subjects."
      ],
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      "id": "yVHRhIsD1pPQ"
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