Bacterial_Growth_simulations.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Bacterial Growth simulations",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mlwright84/bacgrowth/blob/main/Bacterial_Growth_simulations.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rvp3QWyB50bu"
      },
      "source": [
        "# Simulation of Bacterial Growth\n",
        "\n",
        "Matthew Wright and John Chase\n",
        "\n",
        "April 2021\n",
        "\n",
        "This notebook contains code for the simulations in our paper \"Bacterial Growth: Not So Simple\".\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YxstvUWf5iM-"
      },
      "source": [
        "import math\n",
        "import queue\n",
        "import random\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from scipy import stats\n",
        "from scipy.optimize import curve_fit"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V-gA7C927a_z"
      },
      "source": [
        "## Exponentially distributed time-to-division\n",
        "\n",
        "The following code simulates many populations with $\\mathrm{Exp}(1)$ underlying splitting distribution and produces a plot like Figure 2 in the paper."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jrecf2J77qtr"
      },
      "source": [
        "# function to simulate many bacteria populations, each of which has an Exp(1) underlying splitting distribution\n",
        "# parameters:\n",
        "#   numSims: number of populations to simulate\n",
        "#   timeVals: list/array of increasing time values at which to record the population sizes\n",
        "# returns:\n",
        "#   popSizeDF: dataframe containing sizes of each population at each time value\n",
        "#   splitTimeLists\n",
        "\n",
        "def simulateManyPopulations(numSims, timeVals):\n",
        "  # set up a dataframe to store the size of each population at each time\n",
        "  popSizeDF = pd.DataFrame(columns = timeVals)\n",
        "\n",
        "  # set up lists to store the splitting times for each population\n",
        "  splitTimeLists = []\n",
        "\n",
        "  # run simulations and record results in the intervals list\n",
        "  for n in range(numSims):\n",
        "    # list to track size of this population at each time index\n",
        "    sizeAtTime = np.zeros(len(timeVals), dtype='int64')\n",
        "\n",
        "    # list to track splitting times\n",
        "    splitTimes = []\n",
        "\n",
        "    # priority queue for times at which cells split\n",
        "    splits = queue.PriorityQueue()\n",
        "\n",
        "    # generate the splitting time of the first cell\n",
        "    splits.put(random.expovariate(1))\n",
        "\n",
        "    # population starts with 1 bacterium at time 0\n",
        "    time = 0\n",
        "    tIndex = 0\n",
        "    size = 1\n",
        "    \n",
        "    # simulate bacteria splitting until max time index is reached\n",
        "    while tIndex < len(timeVals):\n",
        "      time = splits.get()\t # get the smallest time in the splits queue -- time that population reaches size\n",
        "      size = size + 1      # this is the new population size\n",
        "      splitTimes.append(time)\n",
        "      \n",
        "      # store size at indexes \n",
        "      while tIndex < len(timeVals) and timeVals[tIndex] < time:\n",
        "        sizeAtTime[tIndex] = size - 1\n",
        "        tIndex += 1\n",
        "      \n",
        "      # the current cell has split, creating two new splitting times in the queue\n",
        "      r1 = random.expovariate(1)\n",
        "      r2 = random.expovariate(1)\n",
        "      splits.put(time + r1)\n",
        "      splits.put(time + r2)\n",
        "\n",
        "    # append rows\n",
        "    popSizeDF.loc[n] = sizeAtTime.tolist()\n",
        "    splitTimeLists.append(splitTimes)\n",
        "\n",
        "  # return the dataframe\n",
        "  return popSizeDF, splitTimeLists"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "id": "sfZwvNO29Ybh",
        "outputId": "03013cd7-caa1-4e0c-903e-354a73ae8f41"
      },
      "source": [
        "# run some simluations\n",
        "timeVals = np.linspace(0,8,161)\n",
        "popSizeDF, splitTimes = simulateManyPopulations(5, timeVals)\n",
        "\n",
        "# print population curves from popSizeDF\n",
        "(rows,cols) = popSizeDF.shape\n",
        "plt.figure(figsize=(9,6))\n",
        "\n",
        "for r in range(rows):\n",
        "  yvals = popSizeDF.iloc[r,:]\n",
        "  plt.plot(timeVals,yvals)\n",
        "\n",
        "plt.plot(timeVals, np.exp(timeVals), 'k--', label='e^t')\n",
        "plt.plot(timeVals, np.exp2(timeVals), 'k:', label='2^t')\n",
        "plt.legend()\n",
        "\n",
        "plt.xlim(0,6)\n",
        "plt.ylim(0,100)\n",
        "\n",
        "plt.title(\"Population Growth with Exp(1) Splitting\")\n",
        "plt.xlabel(\"time\")\n",
        "plt.ylabel(\"population size\");"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 648x432 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A_S1wfgq-8F-"
      },
      "source": [
        "## Gamma distributed time-to-division\n",
        "\n",
        "The following code simulates average population sizes when the underlying splitting distribution  is $\\mathrm{Gamma}(\\alpha, 1/\\alpha)$ and produces a plot like Figure 3 in the paper."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VzVMXIEI_l0O"
      },
      "source": [
        "# function to simulate a population until a stopping time\n",
        "# this is used to randomize the \"age\" of the initial bacterium in a population\n",
        "# parameters:\n",
        "#   alpha: underlying splitting distribution is Gamma(alpha, 1/alpha)\n",
        "#   stopTime: time at which the simulation stops\n",
        "# returns: list of time-to-division for each bacterium alive at the stopping time\n",
        "def simulatePopulationAtTime(alpha, stopTime):\n",
        "  # priority queue for times at which cells split\n",
        "  splits = queue.PriorityQueue()\n",
        "\n",
        "  # population starts with 1 bacterium at time 0\n",
        "  time = 0\n",
        "  size = 1\n",
        "\n",
        "  # generate the splitting time of the first cell\n",
        "  # note: Gamma(k, 1/alpha) where k ~ DiscreteUniform[1, alpha]\n",
        "  k = random.randint(1,alpha)\n",
        "  splits.put(random.gammavariate(k,1/alpha)) \n",
        "    \n",
        "  # simulate bacteria splitting until max time index is reached\n",
        "  while time < stopTime:\n",
        "    time = splits.get()\t # get the smallest time in the splits queue -- time that population reaches size\n",
        "  \n",
        "    # the current cell has split, creating two new splitting times in the queue,\n",
        "    #   determined by the underlying distribution\n",
        "    r1 = random.gammavariate(alpha, 1/alpha)\n",
        "    r2 = random.gammavariate(alpha, 1/alpha)\n",
        "    splits.put(time + r1)\n",
        "    splits.put(time + r2)\n",
        "\n",
        "  # convert queue to a list of times until next splits for all currently-alive cells\n",
        "  nextSplits = []\n",
        "  while not splits.empty():\n",
        "    t = splits.get() - stopTime\n",
        "    nextSplits.append(t)\n",
        "\n",
        "  return nextSplits\n",
        "\n",
        "# function to simulate average size of many bacteria populations\n",
        "# uses simulatePopulationAtTime() to choose the time at which the first bacterium splits (if alpha > 1)\n",
        "# parameters:\n",
        "#   numSims: number of populations to simulate\n",
        "#   alpha: underlying splitting distribution is Gamma(alpha, 1/alpha)\n",
        "#   timeVals: list/array of increasing time values at which to record the population sizes\n",
        "# returns: average population size at each time value\n",
        "\n",
        "def simulateAvgPopSizesRandomInitialAge(numSims, alpha, timeVals):\n",
        "  # list for average population size at each time index\n",
        "  avgSizeAtTime = np.zeros(len(timeVals))\n",
        "\n",
        "  # run simulations and record results in the intervals list\n",
        "  for n in range(numSims):\n",
        "    # list to track size of this population at each time index\n",
        "    sizeAtTime = np.zeros(len(timeVals))\n",
        "\n",
        "    # priority queue for times at which cells split\n",
        "    splits = queue.PriorityQueue()\n",
        "\n",
        "    # population starts with 1 bacterium at time 0\n",
        "    time = 0\n",
        "    tIndex = 0\n",
        "    size = 1\n",
        "\n",
        "    # generate the splitting time of the first cell\n",
        "    if alpha == 1:\n",
        "      splits.put(random.expovariate(1))  # since exponential distribution is memoryless\n",
        "    else:\n",
        "      startingDistribution = simulatePopulationAtTime(alpha, 8)   # do the pre-simulation, then\n",
        "      splits.put( random.choice(startingDistribution) )           # choose a random bacterium\n",
        "    \n",
        "    # simulate bacteria splitting until max time index is reached\n",
        "    while tIndex < len(timeVals):\n",
        "      time = splits.get()\t # get the smallest time in the splits queue -- time that population reaches size\n",
        "      size = size + 1      # this is the new population size\n",
        "      \n",
        "      # store size at indexes \n",
        "      while tIndex < len(timeVals) and timeVals[tIndex] < time:\n",
        "        sizeAtTime[tIndex] = size - 1\n",
        "        tIndex += 1\n",
        "      \n",
        "      # the current cell has split, creating two new splitting times in the queue,\n",
        "      #  determined by the underlying distribution\n",
        "      r1 = random.gammavariate(alpha, 1/alpha)\n",
        "      r2 = random.gammavariate(alpha, 1/alpha)\n",
        "      splits.put(time + r1)\n",
        "      splits.put(time + r2)\n",
        "\n",
        "    # add population sizes to master list\n",
        "    avgSizeAtTime = avgSizeAtTime + sizeAtTime\n",
        "\n",
        "  # return the average sizes at each time\n",
        "  return avgSizeAtTime/numSims"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        },
        "id": "uOJovrd5Ca6b",
        "outputId": "856ef9aa-cc60-4745-de2f-cc5c11fe03bd"
      },
      "source": [
        "# this code simulates average population sizes at each of the following time values,\n",
        "#   where underlying splitting distribution is Gamma(alpha, 1/alpha) for each of the following alpha values\n",
        "alphaVals = [1,2,3,10,30,100]\n",
        "timeVals = np.linspace(0, 10, 201)\n",
        "numPopulations = 10000\n",
        "\n",
        "rowList = []\n",
        "\n",
        "for a in alphaVals:\n",
        "  yvals = simulateAvgPopSizesRandomInitialAge(numPopulations, a, timeVals)\n",
        "  rowList.append(yvals)\n",
        "  print(\"finished α =\", a)\n",
        "\n",
        "# show a dataframe containing the results of the simulation\n",
        "colNames = [f\"t={t:.2f}\" for t in timeVals]\n",
        "alphaLabels = [\"α = \"+str(int(a)) for a in alphaVals]\n",
        "avgPopSizeDF = pd.DataFrame(rowList, columns = colNames, index=alphaLabels)\n",
        "pd.set_option('display.max_columns', None)\n",
        "avgPopSizeDF"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "finished α = 1\n",
            "finished α = 2\n",
            "finished α = 3\n",
            "finished α = 10\n",
            "finished α = 30\n",
            "finished α = 100\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "         t=0.00  t=0.05  t=0.10  t=0.15  t=0.20  t=0.25  t=0.30  t=0.35  \\\n",
              "α = 1       1.0  1.0514  1.1076  1.1622  1.2200  1.2817  1.3463  1.4184   \n",
              "α = 2       1.0  1.0409  1.0848  1.1291  1.1745  1.2248  1.2775  1.3320   \n",
              "α = 3       1.0  1.0359  1.0783  1.1212  1.1666  1.2118  1.2599  1.3117   \n",
              "α = 10      1.0  1.0331  1.0739  1.1132  1.1544  1.1948  1.2419  1.2898   \n",
              "α = 30      1.0  1.0301  1.0645  1.1012  1.1401  1.1814  1.2232  1.2684   \n",
              "α = 100     1.0  1.0335  1.0735  1.1148  1.1530  1.1948  1.2319  1.2766   \n",
              "\n",
              "         t=0.40  t=0.45  t=0.50  t=0.55  t=0.60  t=0.65  t=0.70  t=0.75  \\\n",
              "α = 1    1.4897  1.5638  1.6426  1.7221  1.8166  1.9101  2.0052  2.1046   \n",
              "α = 2    1.3902  1.4486  1.5097  1.5694  1.6375  1.7063  1.7796  1.8588   \n",
              "α = 3    1.3650  1.4207  1.4813  1.5376  1.5978  1.6612  1.7285  1.7935   \n",
              "α = 10   1.3366  1.3857  1.4378  1.4883  1.5425  1.5999  1.6569  1.7179   \n",
              "α = 30   1.3154  1.3578  1.4071  1.4583  1.5079  1.5656  1.6216  1.6768   \n",
              "α = 100  1.3216  1.3684  1.4185  1.4698  1.5184  1.5688  1.6229  1.6800   \n",
              "\n",
              "         t=0.80  t=0.85  t=0.90  t=0.95  t=1.00  t=1.05  t=1.10  t=1.15  \\\n",
              "α = 1    2.2125  2.3243  2.4405  2.5625  2.6862  2.8180  2.9587  3.1154   \n",
              "α = 2    1.9415  2.0285  2.1133  2.1975  2.2875  2.3827  2.4894  2.5939   \n",
              "α = 3    1.8695  1.9470  2.0243  2.1022  2.1847  2.2713  2.3589  2.4452   \n",
              "α = 10   1.7815  1.8423  1.9101  1.9808  2.0542  2.1284  2.2073  2.2894   \n",
              "α = 30   1.7401  1.8017  1.8694  1.9374  2.0029  2.0730  2.1478  2.2198   \n",
              "α = 100  1.7372  1.7965  1.8642  1.9330  2.0031  2.0778  2.1559  2.2319   \n",
              "\n",
              "         t=1.20  t=1.25  t=1.30  t=1.35  t=1.40  t=1.45  t=1.50  t=1.55  \\\n",
              "α = 1    3.2757  3.4383  3.6178  3.8050  4.0044  4.2057  4.4163  4.6365   \n",
              "α = 2    2.7073  2.8222  2.9433  3.0692  3.2053  3.3390  3.4791  3.6341   \n",
              "α = 3    2.5441  2.6488  2.7551  2.8654  2.9786  3.0950  3.2222  3.3495   \n",
              "α = 10   2.3679  2.4543  2.5443  2.6342  2.7346  2.8407  2.9453  3.0539   \n",
              "α = 30   2.2977  2.3843  2.4689  2.5538  2.6506  2.7409  2.8396  2.9383   \n",
              "α = 100  2.3079  2.3900  2.4734  2.5576  2.6515  2.7450  2.8384  2.9375   \n",
              "\n",
              "         t=1.60  t=1.65  t=1.70  t=1.75  t=1.80  t=1.85  t=1.90  t=1.95  \\\n",
              "α = 1    4.8846  5.1346  5.3942  5.6745  5.9681  6.2721  6.5943  6.9326   \n",
              "α = 2    3.7903  3.9449  4.1023  4.2760  4.4511  4.6373  4.8322  5.0299   \n",
              "α = 3    3.4828  3.6190  3.7645  3.9110  4.0661  4.2228  4.3842  4.5536   \n",
              "α = 10   3.1650  3.2808  3.3984  3.5212  3.6451  3.7778  3.9159  4.0539   \n",
              "α = 30   3.0470  3.1613  3.2735  3.3878  3.5072  3.6318  3.7600  3.8938   \n",
              "α = 100  3.0448  3.1470  3.2566  3.3702  3.4898  3.6098  3.7373  3.8788   \n",
              "\n",
              "         t=2.00  t=2.05  t=2.10  t=2.15  t=2.20  t=2.25  t=2.30   t=2.35  \\\n",
              "α = 1    7.2754  7.6441  8.0302  8.4428  8.8691  9.3307  9.8043  10.3045   \n",
              "α = 2    5.2474  5.4737  5.7101  5.9462  6.2004  6.4631  6.7392   7.0204   \n",
              "α = 3    4.7354  4.9245  5.1290  5.3368  5.5506  5.7663  5.9912   6.2383   \n",
              "α = 10   4.1994  4.3585  4.5215  4.6902  4.8560  5.0389  5.2281   5.4164   \n",
              "α = 30   4.0367  4.1808  4.3251  4.4781  4.6356  4.8071  4.9720   5.1520   \n",
              "α = 100  4.0162  4.1592  4.3060  4.4576  4.6188  4.7812  4.9560   5.1331   \n",
              "\n",
              "          t=2.40   t=2.45   t=2.50   t=2.55   t=2.60   t=2.65   t=2.70  \\\n",
              "α = 1    10.8419  11.4101  11.9887  12.5931  13.2373  13.9264  14.6506   \n",
              "α = 2     7.3309   7.6306   7.9568   8.2970   8.6468   9.0120   9.3900   \n",
              "α = 3     6.4886   6.7536   7.0214   7.2985   7.5900   7.8924   8.2091   \n",
              "α = 10    5.6156   5.8287   6.0485   6.2595   6.4901   6.7281   6.9741   \n",
              "α = 30    5.3385   5.5313   5.7361   5.9378   6.1512   6.3774   6.6054   \n",
              "α = 100   5.3121   5.4985   5.6849   5.8897   6.0872   6.2999   6.5246   \n",
              "\n",
              "          t=2.75   t=2.80   t=2.85   t=2.90   t=2.95   t=3.00   t=3.05  \\\n",
              "α = 1    15.4165  16.1939  17.0322  17.9130  18.8462  19.7937  20.7903   \n",
              "α = 2     9.7884  10.2131  10.6465  11.0919  11.5677  12.0569  12.5774   \n",
              "α = 3     8.5372   8.8726   9.2340   9.5981   9.9738  10.3759  10.7946   \n",
              "α = 10    7.2288   7.4979   7.7609   8.0505   8.3439   8.6407   8.9584   \n",
              "α = 30    6.8279   7.0738   7.3216   7.5768   7.8485   8.1329   8.4271   \n",
              "α = 100   6.7662   7.0035   7.2457   7.4972   7.7702   8.0519   8.3434   \n",
              "\n",
              "          t=3.10   t=3.15   t=3.20   t=3.25   t=3.30   t=3.35   t=3.40  \\\n",
              "α = 1    21.8573  22.9896  24.1508  25.4102  26.6944  28.0653  29.4966   \n",
              "α = 2    13.1081  13.6719  14.2436  14.8514  15.4770  16.1190  16.7986   \n",
              "α = 3    11.2277  11.6797  12.1550  12.6426  13.1452  13.6574  14.1984   \n",
              "α = 10    9.2782   9.6247   9.9657  10.3335  10.7098  11.0973  11.5038   \n",
              "α = 30    8.7325   9.0423   9.3656   9.7026  10.0437  10.4045  10.7811   \n",
              "α = 100   8.6345   8.9485   9.2656   9.5989   9.9342  10.2847  10.6506   \n",
              "\n",
              "          t=3.45   t=3.50   t=3.55   t=3.60   t=3.65   t=3.70   t=3.75  \\\n",
              "α = 1    30.9870  32.5743  34.2405  36.0263  37.8952  39.8583  41.9090   \n",
              "α = 2    17.5218  18.2601  19.0288  19.8313  20.6712  21.5440  22.4482   \n",
              "α = 3    14.7587  15.3445  15.9521  16.5820  17.2576  17.9508  18.6662   \n",
              "α = 10   11.9173  12.3590  12.8084  13.2739  13.7563  14.2593  14.7842   \n",
              "α = 30   11.1701  11.5588  11.9683  12.4015  12.8443  13.3019  13.7691   \n",
              "α = 100  11.0264  11.4055  11.8068  12.2079  12.6404  13.0927  13.5637   \n",
              "\n",
              "          t=3.80   t=3.85   t=3.90   t=3.95   t=4.00   t=4.05   t=4.10  \\\n",
              "α = 1    44.0650  46.3286  48.7178  51.2341  53.8304  56.5988  59.5153   \n",
              "α = 2    23.3847  24.3654  25.4012  26.5047  27.6159  28.7671  29.9745   \n",
              "α = 3    19.4014  20.1777  20.9775  21.8168  22.6748  23.5930  24.5287   \n",
              "α = 10   15.3441  15.9090  16.4905  17.0939  17.7134  18.3533  19.0258   \n",
              "α = 30   14.2521  14.7616  15.2843  15.8169  16.3893  16.9756  17.5943   \n",
              "α = 100  14.0418  14.5322  15.0454  15.5821  16.1404  16.7094  17.3166   \n",
              "\n",
              "          t=4.15   t=4.20   t=4.25   t=4.30   t=4.35   t=4.40   t=4.45  \\\n",
              "α = 1    62.5538  65.7941  69.1642  72.7473  76.4439  80.3486  84.4506   \n",
              "α = 2    31.2400  32.5717  33.9500  35.3892  36.8915  38.4515  40.0878   \n",
              "α = 3    25.4854  26.4852  27.5310  28.6300  29.7644  30.9674  32.2145   \n",
              "α = 10   19.7140  20.4362  21.1864  21.9546  22.7622  23.6038  24.4757   \n",
              "α = 30   18.2310  18.8805  19.5607  20.2700  20.9998  21.7522  22.5283   \n",
              "α = 100  17.9258  18.5742  19.2380  19.9153  20.6102  21.3489  22.0931   \n",
              "\n",
              "          t=4.50   t=4.55   t=4.60    t=4.65    t=4.70    t=4.75    t=4.80  \\\n",
              "α = 1    88.7824  93.3530  98.1563  103.1656  108.4932  114.0806  119.8918   \n",
              "α = 2    41.7733  43.5369  45.3576   47.2833   49.2929   51.3727   53.5229   \n",
              "α = 3    33.5152  34.8518  36.2373   37.7056   39.1959   40.7623   42.3807   \n",
              "α = 10   25.3710  26.3044  27.2664   28.2525   29.2778   30.3714   31.4635   \n",
              "α = 30   23.3197  24.1498  24.9977   25.8864   26.8113   27.7450   28.7353   \n",
              "α = 100  22.8665  23.6644  24.4937   25.3599   26.2503   27.1852   28.1538   \n",
              "\n",
              "           t=4.85    t=4.90    t=4.95    t=5.00    t=5.05    t=5.10    t=5.15  \\\n",
              "α = 1    126.0120  132.4685  139.3038  146.4492  153.9639  161.8616  170.1581   \n",
              "α = 2     55.7810   58.1537   60.5955   63.1638   65.8255   68.6228   71.5375   \n",
              "α = 3     44.0614   45.8256   47.6270   49.5347   51.4817   53.5134   55.6344   \n",
              "α = 10    32.6122   33.8049   35.0272   36.3081   37.6301   39.0120   40.4484   \n",
              "α = 30    29.7746   30.8424   31.9599   33.1093   34.2858   35.5145   36.7914   \n",
              "α = 100   29.1535   30.1828   31.2620   32.3766   33.5247   34.7310   35.9620   \n",
              "\n",
              "           t=5.20    t=5.25    t=5.30    t=5.35    t=5.40    t=5.45    t=5.50  \\\n",
              "α = 1    178.8964  188.0991  197.7020  207.8475  218.4847  229.6637  241.5076   \n",
              "α = 2     74.5583   77.7308   81.0091   84.4454   88.0189   91.7471   95.6221   \n",
              "α = 3     57.8674   60.1609   62.5709   65.0388   67.6368   70.3264   73.1444   \n",
              "α = 10    41.9367   43.4607   45.0427   46.6954   48.3940   50.1586   51.9845   \n",
              "α = 30    38.0901   39.4486   40.8704   42.3334   43.8228   45.3882   47.0057   \n",
              "α = 100   37.2401   38.5650   39.9253   41.3144   42.7854   44.2813   45.8288   \n",
              "\n",
              "           t=5.55    t=5.60    t=5.65    t=5.70    t=5.75    t=5.80    t=5.85  \\\n",
              "α = 1    253.8857  266.8894  280.5898  294.9800  310.1263  325.9902  342.6846   \n",
              "α = 2     99.6566  103.9027  108.3295  112.9021  117.6736  122.6309  127.8148   \n",
              "α = 3     76.0309   79.0399   82.1584   85.4337   88.8637   92.4021   96.0793   \n",
              "α = 10    53.8642   55.8192   57.8793   60.0206   62.2152   64.4879   66.8456   \n",
              "α = 30    48.6868   50.4174   52.2134   54.0605   56.0018   58.0040   60.0796   \n",
              "α = 100   47.4408   49.1381   50.8583   52.6426   54.5125   56.4303   58.4458   \n",
              "\n",
              "           t=5.90    t=5.95    t=6.00    t=6.05    t=6.10    t=6.15    t=6.20  \\\n",
              "α = 1    360.2797  378.7224  398.1841  418.7112  440.1885  462.7826  486.4879   \n",
              "α = 2    133.2002  138.8350  144.7330  150.8226  157.2171  163.8452  170.7792   \n",
              "α = 3     99.9119  103.8850  108.0034  112.2873  116.7164  121.3310  126.1513   \n",
              "α = 10    69.3068   71.8145   74.4661   77.2062   80.0165   82.9149   85.9283   \n",
              "α = 30    62.2090   64.4225   66.7675   69.1586   71.6162   74.1589   76.7726   \n",
              "α = 100   60.5057   62.6710   64.9053   67.2253   69.6348   72.0948   74.6672   \n",
              "\n",
              "           t=6.25    t=6.30    t=6.35    t=6.40    t=6.45    t=6.50    t=6.55  \\\n",
              "α = 1    511.4141  537.6738  565.2237  594.2321  624.6851  656.7440  690.4455   \n",
              "α = 2    178.0621  185.5578  193.3772  201.5144  210.0495  218.8906  228.1606   \n",
              "α = 3    131.1905  136.4397  141.8527  147.5180  153.4240  159.5238  165.8513   \n",
              "α = 10    89.0450   92.3212   95.6775   99.1909  102.8361  106.5746  110.4826   \n",
              "α = 30    79.5246   82.3653   85.2933   88.3339   91.4877   94.7331   98.1139   \n",
              "α = 100   77.3141   80.0424   82.8619   85.7540   88.7733   91.8961   95.1197   \n",
              "\n",
              "           t=6.60    t=6.65    t=6.70    t=6.75    t=6.80    t=6.85    t=6.90  \\\n",
              "α = 1    725.8122  762.9111  802.1315  843.2312  886.4390  931.9532  979.7212   \n",
              "α = 2    237.7926  247.8899  258.3980  269.3618  280.7625  292.6287  305.0668   \n",
              "α = 3    172.4337  179.2919  186.3875  193.7959  201.5176  209.5270  217.9279   \n",
              "α = 10   114.5039  118.6769  123.0007  127.4850  132.1739  136.9623  141.9613   \n",
              "α = 30   101.5970  105.2246  108.9991  112.9167  116.9413  121.1280  125.4803   \n",
              "α = 100   98.4807  101.9567  105.5503  109.2752  113.1568  117.1651  121.3287   \n",
              "\n",
              "            t=6.95     t=7.00     t=7.05     t=7.10     t=7.15     t=7.20  \\\n",
              "α = 1    1029.9296  1082.7109  1138.2247  1196.6128  1257.8630  1322.4181   \n",
              "α = 2     317.9693   331.4166   345.3545   359.9763   375.1979   391.0442   \n",
              "α = 3     226.5639   235.5528   244.8941   254.6386   264.7586   275.2419   \n",
              "α = 10    147.1678   152.5407   158.0839   163.8632   169.8676   176.1320   \n",
              "α = 30    129.9498   134.6146   139.3891   144.3560   149.5286   154.8533   \n",
              "α = 100   125.6372   130.1030   134.7699   139.5832   144.5629   149.7108   \n",
              "\n",
              "            t=7.25     t=7.30     t=7.35     t=7.40     t=7.45     t=7.50  \\\n",
              "α = 1    1390.1472  1461.3944  1536.2575  1615.0231  1697.7983  1784.6647   \n",
              "α = 2     407.5073   424.7227   442.7038   461.4207   480.9848   501.2686   \n",
              "α = 3     286.2302   297.6602   309.5589   321.8395   334.6402   347.9112   \n",
              "α = 10    182.6034   189.2578   196.1525   203.3326   210.7429   218.4694   \n",
              "α = 30    160.3129   165.9760   171.9194   178.0540   184.4013   190.9362   \n",
              "α = 100   154.9885   160.4411   166.0893   171.9288   177.9959   184.2020   \n",
              "\n",
              "            t=7.55     t=7.60     t=7.65     t=7.70     t=7.75     t=7.80  \\\n",
              "α = 1    1876.1713  1972.4933  2073.6078  2179.8898  2291.5664  2409.0293   \n",
              "α = 2     522.4768   544.5427   567.5548   591.6484   616.6486   642.7949   \n",
              "α = 3     361.7183   376.1171   391.0799   406.6445   422.8512   439.6357   \n",
              "α = 10    226.4307   234.7038   243.2379   252.1245   261.3500   270.9146   \n",
              "α = 30    197.7818   204.8463   212.1944   219.7989   227.6262   235.8096   \n",
              "α = 100   190.7073   197.4359   204.4088   211.6448   219.1281   226.9452   \n",
              "\n",
              "            t=7.85     t=7.90     t=7.95     t=8.00     t=8.05     t=8.10  \\\n",
              "α = 1    2532.5723  2662.3427  2798.5536  2941.9837  3092.8499  3251.6191   \n",
              "α = 2     670.0254   698.3874   727.9190   758.6261   790.7648   824.1858   \n",
              "α = 3     457.1283   475.3498   494.2778   513.9555   534.3989   555.6154   \n",
              "α = 10    280.7623   291.0026   301.6947   312.7411   324.1355   335.9702   \n",
              "α = 30    244.2422   252.9479   261.9334   271.3196   281.0343   291.0662   \n",
              "α = 100   234.9554   243.3080   251.9760   260.9117   270.1926   279.8261   \n",
              "\n",
              "            t=8.15     t=8.20     t=8.25     t=8.30     t=8.35     t=8.40  \\\n",
              "α = 1    3418.2763  3593.4817  3777.6990  3971.5254  4174.9635  4388.8737   \n",
              "α = 2     858.9500   895.2122   933.0901   972.4711  1013.5834  1056.4964   \n",
              "α = 3     577.7726   600.7544   624.6883   649.5742   675.3084   702.1450   \n",
              "α = 10    348.2757   361.0029   374.2248   387.8657   402.0090   416.7136   \n",
              "α = 30    301.4369   312.1451   323.2356   334.7042   346.6703   359.0300   \n",
              "α = 100   289.7973   300.0054   310.6633   321.6493   332.9221   344.6758   \n",
              "\n",
              "            t=8.45     t=8.50     t=8.55     t=8.60     t=8.65     t=8.70  \\\n",
              "α = 1    4613.8843  4850.5095  5099.0124  5360.5483  5635.5603  5924.7625   \n",
              "α = 2    1101.1302  1147.7082  1196.2461  1246.7360  1299.5326  1354.7077   \n",
              "α = 3     729.9556   758.9642   789.1470   820.4414   853.0576   887.0502   \n",
              "α = 10    432.0076   447.7581   464.1031   481.0560   498.6427   516.8799   \n",
              "α = 30    371.8552   385.0784   398.8727   413.0940   427.9119   443.1954   \n",
              "α = 100   356.7450   369.3355   382.3725   395.8798   409.8505   424.3261   \n",
              "\n",
              "            t=8.75     t=8.80     t=8.85     t=8.90     t=8.95     t=9.00  \\\n",
              "α = 1    6228.2520  6547.6301  6883.1559  7236.3223  7607.3100  7997.1309   \n",
              "α = 2    1411.9498  1471.6797  1533.9167  1598.7342  1666.2655  1736.7182   \n",
              "α = 3     922.3957   959.0653   997.2433  1036.9677  1078.1885  1121.0386   \n",
              "α = 10    535.7941   555.2820   575.5989   596.6374   618.4831   641.0741   \n",
              "α = 30    459.0447   475.4861   492.4321   509.9799   528.1921   547.0392   \n",
              "α = 100   439.3620   454.9429   471.1090   487.8066   505.1026   523.1349   \n",
              "\n",
              "            t=9.05     t=9.10     t=9.15     t=9.20      t=9.25      t=9.30  \\\n",
              "α = 1    8407.0545  8838.0011  9291.3353  9767.8820  10268.9896  10795.3903   \n",
              "α = 2    1810.1441  1886.6317  1966.2815  2049.4890   2136.2298   2226.5547   \n",
              "α = 3    1165.6091  1211.7717  1259.9643  1310.0832   1362.2420   1416.3672   \n",
              "α = 10    664.5865   688.8813   714.0129   740.1549    767.1071    795.1301   \n",
              "α = 30    566.5281   586.7386   607.6685   629.3131    651.7484    674.9822   \n",
              "α = 100   541.7202   561.0535   580.9741   601.5440    622.7662    644.7324   \n",
              "\n",
              "             t=9.35      t=9.40      t=9.45      t=9.50      t=9.55  \\\n",
              "α = 1    11348.6101  11930.5008  12542.0623  13185.0031  13860.6458   \n",
              "α = 2     2320.6784   2418.8957   2521.1157   2627.6397   2738.7712   \n",
              "α = 3     1472.7337   1531.2680   1592.1056   1655.3008   1721.0734   \n",
              "α = 10     824.1914    854.3472    885.5031    917.7905    951.3558   \n",
              "α = 30     698.9787    724.0206    749.9023    776.5592    804.2577   \n",
              "α = 100    667.4274    691.0001    715.3629    740.5636    766.6447   \n",
              "\n",
              "             t=9.60      t=9.65      t=9.70      t=9.75      t=9.80  \\\n",
              "α = 1    14571.3094  15318.5545  16103.9996  16929.4693  17797.2913   \n",
              "α = 2     2854.6828   2975.3588   3101.2227   3232.2703   3369.0369   \n",
              "α = 3     1789.4930   1860.5721   1934.5463   2011.3956   2091.5227   \n",
              "α = 10     986.2934   1022.3670   1059.7733   1098.5386   1138.6254   \n",
              "α = 30     832.9161    862.7712    893.5882    925.5358    958.5135   \n",
              "α = 100    793.6738    821.6783    850.7664    880.8608    912.1383   \n",
              "\n",
              "             t=9.85      t=9.90      t=9.95     t=10.00  \n",
              "α = 1    18710.0429  19669.2433  20677.6758  21737.7252  \n",
              "α = 2     3511.5428   3659.8459   3814.7807   3975.9392  \n",
              "α = 3     2174.6608   2261.1735   2351.1060   2444.6576  \n",
              "α = 10    1180.2679   1223.3407   1268.1163   1314.3104  \n",
              "α = 30     992.6846   1028.1106   1064.8524   1102.8501  \n",
              "α = 100    944.4953    977.9433   1012.7850   1048.7237  "
            ],
            "text/html": [
              "<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>t=0.00</th>\n",
              "      <th>t=0.05</th>\n",
              "      <th>t=0.10</th>\n",
              "      <th>t=0.15</th>\n",
              "      <th>t=0.20</th>\n",
              "      <th>t=0.25</th>\n",
              "      <th>t=0.30</th>\n",
              "      <th>t=0.35</th>\n",
              "      <th>t=0.40</th>\n",
              "      <th>t=0.45</th>\n",
              "      <th>t=0.50</th>\n",
              "      <th>t=0.55</th>\n",
              "      <th>t=0.60</th>\n",
              "      <th>t=0.65</th>\n",
              "      <th>t=0.70</th>\n",
              "      <th>t=0.75</th>\n",
              "      <th>t=0.80</th>\n",
              "      <th>t=0.85</th>\n",
              "      <th>t=0.90</th>\n",
              "      <th>t=0.95</th>\n",
              "      <th>t=1.00</th>\n",
              "      <th>t=1.05</th>\n",
              "      <th>t=1.10</th>\n",
              "      <th>t=1.15</th>\n",
              "      <th>t=1.20</th>\n",
              "      <th>t=1.25</th>\n",
              "      <th>t=1.30</th>\n",
              "      <th>t=1.35</th>\n",
              "      <th>t=1.40</th>\n",
              "      <th>t=1.45</th>\n",
              "      <th>t=1.50</th>\n",
              "      <th>t=1.55</th>\n",
              "      <th>t=1.60</th>\n",
              "      <th>t=1.65</th>\n",
              "      <th>t=1.70</th>\n",
              "      <th>t=1.75</th>\n",
              "      <th>t=1.80</th>\n",
              "      <th>t=1.85</th>\n",
              "      <th>t=1.90</th>\n",
              "      <th>t=1.95</th>\n",
              "      <th>t=2.00</th>\n",
              "      <th>t=2.05</th>\n",
              "      <th>t=2.10</th>\n",
              "      <th>t=2.15</th>\n",
              "      <th>t=2.20</th>\n",
              "      <th>t=2.25</th>\n",
              "      <th>t=2.30</th>\n",
              "      <th>t=2.35</th>\n",
              "      <th>t=2.40</th>\n",
              "      <th>t=2.45</th>\n",
              "      <th>t=2.50</th>\n",
              "      <th>t=2.55</th>\n",
              "      <th>t=2.60</th>\n",
              "      <th>t=2.65</th>\n",
              "      <th>t=2.70</th>\n",
              "      <th>t=2.75</th>\n",
              "      <th>t=2.80</th>\n",
              "      <th>t=2.85</th>\n",
              "      <th>t=2.90</th>\n",
              "      <th>t=2.95</th>\n",
              "      <th>t=3.00</th>\n",
              "      <th>t=3.05</th>\n",
              "      <th>t=3.10</th>\n",
              "      <th>t=3.15</th>\n",
              "      <th>t=3.20</th>\n",
              "      <th>t=3.25</th>\n",
              "      <th>t=3.30</th>\n",
              "      <th>t=3.35</th>\n",
              "      <th>t=3.40</th>\n",
              "      <th>t=3.45</th>\n",
              "      <th>t=3.50</th>\n",
              "      <th>t=3.55</th>\n",
              "      <th>t=3.60</th>\n",
              "      <th>t=3.65</th>\n",
              "      <th>t=3.70</th>\n",
              "      <th>t=3.75</th>\n",
              "      <th>t=3.80</th>\n",
              "      <th>t=3.85</th>\n",
              "      <th>t=3.90</th>\n",
              "      <th>t=3.95</th>\n",
              "      <th>t=4.00</th>\n",
              "      <th>t=4.05</th>\n",
              "      <th>t=4.10</th>\n",
              "      <th>t=4.15</th>\n",
              "      <th>t=4.20</th>\n",
              "      <th>t=4.25</th>\n",
              "      <th>t=4.30</th>\n",
              "      <th>t=4.35</th>\n",
              "      <th>t=4.40</th>\n",
              "      <th>t=4.45</th>\n",
              "      <th>t=4.50</th>\n",
              "      <th>t=4.55</th>\n",
              "      <th>t=4.60</th>\n",
              "      <th>t=4.65</th>\n",
              "      <th>t=4.70</th>\n",
              "      <th>t=4.75</th>\n",
              "      <th>t=4.80</th>\n",
              "      <th>t=4.85</th>\n",
              "      <th>t=4.90</th>\n",
              "      <th>t=4.95</th>\n",
              "      <th>t=5.00</th>\n",
              "      <th>t=5.05</th>\n",
              "      <th>t=5.10</th>\n",
              "      <th>t=5.15</th>\n",
              "      <th>t=5.20</th>\n",
              "      <th>t=5.25</th>\n",
              "      <th>t=5.30</th>\n",
              "      <th>t=5.35</th>\n",
              "      <th>t=5.40</th>\n",
              "      <th>t=5.45</th>\n",
              "      <th>t=5.50</th>\n",
              "      <th>t=5.55</th>\n",
              "      <th>t=5.60</th>\n",
              "      <th>t=5.65</th>\n",
              "      <th>t=5.70</th>\n",
              "      <th>t=5.75</th>\n",
              "      <th>t=5.80</th>\n",
              "      <th>t=5.85</th>\n",
              "      <th>t=5.90</th>\n",
              "      <th>t=5.95</th>\n",
              "      <th>t=6.00</th>\n",
              "      <th>t=6.05</th>\n",
              "      <th>t=6.10</th>\n",
              "      <th>t=6.15</th>\n",
              "      <th>t=6.20</th>\n",
              "      <th>t=6.25</th>\n",
              "      <th>t=6.30</th>\n",
              "      <th>t=6.35</th>\n",
              "      <th>t=6.40</th>\n",
              "      <th>t=6.45</th>\n",
              "      <th>t=6.50</th>\n",
              "      <th>t=6.55</th>\n",
              "      <th>t=6.60</th>\n",
              "      <th>t=6.65</th>\n",
              "      <th>t=6.70</th>\n",
              "      <th>t=6.75</th>\n",
              "      <th>t=6.80</th>\n",
              "      <th>t=6.85</th>\n",
              "      <th>t=6.90</th>\n",
              "      <th>t=6.95</th>\n",
              "      <th>t=7.00</th>\n",
              "      <th>t=7.05</th>\n",
              "      <th>t=7.10</th>\n",
              "      <th>t=7.15</th>\n",
              "      <th>t=7.20</th>\n",
              "      <th>t=7.25</th>\n",
              "      <th>t=7.30</th>\n",
              "      <th>t=7.35</th>\n",
              "      <th>t=7.40</th>\n",
              "      <th>t=7.45</th>\n",
              "      <th>t=7.50</th>\n",
              "      <th>t=7.55</th>\n",
              "      <th>t=7.60</th>\n",
              "      <th>t=7.65</th>\n",
              "      <th>t=7.70</th>\n",
              "      <th>t=7.75</th>\n",
              "      <th>t=7.80</th>\n",
              "      <th>t=7.85</th>\n",
              "      <th>t=7.90</th>\n",
              "      <th>t=7.95</th>\n",
              "      <th>t=8.00</th>\n",
              "      <th>t=8.05</th>\n",
              "      <th>t=8.10</th>\n",
              "      <th>t=8.15</th>\n",
              "      <th>t=8.20</th>\n",
              "      <th>t=8.25</th>\n",
              "      <th>t=8.30</th>\n",
              "      <th>t=8.35</th>\n",
              "      <th>t=8.40</th>\n",
              "      <th>t=8.45</th>\n",
              "      <th>t=8.50</th>\n",
              "      <th>t=8.55</th>\n",
              "      <th>t=8.60</th>\n",
              "      <th>t=8.65</th>\n",
              "      <th>t=8.70</th>\n",
              "      <th>t=8.75</th>\n",
              "      <th>t=8.80</th>\n",
              "      <th>t=8.85</th>\n",
              "      <th>t=8.90</th>\n",
              "      <th>t=8.95</th>\n",
              "      <th>t=9.00</th>\n",
              "      <th>t=9.05</th>\n",
              "      <th>t=9.10</th>\n",
              "      <th>t=9.15</th>\n",
              "      <th>t=9.20</th>\n",
              "      <th>t=9.25</th>\n",
              "      <th>t=9.30</th>\n",
              "      <th>t=9.35</th>\n",
              "      <th>t=9.40</th>\n",
              "      <th>t=9.45</th>\n",
              "      <th>t=9.50</th>\n",
              "      <th>t=9.55</th>\n",
              "      <th>t=9.60</th>\n",
              "      <th>t=9.65</th>\n",
              "      <th>t=9.70</th>\n",
              "      <th>t=9.75</th>\n",
              "      <th>t=9.80</th>\n",
              "      <th>t=9.85</th>\n",
              "      <th>t=9.90</th>\n",
              "      <th>t=9.95</th>\n",
              "      <th>t=10.00</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>α = 1</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0514</td>\n",
              "      <td>1.1076</td>\n",
              "      <td>1.1622</td>\n",
              "      <td>1.2200</td>\n",
              "      <td>1.2817</td>\n",
              "      <td>1.3463</td>\n",
              "      <td>1.4184</td>\n",
              "      <td>1.4897</td>\n",
              "      <td>1.5638</td>\n",
              "      <td>1.6426</td>\n",
              "      <td>1.7221</td>\n",
              "      <td>1.8166</td>\n",
              "      <td>1.9101</td>\n",
              "      <td>2.0052</td>\n",
              "      <td>2.1046</td>\n",
              "      <td>2.2125</td>\n",
              "      <td>2.3243</td>\n",
              "      <td>2.4405</td>\n",
              "      <td>2.5625</td>\n",
              "      <td>2.6862</td>\n",
              "      <td>2.8180</td>\n",
              "      <td>2.9587</td>\n",
              "      <td>3.1154</td>\n",
              "      <td>3.2757</td>\n",
              "      <td>3.4383</td>\n",
              "      <td>3.6178</td>\n",
              "      <td>3.8050</td>\n",
              "      <td>4.0044</td>\n",
              "      <td>4.2057</td>\n",
              "      <td>4.4163</td>\n",
              "      <td>4.6365</td>\n",
              "      <td>4.8846</td>\n",
              "      <td>5.1346</td>\n",
              "      <td>5.3942</td>\n",
              "      <td>5.6745</td>\n",
              "      <td>5.9681</td>\n",
              "      <td>6.2721</td>\n",
              "      <td>6.5943</td>\n",
              "      <td>6.9326</td>\n",
              "      <td>7.2754</td>\n",
              "      <td>7.6441</td>\n",
              "      <td>8.0302</td>\n",
              "      <td>8.4428</td>\n",
              "      <td>8.8691</td>\n",
              "      <td>9.3307</td>\n",
              "      <td>9.8043</td>\n",
              "      <td>10.3045</td>\n",
              "      <td>10.8419</td>\n",
              "      <td>11.4101</td>\n",
              "      <td>11.9887</td>\n",
              "      <td>12.5931</td>\n",
              "      <td>13.2373</td>\n",
              "      <td>13.9264</td>\n",
              "      <td>14.6506</td>\n",
              "      <td>15.4165</td>\n",
              "      <td>16.1939</td>\n",
              "      <td>17.0322</td>\n",
              "      <td>17.9130</td>\n",
              "      <td>18.8462</td>\n",
              "      <td>19.7937</td>\n",
              "      <td>20.7903</td>\n",
              "      <td>21.8573</td>\n",
              "      <td>22.9896</td>\n",
              "      <td>24.1508</td>\n",
              "      <td>25.4102</td>\n",
              "      <td>26.6944</td>\n",
              "      <td>28.0653</td>\n",
              "      <td>29.4966</td>\n",
              "      <td>30.9870</td>\n",
              "      <td>32.5743</td>\n",
              "      <td>34.2405</td>\n",
              "      <td>36.0263</td>\n",
              "      <td>37.8952</td>\n",
              "      <td>39.8583</td>\n",
              "      <td>41.9090</td>\n",
              "      <td>44.0650</td>\n",
              "      <td>46.3286</td>\n",
              "      <td>48.7178</td>\n",
              "      <td>51.2341</td>\n",
              "      <td>53.8304</td>\n",
              "      <td>56.5988</td>\n",
              "      <td>59.5153</td>\n",
              "      <td>62.5538</td>\n",
              "      <td>65.7941</td>\n",
              "      <td>69.1642</td>\n",
              "      <td>72.7473</td>\n",
              "      <td>76.4439</td>\n",
              "      <td>80.3486</td>\n",
              "      <td>84.4506</td>\n",
              "      <td>88.7824</td>\n",
              "      <td>93.3530</td>\n",
              "      <td>98.1563</td>\n",
              "      <td>103.1656</td>\n",
              "      <td>108.4932</td>\n",
              "      <td>114.0806</td>\n",
              "      <td>119.8918</td>\n",
              "      <td>126.0120</td>\n",
              "      <td>132.4685</td>\n",
              "      <td>139.3038</td>\n",
              "      <td>146.4492</td>\n",
              "      <td>153.9639</td>\n",
              "      <td>161.8616</td>\n",
              "      <td>170.1581</td>\n",
              "      <td>178.8964</td>\n",
              "      <td>188.0991</td>\n",
              "      <td>197.7020</td>\n",
              "      <td>207.8475</td>\n",
              "      <td>218.4847</td>\n",
              "      <td>229.6637</td>\n",
              "      <td>241.5076</td>\n",
              "      <td>253.8857</td>\n",
              "      <td>266.8894</td>\n",
              "      <td>280.5898</td>\n",
              "      <td>294.9800</td>\n",
              "      <td>310.1263</td>\n",
              "      <td>325.9902</td>\n",
              "      <td>342.6846</td>\n",
              "      <td>360.2797</td>\n",
              "      <td>378.7224</td>\n",
              "      <td>398.1841</td>\n",
              "      <td>418.7112</td>\n",
              "      <td>440.1885</td>\n",
              "      <td>462.7826</td>\n",
              "      <td>486.4879</td>\n",
              "      <td>511.4141</td>\n",
              "      <td>537.6738</td>\n",
              "      <td>565.2237</td>\n",
              "      <td>594.2321</td>\n",
              "      <td>624.6851</td>\n",
              "      <td>656.7440</td>\n",
              "      <td>690.4455</td>\n",
              "      <td>725.8122</td>\n",
              "      <td>762.9111</td>\n",
              "      <td>802.1315</td>\n",
              "      <td>843.2312</td>\n",
              "      <td>886.4390</td>\n",
              "      <td>931.9532</td>\n",
              "      <td>979.7212</td>\n",
              "      <td>1029.9296</td>\n",
              "      <td>1082.7109</td>\n",
              "      <td>1138.2247</td>\n",
              "      <td>1196.6128</td>\n",
              "      <td>1257.8630</td>\n",
              "      <td>1322.4181</td>\n",
              "      <td>1390.1472</td>\n",
              "      <td>1461.3944</td>\n",
              "      <td>1536.2575</td>\n",
              "      <td>1615.0231</td>\n",
              "      <td>1697.7983</td>\n",
              "      <td>1784.6647</td>\n",
              "      <td>1876.1713</td>\n",
              "      <td>1972.4933</td>\n",
              "      <td>2073.6078</td>\n",
              "      <td>2179.8898</td>\n",
              "      <td>2291.5664</td>\n",
              "      <td>2409.0293</td>\n",
              "      <td>2532.5723</td>\n",
              "      <td>2662.3427</td>\n",
              "      <td>2798.5536</td>\n",
              "      <td>2941.9837</td>\n",
              "      <td>3092.8499</td>\n",
              "      <td>3251.6191</td>\n",
              "      <td>3418.2763</td>\n",
              "      <td>3593.4817</td>\n",
              "      <td>3777.6990</td>\n",
              "      <td>3971.5254</td>\n",
              "      <td>4174.9635</td>\n",
              "      <td>4388.8737</td>\n",
              "      <td>4613.8843</td>\n",
              "      <td>4850.5095</td>\n",
              "      <td>5099.0124</td>\n",
              "      <td>5360.5483</td>\n",
              "      <td>5635.5603</td>\n",
              "      <td>5924.7625</td>\n",
              "      <td>6228.2520</td>\n",
              "      <td>6547.6301</td>\n",
              "      <td>6883.1559</td>\n",
              "      <td>7236.3223</td>\n",
              "      <td>7607.3100</td>\n",
              "      <td>7997.1309</td>\n",
              "      <td>8407.0545</td>\n",
              "      <td>8838.0011</td>\n",
              "      <td>9291.3353</td>\n",
              "      <td>9767.8820</td>\n",
              "      <td>10268.9896</td>\n",
              "      <td>10795.3903</td>\n",
              "      <td>11348.6101</td>\n",
              "      <td>11930.5008</td>\n",
              "      <td>12542.0623</td>\n",
              "      <td>13185.0031</td>\n",
              "      <td>13860.6458</td>\n",
              "      <td>14571.3094</td>\n",
              "      <td>15318.5545</td>\n",
              "      <td>16103.9996</td>\n",
              "      <td>16929.4693</td>\n",
              "      <td>17797.2913</td>\n",
              "      <td>18710.0429</td>\n",
              "      <td>19669.2433</td>\n",
              "      <td>20677.6758</td>\n",
              "      <td>21737.7252</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 2</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0409</td>\n",
              "      <td>1.0848</td>\n",
              "      <td>1.1291</td>\n",
              "      <td>1.1745</td>\n",
              "      <td>1.2248</td>\n",
              "      <td>1.2775</td>\n",
              "      <td>1.3320</td>\n",
              "      <td>1.3902</td>\n",
              "      <td>1.4486</td>\n",
              "      <td>1.5097</td>\n",
              "      <td>1.5694</td>\n",
              "      <td>1.6375</td>\n",
              "      <td>1.7063</td>\n",
              "      <td>1.7796</td>\n",
              "      <td>1.8588</td>\n",
              "      <td>1.9415</td>\n",
              "      <td>2.0285</td>\n",
              "      <td>2.1133</td>\n",
              "      <td>2.1975</td>\n",
              "      <td>2.2875</td>\n",
              "      <td>2.3827</td>\n",
              "      <td>2.4894</td>\n",
              "      <td>2.5939</td>\n",
              "      <td>2.7073</td>\n",
              "      <td>2.8222</td>\n",
              "      <td>2.9433</td>\n",
              "      <td>3.0692</td>\n",
              "      <td>3.2053</td>\n",
              "      <td>3.3390</td>\n",
              "      <td>3.4791</td>\n",
              "      <td>3.6341</td>\n",
              "      <td>3.7903</td>\n",
              "      <td>3.9449</td>\n",
              "      <td>4.1023</td>\n",
              "      <td>4.2760</td>\n",
              "      <td>4.4511</td>\n",
              "      <td>4.6373</td>\n",
              "      <td>4.8322</td>\n",
              "      <td>5.0299</td>\n",
              "      <td>5.2474</td>\n",
              "      <td>5.4737</td>\n",
              "      <td>5.7101</td>\n",
              "      <td>5.9462</td>\n",
              "      <td>6.2004</td>\n",
              "      <td>6.4631</td>\n",
              "      <td>6.7392</td>\n",
              "      <td>7.0204</td>\n",
              "      <td>7.3309</td>\n",
              "      <td>7.6306</td>\n",
              "      <td>7.9568</td>\n",
              "      <td>8.2970</td>\n",
              "      <td>8.6468</td>\n",
              "      <td>9.0120</td>\n",
              "      <td>9.3900</td>\n",
              "      <td>9.7884</td>\n",
              "      <td>10.2131</td>\n",
              "      <td>10.6465</td>\n",
              "      <td>11.0919</td>\n",
              "      <td>11.5677</td>\n",
              "      <td>12.0569</td>\n",
              "      <td>12.5774</td>\n",
              "      <td>13.1081</td>\n",
              "      <td>13.6719</td>\n",
              "      <td>14.2436</td>\n",
              "      <td>14.8514</td>\n",
              "      <td>15.4770</td>\n",
              "      <td>16.1190</td>\n",
              "      <td>16.7986</td>\n",
              "      <td>17.5218</td>\n",
              "      <td>18.2601</td>\n",
              "      <td>19.0288</td>\n",
              "      <td>19.8313</td>\n",
              "      <td>20.6712</td>\n",
              "      <td>21.5440</td>\n",
              "      <td>22.4482</td>\n",
              "      <td>23.3847</td>\n",
              "      <td>24.3654</td>\n",
              "      <td>25.4012</td>\n",
              "      <td>26.5047</td>\n",
              "      <td>27.6159</td>\n",
              "      <td>28.7671</td>\n",
              "      <td>29.9745</td>\n",
              "      <td>31.2400</td>\n",
              "      <td>32.5717</td>\n",
              "      <td>33.9500</td>\n",
              "      <td>35.3892</td>\n",
              "      <td>36.8915</td>\n",
              "      <td>38.4515</td>\n",
              "      <td>40.0878</td>\n",
              "      <td>41.7733</td>\n",
              "      <td>43.5369</td>\n",
              "      <td>45.3576</td>\n",
              "      <td>47.2833</td>\n",
              "      <td>49.2929</td>\n",
              "      <td>51.3727</td>\n",
              "      <td>53.5229</td>\n",
              "      <td>55.7810</td>\n",
              "      <td>58.1537</td>\n",
              "      <td>60.5955</td>\n",
              "      <td>63.1638</td>\n",
              "      <td>65.8255</td>\n",
              "      <td>68.6228</td>\n",
              "      <td>71.5375</td>\n",
              "      <td>74.5583</td>\n",
              "      <td>77.7308</td>\n",
              "      <td>81.0091</td>\n",
              "      <td>84.4454</td>\n",
              "      <td>88.0189</td>\n",
              "      <td>91.7471</td>\n",
              "      <td>95.6221</td>\n",
              "      <td>99.6566</td>\n",
              "      <td>103.9027</td>\n",
              "      <td>108.3295</td>\n",
              "      <td>112.9021</td>\n",
              "      <td>117.6736</td>\n",
              "      <td>122.6309</td>\n",
              "      <td>127.8148</td>\n",
              "      <td>133.2002</td>\n",
              "      <td>138.8350</td>\n",
              "      <td>144.7330</td>\n",
              "      <td>150.8226</td>\n",
              "      <td>157.2171</td>\n",
              "      <td>163.8452</td>\n",
              "      <td>170.7792</td>\n",
              "      <td>178.0621</td>\n",
              "      <td>185.5578</td>\n",
              "      <td>193.3772</td>\n",
              "      <td>201.5144</td>\n",
              "      <td>210.0495</td>\n",
              "      <td>218.8906</td>\n",
              "      <td>228.1606</td>\n",
              "      <td>237.7926</td>\n",
              "      <td>247.8899</td>\n",
              "      <td>258.3980</td>\n",
              "      <td>269.3618</td>\n",
              "      <td>280.7625</td>\n",
              "      <td>292.6287</td>\n",
              "      <td>305.0668</td>\n",
              "      <td>317.9693</td>\n",
              "      <td>331.4166</td>\n",
              "      <td>345.3545</td>\n",
              "      <td>359.9763</td>\n",
              "      <td>375.1979</td>\n",
              "      <td>391.0442</td>\n",
              "      <td>407.5073</td>\n",
              "      <td>424.7227</td>\n",
              "      <td>442.7038</td>\n",
              "      <td>461.4207</td>\n",
              "      <td>480.9848</td>\n",
              "      <td>501.2686</td>\n",
              "      <td>522.4768</td>\n",
              "      <td>544.5427</td>\n",
              "      <td>567.5548</td>\n",
              "      <td>591.6484</td>\n",
              "      <td>616.6486</td>\n",
              "      <td>642.7949</td>\n",
              "      <td>670.0254</td>\n",
              "      <td>698.3874</td>\n",
              "      <td>727.9190</td>\n",
              "      <td>758.6261</td>\n",
              "      <td>790.7648</td>\n",
              "      <td>824.1858</td>\n",
              "      <td>858.9500</td>\n",
              "      <td>895.2122</td>\n",
              "      <td>933.0901</td>\n",
              "      <td>972.4711</td>\n",
              "      <td>1013.5834</td>\n",
              "      <td>1056.4964</td>\n",
              "      <td>1101.1302</td>\n",
              "      <td>1147.7082</td>\n",
              "      <td>1196.2461</td>\n",
              "      <td>1246.7360</td>\n",
              "      <td>1299.5326</td>\n",
              "      <td>1354.7077</td>\n",
              "      <td>1411.9498</td>\n",
              "      <td>1471.6797</td>\n",
              "      <td>1533.9167</td>\n",
              "      <td>1598.7342</td>\n",
              "      <td>1666.2655</td>\n",
              "      <td>1736.7182</td>\n",
              "      <td>1810.1441</td>\n",
              "      <td>1886.6317</td>\n",
              "      <td>1966.2815</td>\n",
              "      <td>2049.4890</td>\n",
              "      <td>2136.2298</td>\n",
              "      <td>2226.5547</td>\n",
              "      <td>2320.6784</td>\n",
              "      <td>2418.8957</td>\n",
              "      <td>2521.1157</td>\n",
              "      <td>2627.6397</td>\n",
              "      <td>2738.7712</td>\n",
              "      <td>2854.6828</td>\n",
              "      <td>2975.3588</td>\n",
              "      <td>3101.2227</td>\n",
              "      <td>3232.2703</td>\n",
              "      <td>3369.0369</td>\n",
              "      <td>3511.5428</td>\n",
              "      <td>3659.8459</td>\n",
              "      <td>3814.7807</td>\n",
              "      <td>3975.9392</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 3</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0359</td>\n",
              "      <td>1.0783</td>\n",
              "      <td>1.1212</td>\n",
              "      <td>1.1666</td>\n",
              "      <td>1.2118</td>\n",
              "      <td>1.2599</td>\n",
              "      <td>1.3117</td>\n",
              "      <td>1.3650</td>\n",
              "      <td>1.4207</td>\n",
              "      <td>1.4813</td>\n",
              "      <td>1.5376</td>\n",
              "      <td>1.5978</td>\n",
              "      <td>1.6612</td>\n",
              "      <td>1.7285</td>\n",
              "      <td>1.7935</td>\n",
              "      <td>1.8695</td>\n",
              "      <td>1.9470</td>\n",
              "      <td>2.0243</td>\n",
              "      <td>2.1022</td>\n",
              "      <td>2.1847</td>\n",
              "      <td>2.2713</td>\n",
              "      <td>2.3589</td>\n",
              "      <td>2.4452</td>\n",
              "      <td>2.5441</td>\n",
              "      <td>2.6488</td>\n",
              "      <td>2.7551</td>\n",
              "      <td>2.8654</td>\n",
              "      <td>2.9786</td>\n",
              "      <td>3.0950</td>\n",
              "      <td>3.2222</td>\n",
              "      <td>3.3495</td>\n",
              "      <td>3.4828</td>\n",
              "      <td>3.6190</td>\n",
              "      <td>3.7645</td>\n",
              "      <td>3.9110</td>\n",
              "      <td>4.0661</td>\n",
              "      <td>4.2228</td>\n",
              "      <td>4.3842</td>\n",
              "      <td>4.5536</td>\n",
              "      <td>4.7354</td>\n",
              "      <td>4.9245</td>\n",
              "      <td>5.1290</td>\n",
              "      <td>5.3368</td>\n",
              "      <td>5.5506</td>\n",
              "      <td>5.7663</td>\n",
              "      <td>5.9912</td>\n",
              "      <td>6.2383</td>\n",
              "      <td>6.4886</td>\n",
              "      <td>6.7536</td>\n",
              "      <td>7.0214</td>\n",
              "      <td>7.2985</td>\n",
              "      <td>7.5900</td>\n",
              "      <td>7.8924</td>\n",
              "      <td>8.2091</td>\n",
              "      <td>8.5372</td>\n",
              "      <td>8.8726</td>\n",
              "      <td>9.2340</td>\n",
              "      <td>9.5981</td>\n",
              "      <td>9.9738</td>\n",
              "      <td>10.3759</td>\n",
              "      <td>10.7946</td>\n",
              "      <td>11.2277</td>\n",
              "      <td>11.6797</td>\n",
              "      <td>12.1550</td>\n",
              "      <td>12.6426</td>\n",
              "      <td>13.1452</td>\n",
              "      <td>13.6574</td>\n",
              "      <td>14.1984</td>\n",
              "      <td>14.7587</td>\n",
              "      <td>15.3445</td>\n",
              "      <td>15.9521</td>\n",
              "      <td>16.5820</td>\n",
              "      <td>17.2576</td>\n",
              "      <td>17.9508</td>\n",
              "      <td>18.6662</td>\n",
              "      <td>19.4014</td>\n",
              "      <td>20.1777</td>\n",
              "      <td>20.9775</td>\n",
              "      <td>21.8168</td>\n",
              "      <td>22.6748</td>\n",
              "      <td>23.5930</td>\n",
              "      <td>24.5287</td>\n",
              "      <td>25.4854</td>\n",
              "      <td>26.4852</td>\n",
              "      <td>27.5310</td>\n",
              "      <td>28.6300</td>\n",
              "      <td>29.7644</td>\n",
              "      <td>30.9674</td>\n",
              "      <td>32.2145</td>\n",
              "      <td>33.5152</td>\n",
              "      <td>34.8518</td>\n",
              "      <td>36.2373</td>\n",
              "      <td>37.7056</td>\n",
              "      <td>39.1959</td>\n",
              "      <td>40.7623</td>\n",
              "      <td>42.3807</td>\n",
              "      <td>44.0614</td>\n",
              "      <td>45.8256</td>\n",
              "      <td>47.6270</td>\n",
              "      <td>49.5347</td>\n",
              "      <td>51.4817</td>\n",
              "      <td>53.5134</td>\n",
              "      <td>55.6344</td>\n",
              "      <td>57.8674</td>\n",
              "      <td>60.1609</td>\n",
              "      <td>62.5709</td>\n",
              "      <td>65.0388</td>\n",
              "      <td>67.6368</td>\n",
              "      <td>70.3264</td>\n",
              "      <td>73.1444</td>\n",
              "      <td>76.0309</td>\n",
              "      <td>79.0399</td>\n",
              "      <td>82.1584</td>\n",
              "      <td>85.4337</td>\n",
              "      <td>88.8637</td>\n",
              "      <td>92.4021</td>\n",
              "      <td>96.0793</td>\n",
              "      <td>99.9119</td>\n",
              "      <td>103.8850</td>\n",
              "      <td>108.0034</td>\n",
              "      <td>112.2873</td>\n",
              "      <td>116.7164</td>\n",
              "      <td>121.3310</td>\n",
              "      <td>126.1513</td>\n",
              "      <td>131.1905</td>\n",
              "      <td>136.4397</td>\n",
              "      <td>141.8527</td>\n",
              "      <td>147.5180</td>\n",
              "      <td>153.4240</td>\n",
              "      <td>159.5238</td>\n",
              "      <td>165.8513</td>\n",
              "      <td>172.4337</td>\n",
              "      <td>179.2919</td>\n",
              "      <td>186.3875</td>\n",
              "      <td>193.7959</td>\n",
              "      <td>201.5176</td>\n",
              "      <td>209.5270</td>\n",
              "      <td>217.9279</td>\n",
              "      <td>226.5639</td>\n",
              "      <td>235.5528</td>\n",
              "      <td>244.8941</td>\n",
              "      <td>254.6386</td>\n",
              "      <td>264.7586</td>\n",
              "      <td>275.2419</td>\n",
              "      <td>286.2302</td>\n",
              "      <td>297.6602</td>\n",
              "      <td>309.5589</td>\n",
              "      <td>321.8395</td>\n",
              "      <td>334.6402</td>\n",
              "      <td>347.9112</td>\n",
              "      <td>361.7183</td>\n",
              "      <td>376.1171</td>\n",
              "      <td>391.0799</td>\n",
              "      <td>406.6445</td>\n",
              "      <td>422.8512</td>\n",
              "      <td>439.6357</td>\n",
              "      <td>457.1283</td>\n",
              "      <td>475.3498</td>\n",
              "      <td>494.2778</td>\n",
              "      <td>513.9555</td>\n",
              "      <td>534.3989</td>\n",
              "      <td>555.6154</td>\n",
              "      <td>577.7726</td>\n",
              "      <td>600.7544</td>\n",
              "      <td>624.6883</td>\n",
              "      <td>649.5742</td>\n",
              "      <td>675.3084</td>\n",
              "      <td>702.1450</td>\n",
              "      <td>729.9556</td>\n",
              "      <td>758.9642</td>\n",
              "      <td>789.1470</td>\n",
              "      <td>820.4414</td>\n",
              "      <td>853.0576</td>\n",
              "      <td>887.0502</td>\n",
              "      <td>922.3957</td>\n",
              "      <td>959.0653</td>\n",
              "      <td>997.2433</td>\n",
              "      <td>1036.9677</td>\n",
              "      <td>1078.1885</td>\n",
              "      <td>1121.0386</td>\n",
              "      <td>1165.6091</td>\n",
              "      <td>1211.7717</td>\n",
              "      <td>1259.9643</td>\n",
              "      <td>1310.0832</td>\n",
              "      <td>1362.2420</td>\n",
              "      <td>1416.3672</td>\n",
              "      <td>1472.7337</td>\n",
              "      <td>1531.2680</td>\n",
              "      <td>1592.1056</td>\n",
              "      <td>1655.3008</td>\n",
              "      <td>1721.0734</td>\n",
              "      <td>1789.4930</td>\n",
              "      <td>1860.5721</td>\n",
              "      <td>1934.5463</td>\n",
              "      <td>2011.3956</td>\n",
              "      <td>2091.5227</td>\n",
              "      <td>2174.6608</td>\n",
              "      <td>2261.1735</td>\n",
              "      <td>2351.1060</td>\n",
              "      <td>2444.6576</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 10</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0331</td>\n",
              "      <td>1.0739</td>\n",
              "      <td>1.1132</td>\n",
              "      <td>1.1544</td>\n",
              "      <td>1.1948</td>\n",
              "      <td>1.2419</td>\n",
              "      <td>1.2898</td>\n",
              "      <td>1.3366</td>\n",
              "      <td>1.3857</td>\n",
              "      <td>1.4378</td>\n",
              "      <td>1.4883</td>\n",
              "      <td>1.5425</td>\n",
              "      <td>1.5999</td>\n",
              "      <td>1.6569</td>\n",
              "      <td>1.7179</td>\n",
              "      <td>1.7815</td>\n",
              "      <td>1.8423</td>\n",
              "      <td>1.9101</td>\n",
              "      <td>1.9808</td>\n",
              "      <td>2.0542</td>\n",
              "      <td>2.1284</td>\n",
              "      <td>2.2073</td>\n",
              "      <td>2.2894</td>\n",
              "      <td>2.3679</td>\n",
              "      <td>2.4543</td>\n",
              "      <td>2.5443</td>\n",
              "      <td>2.6342</td>\n",
              "      <td>2.7346</td>\n",
              "      <td>2.8407</td>\n",
              "      <td>2.9453</td>\n",
              "      <td>3.0539</td>\n",
              "      <td>3.1650</td>\n",
              "      <td>3.2808</td>\n",
              "      <td>3.3984</td>\n",
              "      <td>3.5212</td>\n",
              "      <td>3.6451</td>\n",
              "      <td>3.7778</td>\n",
              "      <td>3.9159</td>\n",
              "      <td>4.0539</td>\n",
              "      <td>4.1994</td>\n",
              "      <td>4.3585</td>\n",
              "      <td>4.5215</td>\n",
              "      <td>4.6902</td>\n",
              "      <td>4.8560</td>\n",
              "      <td>5.0389</td>\n",
              "      <td>5.2281</td>\n",
              "      <td>5.4164</td>\n",
              "      <td>5.6156</td>\n",
              "      <td>5.8287</td>\n",
              "      <td>6.0485</td>\n",
              "      <td>6.2595</td>\n",
              "      <td>6.4901</td>\n",
              "      <td>6.7281</td>\n",
              "      <td>6.9741</td>\n",
              "      <td>7.2288</td>\n",
              "      <td>7.4979</td>\n",
              "      <td>7.7609</td>\n",
              "      <td>8.0505</td>\n",
              "      <td>8.3439</td>\n",
              "      <td>8.6407</td>\n",
              "      <td>8.9584</td>\n",
              "      <td>9.2782</td>\n",
              "      <td>9.6247</td>\n",
              "      <td>9.9657</td>\n",
              "      <td>10.3335</td>\n",
              "      <td>10.7098</td>\n",
              "      <td>11.0973</td>\n",
              "      <td>11.5038</td>\n",
              "      <td>11.9173</td>\n",
              "      <td>12.3590</td>\n",
              "      <td>12.8084</td>\n",
              "      <td>13.2739</td>\n",
              "      <td>13.7563</td>\n",
              "      <td>14.2593</td>\n",
              "      <td>14.7842</td>\n",
              "      <td>15.3441</td>\n",
              "      <td>15.9090</td>\n",
              "      <td>16.4905</td>\n",
              "      <td>17.0939</td>\n",
              "      <td>17.7134</td>\n",
              "      <td>18.3533</td>\n",
              "      <td>19.0258</td>\n",
              "      <td>19.7140</td>\n",
              "      <td>20.4362</td>\n",
              "      <td>21.1864</td>\n",
              "      <td>21.9546</td>\n",
              "      <td>22.7622</td>\n",
              "      <td>23.6038</td>\n",
              "      <td>24.4757</td>\n",
              "      <td>25.3710</td>\n",
              "      <td>26.3044</td>\n",
              "      <td>27.2664</td>\n",
              "      <td>28.2525</td>\n",
              "      <td>29.2778</td>\n",
              "      <td>30.3714</td>\n",
              "      <td>31.4635</td>\n",
              "      <td>32.6122</td>\n",
              "      <td>33.8049</td>\n",
              "      <td>35.0272</td>\n",
              "      <td>36.3081</td>\n",
              "      <td>37.6301</td>\n",
              "      <td>39.0120</td>\n",
              "      <td>40.4484</td>\n",
              "      <td>41.9367</td>\n",
              "      <td>43.4607</td>\n",
              "      <td>45.0427</td>\n",
              "      <td>46.6954</td>\n",
              "      <td>48.3940</td>\n",
              "      <td>50.1586</td>\n",
              "      <td>51.9845</td>\n",
              "      <td>53.8642</td>\n",
              "      <td>55.8192</td>\n",
              "      <td>57.8793</td>\n",
              "      <td>60.0206</td>\n",
              "      <td>62.2152</td>\n",
              "      <td>64.4879</td>\n",
              "      <td>66.8456</td>\n",
              "      <td>69.3068</td>\n",
              "      <td>71.8145</td>\n",
              "      <td>74.4661</td>\n",
              "      <td>77.2062</td>\n",
              "      <td>80.0165</td>\n",
              "      <td>82.9149</td>\n",
              "      <td>85.9283</td>\n",
              "      <td>89.0450</td>\n",
              "      <td>92.3212</td>\n",
              "      <td>95.6775</td>\n",
              "      <td>99.1909</td>\n",
              "      <td>102.8361</td>\n",
              "      <td>106.5746</td>\n",
              "      <td>110.4826</td>\n",
              "      <td>114.5039</td>\n",
              "      <td>118.6769</td>\n",
              "      <td>123.0007</td>\n",
              "      <td>127.4850</td>\n",
              "      <td>132.1739</td>\n",
              "      <td>136.9623</td>\n",
              "      <td>141.9613</td>\n",
              "      <td>147.1678</td>\n",
              "      <td>152.5407</td>\n",
              "      <td>158.0839</td>\n",
              "      <td>163.8632</td>\n",
              "      <td>169.8676</td>\n",
              "      <td>176.1320</td>\n",
              "      <td>182.6034</td>\n",
              "      <td>189.2578</td>\n",
              "      <td>196.1525</td>\n",
              "      <td>203.3326</td>\n",
              "      <td>210.7429</td>\n",
              "      <td>218.4694</td>\n",
              "      <td>226.4307</td>\n",
              "      <td>234.7038</td>\n",
              "      <td>243.2379</td>\n",
              "      <td>252.1245</td>\n",
              "      <td>261.3500</td>\n",
              "      <td>270.9146</td>\n",
              "      <td>280.7623</td>\n",
              "      <td>291.0026</td>\n",
              "      <td>301.6947</td>\n",
              "      <td>312.7411</td>\n",
              "      <td>324.1355</td>\n",
              "      <td>335.9702</td>\n",
              "      <td>348.2757</td>\n",
              "      <td>361.0029</td>\n",
              "      <td>374.2248</td>\n",
              "      <td>387.8657</td>\n",
              "      <td>402.0090</td>\n",
              "      <td>416.7136</td>\n",
              "      <td>432.0076</td>\n",
              "      <td>447.7581</td>\n",
              "      <td>464.1031</td>\n",
              "      <td>481.0560</td>\n",
              "      <td>498.6427</td>\n",
              "      <td>516.8799</td>\n",
              "      <td>535.7941</td>\n",
              "      <td>555.2820</td>\n",
              "      <td>575.5989</td>\n",
              "      <td>596.6374</td>\n",
              "      <td>618.4831</td>\n",
              "      <td>641.0741</td>\n",
              "      <td>664.5865</td>\n",
              "      <td>688.8813</td>\n",
              "      <td>714.0129</td>\n",
              "      <td>740.1549</td>\n",
              "      <td>767.1071</td>\n",
              "      <td>795.1301</td>\n",
              "      <td>824.1914</td>\n",
              "      <td>854.3472</td>\n",
              "      <td>885.5031</td>\n",
              "      <td>917.7905</td>\n",
              "      <td>951.3558</td>\n",
              "      <td>986.2934</td>\n",
              "      <td>1022.3670</td>\n",
              "      <td>1059.7733</td>\n",
              "      <td>1098.5386</td>\n",
              "      <td>1138.6254</td>\n",
              "      <td>1180.2679</td>\n",
              "      <td>1223.3407</td>\n",
              "      <td>1268.1163</td>\n",
              "      <td>1314.3104</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 30</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0301</td>\n",
              "      <td>1.0645</td>\n",
              "      <td>1.1012</td>\n",
              "      <td>1.1401</td>\n",
              "      <td>1.1814</td>\n",
              "      <td>1.2232</td>\n",
              "      <td>1.2684</td>\n",
              "      <td>1.3154</td>\n",
              "      <td>1.3578</td>\n",
              "      <td>1.4071</td>\n",
              "      <td>1.4583</td>\n",
              "      <td>1.5079</td>\n",
              "      <td>1.5656</td>\n",
              "      <td>1.6216</td>\n",
              "      <td>1.6768</td>\n",
              "      <td>1.7401</td>\n",
              "      <td>1.8017</td>\n",
              "      <td>1.8694</td>\n",
              "      <td>1.9374</td>\n",
              "      <td>2.0029</td>\n",
              "      <td>2.0730</td>\n",
              "      <td>2.1478</td>\n",
              "      <td>2.2198</td>\n",
              "      <td>2.2977</td>\n",
              "      <td>2.3843</td>\n",
              "      <td>2.4689</td>\n",
              "      <td>2.5538</td>\n",
              "      <td>2.6506</td>\n",
              "      <td>2.7409</td>\n",
              "      <td>2.8396</td>\n",
              "      <td>2.9383</td>\n",
              "      <td>3.0470</td>\n",
              "      <td>3.1613</td>\n",
              "      <td>3.2735</td>\n",
              "      <td>3.3878</td>\n",
              "      <td>3.5072</td>\n",
              "      <td>3.6318</td>\n",
              "      <td>3.7600</td>\n",
              "      <td>3.8938</td>\n",
              "      <td>4.0367</td>\n",
              "      <td>4.1808</td>\n",
              "      <td>4.3251</td>\n",
              "      <td>4.4781</td>\n",
              "      <td>4.6356</td>\n",
              "      <td>4.8071</td>\n",
              "      <td>4.9720</td>\n",
              "      <td>5.1520</td>\n",
              "      <td>5.3385</td>\n",
              "      <td>5.5313</td>\n",
              "      <td>5.7361</td>\n",
              "      <td>5.9378</td>\n",
              "      <td>6.1512</td>\n",
              "      <td>6.3774</td>\n",
              "      <td>6.6054</td>\n",
              "      <td>6.8279</td>\n",
              "      <td>7.0738</td>\n",
              "      <td>7.3216</td>\n",
              "      <td>7.5768</td>\n",
              "      <td>7.8485</td>\n",
              "      <td>8.1329</td>\n",
              "      <td>8.4271</td>\n",
              "      <td>8.7325</td>\n",
              "      <td>9.0423</td>\n",
              "      <td>9.3656</td>\n",
              "      <td>9.7026</td>\n",
              "      <td>10.0437</td>\n",
              "      <td>10.4045</td>\n",
              "      <td>10.7811</td>\n",
              "      <td>11.1701</td>\n",
              "      <td>11.5588</td>\n",
              "      <td>11.9683</td>\n",
              "      <td>12.4015</td>\n",
              "      <td>12.8443</td>\n",
              "      <td>13.3019</td>\n",
              "      <td>13.7691</td>\n",
              "      <td>14.2521</td>\n",
              "      <td>14.7616</td>\n",
              "      <td>15.2843</td>\n",
              "      <td>15.8169</td>\n",
              "      <td>16.3893</td>\n",
              "      <td>16.9756</td>\n",
              "      <td>17.5943</td>\n",
              "      <td>18.2310</td>\n",
              "      <td>18.8805</td>\n",
              "      <td>19.5607</td>\n",
              "      <td>20.2700</td>\n",
              "      <td>20.9998</td>\n",
              "      <td>21.7522</td>\n",
              "      <td>22.5283</td>\n",
              "      <td>23.3197</td>\n",
              "      <td>24.1498</td>\n",
              "      <td>24.9977</td>\n",
              "      <td>25.8864</td>\n",
              "      <td>26.8113</td>\n",
              "      <td>27.7450</td>\n",
              "      <td>28.7353</td>\n",
              "      <td>29.7746</td>\n",
              "      <td>30.8424</td>\n",
              "      <td>31.9599</td>\n",
              "      <td>33.1093</td>\n",
              "      <td>34.2858</td>\n",
              "      <td>35.5145</td>\n",
              "      <td>36.7914</td>\n",
              "      <td>38.0901</td>\n",
              "      <td>39.4486</td>\n",
              "      <td>40.8704</td>\n",
              "      <td>42.3334</td>\n",
              "      <td>43.8228</td>\n",
              "      <td>45.3882</td>\n",
              "      <td>47.0057</td>\n",
              "      <td>48.6868</td>\n",
              "      <td>50.4174</td>\n",
              "      <td>52.2134</td>\n",
              "      <td>54.0605</td>\n",
              "      <td>56.0018</td>\n",
              "      <td>58.0040</td>\n",
              "      <td>60.0796</td>\n",
              "      <td>62.2090</td>\n",
              "      <td>64.4225</td>\n",
              "      <td>66.7675</td>\n",
              "      <td>69.1586</td>\n",
              "      <td>71.6162</td>\n",
              "      <td>74.1589</td>\n",
              "      <td>76.7726</td>\n",
              "      <td>79.5246</td>\n",
              "      <td>82.3653</td>\n",
              "      <td>85.2933</td>\n",
              "      <td>88.3339</td>\n",
              "      <td>91.4877</td>\n",
              "      <td>94.7331</td>\n",
              "      <td>98.1139</td>\n",
              "      <td>101.5970</td>\n",
              "      <td>105.2246</td>\n",
              "      <td>108.9991</td>\n",
              "      <td>112.9167</td>\n",
              "      <td>116.9413</td>\n",
              "      <td>121.1280</td>\n",
              "      <td>125.4803</td>\n",
              "      <td>129.9498</td>\n",
              "      <td>134.6146</td>\n",
              "      <td>139.3891</td>\n",
              "      <td>144.3560</td>\n",
              "      <td>149.5286</td>\n",
              "      <td>154.8533</td>\n",
              "      <td>160.3129</td>\n",
              "      <td>165.9760</td>\n",
              "      <td>171.9194</td>\n",
              "      <td>178.0540</td>\n",
              "      <td>184.4013</td>\n",
              "      <td>190.9362</td>\n",
              "      <td>197.7818</td>\n",
              "      <td>204.8463</td>\n",
              "      <td>212.1944</td>\n",
              "      <td>219.7989</td>\n",
              "      <td>227.6262</td>\n",
              "      <td>235.8096</td>\n",
              "      <td>244.2422</td>\n",
              "      <td>252.9479</td>\n",
              "      <td>261.9334</td>\n",
              "      <td>271.3196</td>\n",
              "      <td>281.0343</td>\n",
              "      <td>291.0662</td>\n",
              "      <td>301.4369</td>\n",
              "      <td>312.1451</td>\n",
              "      <td>323.2356</td>\n",
              "      <td>334.7042</td>\n",
              "      <td>346.6703</td>\n",
              "      <td>359.0300</td>\n",
              "      <td>371.8552</td>\n",
              "      <td>385.0784</td>\n",
              "      <td>398.8727</td>\n",
              "      <td>413.0940</td>\n",
              "      <td>427.9119</td>\n",
              "      <td>443.1954</td>\n",
              "      <td>459.0447</td>\n",
              "      <td>475.4861</td>\n",
              "      <td>492.4321</td>\n",
              "      <td>509.9799</td>\n",
              "      <td>528.1921</td>\n",
              "      <td>547.0392</td>\n",
              "      <td>566.5281</td>\n",
              "      <td>586.7386</td>\n",
              "      <td>607.6685</td>\n",
              "      <td>629.3131</td>\n",
              "      <td>651.7484</td>\n",
              "      <td>674.9822</td>\n",
              "      <td>698.9787</td>\n",
              "      <td>724.0206</td>\n",
              "      <td>749.9023</td>\n",
              "      <td>776.5592</td>\n",
              "      <td>804.2577</td>\n",
              "      <td>832.9161</td>\n",
              "      <td>862.7712</td>\n",
              "      <td>893.5882</td>\n",
              "      <td>925.5358</td>\n",
              "      <td>958.5135</td>\n",
              "      <td>992.6846</td>\n",
              "      <td>1028.1106</td>\n",
              "      <td>1064.8524</td>\n",
              "      <td>1102.8501</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 100</th>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0335</td>\n",
              "      <td>1.0735</td>\n",
              "      <td>1.1148</td>\n",
              "      <td>1.1530</td>\n",
              "      <td>1.1948</td>\n",
              "      <td>1.2319</td>\n",
              "      <td>1.2766</td>\n",
              "      <td>1.3216</td>\n",
              "      <td>1.3684</td>\n",
              "      <td>1.4185</td>\n",
              "      <td>1.4698</td>\n",
              "      <td>1.5184</td>\n",
              "      <td>1.5688</td>\n",
              "      <td>1.6229</td>\n",
              "      <td>1.6800</td>\n",
              "      <td>1.7372</td>\n",
              "      <td>1.7965</td>\n",
              "      <td>1.8642</td>\n",
              "      <td>1.9330</td>\n",
              "      <td>2.0031</td>\n",
              "      <td>2.0778</td>\n",
              "      <td>2.1559</td>\n",
              "      <td>2.2319</td>\n",
              "      <td>2.3079</td>\n",
              "      <td>2.3900</td>\n",
              "      <td>2.4734</td>\n",
              "      <td>2.5576</td>\n",
              "      <td>2.6515</td>\n",
              "      <td>2.7450</td>\n",
              "      <td>2.8384</td>\n",
              "      <td>2.9375</td>\n",
              "      <td>3.0448</td>\n",
              "      <td>3.1470</td>\n",
              "      <td>3.2566</td>\n",
              "      <td>3.3702</td>\n",
              "      <td>3.4898</td>\n",
              "      <td>3.6098</td>\n",
              "      <td>3.7373</td>\n",
              "      <td>3.8788</td>\n",
              "      <td>4.0162</td>\n",
              "      <td>4.1592</td>\n",
              "      <td>4.3060</td>\n",
              "      <td>4.4576</td>\n",
              "      <td>4.6188</td>\n",
              "      <td>4.7812</td>\n",
              "      <td>4.9560</td>\n",
              "      <td>5.1331</td>\n",
              "      <td>5.3121</td>\n",
              "      <td>5.4985</td>\n",
              "      <td>5.6849</td>\n",
              "      <td>5.8897</td>\n",
              "      <td>6.0872</td>\n",
              "      <td>6.2999</td>\n",
              "      <td>6.5246</td>\n",
              "      <td>6.7662</td>\n",
              "      <td>7.0035</td>\n",
              "      <td>7.2457</td>\n",
              "      <td>7.4972</td>\n",
              "      <td>7.7702</td>\n",
              "      <td>8.0519</td>\n",
              "      <td>8.3434</td>\n",
              "      <td>8.6345</td>\n",
              "      <td>8.9485</td>\n",
              "      <td>9.2656</td>\n",
              "      <td>9.5989</td>\n",
              "      <td>9.9342</td>\n",
              "      <td>10.2847</td>\n",
              "      <td>10.6506</td>\n",
              "      <td>11.0264</td>\n",
              "      <td>11.4055</td>\n",
              "      <td>11.8068</td>\n",
              "      <td>12.2079</td>\n",
              "      <td>12.6404</td>\n",
              "      <td>13.0927</td>\n",
              "      <td>13.5637</td>\n",
              "      <td>14.0418</td>\n",
              "      <td>14.5322</td>\n",
              "      <td>15.0454</td>\n",
              "      <td>15.5821</td>\n",
              "      <td>16.1404</td>\n",
              "      <td>16.7094</td>\n",
              "      <td>17.3166</td>\n",
              "      <td>17.9258</td>\n",
              "      <td>18.5742</td>\n",
              "      <td>19.2380</td>\n",
              "      <td>19.9153</td>\n",
              "      <td>20.6102</td>\n",
              "      <td>21.3489</td>\n",
              "      <td>22.0931</td>\n",
              "      <td>22.8665</td>\n",
              "      <td>23.6644</td>\n",
              "      <td>24.4937</td>\n",
              "      <td>25.3599</td>\n",
              "      <td>26.2503</td>\n",
              "      <td>27.1852</td>\n",
              "      <td>28.1538</td>\n",
              "      <td>29.1535</td>\n",
              "      <td>30.1828</td>\n",
              "      <td>31.2620</td>\n",
              "      <td>32.3766</td>\n",
              "      <td>33.5247</td>\n",
              "      <td>34.7310</td>\n",
              "      <td>35.9620</td>\n",
              "      <td>37.2401</td>\n",
              "      <td>38.5650</td>\n",
              "      <td>39.9253</td>\n",
              "      <td>41.3144</td>\n",
              "      <td>42.7854</td>\n",
              "      <td>44.2813</td>\n",
              "      <td>45.8288</td>\n",
              "      <td>47.4408</td>\n",
              "      <td>49.1381</td>\n",
              "      <td>50.8583</td>\n",
              "      <td>52.6426</td>\n",
              "      <td>54.5125</td>\n",
              "      <td>56.4303</td>\n",
              "      <td>58.4458</td>\n",
              "      <td>60.5057</td>\n",
              "      <td>62.6710</td>\n",
              "      <td>64.9053</td>\n",
              "      <td>67.2253</td>\n",
              "      <td>69.6348</td>\n",
              "      <td>72.0948</td>\n",
              "      <td>74.6672</td>\n",
              "      <td>77.3141</td>\n",
              "      <td>80.0424</td>\n",
              "      <td>82.8619</td>\n",
              "      <td>85.7540</td>\n",
              "      <td>88.7733</td>\n",
              "      <td>91.8961</td>\n",
              "      <td>95.1197</td>\n",
              "      <td>98.4807</td>\n",
              "      <td>101.9567</td>\n",
              "      <td>105.5503</td>\n",
              "      <td>109.2752</td>\n",
              "      <td>113.1568</td>\n",
              "      <td>117.1651</td>\n",
              "      <td>121.3287</td>\n",
              "      <td>125.6372</td>\n",
              "      <td>130.1030</td>\n",
              "      <td>134.7699</td>\n",
              "      <td>139.5832</td>\n",
              "      <td>144.5629</td>\n",
              "      <td>149.7108</td>\n",
              "      <td>154.9885</td>\n",
              "      <td>160.4411</td>\n",
              "      <td>166.0893</td>\n",
              "      <td>171.9288</td>\n",
              "      <td>177.9959</td>\n",
              "      <td>184.2020</td>\n",
              "      <td>190.7073</td>\n",
              "      <td>197.4359</td>\n",
              "      <td>204.4088</td>\n",
              "      <td>211.6448</td>\n",
              "      <td>219.1281</td>\n",
              "      <td>226.9452</td>\n",
              "      <td>234.9554</td>\n",
              "      <td>243.3080</td>\n",
              "      <td>251.9760</td>\n",
              "      <td>260.9117</td>\n",
              "      <td>270.1926</td>\n",
              "      <td>279.8261</td>\n",
              "      <td>289.7973</td>\n",
              "      <td>300.0054</td>\n",
              "      <td>310.6633</td>\n",
              "      <td>321.6493</td>\n",
              "      <td>332.9221</td>\n",
              "      <td>344.6758</td>\n",
              "      <td>356.7450</td>\n",
              "      <td>369.3355</td>\n",
              "      <td>382.3725</td>\n",
              "      <td>395.8798</td>\n",
              "      <td>409.8505</td>\n",
              "      <td>424.3261</td>\n",
              "      <td>439.3620</td>\n",
              "      <td>454.9429</td>\n",
              "      <td>471.1090</td>\n",
              "      <td>487.8066</td>\n",
              "      <td>505.1026</td>\n",
              "      <td>523.1349</td>\n",
              "      <td>541.7202</td>\n",
              "      <td>561.0535</td>\n",
              "      <td>580.9741</td>\n",
              "      <td>601.5440</td>\n",
              "      <td>622.7662</td>\n",
              "      <td>644.7324</td>\n",
              "      <td>667.4274</td>\n",
              "      <td>691.0001</td>\n",
              "      <td>715.3629</td>\n",
              "      <td>740.5636</td>\n",
              "      <td>766.6447</td>\n",
              "      <td>793.6738</td>\n",
              "      <td>821.6783</td>\n",
              "      <td>850.7664</td>\n",
              "      <td>880.8608</td>\n",
              "      <td>912.1383</td>\n",
              "      <td>944.4953</td>\n",
              "      <td>977.9433</td>\n",
              "      <td>1012.7850</td>\n",
              "      <td>1048.7237</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "id": "1PJB4suXDI2Z",
        "outputId": "b8d9446e-ba96-4cc3-f2a6-f3235ee2d494"
      },
      "source": [
        "# plot the average population size functions from the simulation\n",
        "(rows,cols) = avgPopSizeDF.shape\n",
        "\n",
        "plt.figure(figsize=(9,6))\n",
        "plt.grid(color='0.7')\n",
        "for r in range(rows): \n",
        "  yVals = avgPopSizeDF.iloc[r,:]\n",
        "  plt.plot(timeVals, yVals)\n",
        "\n",
        "plt.xlim(0,10)\n",
        "plt.ylim(0, 1000)\n",
        "\n",
        "plt.title(\"Average Population Size for Gamma Splitting\")\n",
        "plt.xlabel(\"time\")\n",
        "plt.ylabel(\"population size\")\n",
        "plt.legend([\"α = \"+str(int(a)) for a in alphaVals]);"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 648x432 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "znjkXD0nRctR"
      },
      "source": [
        "We now fit curves to the average population size data above. In the next code cell, we compute linear regressions on the log of the average population sizes over time."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 235
        },
        "id": "Rz19JBf_DTzQ",
        "outputId": "8a4c41bf-9103-4ca1-98df-2d25225724c7"
      },
      "source": [
        "# compute exponential regression\n",
        "(rows,cols) = avgPopSizeDF.shape\n",
        "yvals = [math.log(y) for y in range(1,cols)]\n",
        "\n",
        "rowList = []\n",
        "for r in range(rows):\n",
        "  slope, intercept, rval, pval, stderr = stats.linregress(timeVals, np.log(avgPopSizeDF.iloc[r,:]))\n",
        "  rowList.append([slope, math.exp(slope), intercept, math.exp(intercept), rval])\n",
        "\n",
        "# display the regression data in a table\n",
        "alphaLabels = [\"α = \"+str(int(a)) for a in alphaVals]\n",
        "colLabels = [\"slope\",\"exp(slope)\",\"intercept\",\"exp(intercept)\",\"correlation\"]\n",
        "regDF = pd.DataFrame(rowList, columns=colLabels, index=alphaLabels)\n",
        "regDF"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "            slope  exp(slope)  intercept  exp(intercept)  correlation\n",
              "α = 1    0.999632    2.717281  -0.010873        0.989186     0.999999\n",
              "α = 2    0.828822    2.290618   0.001275        1.001276     1.000000\n",
              "α = 3    0.780372    2.182284  -0.000902        0.999098     1.000000\n",
              "α = 10   0.717940    2.050206   0.002030        1.002032     1.000000\n",
              "α = 30   0.701343    2.016459  -0.007551        0.992477     1.000000\n",
              "α = 100  0.695541    2.004794  -0.000277        0.999723     1.000000"
            ],
            "text/html": [
              "<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>slope</th>\n",
              "      <th>exp(slope)</th>\n",
              "      <th>intercept</th>\n",
              "      <th>exp(intercept)</th>\n",
              "      <th>correlation</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>α = 1</th>\n",
              "      <td>0.999632</td>\n",
              "      <td>2.717281</td>\n",
              "      <td>-0.010873</td>\n",
              "      <td>0.989186</td>\n",
              "      <td>0.999999</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 2</th>\n",
              "      <td>0.828822</td>\n",
              "      <td>2.290618</td>\n",
              "      <td>0.001275</td>\n",
              "      <td>1.001276</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 3</th>\n",
              "      <td>0.780372</td>\n",
              "      <td>2.182284</td>\n",
              "      <td>-0.000902</td>\n",
              "      <td>0.999098</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 10</th>\n",
              "      <td>0.717940</td>\n",
              "      <td>2.050206</td>\n",
              "      <td>0.002030</td>\n",
              "      <td>1.002032</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 30</th>\n",
              "      <td>0.701343</td>\n",
              "      <td>2.016459</td>\n",
              "      <td>-0.007551</td>\n",
              "      <td>0.992477</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>α = 100</th>\n",
              "      <td>0.695541</td>\n",
              "      <td>2.004794</td>\n",
              "      <td>-0.000277</td>\n",
              "      <td>0.999723</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "owFtwFHwYvlR"
      },
      "source": [
        "In the next code cell, we use `scipy.optimize.curve_fit` to fit a function $f(t) = r^t$ to the average population sizes over time. This produces regression functions like those in Table 1 in the paper."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jNAW7cZvXrYy",
        "outputId": "dca8d423-f460-4bb2-e2ac-f21326a8faa7"
      },
      "source": [
        "# exponential regression f(t) = 1 r^t\n",
        "def f_rt(t, r):\n",
        "  return r**t\n",
        "\n",
        "(rows,cols) = avgPopSizeDF.shape\n",
        "rvals = [0]*6\n",
        "for r in range(rows):\n",
        "  popt, pcov = curve_fit(f_rt, timeVals, avgPopSizeDF.iloc[r,:])\n",
        "  rvals[r] = popt[0]\n",
        "  print(\"r = \",popt[0])\n",
        "  print(\"variance of estimate:\", pcov[0,0])"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "r =  2.714535051152477\n",
            "variance of estimate: 1.7729954517697125e-10\n",
            "r =  2.2906405508944667\n",
            "variance of estimate: 3.040498844771594e-11\n",
            "r =  2.181879965310666\n",
            "variance of estimate: 1.9406024775176035e-11\n",
            "r =  2.0505840831477937\n",
            "variance of estimate: 9.316995222451666e-12\n",
            "r =  2.014788890198907\n",
            "variance of estimate: 6.614218590863755e-11\n",
            "r =  2.004743228515968\n",
            "variance of estimate: 3.000973889998387e-11\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jl1BEYBj_lKO"
      },
      "source": [
        "## Asymptotics\n",
        "\n",
        "The following code simulates the ratio $Z(t)/b^2$, where $Z(t)$ is the aggregate population growth function and $b$ is the aggregate growth factor. Computing this ratio for a large number of simulations, we obtain a figure like Figure 4 in the paper."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oQJLgWriHQLd"
      },
      "source": [
        "# simulate population growth until a specified stopping time\n",
        "# parameters:\n",
        "#   stopTime: time at which the simulation stops\n",
        "#   alpha: underlying splitting distribution is Gamma(alpha, 1/alpha)\n",
        "# returns: population size at the stopping time\n",
        "\n",
        "def simulateSizeAtTime(stopTime, alpha):\n",
        "  # priority queue for times at which cells split\n",
        "  splits = queue.PriorityQueue()\n",
        "\n",
        "  #population starts with 1 bacterium at time 0\n",
        "  time = 0\n",
        "  size = 1\n",
        "\n",
        "  # generate the splitting time of the first cell\n",
        "  if alpha == 1:\n",
        "    splits.put(random.expovariate(1))  # since exponential distribution is memoryless\n",
        "  else:\n",
        "    startingDistribution = simulatePopulationAtTime(alpha, 8)   # do the pre-simulation, then\n",
        "    splits.put( random.choice(startingDistribution) )           # choose a random bacterium\n",
        "    \n",
        "  # simulate bacteria splitting until stopTime is reached\n",
        "  while time < stopTime:\n",
        "    time = splits.get()\t # get the smallest time in the splits queue -- time that population reaches size\n",
        "    size = size + 1      # this is the new population size\n",
        "      \n",
        "    # the current cell has split, creating two new splitting times in the queue,\n",
        "    #  determined by the underlying distribution\n",
        "    r1 = random.gammavariate(alpha, 1/alpha)\n",
        "    r2 = random.gammavariate(alpha, 1/alpha)\n",
        "    splits.put(time + r1)\n",
        "    splits.put(time + r2)\n",
        "\n",
        "  return size"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "smfM-O89H5Ou",
        "outputId": "dd349ee1-f722-4a8a-a27d-818f1390c1d0"
      },
      "source": [
        "# now simulate 10,000 populations with Gamma(3, 1/3) underlying splitting distribution\n",
        "finalSizes = np.array([simulateSizeAtTime(8,3) for _ in range(10000)])\n",
        "\n",
        "# aggregregate growth factor for Gamma(3, 1/3)\n",
        "b = 2.18095564\n",
        "\n",
        "ratios = finalSizes/(b**8)\n",
        "print(\"mean ratio is:\",np.mean(ratios))\n",
        "\n",
        "counts, bins, patches = plt.hist(ratios, range=(0,4.5), bins=36, edgecolor='black')"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "mean ratio is: 1.0070838641745457\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}