From ae741b4143bfc05005d7a110bf0d468c36252785 Mon Sep 17 00:00:00 2001 From: MatthieuGilson <matthieu.gilson@univ-amu.fr> Date: Wed, 5 Jul 2023 20:57:54 +0200 Subject: [PATCH] add notebooks --- DESU_corr_param_nonparam.ipynb | 82 ++ DESU_distributions.ipynb | 802 +++++++++++++++++ DESU_distributions_corrected.ipynb | 1353 ++++++++++++++++++++++++++++ 3 files changed, 2237 insertions(+) create mode 100644 DESU_corr_param_nonparam.ipynb create mode 100644 DESU_distributions.ipynb create mode 100644 DESU_distributions_corrected.ipynb diff --git a/DESU_corr_param_nonparam.ipynb b/DESU_corr_param_nonparam.ipynb new file mode 100644 index 0000000..2b1ca93 --- /dev/null +++ b/DESU_corr_param_nonparam.ipynb @@ -0,0 +1,82 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "910b76de-7f01-4548-be82-48845592ea79", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import scipy.stats as stt\n", + "\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import seaborn as sb\n", + "\n", + "sb.set_style('whitegrid')\n", + "sb.set(font_scale=1.5)" + ] + }, + { + "cell_type": "markdown", + "id": "90388ab5-77ae-4af4-90b4-79251f37a0d0", + "metadata": {}, + "source": [ + "We generate 2 time series with a linear relationship between them (via a common input).\n", + "\n", + "### EXERCICE\n", + "- Calculate the Pearson correlatrion between the time series (cd `stt.prearsonr`), which also provides you with a p-value for significance.\n", + "- Calculate surrogate time series by manipulating the temporal distribution of the time series.\n", + "- Make a non-parametric test by comparing the distribution of surrogate correlation values with the value obtained from the original time series." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "f1e1d19c-066c-4d71-963c-b702e2363f96", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# duration of time series\n", + "T = 100\n", + "\n", + "# generate two sets of normally distributed random variables (white noise)\n", + "x1 = stt.norm.rvs(size=T)\n", + "x2 = stt.norm.rvs(size=T)\n", + "\n", + "# add to create correlation between the two time series\n", + "x0 = stt.norm.rvs(size=T)\n", + "# desired level of correlation\n", + "c = 0.1\n", + "x1 = np.sqrt(1.0-c) * x1 + np.sqrt(c) * x0\n", + "x2 = np.sqrt(1.0-c) * x2 + np.sqrt(c) * x0" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/DESU_distributions.ipynb b/DESU_distributions.ipynb new file mode 100644 index 0000000..2130f23 --- /dev/null +++ b/DESU_distributions.ipynb @@ -0,0 +1,802 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "046cefd5-f821-4613-8660-b5e296eb5a88", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import scipy.stats as stt\n", + "import pandas as pd\n", + "\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import seaborn as sb\n", + "\n", + "sb.set_style('whitegrid')\n", + "sb.set(font_scale=1.5)\n", + "\n", + "# check help on package\n", + "#help(stt)" + ] + }, + { + "cell_type": "markdown", + "id": "ed78ded5-0cd8-4b61-9866-c3b804ffcf9b", + "metadata": {}, + "source": [ + "## Random Samples\n", + "\n", + "Let's first randomly generate samples from a given distribution (normal or Gaussian, centered in zero with unit variance), then calculate summary statistics on these samples." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "cf7ba0e0-4068-42e7-8b5a-a871e9629e87", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "#number of samples\n", + "n = 1000\n", + "\n", + "# generate random samples\n", + "samples = stt.norm.rvs(size=n)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "ac6fd30c-8c07-48fa-859b-02b8b6e7b11a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# variable range\n", + "vx = np.linspace(-3.0,3.0,50)\n", + "dx = np.diff(vx)[0]\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples, bins=vx)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx, stt.norm.pdf(x=vx)*n*dx)\n", + "\n", + "# show percentiles from samples, top and bottom 5%\n", + "if False:\n", + " top_lim = stt.scoreatpercentile(samples, 95.0)\n", + " bottom_lim = stt.scoreatpercentile(samples, 5.0)\n", + " l = max(stt.norm.pdf(x=vx)*n*dx)\n", + " plt.plot([top_lim]*2, [0,l], ls='--', c='gray')\n", + " plt.plot([bottom_lim]*2, [0,l], ls='--', c='gray')\n", + "\n", + "# show percentiles from samples, top and bottom 5%\n", + "if False:\n", + " top_lim_th = stt.norm.isf(0.05)\n", + " bottom_lim_th = stt.norm.isf(0.95)\n", + " l = max(stt.norm.pdf(x=vx)*n*dx)\n", + " plt.plot([top_lim_th]*2, [0,l], ls='--', c='k')\n", + " plt.plot([bottom_lim_th]*2, [0,l], ls='--', c='k')\n", + " \n", + "plt.tight_layout()\n", + "#plt.savefig('figs/ex_hist_norm_perc_th_n100000.png')" + ] + }, + { + "cell_type": "markdown", + "id": "1bfdb6a3-c880-41fa-9056-a2696ace2a9f", + "metadata": {}, + "source": [ + "With the cumulative density function" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "7c0a36c0-59a3-42ec-aec1-bb84e7d92bdc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(samples, bins=vx, cumulative=True)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx, stt.norm.cdf(x=vx)*n)\n", + "\n", + "# show percentiles, top and bottom 5%\n", + "top_lim = stt.norm.isf(0.05)\n", + "bottom_lim = stt.norm.isf(0.95)\n", + "plt.plot([top_lim]*2, [0,n], '--k')\n", + "plt.plot([bottom_lim]*2, [0,n], '--k')\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "id": "304a427a-c94b-4995-a24e-ff26c4f8b07f", + "metadata": {}, + "source": [ + "In this way, we can find boundaries for the probability of finding a random samples that follow the concerned distribution. This leads to the notion of statistical testing, which we will see in detail later." + ] + }, + { + "cell_type": "markdown", + "id": "b5be9b02-17d6-4407-aa71-53a31a6b224c", + "metadata": {}, + "source": [ + "## Summary statistics\n", + "\n", + "Let's now look at the summary statistics of the $n$ samples:\n", + "- mean: $\\mu = E[X] = \\frac{1}{n} \\sum_i x_i$\n", + "- variance: $\\sigma^2 = E[(X-\\mu)^2] \\simeq \\frac{1}{n-1} \\sum_i (x_i - \\mu)^2$\n", + "\n", + "Here $\\sigma$ is the standard deviation, whose square is the variance. Note that the denominator of the sample variance is $n-1$ and not $n$, to correct a bias.\n", + "\n", + "The skew and kurtosis measure deviations from normality:\n", + "- skew: $E[\\frac{(X-\\mu)^3}{\\sigma^3}] = \\frac{m_3}{\\sigma^3}$\n", + "- kurtosis: $E[\\frac{(X-\\mu)^4}{\\sigma^4}] = \\frac{m_4}{\\sigma^4}$\n", + "\n", + "They also correspond to standardized moments, including a normalization by $\\sigma$.\n", + "\n", + "In the previous definitions, we see some powers of the demeaned variables. This is generalized by moments, which have several variations. In scipy.stats they correspond by default to the central moments of samples (without removing the bias)\n", + "$$ m_k = \\frac{1}{n} \\sum_{i = 1}^n (x_i - \\bar{x})^k $$\n", + "where $\\bar{x} = \\mu$ is the mean. Note that this convention implies that the first centralized moment is 0.0.\n", + "\n", + "Scipy.stats has a large range of summary statistics ([link](https://docs.scipy.org/doc/scipy/reference/stats.html#summary-statistics)). For further details, check also the moment generation function and cumulants." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "9fa8b512-f6ba-4396-a0a3-9cc54646f6cc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean:\t\t 0.024246059522653948\n", + "variance:\t 1.0090602557851374\n", + "skew:\t\t -0.05750931258530448\n", + "kurtosis:\t -0.20065505984460552\n" + ] + } + ], + "source": [ + "print('mean:\\t\\t', np.mean(samples))\n", + "print('variance:\\t', np.var(samples))\n", + "print('skew:\\t\\t', stt.skew(samples))\n", + "print('kurtosis:\\t', stt.kurtosis(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "5812c419-861a-4733-97ff-e532deb2c3eb", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "central moments:\n", + "order 1: 0.0\n", + "order 2: 1.0090602557851374\n", + "order 3: -0.05829265385840662\n", + "order 4: 2.850300295817662\n" + ] + } + ], + "source": [ + "print('central moments:')\n", + "for k in range(1,5):\n", + " print('order {0}:'.format(k), stt.moment(samples, moment=k))" + ] + }, + { + "cell_type": "markdown", + "id": "b6579e85-c7c4-47bf-81fd-24c94a104771", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Change the `loc` and `scale` parameters (see the doc of `norm`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm))" + ] + }, + { + "cell_type": "markdown", + "id": "1133965f-51e0-490e-984e-c917b4ef6583", + "metadata": {}, + "source": [ + "Let's try with another type of distribution, like lognormal (`lognorm`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html#scipy.stats.lognorm)). There is a shape argument $s$, so let's see its effect." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "53914dd6-b0ee-43ad-80b3-9533367d28d5", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean:\t\t 1.0029206619333029\n", + "variance:\t 0.010281620586461631\n", + "skew:\t\t 0.32174326148243954\n", + "kurtosis:\t 0.5768071883838695\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate random samples with shape s\n", + "s = 0.1\n", + "samples2 = stt.lognorm.rvs(s=s, size=n)\n", + "\n", + "# variable range\n", + "vx2 = np.linspace(0.0,3.0,50)\n", + "dx2 = np.diff(vx2)[0]\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples2, bins=vx2)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx2, stt.lognorm.pdf(x=vx2, s=s)*n*dx2)\n", + "\n", + "plt.tight_layout()\n", + "\n", + "print('mean:\\t\\t', np.mean(samples2))\n", + "print('variance:\\t', np.var(samples2))\n", + "print('skew:\\t\\t', stt.skew(samples2))\n", + "print('kurtosis:\\t', stt.kurtosis(samples2))" + ] + }, + { + "cell_type": "markdown", + "id": "22149ced-544b-49ea-9a1b-33773c523560", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Change the `s` shape parameter and see its effect on the skew and kurtosis" + ] + }, + { + "cell_type": "markdown", + "id": "83b5a55f-7889-49d2-8f85-42030e930018", + "metadata": {}, + "source": [ + "## Statistical test about the mean of a distribution\n", + "\n", + "We want to test whether observations could come from a distribution with a given mean.\n", + "\n", + "According to the law of large numbers, for independent random variables $X_i$ following a same distribution $P(X_i) = P(X)$, the sample mean is distributed normally with:\n", + "- a mean equal to the mean of $E[X]$\n", + "- a standard deviation equal to $\\sigma / \\sqrt{n}$ with $n$ the number of samples and the standard deviation $\\sigma = \\sqrt{E[(X-E[X])^2]}$.\n", + "\n", + "Student's t-test focuses on the following statistics that involves the sample mean $\\bar{x}$, tested against a given value $\\mu$, and the sample standard deviation $s$:\n", + "$$ t = \\frac{\\bar{x} - \\mu}{s / \\sqrt(n)} $$\n", + "According to what is said above, $t$ becomes normally distributed with unit variance when the number of samples increases." + ] + }, + { + "cell_type": "markdown", + "id": "4320932d-787a-4f9f-a489-7fb9ae38a8d8", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Verify empirically the law of large number for a normal distribution, then for a lognormal distribution." + ] + }, + { + "cell_type": "markdown", + "id": "68502cc8-e6fe-48d7-a2ac-97d22a955f4f", + "metadata": {}, + "source": [ + "We can use Student's test to check whether observations come from a distribution away from 0 (i.e. there is some effect)." + ] + }, + { + "cell_type": "code", + "execution_count": 184, + "id": "4d970957-a64b-4dd8-9d58-53d818b00fa0", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t statistics: -3.215283932145039\n", + "p value: 0.0013031555669454908\n", + "TtestResult(statistic=-3.1991671192150877, pvalue=0.0018519030887166896, df=99)\n" + ] + }, + { + "data": { + "text/plain": [ + "[<matplotlib.lines.Line2D at 0x7fa4fe7e8210>]" + ] + }, + "execution_count": 184, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate random samples\n", + "n = 100\n", + "samples = stt.norm.rvs(loc=0.1, scale=1.0, size=n)\n", + "\n", + "# t statistics\n", + "t = np.mean(samples) * np.sqrt(n) / np.std(samples) # n should be replaced by n-1\n", + "print('t statistics:', t)\n", + "print('p value:', 1.0 - np.abs(0.5 - stt.norm.cdf(t))*2)\n", + "print(stt.ttest_1samp(samples, popmean=0.0))\n", + "\n", + "plt.figure()\n", + "plt.hist(samples, bins=50)\n", + "plt.title('sample mean {:.4f}'.format(samples.mean())) \n", + "\n", + "vx = np.linspace(-4.0,4.0,100)\n", + "plt.figure()\n", + "plt.plot(vx, stt.norm.cdf(x=vx))\n", + "plt.plot(t, 1.0, 'x')" + ] + }, + { + "cell_type": "markdown", + "id": "c6f9c939-ba4e-474e-89bb-a3cae4c6fe46", + "metadata": {}, + "source": [ + "## Statistical testing: is a distribution normal?\n", + "\n", + "Several tests exists to compare distributions:\n", + "- D’Agostino-Pearson (`normaltest`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html#scipy.stats.normaltest))\n", + "- Shapiro-Wilk (`shapiro`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html#scipy.stats.shapiro))\n", + "- Anderson-Darling (`anderson`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html#scipy.stats.anderson))\n", + "\n", + "For example, the `normaltest` rely on the combined `kurtosistest` and `skewtest` that check how close to zero these statistics are (to match a normal distribution).\n", + "\n", + "From the doc: If the p-value is “small”, there is a low probability of sampling data from a normally distributed population. In other words, this may be taken as evidence against the null hypothesis in favor of the alternative: the weights were not drawn from a normal distribution.\n", + "\n", + "*Importantly:* The inverse is not true; that is, these tests are not used to provide evidence for the null hypothesis.\n", + "\n", + "In contrast, the `anderson` test fits to a given distribution and evaluates the goodness of fit. In this way, you get an estimation of the mean and variance of the estimated distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "d4f3f64e-cfa8-4b58-b27c-3ac289ffb5c3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SkewtestResult(statistic=-0.7473091515071377, pvalue=0.4548769696331981)\n", + "KurtosistestResult(statistic=-1.339055153956115, pvalue=0.18055271842563614)\n" + ] + } + ], + "source": [ + "print(stt.skewtest(samples))\n", + "print(stt.kurtosistest(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "395d152c-becb-4fed-b755-e5af7c94983e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NormaltestResult(statistic=2.3515396732627534, pvalue=0.30858133101205654)\n" + ] + } + ], + "source": [ + "print(stt.normaltest(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "bf09163c-0c14-434a-bc20-3fa5d3ab34e8", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ShapiroResult(statistic=0.9983673691749573, pvalue=0.47113797068595886)\n" + ] + } + ], + "source": [ + "print(stt.shapiro(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "6b57ebfd-4cea-4143-8348-cf849531c4ab", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AndersonResult(statistic=0.4331062623048183, critical_values=array([0.574, 0.653, 0.784, 0.914, 1.088]), significance_level=array([15. , 10. , 5. , 2.5, 1. ]), fit_result= params: FitParams(loc=0.024246059522653948, scale=1.0050225500511163)\n", + " success: True\n", + " message: '`anderson` successfully fit the distribution to the data.')\n" + ] + } + ], + "source": [ + "print(stt.anderson(samples, dist='norm'))" + ] + }, + { + "cell_type": "markdown", + "id": "0e840030-3d48-4313-9ef9-c543c6c25fe6", + "metadata": {}, + "source": [ + "### *EXERCISES*\n", + "- Apply these tests for various sample sizes and check the robustness of these tests\n", + "- Redo these steps with the lognormal distribution, playing with the shape $s$\n", + "- Try to fit the data *NeuroCog* (cognitive scores from patients and controls, see below), using the `fit` method of distributions (e.g. `norm.fit(...)`, `lognorm.fit(...)`, etc.)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "3239e1ef-7c45-47a6-b1aa-0573fa2214f6", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# load NeuroCog data \n", + "import pandas as pd\n", + "df = pd.read_csv('NeuroCog_dataset.csv', sep=',')\n", + "\n", + "# select memory scores for control subjects\n", + "sel_df = df['Dx']=='Control'\n", + "samples = np.array(df[sel_df]['Memory'])\n", + "n = samples.size" + ] + }, + { + "cell_type": "markdown", + "id": "12cd9759-5bf4-4ab7-a75b-5cba2122f1df", + "metadata": {}, + "source": [ + "## Statistical testing to compare two distributions\n", + "\n", + "We can now consider the distributions of real data across several conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 188, + "id": "a83ce97d-6fc3-46d0-906c-d0eec135e514", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sb.violinplot(data=df, x='Dx', y='Memory', order=('Control','Schizophrenia','Schizoaffective'))\n", + "plt.xticks(fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 189, + "id": "3d8e7686-8ae6-404c-886e-669873077ac6", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# get memory scores for controls and schizophrenia patients\n", + "score_measure = 'Memory'\n", + "sel_df = df['Dx']=='Control'\n", + "samples_ctrl = np.array(df[sel_df][score_measure])\n", + "sel_df = df['Dx']=='Schizophrenia'\n", + "samples_pat = np.array(df[sel_df][score_measure])\n", + "n_ctrl = samples_ctrl.size\n", + "n_pat = samples_pat.size\n", + "\n", + "# range of values\n", + "samples = np.concatenate((samples_ctrl, samples_pat))\n", + "vx = np.linspace(samples.min(),samples.max(),50)\n", + "dx = np.diff(vx)[0]\n", + "\n", + "plt.hist(samples_ctrl, bins=vx, histtype='step', label='ctrl')\n", + "plt.hist(samples_pat, bins=vx, histtype='step', label='pat')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "2cb261b3-1444-44f6-ad28-d4177628c3d4", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ttest_indResult(statistic=4.707384156121897, pvalue=4.667384543620185e-06)\n" + ] + } + ], + "source": [ + "# Student's t-test (parametric: normal distributions with equal variances)\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat))" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "3418daca-4220-4b81-82ce-d8bc59bc691e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "variances\n", + "controls: 88.48104637336505\n", + "patients: 80.91557669441141\n" + ] + } + ], + "source": [ + "print('variances')\n", + "print('controls:', np.var(samples_ctrl))\n", + "print('patients:', np.var(samples_pat))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "f63fc195-1845-4eb0-86c7-1fbcb1650f76", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ttest_indResult(statistic=4.580013245897252, pvalue=1.3509339537040669e-05)\n" + ] + } + ], + "source": [ + "# Welch's t-test (parametric: normal distributions with unequal variances)\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat, equal_var=False))" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "0818927a-7d17-41b3-b21f-fac1e7cb5113", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MannwhitneyuResult(statistic=5934.5, pvalue=4.707083559908631e-06)\n" + ] + } + ], + "source": [ + "# Mann-whitney test or Wilcoxon unsigned test (non-parametric)\n", + "print(stt.mannwhitneyu(samples_ctrl, samples_pat))" + ] + }, + { + "cell_type": "markdown", + "id": "d4508eb8-e3b6-489c-9890-3ff65d7470ea", + "metadata": {}, + "source": [ + "### Exercise\n", + "- Redo the comparison of statistical tests for other cognitive scores\n", + "- Redo the comparison of statistical tests for normal and lognormal distributions (playing with the shape)" + ] + }, + { + "cell_type": "markdown", + "id": "55084553-673a-48f5-874f-58351613107f", + "metadata": {}, + "source": [ + "## Miscellanous\n", + "\n", + "We can also generate a random variable from empirical observations ([link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_histogram.html#scipy-stats-rv-histogram)). But this method doesn't generalize well in the sense of smoothing the histogram for small number of observed samples..." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "0cfe8571-012e-4ab2-8ea1-861aea6a17df", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "<matplotlib.legend.Legend at 0x7fa503555650>" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmIAAAHHCAYAAAAcbzQmAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABlC0lEQVR4nO3deVxU5f4H8M85MzDsi4oouaCWkHq5KmVa3hb0l2iblWGWGdWV0rR7s7paprlclzZvZldaXfJmqW1quZC5lCmVpKCmmQuhoCA7A8x6zu8PGpKYGYZh9vm8Xy9fxZzvec73zJw5fDnnOc8jyLIsg4iIiIhcTnR3AkRERET+ioUYERERkZuwECMiIiJyExZiRERERG7CQoyIiIjITViIEREREbkJCzEiIiIiN2EhRkREROQmLMSIiIiI3ETp7gTIOlmWIUkNkx+IotD4/0Q8HujPeEzQn/GYcA9RFCAIgk2xLMQ8nCTJKC+vhVIpIjo6FNXVdTAYJHenRW7G44H+jMcE/RmPCfdp1y4UCoVthRhvTRIRERG5CQsxIiIiIjdhIUZERETkJizEiIiIiNyEhRgRERGRm7AQIyIiInITFmJEREREbsJCjIiIiMhNOKCrj5JlGUajEbLMQfx8kSQJ0GgUMBqNAGwbNJCIiDwPCzEfI0kS1OoqaDR1kCSDu9MhJyotFSFJEgIDgxAWFoXAQJW7UyIiolZiIeZDJElCRUUJDAY9goJCoVIFQ6EQwSsmvkmhEKDValFbW4OKihK0b98JSmWAu9MiIqJWYCHmQ9TqKhgMerRr1xEBAbw64uuUShGiGACVKgRlZeehVlciKirG3WkREVErsLO+j5BlGRpNHYKCQlmE+RlRFBEUFAqtVgNZlt2dDhERtQILMR9hNBohSQaoVMHuToXcIDBQBVmWYDSyXyARkTfhrUkfYXo6sqFPGPkbUWz43HlFjBxNUpdB1tS0GCcEhUMMa++CjIh8i9cVYtnZ2Vi5ciVyc3NRV1eHuLg4pKamIiMjAyEhIS5vs76+Hv/73/+wfft2/Pbbb9BqtejQoQP69u2LO+64A8OHD7crJ/uxY75/4udOjiepy1C7/lnAoGs5WBmI0LRFLMaIWsmrCrE1a9ZgwYIFkGUZnTp1QufOnXHy5ElkZmYiKysLa9euRVRUlMvaPHXqFCZOnIjCwkIoFAr06NEDKpUKJSUlyMrKgiAIbijEiIgcQ9bUAAYdgm7KgBgdZzFOqiiCZtfbDfEsxIhaxWsKsSNHjmDhwoUAgHnz5iEtLQ2CIKC4uBiTJk3C0aNHMWvWLCxbtswlbZaXl+PBBx/ExYsXMX78eEydOrVJwVZUVIRz5861baeJiDyAGB0HRYd4d6dB5JO8pkPR8uXLIUkS7rjjDowdOxaC0HArJjY2FkuWLIEoisjKysLx48dd0uaLL76Iixcv4t5778WsWbOaXTWLi4vDoEGD7N9hIiIi8nleUYjV1tbi22+/BQCkpaU1Wx4fH4/BgwcDALZt2+b0Ni9evIgvv/wSAQEBeOKJJ2zfEQ8higKUStGr/omi9/SB2rJlM4YOvQoLFsxxdypEROThvOLW5LFjx6DT6RAYGIikpCSzMcnJydi3bx9yc3Od3uaePXug1+tx9dVXIzIyEp9++in27NmDyspKxMTEYOjQobj11luhVHre2yuKAqKiQrzu6UqjUUJlZR0kiU8FEhGR7/C8SsGMM2fOAGi43RcQYH4Kl27dujWJdWabhw8fblx3/PjxOHjwYJPlmzdvxsqVK/H2228jNjbWpnysUSrFxsLJUgElSbZdMRJFAQqFiFc+yMG54pYfSfcEXWLD8fT9yRBFwSsKsdDQMHTr1h3t23dw2jZ+v4sOQQAuHbFCoWi42kn+p6VzhH2N/tGm1ePK1jhyKaccE+RwXlGIVVVVAQAiIyMtxpiWmWKd2ebFixcBAFu2bIHBYMDkyZNx3333ISIiAtnZ2ZgzZw6OHz+OJ554Ah999FFj3zN7iKKA6OjQxp8jIswP2KrRKFBaKrb4i9j0hTxXXINThba9V57CW04mw4YNw7Bhw1yyLdN7IkkCRFFEZGQIgoKCXLJt8kyWzhH20GqCUQMgIjwYqkvOQ/bGkXs48pggx/OKQkyr1QKAxStXABAYGNgk1plt1tXVAQD0ej3Gjh2Lf/zjH43LbrjhBrzxxhu4++67cejQIXzzzTe44YYbbMrJHEmSUV1dB4VCREREMKqr62E0Ss3idDotJEmC0SjDYGi+3BcYjZLP7ltrCUJDEWY0SpBlwGiUIUkSqqrqUF9vdHd65AYtnSPsYaipBwBU19RDGVTb5jhyLWccE2SbiIhgmy8eeEUhplI1zJ2o1+stxuh0uiaxzmzz0p8ffvjhZuv17dsXgwYNwvfff9/mQgxAk+LDUjFiNHr+LTtPVFdXi3Xr1mL37p0oKmoYbuSyy7rixhtTkJZ2X7MBfceMuQ0XLpzH66+/ifDwCLz//grk5h5EZWUFpkz5J9LS7sOWLZuxcOFcjBx5K2bOnNNsm0eOHMbq1e/i8OE8GI0GdOsWj7vuuge33HJ7Y/sbNmxC586Wx20y3Y7880D6vlyIk20c+QeL6Ze30SgBVtq0NY7cg3/EejavKMRsue1oy61GR7UZEREBoOFqmqkf2Z/16tUL33//PccS82AlJcX4xz8m4ezZAoiiiPj4HhAEAadPn8TJkyewY8d2vPbacnToENNs3dzcg1izZiVEUUT37j1svh24e/fXeOGF52A0GhEaGoru3XugvLwMixbNw+nTpxy9i0RE5OG8ohCLj48H0DBIql6vN3s7saCgoEmsM9vs2bMngIZCzDTH35+ZrpoZjbxN5KnmzZuFs2cLcPnlvbFgwUu47LIuAICzZwvw3HNP48yZ05g3bxZef/3NZuuuWvUuUlNvwT//+QyCgxv6X2i1GqvbKy0txaJF82A0GjF69N2YOnVa43GSlbUVCxfOdfAeEhGRp/OK3s99+vRBQEAAdDod8vLyzMbk5OQAAPr37+/0NgcOHAigoa9YaWmp2XVNRZwjnpokxzt4MAeHDv0EURQxd+7CxiIMALp27YY5cxZCEAT89NMB5OYearZ+fHxP/OtfMxuLMABQqaxfFdu48RPU1tYiIeFKPPXUjCa3uG++eSTGjXsABoOh7TtHRERewysKsdDQUAwdOhQAsH79+mbL8/PzkZ2dDQBITU11eptXXXUVYmIabld98sknzdYtLi7G3r17AQBDhgyxKR9yrezsfQCAQYMGo3v3+GbLe/W6HFdffc3vsd81Wz5ixCgoFAq7tjlq1G1mn6S97bbRrWqPiIi8n1cUYgAwefJkCIKAjRs3Yt26dZB/76VcUlKCadOmQZIkDB8+HImJiU3WGzduHFJSUrBq1SqHtalQKBpH1H/zzTfx3Xd//KIuLy/H9OnTodVqER8fjxEjRjjybSAHKSj4DQDQs2cvizE9e14OAPjtt/xmy+Lje7R6m2fPNlwlvfzy3maXx8VdhtBQPvpPRORPvKKPGAAkJSVhxowZWLx4MWbPno3MzExER0fj5MmT0Ol06NGjB+bPn99sveLiYhQWFqKmpvngpfa2CTRMi3T48GGsX78eDz/8MLp3746wsDD8+uuv0Ol0iImJwbJly6wOj0HuYxqCJDq6vcWYdu3a/x7b/HF8e8bqqq9v2Oafn8S8VGhoGGpr+fg/EZG/8JpCDADS09ORkJCAFStWIC8vD2VlZYiLi0NqaioyMjLsuprQljbnz5+PIUOG4MMPP8Qvv/yCoqIixMXF4aabbsLEiRPRoYPzRlantjEVQxUVZRZjysvLfo91zFWq4OBgqNXqxoLMHHNFHxER+S6vKsSAhj5Xrel3tXPnToe3ealRo0Zh1KhRdq1L7tOtW3cAwKlTloeMMA0nYa4PmT26du2GY8d+xsmTvyIpqX+z5RcunIdarXbItoiIyDt4TR8xIkcaPPhaAMAPP+w32wfs9OlT+PHH7CaxbXXNNQ3tbN26ubE/4qU2b/7cIdshIiLvwUKM/NKAAclISuoPWZYxZ85zKCz8Y+DdwsJzmDt3JmRZRv/+A/HXvw5wyDZHj74bISGhOHbsZ/znPy81mTprx47tWLv2fSiVXneRmoiI2oBnfT/VJTbc3SnYzFm5zp79b/zzn5Pw668nMG7cXejRoxcAGWfOnIYkSejatRtmzzb/sIY9OnSIwXPPzcYLLzyHTz/dgKysrejatRvKyspQUlKMsWPvw549u3DhwnmLAwUTEZFvYSHmZyRJhtEo4en7k92dSqsYjRIkybHzaXbq1AnvvbcGH330Afbs2YnCwrMAgB49euLGG4dh7Nj7HNZR3+TGG4fhv/99B6tWvYsjR/Jw5sxpdOsWj/T0v+P22+/E9u1bADQ8PUlERL6PhZifkSQZlZV1EMXmA4p6MkmSHV6IAQ0FzyOPPIpHHnnUpviPP97cYsyoUbdh1KjbLC7v1y8Jr7zyerPXKysrUVlZifDwCISFsRAjIvIHLMT8kLOKGmqbL7/cCAD461/7uzcRIiJyGRZiRC60d+83MBoNuO666xs75huNRmzd+gXee+9tAMBdd6W5M0UiInIhFmJELlRQ8BuWL1+KgIAAdOrUGaGhYTh37izU6oaZH8aNewCDBg12c5ZEROQqLMSIXGjw4GtRVHQOhw79hLKyMhQVFSI8PAJDhlyHO+64C0OH3uDuFImIyIVYiBG5UM+evfD008+6Ow0iIvIQHKyIiIiIyE1YiBERERG5CQsxIiIiIjdhIUZERETkJizEiIiIiNyEhRgRERGRm7AQIyIiInITFmJEREREbsJCjIiIiMhNWIgRERERuQkLMSIiIiI34VyTfkhSl0HW1Lg7jVYRgsIhhrV3dxpEREQOxULMz0jqMtSufxYw6NydSusoAxGatojFGBER+RQWYn5G1tQABh2CbsqAGB3n7nRsIlUUQbPr7YbcWYgREZEPYSHmp8ToOCg6xLs7DSIiIr/Gzvrkt0pLS/Haa69g3Li7kJJyHYYNuw533XUL/vGPSfjf/1bBYDAAAM6fL8LQoVdhzJjbLLa1YMEcDB16FbZs2dzk9S1bNmPo0KswZUoGDAYD1q5dgwcfHIfhw4ciNfVGAMBPPx1o0v4XX3yOiRMfxM0334ChQ69CTY139ecjIiLb8YoY+aWSkmJMnDgBZWVlUCqV6NKlK4KCgnHxYgl++ukAcnJ+xB133I3w8HCHbfO5557Gvn170bnzZejWLR4VFeXNYl55ZTE+//xjxMR0RLdu3XHu3FmHbZ+IiDwPCzHySx9++D+UlZXhqqsGYc6chYiKimpcVl5ehh07tiMgIMBh2zt8OBfh4eH473/fwV//OgAAoNVqmsRcvFiCrVs3Y8GCl3DDDSkAAJ1OB6WSX1N/IooCRFGwGiNJMiRJdlFGgEIhQqm0cgNF4dqbK65+jzzxMyHfwTM8+aXffssHANx9d1qTIgwA2rVrj7S0+xy6PaPRiKeemtFYhAGAShXULObRR6c0FmEAEBgY6NA8yLOJooCoqBAoWihsjEYJlZV1Tv/FLwoNxUdEeDBU0aEW47SaYNRcEu/UnFz8HnnaZ0K+h4UY+aXY2FgAwO7dX2Pw4OscevXLnNDQUFx//U0txo0ceatT8yDPJooCFAoRr3yQg3PF5vsGdokNx9P3J0MUBaf/0hd+vwq0ZusxHKkssBjXL6oWKZfEO5Or3yNP+0zI97AQI790991jsW3bl9i+fSuys/dh8OBr0a/fXzFgQDLi43s4fHtdu3aHQqGwGhMVFYXo6GiHb5u8i6HqIrTnT0Fboja7XCuFwVDVDUCIy3IqLq/FqfMGi8tjJK3LcjE5V1yDU4VVPrs98h8sxMgvXX75FVi+/F2sXPkOfvzxe2zfvhXbt28FAPTqdQUmTZqKwYOvddj2goKCbIgJdtj2yDtJNaU4+9GzGKfXApEWgrTA2bc+R8S9i4Dgdi7Nj4gcj4UY+a0rr+yLl156DVqtBkePHsHBgznYtWsHTp36FdOnP4n//vdd9Ov3Fwi/93uRJMliW/X19a5Km3yYpFFD1muxPeBm5JWav12e1EGPEfosSBo1CzEiH8BxxMjvqVRBGDjwKjzyyKN4//11GDz4WhiNRmze/BmAP65UVVZWWGzj7FnL/WeIWqtcjMY5Y3uz/8pF3r4m8iUsxIguIYoi+vVLAgCUlZUCaOi7FR4eAZ1OhxMnjjdbJy/vEE6d+tWleRIRkW9gIUZ+6aWXFiAraxvq6mqbvF5Q8Bu2bv0CAJCY2Kfx9WuvvQ4AsHTpq6iqqmx8/cSJ4/j3v1/gWF9ERGQX/vYgv/Tzz0exadNnUCgUiIu7DOHhEaiurkZh4VnIsozLL++NcePGN8Y//PCj2LfvO+TmHsSdd96Cbt26Q6PR4Ny5Alx11SD07fsXfPXVNjfuEREReSMWYn5Kqihydwo2c0auTzwxDd999w1ycw/h4sViFBUVQqUKQmJiH9x00zDcfXdakwFXL7usC958cwXeeScTP/10AAUF+ejcOQ6PPvo4xo17AC+++G+H50hERL6PhZifEYLCAWUgNLvedncqraMMbMjdQQYOvAoDB17VqnW6d4/Hv//9otllM2fOwcyZc5q9PmrUbRg1yvJk4aZc9u490KpciMg6Q9VFGC6WwGi0/LQz0HBOFMPauygroua8rhDLzs7GypUrkZubi7q6OsTFxSE1NRUZGRkICbFvgEN72kxJSUFhYaHVdvPy8qBSqezKyVnEsPYITVsEWWN+hGhPxZMlEdkqTKrB2bf+AVlvw0CzykCEpi3i+YXcxqsKsTVr1mDBggWQZRmdOnVC586dcfLkSWRmZiIrKwtr165tNm+gs9vs3bs3wsLCzC4TXDDvmj3EsPYATzpE5KOCUQ9Zr0XI8MeAiE4W46SKImh2vd3whynPieQmXlOIHTlyBAsXLgQAzJs3D2lpaRAEAcXFxZg0aRKOHj2KWbNmYdmyZS5t8/nnn8c111zTtp0jIiKHU0THAdHd3J0GkVVeM3zF8uXLIUkS7rjjDowdO7bxalNsbCyWLFkCURSRlZWF48ebj/PkyjaJiIiIbOUVhVhtbS2+/fZbAEBaWlqz5fHx8Rg8eDAAYNs224YQcEabRERERK3hFbcmjx07Bp1Oh8DAQCQlJZmNSU5Oxr59+5Cbm+vSNj/66COsWLECGo0GHTp0wFVXXYXbbrvNYr8xIiIiIhOvKMTOnDkDAIiLi0NAgPmJcLt169Yk1lVtbtmypcnPX3zxBZYuXYpXX30V1113nU25EBERkX/yikKsqqoKABAZGWkxxrTMFOvsNgcMGIDHHnsMycnJiIuLg16vR05ODl5//XX8/PPPmDRpEj788EP07dvXpnysUSpFKBQNd5FN//0zSfLMJzTJOUwP5AoCIMt/vK5QCFAqvaLHAZkhi7Z/jxWiAOGSz7qlc4Sz8zGXkzO0Zv9azOeS98zS96ZV23Pge+8IzjgmyPG8ohDTahvGgrF05QoAAgMDm8Q6u81XX321yc/BwcG46aabMGTIENx33304evQoXnnlFaxcudKmfCwRRQHR0aGNP0dEBJuN02gUKC0V+YvYz5hOsJIkQBRFREaGICgoqIW1yFNpNUGotDE2NDQIqkvODSaWzhHOzsdaTu7SUj5aTTBqAESEBzskb0e+947kqXlRA68oxEyDour1eosxOp2uSaw72gSAoKAg/POf/8TEiRORnZ2N6upqRERE2Lz+n0mSjOrqOigUIiIiglFdXW92pGiDQQ9JkqDTGSCKlotL8g2C0FCEGY0SZBnQ6w2QJAk1NRrU1xvdnR7ZSa7V2BxbW6tBXcUfk9a3dI5wdj7mcnIG037aoq5eC211vcXlht/3r7qmHsog83m3ZnuOfO8dwRnHBNkmIiLY5iuRXlGI2XLb0ZZbjc5u02TgwIEAAEmSUFBQgH79+rVq/T8zGP74AhmNUpOfTWRZhCgqodXWIyiIf/34OtPtSNN/dTotBEGELItmjw/yEpLccszvjJIMmPmsLZ0jnJ2PtZxcLTwkENACIcEqqKwUUdrahit+siQ75D1z6HvvQJ6aFzXwikIsPj4eAFBUVAS9Xm/2dmJBQUGTWHe0aXJpW0aja65OCIKAoKAQ1NerERISioAAz5paiZxHkiRoNLVQqYI8djYHIlcKUTX8aluz9RiOVBZYjOsXVYsUAEIr+8IROZJXFGJ9+vRBQEAAdDod8vLykJyc3CwmJycHANC/f3+3tWly4sSJxv+PjY1t1bptERYWCb1ei/LyEgQFhUKlMl0a5UnGF0mSAK1Wi9raGkiShLCwKHenRORRistrceq8weLyGMm2PsVEzuQVhVhoaCiGDh2KXbt2Yf369c2Kpvz8fGRnZwMAUlNT3damybvvvgsAuPzyy9Gpk+V5zhxNFEVER3eEWl0FjaYO9fXeNbE3tY4oipAkCYGBQYiI6Ailkn0DiYi8jVcUYgAwefJk7N69Gxs3bsTAgQMb54UsKSnBtGnTIEkShg8fjsTExCbrjRs3DsXFxZgwYQLS09Md0uZ7772HwMBA3HrrrYiOjm58vaKiAv/5z38aR+KfOnWqc94MK0RRRERENMLDo2A0GiHL7BfgixQKAZGRIVCrdZBlXvEkIvJWXlOIJSUlYcaMGVi8eDFmz56NzMxMREdH4+TJk9DpdOjRowfmz5/fbL3i4mIUFhaipqb51SF727xw4QLef/99LFiwAJdddhnatWsHjUaD06dPw2AwQBRFTJs2rdVX0hxJEAQolV7z8VIrKZUigoKCUF9vZCdcIiIv5lW/qdPT05GQkIAVK1YgLy8PZWVliIuLQ2pqKjIyMhAa2vpxYOxp85ZbboEsyzh8+DCKiopw/PhxKBQKdOnSBYMGDcJ9992HK6+80hG7TERERD7MqwoxABgyZAiGDBlic/zOnTsd3mb//v1b3YGfiIiI6M84BDsRERGRm7AQIyIiInITFmJEREREbsJCjIiIiMhNWIgRERERuYnXPTVJRETeSVKXQdZYn/FDCAqHGNbeRRkRuR8LMSIicjpJXYba9c8CBp31QGUgQtMWsRgjv8FCjIiInE7W1AAGHYJuyoAYHWc2RqoogmbX2w2xLMTIT7AQIyIilxGj46DoEO/uNIg8BjvrExEREbmJ3YVYYmIi/va3v9kcn5KSgj59+ti7OSIiIiKf06Zbk7IsOzWeiMgbiKIAURSsxkiSDEny7XOgQhQgKC38fa/gDRgic1zWR0yv10MU+UUkIt8iigKiokKgaKHQMBolVFbW+WQxFh4SCGiB0NAgqKJDzcZoNcGoASAK1gtWIn/jkkKsuroa5eXlCA8Pd8XmiIhcRhQFKBQiXvkgB+eKzY+R1SU2HE/fnwxRFHyyEAtRNfwqWbP1GI5UFpiN6RdVixQAQgtXDon8jc2F2PHjx3H8+PEmr2m1Wnz++ecW15FlGdXV1di+fTskSULfvn3tTpSIyJOdK67BqcIqd6fhVsXltTh13mB2WYykdXE2RN7B5kJsx44d+O9//9vkNbVajWeffbbFdWVZhiAISE9Pb3WCRERERL7K5kIsPDwcnTt3bvy5qKgIoigiNjbW4jqiKCIsLAxXXHEFxo4di6uuuqpt2RIRERH5EJsLsQcffBAPPvhg48+JiYmIjo7Gzp07nZIYERERka+zu7P+lClTEBIS4shciIiIiPxKmwoxIiICDFUXESOVQKtQm10eI2lhqLoIgH+8ElFTnGuSiKgNpJpSnP3oWYzTa4FIC0Fa4OxbnyPi3kVAcDuX5kdEnq3NhVhBQQG2bt2KX375BVVVVdDr9RZjBUHA6tWr27pJIiKPIWnUkPVabA+4GXmlAWZjkjroMUKfBUmjZiFGRE20qRB74403kJmZCUmSbJq+SOCIykTko8rFaJwzqswu6yJyDC0iMs/uQmzTpk144403AAAdO3bE0KFD0bFjRyiVvNtJREREZAu7q6a1a9cCAFJSUvDaa68hMDDQYUkRERER+QO7Z+E+ceIEBEHACy+8wCKMiIiIyA52F2KCICAsLMzqyPpEREREZJndhVjPnj1RX18PnU7nyHyIiIiI/Ibdhdg999wDg8GArVu3OjIfIiIiIr9hdyGWlpaGlJQULFiwAD/++KMjcyIiIiLyC3Y/NfnGG28gMTEROTk5mDBhAgYOHIikpCSEhoZaXY9TIxERERE1aFMhZhqgVZZl5OTk4KeffmpxPRZiRESeQRQFiKLlgbZlK8uIyDHsLsSuvvpqR+ZBREQuJIoCoqJCoFBY7qGi1QSh0nUpEfkluwuxNWvWODIPIiJyIVEUoFCIeOWDHJwrrjEb87duBgxwcV5E/obzERER+bFzxTU4VVhldlm/SIWLsyHyP3Y/NUlEREREbcNCjIiIiMhN7L41OWHChFavIwgCVq9ebe8miYiIiHyK3YXYDz/8YFPcpUNcmP6fiIiIiNpQiLU0HlhNTQ1yc3Nx6NAhREVFYdy4cVAo2PGTiIiIyMRphZjJ/v37MXXqVJw6dQqvv/66vZtrlJ2djZUrVyI3Nxd1dXWIi4tDamoqMjIyEBIS4tY2n3jiCWzfvh1Aw/szdepUu/IhIiIi/+D0zvpDhgzBzJkz8dVXX2HDhg1tamvNmjVIT0/H7t27oVKp0KtXLxQWFiIzMxNjxoxBZWWl29rcsWNHYxFGREREZAuXPDU5atQoKBSKNhViR44cwcKFCwEA8+bNw+7du/HZZ59hx44d6Nu3L06dOoVZs2a5pc2amhrMnTsXnTt3Rt++fVu/c0REROSXXFKIqVQqBAcH49SpU3a3sXz5ckiShDvuuANjx45t7PgfGxuLJUuWQBRFZGVl4fjx4y5v88UXX0RJSQlmzZrV4qTnRERERCYuKcSKi4tRU1MDWZbtWr+2thbffvstACAtLa3Z8vj4eAwePBgAsG3bNpe2mZ2djY8//hg333wzhg0bZtO2iYiIiAAXFGIajQZz5swBAPTu3duuNo4dOwadTofAwEAkJSWZjUlOTgYA5ObmuqxNjUbTeBXs+eeft2m7RERERCZ2PzX5xhtvWF2u0+lw/vx57N27F5WVlRAEAffff79d2zpz5gwAIC4uDgEBAWZjunXr1iTWFW0uXboUBQUFmD17NmJjY23arj2UShEKRUPNbPov+TceD55DFm0fH1EhChCUlj+ztrTV2mPCXceO1ffgkn1QWohxRt7WcmrN9jzt+8jzhHdoUyFmywCtsixDFEU89thjuO222+zaVlVVw4S0kZGRFmNMy0yxzm7z8OHDWL16Nf76179i3LhxNm3THqIoIDr6j35nERHBTtsWeR8eD+6n1QSh0sbY0NAgqKIt9yN1RFuefkxYew+0mmDUAIgID7b6Prkyp9bw1PfeU/OiBnYXYldffbX1hpVKREREIDExESNHjkR8fLy9m4JWqwUAi1euACAwMLBJrDPb1Ov1mDlzJgRBwLx58yCKzvtrQ5JkVFfXQaEQERERjOrqehiNktO2R96Bx4PnkGs1NsfW1mpQV1HrlLZae0yY4l3N2ntgqKkHAFTX1EMZZD7GGXlby6k12/O07yPPE+4TERFs85VIuwuxNWvW2Ltqq6lUKgANBZAlOp2uSawz23znnXfwyy+/YOLEiUhMTLRpe21hMPzxBTIapSY/k3/j8eABJNsfQjJKMmDt83JAW55+TFh7D0zFgtEoWX+fXJhTq9rx0PfeU/OiBl5x49iW24623Gp0RJu//fYbMjMz0bVrV5tnFyAiIiIyx+4rYq5kuq1ZVFQEvV5v9nZiQUFBk1hntfnrr79Cp9OhtLTU7HAVpuJtxYoV+Oijj9CpUyd88sknNuVERERE/sUhhVhpaSm2b9+OI0eOoKysDIIgoF27dujXrx9GjBiBDh06tKn9Pn36ICAgADqdDnl5eY3DSlwqJycHANC/f3+XtFlfX4/6+nqL7dfV1aGurs7mW6VERP7AlqcmifxJmwoxo9GIpUuXYuXKlTAYDADQOGirIAj4/PPPsXjxYjz88MN44oknoFAo7NpOaGgohg4dil27dmH9+vXNiqb8/HxkZ2cDAFJTU53a5vDhw/HLL79YbPeBBx7ADz/8wEm/iYguER4SCGhte2pStOGJfCJf0aZC7F//+he2bNkCWZYRGBiIfv36oVOnTgCACxcu4MiRI9DpdHj77bdRVFSEl19+2e5tTZ48Gbt378bGjRsxcOBApKWlQRAElJSUYNq0aZAkCcOHD2/WeX7cuHEoLi7GhAkTkJ6e7pA2iYiodUJUDb9u1mw9hiOVBWZj+kXVIgWA0Irx1Ii8nd2F2I4dO/Dll18CAB566CFMmjQJERERTWJqamqQmZmJFStW4IsvvkBqaqrd0wAlJSVhxowZWLx4MWbPno3MzExER0fj5MmT0Ol06NGjB+bPn99sveLiYhQWFqKmpsZhbRIRkX2Ky2tx6rzB7LIYybbhh4h8id035D/++GMIgoDHHnsM06dPb1aEAUB4eDj+9a9/4bHHHoMsy9iwYUObkk1PT8fKlStx/fXXo76+HidPnkRcXBwee+wxfPLJJ2jXrp1HtElERERkC7uviB0+fBiiKOKRRx5pMfaRRx7B22+/jcOHD9u7uUZDhgzBkCFDbI7fuXOnw9u0xpXjqxEREZF3s/uKWFVVFcLCwhAeHt5ibHh4OMLDw22efoiIiIjIH9h9RSwyMhKVlZVQq9UICwuzGltTU4OamhpER0fbuzkiInIwQ9VFxEgl0CrUZpeH6zmcBJGz2V2I/eUvf8GePXuwatWqFkeYX7VqFSRJQr9+/ezdHBEROZBUU4qzHz2LcXotYGlCkjJACFChHsEAOEUOkTPYXYjddddd2L17N5YvXw6DwYCJEyciNLTp2DBqtRrvvPMO3n77bQiCgHvuuafNCRMRUdtJGjVkvRbbA25GXmnzmUUAIDmhI9LHXAP1e0cBsGsJkTPYXYjdfPPNGDlyJLZu3Yq33noLq1atwl/+8hd07NgRgiA0jiOm1WohyzJGjRqF4cOHOzJ3IiJqo3IxGueM5mcA6aXqBGVkjIszIvIvbRrQ9aWXXkKnTp2wZs0aaDQa/PjjjxB+HxHZNMK+UqnEAw88gGnTprU9WyIiIiIf0qZCLCAgANOnT0d6ejqysrIa55oEgPbt26Nfv364+eabERsb65BkiYiIiHyJQyb9jo2NxQMPPOCIpoiIiIj8Bp9NJiIiInITu6+IqdVqfP/99wgNDcXgwYOtxu7fvx91dXUYPHhwsycriYiIiPyV3VfEvvjiC0yZMgXffPNNi7Hbtm3DlClTsGXLFns3R0RERORz7C7EvvrqKwDALbfc0mLsXXfdBVmWkZWVZe/miIiIiHyO3YXYmTNnAACXX355i7EJCQlN1iEiIiKiNvQRKy0tRUREBFQq8wMBXiooKAiRkZEoLS21d3NERERu0dKcnDGSFoaqiwBCXJsY+QS7C7Hg4GDU1tbCaDRCoVBYjTUYDKitrUVwcLC9myMiInI5m+bk1AJn3/ocEfcuAoLbuTQ/8n52F2Ldu3fH4cOHsX//fgwdOtRq7P79+2EwGNC1a1d7N0dERORytszJmdRBjxH6LEgaNQsxajW7+4hdf/31kGUZL730EtRq85drAaC2thYvvfQSBEHADTfcYO/miIiI3KZhTs72Zv+Vi9HuTo+8mN2F2Pjx4xEZGYlff/0VY8aMwVdffQWNRtO4XKPRICsrC3fffTd+/fVXhIeHY8KECQ5JmoiIiMgX2H1rMioqCq+++ioef/xx5Ofn44knnoBCoUBUVBQEQUBFRQWMRiNkWYZKpcJrr72G6Gj+1UBERERk0qYpjoYOHYoPP/wQAwcOhCzLMBgMKC0txcWLF2EwGCDLMq6++mqsW7cO1157raNyJiIiIvIJbZ70u0+fPli7di1+++03HDx4EBcvXgQAxMTEYODAgejWrVubkyQiIiLyRW0uxEy6d++O7t27O6o5IiIiIp/XpluTRERERGQ/FmJEREREbsJCjIiIiMhNHNZHjIiIyBVamvsxXM9rDOQ9WIgREZHXsGnuxzJACFChHsEAJFemR9RqLMSIiMhr2DL3Y3JCR6SPuQbq944CqHJtgkStxEKMiIi8TsPcjyqzy3qpOkEZGePijIjswxvpRERERG7CQoyIiIjITRxya/Lrr7/G3r17UVRUBI1Gg9WrVzcuq6urw/HjxyEIAgYMGOCIzRERERH5hDYVYufPn8eUKVPw888/AwBkWYYgCE1iAgMD8dRTT+HChQv4/PPPkZCQ0JZNEhEREfkMu29N1tfX4+GHH8bRo0cRGxuL+++/H8HBwc3ilEolxowZA1mW8fXXX7cpWSIiIiJfYnch9sEHH+DMmTPo06cPtmzZgueffx6hoaFmY4cNGwYA+O677+zdHBEREZHPsbsQ2759OwRBwLPPPouQkBCrsb1794ZSqUR+fr69myMiIiLyOXb3ETtz5gwUCgUGDhzYYqwoiggLC0NVFQfWIyIiz2KsKAKMFkbgr77g2mTI79hdiOl0OqhUKigUCpvi6+vrERgYaO/miIiIHKoewRACVKjb8abVOE6XRM5kdyHWvn17XLhwAdXV1YiIiLAae/z4cWi1WvTs2dPezRERETmUWgxH14lLUVFcAqOFK2IKhYjo2I6cLomcxu5CbMCAAdi6dSu2bt2KsWPHWo3NzMyEIAi4+uqr7d1co+zsbKxcuRK5ubmoq6tDXFwcUlNTkZGR0WJfNUe1WV9fj7Vr1+Lw4cM4ceIEysrKoFarERYWht69e2PkyJG45557EBBgfh40IiLyDMrIGCilEMBgvhBTKkUoI80/iEbkCHZ31r/33nshyzKWLVuGkydPmo2pr6/H3LlzsX37dgDAuHHj7N0cAGDNmjVIT0/H7t27oVKp0KtXLxQWFiIzMxNjxoxBZWWlS9osKyvDSy+9hK1bt6K4uBjt2rVDQkICBEHADz/8gLlz5+Lee+9FdXV1m/aXiIiIfJvdV8QGDRqEMWPG4OOPP8Y999yDG2+8EXV1dQCAd999FydOnMCePXsai5EHH3wQiYmJdid65MgRLFy4EAAwb948pKWlQRAEFBcXY9KkSTh69ChmzZqFZcuWOb3NsLAwzJw5E9dddx169erV+LpprLRnnnkGR44cwauvvoq5c+favc9ERETk29o01+TcuXPxwAMPQKPRYOvWrY2F2KuvvorNmzc3PiX50EMPYfr06W1KdPny5ZAkCXfccQfGjh3bOIJ/bGwslixZAlEUkZWVhePHjzu9zaioKEyYMKFJEQYAgiBg+PDhmDx5MgDgq6++assuExERkY9rUyGmUCgwc+ZMbNq0CRMmTEC/fv0QExOD9u3bIyEhAffddx8+++wzTJ8+vdnUR61RW1uLb7/9FgCQlpbWbHl8fDwGDx4MANi2bZvb2jQxFWj19fWtWo+IiIj8i0Mm/b7iiivw3HPPOaIps44dOwadTofAwEAkJSWZjUlOTsa+ffuQm5vrtjZNcnJyAAD9+vVr1XpERETkXxxSiDnbmTNnAABxcXEWn0Ts1q1bk1hXt6nT6XDhwgVs2rQJK1euREhICJ555hmbciEiIiL/5BWFmKmvWWRkpMUY0zJbR+93VJvp6enYv39/k9dGjRqFKVOmNOtDZi+lUoRC0XAX2fRf8m88HjyHLNre7UIhChCUlj+ztrTV2mOiNduyVTupAl0U5v+wDdfbfqxae5+ckbe196w137GWPl9X43nCO9hUiP34448O26A9Y4lptVoAsDoul2nUflOsq9rs3bs3tFotNBoNCgsLUVVVhX379qFnz554/PHHIYpt+wKIooDo6D/GsImICG5Te+RbeDy4n1YThEobY0NDg6CKtjwmlSPasvWYaM22WmxL0TBC/Qh9FkZY+tu2zPYR6q29T47M28RR36OWPl934XnCs9lUiD3wwANt6mxvIggCfv7551avp1KpAAB6vd5ijE6naxLrqjb/3Dfu66+/xvz58/HGG2+gsrISs2bNsikfSyRJRnV1HRQKERERwaiurrc4AjT5Dx4PnkOu1dgcW1urQV1FrVPaau0x0ZpttaReGYmujy7Fi+/swrkStdmY5ISOSB9zjU0j1Ft7nxyZt4m198z0vtqipc/X1XiecJ+IiGCbr0TafGtSlmW7E2prG7bcIrTlVqOz2wSAYcOGoX379hg7diw+/PBDPPLII4iLi7N5fXMMl4z4bDRKTX4m/8bjwQNItp/XjJJscQR3R7Vl8zHRim3ZQhkZg4tiR5wzmv/DtZeqE5SRMTa1ZfV9cnDegOO+Ry1+vm7C84Rns6kQa83YXM4QHx8PACgqKoJerzd7O7GgoKBJrDvaNOnfvz+io6NRUVGBn3/+uc2FGBEREfkmr+jB16dPHwQEBECn0yEvL89sjGnIiP79+7utzUsZjUYAjrmSSERERL7JKwqx0NBQDB06FACwfv36Zsvz8/ORnZ0NAEhNTXVbmyb79+9vnNrpyiuvbNW6RERE5D8cWogVFhYiLy8PeXl5KCwsdGTTmDx5MgRBwMaNG7Fu3brGK00lJSWYNm0aJEnC8OHDm81nOW7cOKSkpGDVqlUOa3PFihXYtGkT1OqmnVKNRiO++uorTJs2DQDwf//3f+jSpYuj3gIiIiLyMW0eR6y4uBhvv/02tmzZgsrKyibLIiMjccstt2DixIno1KlTm7aTlJSEGTNmYPHixZg9ezYyMzMRHR2NkydPQqfToUePHpg/f77Z/AoLC1FTU+OwNk+cOIEXX3wRoiiia9euiIqKgl6vR0FBQWNxNmjQICxatKhN+0xERES+rU2F2N69e/Hkk09CrVab7QtVWVmJtWvXYuPGjViyZAmuv/76tmwO6enpSEhIwIoVK5CXl4eysjLExcUhNTUVGRkZCA1t/fgt9rT5wAMPIDY2FgcOHMC5c+dw7NgxCIKADh064Nprr8Utt9yCESNGOGTIDyIiIvJddhdip0+fxuOPPw6tVovIyEjce++9GDx4MGJjYwE0XIn6/vvvsW7dOlRUVGDq1Kn47LPP0LNnzzYlPGTIEAwZMsTm+J07dzq8zb59+6Jv3742xxMRERGZY3chtnz5cmi1WiQkJGDlypVo165dk+U9e/bEkCFDMGHCBDz00EM4ceIEMjMz8fLLL7c5aSIiIiJfYHdn/ezsbAiCgH//+9/NirBLtWvXDvPnz4csy83mZCQiIiLyZ3YXYtXV1QgJCcFf/vKXFmOTkpIQEhLSOKQDEREREbWhEIuJiYEk2T5lgizLiImxbXoLIiIiIn9gdyF2ww03QKPR2HS7cf/+/aivr8dNN91k7+aIiIiIfI7dhdjkyZPRvn17zJw5E2fOnLEYl5+fj+effx4xMTGYNGmSvZsjIiIi8jl2PzV55swZTJs2DYsWLcIdd9yB1NTUxuErBEHAhQsX8P3332Pbtm1QqVSYMWMGTp8+jdOnTzdr6+qrr27TThARERF5I7sLsQceeKDJgKWbN2/G5s2bzcbqdDrMnDnT7DJBEPDzzz/bmwYRERGR12rTyPrmRtN3RxtERERE3sjuQuz48eOOzIOIiIjI79jdWZ+IiIiI2oaFGBEREZGbsBAjIiIicpM2ddYHALVajV27duGXX35BdXU19Hq9xVhBELBw4cK2bpKIiIjIJ7SpEFu3bh1efPFF1NfXN75m7ilIQRAgyzILMSIiIqJL2F2IbdmyBS+88AIAIDg4GAMGDED79u2hVLb5IhsRERGRX7C7alqxYgUA4Prrr8eSJUsQFhbmsKSIiIiI/IHdnfVPnjzZeKuRRRgRERFR69l9RSw4OBiBgYHo0KGDI/MhIiIbyFXnIVz6syhAqwmCXKsBJBkIDANC27ktP2pOFAWIomA1RpJkSBJnnPEndhdiiYmJ+OGHH6BWq3lFjIjIRQLDIiFIKqizMpstq7zk/4UAFcLSFrEY8xCiKCAqKgQKhfUbUUajhMrKOhZjfsTuQuzBBx/E/v37sXbtWmRkZDgyJyIiskAIa4+u45Zi1Sc/oLi81mzM5eH1uLp0E6BTsxBzIWNFEWCUzC9UiJCVHfHKFwU4V1xjNqRLbDievj8ZoiiwEPMjdhdiN954IyZPnoylS5cCACZMmICgoCCHJUZEROYpI2NwpDIUp84bLMZc7cJ8/F09giEEqFC3402rceoAFSrFcTh13kKxRn6pTWNNPPHEEwgJCcErr7yC5cuXo1evXggNDbUYLwgCVq9e3ZZNEhEReRS1GI6uE5eiorgERktXxKovoG7HmwhW1QNQuTQ/8mxtKsT+85//4N1334UgCNBoNDh69KjVeEGw3kmRiIjIGykjY6CUQgCD5VuTRObYXYh9/PHHeOuttwAAXbp0wZAhQzigKxEREVEr2F01ffDBBxAEAaNHj8aCBQsgiqz2iYiIiFrD7uopPz8fAPDss8+yCCMiIiKyQ5sGdA0ICEBERIQj8yEiIiLyG3ZfykpKSoJarUZFRYUj8yEiIiLyG3YXYn//+98BAG++aX3cFCIiIiIyz+5C7KqrrsLcuXPx4YcfYvbs2Th79qwj8yIiIiLyeXb3ERs2bBgAQKFQYMOGDdiwYQMiIyNbHNB1x44d9m6SiIiIyKfYXYgVFhY2e62yshKVlZUW1+GArkRERER/sLsQW7RokSPzICIiIvI7dhdid955pyPzICIiIvI7HImViIiIyE1YiBERERG5icNm6JZlGVVVVaivr4csyxbj4uLiHLVJIiIiIq/W5kJs165dWLNmDQ4ePAiNRmM1VhAE/Pzzz23dJBEREZFPaFMh9tJLL2HlypVWr4BdytY4IiIiIn9gdyH2zTffYMWKFVAqlXjqqadw/fXX45ZbbkG7du2wbt06XLx4Efv27cOaNWsgiiIWLVqEK664os0JZ2dnY+XKlcjNzUVdXR3i4uKQmpqKjIwMhISEuKTN2tpa7Nq1C3v37kVeXh4KCwshSRJiY2MxaNAgpKeno3fv3m3dVSIiIvJxdnfWX7duHQRBwOTJk/HQQw+hV69eDQ2KIrp27YqBAwdiypQp2LhxI8LDwzFz5kwEBga2Kdk1a9YgPT0du3fvhkqlQq9evVBYWIjMzEyMGTPG6mCyjmxzzpw5eOqpp/DZZ5+hsLAQ3bt3R3x8PIqLi/HJJ5/grrvuwieffNKmfSUiIiLfZ3chlpeXBwBIS0uzGtepUyfMmjULZWVleOedd+zdHI4cOYKFCxcCAObNm4fdu3fjs88+w44dO9C3b1+cOnUKs2bNclmbN954I95++238+OOP2LRpEzZv3oy9e/fi1ltvhV6vx6xZs3DixAm795eIyF8ZK4pgLM03/6+iyN3pETmU3bcmKysrERQUhA4dOjS+plAoUF9f3yz2uuuug0qlwp49e/Dcc8/Ztb3ly5dDkiSMHj0aY8eObXw9NjYWS5YswciRI5GVlYXjx48jMTHRqW0+99xziI6ObtZeZGQkFi9ejF9++QW//vorNmzYgJkzZ9q1v0RE/qYewRACVKjb8abVOCFAhXoEA5BckxiRE9ldiIWFhTV7SjIsLAzV1dWoq6tr0rdKFEUoFAoUFxfbta3a2lp8++23AMxfgYuPj8fgwYOxb98+bNu2zaZCrC1tmivCTAICAjB48GD8+uuvOHPmTIt5EBFRA7UYjq4Tl6KiuARGo/kiS6EQER3bEer3jgKocm2CRE5g963J2NhYaDQaVFX98UXo0aMHAOCnn35qEpufn4+6ujooFAq7tnXs2DHodDoEBgYiKSnJbExycjIAIDc3121tmuh0OgBAcHBwq9YjIvJ3ysgYKGPioehg/p8yJh7KyBh3p0nkMHZfEevXrx9++eUXnDhxAldffTUA4Nprr8WhQ4ewZMkSJCQkICYmBuXl5Zg1axYEQUC/fv3s2pbpylJcXBwCAgLMxnTr1q1JrDvaBACNRoOvv/4awB+FXFsplSIUioaa2fRf8m88HjyHLAo2xypEAYLS8mfWmrbauj1Hb8uRrB3XzjjmHbU9a7GtOk4ctI88T3gHuwuxlJQUfPzxx/jiiy8aC7H7778f//vf/3Ds2DHcdNNNiI6ORllZWeP4YY888ohd2zJddYuMjLQYY1p26RU6V7cJAK+99hpKS0vRrl07jBkzxub1LBFFAdHRoY0/R0TwKhv9gceD+2k1Qai0MTY0NAiqS77PbWmrrdtz9LYcydXHtaO2Z62d1rzfjt5/nic8m92F2HXXXYdFixYhPDy88bX27dvjrbfewlNPPYWioiJcvHgRQMMtuunTp+P666+3a1tarRYALF65AtA4NIYp1h1tfvnll1i5ciUAYP78+QgLC7NpPWskSUZ1dR0UChEREcGorq632HeC/AePB88h11qfUeRStbUa1FXUOqSttm7P0dtyJGvHtenY98TtWWunNe+3o77XPE+4T0REsM1XIu0uxFQqFe68885mrw8YMABfffUVDh48iAsXLiA8PBzJycltKkpUKhUAQK/XW4wx9csyxbq6ze+++w7Tp08HADz55JMYPny4TXnYwmD44wtkNEpNfib/xuPBA0i2zxhilGTA2ufVirbavD0Hb8uRXH1cO2p7VttpzXHi4P3necKzOWzS70spFApcddVVDmvPlluEttxqdFabP/74Ix5//HHo9XpkZGTgsccesykHIiIi8m9e0YMvPj4eAFBUVGTxClZBQUGTWFe1efDgQWRkZKC+vh4PPPAAnnrqKZu2T0RERGR3IabT6Zr0A7tUbW0tXnzxRdx+++2488478dprrzUbc6w1+vTpg4CAAOh0usYR/f8sJycHANC/f3+XtXnkyBFMnDgRdXV1SEtL4+CtRERE1Cp2F2IbNmzAsGHDsGTJkmbLHn30UaxatQonTpzAsWPH8NZbb2HixImNT0+2VmhoKIYOHQoAWL9+fbPl+fn5yM7OBgCkpqa6pM1ffvkFjzzyCGpqanDHHXdg7ty5EATPfRyciIiIPI/dhdjevXsBALfddluT17/++mscOHAAgiDgtttuwz333AOlUokDBw5g48aNdic6efJkCIKAjRs3Yt26dY1FXUlJCaZNmwZJkjB8+PBmo+qPGzcOKSkpWLVqlcPazM/Px8MPP4zKykqMHDkSixYtgih6xV1eIiIi8iB2d9Y/ffo0AKBv375NXv/iiy8gCAImTpyIJ598EkDDbcC5c+di8+bNGD16tF3bS0pKwowZM7B48WLMnj0bmZmZiI6OxsmTJ6HT6dCjRw/Mnz+/2XrFxcUoLCxETU2Nw9qcP38+SktLATT0MRs/frzZnGNiYvD666/btb9ERETk++wuxMrLyxEUFNTsicLvv/8eAJoMZmq6dffLL7/YuzkAQHp6OhISErBixQrk5eWhrKwMcXFxSE1NRUZGBkJDLQ+U6Mg2TcNaANanP7rssstanQ8RERH5D7sLsfr6+mbja507dw7l5eWIi4tD165dG18PCQlBREQEKisr7U7UZMiQIRgyZIjN8Tt37nR4m2vWrLE5loiIyFaGqoswXLQ86bmJEBQOMay9i7IiZ7K7EIuMjER5eTmqq6sREREBAI2d2wcMGNAs3mAw2HXFiog8n6Qug6xpfvv/UvzFQWRdmFSDs2/9A7LehtlclIEITVvE75QPsLsQ69OnD/bu3YuPP/4YDz/8MCRJwscffwxBEHDNNdc0iS0vL0ddXR169erV5oSJyLNI6jLUrn8WMOisB/IXB5FVwaiHrNci7OZJECI7W4wzVhShbsebDX/88Pvk9ewuxO688058++23ePXVV7Fv3z6Ul5fj559/RmhoaLPhHg4cOAAALMSIfJCgVQMGHWLu+AcC23cxG6MrO4eLG5c2xPIXB5FZ4SGBgBaI7NITqs49LcZpzwejDoDIIZN8gt2F2KhRo7B37158+umnjUNZqFQqzJ07t/FWpcmWLVvMXikjIu8niA2/DNb9UIMjlQVmY/pF1SLlklgiai5E1fArec3WYxa/SwC/T76mTXNNLly4EHfffTcOHjyIiIgIDBkypEknfaDhCcPw8HCMHj0a119/fZuSJSLPVVxei1PnDWaXxUg29HkhIgDWv0sAv0++ps2TficnJyM5Odni8sDAQLNjcRERERH5Ow4HT0REROQmLMSIiIiI3ISFGBEREZGbsBAjIiIichMWYkRERERuwkKMiIiIyE1YiBERERG5CQsxIiIiIjdp84CuROR5JHVZw4TAVghB4ZyA28WMFUWAUbIcUH3BdckQkUdgIUbkYyR1GWrXPwsYdNYDlYEITVvEYswF6hEMIUCFuh1vthgrBKhQj2AAVgo2IvIZLMSIfIysqQEMOgTdlAExOs5sjFRRBM2utxtiWYg5nVoMR9eJS1FRXAKjlStiCoWI6NiOUL93FECV6xIkIrdhIUbko8ToOCg6xLs7DfqdMjIGSikEMFguxJRKEcrIUBdmRUTuxkKMiIiILGKfU+diIUZERERmsc+p87EQIyIiIrPY59T5WIgRERGRVexz6jwsxIh8lEIhQqm0MGazwjPHchZFAaIoWI2RJBmSJLsoI8dStPC+t7ScnMPa++7Nn4kgNHyXrO2Drd8nbzyfeAsWYkQ+Rvz95BsRHgxVtPkn8LSaYNRcEusJRFFAVFRIi7/4jEYJlZV1XlWMRYWrIEkyIiKC3Z0KXcKXPxdRFBAeHgQAVvevpe+Tt55PvAkLMSIfI/x+RWnN1mM4UllgNqZfVC1SLon1BKIoQKEQ8coHOThXbP4JrS6x4Xj6/mSIouBVhVhYcABEUbC6bwAwMLEjJozq48LM/Jstn4u3fiaO+j556/nEm7AQI/JRxeW1OHXeYHZZjKR1cTa2O1dcg1OFvjmYaUv71qVjmAuzIRNrn4u3fyaO+j556/nEG/DGLhEREZGbsBAjIiIichPemiQilzFWFAGW5lpUiDCIHV2bEBGRm7EQI7KCU3s4Rj2CIQSoULfjTatx6gAVwsRxLsqKiMj9WIgRWcCpPRxHLYaj68SlqCgugdHSFbHqC6jb8SaCVfUAVC7Nj4jIXViIEVnAqT0cSxkZA6UUAhgs35okIvI3LMSIWsCpPYiIyFn4JygRERGRm7AQIyIiInITFmJEREREbsJCjIiIiMhNWIgRERERuQkLMSIiIiI38brhK7Kzs7Fy5Urk5uairq4OcXFxSE1NRUZGBkJCQlzW5uHDh5GTk4MjR47g8OHD+O233yDLMmbNmoXx48e3ZReJiIjIT3hVIbZmzRosWLAAsiyjU6dO6Ny5M06ePInMzExkZWVh7dq1iIqKckmbzz//PI4fP+6YHSMiIiK/5DW3Jo8cOYKFCxcCAObNm4fdu3fjs88+w44dO9C3b1+cOnUKs2bNclmbXbt2xahRo/Cvf/0L77//Pvr379+m/SMiIt/XTqpAF0WZ2X/h+lJ3p0du4DVXxJYvXw5JkjB69GiMHTu28fXY2FgsWbIEI0eORFZWFo4fP47ExESnt/nGG280+TkwMLANe0eeTKEQoVRa+JvFDdPyiKIAxe/bVZjZviwKrk7JZubyNXF43rXlgE5tPSYwDAht59jtkt+ydnwjNAJCgAoj9FkYEWkhpgwQAlSoRzAAC1OBkc/xikKstrYW3377LQAgLS2t2fL4+HgMHjwY+/btw7Zt22wqxJzRJvkWUWgoDCLCg6GKDjUbo9UEo+aSWKfnJAqIigppPOFHRASbySkIlS7JxnZR4SpIkmw2XxOH5l1bDvX6ZyHrtVbDhAAVwtIWsRijNrHl+EZ0KMIfXYoX39mFcyXm/0BITuiI9DHXQP3eUQBVzkmWPI5XFGLHjh2DTqdDYGAgkpKSzMYkJydj3759yM3NdVub5FuE36/QrNl6DEcqC8zG9IuqRcolsc5muhr2ygc5OFdcYzbmb90MGOCSbGwXFhwAURRcl7dODVmvxY8dbsfJGvO/HC8Pr8fVpZsarpqxEKM2sOX4HpjYERNG9cFFsSPOGVVmY3qpOkEZGePMVMkDeUUhdubMGQBAXFwcAgICzMZ069atSaw72iTfVFxei1PnDWaXxUjWr7g4y7niGpwqNP8Xc79IhYuzsZ2r8z5ZE4zs8+Z/6QHA1Q7fIvkza8d3l45hLs6GvIVXFGJVVQ0HdmSkpRvrfywzxbqjTWdRKkWrfYLIOVrTZ0khChAs9SNzIEd//o7I2x190lp6H1z52Xl0nzwr++bReVv5fHkO/IO1z7c175Oj+m666jzoa7yiENNqG646WLpyBfzRWd4U6442nUEUBURf0j/Jah8EcqjW9FkKDQ2y2I/Mkzkib3f0SWvpe+DKz84T++SZWNs3T86b5znbOOq846i+m956HnQ3ryjEVKqGWwt6vd5ijE6naxLrjjadQZJkVFfXQaEQERERjOrqehiNfJrGFeRajc2xtbUa1FXUOjGbBqbjwFEckXdr3idHael74MrPzh37bytr++bJeVv7fB39HfBm1j7f1rxP1t5vTzwPeoOIiGCbr0p6RSFmyy1CW241OrtNZzEY/viCGI1Sk5/JiSTZ5lCjJANe+Lk4JO9WvE+2aBhnyfyV6hhJC0PVRRilEOvfA1d+dg7ef0eyum+enDfPczZxxPfXUHUR2uISy3/YVF9waT7+yCsKsfj4eABAUVER9Hq92duJBQUFTWLd0SYR2U+rCG55nCUtcPatzxFx7yIgmE86ErVFmFSDs2/9w6ZhXji2mfN4RSHWp08fBAQEQKfTIS8vD8nJyc1icnJyAMDmEe6d0SYR2a9eGYmuLYyzlNRBjxH6LEgaNQsxojYKRj1kvRYhwx8DIjqZjVEoRETHduTYZk7kFY83hIaGYujQoQCA9evXN1uen5+P7OxsAEBqaqrb2iSitlFGxvw+zlJ7s//KxWh3p0jkcxTRcVB0iDf7TxkTz7HNnMwrCjEAmDx5MgRBwMaNG7Fu3TrIckP/hpKSEkybNg2SJGH48OHNRsAfN24cUlJSsGrVKoe1SeROhqqLiJFKOF8dEZEP8IpbkwCQlJSEGTNmYPHixZg9ezYyMzMRHR2NkydPQqfToUePHpg/f36z9YqLi1FYWIiamuajHdvbJgC88847ePfddxt/VqsbbqW8+uqrWLZsWePrn3/+OTp37tzW3ScCAEg1pTj70bMYp9cCnK+OiMjreU0hBgDp6elISEjAihUrkJeXh7KyMsTFxSE1NRUZGRkIDW39+CX2tqnRaFBZWdns9bq6OtTV1TX+bDQaW50TkSWSpmHqnu0BNyOv1PyThZyvjojIe3hVIQYAQ4YMwZAhQ2yO37lzp8PbBICpU6di6tSprVqHyFHKxWjOV0dE5AO8po8YERERka9hIUZERETkJizEiIiIiNyEhRgRERGRm3hdZ30iIiJqmWnMQa3C/EwV7SS9izMic1iIEbmIKAoQRcFqjCTJkDx4MmZfpBAFCErLNwf4mZA3smnMQX3DmIPK0AjAwndAobD9xllL3yWA3ydzWIgRuYAoCoiKCmnxpGY0SqisrOOJygXCQwIBLRAaGgRVtOUxCPmZkDeyZczBK+Pb4bFx1yIwumObtmXrdwng98kcFmJELiCKAhQKEa98kINzxc1neQCALrHhePr+ZIiiwJOUC4SoGk5/a7Yew5HKArMx/EzI21kdczDiMgRGd7R6XhqY2BETRvWxug1bvksAv0+WsBAjcqFzxTU4VcjR7j1JcXktTp03uDsNIrexdl7q0jHM5nb4XbIPn5okIiIichNeESMiv9ZOqkAXhfk+NDGSFoaqiwBCXJsUEfkNFmJE5Je0imAIASqM0GdhhKWnyrTA2bc+R8S9i4Dgdi7Nj4j8AwsxIvJL9cpIdH10KV58ZxfOlZgfZympgx4j9FmQNGoWYkQtsHZ1GeAVZktYiBGR31JGxuCi2NHiU2VdRK2LMyLyPjZdXQZ4hdkCFmJE5HWMFUWAUbIcUH3BdckQ+Tlbri4DvMJsCQsxIvIa9Wj4y7tux5stxgoBKtQjGICVgo2IHKKlq8sArzBbwkKMiLyGWgxH14lLUVFcAqOVK2IKhYjo2I5Qv3cUAMdtIyLPxUKMiLyKMjIGSikEMFguxJRKEcpI61Ot+AOrt3B5+5bII7AQIyLyMbbewuXtW+/GQts3sBAjIvIxttzC5e1b78VC27ewECMi8kEt3cLl7VvvxULbt7AQIyIi8jIstH0HCzEiFzFUXUSMVAKtwvw4Oxx1mojI/7AQI3IBqaYUZz96FuP0WoDzGhIROZ2kLoOsqbEaIwSFQwxr76KMzGMh5se85SD1BZJGDVmvxfaAm5FXan4uNo46TUTkGJK6DLXrnwUMOuuBykCEpi1y6+85FmJ+ypsOUl9SLkZzXkMiIieTNTWAQYegmzIgRseZjZEqiqDZ9XZDLAsxcjXTQRoy/DEoLBykxooi1O140+0H6Z+JogBRFKzGSJIMSZLb1I7cwjacRa46D0tblqvOuzQXwDPfJ4VCbNNy8mzWPj9+tgTY8Hvg9+MkoEMXKGPizYYYFCI0TsittViI+SlRaDiAo7v1gqpzT7Mx2vPBqLsk1hOIooCoqJAWT8ZGo4TKyjqLxZgt7Wg1QahsS7KtFBgWCUFSQZ2VaTXOlWMDedr7FBWugiTJiIgIdtEWyZX4+ZItbDsvBaMGQER4MFTR5p8eNcW4+3ccCzE/Jfz+l8SarcdwpLLAbEy/qFqkXBLrCURRgEIh4pUPcnCu2Hz/ti6x4Xj6/mSIomC1EGupnb91M2CAwzJvmRDWHl3HLcWqT35AcXmt2ZjE+Ha44//+6rKxgTztfQoLDoAoClbzAYCBiR0xYVQfF2VFjmLL58vPlkRRgKwuw7tWzpUDOxmRAO/4HcdCzM8Vl9fi1HmD2WUxkmf2WTJUXYT2/CloS8wPA6GVwmCo6gZbhoE4V1yDU4XmC5p+kYq2pGkXZWQMjlSGWvxMVJ2ioIyMcXFWnvc+WcsHALp0DHNhNuRo1j5ffrZkego9RW/ld9RvDXcP8sslnDpv/ljylN9xLMTIq3jqMBBW53wDOO8bEZGD2PIUenJCR6SPucYrZhZgIUZexdOGgbB1zjeA874RETmStafQe6k6ueXugT1YiJFX8pRhIGyZ8w3gvG9ERGQeCzGiNmppzjeA874REZF5LMSI/FiLfdsUIgxiR9clRETkZ1iIEfmh1vRtUweoECaOc0FWRET+h4UYkR+ytW8bqi+gbsebCFbVAzDfJ4+IiOzHQozIT9nStw2cToaIyKlYiBEREZHLtNQ3VQgKh+hB8xs7GwsxImpRO6kCXRTmx20L1/OqGRG1zOa+qcpAhKYt8ptizOsKsezsbKxcuRK5ubmoq6tDXFwcUlNTkZGRgZCQlqe0cWSber0eq1evxqZNm1BQUIDAwEAkJiZi/PjxuPnmm+3dRXIRQ9VFxEgl0CrMT5XEAgMQg8IgBKgwQp+FEZZmMijjYLVE1DJb+qZKFUXQ7HobsqYGYCHmedasWYMFCxZAlmV06tQJnTt3xsmTJ5GZmYmsrCysXbsWUVFRLmlTq9XioYceQk5ODhQKBS6//HLU19fj+++/x/fff4+JEyfi6aefdsyOk8PZNFUSCwyI4R3Q9dGlePGdXThnYW5Pb5pKhIjcy6a+qX7GawqxI0eOYOHChQCAefPmIS0tDYIgoLi4GJMmTcLRo0cxa9YsLFu2zCVtvvzyy8jJyUGXLl3wzjvvoGfPngCAr7/+Gv/85z/xzjvvYODAgUhJSXHA3vsHSV3W8FeQNQ6as9HX5ipzJmVkDC6KHX1iKhF7We3TwnlEiagNvKYQW758OSRJwujRozF27NjG12NjY7FkyRKMHDkSWVlZOH78OBITE53aZmlpKT766CMAwIIFCxqLMAAYNmwY/v73v2P58uV44403WIjZSFKXoXb9s4BB12KsI69S+cpcZeQctvZp8fcrp0RkP68oxGpra/Htt98CANLS0potj4+Px+DBg7Fv3z5s27bNpkKsLW3u3LkTer0e3bt3x+DBg5ute++992L58uU4evQoCgoK0K1bN5v31V/JmhrAoEPQTRkQo+MsxnHORnIlW/q08JgkorbwikLs2LFj0Ol0CAwMRFJSktmY5ORk7Nu3D7m5uU5v89ChQ43LzYmNjUWXLl1w7tw5HDp0iIVYK4jRcVB0iLe4nHM2kqu11KeFxyQRtYUgy7Ls7iRasmHDBjz//POIj4/H9u3bzcZs2rQJzzzzDDp37ozdu3c7tc377rsPOTk5ePLJJ/HYY4+ZXfehhx7Cvn37MHnyZPzjH/9oMR9LZFmGJMkQBEAURUiSBId8YpIBkroC9cpw6IyC2ZBAhYxgQw3EkAhAVDhgo1YYDZDqayCGRUNQWP/7QBRFVNZoYbBwhcKmvCUjpLpqq/uvClQgPCTQ6raUChFR4SpIUsu3pFrK25btOSrGW/O2JcaRbdn6PjniPWLe3nucuDpvV36+rs5bNjb8bhKDwwFLvwscdP5u/F0RFg2Ijr0uJYoCBMF8bn/mFVfEqqoaLvdHRlp6vO2PZaZYZ7bZmnWrq6ttyscSQRCgUPzxYYqig4ZUUARCER0L893UL2XfkCCtFhAIRZDt24oKb2m6nZbbUqiCbdh/W7Zl++diS1uujPHWvG2JcWRbtrxPzNvzjgFfz9uVn6/L8hYbfje1xHHnbxf9jrPCKwZK0mq1AICAAMtve2BgYJNYZ7bZmnU1Go1N+RAREZH/8YpCTKVqqGj1er3FGJ1O1yTWmW22Zt2goCCb8iEiIiL/4xWFmC23HW25XeioNiMiImxe1xRLRERE9GdeUYjFx8cDAIqKiixehSooKGgS68w2TT//9ttvFttvbT5ERETkf7yiEOvTpw8CAgKg0+mQl5dnNiYnJwcA0L9/f6e3afr5p59+MrtecXExzp0716p8iIiIyP94RSEWGhqKoUOHAgDWr1/fbHl+fj6ys7MBAKmpqU5vc9iwYQgICGgScynTqPt9+vRB9+7dbcqHiIiI/I9XFGIAMHnyZAiCgI0bN2LdunUwDX9WUlKCadOmQZIkDB8+vNmo+uPGjUNKSgpWrVrlsDY7dOjQOCXSzJkzcfr06cZlO3fuxLvvvgsAePzxxx22/0REROR7vGJAV5NVq1Zh8eLFkGUZnTt3RnR0NE6ePAmdTocePXpg7dq1aNeuXZN1UlJSUFhYiClTpmDq1KkOaRNoGJYiPT0dBw8ehEKhwBVXXIG6urrGvmEPP/wwpk+f7pw3goiIiHyCVwzoapKeno6EhASsWLECeXl5KCsrQ1xcHFJTU5GRkYHQ0NZPM2Jvm0FBQXj//fexevVqbNq0Cfn5+QgICMCgQYMwfvx4jBgxoq27S0RERD7Oq66IEREREfkSr+kjRkRERORrWIgRERERuQkLMSIiIiI3YSFGRERE5CZe9dSkP8rOzsbKlSuRm5uLurq6Jk90hoSEuDs9chBZlnHw4EHs3LkTOTk5OH36NNRqNcLDw9GnTx+MHj0at912GwRBMLu+Xq9vfIK3oKAAgYGBSExMxPjx43HzzTe7eG/IWfbs2YOMjAwAwGWXXYadO3eajePx4B/27NmDDRs24NChQ6isrERERAS6deuGa665BlOnToVS2fRXPI8Lz8SnJj3YmjVrsGDBAsiyjE6dOqFdu3aNY5z16tULa9euRVRUlLvTJAfYv38/0tPTG3/u2rUrIiIiUFhYiMrKSgDAjTfeiGXLliEwMLDJulqtFg899BBycnKgUChw+eWXo76+vnFMu4kTJ+Lpp5921a6Qk6jVatx66604f/48AMuFGI8H32cwGPDss89i06ZNAIBOnTohJiYGlZWVuHDhAvR6PX766acmwy/xuPBgMnmkw4cPy4mJiXJCQoL80UcfyZIkybIsyxcuXJDvvPNOuXfv3vKUKVPcnCU5ynfffSenpKTIq1evlktLS5ss++yzz+R+/frJvXv3ll9++eVm686fP1/u3bu3nJKSIp86darx9R07djSu9/XXXzt9H8i5XnjhBbl3797y5MmT5d69e8s33XST2TgeD75v5syZcu/eveXbb79dzs3NbbKsrq5O3rFjh6zT6Zq8zuPCc7EQ81CTJk2Se/fuLf/rX/9qtuzMmTNyYmKi3Lt3b/nYsWNuyI4craamptmJ81KZmZly79695UGDBslGo7Hx9YsXL8p9+/aVe/fuLe/fv7/Zeq+99prcu3dv+c4773RK3uQaP/74o5yQkCA//vjj8ieffGKxEOPx4Pv2798v9+7dWx46dKhcUVFh0zo8LjwbO+t7oNraWnz77bcAgLS0tGbL4+PjMXjwYADAtm3bXJobOUdYWBgCAgIsLr/++usBAJWVlSgvL298fefOndDr9ejevXvjMXGpe++9FwBw9OjRxlsQ5F20Wi2ef/55hISEYNasWVZjeTz4PtO8yY888ojNXVN4XHg2FmIe6NixY9DpdAgMDERSUpLZmOTkZABAbm6uK1MjN9FqtY3/HxQU1Pj/hw4dAvDH8fBnsbGx6NKlS5NY8i7//e9/cebMGUybNg2xsbFWY3k8+DatVou9e/cCAIYNG4a8vDzMmTMHDz30EB577DG88cYbuHDhQrP1eFx4NhZiHujMmTMAgLi4OItXSbp169Yklnzbl19+CQBITExEWFhY4+v5+fkAgO7du1tcl8eK9zp27Bjee+89JCUl4b777msxnseDbzt+/Dj0ej1CQkKwfft2jB07Fh9++CH27duHXbt2YdmyZRgxYgS2bt3aZD0eF56NhZgHqqqqAgBERkZajDEtM8WS7zp69Cg++ugjAGgcusCkNcdKdXW1kzIkZzAajZg5cyYAYP78+RDFlk/XPB5828WLFwEAOp0OL7/8MgYMGIBPP/0Uhw8fxvbt25GamgqNRoNnnnkGx48fb1yPx4VnYyHmgUy3oaz1GTINYXDpLSvyPaWlpZgyZQr0ej3+7//+D7fcckuT5a05VjQajfMSJYd77733cPToUaSnpyMxMdGmdXg8+Lba2loADcNXREdH4+2330bfvn0RGBiI+Ph4/Oc//8GVV14JvV6PzMzMxvV4XHg2FmIeSKVSAWgYfM8SnU7XJJZ8T01NDSZOnIiioiL07dsXixcvbhbTmmPl0r5l5Nny8/PxxhtvoEuXLpgyZYrN6/F48G2Xnu/Hjh3bpJsCAIii2Dge4d69eyFJUpP1eFx4JhZiHsiW2462XGom71VbW4u///3v+Pnnn3HFFVfgvffea3bSBYCIiAgAth0rpljyfC+88AK0Wi3mzJmD4OBgm9fj8eDbLj3f9+zZ02yM6XW1Wt04GDSPC8/GKY48UHx8PACgqKgIer3e7OVk0yPGpljyHfX19Xj00Udx6NAhxMfHY+XKlYiOjjYbGx8fj59++gm//fabxfZ4rHifo0ePQhAEzJgxo9ky062j8+fP47rrrgMALFu2DAMHDuTx4OMuLb4s3Q259HXTFTEeF56NV8Q8UJ8+fRAQEACdToe8vDyzMTk5OQCA/v37uzAzcjatVovJkyfjxx9/xGWXXYbVq1cjJibGYrzp8//pp5/MLi8uLsa5c+eaxJJ3kGUZpaWlzf6p1WoADb9kTa+ZbjnxePBtsbGxuOyyywDA4nhfZ8+eBdDQ58s0zhiPC8/GQswDhYaGYujQoQCA9evXN1uen5+P7OxsAEBqaqpLcyPn0ev1mDp1Kvbt24dOnTph9erV6NSpk9V1hg0bhoCAgCbHxKVMT1v26dPH6qPr5FkOHDiAX375xey/RYsWAWiYa9L02jXXXAOAx4M/GDlyJADg888/b7zidamPP/4YADBo0KDGSb95XHg2FmIeavLkyRAEARs3bsS6desg/z43e0lJCaZNmwZJkjB8+HCbn6Yiz2Y0GvH0009jz549iImJwerVq9G1a9cW1+vQoQPGjh0LAJg5cyZOnz7duGznzp149913AQCPP/64cxInj8Ljwfc98sgjCA8Px6lTp7Bw4cLGTvayLGP16tXYtWsXBEFoMtQNjwvPJsim3/DkcVatWoXFixdDlmV07twZ0dHROHnyJHQ6HXr06IG1a9eiXbt27k6THOCLL77AU089BaDhSoe1EdRnzZqFPn36NP6s0WiQnp6OgwcPQqFQ4IorrkBdXV3jrYuHH34Y06dPd+4OkMt8+umnePbZZ3HZZZdh586dzZbzePB9+/btw6RJk6DRaBAZGYnu3bvj/PnzuHjxIgRBwDPPPINHHnmkyTo8LjwXO+t7sPT0dCQkJGDFihXIy8tDWVkZ4uLikJqaioyMDISGhro7RXIQ01+1AFBYWIjCwkKLsTU1NU1+DgoKwvvvv4/Vq1dj06ZNyM/PR0BAAAYNGoTx48djxIgRTsubPA+PB9937bXXYuPGjXjrrbewb98+HDt2DGFhYUhJScFDDz2EQYMGNVuHx4Xn4hUxIiIiIjdhHzEiIiIiN2EhRkREROQmLMSIiIiI3ISFGBEREZGbsBAjIiIichMWYkRERERuwkKMiIiIyE1YiBERERG5CQsxIiIiIjdhIUZE5GIzZsxAQkICZsyY4e5UiMjNWIgRERERuQkLMSIiIiI3YSFGRERE5CYsxIiIiIjchIUYEfmlsrIy9O3bFwkJCfj666+txr722mtISEjA//3f/zW+VlRUhA8++AAZGRkYMWIE+vfvjwEDBmDUqFFYsGABioqK7MorJSUFCQkJ+PTTTy3G2NLZv6CgAPPnz8fIkSMxYMAA/PWvf8XIkSPblBsROR4LMSLyS+3bt8fQoUMBABs3brQYJ8syNm/eDAC44447Gl+fPn065s2bhz179iA/Px9KpRIajQanTp3C+++/j9tvvx0HDhxw7k5YsH79eowaNQr/+9//cPr0aRgMBgDA6dOn8f777+O2227Dd99955bciKgpFmJE5LdMhdWuXbtQXV1tNiYnJwfnzp1rEg8AV1xxBZ566ils2bIFubm5OHDgAA4fPowNGzbgb3/7G2pqavDkk09Co9E4f0cusWPHDsyaNQsAkJGRgZ07dyIvLw+HDh3C1q1bkZqaCrVajSeeeIJXxog8AAsxIvJbw4YNQ3h4OHQ6HbZu3Wo2ZtOmTQCA5ORkdO3atfH12bNnIyMjA7169UJQUBAAQKlUIikpCW+99RYSEhJQUlKC7du3O39HfqfT6TBv3jwAwJw5c/DUU0/hsssugyAIEAQBPXv2xNKlS5GSkgK1Wo2VK1e6LDciMo+FGBH5LZVKhdTUVADmb09eWqBdejWsJQqFAn/7298ANFxRc5VvvvkGxcXF6NChA+6++26LcaNHjwYA7N2710WZEZElSncnQETkTqNHj8aGDRvw008/4ezZs02uepluWQYGBmLkyJHN1j1w4AA+/vhjHDp0CMXFxairq2sWU1xc7NT8L2Uq+qqqqhr7v5mj1+sBgLcmiTwACzEi8mvJycno0qULzp07h02bNuHxxx9vXGa6SpaSkoKIiIgm67388st49913G39WKBSIjIxEQEAAAKCurq7xn6uUlJQAaCi0SktLW4x3df81ImqOhRgR+TVBEHD77bdj+fLlTQqxiooKfPPNNwD+uJVn8t133zUWYffddx/GjRuHXr16QaFQNMa89tpryMzMdM1O/E6SJADA3/72tyZFIhF5LvYRIyK/Zyq08vPzcejQIQDAli1boNfr0a5du8b+XiZffvklAGDo0KF44YUX0Lt37yZFGACbrkiZY2pHq9VajKmpqTH7eocOHQAAJ06csGvbROR6LMSIyO91794dAwYMAPDH7UjT05K33HILlMqmNw8uXLgAAOjTp4/Z9mRZRnZ2tl25mG6BmrbxZ5Ik4ciRI2aXDRw4EEBDvzR3jWFGRK3DQoyICH88FbllyxacPHmy8crYn29LAkBYWBgA4Pjx42bb+vDDD3H27Fm78khMTAQAfPXVV5Bludnyzz77zGKRlpKSgpiYGADAwoULUV9fb3VblZWVduVIRI7DQoyICMCoUaMQEBCAyspKTJ8+HQDQq1cv9OvXr1ms6VblN998g//+97+NHfKrq6vx5ptv4t///jeioqLsyuPWW28FAJw6dQqzZs1CRUUFAECtVmPVqlV44YUXLLatUqkwZ84cCIKAo0ePYty4cfj222+h0+kaY86ePYuPPvoIY8aMwdq1a+3KkYgch531iYgAREZG4qabbkJWVlbjrT9zV8NMr3/++ec4cOAAXn/9dSxbtgwRERGoqamBJEm48cYbceWVV9rVWX/IkCGN7W/YsAEbNmxAREQE1Go1JEnC+PHjUVtbi88++8zs+sOHD8dLL72E2bNn49ixY/j73/8OpVKJsLAw1NXVNSnKhg0b1ur8iMixeEWMiOh3lw7aKooibr/9drNxAQEBWLFiBaZMmYL4+HgolUrIsoykpCTMmTMHmZmZzTrvt8bChQsxc+ZMXHnllQgKCoIkSRg4cCD+85//NE5fZM3tt9+OrKwsTJo0Cf369UNISAhqamqgUqlw5ZVXYvz48Vi1ahUmTpxod45E5BiCbK4TAhERERE5Ha+IEREREbkJCzEiIiIiN2EhRkREROQmLMSIiIiI3ISFGBEREZGbsBAjIiIichMWYkRERERuwkKMiIiIyE1YiBERERG5CQsxIiIiIjdhIUZERETkJizEiIiIiNyEhRgRERGRm7AQIyIiInKT/weEnquRGd/BigAAAABJRU5ErkJggg==", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create a generator of random variables from the empirical samples\n", + "hist = np.histogram(samples, bins=100)\n", + "emp_rv = stt.rv_histogram(hist)\n", + "\n", + "# generate surrogate samples\n", + "surr_samples = emp_rv.rvs(size=100000)\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples, bins=vx, density=True, label='orig')\n", + "plt.hist(surr_samples, bins=vx, histtype='step', density=True, label='surr')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/DESU_distributions_corrected.ipynb b/DESU_distributions_corrected.ipynb new file mode 100644 index 0000000..5a2e283 --- /dev/null +++ b/DESU_distributions_corrected.ipynb @@ -0,0 +1,1353 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 10, + "id": "046cefd5-f821-4613-8660-b5e296eb5a88", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import scipy.stats as stt\n", + "import pandas as pd\n", + "\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import seaborn as sb\n", + "\n", + "sb.set_style('whitegrid')\n", + "sb.set(font_scale=1.5)\n", + "\n", + "# check help on package\n", + "#help(stt)" + ] + }, + { + "cell_type": "markdown", + "id": "ed78ded5-0cd8-4b61-9866-c3b804ffcf9b", + "metadata": {}, + "source": [ + "## Random Samples\n", + "\n", + "Let's first randomly generate samples from a given distribution (normal or Gaussian, centered in zero with unit variance), then calculate summary statistics on these samples." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "cf7ba0e0-4068-42e7-8b5a-a871e9629e87", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "#number of samples\n", + "n = 1000\n", + "\n", + "# generate random samples\n", + "samples = stt.norm.rvs(size=n)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "ac6fd30c-8c07-48fa-859b-02b8b6e7b11a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# variable range\n", + "vx = np.linspace(-3.0,3.0,50)\n", + "dx = np.diff(vx)[0]\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples, bins=vx)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx, stt.norm.pdf(x=vx)*n*dx)\n", + "\n", + "# show percentiles from samples, top and bottom 5%\n", + "if False:\n", + " top_lim = stt.scoreatpercentile(samples, 95.0)\n", + " bottom_lim = stt.scoreatpercentile(samples, 5.0)\n", + " l = max(stt.norm.pdf(x=vx)*n*dx)\n", + " plt.plot([top_lim]*2, [0,l], ls='--', c='gray')\n", + " plt.plot([bottom_lim]*2, [0,l], ls='--', c='gray')\n", + "\n", + "# show percentiles from samples, top and bottom 5%\n", + "if False:\n", + " top_lim_th = stt.norm.isf(0.05)\n", + " bottom_lim_th = stt.norm.isf(0.95)\n", + " l = max(stt.norm.pdf(x=vx)*n*dx)\n", + " plt.plot([top_lim_th]*2, [0,l], ls='--', c='k')\n", + " plt.plot([bottom_lim_th]*2, [0,l], ls='--', c='k')\n", + " \n", + "plt.tight_layout()\n", + "#plt.savefig('figs/ex_hist_norm_perc_th_n100000.png')" + ] + }, + { + "cell_type": "markdown", + "id": "1bfdb6a3-c880-41fa-9056-a2696ace2a9f", + "metadata": {}, + "source": [ + "With the cumulative density function" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "7c0a36c0-59a3-42ec-aec1-bb84e7d92bdc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(samples, bins=vx, cumulative=True)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx, stt.norm.cdf(x=vx)*n)\n", + "\n", + "# show percentiles, top and bottom 5%\n", + "top_lim = stt.norm.isf(0.05)\n", + "bottom_lim = stt.norm.isf(0.95)\n", + "plt.plot([top_lim]*2, [0,n], '--k')\n", + "plt.plot([bottom_lim]*2, [0,n], '--k')\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "id": "304a427a-c94b-4995-a24e-ff26c4f8b07f", + "metadata": {}, + "source": [ + "In this way, we can find boundaries for the probability of finding a random samples that follow the concerned distribution. This leads to the notion of statistical testing, which we will see in detail later." + ] + }, + { + "cell_type": "markdown", + "id": "b5be9b02-17d6-4407-aa71-53a31a6b224c", + "metadata": {}, + "source": [ + "## Summary statistics\n", + "\n", + "Let's now look at the summary statistics of the $n$ samples:\n", + "- mean: $\\mu = E[X] = \\frac{1}{n} \\sum_i x_i$\n", + "- variance: $\\sigma^2 = E[(X-\\mu)^2] \\simeq \\frac{1}{n-1} \\sum_i (x_i - \\mu)^2$\n", + "\n", + "Here $\\sigma$ is the standard deviation, whose square is the variance. Note that the denominator of the sample variance is $n-1$ and not $n$, to correct a bias.\n", + "\n", + "The skew and kurtosis measure deviations from normality:\n", + "- skew: $E[\\frac{(X-\\mu)^3}{\\sigma^3}] = \\frac{m_3}{\\sigma^3}$\n", + "- kurtosis: $E[\\frac{(X-\\mu)^4}{\\sigma^4}] = \\frac{m_4}{\\sigma^4}$\n", + "\n", + "They also correspond to standardized moments, including a normalization by $\\sigma$.\n", + "\n", + "In the previous definitions, we see some powers of the demeaned variables. This is generalized by moments, which have several variations. In scipy.stats they correspond by default to the central moments of samples (without removing the bias)\n", + "$$ m_k = \\frac{1}{n} \\sum_{i = 1}^n (x_i - \\bar{x})^k $$\n", + "where $\\bar{x} = \\mu$ is the mean. Note that this convention implies that the first centralized moment is 0.0.\n", + "\n", + "Scipy.stats has a large range of summary statistics ([link](https://docs.scipy.org/doc/scipy/reference/stats.html#summary-statistics)). For further details, check also the moment generation function and cumulants." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "9fa8b512-f6ba-4396-a0a3-9cc54646f6cc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean:\t\t 0.024246059522653948\n", + "variance:\t 1.0090602557851374\n", + "skew:\t\t -0.05750931258530448\n", + "kurtosis:\t -0.20065505984460552\n" + ] + } + ], + "source": [ + "print('mean:\\t\\t', np.mean(samples))\n", + "print('variance:\\t', np.var(samples))\n", + "print('skew:\\t\\t', stt.skew(samples))\n", + "print('kurtosis:\\t', stt.kurtosis(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "5812c419-861a-4733-97ff-e532deb2c3eb", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "central moments:\n", + "order 1: 0.0\n", + "order 2: 1.0090602557851374\n", + "order 3: -0.05829265385840662\n", + "order 4: 2.850300295817662\n" + ] + } + ], + "source": [ + "print('central moments:')\n", + "for k in range(1,5):\n", + " print('order {0}:'.format(k), stt.moment(samples, moment=k))" + ] + }, + { + "cell_type": "markdown", + "id": "b6579e85-c7c4-47bf-81fd-24c94a104771", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Change the `loc` and `scale` parameters (see the doc of `norm`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm))" + ] + }, + { + "cell_type": "markdown", + "id": "1133965f-51e0-490e-984e-c917b4ef6583", + "metadata": {}, + "source": [ + "Let's not w try with another type of distribution, like lognormal (`lognorm`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html#scipy.stats.lognorm)). There is a shape argument $s$, so let's see its effect." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "53914dd6-b0ee-43ad-80b3-9533367d28d5", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean:\t\t 1.0029206619333029\n", + "variance:\t 0.010281620586461631\n", + "skew:\t\t 0.32174326148243954\n", + "kurtosis:\t 0.5768071883838695\n" + ] + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl4AAAG+CAYAAABCjQqZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABguElEQVR4nO3dd5xU9b3/8deZ2Z3tjS4sJShFQKKAvcSAUWJJEFtsRLmgASUPr5qY/IwCyTV6Y4kKF00sgEaEoBiNCDasIEQQlCoKLAuLIAhbZ3ennPP7Y5lh1y3MTi/v5+PBw92ZUz5zOKzv/X6/5/s1LMuyEBEREZGIs8W6ABEREZFUoeAlIiIiEiUKXiIiIiJRouAlIiIiEiUKXiIiIiJRouAlIiIiEiUKXiIiIiJRouAlIiIiEiUKXiIiIiJRkhbrAgQsy8I0w7+AgM1mROS4yUrXq310vQKna9U+ul7to+sVuEhdK5vNwDCMgLZV8IoDpmlx8GBNWI+ZlmajqCiHykonHo8Z1mMnI12v9tH1CpyuVfvoerWPrlfgInmtOnTIwW4PLHipq1FEREQkShS8RERERKIkIboaLcti7dq1LFu2jDVr1rB9+3aqq6vJy8tj0KBBjBkzhksuuaTF/tWRI0dSVlbW5vG/+OILMjIyWnxv165dzJo1i+XLl3Pw4EE6duzImWeeyaRJk+jZs2dYPp+IiIikhoQIXitXruSGG27wf9+zZ0969OhBWVkZy5cvZ/ny5SxevJgZM2bgcDhaPEb//v3Jzc1t8b3WBsStXbuW8ePH43Q6KSgooH///uzatYuXX36ZpUuXMmfOHIYOHRry5xMREZHUkBDBy7IsiouL+eUvf8lFF11Ex44d/e/961//4p577uH999/n8ccf584772zxGH/4wx849dRTAz5nbW0tU6ZMwel0ctlllzF16lQyMjKor69n2rRpLFq0iClTpvDmm2+SmZkZ8mcUERGR5JcQY7yGDh3K0qVLGTduXJPQBTBmzBhuueUWABYuXIhphudJhQULFrB//3569+7NtGnT/F2RGRkZTJ8+nV69erF3714WLlwYlvOJiIhI8kuI4JWbm0t6enqr759zzjkAlJeXc/DgwbCcc+nSpQBceumlzbovHQ4HY8eOBWDJkiVhOZ+IiIgkv4Toajya+vp6/9etdfvNnz+fZ599lrq6Ojp16sSIESO45JJLWhz35fV62bBhAwAjRoxo8Xi+19evX4/X68Vut4f6MURERCTJJUXwWrx4MQADBw5sdQD9G2+80eT7119/nccee4yHH36YM888s8l7ZWVluN1uAHr16tXi8Xyvu1wu9uzZoyccRURE5KgSPnht3LiR+fPnA3DTTTc1e/+kk07iV7/6FcOHD6d79+643W7WrFnD448/zqZNm5g0aRIvvvgigwcP9u9TXl7u/7qwsLDF8xYUFPi/rqioCDl4paWFt9fXbrc1+a+0TderfXS9Aqdr1T66Xu2j6xW4eLlWhmVZCbvA04EDB7jiiivYs2cPP/nJT5g5c2bA+9bV1XHNNdewceNGzjjjDGbPnu1/b/Xq1Vx77bUAbN68GZut+V+SaZocf/zxALzwwgutdkkGwrKsgNd4EhERkcSVsC1eVVVVTJw4kT179jB48GAeeOCBdu2fmZnJbbfdxsSJE1m5ciWVlZXk5+cDNBlM73a7W5xc1eVyNTlWKEzTorLSGdIxvs9ut5Gfn0VlZS1er9bvOhpdr/bR9QqcrlX76Hq1j65X4CJ5rfLzswJuSUvI4FVTU8OECRPYtGkT/fr145lnnml1bFdbhg0bBjS0XpWWljJkyBCgaTdieXk5Xbt2bbZvRUWF/+vG2wcrUouber2mFk5tB12v9tH1CpyuVfvoerWPrlfgYn2tEq5TuLa2lptvvpl169bRp08fZs+eTVFRUVDHajxFhdfr9X/do0cP/3ulpaUt7ut73eFw0L1796DOLyIiIqkloYJXfX09kydP5tNPP6VHjx7MnTuXzp07B328rVu3+r9u3KqVlpbmb/1avXp1i/v6Xj/hhBM0lYQkPJvNIC3NdtQ/NpvGIoqIhCJhgpfb7WbKlCmsWLGCbt26MXfuXLp16xbSMZ9++mkAjjvuuGbHuuCCCwB45ZVX/FNL+LhcLhYtWgTA6NGjQ6pBJNZsNoPCwmyKinKO+qewMFvhS0QkBAkxxsvr9XLnnXfywQcf0LlzZ+bOnRvQ9A3PPPMMDoeDiy++uEl35KFDh/jrX//qn51+ypQpzfa96qqreOaZZ9i5cydTp05ttlZjaWkpXbp04YorrgjfBxWJAZvNwG638dALa9i9r6rljSyLfp0sJo87V8FLRCQECRG8lixZ4g9JDoeD3//+961ue8899zBo0CAA9u7dy3PPPcd9991Hjx496NChA3V1dWzfvh2Px4PNZuP2229vsdUqOzubxx57jAkTJvDyyy/zzjvvUFxczO7du6moqCA7O5sZM2aQlZUVmQ8tEmW791Wxrayixfd+mL6Tn9Z9QMXKSuyDL/C/3tJTPKZpYZoJO0uNiEhEJUTwajx1Q1lZGWVlZa1uW1V15Df2iy66CMuyWL9+PXv27GHLli3Y7XaKi4s55ZRTuOaaa/xzcbVk+PDhvPrqq8yaNYvly5ezdetWioqKGDt2LJMnT9Zs9ZIyjk3fB0D1puUUnz7G/3p+fvNfPLxek/Jyp8KXiEgLEiJ4jR071r8odXuceOKJnHjiiSGdu1evXu2eI0wk2RTaGuaZc+0r4dHnV1Cy39XidsVd87jz2uHYbIaCl4hICxIieIlIbBXZahq+sEysvV+xbW9hTOsREUlUCfNUo4jETqEveAHdzda7+kVEpG0KXiLSJjte8m11/u97mHtiWI2ISGJT8BKRNhXYmq4j2tXcRzqeGFUjIpLYFLxEpE1Fh4NXdVoh9twO2DHpnXYgxlWJiCQmBS8RaZNvfFetPZ/MXg3Trxybti+WJYmIJCwFLxFpk++JRmdaPlm9GiYn9s3rJSIi7aPgJSJt8o3xamjxaghefdIOYMOMZVkiIglJwUtE2uRr8apNyyO9UzG1ZJJheOhp/y7GlYmIJB4FLxFpU2GjFi/DsLHH1h1Qd6OISDAUvESkTY1bvADK7IeDV9q3MatJRCRRKXiJSKvS8ZBrqwfAac8HoMzWA4C+afswNM5LRKRdFLxEpFW+bsZ6Kw23LROAA0Yn6qw0sm1ujrGXx7A6EZHEo+AlIq3yPdFYbmaDYQBgGTZ2uLsAms9LRKS9FLxEpFW+8V3lZk6T17d5ugJwbLrGeYmItIeCl4i0qtAfvLKbvL7N09DidVzaPsCKdlkiIglLwUtEWuVbp/HQ91q8dno64bZs5Nnq6GKrjEVpIiIJScFLRFrVWouXFzslns6A5vMSEWkPBS8RaVVhKy1e0Gicl+bzEhEJmIKXiLSqsJXB9QDbDj/Z2FdPNoqIBEzBS0Ra5MBNjs0FNO9qBCjxdMZrGXS011Bkq452eSIiCUnBS0Ra5OtmrLPSqbMczd53kc4ub0dA3Y0iIoFS8BKRFvnm8Drkbd7a5bPN7Rvnpe5GEZFAKHiJSIvaGt/l45vPS082iogERsFLRFp05InG1lu8tnu6YFrQ1V5JnlEbrdJERBKWgpeItCiQFq9aK4NvvEUA9NU4LxGRo1LwEpEWFTVeILsN6m4UEQmcgpeItCiQFi/QAHsRkfZQ8BKRFhXZW5+1vjHfDPbd7YfIsOoiXpeISCJT8BKRZjINF5mGGzh6V2OVlcU+bz42A44xv4lGeSIiCUvBS0Sa8T3RWGM6cJF+1O19ywf1MPdEtC4RkUSn4CUizfjGd1UcpbXLx9/d6FXwEhFpi4KXiDTjn7X+KOO7fHzBq4v1LaZL47xERFqj4CUizRT6p5IILHgdMnM56M3Bjkl92dZIliYiktAUvESkmSMtXoF1NULDLPYAtaWbIlKTiEgyUPASkWba2+IF8PXh7sY6BS8RkVYpeIlIM0cmTw28xWuXpyMA7u/KIlKTiEgyUPASke+xgmrxqjSzAPDWVmFZZkQqExFJdApeItJEtuEiw/AA7WvxqrEyGr4wvVj1zkiUJiKS8BS8RKQJXzdjtZmBm7SA9/Nip46G8GXVVkakNhGRRKfgJSJNFNkCW6OxJbVGQ3ejqeAlItIiBS8RaSKYgfU+vuBl1VaFtSYRkWSh4CUiTQQzsN7HiS94qcVLRKQlCl4i0kRoLV4N+6irUUSkZQpeItJEe9dpbExdjSIibVPwEpEmQupq1OB6EZE2KXiJSCOWv6uxPes0+tRqjJeISJsUvETEL8eoJ91omHW+IoSnGk11NYqItEjBS0T8fOO7Ks1MvNjbvb/z8OB6tXiJiLRMwUtE/I480dj+8V3QaHB9XTWW6Q1bXSIiyULBS0T8Qpm1HqCOTMAALKy66vAVJiKSJAJfiC2GLMti7dq1LFu2jDVr1rB9+3aqq6vJy8tj0KBBjBkzhksuuQTDMFrc3+12M3fuXF577TVKS0txOBwMHDiQ6667jvPPP7/Nc+/atYtZs2axfPlyDh48SMeOHTnzzDOZNGkSPXv2jMTHFYmZUObwArAMG7bsPExnJVZdFWQXhLM8EZGElxDBa+XKldxwww3+73v27EmPHj0oKytj+fLlLF++nMWLFzNjxgwcDkeTfevr67nxxhtZs2YNdrud4447jtraWlatWsWqVauYOHEid955Z4vnXbt2LePHj8fpdFJQUED//v3ZtWsXL7/8MkuXLmXOnDkMHTo0kh9dJKqOTCURXPACsGfnNwQvjfMSEWkmIboaLcuiuLiYu+++mxUrVvDOO++waNEiVq1axf/+7//icDh4//33efzxx5vt++CDD7JmzRqKi4t5/fXXee2113j77beZNWsWDoeDp556imXLljXbr7a2lilTpuB0Ornsssv46KOPWLRoER9//DFjx46lpqaGKVOmUFdXF41LIBIVhSFMnupjz2lo5VLwEhFpLiGC19ChQ1m6dCnjxo2jY8eOTd4bM2YMt9xyCwALFy7ENE3/ewcOHGD+/PkA3HffffTt29f/3qhRo5gwYQIAM2fObHbOBQsWsH//fnr37s20adPIyMgAICMjg+nTp9OrVy/27t3LwoULw/thRWKoKITJU33s2fkADV2NIiLSREIEr9zcXNLT01t9/5xzzgGgvLycgwcP+l9ftmwZbreb3r17c9pppzXb7xe/+AUAGzdupLS0tMl7S5cuBeDSSy9t1n3pcDgYO3YsAEuWLAniE4nEIcuiICxdjWrxEhFpTUIEr6Opr6/3f52Zmen/et26dQAMHz68xf26du1KcXFxk20BvF4vGzZsAGDEiBEt7ut7ff369Xi9emxeEl82TtIME9Mygpo81edIV6NavEREvi8pgtfixYsBGDhwILm5uf7XS0pKAOjdu3er+/bq1QuAHTt2+F8rKyvD7XY3eb+1/VwuF3v27Am+eJE4kWs1TP9QaWVhhvCjQV2NIiKtS4inGtuyceNG/zium266qcl7FRUVABQUtP5Iu++9ysoj3SLl5eX+rwsLC9vcz3eeUKeWSEsLbwa2221N/ittS+Xr5fvMeVZDUAqlmxHA5mvxqqsM+32diFL53gqGrlf76HoFLl6uVUIHrwMHDnDrrbfidrv5yU9+wkUXXdTkfV8XZFvjw3zjtxo/nehyufxft7Zv43FfoT7ZaLMZFBUFP5i5Lfn5WRE5brJK5evla/EK5YlGODLGy+aqjth9nYhS+d4Khq5X++h6BS7W1yphg1dVVRUTJ05kz549DB48mAceeKDZNr4nEX3dhi3xhazGY8Mahyq32+0/Tkv7fX/fYJimRWWlM6RjfJ/dbiM/P4vKylq8XvPoO6S4VL5evs+edzh4hdri5etq9NRUcOhQTcj1JbpUvreCoevVPrpegYvktcrPzwq4JS0hg1dNTQ0TJkxg06ZN9OvXj2eeeabJ2C6f/PyG/wH4uhxb4nvPty007UYsLy+na9eure73/e2D5fFE5h+M12tG7NjJKJWvV66vq9EbYouXr6ux3om73oVhT8gfM2GXyvdWMHS92kfXK3CxvlYJ1ylcW1vLzTffzLp16+jTpw+zZ8+mqKioxW379OkDwM6dO1s9nm8aCd+2AD169PB3MX5/monv7+dwOOjevXt7P4ZI3MkLU1ejLTMHbHZAA+xFRL4voYJXfX09kydP5tNPP6VHjx7MnTuXzp07t7r9iSeeCMBnn33W4vv79u1j9+7dTbYFSEtLY8iQIQCsXr26xX19r59wwgnY7fb2fhSRuJMbpq5Gw7BhZOYBmstLROT7EiZ4ud1upkyZwooVK+jWrRtz586lW7dube4zatQo0tPTKSkpYeXKlc3e9z0NOWjQoGZTTlxwwQUAvPLKK83GiLlcLhYtWgTA6NGjg/5MIvHCMr3kWL4FskMfEG/LOhy81OIlItJEQgQvr9fLnXfeyQcffEDnzp2ZO3duQNM3dOrUiauuugqAu+++m+3bt/vfW7ZsGU8//TSAf8mhxq666io6d+7Mzp07mTp1qv8Jyfr6eqZOnUppaSldunThiiuuCMdHFIkpb3U5Niy8lkGlFdrDIgBG1uG5vNTiJSLSREKMel2yZIl/CR+Hw8Hvf//7Vre95557GDRokP/73/zmN2zcuJG1a9dy8cUX069fP5xOp3+M1vjx4znvvPOaHSc7O5vHHnuMCRMm8PLLL/POO+9QXFzM7t27qaioIDs7mxkzZpCVpUd4JfF5Kg8AUGFmY4Xh9zGbgpeISIsSIng1nrqhrKyMsrKyVretqmratZGZmclzzz3H3Llzee211ygpKSE9PZ1TTjmF6667zt+l2JLhw4fz6quvMmvWLJYvX87WrVspKipi7NixTJ48OeRJU0XihS94hTq+y8dQV6OISIsSIniNHTvWvyh1MBwOBxMnTmTixInt3rdXr14tzhEmkkw8Vd8B4RnfBepqFBFpTUKM8RKRyPJUNgSvQ2Fq8fJ1NZoKXiIiTSh4iQhef1djuFq81NUoItISBS8R8bd4hSt4HRlcr+AlItKYgpeI+AfXh6urUWO8RERapuAlkuIsrwdvdTkQ/hYvPPVYnvqwHFNEJBkoeImkONNZDlh4sVEdhslTAUjPhMOLY6u7UUTkiKCD18CBAzn77LMD3n7kyJFNJjYVkfhgVTeM76o2crEwwnJMwzAwMtXdKCLyfSG1eFmWFdHtRSTyzOqDQEPwCif/OK86BS8REZ+odTW63W5sNvVsisQbX/CqMvLCelz/lBLqahQR8YtKEqqsrOTgwYPk5YX3B7uIhM5s1NUYTr6uRlPBS0TEL+Alg7Zs2cKWLVuavFZfX8+//vWvVvexLIvKykrefPNNTNNk8ODBQRcqIpFhVh8CItHV6JtEVV2NIiI+AQevd955h//7v/9r8lp1dTW///3vj7qvZVkYhsENN9zQ7gJFJLIanmqEGiM8c3j5HBlcrxYvERGfgINXXl4exxxzjP/7PXv2YLPZ6Nq1a6v72Gw2cnNz6devH1dddRUjRowIrVoRCTur3glAHWGaSuIwm1q8RESaCTh4/fKXv+SXv/yl//uBAwdSVFTEsmXLIlKYiESHVV8NQJ0R3uCl2etFRJoLOHh936233kp2dni7JkQkuizL8rd41ZMBmGE7tpGppxpFRL4vpOAlIgnOUw+mF4B6IwOoDduhG8/j5RvnKSKS6jSxlkgKs+prGr6wpeEmPazH9j3ViNcD7rqwHltEJFEF3eLlU1paypIlS/jyyy+pqKjA7Xa3uq1hGMydOzfUU4pImPiClz0rB8zwtkgZaRkNaza667BqKzEcWWE9vohIIgopeM2cOZMnnngC0zQDWg5IXQ0i8cUXvGyZOeAM//GNzDwsdx1WXRUUtP4EtIhIqgg6eL322mvMnDkTgC5dunDWWWfRpUsX0tJCbkQTkSjxDay3ZeZFJnhl5WFV7cesrcQe/sOLiCScoFPSvHnzABg5ciSPPvooDocjbEWJSHT4ppKwZeZE5PhHJlHVlBIiIhDC4PqtW7diGAZTp05V6BJJVIdbvOxZ4V0uyOfIJKqaUkJEBEIIXoZhkJub2+bM9SIS346M8YpM8NIkqiIiTQUdvPr27UttbS0ulyuc9YhIFDUZXB8BWq9RRKSpoIPXFVdcgcfjYcmSJeGsR0Si6Mh0EpFq8dJ6jSIijQUdvK688kpGjhzJfffdx6effhrOmkQkSiyX76nGCLV4ZanFS0SksaCfapw5cyYDBw5kzZo1jBs3jmHDhjF06FByctr+Aa6lhkTiR9MxXjVhP/6R9RrV4iUiAiEGL9+EqJZlsWbNGj777LOj7qfgJRI/mnY1RiB4+ddrrMKyTAxDq5SJSGoLOnidfPLJ4axDRGIg8oPrD6/XaJkNU1dE6OlJEZFEEXTwev7558NZh4hEmeULQxyeuT4CDHsaOLLB5cSsq8Su4CUiKU7t/iKpylULNKyxasuKTIsXaIC9iEhjCl4iKcq3TiP2dGxpkVt9wqYB9iIifgpeIinKN77LiHD3X+MB9iIiqS7oMV7jxo1r9z6GYTB37txgTykiYeQPXhnZET2PfxJVtXiJiAQfvP7zn/8EtF3jKSd8X4tI7Fmuw080ZkRufBc0nstLLV4iIkEHr6PNx1VVVcXnn3/OunXrKCws5Oqrr8Zutwd7OhEJM98YLyPSwcvf1agWLxGRiAUvn08++YQpU6awbds2Hn/88WBPJyJhZtVXA1EMXupqFBGJ/OD6008/nbvvvpu3336bhQsXRvp0IhKoaLV4qatRRMQvKk81XnjhhdjtdgUvkThy5KnGaHU1KniJiEQleGVkZJCVlcW2bduicToRCcCRpxqjFbyqsUxvRM8lIhLvohK89u3bR1VVFZZlReN0IhKAqAWvjFzAACysuuqInktEJN5FPHjV1dUxbdo0APr37x/p04lIgHxPNUZ8OgmbzT9Jq7obRSTVBf1U48yZM9t83+Vy8c033/Dxxx9TXl6OYRhce+21wZ5ORMIsWk81QsMkqlZdlZ5sFJGUF1LwCmRCVMuysNls/OpXv+KSSy4J9nQiEmbRmscLwMjMB/YoeIlIygs6eJ188sltHzgtjfz8fAYOHMhPf/pT+vTpE+ypRCTMLNML7logei1eoK5GEZGgg9fzzz8fzjpEJIosl9P/daTXagRfi5cmURURicpTjSISZw4/0Uh6JoY96N+/AnZk9nq1eIlIalPwEklB/vFdjsi3dkHjrka1eIlIagvLr7oHDhzgzTffZMOGDXz33XcYhkGHDh0YMmQIF1xwAZ06dQrHaUQkTPxPNEZ41nofLRskItIgpODl9Xp57LHHmD17Nh6PB8A/SaphGPzrX//igQceYPz48fz617/GbreHXrGIhOxIi1eUgtfhrkZTLV4ikuJCCl6//e1veeONN7AsC4fDwZAhQ+jWrRsAe/fuZcOGDbhcLv7+97+zZ88eHnzwwbAULSKhidas9T7+rkYNrheRFBd08HrnnXdYvHgxADfeeCOTJk0iPz+/yTZVVVU88cQTPPvss7z++uuMHj2aUaNGhVaxiIQs2sHLdvipRly1WF5PVAb0i4jEo6B/+r300ksYhsHNN9/Mbbfd1uI2eXl5/Pa3v8XhcPDkk0+ycOHCoIPX/v37WbFiBevXr2fDhg1s3ryZuro6Bg8ezKJFi1rdb+TIkZSVlbV57C+++IKMjIwW39u1axezZs1i+fLlHDx4kI4dO3LmmWcyadIkevbsGdRnEYk1X/AiClNJ+M9j2MHyYtVVYeQURee8IiJxJujgtX79emw2G//1X/911G3/67/+i7///e+sX78+2NOxePFi7r///qD379+/P7m5uS2+19oM/GvXrmX8+PE4nU4KCgro378/u3bt4uWXX2bp0qXMmTOHoUOHBl2TSKxEc9Z6AMOwNSwb5Cxv6G5U8BKRFBV08KqoqCA3N5e8vLyjbpuXl0deXh4VFRXBno7c3FzOOOMMhgwZwpAhQygpKeGRRx4JeP8//OEPnHrqqQFvX1tby5QpU3A6nVx22WVMnTqVjIwM6uvrmTZtGosWLWLKlCm8+eabZGZmBvORRGLHFd2uRmh4stFylmv2ehFJaUHP41VQUEB1dTXV1dVH3baqqoqqqioKCgqCPR2XX345s2fP5o477uCCCy6gc+fOQR8rEAsWLGD//v307t2badOm+bsiMzIymD59Or169WLv3r0sXLgwonWIREK0x3hB40lUNcBeRFJX0MHrhBNOwDRN5syZc9Rt58yZg2maDBkyJNjTRd3SpUsBuPTSS3E4HE3eczgcjB07FoAlS5ZEvTaRUEU6eNntNtLSmv6xZzcEL6O+Cput5e59EZFkF3RX49ixY3n//feZNWsWHo+HiRMnkpPT9Id4dXU1Tz31FH//+98xDIMrrrgi5IKDNX/+fJ599lnq6uro1KkTI0aM4JJLLmlx3JfX62XDhg0AjBgxosXj+V5fv349Xq9Xc5RJQonUGK/CvAxM0yI/P6vZe97CDrgAh1VLYWE25eVOTNMK6/lFROJd0MHr/PPP56c//SlLlizhb3/7G3PmzOGEE06gS5cuGIbhn8ervr4ey7K48MILOe+888JZe7u88cYbTb5//fXXeeyxx3j44Yc588wzm7xXVlaG2+0GoFevXi0ez/e6y+Viz549esJREop/5vowB6/crHRsNoOHXljD7n1Nx3KNcH/HGcDn63cwcqQNm81Q8BKRlBPSZDp/+ctf6NatG88//zx1dXV8+umn/icEfTPYp6Wlcf3113P77beHXm0QTjrpJH71q18xfPhwunfvjtvtZs2aNTz++ONs2rSJSZMm8eKLLzJ48GD/PuXl5f6vCwsLWzxu4/FqFRUVIQevtLTwLptpt9ua/FfalkrXy/J6wOMCIC07NyKfefe+KraVNX2YpnOGwRk5YDkbXk+Faw2pdW+Fg65X++h6BS5erlVIwSs9PZ277rqLG264gbfeesu/ViNAx44dGTJkCOeffz5du3YNS7HBePjhh5t8n5WVxY9//GNOP/10rrnmGjZu3MhDDz3E7Nmz/du4XC7/1+np6S0et/G4r7q6upBqtNkMiooiM9ampS4faV0qXC9PdTnlABh06NoJwxadbvJqs+EBlSyrFkiNa91Yqn3eUOl6tY+uV+Bifa3CMn10165duf7668NxqKjJzMzktttuY+LEiaxcuZLKykr/zPuNQ5Xb7W5xctXG4SzU6SRM06Ky0hnSMb7PbreRn59FZWUtXq8Z1mMno1S6Xt6D3wJgZGRRXlHn/+yRVm01nCOLhuCVCtcaUuveCgddr/bR9QpcJK9Vfn5WwC1pKb1ux7BhwwAwTZPS0lL/U5eNuxHLy8tbbLFrPCdZKNNk+Hg8kfkH4/WaETt2MkqF6+V1Hp4CxpET1c9aZTb8guJr8UqFa91Yqn3eUOl6tY+uV+Bifa2C7uisrq7m3XffZeXKlUfd9pNPPuHdd9+lpqYm2NNFRONuRK/X6/+6R48e/vdKS0tb3Nf3usPhoHv37hGsUiS8LP/kqVFaLugwX1ejAzemuz6q5xYRiRdBB6/XX3+dW2+9lQ8//PCo2y5dupRbb7212ZOFsbZ161b/141btdLS0vytX6tXr25xX9/rJ5xwgqaSkIRi1fmCV8tLaEVKPem4rYYfOV5n8KtYiIgksqCD19tvvw3ARRdddNRtx44di2VZvPXWW8GeLiKefvppAI477ji6devW5L0LLrgAgFdeecU/tYSPy+XyL8w9evToKFQqEj6WyzeHV3RbvMCg+nB3o7dGs9eLSGoKOnjt2LEDaAgtRzNgwIAm+0TLM888w/PPP8+hQ4eavH7o0CHuvfde/+z0U6ZMabbvVVddRefOndm5cydTp06lvr6ha6S+vp6pU6dSWlpKly5dYjoprEgw/LPWO6K3XJBP1eEB9maNWrxEJDUFPbj+wIED5Ofnt/jE3/dlZmZSUFDAgQMHgj0d33zzDWPGjPF/73uq8Msvv2yy+PWECROYOHEiAHv37uW5557jvvvuo0ePHnTo0IG6ujq2b9+Ox+PBZrNx++23t9hqlZ2dzWOPPcaECRN4+eWXeeeddyguLmb37t1UVFSQnZ3NjBkzyMrSI7ySWPzBKzP6wcs3zktdjSKSqoIOXllZWdTU1AS0XI7H46GmpiakkOL1eptMbNr42I1fbzyn1kUXXYRlWaxfv549e/awZcsW7HY7xcXFnHLKKVxzzTUcf/zxrZ5z+PDhvPrqq8yaNYvly5ezdetWioqKGDt2LJMnT9Zs9ZKQfMGLGLR4VVuHuxqd6moUkdQUdPDq3bs369ev55NPPuGss85qc9tPPvkEj8cTUlApLi7myy+/bNc+J554IieeeGLQ54SGpYEeeOCBkI4hEk+OLJAd7TFeR6aU8NZUBD/OQUQkgQX9s++cc87Bsiz+8pe/UF1d3ep2NTU1/OUvf8EwDH70ox8FezoRCZcILZAdiCMtXupqFJHUFHTwuu666ygoKOCrr77i8ssv5+23327SzVdXV8dbb73FZZddxldffUVeXh7jxo0LS9EiErwjLV6xGOOlpxpFJLUF3dVYWFjIww8/zC233EJJSQm//vWvsdvtFBYWYhgGhw4dwuv1YlkWGRkZPProoxQVFYWzdhEJQkyDl1q8RCTFhTTM4qyzzuLFF19k2LBhWJaFx+PhwIED7N+/H4/Hg2VZnHzyySxYsIAzzjgjXDWLSJAsy2o0c30sW7wUvEQkNYW8VuOgQYOYN28eO3fuZO3atezfvx+Azp07M2zYMHr16hVykSISJl4XeD1AbIJX1eEWL9NZiWVZUT+/iEishW2R7N69e9O7d+9wHU5EIsA6PLAewwbpmVE/v6/Fy/K6wV0HtqPPAygikkz0RLdICmk8vsswjKif300aLhoWoDc1zktEUpCCl0gK8U+eGoM5vHycRsO5rVoFLxFJPQpeIikklus0+viCl1q8RCQVKXiJpJIYrtPo40TBS0RSl4KXSAqJhxavGl9Xo4KXiKQgBS+RFBLLdRp9nEZD6FOLl4ikIgUvkRRixXCdRh+nkdVQi4KXiKQgBS+RFBLL5YJ81OIlIqlMwUskhcRyuSCfGj3VKCIpLCwz17/77rt8/PHH7Nmzh7q6OubOnet/z+l0smXLFgzD4KSTTgrH6UQkSHExjxdH5vGyLCsmE7mKiMRKSMHrm2++4dZbb2XTpk0ALf4QdTgc3HHHHezdu5d//etfDBgwIJRTikgIjnQ15sashtrDLV6Y3obpLTJjV4uISLQF3dVYW1vL+PHj2bhxI127duXaa68lKyur2XZpaWlcfvnlWJbFu+++G1KxIhIi/+D62LV4eQ07tqyGsGVq9noRSTFBB68XXniBHTt2MGjQIN544w3+8Ic/kJPT8riRUaNGAbB8+fJgTyciIbIsKy7m8QKw5xQCerJRRFJP0MHrzTffxDAMfv/735Od3fZvz/379yctLY2SkpJgTycioXLXgWUCsZ25HhoFL7V4iUiKCTp47dixA7vdzrBhw45+EpuN3NxcKir0Q1YkVvwD621pYHfEtBZ7biGgFi8RST1BBy+Xy0VGRgZ2uz2g7Wtra3E4YvvDXiSVNZ61PtZPEqYdbvHSlBIikmqCDl4dO3bE6XRSWVl51G23bNlCfX093bp1C/Z0IhIiy+UbWB/7pwjtuUWAuhpFJPUEHbx8c3ItWbLkqNs+8cQTGIbBySefHOzpRCREVl11wxcxfKLR58gYr6P/4iYikkyCDl6/+MUvsCyLGTNm8PXXX7e4TW1tLdOnT+fNN98E4Oqrrw72dCISoiMtXrEdWA8a4yUiqSvoCVRPOeUULr/8cl566SWuuOIKzj33XJzOhh/sTz/9NFu3buWDDz7wd0X+8pe/ZODAgeGpWkTaLw7WafTRU40ikqpCmrl++vTpZGVl8Y9//MPf5WgYBg8//DBwZCb7G2+8kd/+9rehVysiQYuHBbJ9jgSvKizTi2EL7CEdEZFEF1Lwstvt3H333Vx55ZUsXLiQzz77jG+//RbTNOnUqRPDhg3jyiuvVEuXSBw4MnlqHIzxys4DwwDLwqqrwsgujHVJIiJREZZFsvv168f/+3//LxyHEpEIsXzLBcXB2oiGzY6RlY/lrGgY56XgJSIpIujB9SKSWOKpxQvAll0AaJyXiKQWBS+RFBFPY7wAf/einmwUkVQSUFfjp59+GrYTai4vkdjwLxkUJ8HLlpUPgKkWLxFJIQEFr+uvvz4sS4wYhsGmTZtCPo6ItF/8tXgd7mpUi5eIpJCAB9dblhXyycJxDBFpP8sywVULNKzVGA9sCl4ikoICCl5btmyJdB0iEkmuWqDhF594afGy+cZ4qatRRFKIBteLpAD/+K40B4Y9PbbFHKauRhFJRWGZx0tE4pfNZoDnyDqNaWlNf9+y22Pz+5evq9HUQtkikkLCGrzKysr47rvvAOjYsSM9evQI5+FFpJ1sNoPCwmzqK0yqgLTsPIqK4qOr0chqCF64nFgeF0aaI7YFiYhEQcjBa9++ffz973/njTfeoLy8vMl7BQUFXHTRRUycOJFu3bqFeioRaSebzcBut/HqO19wKlDynYeHH3m/yTbDBnZh3IWDol6bkZENtjQwPVi1lRh5naJeg4hItIXUx/Dxxx9z8cUXM2/ePA4dOoRlWU3+lJeXM2/ePC6++GI+/PDDcNUsIu1Uc/iXou/q7Gwrq2jy59uDzpjUZBjGkXFeGmAvIiki6Bav7du3c8stt1BfX09BQQG/+MUvOO200+jatSvQ0BK2atUqFixYwKFDh5gyZQqvvPIKffv2DVvxIhKYTKsegForvrrzjKwCrOrvMJ0V2GNdjIhIFAQdvGbNmkV9fT0DBgxg9uzZdOjQocn7ffv25fTTT2fcuHHceOONbN26lSeeeIIHH3ww5KJFpH0yaAheTjMjxpU0ZcsuwERPNopI6gi6q3HlypUYhsH//M//NAtdjXXo0IE//elPWJbFJ598EuzpRCQEmVYdAM44bPECsPRko4ikiKCDV2VlJdnZ2ZxwwglH3Xbo0KFkZ2dTWakfriKxkHG4qzHugld2w3qNGuMlIqki6ODVuXNnTNMMeHvLsujcuXOwpxOREPi7Gq346mr0t3ipq1FEUkTQwetHP/oRdXV1AXUffvLJJ9TW1vLjH/842NOJSAjitqvRP4mqgpeIpIagg9fkyZPp2LEjd999Nzt27Gh1u5KSEv7whz/QuXNnJk2aFOzpRCQEvhavWjN+gpfdbiM9t6jhm9oK0tJsTf7YbEZsCxQRiYCgn2rcsWMHt99+O/fffz8///nPGT16tH86CcMw2Lt3L6tWrWLp0qVkZGTwu9/9ju3bt7N9+/Zmxzr55JND+hAi0rYjLV6x72oszMvANC3y87NwH9ONKhq6GgsLszGMI2HL6zUpL3dimlbsihURCbOgg9f111/f5Ifkv//9b/7973+3uK3L5eLuu+9u8T3DMNi0aVOwZYjIUVheDw7cQHx0NeZmpWOzGTz0whr27j3IZMDyuPjtI2/jNhrqK+6ax53XDsdmMxS8RCSphLRkkGWF/gMxHMcQkdaZdTX+r+NpAtXd+6rYtsdJXVEamYaH7/buY7+ZH+uyREQiKujgtWXLlnDWISIR4j0cvOqsdMzQVgmLiCozi0x7FXm2WgUvEUl68fdTWETCyqyrBqAmjgbWN1ZpZgGQb9TGuBIRkcgLqasxmvbv38+KFStYv349GzZsYPPmzdTV1TF48GAWLVrU5r5ut5u5c+fy2muvUVpaisPhYODAgVx33XWcf/75be67a9cuZs2axfLlyzl48CAdO3bkzDPPZNKkSfTs2TOcH1EkIszahuAVT92MjVVaDcErz6bgJSLJL2GC1+LFi7n//vvbvV99fT033ngja9aswW63c9xxx1FbW8uqVatYtWoVEydO5M4772xx37Vr1zJ+/HicTicFBQX079+fXbt28fLLL7N06VLmzJnD0KFDQ/1oIhHlG+MVD080tqTKzAQg31YX40pERCIv5OBVXV3Ne++9x5dffkllZSVut7vVbQ3D4M9//nNQ58nNzeWMM85gyJAhDBkyhJKSEh555JGj7vfggw+yZs0aiouLeeqpp+jbty8A7777LrfddhtPPfUUw4YNY+TIkU32q62tZcqUKTidTi677DKmTp1KRkYG9fX1TJs2jUWLFjFlyhTefPNNMjMzg/pMItHgPdzVGA9PNLbE39WoFi8RSQEhBa8FCxbwv//7v9TWHvmB2dJTioZhYFlWSMHr8ssv5/LLL/d/f7TuRYADBw4wf/58AO677z5/6AIYNWoUEyZMYNasWcycObNZ8FqwYAH79++nd+/eTJs2DYej4X9aGRkZTJ8+ndWrV1NaWsrChQu5/vrrg/pMItHg62p0xukYrypfV6PGeIlICgg6eL3xxhtMnToVgKysLE466SQ6duxIWlr89F4uW7YMt9tN7969Oe2005q9/4tf/IJZs2axceNGSktL6dWrl/+9pUuXAnDppZf6Q5ePw+Fg7NixPProoyxZskTBS+Kab3B9bdx2NfrGeKmrUUSSX9Ap6dlnnwXgnHPO4ZFHHiE3NzdsRYXLunXrABg+fHiL73ft2pXi4mJ2797NunXr/MHL6/WyYcMGAEaMGNHivr7X169fj9frxW63h7l6kfDw+sd4xWeLV6V/jJdavEQk+QU9ncTXX3/t7zqMx9AFDetEAvTu3bvVbXxhq/F6k2VlZf6xao1bwVraz+VysWfPnnCUKxIR/q7GOG3x8o3xyjNqMdCEyiKS3IJu8crKysLhcNCpU6dw1hNWFRUVABQUFLS6je+9yspK/2vl5eX+rwsLC9vcz3eeUKeWSEsL75RqdrutyX+lbcl6vex2m7+rMV5bvKqthhYvu2GRbdRTYx15WCUZ/j6S9d6KFF2v9tH1Cly8XKugg9fAgQP5z3/+Q3V1ddy2eNXX1wOQnp7e6ja+8Vt1dUfGl7hcLv/Xre3beNxX432DYbMZFBXlhHSM1uTnZ0XkuMkqGa9Xha+rMU4H13uxU21mkGurJ99WS433SPBKpr+PZPos0aDr1T66XoGL9bUKOnj98pe/5JNPPmHevHncdNNN4awpbDIyGrpW2priwheyGk8J0ThUud1u/3Fa2u/7+wbDNC0qK50hHeP77HYb+flZVFbW4vWaYT12MkrW62W32+K+qxEa5vLKtdWTZ9TxTaPXk+HvI1nvrUjR9WofXa/ARfJa5ednBdySFnTwOvfcc5k8eTKPPfYYAOPGjYu7+azy8xvWffN1ObbE955vW2jajVheXk7Xrl1b3e/72wfL44nMPxiv14zYsZNRMl6vI081xmeLFzRMKXEMFc1mr0+mv49k+izRoOvVPrpegYv1tQpp7odf//rXZGdn89BDDzFr1iyOPfZYcnJa7zIzDIO5c+eGcsp26dOnD5999hk7d+5sdZvS0lL/tj49evQgPT0dt9tNaWlpi8HLt5/D4aB79+7hLVwkTCyPC8vT0Dobzy1emkRVRFJFSMHrr3/9K08//TSGYVBXV8fGjRvb3N4wjFBO124nnngiixYt4rPPPmvx/X379rF7927/tj5paWkMGTKEtWvXsnr1ak4++eRm+65evRqAE044QVNJSNyy6hu6sC2gzmp9rGOsVZmaRFVEUkPQweull17ib3/7GwDFxcWcfvrpcTeB6qhRo/jTn/5ESUkJK1eubDaJqm9W+0GDBjWbcuKCCy5g7dq1vPLKK0yYMKHJIHuXy+WfOX/06NER/hQiwbPqGwbW15OBRXR/8WmPSkvrNYpIagg6Jb3wwgsYhsGYMWO47777sNni71HWTp06cdVVV/GPf/yDu+++u8lajcuWLePpp58G4JZbbmm271VXXcUzzzzDzp07mTp1arO1GktLS+nSpQtXXHFFVD+TSHv4gledEV/jL79PXY0ikiqCDl6+yUl///vfRyV0ffPNN4wZM8b/ve+pwi+//JJTTz3V//qECROYOHGi//vf/OY3bNy4kbVr13LxxRfTr18/nE6nf4zW+PHjOe+885qdLzs7m8cee4wJEybw8ssv88477/hnua+oqCA7O5sZM2aQlaVHeCV+mY1avOKZuhpFJFWENIFqenp6k6cBI8nr9TaZ2NTH4/E0ef37c2plZmby3HPPMXfuXF577TVKSkpIT0/nlFNO4brrruOCCy5o9ZzDhw/n1VdfZdasWSxfvpytW7dSVFTE2LFjmTx5csiTpopEmnV4Dq96I86Dl6X1GkUkNQQdvIYOHcqHH37IoUOHKCoqCmdNLSouLubLL78Mal+Hw8HEiRObtIQFqlevXjzwwANBnVck1o50NcZ38PKt15hj1GFDj8SLSPIKuo9wwoQJADz55JNhK0ZEwssfvIjvMV41VgZey8BmQK6hVi8RSV5BB68RI0Ywffp0XnzxRe6991527doVzrpEJAz8TzXGeYuXhc2/ZqMG2ItIMgu6q3HUqFEA2O12Fi5cyMKFCykoKDjqBKrvvPNOsKcUkXY6Mp1EfLd4QcOTjQW2WvJttdTHuhgRkQgJOniVlZU1e628vLzFAfA+0Z5AVSTVJcoYL2hYrxEanmxU8BKRZBV08Lr//vvDWYeIRICZIE81QtMnGw/EuBYRkUgJOnhdeuml4axDRCIg0boaQWO8RCS5xd908yISNr61GhOjq1GTqIpI8lPwEklSlmVh1VcD8T+dBGi9RhFJDWFb0dqyLCoqKqitrcWyrFa36969e7hOKSJtcdeC6QV8azU6Y1vPUfi6GvPU1SgiSSzk4PXee+/x/PPPs3bt2mbL9XyfYRhs2rQp1FOKSADMmkMA2DJz8BjpMa7m6HxdjfnqahSRJBZS8PrLX/7C7Nmz22zhaizQ7UQkdFZNOQD23CKoiW0tgfA91Zhlc2O3PDGuRkQkMoIe4/Xhhx/y7LPPYrfbueuuu1i8eDEAHTp04O2332bevHnceuutFBQUUFRUxJNPPsm7774btsJFpG2Ws6HFKy2vY4wrCUytlY7baviRlG3Fd7eoiEiwgg5eCxYswDAMJk+ezI033sixxx7bcECbjZ49ezJs2DBuvfVWXn31VfLy8rj77rtxOBxhK1xE2mb6WrzyIr+IfXgY/nFeOXE+Hk1EJFhBB68vvvgCgCuvvLLN7bp168Y999zDd999x1NPPRXs6USknazDY7zScjvEuJLA+bobs60E6BsVEQlC0MGrvLyczMxMOnXq5H/NbrdTW9t8YOyZZ55JRkYGH3zwQbCnE5F2spzlANjzEid4+Vq81NUoIskq6OCVm5vb4mtOpxOns+kPTZvNht1uZ9++fcGeTkTayfdUY1oCBS/feo05Cl4ikqSCDl5du3alrq6OiooK/2s/+MEPAPjss8+abFtSUoLT6cRutwd7OhFpJ3+LV0J2NSp4iUhyCjp4DRkyBICtW7f6XzvjjDOwLItHHnmE/fv3A3Dw4EHuueceDMPw7yMikWWZpj94JVKLl7oaRSTZBR28Ro4ciWVZvP766/7Xrr32WvLz89m8eTM//vGPOfvssznrrLNYvXo1AP/1X/8VesUiclRWXSVYJhgG9tzCWJcTsCoFLxFJckEHrzPPPJP777+fs88+2/9ax44d+dvf/sYxxxyDx+Nh//79mKZJZmYmU6dO5ZxzzglL0SLSNt/kqUZWAYYtcbr4K31djZpOQkSSVNAz12dkZHDppZc2e/2kk07i7bffZu3atezdu5e8vDyGDx/e4mB8EYkM3+SptpzC2BbSTpX+wfU1WulCRJJS2BbJbsxutzNixIhIHFpEAuBfpzEnUSZPbeDrakzDi1WvVi8RST5BdzWKSPzyDaw3Eix4uUmjzmpY0NtzuLtURCSZBN3i5XK5OHDgAOnp6XTu3LnJezU1NcycOZPly5djt9v50Y9+xK9+9SsyMzNDLlhEjs5K0BYvaOhuzLS78daUQ15hrMsREQmroFu8Fi5cyKhRo3jkkUeavXfzzTczZ84ctm7dyubNm/nb3/7GxIkTNWZDJErMwy1eiTbGC45MKeGtLo9tISIiERB08Pr4448BuOSSS5q8/u6777J69WoMw+CSSy7hiiuuIC0tjdWrV/Pqq6+GVq2IBCSRW7x847y86moUkSQUdFfj9u3bARg8eHCT119//XUMw2DixIn893//NwCDBg1i+vTp/Pvf/2bMmDHBVysiAfFNJ5GIwcs3pYS3uhwjxrWIiIRb0C1eBw8eJDMzk4KCgiavr1q1CoDLL7/c/9rPf/5zAL788stgTyciAbI8Lqz6aiDxBtfDkRYvj7oaRSQJBR28amtrsdma7r57924OHjzIMcccQ8+ePf2vZ2dnk5+fT3l5edCFikhgLOfh9VPtaRgZObEtJgi+hbK9h7tLRUSSSdDBq6CgAKfTSWVlpf+1lStXAg2TqH6fx+MhJyfx/icgkmjMw5OnGtlFGEbiddY17moUEUk2QQevQYMGAfDSSy8BYJomL730EoZhcOqppzbZ9uDBgzidTjp16hRCqSISiEQe3wWNnmqsqYhxJSIi4Rf04PpLL72Ujz76iIcffpgVK1Zw8OBBNm3aRE5ODqNHj26yrW+R7GOPPTa0akXkqHxPNBrZhbEtJEiNn2q0LDPG1YiIhFfQLV4XXnghY8eOxev18vHHH7Np0yYyMjKYPn06+fn5TbZ94403WmwJE5Hw83c1JmiLV5V1eKJly8Sqq45tMSIiYRbSWo1//vOfueyyy1i7di35+fmcfvrpTQbVQ8MM93l5eYwZM4ZzzjknpGJF5Oj8XY0J2uJlYqOWTLKoa3hQoCA31iWJiIRNyItkDx8+nOHDh7f6vsPh4E9/+lOopxGRAFkJ3uIF4DSyybLqMJ0VGAU9Yl2OiEjYaJFskSRjHm7xStQxXgA1RjZw5LOIiCQLBS+RJGJZlr/FK1GfagSoMhrGiZqV38a4EhGR8FLwEkkmLid4XAAYCbhAts9BoyE0eg/tiXElIiLhpeAlkkRMZ3nDF45sjLSMmNYSioO2DoCCl4gkHwUvkSTim8PLlsCtXQCHDrd4meXfYJneGFcjIhI+Cl4iScQ63OJlZCfu+C6ASiMfI80Bphercn+syxERCRsFL5EkYvpmrU/wFi8Mg/SODdNIeMvV3SgiyUPBSySJHJk8NbFbvAAcnYoBMBW8RCSJKHiJJJEjk6cWxraQMEj3BS8NsBeRJKLgJZJE/JOnJvAcXj7pnRq6Gs3yb2JciYhI+Ch4iSQR/+SpSdHV2LDuq1n+DZZlxbgaEZHwUPASSWA2m0Famo20NBt2Gw2LSgPp+R0aXrMn7j/x9KJuYLODuw6r5mCsyxERCYuQF8kWkdiw2QwKC7P94cpTdYhyywTDRoce3TFs9hhXGBrDnoYtvwtm+TeY5d9gy+0Y65JEREKm4CWSoGw2A7vdxkMvrGH3vio6m99yNVBtZfHfj34EwLCBXRh34aDYFhoCe1H3huB1qAyKh8S6HBGRkCVuP4SIALB7XxXbyiqoPtCwoPRBTybbyirYVlbBtwedMa4uNPYOhwfYH9IAexFJDgpeIkmiwNYQsirMrBhXEj62ou6A5vISkeSh4CWSJI4Er+wYVxI+dn/wUouXiCSHlBjjNWPGDGbOnNnmNtOmTePqq69u9rrb7Wbu3Lm89tprlJaW4nA4GDhwINdddx3nn39+pEoWabcCWy2QZMGr8BgArLoqzNpKbFn5Ma5IRCQ0KRG8fDp27Ejv3r1bfK9z587NXquvr+fGG29kzZo12O12jjvuOGpra1m1ahWrVq1i4sSJ3HnnnZEuWyQgBUbydTUa6RkYuR2xqr9reLJRwUtEElxKBa9zzjmHBx54IODtH3zwQdasWUNxcTFPPfUUffv2BeDdd9/ltttu46mnnmLYsGGMHDkyUiWLBMzf1WglT4sXgK2oB97q7xqWDjpmQKzLEREJicZ4teLAgQPMnz8fgPvuu88fugBGjRrFhAkTAI7ahSkSLck4xgvAdri7UQPsRSQZKHi1YtmyZbjdbnr37s1pp53W7P1f/OIXAGzcuJHS0tJolyfSRBpecmwuIAmDlwbYi0gSSamuxi1btnDHHXewf/9+cnJyGDBgABdddBH9+vVrtu26desAGD58eIvH6tq1K8XFxezevZt169bRq1evSJYu0iZfa5fbsuG0HDGuJrxshYeD1yG1eIlI4kup4LV582Y2b97s/37ZsmU8+eSTjBs3jrvuugu7/cgSKyUlJQCtDsYH6NWrF7t372bHjh0Rq1kkEE27GY3YFhNm/icbaw5iuWoxHMnz8ICIpJ6UCF6dOnViwoQJnH/++fTs2ZPc3Fx27NjBvHnzmD9/PnPnziU9PZ3f/OY3/n0qKhoWGy4oKGj1uL73KisrQ64xLS28vb6+9fsSeZHkaErE69W41mQd32W32yA3HyOrAKu2AqNqH2ld+x59xziSiPdWLOl6tY+uV+Di5VqlRPBqaX6uAQMGMH36dIqLi3nooYeYM2cOV199NcXFxUDDVBIA6enprR7X4Wjo0qmrqwupPpvNoKgoJ6RjtCY/X60D7ZGo16vASL45vODI30dtl2LqdlaQ6fqOvKITYlxVcBL13ooVXa/20fUKXKyvVUoEr7aMHz+e5557jm+//Zb33nuP66+/HoCMjAygYQLV1rhcDYOZMzMzQ6rBNC0qK8O7pp7dbiM/P4vKylq8XjOsx05GiXi9fDVD46kkkuuHr+/vw8rtCmykavcOPD1PjnVZ7ZKI91Ys6Xq1j65X4CJ5rfLzswJuSUv54GW32/nhD3/I22+/7R/XBZCf3zBRo6/LsSW+93zbhsLjicw/GK/XjNixk1GiXq9k7Wr0/30UNAyw9xwsS8i/H0jceytWdL3aR9crcLG+VuoU5kh3osfj8b/Wp08fAHbu3Nnqfr5pJHzbisRKMi4X1JhvSgmv5vISkQSn4AV89dVXAHTr1s3/2oknngjAZ5991uI++/btY/fu3U22FYmVZG3x8vFNompVfovlbb37X0Qk3qV88Hr//ff9wevMM8/0vz5q1CjS09MpKSlh5cqVzfbzzWo/aNCgNqecEIk4yyLf3+KVXGO8fIzsQkjPAsvCrNgX63JERIKW9MHrq6++4t5772XLli1NXjdNk9dff5077rgDgHPPPZehQ4f63+/UqRNXXXUVAHfffTfbt2/3v7ds2TKefvppAG655ZZIfwSRNjlwkWE0dJMna4uXYRjYig4vHaSJVEUkgSX94HqPx8OCBQtYsGABhYWFdO/eHbvdTmlpqX9w/IgRI3jwwQeb7fub3/yGjRs3snbtWi6++GL69euH0+n0j+0aP3485513XlQ/j8j35Vo1ADhNB+4k/idtK+yB+e12rdkoIgkteX9KH9ajRw9uu+021q1bx7Zt29i5cycul4uCggLOOeccLr74Yi6++OIms9b7ZGZm8txzzzF37lxee+01SkpKSE9P55RTTuG6667jggsuiMEnEmkqx6oGkre1y8dedAwe1OIlIokt6YNXfn4+kyZNCnp/h8PBxIkTmThxYhirEgmfnMMtXsk2h9f3+dds1GLZIpLAkn6Ml0iyy02RFi/flBJmxTdYpuYrEpHEpOAlkuD8LV5JHryM3E5gTwevB6tqf6zLEREJioKXSILL9Qev5O5qNGw2bIUNc+1pgL2IJCoFL5EElyotXnBknJf3kMZ5iUhiUvASSXCpMsYLGg+wV4uXiCQmBS+RBGaZXrJJ7uWCGvMPsNeUEiKSoBS8RBKYt6YSGxamZVBlZca6nIhr3OJlWVaMqxERaT8FL5EE5q0+CECVlYmZAv+cbQVdwbCBuw7LWR7rckRE2i35f1KLJDFPVUPwStZuRrvdRlrakT/pGQ5sBV0AMCq/IS3Nhs1mxLhKEZHAJf3M9SLJzOsPXsk1lURhXgamaZGf3/xz1XfphbN8Lxn131FQlIPXa1Je7sQ01fUoIvFPwUskgSVri1duVjo2m8FDL6xh976qJu+d7vZyMvDeu6v4emtX7rx2ODaboeAlIglBwUskgfnGeCVb8PLZva+KbWUVTV4rcmRyci5k1e1vFspEROKdxniJJLBkbfFqyz5vAQDd7BVH2VJEJP4oeIkkMH+Ll5VcY7za4gteebY6Mqy6GFcjItI+Cl4iCSwVW7xcpHPQmwNAB/NgjKsREWkfBS+RBGV5XJi1qbNcUGO+Vq8OloKXiCQWBS+RBGXWlAPgwY7TcsS2mCjbZx4OXuahGFciItI+Cl4iCcpyNoSOGiMHSK1JRPcebvEqUouXiCQYBS+RBGVWNwSvaiM3xpVE35GuRrV4iUhiUfASSVDm4bUKG1q8UouvxSvfqsJ01ca4GhGRwCl4iSSoIy1eqRe8nFYmVWYmAO7v9sS4GhGRwCl4iSQo0zfGi9QLXnCku9F1YHeMKxERCZyCl0iCsmpSd4wXHOludCt4iUgCUfASSVC+6SRScYwXwF5vIQB1u7fEthARkXZQ8BJJQJZlYdb4ppNIzRavDe5iLKCudBPeim9jXY6ISEAUvEQSkcsJHheQmoPrAQ6Zueyy9QTA9eXHMa5GRCQwCl4iCcjXzWjLzMVrpMW2mBjaZD8eaAhelmXGuBoRkaNT8BJJQGblXgDseR1iXElsbbMfiy0jG7PqAN49GuslIvFPwUskAXl2fAZAVu8hMa4ktrxGGjmDzgLA/eVHMa5GROToFLxEEozldeMpaQheuYPOiHE1sZf3wx8D4NmxBsvljHE1IiJtU/ASSTDe3RvAXYuRU0RG8YBYlxNzGd37YSs8Brwu3Ns/jXU5IiJtUvASSTC+cOE49mQMQ/+EDcMg4/hzAHU3ikj8009tkQRieVx4StYC4Dj21BhXEz8c/c8Ew8Dc9zVm+TexLkdEpFUKXiIJxLt74+Fuxg7Yux0b63Lihi2nEHvxCQC4t2pOLxGJXwpeIgnEvf0/AKT1VTfj96UPOBsA99blWKbm9BKR+KSf3CIJwvK48Oxs6GZM73tyjKuJL3a7jcxjh2Fk5GA5y2HvJtLSbP4/NpsR6xJFRAAFL5GE4dm9Htx1GDkdsHXpG+ty4kJhXgamaZGfn0WHToXkndAwyN7atoKiohz/n8LCbIUvEYkLqbvWiEiC8WxreJpR3YxH5GalY7MZPPTCGnbvq6Kzmc/VQOXmlTzy8FLqjUyKu+Zx57XDsdkMTNOKdckikuL001skATTpZjz2lBhXE39276tiW1kFK79xUOYpwo5Jh+8+Z1tZBbv3VcW6PBERPwUvkQTg2bUePPUYuR2xdVY3Y+sMVtU3PO15asa2GNciItKcgpdIAvA0eZpRY5XastrVF69l0CvtO46xH4p1OSIiTSh4icQ5y1OPZ+c6ANL7qpvxaGqsTDa6iwE4xaFWLxGJLwpeInHOU/pFQzdjXidsnX8Q63ISwqr64wA4OWM7Nssb42pERI7QU40iccpmM7DZDOp2+NZmPIX0dLv/fbtdvze1ZpO7B1VmJnm2OnqbO2NdjoiIn4KXSByy2QwKC7MxvC7KSz8HoNNJPyKjKCfGlSUGExur6/vy46xNHO/ZHOtyRET8FLxE4pDNZmC323jxmZc41V1PhZHP4y/uAmO3f5thA7sw7sJBMawyvq1yHcuPszbxA7MEb00F+nEnIvFAP4lE4liH79YD8KmzJ9u+q2zyXnGX3FiUlDC+8RZR6ulIr7TvqN74EfT7caxLEhHR4HqReGW66uhjlgCw1tUnprUkKt+cXhWfvoFZUx7bYkREUPASiVvOr9eQjof93jx2ezvEupyEtMbVl2py8JTvo2rRH/GW74l1SSKS4hS8ROJUzeYVAKxz9QY0aWowai0HL2VcRnqHYzCrDuB89T68e7+KdVkiksIUvETikOWuw/n1ZwCsdfWOcTWJrdJWQPdx92Hv0hfqa3Au/guekrWxLktEUpSCVwBWrlzJzTffzGmnncbQoUMZPXo0jz76KE6nM9alSZJyl6zD8rgoNwooUzdjyOw5BRSO/X+k9/4heN3Uvv043i/fJy3N5v9js6lVUUQiT8HrKJ5//nluuOEG3n//fTIyMjj22GMpKyvjiSee4PLLL6e8vDzWJUoScn29CoCv7P1QN2NoCvMyME2Lgo5FFF9zN3k/HAWWhfODOVhfvEZhYTZFRTkUFmYrfIlIxGk6iTZs2LCBP//5zwD88Y9/5Morr8QwDPbt28ekSZPYuHEj99xzDzNmzIhxpZJMLFct7tIvAPjKflyMq0l8uVnp2GwGD72wht37qsA6nlPTqjjV8x/KP36J5Z9sYmvxJdxx3SnYbAamacW6ZBFJYmrxasOsWbMwTZOf//znXHXVVRhGw2/DXbt25ZFHHsFms/HWW2+xZcuWGFcqicRmM5p0cTXp7nJV416zCLxu0jt054DRKdblJo3d+6rYVlbBtj2VzPt2IPNrTsO0DAZ7N3HirvmYrrpYlygiKUAtXq2oqanho48+AuDKK69s9n6fPn047bTTWLFiBUuXLmXgwIHRLlESkG8poMbrLFqWRd2uTVSueZOaLavA9ACQd+Io+ERdX5HySX1/Ks0sbsj9kB+YOymb8zvsPzgZo+sA7F36YtjTm+3jWz/zaEzTUsuZiLRIwasVmzdvxuVy4XA4GDp0aIvbDB8+nBUrVvD5559HuTpJVL6lgB56YQ3f7j3AQO8WTvBsoKN10L/NXqMrlT3P5ILTfgaffBjDapPfRndPZlaez6SC92D/Ltz7dzW8YU/H3vU47McMxN59IPbOP8DuyGgWmlvj9ZqUlzsVvkSkGQWvVuzYsQOA7t27k57e/DdfgF69ejXZViQQ9d9sp/+uf3GRZysZRkPrVr2Vxpr6H7C8vj+7vR35Ua8ejDY0EiAadno780LmNfzuXDsVX32OZ88WrNpKvHs2492zGdYA9jTSuvbD+MEg3t9cybdVFvVGBi4yqDccuHAc/t5Bj24F3HntcI0XE5EWGZZl6SdDC55++mkefPBBfvjDH/LPf/6zxW0++OADbrrpJrKzs1m7Nvh5gSwrAt0SHheWywkB/PVaHP25uWhuE7OajMPfBHksq/FXVqNX/H8HVrPje7HhNhy4SMdqdPQMh528bAflVfV4vGaL54vmNsleU5rddvjpx4b3La8Xy+sCjxvL6waz9Rq+zwL/eFAO/7fh1mp09xjNvmhVIv6bCvlYjf4txk1NEdgmbMc6ys+umNQUr+ez2TCy8gOsLHA2m3Hk3/1RqMWrFfX19QCttnYBOByOJtsGyzAM7PYwj+WxZ0JGZniPKWGXDrT1t1SYl3HUY0Rzm2SvyWaz+b6ANv7ti4gES30ZrcjIaPgh7Xa7W93G5XI12VZERESkLQperSgoKACgoqKi1W187/m2FREREWmLglcr+vTpA8CePXtabfUqLS1tsq2IiIhIWxS8WjFo0CDS09NxuVx88cUXLW6zZs0aAE488cQoViYiIiKJSsGrFTk5OZx11lkALT7VWFJSwsqVKwEYPXp0VGsTERGRxKTg1YbJkydjGAavvvoqCxYswDfzxrfffsvtt9+OaZqcd955mrVeREREAqJ5vI5izpw5PPDAA1iWxTHHHENRURFff/01LpeLH/zgB8ybN48OHTrEukwRERFJAApeAfjkk0949tln+eKLL3A6nXTv3p3Ro0dz0003kZOTE+vyREREJEEoeImIiIhEicZ4iYiIiESJgpeIiIhIlCh4iYiIiESJgpeIiIhIlKTFugAJzMqVK5k9ezaff/55sycrs7Oz4+aY8SCcn2vGjBnMnDmzzW2mTZvG1VdfHUrJMbF//35WrFjB+vXr2bBhA5s3b6auro7BgwezaNGikI6djPdWJK5XMt5flmWxdu1ali1bxpo1a9i+fTvV1dXk5eUxaNAgxowZwyWXXIJhGEEdP9nurUhdr2S8t3yWLVvGRx99xMaNG9m7dy+HDh0iLS2NHj16cPrpp3PDDTfQo0ePoI4djftLwSsBPP/889x3331YlkW3bt045phj+Prrr3niiSd46623mDdvHoWFhTE/ZjyI1Ofq2LEjvXv3bvG9zp07h1h1bCxevJj7778/7MdN1nsrUtcLkuv+WrlyJTfccIP/+549e9KjRw/KyspYvnw5y5cvZ/HixcyYMQOHw9GuYyfjvRXJ6wXJdW/5zJ49m//85z+kp6fTuXNn+vfvz6FDh9i2bRtfffUVCxcuZObMmf7VZwIVtfvLkri2fv16a+DAgdaAAQOs+fPnW6ZpWpZlWXv37rUuvfRSq3///tatt94a82PGg0h8rscff9zq37+/ddddd0Wi5JhauHChdcMNN1gPPfSQtXTpUuvJJ5+0+vfvb1166aVBHzNZ7y3Lisz1Ssb7a/ny5dbIkSOtuXPnWgcOHGjy3iuvvGINGTLE6t+/v/Xggw+267jJem9F6nol473l88orr1grVqyw6uvrm7y+c+dO69prr7X69+9vnXrqqVZNTU3Ax4zm/aXgFecmTZpk9e/f3/rtb3/b7L0dO3ZYAwcOtPr3729t3rw5pseMB5H4XMn8w+v7Xn755ZCDRLLeWy0Jx/VKxvurqqrKcrlcrb7/xBNPWP3797dOOeUUy+v1BnzcZL23InW9kvHeCsT+/fut/v37W/3797fef//9gPeL5v2lwfVxrKamho8++giAK6+8stn7ffr04bTTTgNg6dKlMTtmPEjWz5VI9HcgALm5uaSnp7f6/jnnnANAeXk5Bw8eDOiYyXxvReJ6pbJOnTr5uwPr6uoC2ifa95fGeMWxzZs343K5cDgcDB06tMVthg8fzooVK/j8889jdsx4EOnPtWXLFu644w72799PTk4OAwYM4KKLLqJfv36hlp40kvXeioZUur/q6+v9X2dmZga0TyrfW8Fcr8ZS6d4C2LZtG+Xl5dhsNgYNGhTQPtG+vxS84tiOHTsA6N69e6u/EfXq1avJtrE4ZjyI9OfavHkzmzdv9n+/bNkynnzyScaNG8ddd92F3W4Pourkkqz3VjSk0v21ePFiAAYOHEhubm5A+6TyvRXM9WosFe4ty7I4ePAga9as4aGHHgJg/Pjx9OzZM6D9o31/KXjFsYqKCgAKCgpa3cb3nm/bWBwzHkTqc3Xq1IkJEyZw/vnn07NnT3Jzc9mxYwfz5s1j/vz5zJ07l/T0dH7zm9+E9gGSQLLeW5GUavfXxo0bmT9/PgA33XRTwPul6r0V7PWC1Li3Xn31VX772982ea1v37489NBDXHLJJQEfJ9r3l4JXHPM1MbfV/+97vLhxc3S0jxkPIvW5WprjZsCAAUyfPp3i4mIeeugh5syZw9VXX01xcXE7q04uyXpvRVIq3V8HDhzg1ltvxe1285Of/ISLLroo4H1T8d4K5XpBatxbHTt2ZNiwYViWxd69e9m3bx8lJSX8+9//5uSTT6Zbt24BHSfa95cG18exjIwMANxud6vbuFyuJtvG4pjxIBafa/z48XTp0gWPx8N7770XlmMmsmS9t2Ilme6vqqoqJk6cyJ49exg8eDAPPPBAu/ZPtXsr1Ot1NMlyb5111lm8+OKLzJ8/n/fff5+33nqLkSNH8sEHH3DllVdSVVUV0HGifX8peMWxQJo2A2kijfQx40EsPpfdbueHP/whACUlJWE5ZiJL1nsrVpLl/qqpqWHChAls2rSJfv368cwzz7R7rFIq3VvhuF5Hkyz31vf17NmTxx9/nH79+rFv3z7+8Y9/BLRftO8vBa841qdPHwD27NnTahIvLS1tsm0sjhkPYvW5fE3THo8nbMdMVMl6b8VSot9ftbW13Hzzzaxbt44+ffowe/ZsioqK2n2cVLm3wnW9ApHo91Zr7HY7Z599NgAbNmwIaJ9o318KXnFs0KBBpKen43K5+OKLL1rcZs2aNQCceOKJMTtmPIjV5/rqq68AAh5LkMyS9d6KpUS+v+rr65k8eTKffvopPXr0YO7cuUEvUZMK91Y4r1cgEvneOhpfmDRNM6Dto31/KXjFsZycHP9aU//85z+bvV9SUsLKlSsBGD16dMyOGQ9i8bnef/99/w+vM888MyzHTGTJem/FSiLfX263mylTprBixQq6devG3LlzQ/offLLfW+G+XkeTyPfW0bhcLt5//32AgOfxivb9peAV5yZPnoxhGLz66qssWLAAy7IA+Pbbb7n99tsxTZPzzjuPgQMHNtnv6quvZuTIkcyZMydsx4x34b5WX331Fffeey9btmxp8rppmrz++uvccccdAJx77rmtTrqXjFLx3gpFqt1fXq+XO++8kw8++IDOnTszd+7cgOdTSsV7KxLXK1nvLYD169fz6KOPtjg2bceOHUyaNInS0lKys7ObzUIfL/eXYfmOLnFrzpw5PPDAA1iWxTHHHENRURFff/01LpeLH/zgB8ybN48OHTo02WfkyJGUlZVx6623MmXKlLAcMxGE81pt3ryZMWPGAFBYWEj37t2x2+2Ulpb6B1qOGDGCJ554gvz8/Kh9xnD55ptv/J8PGn5TdDqdpKWlNRnMO2HCBCZOnOj/PlXvrXBfr2S9vxr/j71Hjx507dq11W3vueeeJq0SqXhvReJ6Jeu9BbBq1SrGjRsHQIcOHTjmmGNIS0tj//797NmzB2j4zI8++iinn356k33j5f7SPF4J4IYbbmDAgAE8++yzfPHFF3z33Xd0796d0aNHc9NNN5GTkxMXx4wH4fxcPXr04LbbbmPdunVs27aNnTt34nK5KCgo4JxzzuHiiy/m4osvTtiZn71eL+Xl5c1e93g8TV4PdL0zn2S9t8J9vZL1/vI9dg9QVlZGWVlZq9sG+ri/TzLeW5G4Xsl6b0HDDP5/+MMf+M9//sPWrVvZuXMndXV15ObmMnz4cM4++2yuuuqqoAJStO4vtXiJiIiIRInGeImIiIhEiYKXiIiISJQoeImIiIhEiYKXiIiISJQoeImIiIhEiYKXiIiISJQoeImIiIhEiYKXiIiISJQoeImIiIhEiYKXiIiISJQoeImIRMjvfvc7BgwYwO9+97tYlyIicULBS0RERCRKFLxEREREokTBS0RERCRKFLxEREREokTBS0SS2nfffcfgwYMZMGAA7777bpvbPvroowwYMICf/OQn/tf27NnDCy+8wE033cQFF1zAiSeeyEknncSFF17Ifffdx549e4Kqa+TIkQwYMIBFixa1uk0gg/NLS0v505/+xE9/+lNOOukkfvjDH/LTn/40pNpEJHIUvEQkqXXs2JGzzjoLgFdffbXV7SzL4t///jcAP//5z/2v33XXXfzxj3/kgw8+oKSkhLS0NOrq6ti2bRvPPfccP/vZz1i9enVkP0Qr/vnPf3LhhRfyj3/8g+3bt+PxeADYvn07zz33HJdccgnLly+PSW0i0jIFLxFJer4g9d5771FZWdniNmvWrGH37t1Ntgfo168fd9xxB2+88Qaff/45q1evZv369SxcuJCzzz6bqqoq/vu//5u6urrIf5BG3nnnHe655x4AbrrpJpYtW8YXX3zBunXrWLJkCaNHj6a6uppf//rXavkSiSMKXiKS9EaNGkVeXh4ul4slS5a0uM1rr70GwPDhw+nZs6f/9XvvvZebbrqJY489lszMTADS0tIYOnQof/vb3xgwYADffvstb775ZuQ/yGEul4s//vGPAEybNo077riDHj16YBgGhmHQt29fHnvsMUaOHEl1dTWzZ8+OWm0i0jYFLxFJehkZGYwePRpoubuxcSBr3Np1NHa7nbPPPhtoaDGLlg8//JB9+/bRqVMnLrvssla3GzNmDAAff/xxlCoTkaNJi3UBIiLRMGbMGBYuXMhnn33Grl27mrRq+bogHQ4HP/3pT5vtu3r1al566SXWrVvHvn37cDqdzbbZt29fROtvzBfyKioq/OPXWuJ2uwHU1SgSRxS8RCQlDB8+nOLiYnbv3s1rr73GLbfc4n/P1wo2cuRI8vPzm+z34IMP8vTTT/u/t9vtFBQUkJ6eDoDT6fT/iZZvv/0WaAhWBw4cOOr20R5/JiKtU/ASkZRgGAY/+9nPmDVrVpPgdejQIT788EPgSNecz/Lly/2h65prruHqq6/m2GOPxW63+7d59NFHeeKJJ6LzIQ4zTROAs88+u0koFJH4pzFeIpIyfMGqpKSEdevWAfDGG2/gdrvp0KGDf7yWz+LFiwE466yzmDp1Kv37928SuoCAWpxa4jtOfX19q9tUVVW1+HqnTp0A2Lp1a1DnFpHYUfASkZTRu3dvTjrpJOBI96LvacaLLrqItLSmnQB79+4FYNCgQS0ez7IsVq5cGVQtvi5N3zm+zzRNNmzY0OJ7w4YNAxrGlcVqDjERCY6Cl4ikFN9Ti2+88QZff/21v+Xr+92MALm5uQBs2bKlxWO9+OKL7Nq1K6g6Bg4cCMDbb7+NZVnN3n/llVdaDWUjR46kc+fOAPz5z3+mtra2zXOVl5cHVaOIhJ+Cl4iklAsvvJD09HTKy8u56667ADj22GMZMmRIs219XY8ffvgh//d//+cfQF9ZWcmTTz7J//zP/1BYWBhUHRdffDEA27Zt45577uHQoUMAVFdXM2fOHKZOndrqsTMyMpg2bRqGYbBx40auvvpqPvroI1wul3+bXbt2MX/+fC6//HLmzZsXVI0iEn4aXC8iKaWgoIAf//jHvPXWW/6uvJZau3yv/+tf/2L16tU8/vjjzJgxg/z8fKqqqjBNk3PPPZfjjz8+qMH1p59+uv/4CxcuZOHCheTn51NdXY1pmlx33XXU1NTwyiuvtLj/eeedx1/+8hfuvfdeNm/ezIQJE0hLSyM3Nxen09kkhI0aNard9YlIZKjFS0RSTuNJUm02Gz/72c9a3C49PZ1nn32WW2+9lT59+pCWloZlWQwdOpRp06bxxBNPNBts3x5//vOfufvuuzn++OPJzMzENE2GDRvGX//6V/9yQG352c9+xltvvcWkSZMYMmQI2dnZVFVVkZGRwfHHH891113HnDlzmDhxYtA1ikh4GVZLgwtEREREJOzU4iUiIiISJQpeIiIiIlGi4CUiIiISJQpeIiIiIlGi4CUiIiISJQpeIiIiIlGi4CUiIiISJQpeIiIiIlGi4CUiIiISJQpeIiIiIlGi4CUiIiISJQpeIiIiIlGi4CUiIiISJQpeIiIiIlHy/wHeAQAF0rJKrwAAAABJRU5ErkJggg==", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate random samples with shape s\n", + "s = 0.1\n", + "samples2 = stt.lognorm.rvs(s=s, size=n)\n", + "\n", + "# variable range\n", + "vx2 = np.linspace(0.0,3.0,50)\n", + "dx2 = np.diff(vx2)[0]\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples2, bins=vx2)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx2, stt.lognorm.pdf(x=vx2, s=s)*n*dx2)\n", + "\n", + "plt.tight_layout()\n", + "\n", + "print('mean:\\t\\t', np.mean(samples2))\n", + "print('variance:\\t', np.var(samples2))\n", + "print('skew:\\t\\t', stt.skew(samples2))\n", + "print('kurtosis:\\t', stt.kurtosis(samples2))" + ] + }, + { + "cell_type": "markdown", + "id": "22149ced-544b-49ea-9a1b-33773c523560", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Change the `s` shape parameter and see its effect on the skew and kurtosis" + ] + }, + { + "cell_type": "markdown", + "id": "83b5a55f-7889-49d2-8f85-42030e930018", + "metadata": {}, + "source": [ + "## Statistical test about the mean of a distribution\n", + "\n", + "We want to test whether observations could come from a distribution with a given mean.\n", + "\n", + "According to the law of large numbers, for independent random variables $X_i$ following a same distribution $P(X_i) = P(X)$, the sample mean is distributed normally with:\n", + "- a mean equal to the mean of $E[X]$\n", + "- a standard deviation equal to $\\sigma / \\sqrt{n}$ with $n$ the number of samples and the standard deviation $\\sigma = \\sqrt{E[(X-E[X])^2]}$.\n", + "\n", + "Student's t-test focuses on the following statistics that involves the sample mean $\\bar{x}$, tested against a given value $\\mu$, and the sample standard deviation $s$:\n", + "$$ t = \\frac{\\bar{x} - \\mu}{s / \\sqrt(n)} $$\n", + "According to what is said above, $t$ becomes normally distributed with unit variance when the number of samples increases." + ] + }, + { + "cell_type": "markdown", + "id": "4320932d-787a-4f9f-a489-7fb9ae38a8d8", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Verify empirically the law of large number for a normal distribution, then for a lognormal distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 125, + "id": "0aeebbcf-26d8-491a-aee4-787123cc38bc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# random samples to generate at each repetition\n", + "n = 1000\n", + "\n", + "# repetition to evaluate the distirbution of sample mean\n", + "n_rep = 100\n", + "\n", + "# standard deviation of the normal distribution\n", + "sig = 1.0\n", + "\n", + "m_hat = np.zeros([n_rep])\n", + "for i_rep in range(n_rep):\n", + " samples = stt.norm.rvs(scale=sig, size=n)\n", + " m_hat[i_rep] = samples.mean()\n", + "\n", + "vx = np.linspace(m_hat.min(), m_hat.max(), 50)\n", + "dx = np.diff(vx)[0]\n", + "plt.figure()\n", + "plt.hist(m_hat, bins=vx)\n", + "plt.plot(vx, stt.norm.pdf(x=vx, scale=sig/np.sqrt(n))*n_rep*dx)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 136, + "id": "e9c978a7-b08e-4155-a4b7-b558049b92f5", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# random samples to generate at each repetition\n", + "n = 1000\n", + "\n", + "# repetition to evaluate the distirbution of sample mean\n", + "n_rep = 100\n", + "\n", + "# standard deviation of the normal distribution\n", + "s = 1.0\n", + "\n", + "m_hat = np.zeros([n_rep])\n", + "for i_rep in range(n_rep):\n", + " samples = stt.lognorm.rvs(s=s, size=n)\n", + " m_hat[i_rep] = samples.mean()\n", + "\n", + "vx = np.linspace(m_hat.min(), m_hat.max(), 50)\n", + "dx = np.diff(vx)[0]\n", + "plt.figure()\n", + "plt.hist(m_hat, bins=vx)\n", + "plt.plot(vx, stt.norm.pdf(x=vx,\n", + " loc=np.mean(m_hat), # here we use the actual mean of m_hat\n", + " scale=np.std(samples)/np.sqrt(n))*n_rep*dx) # but here we use the std of a single batch of samples\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5404b927-e644-41fd-805d-4b9fb5a59310", + "metadata": {}, + "source": [ + "We can use Student's test to check whether observations come from a distribution away from 0 (i.e. there is some effect)." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "4d970957-a64b-4dd8-9d58-53d818b00fa0", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t statistics: 1.4823831806538128\n", + "p value: 0.13823836670142775\n", + "TtestResult(statistic=1.474952641728697, pvalue=0.14339847241619527, df=99)\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjUAAAGpCAYAAAB1Wcc9AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABGwElEQVR4nO3de3xU9b3v/9fMZCbkTsIlFwIkIBICxgheUKlWQE2rVrQe2Lb7tOyjTSu1u79N6zn2YaE9erT0tMVWLHh2q0DZtaItiq0tReRSFKNcEwNBBRMCARJyIffMba3fHyEpESKZ3NbM5P18PNJJZn3ny8d+meGd71rf77KZpmkiIiIiEuLsVhcgIiIi0h8UakRERCQsKNSIiIhIWFCoERERkbCgUCMiIiJhQaFGREREwoJCjYiIiIQFhRoREREJCxFWFzDYTNPEMPp/v0G73TYg/crg0RiGPo1h6NMYhraBGj+73YbNZrtkuyEXagzDpLa2uV/7jIiwk5gYQ0NDCz6f0a99y+DQGIY+jWHo0xiGtoEcv6SkGByOS4canX4SERGRsKBQIyIiImFBoUZERETCgkKNiIiIhAWFGhEREQkLCjUiIiISFhRqREREJCwo1IiIiEhY6NXme2fOnGHXrl188MEHFBcXU1JSQltbG1OnTmXDhg19KqigoIDVq1dTWFhIS0sLaWlp5OXlkZ+fT3R0dJ/6FhERkfDVq1Dzxhtv8JOf/KS/a2HdunU8+eSTmKZJSkoKqampHDlyhFWrVrF582ZefPFFhg8f3u9/roiIiIS+XoWa2NhYbrjhBqZNm8a0adMoKytj+fLlfSqkuLiYp556CoDHH3+c+fPnY7PZqKys5KGHHuLgwYMsWbKEFStW9OnPERERkfDUq1Bz3333cd9993X+3NdTTgArV67EMAzmzZvHggULOp9PTk5m+fLlfOELX2Dz5s0cPnyYrKysPv95IiLyT+49r4LdTuT0uy88tm8jGAaRV99jQWUiPRcUFwo3Nzezc+dOAObPn3/B8YyMDGbOnAnApk2bBrU2EZEhwW7Hs+fV9gBzHve+jXjOBR6RYBcUd+kuKSnB4/HgcrnIycm5aJsZM2awa9cuCgsLB7k6EZHw1zFD49nzaufPHYHGdfU9F53BkfBimmb7Y+f/gNnxDWCaF77m/OdNwG9002iQBEWoKS0tBSAtLQ2n03nRNuPGjevSti8iIvr3Nw6Hw97lUUKPxjD0aQz7LuLae7DbbbS9vwHPvj+D4WPYtfcSdfW8QfnzQ2UMfX6DNo+fVrePNo8ft8eP23vuy+PH4/Pj9Rl4fQYe77nv/SY+v4HPZ+D1G/j8Bn6j/Tm/38RvmBhG+6PfMDp/NgwTw+Tco9n5aJp0PppmexvTNM99tQcNExPO+74zfJx/rJ//v0mIdfH4g9eRGBvZzz33TFCEmvr6egASEhK6bdNxrKNtb9ntNhITY/rUR3fi46MGpF8ZPBrD0Kcx7JvEW7/KJ3tfB78PHBGk3frVQa9hMMfQ4/VT29BGXYObs01uGprPPTZ5aGjx0NTipanFQ1Orl6ZWLy1tPjxe/6DVF2r8fpPo6MgB+3f2UoIi1LjdboBuZ2kAXC5Xl7a9ZRgmDQ0tferj0xwOO/HxUTQ0tOL3G/3atwwOjWHo0xj2j9Y9r7UHGnsE+H2cfPP3gzpT099j2NTqpbK2her6NqrPtnLmbCvV9W3UNbqpbXTT3Ortdd/OCDvDXA4inQ4iOx6dDlxOO64IB84IOy5n+2OEw47TYSMiwo7TYcfhsBPhsOGwdzzacDjs2O3nvrfbsNts2O027Daw2+3nHm3YbDbsdtqP22xgo/05W3tddpvtn4/njtmAc093/kz7YWwdB85rw3nPn/fUp34A23lPOBw2RiTF0tripq6uudf/v15MfHxUj2bwgiLUREa2T1N5vd3/5fJ4PF3a9oXPNzAfeP5zU4sSujSGoU9j2HufvobGvW8jbe9vwDDMQb2mpjdjWN/s4XhVIyeqmjlV08zp2hZO17bQ2HLp0OKMsJMQ4yI+xkVclJO4GBdx0U5io5zEDHMSMyyC6HOPUZHtX8NcDiKC/DTZYIuIsOOMsNNk4XswKEJNT04t9eQUlYiI9M7FLgq+2MXDwaCh2cPRk/V8crKBstONHK9qoqHZ02374bEuRg6PYmTCMEYmtD8mxUUyPC6S4bGRxAyL6DJbIaErKEJNRkYGACdPnsTr9V70NFR5eXmXtiIi0o8M46KrnDp/Nqyb/TpztpWSY3UcLq/jaEU9Z862XdDGBoxOimbsqBjSRsaQMiKa1KQYkpOiGOYKin/qZBAExUhnZ2fjdDrxeDwUFRUxY8aMC9rs3bsXgNzc3EGuTkQk/H3WxnqDPUPT6vZx4ONqDpbWcKisjur6C0NM2sgYJqbFk5kaz9jkWNJHxhLpcgxqnRJ8giLUxMTEMGvWLLZt28bLL798QagpKyujoKAAgLy8PCtKFBGRAVTX6Kbokxo++KSWwo/PdNnvxGG3kZkWT/b4RCalDyczNY7oYd0vLJGha1BDzf33309lZSVf+9rXWLhwYZdjixYtYvv27WzcuJHp06d33vupqqqKxYsXYxgGc+fO1S0SRETCRHOblz2Hq3i3+DQfneh6TWVyUjRXThxBdkZ7kImKDIrfwSXI9epvyalTp5g3b17nzx0rkz788EOuu+66zucffPBBvvGNb3T+XFlZSUVFBY2NjRf0mZOTw6OPPsqyZctYunQpq1atIjExkSNHjuDxeMjMzOSJJ57oTbkiIhIkDMOk6GgN7xSfovBINT5/+4yMDZiYnsCNV45hytgERg/XfkMSuF6FGr/fz9mzZy943ufzdXm+re3C86CfZeHChUyePJkXXniBoqIiampqSEtLIy8vj/z8fGJirNnMR0RE+qap1cvOwpNs3VdBTcM//20YMyqGG6amcF12MqOToklMjKGurlnL8qVXbKbZ3d0cwpPfb1Bb27+bAkVE2PVGDHEaw9CnMQxOJ840sfn947xXUon33LjEDIvgxitSuWFaCmNHx3Yup9YYhraBHL+kpJjQ2XxPRETCy7HTjfx5Vxn7PjrT+dy45FjmzEjnuinJuJxaqST9T6FGRET6TempBl5/u5TCozVA+7UyMyaP4rZrxzExLV6b3MmAUqgREZE+O3O2lVe2H2XP4Sqg/R5C101J5o4bMhgzUtdDyuBQqBERkV5rafPxxrtlvLnnOD6/iQ24floKd96QQUpStNXlyRCjUCMiIgEzTZOdRaf4046jnTeNnDI+kQWzL2NccpzF1clQpVAjIiIBqaxrYe3fDnO4/CwAKUnRLJh9GTkTR+iaGbGUQo2IiPSI3zD4+/vH2fh2KV6fgctp557PTWDOjHQierDcVmSgKdSIiMglVVQ389s/H+JYZfuO8NkZiXw9L4tR2vlXgohCjYiIdKvj2pkX3/wIj88gOjKCf5kziRuvSNGpJgk6CjUiInJRLW0+1m46zO5zy7SnZiTywJ3ZDI+NtLgykYtTqBERkQscPVnP/9t4kOr6Nhx2G/feNIHbrxuHXbMzEsQUakREpIu3i06xdtNh/IbJyIRhfPPuqUxMS7C6LJFLUqgREREADMPkle1H+Pv7xwGYcfko/u2LU4gepn8qJDTob6qIiNDS5uP/vX6QDz5pv2fTl27M4EuzMnW6SUKKQo2IyBBXdbaVX71SyKmaFlwRdh64M5trskZbXZZIwBRqRESGsONVTSxff4D6Zg+JcZH8+5dzGJ+i2xxIaFKoEREZoo6cqOeXrxTS4vaRPiqWxQuu1HJtCWkKNSIiQ9AHn9Tw6w0f4PEZXJaewP93Xw7Rw5xWlyXSJwo1IiJDzHuHKvntXw7hN0yumDCCRfdMI9LpsLoskT5TqBERGUIKDp3mN38+hGnCddnJPHDHFN2MUsKGQo2IyBCx53AVv/1zCaYJN12ZxtfyJmvJtoQVxXMRkSHgwMfV/L/XD2KYJjdekaJAI2FJoUZEJMwVl9aw8rUP8Bsm104Zzb99YYoCjYQlhRoRkTD2YXkdK/70AT6/yYzLR/HgndnY7Qo0Ep4UakREwtSJM00886cP8PoMrpw4gm/ePVUXBUtY099uEZEwVNfo5pevFNLq9jEpPYFF90xToJGwp7/hIiJhptXt41evFFLb4CYlKZrvfDkHZ4T2oZHwp1AjIhJGfH6DVa8VU17VRHy0k/9v/pXERmmnYBkaFGpERMKEaZr81+YPKS6txeW0893/diWjh0dZXZbIoFGoEREJE1v2nOAfhaew2eBbX5pGZmq81SWJDCqFGhGRMHD4WB3rtx4B4F9mTyJ30kiLKxIZfAo1IiIhrqa+jVUbizFMk+unpjD36nSrSxKxhEKNiEgI83j9PPvqBzS2eBmXHMvX8yZj027BMkQp1IiIhCjTNFn39w85drqR2CgnD997BS6nlm7L0KVQIyISorbtr+Cd4tPYbPDQ3VMZmaCVTjK0KdSIiISgY6cbeemtjwH4b5+/jCkZSRZXJGI9hRoRkRDT5vHx3OsH8flNrpo0ktuvHWt1SSJBQaFGRCTE/P7Nj6isbSExLpJ/++IUXRgsco5CjYhICCk4eJp3Pmi/jib/rmzdAkHkPAo1IiIhoqquhd/9/UMA7rohg8njEi2uSCS4KNSIiIQAn9/guY0HafP4uTw9gbtuzLC6JJGgo1AjIhIC/vxOGWWnG4kZFkH+l6bisOvjW+TT9K4QEQlyZacbeOPdYwD899snkxQ/zOKKRIKTQo2ISBDz+gye/0sJhmlyTdZorp2SbHVJIkFLoUZEJIhtfLuUiupm4qOd/Ottl1tdjkhQU6gREQlSR0/W87f3Ok47ZREX7bK4IpHgplAjIhKEPF4/L7xRgmnCzKnJzJg8yuqSRIKeQo2ISBB6bWcpp2paSIhx8ZW5Ou0k0hMKNSIiQebY6Ub+vrscgK/nZWnXYJEeiujLiwsKCli9ejWFhYW0tLSQlpZGXl4e+fn5REdHB9zf2bNnWb16Ndu3b6e8vByv10tiYiK5ubl89atfZebMmX0pV0Qk6BmGydpNhzFNuHbKaHInjbS6JJGQ0euZmnXr1rFw4UK2b99OZGQkEydOpKKiglWrVnHfffdx9uzZgPorKyvjrrvu4rnnnuOjjz5ixIgRTJo0iZaWFjZv3szXv/51Vq5c2dtyRURCwtZ9Jyg73UhUZAT3z5lkdTkiIaVXoaa4uJinnnoKgMcff5zt27fz6quvsmXLFqZOncrRo0dZsmRJQH3+6Ec/oqqqioyMDF5//XW2bNnCq6++yrvvvsuiRYsAeOaZZzh8+HBvShYRCXq1DW1s+McnANz3+YkkxEZaXJFIaOlVqFm5ciWGYXD33XezYMGCztveJycns3z5cux2O5s3b+5xAGlqauK9994D4H/+z//JpEn//O3E5XLx3e9+lylTpmCaJv/4xz96U7KISND7w5aPafP4mZgWz825aVaXIxJyAg41zc3N7Ny5E4D58+dfcDwjI6Pz2pdNmzb1qE+Px4NpmgCMHTv2om06nvd6vYGWLCIS9A58XM3ej87gsNv4el4W9nO/LIpIzwUcakpKSvB4PLhcLnJyci7aZsaMGQAUFhb2qM+kpCRSU1MB2Ldv3wXH3W43xcXFAFx55ZWBliwiEtTaPD5+/+aHANx2zVjSR8daXJFIaAp49VNpaSkAaWlpOJ0XX2Y4bty4Lm174pFHHuF73/seP/vZz7Db7dxyyy3ExsZy9OhRfvWrX3Hy5Eluv/12Zs2aFWjJF4iI6N+V7A6HvcujhB6NYegL5TH86z/KqWlwMzJhGPfePLHfP6NCRSiPoQTH+AUcaurr6wFISEjotk3HsY62PXHHHXcQExPDs88+e8FFxomJiSxdupT7778/0HIvYLfbSEyM6XM/FxMfHzUg/crg0RiGvlAbw5PVTWx6r31Pmm/dm0NKcrzFFVkv1MZQurJy/AIONW63G6DbWRpov7j3/LY9VV5eTn19PTabjdTUVOLj4ykvL6euro7169eTnZ3NVVddFWjJXRiGSUNDS5/6+DSHw058fBQNDa34/Ua/9i2DQ2MY+kJ1DJ/7YyE+v8EVE0YwKS2Ourpmq0uyTKiOobQbyPGLj4/q0QxQwKEmMrJ9ieFnXbDr8Xi6tO2J//2//zcvvvgiWVlZbNy4kcmTJ3f+OatXr+YXv/gFX//61/nDH/7A1KlTAy27C59vYN4sfr8xYH3L4NAYhr5QGsPiT2rY/3E1DruNf5lzGX6/CZhWl2W5UBpDuZCV4xfwia+enFrqySmq8x0+fJg//OEPREREsGLFis5AA+0zQvn5+dxzzz243W5++ctfBlqyiEjQ8fkNXtzyMQBzZqSTOmJgTouLDCUBh5qMjAwATp482e1sTXl5eZe2l7J3715M02T8+PGdFxl/2k033QRAUVFRYAWLiASht/ae4HRtC3HRTr50Y4bV5YiEhYBDTXZ2Nk6nE4/H023A2Lt3LwC5ubk96rO5uf0csq0H+zJ0nNoSEQlV9c0eXn+nfXXol2+eSPQw3bBSpD8EHGpiYmI6l1W//PLLFxwvKyujoKAAgLy8vB71mZmZ2fna48ePX7RNx4Z/HW1FRELVhh1HaXX7GZ8Sx6wrUq0uRyRs9Gox+aJFi7DZbGzcuJH169d37gZcVVXF4sWLMQyDuXPnkpWV1eV1999/P7Nnz2bNmjVdnp81axYjR47E5/Px7//+73z88cedx7xeL7/97W/ZsGEDAPPmzetNySIiQeF4VRNvF50C4KtzL8du187BIv0l4NVPADk5OTz66KMsW7aMpUuXsmrVKhITEzly5Agej4fMzEyeeOKJC15XWVlJRUUFjY2NXZ6Piori5z//OYsWLeLQoUPcddddpKWldS7p7jg9ddttt/HVr361NyWLiASFV7YdwQSuyRrNZek9W0whIj3Tq1ADsHDhQiZPnswLL7xAUVERNTU1pKWlkZeXR35+PjExgV3Jf/311/OXv/yFtWvXsmvXLk6cOEFlZSUJCQlMnz6de+65hzvuuKO35YqIWO5gaS3FpbU47Da+fPMEq8sRCTs2s+Pc0RDh9xvU1vbv5lYREXYSE2Ooq2vW3gohSmMY+oJ9DA3T5PHVuymvamLujHS+cuvlVpcUdIJ9DOWzDeT4JSXF9GjzPd1gQ0RkELx3sJLyqiaiIh3cpSXcIgNCoUZEZIB5fX42/OMoAF+cOZ64aJfFFYmEJ4UaEZEBtmXvCWoa3CTGRXLr1WOtLkckbCnUiIgMoKZWL3/ZdQyAez43AZfTYXFFIuFLoUZEZAD99d1jtLp9pI+K5YZpKVaXIxLWFGpERAZIXaObt/adAOC+z0/QRnsiA0yhRkRkgLzxbhlen8FlYxK4YsIIq8sRCXsKNSIiA6D6bCs7DpwE4J6bJvTohr0i0jcKNSIiA+D1d8rwGyZTxicyZXyi1eWIDAkKNSIi/ex0bQvvFLfftPJe3Q5BZNAo1IiI9LPXdn6CaULuZSOZmKabVooMFoUaEZF+dLyqifdLqgCY97lMi6sRGVoUakRE+tFrOz8B4Jqs0YxLjrO4GpGhRaFGRKSfHDvdyP6Pq7HZNEsjYgWFGhGRfvL6O6UAzMxOJnVEjMXViAw9CjUiIv2gvPLcLA1w5w0ZVpcjMiQp1IiI9IM/7yoD4FrN0ohYRqFGRKSPTlQ1sffDM+2zNNePt7ockSFLoUZEpI86ZmlmZI1mzKhYa4sRGcIUakRE+qCiupk9h9v3pfmSrqURsZRCjYhIH/xlVxkmMOPyUaSP1iyNiJUUakREeulUTTPvH6oE4K4bM6wtRkQUakREeuuNd49h0n6PJ+0eLGI9hRoRkV6oPttKwUHN0ogEE4UaEZFe2PR+OYZpkp2RSGZqvNXliAgKNSIiAatv9rCz6BQAd8zUvjQiwUKhRkQkQFv2HMfrM8hMjSdrfKLV5YjIOQo1IiIBaGnzsXXfCQDuuH48NpvN4opEpINCjYhIALbtP0Gr20/ayBhyJ420uhwROY9CjYhID3m8ft7cfRyAL1w3DrtmaUSCikKNiEgPvf3BKRpavIyIH8Z12clWlyMin6JQIyLSAz6/wd8KygHIu24cEQ59fIoEG70rRUR6YM/hKmoa2oiLdjIrJ9XqckTkIhRqREQuwTRNNr3XPkszd0Y6kU6HxRWJyMUo1IiIXMKhY3WUVzXhctq5ZXq61eWISDcUakRELqFjluZzV6QRG+W0uBoR6Y5CjYjIZzhe1cTB0lpsNrjt2rFWlyMin0GhRkTkM3TM0lw9eTSjhkdZXI2IfBaFGhGRbtQ2tPF+SSXQvoxbRIKbQo2ISDfe3HMcv2GSNW44manxVpcjIpegUCMichEtbT52HDgJaJZGJFQo1IiIXMSOwgraPO03rpw2YYTV5YhIDyjUiIh8is9vsGXPCQBuv3asblwpEiIUakREPmXPh1XUNbqJj3ExMzvF6nJEpIcUakREzmOaJpvfPw7A7OljcEboY1IkVOjdKiJyno9P1FN2uhFnhJ3PXzXG6nJEJAAKNSIi59m8u32W5vqpKcRHuyyuRkQCoVAjInJOVV0L+z86A8Ct1+iWCCKhRqFGROScLXtOYALTJiQxZmSM1eWISIAi+vLigoICVq9eTWFhIS0tLaSlpZGXl0d+fj7R0dG97nfHjh288sorHDhwgLNnzxIfH8+4ceO47rrr+M53vkNERJ/KFhG5QEubl51FpwC4TbM0IiGp1zM169atY+HChWzfvp3IyEgmTpxIRUUFq1at4r777uPs2bMB9+nz+XjkkUfIz8/nzTffxOFwkJWVRXR0NMXFxTz33HO43e7eliwi0q1/FJ7C7fUzZmQMUzOSrC5HRHqhV1MexcXFPPXUUwA8/vjjzJ8/H5vNRmVlJQ899BAHDx5kyZIlrFixIqB+f/zjH/P666+TlZXFE088QU5OTuex1tZWdu3ahculC/dEpH/5DYMte9svEL71mrHYtNmeSEjq1UzNypUrMQyDu+++mwULFnR+ACQnJ7N8+XLsdjubN2/m8OHDPe6zoKCAV155hdGjR7N27dougQYgKiqKOXPm4HQ6e1OyiEi39n54htoGN3HRTq6fmmx1OSLSSwGHmubmZnbu3AnA/PnzLziekZHBzJkzAdi0aVOP+12zZg0ADzzwAMOHDw+0LBGRXuu4JcItV43BGeGwuBoR6a2ATz+VlJTg8XhwuVwXzKZ0mDFjBrt27aKwsLBHfbrdbt5++20A5syZQ1FRERs2bODYsWNERkYybdo07rvvPlJStF25iPSv0lMNHKmox2G3cYs22xMJaQGHmtLSUgDS0tK6PRU0bty4Lm0v5fDhw3i9XqKjo/n73//OL37xCwzD6Dy+bds2fvOb37Bs2TK+8IUvBFryBSL6edtzh8Pe5VFCj8Yw9PV2DN/a2z5Lc112MiOGR/V7XdJzeh+GtmAYv4BDTX19PQAJCQndtuk41tH2Us6cad/syuPx8LOf/YwZM2bw2GOPMWnSJE6ePMnTTz/Npk2beOSRR8jMzCQrKyvQsjvZ7TYSEwdm/4n4eH0ghjqNYegLZAxrG9p4v6QSgC/PuXzAPhskMHofhjYrxy/gUNOxpPqzLtjtWKHU0+XXzc3NQPuS7sTERP7zP/+T2NhYoP0anaeffppjx45RUlLCqlWr+NWvfhVo2Z0Mw6ShoaXXr78Yh8NOfHwUDQ2t+P3GpV8gQUdjGPp6M4av7jiKz29yWXoCo+Jc1NU1D3CV8ln0PgxtAzl+8fFRPZoBCjjUREZGAuD1ertt4/F4urTtaZ8ACxYs6Aw0Hex2OwsXLuR//a//xdtvv41hGNjtvZ/e8vkG5s3i9xsD1rcMDo1h6OvpGHp9BlvPnXqaOyNd4x5E9D4MbVaOX8DJoCenlnpyiupifQJMmDDhom06nm9qaurVxn4iIud7v6SShhYviXGRTL98lNXliEg/CDjUZGRkAHDy5MluZ2vKy8u7tL2U84NMd7M75z9//kXEIiKBMk2zcxn37OljiNCFqSJhIeB3cnZ2Nk6nE4/HQ1FR0UXb7N27F4Dc3Nwe9ZmcnMyYMe1LKTsC0acdP96+26fL5dI+NiLSJx+fqOdYZSPOCDs352oZt0i4CDjUxMTEMGvWLABefvnlC46XlZVRUFAAQF5eXo/77Viq/dprr110JuaPf/wjANdee61uaCkifbLl3LU0109NJjZKu5SLhItezbkuWrQIm83Gxo0bWb9+PaZpAlBVVcXixYsxDIO5c+desPT6/vvvZ/bs2Z27B5/vgQceIC4ujqNHj/LUU091XmxsmiZr165l27Zt2Gw28vPze1OyiAjQvox734ft20jMmaG7cYuEk15NeeTk5PDoo4+ybNkyli5dyqpVq0hMTOTIkSN4PB4yMzN54oknLnhdZWUlFRUVNDY2XnAsKSmJZ555hoceeoh169bx+uuvM378eE6dOsWZM2ew2Ww88sgjXHfddb0pWUQEgG37KzBMk6xxwxk7OvbSLxCRkNHrq+MWLlzI6tWruemmm2htbeXIkSOkpaXxrW99iz/96U8kJSUF3OcNN9zAxo0buffee4mKiqKkpASfz8fs2bP53e9+xwMPPNDbckVE8Pr87DhwEoA5M9ItrkZE+lufLk65/vrruf7663vcfuvWrZdsk5GRwU9+8pO+lCUiclHvl1TR1OolKT6S3EkjrS5HRPqZ1jGKyJBw/jLuW64ag6MPG3iKSHDSu1pEhoSjFQ0cq2wkwmHnpivTrC5HRAaAQo2IDAlb9rbvdTUzO5m4aJfF1YjIQFCoEZGwV9foZm/nMm5dICwSrhRqRCTs7ThQgd8wmZSewPiUOKvLEZEBolAjImHN5zfYrmXcIkOCQo2IhLXdh6toaPbobtwiQ4BCjYiEta3n7vN0c26a7sYtEub0DheRsFV6qoGjJxtw2G26G7fIEKBQIyJha+u+9lmaa6aMJiFGy7hFwp1CjYiEpcYWD+8dqgJgznRdICwyFCjUiEhY2ll0Cp/fYHxKHBPS4q0uR0QGgUKNiIQdwzDZdu7U05zp6dhsNosrEpHBoFAjImGn8Eg1NQ1uYqOcXDtltNXliMggUagRkbDz1rlZms9dmYrL6bC4GhEZLAo1IhJWKqqbOVRWh80Gt2gZt8iQolAjImHlrT3td+POvWwkI4dHWVyNiAwmhRoRCRstbV7eLjoFwGwt4xYZchRqRCRsbNtznDaPn5SkaKZkJFpdjogMMoUaEQkLpmnyxq5SAGZPH4Ndy7hFhhyFGhEJCyVldRyvbGKYy8GNV6RaXY6IWEChRkTCwpvnLhC+4YpUoiIjLK5GRKygUCMiIa+mvo19H50BYO7VukBYZKhSqBGRkLf9QAWmCTmXjSR9VKzV5YiIRRRqRCSkeX0G/yg8CcAXb8y0uBoRsZJCjYiEtD2Hq2hs8ZIUF8nMqSlWlyMiFlKoEZGQ1nGfp9kz0nE49JEmMpTpE0BEQlbpqQY+OdmAw27j5tw0q8sREYsp1IhIyNp6bpbmmqzRJMRGWlyNiFhNoUZEQlJji4f3DlUBMGeGlnGLiEKNiISonUWn8PkNxqfEMSEt3upyRCQIKNSISMjxGwbbzp16mjM9HZvu8yQiKNSISAgqPFJDTYOb2Cgn104ZbXU5IhIkFGpEJOS8tbd9luZzV6bicjosrkZEgoVCjYiElJPVzZQcq8Nmg1uuGmN1OSISRBRqRCSkdCzjzr1sJCMToiyuRkSCiUKNiISMVrePd4pPA1rGLSIXUqgRkZCxq/g0bo+f1BHRTBmfaHU5IhJkFGpEJCSYptl56mm2lnGLyEUo1IhISDhUVsepmhYiXQ5umKa7cYvIhRRqRCQkdCzjnjUtlajICIurEZFgpFAjIkGv6mwrhUeqAZg9Q8u4ReTiFGpEJOht23cCE5iamUTqiBiryxGRIKVQIyJBze3xs7PwFKBl3CLy2RRqRCSovXvoNC1uH6OGDyNnwgiryxGRIKZQIyJByzTNzguE50xPx27XMm4R6Z5CjYgErQ/Lz1JxphmX086snFSryxGRIKdQIyJBq2OW5oZpqUQPc1pcjYgEO4UaEQlKNfVt7Pv4DABzpmsZt4hcWp9CTUFBAd/85jeZOXMmOTk55OXl8ctf/pKWlpZ+KW7Hjh1MnjyZyZMnM3v27H7pU0RCw7b9FZgmTBmfyJhRsVaXIyIhoNehZt26dSxcuJDt27cTGRnJxIkTqaioYNWqVdx3332cPXu2T4U1NTXxox/9qE99iEhocnv97DhQAWgZt4j0XK9CTXFxMU899RQAjz/+ONu3b+fVV19ly5YtTJ06laNHj7JkyZI+Ffbzn/+cU6dOMXfu3D71IyKhp+DgaZrbfIxMGEbuZSOtLkdEQkSvQs3KlSsxDIO7776bBQsWdN4tNzk5meXLl2O329m8eTOHDx/uVVF79uzhpZde4tZbb2XOnDm96kNEQpNpmmzZc24Z9wwt4xaRngs41DQ3N7Nz504A5s+ff8HxjIwMZs6cCcCmTZsCLsjtdvPDH/6Q6OjoPs/2iEjoKTlWR0V1M5FOB5/TMm4RCUDAoaakpASPx4PL5SInJ+eibWbMmAFAYWFhwAX9+te/prS0lMWLF5OcnBzw60UktHXM0tx4RYqWcYtIQAIONaWlpQCkpaXhdF78A2fcuHFd2vZUSUkJzz//PDk5OXzlK18JtDQRCXFVdS2dd+PWBcIiEqiIQF9QX18PQEJCQrdtOo51tO0Jv9/PY489BsATTzyB3T5wW+hERPRv3w6HvcujhB6NYXDYtr8CE8iZOIKxyXEBvVZjGPo0hqEtGMYv4FDjdrsBup2lAXC5XF3a9sTzzz/PwYMHefDBB8nKygq0rB6z220kJsYMSN/x8VED0q8MHo2hdVravOwsar8b972zJ/X6faoxDH0aw9Bm5fgFHGoiIyMB8Hq93bbxeDxd2l5KWVkZzz77LOnp6Tz88MOBlhQQwzBpaOifzQE7OBx24uOjaGhoxe83+rVvGRwaQ+tt3l1OS5uP1BHRZIyOoa6uOaDXawxDn8YwtA3k+MXHR/VoBijgUNOTU0s9OUV1vh/96Ee43W5+/OMfExU18AnP5xuYN4vfbwxY3zI4NIbWMEyTN98/DrRfS2P4TQzMXvWlMQx9GsPQZuX4BRxqMjIyADh58iRer/eip6HKy8u7tL2UgwcPYrPZePTRRy841tbWBsCpU6e48cYbAVixYgXTp08PtHQRCVJFR2uorGslKjKCG6alWF2OiISogENNdnY2TqcTj8dDUVFR5/Lt8+3duxeA3NzcHvdrmibV1dXdHjcMo/P4Z536EpHQ8+bu9lmam3PTGOYK+GNJRAToRaiJiYlh1qxZbNu2jZdffvmCUFNWVkZBQQEAeXl5Pepzz5493R7bsGEDP/jBDxgzZgxbt24NtFwRCXLllY2UHKvDbrMxV8u4RaQPerXuatGiRdhsNjZu3Mj69esxzfZz31VVVSxevBjDMJg7d+4Fq5juv/9+Zs+ezZo1a/pcuIiEh45ZmquzRpEUP8ziakQklPUq1OTk5HRe/7J06VJuueUW7rnnHubMmcPBgwfJzMzkiSeeuOB1lZWVVFRU0NjY2LeqRSQsnG1yU3CoEoDbrhlncTUiEup6ffJ64cKFTJ48mRdeeIGioiJqampIS0sjLy+P/Px8YmIGZi8YEQkfW/dV4DdMLktPYEJavNXliEiIs5kd546GCL/foLY2sP0vLiUiwk5iYvu+GlqGGJo0hoPP4/Xz/ZW7aGr1smjeNK7OGt2n/jSGoU9jGNoGcvySkmJ6tE+N9qIWEUvsOniaplYvIxOGMf3yUVaXIyJhQKFGRAadYZqdFwjPvXosdrvN4opEJBwo1IjIoCv+pJZTNS0Mczn4XE6q1eWISJhQqBGRQbd5d/uu4zddmUZUpDbbE5H+oVAjIoPq2OlGDpWd22zvam22JyL9R6FGRAbV399vn6W5ZspoRiYM/A1sRWToUKgRkUFTXd/K+yVVAORdq832RKR/KdSIyKB5c/cJDNNkyvhExqfEWV2OiIQZhRoRGRTNbV7+UXgSgC9cp1kaEel/CjUiMii276/A7fWTPiqGqZlJVpcjImFIoUZEBpzXZ7BlzwkAbr92HDabNtsTkf6nUCMiA67g4Gnqmz0kxkVyXXay1eWISJhSqBGRAWWYJpvOLeO+9eqxRPTgpnQiIr2hTxcRGVBFR2o4VdNCVKSDm3PTrC5HRMKYQo2IDBjTNHmjoAyAz+eO0S0RRGRAKdSIyID56PhZjlY0EOGwc9s1Y60uR0TCnEKNiAyYN949BsCsnFQSYiMtrkZEwp1CjYgMiGOnGykurcVmgzxtticig0ChRkQGxBsF7bM0101JZvRw3bhSRAaeQo2I9LvTtS3sPdx+48ovzhxvcTUiMlQo1IhIv/tbwTFMIPeykaSPjrW6HBEZIhRqRKRf1Ta0sav4NABfvF6zNCIyeBRqRKRfbd59HL9hMnnscC4bk2B1OSIyhCjUiEi/aWj2sH1/BQB3aJZGRAaZQo2I9Ju/v1+Ox2eQmRrH1Mwkq8sRkSFGoUZE+kVji4et+9pnae66MRObzWZxRSIy1CjUiEi/2Lz7OG6vn/HJcVw5cYTV5YjIEKRQIyJ91tTqZcveEwB86cYMzdKIiCUUakSkz97cfRy3x8/Y0bHkThppdTkiMkQp1IhInzS3edmy9zigWRoRsZZCjYj0yZY9J2h1+xkzKoarLh9ldTkiMoQp1IhIr7W0+Xhzd/sszV03ZGDXLI2IWEihRkR67c09x2lx+0gbGcPVWaOtLkdEhjiFGhHplaZWL5t3lwPt19JolkZErKZQIyK98rf3jtHqbl/xpFkaEQkGCjUiErD6Jjdv7Wnfl+aez03QLI2IBAWFGhEJ2BvvHsPjM5iQFs+Vl2n3YBEJDgo1IhKQmvo2th9ov8fTvTdN0L40IhI0FGpEJCB/3lWKz2+SNW442Rm6E7eIBA+FGhHpscq6Ft4uOg3AvTdNtLgaEZGuFGpEpMc2vl2KYZrkTBzBZekJVpcjItKFQo2I9Eh5ZSPvHawE2lc8iYgEG4UaEemRV7YfxQSuy05mfEqc1eWIiFxAoUZELqm4tIaDpbU47DbuvUmzNCISnBRqROQzGYbJK9uOAjBnRjqjhkdZXJGIyMUp1IjIZ3r34GmOVzURFRnBnTdkWF2OiEi3FGpEpFser59Xd34CwJ03jCc2ymlxRSIi3VOoEZFubdl7gtoGNyPiI5k7I93qckREPpNCjYhcVGOLhzfeLQPgnpsm4IxwWFuQiMglKNSIyEW9/nYZrW4/40bHMnNqitXliIhcUkRfXlxQUMDq1aspLCykpaWFtLQ08vLyyM/PJzo6usf9mKbJ/v372bp1K3v37uWTTz6hqamJuLg4srOzmTdvHnfddZdunCcySE6caWLb/vabVi6YfRl2vfdEJAT0OtSsW7eOJ598EtM0SUlJITU1lSNHjrBq1So2b97Miy++yPDhw3vUV0FBAQsXLuz8eezYsYwZM4aKigreeecd3nnnHd544w1WrFiBy+Xqbcki0gOmafKHLR9jmCYzJo9iim5aKSIholenn4qLi3nqqacAePzxx9m+fTuvvvoqW7ZsYerUqRw9epQlS5b0uD/TNElPT+exxx5j165dbNmyhQ0bNvDee+/x05/+FJfLxfbt23nmmWd6U66IBGDfR2coOVaHM8LOglsus7ocEZEe61WoWblyJYZhcPfdd7NgwYLO00LJycksX74cu93O5s2bOXz4cI/6y8nJYdOmTXzta19jxIgRXY7NmzePb3/72wC88sorGIbRm5JFpAc8Xj8vvXUEgLxrxzFSG+2JSAgJONQ0Nzezc+dOAObPn3/B8YyMDGbOnAnApk2betRnbGwsTmf3+1/cdNNNAJw9e5ba2tpASxaRHtr0fjk1DW0kxkXyxZnjrS5HRCQgAYeakpISPB4PLpeLnJyci7aZMWMGAIWFhX2r7hy32935/bBhw/qlTxHpqrahjb++ewxovzg40qUl3CISWgK+ULi0tBSAtLS0bmdXxo0b16VtX73xxhsAZGVlERsb2+f+IiL6dyW7w2Hv8iihR2MIf9x+FI/PYPK44Vw/LSXkVhtqDEOfxjC0BcP4BRxq6uvrAUhISOi2TcexjrZ9cfDgQV566SUA8vPz+9yf3W4jMTGmz/1cTHy8rj8IdUN1DA98VEXBoUpsNlh0Xy5JSX3/5cEqQ3UMw4nGMLRZOX4Bh5qOU0GfdQ1Mx7Lr808b9UZ1dTUPP/wwXq+XW2+9lTvuuKNP/UH7HYcbGlr63M/5HA478fFRNDS04vfrQuZQNJTH0OPz8+zLBwCYe/VYEqMjqKtrtraoXhjKYxguNIahbSDHLz4+qkczQAGHmsjISAC8Xm+3bTweT5e2vdHY2Mg3vvENTp48ydSpU1m2bFmv+/o0n29g3ix+vzFgfcvgGIpjuPEfpVTWtTI81sW8WZkh/98/FMcw3GgMQ5uV4xfwia+enFrqySmqz9Lc3MyDDz7IoUOHmDRpEs8//3y/XEsjIl2drG7mrwXtFwd/Ze7lREX2aZNxERFLBRxqMjIyADh58mS3szXl5eVd2gaitbWVb37zmxw4cICMjAxWr15NYmJiwP2IyGczTJPfbTqM3zC5cuIIZkweZXVJIiJ9EnCoyc7Oxul04vF4KCoqumibvXv3ApCbmxtQ3263m0WLFrF7927GjBnD2rVrGTVKH7QiA+GdolN8dKIel9POV2+7PORWO4mIfFrAoSYmJoZZs2YB8PLLL19wvKysjIKCAgDy8vJ63K/X6+U73/kOu3btIiUlhbVr15KSojsDiwyEhmYPL29r3zl43qwJjEzQahMRCX29Wky+aNEibDYbGzduZP369ZimCUBVVRWLFy/GMAzmzp1LVlZWl9fdf//9zJ49mzVr1nR53u/38/3vf58dO3YwatQo1q5dy9ixY3v3XyQil/SHtz6muc3H2NGx3HpNutXliIj0i15dFZiTk8Ojjz7KsmXLWLp0KatWrSIxMZEjR47g8XjIzMzkiSeeuOB1lZWVVFRU0NjY2OX5v/3tb523VHC5XPzgBz/o9s9esmQJ2dnZvSlbRIC9H1bx3rk9aRZ+IQuHXRudiUh46PVSh4ULFzJ58mReeOEFioqKqKmpIS0tjby8PPLz84mJ6fkGdx1LwAEqKiqoqKjotu2nA5GI9FxDi4ff/f1DAL44czyZqfEWVyQi0n9sZse5oyHC7zeore3fjcUiIuwkJsZQV9esvRVC1FAZw5WvFbPncBVjRsWw9OvX4OznW4ZYaaiMYTjTGIa2gRy/pKSYHm2+Fz6faCLymd4vqWTP4SocdhsP3pEdVoFGRAQUakSGhPpmD/+1+SMA7rh+PONT4iyuSESk/ynUiIQ50zRZ9/cPaWr1Mm50LHfekGF1SSIiA0KhRiTM7Sw6xb6PzuCw23jgzmwienBeWkQkFOnTTSSMnaxu5sU320873XvTBMaO1j3URCR8KdSIhCmvz89zGw/i8RlMzUzi9uvGWV2SiMiAUqgRCVPrtx7hxJkm4qOdPHjHFOy6t5OIhDmFGpEwtO+jM2zd176J5YN3ZpMQG2lxRSIiA0+hRiTM1Da0sfqvJQDkXTuOaRNGWFyRiMjgUKgRCSM+v8GqjcU0t/nITI3j3psnWF2SiMigUagRCSMvvvkRRysaiIqM4Jtfmqrl2yIypOgTTyRM7DhQwfYDJ7EB3/xSNqMTo60uSURkUCnUiISBoxX1/P7cfjTzbppAzsSRFlckIjL4FGpEQlx9k5tfv/oBPr/J9MtHccf1460uSUTEEgo1IiHM5zdY+VoxZ5s8pI6I5gHtRyMiQ5hCjUiIMk2T1X89zMcn6omKdPDwvVcQFRlhdVkiIpZRqBEJUa/uLOXdg6ex22x86+5ppI6IsbokERFLKdSIhKB/FJ7kL7vKAPha3mSu0AZ7IiIKNSKh5oNPavjdpg8BuPOGDG66Ms3iikREgoNCjUgIOXa6kZWvFWOYJtdPTeGez2VaXZKISNBQqBEJEadqmnn65QO4PX6mjE/k376YhU0rnUREOinUiISAyroW/u8f9tPQ4mVccizfvucK3QJBRORT9KkoEuSqz7bysz/sp77Jw5hRMXxvQS7Rw7R0W0Tk0xRqRIJYbUMb//cP+6ltcJM6Iprv/8tVxEW7rC5LRCQoKdSIBKm6Rjc/+8N+quvbGD08iu//y1UkxCjQiIh0R3PYIkGosraFX6w/QHV9GyPih/HI/VeRGBdpdVkiIkFNoUYkyJRXNrJ8/QEaWryMTozi+wtyGZEwzOqyRESCnkKNSBD56PhZfvXHIlrdPsaNjuU/FuTqlJOISA8p1IgEicIj1ax8rRivz+Dy9AT+/b4rtcpJRCQA+sQUsZhpmry55wTrt36MaULOxBE8NG8akU6H1aWJiIQUhRoRC3l9Bus2f8jbRacAmHVFKl/Lm6yN9UREekGhRsQiDc0efv3qB3x8oh6bDebfchm3XTNWtz4QEeklhRoRC5SdbuDXGz6gpsFNVKSDb35pGjkTR1hdlohISFOoERlEpmny5u7jvLL9KH7DZHRiFP/+5RzSRsZYXZqISMhTqBEZJA0tHl54o4SiozUAXDVpJP/2xSnERjktrkxEJDwo1IgMgpKyWv7zL4eob/IQ4bDzL3Mu45arxuj6GRGRfqRQIzKAWtp8/HHHUbbvrwAgdUQ037p7GmNHx1pcmYhI+FGoERkg+z8+w39t/oi6RjcAn89NY8HsSUS6tP+MiMhAUKgR6Wdnm9y89NbHvF9SBcDoxCgW5mWRNT7R4spERMKbQo1IP/F4/fz9/XL+WlCO2+vHbrNx+7VjuXtWJi7tDiwiMuAUakT6yDBN3jtUyZ92HKW2of1UU2ZqPP/99svJSIm3uDoRkaFDoUakl0zTpPBoDa+/XUrZ6UYARsRH8uXPT+TaKcnYtbJJRGRQKdSIBMgwTfZ/VM2fd5VSXtkEQKTLwZ3Xj+fWq8fqVJOIiEUUakR6yOsz2H24kk3vlXPiTDMAkU4Ht0wfw+3XjiMhxmVxhSIiQ5tCjcgl1Da0sf1ABTsOnKSxxQvAMJeDOTPSue2ascRFK8yIiAQDhRqRi/D5DYo/qeWd4lPs/6gawzQBSIyL5PNXjWH29DHEDNPtDUREgolCjcg5pmlytKKetwtP8V5JJU2t3s5jk8cOZ86MdHInjSTCYbewShER6Y5CjQxpfsPg4+P1FB6t5sCRGiprWzqPxce4uG5KMrNyUnVbAxGREKBQI0NOXaObkmO1HCyto+hoNc1tvs5jrgg70y8fxfXTUsjOSMRh16yMiEio6FOoKSgoYPXq1RQWFtLS0kJaWhp5eXnk5+cTHR0dNH3K0Fbb0MaRino+PH6WkrI6Tp83GwMQG+Xkqkkj+dz0sWSOjsFh1/4yIiKhyGaa566ADNC6det48sknMU2TlJQUkpKSOHLkCB6Ph4kTJ/Liiy8yfPhwy/v8NL/foLa2uU99fFpEhJ3ExBjq6prx+Yx+7VsC09Di4XhVE8crmzh6sp5PTjZ03lCygw0YnxLHlIxEciaM4LL0BCJdERrDEKf3YejTGIa2gRy/pKQYHD24nrFXMzXFxcU89dRTADz++OPMnz8fm81GZWUlDz30EAcPHmTJkiWsWLHC0j4lfDW2eDhV08Lp2vavijPNHK9q5GyT54K2dpuN9NExXDYmgSnjk8gaP1wrl0REwlCvQs3KlSsxDIN58+axYMGCzueTk5NZvnw5X/jCF9i8eTOHDx8mKyvLsj4lNBmmSWOLl7ONbuqa3NTUt1FT30Z1fSvV9W2cOdva5TqYTxs9PIqxo2PJTItnYlo8GSnxRLq0y6+ISLgLONQ0Nzezc+dOAObPn3/B8YyMDGbOnMmuXbvYtGlTjwLIQPQpwcHnN2jz+Gl1+2hp89HS5qW5zUdzm5eWNh+NLV4aWzw0dD56qG/y4DcufVZ0RHwkKUnRpCTFkDYymrGj4xgzKoaoSF3/LiIyFAX86V9SUoLH48HlcpGTk3PRNjNmzGDXrl0UFhZa1udg8/r8uL3+f55HPO/fZPPcDxe7eqn9ObPzJee36bjcqaOJaZpd2pimidnl+fafjfOeNzof25/zGyaGYWKaZvv3ponf3/6c/9yXz2+0f+838Bntx71+A5/PwOc38PoNvD4Dj9fA6/Pj8Rl4vH7c3o7H9q82jx9vL8+r2mhfUj08NpKk+EhGJkQxMmEYI4cPY2RCFKMTo4jUPZZEROQ8AYea0tJSANLS0nA6L35dwrhx47q0taLPzxIR0b/LdLfuO8HvNn2I0YPZhaHK5bQTFRlB7DAn0cMiiIlyEjMsgrhoF/ExLuKincTHuIiPdpEYF0lCrGtQl1N3XIDWkwvRJDhpDEOfxjC0BcP4BRxq6uvrAUhISOi2TcexjrZW9Nkdu91GYmJMn/r4tGGRzotPw/Qzm619BgObDRtgs9mw2879bGu/INZua3/eZmv/b21vc+55uw2H/dzP9vavCLsdu6P9+fYvOxEOGw6HHWeEHYfdRkSEHee5n50RDpwRdlxOB5HO9sf27x0MczkY5oogMrL9MToyguhhEURFRoTMh1R8fJTVJUgfaQxDn8YwtFk5fgGHGre7fXlsdzMqAC6Xq0tbK/rsjmGYNDS0XLphAD6Xk8qt143nbH0Lhv+8cGO7yLe2jod/HrR9aluU9vBiO69te1AJPSZetxev23vpphZzOOzEx0fR0NCK36+lpKFIYxj6NIahbSDHLz4+amCWdEdGRgLg9Xb/D5XH4+nS1oo+P8tA7H/gcjpwOuz4zF70/alJHtP853U43TaSAeE/d+2QhC6NYejTGIY2K8cv4HMCPTkN1JPTSQPdp4iIiAwtAYeajIwMAE6ePNntzEp5eXmXtlb0KSIiIkNLwKEmOzsbp9OJx+OhqKjoom327t0LQG5urmV9ioiIyNAScKiJiYlh1qxZALz88ssXHC8rK6OgoACAvLw8y/oUERGRoaVX62wXLVqEzWZj48aNrF+/vnOTuKqqKhYvXoxhGMydO/eCnX/vv/9+Zs+ezZo1a/qtTxERERHow12616xZw7JlyzBNk9TUVBITEzvvqJ2ZmcmLL75IUlJSl9fMnj2biooKHn74Yb7zne/0S5+B0l265WI0hqFPYxj6NIahLWTv0g2wcOFCJk+ezAsvvEBRURE1NTWkpaWRl5dHfn4+MTGBb3A3EH2KiIjI0NDrmZpQpZkauRiNYejTGIY+jWFoC4aZmtDYu15ERETkEhRqREREJCwo1IiIiEhYUKgRERGRsKBQIyIiImFhyK1+Mk0Tw+j//2SHw97vt1qXwaUxDH0aw9CnMQxtAzV+drsNm812yXZDLtSIiIhIeNLpJxEREQkLCjUiIiISFhRqREREJCwo1IiIiEhYUKgRERGRsKBQIyIiImFBoUZERETCgkKNiIiIhAWFGhEREQkLCjUiIiISFhRqREREJCwo1IiIiEhYUKgRERGRsKBQIyIiImEhwuoChpLKykruuOMOGhsbAXjrrbdIT0+3uCrpTllZGW+++SbvvfceH374IXV1dURGRpKZmcltt93GV7/6VWJiYqwuc8grKChg9erVFBYW0tLSQlpaGnl5eeTn5xMdHW11edIN0zTZv38/W7duZe/evXzyySc0NTURFxdHdnY28+bN46677sJms1ldqgRgx44d5OfnAzBmzBi2bt06qH++zTRNc1D/xCFs0aJFvPXWW50/K9QEL7/fT3Z2dufPo0aNIjk5merqak6fPg3AuHHjWLNmDWPGjLGqzCFv3bp1PPnkk5imSUpKCklJSRw5cgSPx8PEiRN58cUXGT58uNVlykW8++67LFy4sPPnsWPHEh8fT0VFBWfPngXg85//PCtWrMDlcllTpASkqamJO++8k1OnTgHWhBqdfhokf/3rX3nrrbeYO3eu1aVID5imSWxsLA8++CB//etfefvtt/nTn/7Ejh07WL9+Penp6ZSXl/Mf//EfVpc6ZBUXF/PUU08B8Pjjj7N9+3ZeffVVtmzZwtSpUzl69ChLliyxuErpjmmapKen89hjj7Fr1y62bNnChg0beO+99/jpT3+Ky+Vi+/btPPPMM1aXKj3085//nFOnTln675xCzSA4e/YsTz75JKmpqXz3u9+1uhzpAYfDwVtvvcUjjzzCxIkTuxzLzc3lZz/7GQCFhYWUlJRYUeKQt3LlSgzD4O6772bBggWdpymSk5NZvnw5drudzZs3c/jwYYsrlYvJyclh06ZNfO1rX2PEiBFdjs2bN49vf/vbALzyyisYhmFFiRKAPXv28NJLL3HrrbcyZ84cy+pQqBkEP/nJT6iurmbp0qU6xx8ibDbbZ562mD59OnFxcQCUlpYOUlXSobm5mZ07dwIwf/78C45nZGQwc+ZMADZt2jSotUnPxMbG4nQ6uz1+0003Ae2/FNbW1g5WWdILbrebH/7wh0RHR1s+O6pQM8DefvttXnvtNW6//XZmz55tdTnST/x+Pz6fD4Bhw4ZZXM3QU1JSgsfjweVykZOTc9E2M2bMANpn0yT0uN3uzu/1Hgtuv/71ryktLWXx4sUkJydbWotCzQBqaWlh6dKlxMbG8thjj1ldjvSjt956i9bWViIiIsjNzbW6nCGnY3YsLS2t29/2x40b16WthJY33ngDgKysLGJjYy2uRrpTUlLC888/T05ODl/5ylesLkehZiAtX76cioqKoEiv0n+ampr46U9/CsCXv/xlkpKSLK5o6KmvrwcgISGh2zYdxzraSug4ePAgL730EkDn8mAJPn6/v/MX9ieeeAK73fpIYX0FYWr//v38/ve/Jzc3l/vvv9/qcqSf+P1+Fi9ezIkTJxgzZgyPPPKI1SUNSR2nJj7rmoyOZcDnn8aQ4FddXc3DDz+M1+vl1ltv5Y477rC6JOnG888/z8GDB1m4cCFZWVlWlwNo870LLF26lPXr1wf8umuvvZZ169YB4PF4+OEPf4jdbufxxx8PivQ6lPTHGF6MaZosWbKEHTt2kJCQwHPPPdd5sbAMrsjISAC8Xm+3bTweT5e2EvwaGxv5xje+wcmTJ5k6dSrLli2zuiTpRllZGc8++yzp6ek8/PDDVpfTSaHmU+Li4hg5cmTArzt/Gvw3v/kNR44cIT8/n8mTJ/dnedID/TGGF/N//s//4U9/+hMxMTH89re/5fLLL+9tidJHPTm11JNTVBI8mpubefDBBzl06BCTJk3i+eef17U0QexHP/oRbrebH//4x0RFRVldTiftKDwAOnYOHj58OBERXXOj3++nrq4OgMTERBwOB//jf/wPHnjgAStKlR766U9/ygsvvEBUVBS//e1vufrqq60uaUjbvXs3//qv/4rL5WLfvn0XPQ317LPPsmLFCq6//nrWrFkz+EVKj7W2tvKNb3yD3bt3k5GRwX/9138xatQoq8uSz3D11VfT1NR0wR5DAG1tbTQ1NWG32zuvOVyxYgXTp08f8Lo0UzOAOrb67k5HuGlpaRmEaqS3nn76aV544QUiIyNZtWqVAk0QyM7Oxul04vF4KCoq6ly+fb69e/cCaHVakHO73SxatIjdu3czZswY1q5dq0ATIkzTpLq6utvjhmF0Hv+sU8X9SaFmAKxcubLbYydOnOjcbVH3fgp+zz33HM899xxOp7Pzt36xXkxMDLNmzWLbtm28/PLLF4SasrIyCgoKAMjLy7OiROkBr9fLd77zHXbt2kVKSgpr164lJSXF6rKkB/bs2dPtsQ0bNvCDH/xA934SCSa/+93vePrpp4mIiODpp5/m5ptvtrokOc+iRYuw2Wxs3LiR9evX03EmvaqqisWLF2MYBnPnzg2aVRnSld/v5/vf/z47duxg1KhRrF27lrFjx1pdloQ4XVMzyDRTExoqKyu5+eabMU2ThISEC+7/dL4vf/nL3HfffYNYnXRYs2YNy5YtwzRNUlNTSUxM7LxLd2ZmJi+++KL2EQpSf/nLX/je974HtN/N+bP28lqyZAnZ2dmDVZr0kZUzNTr9JHIRXq+38zf/+vp69u3b123bG264YbDKkk9ZuHAhkydP5oUXXqCoqIiamhrS0tLIy8sjPz+fmJgYq0uUbnQsuQeoqKigoqKi27aNjY2DUZKEAc3UiIiISFjQNTUiIiISFhRqREREJCwo1IiIiEhYUKgRERGRsKBQIyIiImFBoUZERETCgkKNiIiIhAWFGhEREQkLCjUiIiISFhRqREREJCwo1IiIiEhYUKgRERGRsKBQIyIiImHh/wehWB1kH7MFQAAAAABJRU5ErkJggg==", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate random samples\n", + "n = 100\n", + "samples = stt.norm.rvs(loc=0.1, scale=1.0, size=n)\n", + "\n", + "# t statistics\n", + "t = np.mean(samples) * np.sqrt(n) / np.std(samples) # n should be replaced by n-1 for unbiased estimate\n", + "print('t statistics:', t)\n", + "print('p value:', 1.0 - np.abs(0.5 - stt.norm.cdf(t))*2)\n", + "print(stt.ttest_1samp(samples, popmean=0.0))\n", + "\n", + "plt.figure()\n", + "plt.hist(samples, bins=50)\n", + "plt.title('sample mean {:.4f}'.format(samples.mean())) \n", + "\n", + "vx = np.linspace(-4.0,4.0,100)\n", + "plt.figure()\n", + "plt.plot(vx, stt.norm.cdf(x=vx))\n", + "plt.plot(t, 1.0, 'x')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c6f9c939-ba4e-474e-89bb-a3cae4c6fe46", + "metadata": {}, + "source": [ + "## Statistical testing: is a distribution normal?\n", + "\n", + "Several tests exists to compare distributions:\n", + "- D’Agostino-Pearson (`normaltest`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html#scipy.stats.normaltest))\n", + "- Shapiro-Wilk (`shapiro`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html#scipy.stats.shapiro))\n", + "- Anderson-Darling (`anderson`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html#scipy.stats.anderson))\n", + "\n", + "For example, the `normaltest` rely on the combined `kurtosistest` and `skewtest` that check how close to zero these statistics are (to match a normal distribution).\n", + "\n", + "From the doc: If the p-value is “small”, there is a low probability of sampling data from a normally distributed population. In other words, this may be taken as evidence against the null hypothesis in favor of the alternative: the weights were not drawn from a normal distribution.\n", + "\n", + "*Importantly:* The inverse is not true; that is, these tests are not used to provide evidence for the null hypothesis.\n", + "\n", + "In contrast, the `anderson` test fits to a given distribution and evaluates the goodness of fit. In this way, you get an estimation of the mean and variance of the estimated distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "d4f3f64e-cfa8-4b58-b27c-3ac289ffb5c3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SkewtestResult(statistic=-0.7473091515071377, pvalue=0.4548769696331981)\n", + "KurtosistestResult(statistic=-1.339055153956115, pvalue=0.18055271842563614)\n" + ] + } + ], + "source": [ + "print(stt.skewtest(samples))\n", + "print(stt.kurtosistest(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "395d152c-becb-4fed-b755-e5af7c94983e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NormaltestResult(statistic=2.3515396732627534, pvalue=0.30858133101205654)\n" + ] + } + ], + "source": [ + "print(stt.normaltest(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "bf09163c-0c14-434a-bc20-3fa5d3ab34e8", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ShapiroResult(statistic=0.9983673691749573, pvalue=0.47113797068595886)\n" + ] + } + ], + "source": [ + "print(stt.shapiro(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "6b57ebfd-4cea-4143-8348-cf849531c4ab", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AndersonResult(statistic=0.4331062623048183, critical_values=array([0.574, 0.653, 0.784, 0.914, 1.088]), significance_level=array([15. , 10. , 5. , 2.5, 1. ]), fit_result= params: FitParams(loc=0.024246059522653948, scale=1.0050225500511163)\n", + " success: True\n", + " message: '`anderson` successfully fit the distribution to the data.')\n" + ] + } + ], + "source": [ + "print(stt.anderson(samples, dist='norm'))" + ] + }, + { + "cell_type": "markdown", + "id": "0e840030-3d48-4313-9ef9-c543c6c25fe6", + "metadata": {}, + "source": [ + "### *EXERCISES*\n", + "- Apply these tests for various sample sizes and check the robustness of these tests\n", + "- Redo these steps with the lognormal distribution, playing with the shape $s$\n", + "- Try to fit the data *NeuroCog* (cognitive scores from patients and controls, see below), using the `fit` method of distributions (e.g. `norm.fit(...)`, `lognorm.fit(...)`, etc.)" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "id": "5d42fe82-e5d6-44f4-915e-a46f21f83a96", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 10\n", + "skew:\t\t -0.4056769282907124\n", + "kurtosis:\t -0.6186397927189051\n", + "NormaltestResult(statistic=0.529642403163842, pvalue=0.7673431374501384)\n", + "ShapiroResult(statistic=0.9712831377983093, pvalue=0.90248042345047)\n", + "\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/INT/gilson.m/.conda/envs/course/lib/python3.11/site-packages/scipy/stats/_stats_py.py:1736: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", + " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 100\n", + "skew:\t\t 0.0882717421381724\n", + "kurtosis:\t -0.4086837585969967\n", + "NormaltestResult(statistic=0.7407235723064387, pvalue=0.6904844777203649)\n", + "ShapiroResult(statistic=0.9915692806243896, pvalue=0.7892195582389832)\n", + "\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 1000\n", + "skew:\t\t 0.03648349165645193\n", + "kurtosis:\t -0.0058636379577423625\n", + "NormaltestResult(statistic=0.23071365915424577, pvalue=0.8910481348435335)\n", + "ShapiroResult(statistic=0.9987481236457825, pvalue=0.7207890152931213)\n", + "\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 10000\n", + "skew:\t\t -0.005099974965489589\n", + "kurtosis:\t 0.03517605226874165\n", + "NormaltestResult(statistic=0.5956030068563615, pvalue=0.7424486986436052)\n", + "ShapiroResult(statistic=0.9998794794082642, pvalue=0.914222002029419)\n", + "\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/INT/gilson.m/.conda/envs/course/lib/python3.11/site-packages/scipy/stats/_morestats.py:1816: UserWarning: p-value may not be accurate for N > 5000.\n", + " warnings.warn(\"p-value may not be accurate for N > 5000.\")\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 100000\n", + "skew:\t\t -0.01271014498484355\n", + "kurtosis:\t 0.013970144638268067\n", + "NormaltestResult(statistic=3.5157215664715156, pvalue=0.17241329902081415)\n", + "ShapiroResult(statistic=0.9999722838401794, pvalue=0.6788431406021118)\n", + "\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# loop to generate samples with various sizes\n", + "v_n = [10,100,1000,10000,100000]\n", + "\n", + "for n in v_n:\n", + " print('sample size:', n)\n", + " samples2 = stt.norm.rvs(size=n)\n", + "# samples2 = stt.lognorm.rvs(s=0.1, size=n)\n", + "# samples2 = stt.lognorm.rvs(s=0.5, size=n)\n", + "\n", + " # variable range\n", + " vx2 = np.linspace(-3.0,3.0,50)\n", + " dx2 = np.diff(vx2)[0]\n", + "\n", + " # comparison between sample histogram and ground truth (probability density function)\n", + " plt.figure()\n", + " plt.hist(samples2, bins=vx2)\n", + " plt.xlabel('value')\n", + " plt.ylabel('sample count')\n", + " plt.tight_layout()\n", + "\n", + " # summary statistics\n", + " print('skew:\\t\\t', stt.skew(samples2))\n", + " print('kurtosis:\\t', stt.kurtosis(samples2))\n", + " \n", + " # tests for normality\n", + " print(stt.normaltest(samples2))\n", + " print(stt.shapiro(samples2))\n", + " \n", + " print()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "3239e1ef-7c45-47a6-b1aa-0573fa2214f6", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# load NeuroCog data \n", + "import pandas as pd\n", + "df = pd.read_csv('NeuroCog_dataset.csv', sep=',')\n", + "\n", + "# select memory scores for control subjects\n", + "sel_df = df['Dx']=='Control'\n", + "samples = np.array(df[sel_df]['Memory'])\n", + "n = samples.size" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "3a3e6bfe-2508-4b64-a3ca-3d64a7099b11", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# range of values\n", + "vx = np.linspace(samples.min(),samples.max(),50)\n", + "dx = np.diff(vx)[0]\n", + "\n", + "plt.hist(samples, bins=vx)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "# show percentiles from samples, top and bottom 5%\n", + "if True:\n", + " top_lim = stt.scoreatpercentile(samples, 95.0)\n", + " bottom_lim = stt.scoreatpercentile(samples, 5.0)\n", + " l = 10\n", + " plt.plot([top_lim]*2, [0,l], ls='--', c='gray')\n", + " plt.plot([bottom_lim]*2, [0,l], ls='--', c='gray')" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "8cd1d6fd-f2ca-4f27-a4f8-420fa9c03013", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SkewtestResult(statistic=-3.093498102795657, pvalue=0.0019781181783180414)\n", + "KurtosistestResult(statistic=1.47635115293601, pvalue=0.13984964859269813)\n", + "NormaltestResult(statistic=11.749343238775817, pvalue=0.002809716699540441)\n", + "ShapiroResult(statistic=0.967986524105072, pvalue=0.0018053010571748018)\n" + ] + } + ], + "source": [ + "print(stt.skewtest(samples))\n", + "print(stt.kurtosistest(samples))\n", + "print(stt.normaltest(samples))\n", + "print(stt.shapiro(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "a2eaebb2-3ce1-4c2e-b78a-1cd9237c986d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AndersonResult(statistic=1.4625728239705609, critical_values=array([0.561, 0.639, 0.767, 0.894, 1.064]), significance_level=array([15. , 10. , 5. , 2.5, 1. ]), fit_result= params: FitParams(loc=45.66206896551724, scale=11.182340175507374)\n", + " success: True\n", + " message: '`anderson` successfully fit the distribution to the data.')\n", + "AndersonResult(statistic=38.501451395049344, critical_values=array([0.918, 1.074, 1.335, 1.599, 1.949]), significance_level=array([15. , 10. , 5. , 2.5, 1. ]), fit_result= params: FitParams(loc=0.0, scale=45.66206896551724)\n", + " success: True\n", + " message: '`anderson` successfully fit the distribution to the data.')\n" + ] + } + ], + "source": [ + "for dist_type in ['norm', 'expon']:\n", + " print(stt.anderson(samples, dist=dist_type))" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "fd2f6d0e-22ac-44c2-99dc-911a8a6712b9", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[<matplotlib.lines.Line2D at 0x7fa5037f58d0>]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# fit a normal distribution to the empirical data\n", + "fitted_loc, fitted_scale = stt.norm.fit(data=samples)\n", + "\n", + "plt.hist(samples, bins=vx)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx, stt.norm.pdf(x=vx, loc=fitted_loc, scale=fitted_scale)*n*dx)" + ] + }, + { + "cell_type": "markdown", + "id": "12cd9759-5bf4-4ab7-a75b-5cba2122f1df", + "metadata": {}, + "source": [ + "## Statistical testing to compare two distributions\n", + "\n", + "We can now consider the distributions of real data across several conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a83ce97d-6fc3-46d0-906c-d0eec135e514", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'sb' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43msb\u001b[49m\u001b[38;5;241m.\u001b[39mviolinplot(data\u001b[38;5;241m=\u001b[39mdf, x\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mDx\u001b[39m\u001b[38;5;124m'\u001b[39m, y\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mMemory\u001b[39m\u001b[38;5;124m'\u001b[39m, order\u001b[38;5;241m=\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mControl\u001b[39m\u001b[38;5;124m'\u001b[39m,\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mSchizophrenia\u001b[39m\u001b[38;5;124m'\u001b[39m,\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mSchizoaffective\u001b[39m\u001b[38;5;124m'\u001b[39m))\n\u001b[1;32m 2\u001b[0m plt\u001b[38;5;241m.\u001b[39mxticks(fontsize\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m14\u001b[39m)\n\u001b[1;32m 3\u001b[0m plt\u001b[38;5;241m.\u001b[39mshow()\n", + "\u001b[0;31mNameError\u001b[0m: name 'sb' is not defined" + ] + } + ], + "source": [ + "sb.violinplot(data=df, x='Dx', y='Memory', order=('Control','Schizophrenia','Schizoaffective'))\n", + "plt.xticks(fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "3d8e7686-8ae6-404c-886e-669873077ac6", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# get memory scores for controls and schizophrenia patients\n", + "score_measure = 'Memory'\n", + "sel_df = df['Dx']=='Control'\n", + "samples_ctrl = np.array(df[sel_df][score_measure])\n", + "sel_df = df['Dx']=='Schizophrenia'\n", + "samples_pat = np.array(df[sel_df][score_measure])\n", + "n_ctrl = samples_ctrl.size\n", + "n_pat = samples_pat.size\n", + "\n", + "# range of values\n", + "samples = np.concatenate((samples_ctrl, samples_pat))\n", + "vx = np.linspace(samples.min(),samples.max(),50)\n", + "dx = np.diff(vx)[0]\n", + "\n", + "plt.hist(samples_ctrl, bins=vx, histtype='step', label='ctrl')\n", + "plt.hist(samples_pat, bins=vx, histtype='step', label='pat')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "336eb4c9-ea1a-4e9a-8a8b-da9ada5aa639", + "metadata": {}, + "source": [ + "\n", + "\n", + "https://en.wikipedia.org/wiki/Student%27s_t-test\n", + "\n", + "$\\chi$2 distibution [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html#scipy.stats.chi2)" + ] + }, + { + "cell_type": "markdown", + "id": "e0bfb221-6a9e-4905-a6bf-a3c5c7b5ba0e", + "metadata": {}, + "source": [ + "\n", + "\n", + "$$ f(x, k) = \\frac{1}{2^{k/2} \\Gamma \\left( k/2 \\right)}\n", + " x^{k/2-1} \\exp \\left( -x/2 \\right)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "2cb261b3-1444-44f6-ad28-d4177628c3d4", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ttest_indResult(statistic=4.707384156121897, pvalue=4.667384543620185e-06)\n" + ] + } + ], + "source": [ + "# Student's t-test (parametric: normal distributions with equal variances)\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat))" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "3418daca-4220-4b81-82ce-d8bc59bc691e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "variances\n", + "controls: 88.48104637336505\n", + "patients: 80.91557669441141\n" + ] + } + ], + "source": [ + "print('variances')\n", + "print('controls:', np.var(samples_ctrl))\n", + "print('patients:', np.var(samples_pat))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "f63fc195-1845-4eb0-86c7-1fbcb1650f76", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ttest_indResult(statistic=4.580013245897252, pvalue=1.3509339537040669e-05)\n" + ] + } + ], + "source": [ + "# Welch's t-test (parametric: normal distributions with unequal variances)\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat, equal_var=False))" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "0818927a-7d17-41b3-b21f-fac1e7cb5113", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MannwhitneyuResult(statistic=5934.5, pvalue=4.707083559908631e-06)\n" + ] + } + ], + "source": [ + "# Mann-whitney test or Wilcoxon unsigned test (non-parametric)\n", + "print(stt.mannwhitneyu(samples_ctrl, samples_pat))" + ] + }, + { + "cell_type": "markdown", + "id": "d4508eb8-e3b6-489c-9890-3ff65d7470ea", + "metadata": {}, + "source": [ + "### Exercise\n", + "- Redo the comparison of statistical tests for other cognitive scores\n", + "- Redo the comparison of statistical tests for normal and lognormal distributions (playing with the shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "9fd0d37b-f800-48dd-9586-70e5bc6a412f", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ttest_indResult(statistic=6.413417601062506, pvalue=9.972764687201873e-10)\n", + "Ttest_indResult(statistic=6.523279590300689, pvalue=2.2290120236851023e-09)\n", + "MannwhitneyuResult(statistic=6530.0, pvalue=7.415691530325375e-10)\n" + ] + } + ], + "source": [ + "# get memory scores for controls and patients\n", + "score_measure = 'Verbal' # 'Attention', 'Memory', 'Verbal', 'Visual'\n", + "sel_df = df['Dx']=='Control'\n", + "samples_ctrl = np.array(df[sel_df][score_measure])\n", + "sel_df = df['Dx']=='Schizophrenia'\n", + "samples_pat = np.array(df[sel_df][score_measure])\n", + "n_ctrl = samples_ctrl.size\n", + "n_pat = samples_pat.size\n", + "\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat))\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat, equal_var=False))\n", + "print(stt.mannwhitneyu(samples_ctrl, samples_pat))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c573b539-9003-414d-9d84-88743206b8e4", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample mean and variance:\n", + "sample1: -0.22844978193811102 1.1215425191224164\n", + "sample2: 0.37244619026073855 1.920809638872736\n", + "\n", + "theoretical t-statistics: -3.1739916913162465\n", + "Ttest_indResult(statistic=-4.150609995090302, pvalue=4.332082274870572e-05)\n", + "Ttest_indResult(statistic=-3.797514073026098, pvalue=0.00020792378728388963)\n", + "MannwhitneyuResult(statistic=7314.0, pvalue=0.00014970606933548852)\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create 2 normal distribution with variances sig1 and sig2, and mean separation of d_mu\n", + "d_mu = 0.5\n", + "sig1 = 1.0\n", + "sig2 = 1.5\n", + "n1 = 200\n", + "samples1 = stt.norm.rvs(loc=-0.5*d_mu, scale=sig1, size=n1)\n", + "n2 = 100\n", + "samples2 = stt.norm.rvs(loc=0.5*d_mu, scale=sig2, size=n2)\n", + "\n", + "print('sample mean and variance:')\n", + "print('sample1:', np.mean(samples1), np.var(samples1))\n", + "print('sample2:', np.mean(samples2), np.var(samples2))\n", + "\n", + "vx = np.linspace(-5.0,5.0,50)\n", + "plt.hist(samples1, bins=vx, histtype='step', label='norm1')\n", + "plt.hist(samples2, bins=vx, histtype='step', label='norm2')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()\n", + "\n", + "print()\n", + "print('theoretical t-statistics:', -d_mu / np.sqrt(np.var(samples1)/n1 + np.var(samples2)/n2))\n", + "print(stt.ttest_ind(samples1, samples2))\n", + "print(stt.ttest_ind(samples1, samples2, equal_var=False))\n", + "print(stt.mannwhitneyu(samples1, samples2))" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "id": "9f6440ed-d77d-46f5-a1a9-caf16a6c75ce", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean, variance:\n", + "sample1: -0.006983318346723335 0.9693682659115377\n", + "sample2: -1.3145040611561853e-16 1.0000000000000002\n", + "Ttest_indResult(statistic=-0.15728275832365698, pvalue=0.8750379000166193)\n", + "Ttest_indResult(statistic=-0.15728275832365698, pvalue=0.8750379038611265)\n", + "MannwhitneyuResult(statistic=532053.0, pvalue=0.013059026877977283)\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create \n", + "n1 = 1000\n", + "samples1 = stt.norm.rvs(loc=0.0, scale=1.0, size=n1)\n", + "n2 = 1000\n", + "samples2 = stt.lognorm.rvs(s=0.5, size=n2)\n", + "# z-score to center and get standard deviation equal to 1\n", + "samples2 -= samples2.mean()\n", + "samples2 /= samples2.std()\n", + "\n", + "print('mean, variance:')\n", + "print('sample1:', np.mean(samples1), np.var(samples1))\n", + "print('sample2:', np.mean(samples2), np.var(samples2))\n", + "\n", + "vx = np.linspace(-5.0,10.0,50)\n", + "plt.hist(samples1, bins=vx, histtype='step', label='lognorm')\n", + "plt.hist(samples2, bins=vx, histtype='step', label='norm')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()\n", + "\n", + "print(stt.ttest_ind(samples1, samples2))\n", + "print(stt.ttest_ind(samples1, samples2, equal_var=False))\n", + "print(stt.mannwhitneyu(samples1, samples2))" + ] + }, + { + "cell_type": "markdown", + "id": "55084553-673a-48f5-874f-58351613107f", + "metadata": {}, + "source": [ + "## Miscellanous\n", + "\n", + "We can also generate a random variable from empirical observations ([link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_histogram.html#scipy-stats-rv-histogram)). But this method doesn't generalize well in the sense of smoothing the histogram for small number of observed samples..." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "0cfe8571-012e-4ab2-8ea1-861aea6a17df", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "<matplotlib.legend.Legend at 0x7fa503555650>" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create a generator of random variables from the empirical samples\n", + "hist = np.histogram(samples, bins=100)\n", + "emp_rv = stt.rv_histogram(hist)\n", + "\n", + "# generate surrogate samples\n", + "surr_samples = emp_rv.rvs(size=100000)\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples, bins=vx, density=True, label='orig')\n", + "plt.hist(surr_samples, bins=vx, histtype='step', density=True, label='surr')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} -- GitLab