analysis.ipynb

{
 "cells": [
  {
   "source": [
    "# Matematično ozadje"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "Analiza glavnih komponent (*angl.* Principal Component Analysis oz. PCA) je metoda za analizo podatkov. Navadno se uporablja za podatkovne nabore, ki imajo visoko dimenzijo. Z analizo glavnih komponent lahko dimenzijo nabora podatkov občutno zmanjšamo, kljub temu pa ohranimo večino informacij, ki jih vsebuje celoten nabor. To nam pogosto močno olajša analizo podatkov in nam omogoči, da iz njih lažje sklepamo kaj konkretnega."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "V matematičnem jeziku je PCA preprosto linearni automorfizem nabora podatkov. Po transformaciji dobimo podatke zapisane v novi bazi, za katero velja, da imajo njeni bazni vektorji (ki jim pravimo glavne komponente) določeno urejenost. Prva glavna komponenta je vektor, v smeri katerega se ohrani največji delež variance, če nabor podatkov projiciramo nanj. Podobno velja za nadaljne glavne komponente."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "Izkaže se, da so tako definirane glavne komponente ravno lastni vektorji kovariančne matrike nabora podatkov, urejene po velikostih njihovih lastnih vrednosti. Za računanje lastnih vektorjev obstaja veliko metod, ena izmed najbolj stabilnih je kar SVD razcep. Izračun glavnih komponent torej ni nič drugega kot SVD razcep kovariančne matrike nabora podatkov. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "# Reševanje"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "Analizirali bomo mutacije, ki se pojavljajo na genomih posameznikov, ki prihajajo iz različnih populacij. Z analizo PCA bomo poskusili identificirati glavne dejavnike za temi mutacijami. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "Najprej naložimo vse potrebne pythonove knjižnice, ki jih bomo potrebovali."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "\n",
    "from sklearn.decomposition import PCA\n"
   ]
  },
  {
   "source": [
    "Preberemo nabor podatkov iz priložene datoteke ter mu dodamo ustrezno glavo, ki nam opiše kategorije posameznih parametrov. Nato izračunamo najpogostejše nukleobaze na posameznih mestih, saj bomo to potrebovali za analizo mutacij."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10101\n",
    "head = ['id', 'sex', 'population'] + list(range(n))\n",
    "dataset = pd.read_csv(\"dataset.txt\", delimiter=' ', header=None, names=head)\n",
    "mode_nucleobase = dataset.mode(axis=0, numeric_only=False).iloc[:1, 3:].values.tolist()[0]"
   ]
  },
  {
   "source": [
    "Sestavimo 995x10101 matriko, ki predstavlja mutacije na sekvencah genomov posameznikov iz nabora podatkov. Če se na j-tem mestu v sekvenci pojavi mutacija, je v matriki na tem mestu 1, drugače pa 0. To je dejanska numerična matrika podatkov, ki jo bomo analizirali."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "matrix = np.array([\n",
    "        [int(row[j] != mode) for j, mode in enumerate(mode_nucleobase)] for i, row in dataset.iterrows()]\n",
    ")\n",
    "        "
   ]
  },
  {
   "source": [
    "Na dobljeni matriki mutacij zdaj izvedemo algoritem PCA ter shranimo prve 3 komponente."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=3, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=3)\n",
    "pca.fit(matrix)"
   ]
  },
  {
   "source": [
    "Naš prvi graf prikazuje projekcijo nabora podatkov na prostor, ki ga napenjata prvi dve glavni komponenti. Vsak posameznik je predstavljen s točko in ima določeno barvo glede na populacijo, kateri pripada."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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A94GbgMuBaL9/LmBQ7jE3owz59UAVVyVrTitOy0Ct1W7h7tcvxV7I07XYTCSkOLjh8T4h+677cUdMi29acchwe2N5FFNY0ZEn28f+bVVXWaqpbJzAKMAN5PWMzQZ+Ab6IcswYYHHuMRmAB/gOeL5CZ6qpXsRUa0VKuQhYFMsxozHo7q40bF2Tmf9axvF9WXS9tBXXPtabmg1UVyBfToDj+zNxJNpwZniLHa9us2Q6XtAMZ4aH1XO3EwxILmE1I/iJ2mRxiJpM5lIyiacW2RHHu3AQDLsvxiXaaHVu/dhcsOY0YAnGf1JOYCowImx7EPgYZbwL4wb+C7wY6wlqqimntWhW5/4t6Ny/RcT22W/9yqd/X0QwECTH48dkEQT9UbxyAcm143lz1d3UqJvAew/ORUrJZfzK3czDketZNSKdsczkZzpxIRvytwPIuHh+ShqA5aQZf46K25utJlLqJ3DeVW1jfNWaUxd7Ee/FG2wLANGcDGf5p6M5YzgtQytFsXT6JqY8sRBXpheP06fi1hJMZkF8DTv2OAtNO9ShRae61GtRgyEP9uDdDfdSo24CAIs+3UDj4BHu47sQYw2qQrQt+5hNL7xY8ZodSLsDcd+99E/7nEvv6kJCioP4GnYGjOzMuBV3YrWdepromoriAsBmsD0BuNtguxXobrBdABfFblqaas9p7ZEb8fkLS/C6Qg1wMCCx2s08MvlKmrarTdP20bvzmN3ZvMZEzFFEthqSztJuI7lh8VzEvn3QuDEkJpIAjH73cka/e3m+TO3+rcdZ/tVmkmvHkTq4DTZHtfu4NSFYgDmoxctg7isAPABcEuWY/6KMthcVV7ejkr/eqOC5aqoT1c6yHD+QZbhdCEH7Pk2oWT8Rjh2DzExo0QJMoQ8lg+LTiMvxRi0APURNDu88gUhIgLYqbHJ0bwbv3T+X1d9vR5ig19VtsdktLJ2RhhBgMpuwWM28tOCWKm92oalozgMOohYsM4ABQIsi9u8ObATGA+uBnsCDQKMKnaWmelHtDPnZPRuxeu52AM4jjZEsoB4n2eupy+8PBeiXvhjTksVKkyU5GT74AIYUFKL2a+fDusI4nu5HMIVLqOM/oYqNWrXC4/Yz9rwPOXnEmZ9+uGzmZmRQEl40+/zQaXy4+6H8KlBNdSUOuK4U+zcHXq+guWjOBKqdIb/tlQFsXLyH3s5VPMjs/Dh3W/bT5otnkAjIC5u4XDBsGCxfDp07A9CsfR3kikhJFgnspg4PMJtaWdnQ5lVISWH5ff/BleUNzSEPGN8Isk962LH2EGd1bxjjq9ZoNGcy1W6xs1XmNj4auJaHxKyIxUoTMjL27fHAE09AMAjHj2NeuTzq2C04Ri2ylZGXEk6c4Jx/3kdOdvHpjaB0WXze2BQmaTQaTR7VyyN/5hl4/XWSXC4i4hrRCAZh3jxV1l+zJmzdahgfDwozJhmIeK+mzKKPZStL/e2KPZXJLGjTQ8c+NRpNbKk+Hvnu3fCvf4HTWXIjnkcgoI7//XfwG3jMJhPmczoYHmohyLliJ2ZLgYm32EzY4izYEyy5P5uxx1t47NNrsFh1OqKmMshGFSH9F/izCs6/M/e8uqVhZVB9PPIff4zIQAnHj0AgiWpKo90Aunfn4LkX0mDDhshDgH7Xnc0WZ0O8cxfiNMXRfHAqw25qxNbMZFascZFSP4GLbz+Xes1TSnVJmlMbr9/L/zb8jy/TvqRufF1G9xhNz8Y9q3paKEmAy3P/neeYjEbpv1T0QvsfwA3ArtxzNQCmARHKq2cYacC/UJ9PT+Ax1CJ3bKg+hjwpybA7kCQvo9eEpSwNmB0OuOIK/jmtJuMwYyE0vCIRJLRsxCNvPAhxVrWA+vUkmJ9IN7+fbtdcA+OngFUrIFYnPH4P5394PpuPbcbpc2ISJr7Y9AXjLhnH6B6jq3BmPmAoEJ6G+z4qv/3SsO0B4CvgcwoKly4o47ldwIUo1cc8p2gHMBBl2GuWcdzTnSXAZahagQCwFiXNsBwlklZ+qk9oZUhELwsARFwc8qprsJgFglL6I0JAXBzBa69je9pJHuFeTpKQX+qRjZ1J4jIYP14tmmZlFfQLzc5W277+Gl7UmhmnL5mogp5aQApwF3CMj3//mLRjaTh9qpQ+KIO4fC7G/jCWTG9V9mNdjDIW4TiBSWHbgiijfzswE/gEZXCeK+O5v0YZq/AnWz8qzHOmci/qJpf3vfhQN9qxMTtD9fHIExJgzhy48sqCEInPB+++i+XBByMaMocghHFYJTczxdS5E98AGcTzEZfwB80RSA5Qh8dNM5AuV/QbhNsN//kPPFfWPw5N1REE+gGbKdBE+QT4mVmbW+LyuSKOsJqtLNu7jMvOuqzyphlCUfK34eJc36EMf56ui0QZnH+iblhNSnnugxhrx7iAfaUcq7rgRmnNhyNRn31sqD6GHKBfPzh8GBYuVN7whRfC669H9vAsjBAqLJNZtBclgBRcPMQsBODEwUz6Eh9wFu/lZxlXm2pOdeYD2wk1Tj7gMJe2rs/cPwUyzPuUUlLDXqMS5xhOP4y1zxNQeueFmYWxOJcZWADcVsR53MDTwGTU5zMIuAWlNeML2zcR1X/mTMSa+zJyJGO3ZlZ9QisAOTnKC+/fH3r0gL//Hd4oRrOiTx9l9EuICWXUE/EwjMX4sOCmiPi3EOoGozkNWY+xh5nNNe1bEmeNC9kqEKQ4UjivyXmVMjtjElDGNQ7yfy8TUFIB4dWmKRj7ciZU+92iGAL8BziB8rhnAfehFvIKKz3GAR1RIZszEQtwK0o/pzDxwMMxO0v1MORZWTBypPKsk5MhPh5at1YhjaK8casV0tLUDaAMOPDRmZ0cJwl/7kcZ4p/ZbGpOb75ZpvE1Vc1ZRP4BAiTQrMZAnr/oeRwWB8n2ZJJsSTRKasS8W+ZhElX9Z3UjSr/lKeAh1GLmLIjI17oDDJ0QEwVZL0asBVYQGqoJorz7wcDLKOPdDngW+Mng3GcSb6JuZA6gBkoYbQSxjJELWdqc6xiQmpoqV61aFbsB+/dXZfbeklVYYsuVGvX5Sp9zHkYQgRcTcQTyjbioXRuaN1fnOXhQ/f/22+HRR1UWjOY0wQe0QcV38x6NTUAdVDZGAunudJbuWUqKI4Xzm51/ChjxotgLvEOBONf9wLcoka48g27O3da7iHE+yT02ssGKam33WYzmW93Yg/q9aQ+UreGMEGK1lDIil/P0N+RpaZCaWrTnXYFIomTCmM1gsRTcXOLi1Dx//lmFWzSnCQdQKXk/kls1AEwEWlXlpMrAWtTcc3JfjtzXr0A9VGOvOKA/xl56YVYAFxMZX3cAzwBPxGrSmjCiGfJT2X0oGdu3V2mOdlSTHAiEPiG43bB2rTLkmtOIRqjsDmfuayGnnxEHlQKXTUFWiwclszsG9bh/FSrHvCR/S+ehwiaFm2gIVMjAqIGGpqI5/Q15p06qLP90wOOBX3+t6lloyoSNolu5ncr4gNUG2yXqxlRaBCqj53qU4TehQjG/ANGbtmgqjnIbciFEUyHET0KITUKIP4QQsVuKLQkWi7E+yqmIwwFNSpubqymaHFSe7okqOPcsVCiiEyqccLwK5lASzET3tI16iZaEFOB/qDRED8qIdyzjWJryEguP3A+MlVJ2AHoBDwghYlN3WhxSwsUXV8qpyo0QypBfc01Vz6Qa8R7KA+wONASGo1LhKoMXUHnZi1AZIq8DXYGTlXT+0mBC5XiHP1HEAfeUc+yibhKayqLchlxKeVBKuSb331kodZjG5R23RKxaBftOwYoxIWDUKOjQQRlvu101rliyRC16lhKv38uTC56k7r/qkvByAld9fhU7TuyogImXnRPuE4xbNo5hM4bx4uIXOZx9uILP+C1KeCgTFfv1ojzkuyr4vKC8/5cJXezLAY6icqtPRd5EFeXEAcmohclBwD+qcE6aWBHTyk4hRAuUW7IyluNG5dChYhUPqwSTCc46CyZMUDcakwkalV2H/IbpNzB/x3zcfjcAc7bOYemepWx5cAt14uvEatZlZvfJ3aR+kIozx4nb72b2ltmMWzaOpXcu5Zx651TQWV8m0vv2oHKmTxLLqrlIVqO82/BCMg8wF3gyf4uUkoU7F/LD9h+oHV+bmzvdTOPkyvFzQklEVWtuArahwiBnVcE8NBVBzKygECIRpbzziJQyot5dCHGPEGKVEGLV0aNHY3PS1NSS545XJvHx0L69+neTJuUy4puPbQ4x4lAg0PT+qvfLO9OY8Oi8R0l3p+fP0eP3kOHNYNQ3oyrwrNGexKwoz7giaUBkGTqoRcBm+T8FggGGTh3KVZ9fxWvLXuOZn56hzdttmLttbgXPryg6oDJUtBGvTsTEkAshrCgj/j8p5ZdG+0gpJ0gpU6WUqXXrxmhlu2FDeOABJZhVHHFxlZOmaDKpUEqH2CwTbDyyEas5ct4ev4cV+1fE5BzlZd72eQRlpETwr/t/JSdQtqrZ4rkA42pBMwVd6/3ABFRGRW/gA8BPIBhg6oapXPbpZVzxvyuYuWkmpaunOAc4m8gH2jgKl11P3TiVRbsW5SskegNe3H43N828qQI/F82ZSCyyVgRKHzNNSln5rcDHjYOJE6FXL2jXDpo2VZkshYmPhwULoGXLyplTVhacc46SCCgnbWq1wR+MzMqxm+2cW//cco8fC+yWyLS8u7rCH/cHsZqaohYFd5Vh5MMo3eZpROpr/wOlIVL4VzgeeBXllUuUROsYVAHLCuARpLya66dfx6hvRjFv+zy++/M7bvv6Nu6YdUcp5zYX1SzBgdIlSUZpfhc0lvj494/zjXhh2tf1szfjEdRNJr2U59VoIomFR94XGAkMEEKsy30NjsG4JUMIGD5cleinpcG6dTBggPKKExNVH85Jk6B3b2XkK4q8WH0wqMI9Hg+MHatayJWDcxucS7eG3bCbQ42lzWxjdGpVNjAo4M6ud+KwFEgP/PtSGH8ZtKsDQhxBNS3ojpI5LSlvozzrB4BRqKyUeYXePwtYg7pJtADOB2agCl9AifkvITSO7iIoF5DtnRdiYJ0+J9M3TWfdoXWlmF8DVGOANOBnVDjnlpA9rKbIJ6l3B8OCW520rPkB6ibTFPihFOfVaCKJRdbKUimlkFJ2llJ2yX19F4vJlZrjx+GJJ1Q2S0ICXHutqvwcPly9//DDyjuvCIIG3YekhK++KvfQ3434jmHnDMNmtmESJno06sHiOxZX0aJZJC/0f4ELml1AvDWe5jUSuL8HJBQu+sttwwHFKFHmsxH4G2rxMBvljTtR6n2FPfPWKI99J8poFxZ6+hnjVEQvPRpHql36g37m75hfwvkVpgVqfd8W8c5d3e4iwVoQ9hvUGm49F+KtYBL+3Pm5UIU1JVfg1GjCOQVTPspITo4Kr0yeDOnp6jVtGlxySYEw1tChykuuzEyXGGjZJNmTmHL1FFxPunA/5ebXUb/SpUGXGEwuNjgsDn4Y+QPL71rOB0MfxmJKNNgrh5IL6X+CcYMEEzCnhGPUQ8WsQwlIKyc8kclaVpOVWnG1Sjh2ybim3TUMO2cYcZY47GY7d3czkxhp71GLpItieu6i8aP6d56FyhT+C3CsEs+viTXVx5B/9ZVKR/QVyibwemHLFtVoIo9nn1Uee2UsfAoBV18ds+HMJjM2s6ElOCXoXL8zl7S+C4vJSETfhFISLAlOjIX4g6hKwpIwDKPFUIvJxtebI797IQTXtQ/X6y4fQggmXTmJlXev5NWLXyW1Ubci9i5DP9kyMwwlL7sdJQo2ARXvP02kLjQRVB9DvmaN6pMZTk6OEqu6+mplWC0W6NYt1ODHGqtVZcm88krlLbCWgaAMsvbgWtYcXGOYdVI2WqGWTcIXQB2oAp6ScB1qITOcAGoxcRKqqnNPEWOkoFqWhXrfJuEk7f7mnNc4kWR7Msm2ZGrF1eLbEd9Sw1FUZ5+8JsU3oxoo/FbCa4FO9TvxcK+HaZHydBHXdVGJxysfm1ALtYXDTjkoj/zTSpqDJuZIKSv91b17dxlzJk6UMiFBShXMKHjZbFI6HJHbK/J1xx1S/vln7K8xhqzYu0I2GtdIJr6cKBNfTpQN/tVALtm9JEajZ0gpb5BS2qWUDillEynlt6U4PiilHNgpcH0AACAASURBVCmlTJDqV8YkpYyTUt6a+/+E3P87pJSvRhljtZQyXkb7NQwGa8glu7+Wi3ctlr6AL/cYp5RymZRyS9hYfinl5WHziZdS/rsU15R3XTfnjiOk+nzipJRfl3Kc8jBFSpkojT+XEZU4D01ZAFZJgy/v9NcjzyM7W3m/6enGC4+VSb16qqHEqVh1CmR4Mmj2RjMyc0LrthJtiex+ZHcMY8V5C5UNKELwNwp5ynzTUWmFV6EWM8NDK3Go1MLOYduvRXV1L+r3uweq2jEJFV54FBWO8aNkWr9Bydh+jUrMCn/is6OaNZSmLkKiCp/nouRjh+eeo7JYhErLNLqWJ1AhF82pSvXVI88jMRGWLVM9OC0WZUTNFdteKqqJcDph8+YKPXd5mLFpBgEZGYMOBoNM2zgthmdKRKUNlqWRhgAGAv9FCVLtwrgAKAelwhfOBoo24qBK7S9HZbyMQcWIM1Fhh99RbctA1boZdcOxoW4EpUGgtOWeQ4Vp9lG5yo39UN9J+GdpRWuJn75UH0MO0KaNEqbKyIDRo1VzhwpCUoSZCARKVm1aRRx1HcUbiJQ2cPvdHHEeKcVIXowNXHGsR3l+LwAlveH5MV4QDGJcLn8uxd9AgsA6VHFReKpiAH9wM++veogtxw4ipdGfimrDXXq8qJ6NzVHNHBqhKkIr40nShErN7EeBxnobVAekUyOdVVN6qpchzyM+Hpo1q9D+mAL14UUYc7NZlec3b15h5y4vFza/MKLACCDeGs+FLS4swQjpqAXJJKAmKo96bQnP/jTKI30JeB7ohvK4QS0gfoDycsON2mCDbaDCLtcbbP87JdOEM6HCI5E4c7xM++Md7pq9DLff6Nwm4BKD7etRBjoJZazfJvQ35f9Q4RovqkuPB9U+rrKadDdEha0OoXLwt6C+E83pSvU05AAjR1ZKb8yIMwSDsG1bTMrzY0M64V5zrya9GNhqYEixSrw1nguaXcCFzYsz5BLVr/EblCfsR3m1F1J85eZ6lNF2ozI1/Ln/fhLog8rceAS4BtWgtrAUbkNU7nMcykALlBG/I/dYN6pCcgEq3HIuqoN8cb/iAZSca+RN32qGVQckv+x18/iP4PULCsrxk1E3l/OAKyjIA9+Gytr5EfW57wEeRxnvvPNNJDLW76LkBVOxoiZlD31pTiWqz2KnEdOmFVR1Vjbx8fDpp1XYSGIVcBvwJ8r4DgSmoApllDLfx79/zKS1k5BSckfXO7i9y+1YTMV5sStQXqjRYtmTqOa70XgOFU4JD3mZUQa3cIjEknue8CLhzcBUlDd7DcqQzkGFKvIMkkClCp6DqryM1mzCgboJzAS6oG4cqsIyOwee+QneKKRL1jDRyuYH/kOyw4FaGM2goHApHuVRL0dVm4ZfowPlAVtRNwGjsF88OpdbUxTRFjtjqkd+yrF0adWd2+WCF16oIkN+ENWCrLCxXQAMQC0CCswmM3d0vYM7upZWLOpnjKsuvcAfxRwbrQw9QKRh86P6QroIbUfWDnVDyOMAcCORHu6VqJDJNFRmSF4gzJX77zxv/hWUl78WFQKZzcKdf/DKUg/zw3p3HHcLvIGrUFroJwm98biAsUATg2sBFY/+E6U50xrVni6c3gbbNJriqd6G/LPPYjteXhZMSRdR9++P7fmLxQe8lvsK95h9wG5Ub8XzC23PQYlPxaFS+Ip6zP4bMB5jQx5P0XHWN1BhldIuQBfXj3UqxrFzifK070J52vMpCAsZLVDWRD1NPMP8HU+ydM8bFL7xCAQd63akbkJdlHhXtIKyRqinhvAnXS9KIAtUMdPQ3PGDqCeSOODfRV3oGYvP52Pfvn14PGeOHo3D4aBJkyZYS1iBXr0NeUlj5EKUTBNFSjhxAu65B6ZPVymOFouSAgg/Xgg477zSz7lc3IgyMkWVse+kwJDPRoVfgigDWxcV+zbq6rMSeAdlkEKRUiBEEnBnlHOuQi1yGt0AHKh87uVEGu1OqDBEUZyIMq4PFfoAVU15VTHjFPDUBU/xw/Yf2HJ8C9k52STaErGb7Xx2XZ5j0AClemh0zkdR11I4nBOHCgPVy/15AOqG+gqq0rInKo5eUgmDM4t9+/aRlJREixYtEJWw7lXVSCk5fvw4+/bto2VJK8ONqoQq+lUhlZ1GPPigquyMVcWm1Srl44+HVpDGxUnZvbv6f942IdQ+69dXznVKKaX8Q6oqwaI++jgp5cbc/bdL48rHelLKHIPxH5aqojG8QhJ5KBPZ4d1k+Y+f/iH9Ab/BsfcZHqsqM6dIKQ9LKZvJgsrJOCllDSllST6/JYWOK/yKl1JuKMHxxvgDfvnt1m/lP376h5y8drLM9mYXevdbGfnZ2aSU/XPfnyelbC2ltORey4NSSk+Z53Kms2nTJhkMBqt6GpVKMBiUmzZtithOlMrO6u2Rv/giLFqkNMGzwhsTlIFgEN54I7S9nNutin/+/neYPVudq1cveP551Vyi0liDccFMHnGoxcOOuT9PxDg84EJlcazLPWYUahHTOHNeCKgZBy5fJq8te410TzrjLxsftlcmxuEPK2qRtB7Kw52KWkxtC9wOFNePVKIWKwejFkXzFgoTUMU2Zf/8zSYzg9sMZnAbI2n9wcCLqKcMC+qJ4DyUHjqo1MM/UeEtB9X9wbcyOBM88cKU9nqrb/ohQI0aqtHEZ58poz5sWGi1Z2k72ptMxuEapxOOHFHNLQ4cgC+/rGQjDlDUI1gy8BQFhiYdlbNtZMizUQuaJ1ALia+hyt1vItqvizcAPRuDy+diwuoJZHnDb5o3YCwW5UNl04CKsd+FShlcgMq/tuWeswHwFgU3ki2o8IQld9wEVHy5Pyr2/FTuNQ5EdbUvqWJiaRgDHEGlPKah0g/DpQ0SKZ0RD6AWUuvmHtcDWFbeiWpiQGJi6LrKyZMnqV27NjI3pLp8+XKEEOzbp3rJZmRkUKtWLYLBILfffjszZqi/vfT0dLp27crkyZNjOr/q7yqYzTBkiHqBWqhctQqSkpShb9Kk5GM5HMaxdKsVUmLTtT0QDHAw+yApjhQSbaWpGuyDSrXbTGisORFlaPL0PP6FWtQzvuNLCUIU9p7dSLmQDM/jBGUrasZtM7yXHci13VaTlb2Ze+lQt3DP0qGoPPPFqBuFGeWJ/5NQr3tL7nWEL9QeRumAZKGMfTcKYtAeVLrfFFSOtwulY5L3GaxA6agsx0ifvHwkoDzxWDEGpeyYd22rUE9Ry4nUkjlzadAADh8ufr+SUr++UsAuDSkpKTRs2JC0tDQ6dOjAsmXL6Nq1K8uWLePGG29kxYoV9OzZE1MhvaWMjAwGDRrEPffcwx13lDZbrGiqt0duhNmsFiE7dIDGjUvnlUfLVrFY4JZbjN8rBVM3TqXhvxty9ttnU+e1Otz61a24fSX1JgWqWu9SVMjChuqYvpACI/4Tqhzdg5GXqox45Mgun5cxP/Tntln78IatR/oCcCgbluYqyvqDfprVaBY2ghm1sPopSnzqPuAjlEf+AQV9K18wnFfuLFCG/wIi88KDKG89E2XA/WHHbUM1qziVyUB9FuHX5kGFcTR5xNKIl2e8Pn36sGyZemJatmwZY8aMCfm5b9+++ftmZ2dz+eWXM2LECEaPjn2LxjPPkIfz/PMl39digaefVp58crJ6xcfDBx9A69ZRDzuYdZD3V73Pe7+9x/5M45TEn3f9zN2z7+ao6yhuvxtvwMv0TdO5fdbtpbiYusC3KMN4EJXXnYqKH1+DCo9EK44pKnknyAv9/Xx+nRsJ+IPg8oHbB6sPwoCP1V4Os4MHez4Y5UnCjMocmYK66dyG8rIfoaBv5XyKTk/MRjVDKC0uVIFQUQRRGT/jgFkUn/YYa3Zh1C5Ozev3yp2KpkT07ds333Dv2LGDG264gbxCx2XLltGnT5/8fR999FHOP/98xowZUyFzqf6hleIYOxY2boQpU4rf1++HL75QRrtjR7jsMtU+Likp6iGT107m/u/uxyRMSCl59IdHef3S1xndI/Su/PKSl3H5Qo2sx+9h9ubZHHUezc1fLimFDekY1MJmySoGwz3yHD/YLdAoCUyF3nP7oMcHsOV4wbY2tdvwz4v/CcBx13ECMkC9hD2oG8rZqDzzH4HJFHjeeamDgylZjnlZKpEFHl8WT//0CL/sWUn7uu0Z23ssHevlLfxmoESkdqDSKx1AbVR8umEZzlcWmmOcRilQaZiaU40+ffrwyiuvsHPnTlq0aIHD4UBKSXZ2NqtXr+a8QunHAwYMYNasWTz22GPUq1eviFHLhvbIhYCPPlKLlC+8oLzuaLhcqhPRmjUqj/zvfy8y/3xf5j7u/+5+PH4PLp8Lt9+Nx+/h0R8eZXt6qGe58+ROwzEsJgvv/vYu//rlX6w9GCpMlZ2TzdbjWyNuAAVsA96ntGXfUqqQidcPfxwFjy/UiIP62PqF6YLFW+PZk7GHPpP6cNbbDdlyrAEuX08CwdGokE8Pot9UKlCpUkoC8hce6DGe3Rkr+Pj3j+k5sSc/7fwpd4/HUWsL2ahwTxZKXnZUhc0pkhRUHn54c/A4VHaM5lSjTZs2nDx5km+++YbevVVVbvfu3Zk8eTItWrQIWSAdPnw49913H4MHDyYrFhl0YcTEkAshLhNCbBFC/CmEeDwWY1Y6DRuq2HlJ5Wc9HtU8YsKEqLt8lWb8OB8IBpixaUbItr5N+2IWkemD2b5sxi0bx1MLn6LPh31o/kZzLvm4Du+sTOT9VTUY9U0X6rxWh6cWPJW/gg4qVh2U8ynqK452DwpKGP0tpLwK0zcJ7Ab3tngrNCz0IOKwOLi09aWc/+H5rNy/kn9c6CO1kSTeKjGb3CgjuQH4Nep8YkvBZykEJNigSTJMvgoCMoDL5+KeOffkfmZTifSG/RRdwVkRvIUS10pBeeLnohZuT51G25pQevXqxfjx4/MNee/evXnzzTdD4uN5jBkzhoEDB3LttdeSk2P09FV2ym3IhRBm4F2UQn8H4CYhRIeijzpFad5c9fg0wshTd7vhm2+iDucP+kOMax5BGcQfDI3BPt3vaRJsCZhE5Ffi9DnxBX14/B5u67KHr4cf574eTh7pFeS7EW6evcjNmyvf5M2Vb7Lh8Ab6TOqD/UU7t371EG6f0fWYceY05KjT2JgHJTRKEkhpp3GScdm9Mwd+yV3gtJvt1I6rTZtabcj0ZhKUQW7rAnER1cU5KE+3PFrtVpSXmoxxTDlvn8hwl9UM/VtCXO5XufvkbjK90XLcoWxhnPJgRi1Gn0A9oaxDhXw0VY3L5aJJkyb5r9dfV9LLffv2Ze/evaSmKh2r3r17s2PHjpD4eGFeffVVmjRpwsiRIwnGsJNZudUPhRC9gX9IKQfl/vwEgJTylWjHVJr6YVm46CKVD17YoDscyq1zh2VUCKFy06dONRxqe/p2znnvHDz+UI2IOEscv436rVCMVrH1+FaeWvgUS3YvIdGWyIGsA7j9Bec8qxasvy/SQLp80GsiHHHWx+135xonZbAOjoUaEQqtcdzzTV8SbfP596WRcXEpwR8UmEQvzKZ1SOkO2ceZA6sPCp6c34DLzjLRrk5XBrQczyfrv+Fv8/+GN+DF9aSRIc9jMCpXvSQhHwvKOxYoA/5PVAhiCSqePRrVODjPc7ah8sl/oyAbpoCcANR+Takb2s12Mp/IxGa+B/iMUO/blDvO/BLMUVORpKWl0b59+/yfT4X0w8og/LqhYlu9NSZUmX8fBq1GhBD3CCFWCSFWHT16NAanrSBmzVI55zabMuBNm8JXX0GrVpGt4+Li4OGHow7VulZrnrnwGeIscZiFGbMwE2eJC1toK+Ds2mcz/YbpHHrsEBOvnIjVHGoJh5xtnP1tNcGVbXM7//gLqk7dfrj0UzjqhEAwAeXFJgKfsP1EkGvbG6cbCgFWs8QklgOhRjwYhMW7YeFOyY+3HuTJfse5vuMiasV34pLWgXwZ3O//LKp16gmUgSyuN+ilKKGt/qiionnAX1Ae/WWoLJi1KGNeC/XpCGApagEz9PuSEgJBsJhUhs3wc4ZjM9tQufVNKFgkTkDlt39QzPw0VcGhQ7Htln4qGvHSUmlZK1LKCajKDFJTUytfBL2k1KgBM2eqkv7sbHX7F0JVag4ZoppGWCzKSo0fr8rxi+CJ85/gyrOvZNof05BScn2H6zm3wbnFTqNP0z4Rj16+QJRmZ1J5msm2ZE56T4a89+t+aPt2EjOGPcqAluejmh7EcdM5J+hYd2GRczAy8iYTnF1bLXQqj7vgaaNZjbHYTFZyTFYemefj6nbRRl6JSoschJKZDb8qM8qj9qMKeh4AhqCKiMKpD9yLMroS5aVHCnvlXY9ZwCsDzXyzdQDvDn439526qMXOL1Gpfm1RAmThC48azalJLAz5fgr0OUG5NpWt3xp7kpJC0wqbNFHl/ps3KwXELl1KXEzUsV5Hnq9Xinx1wGa20bpWa34/XJBDPDMNXjPoLBaQMGerg+s7XM+nGz6NCOV4An7qJ9xAgc4K3HrurfyZ/jA146LnlUejTjw4DH5zgkEY0MrHzDTYn2kmwxskxWF0z7aiHgafQhUKFQ6xxKMM89Oo8IsfFS6JQ4VTzjYYLzwsEh2bBUZ1S+a+1G/D30HplldRIxKNphzEIrTyG9BGCNFSCJH31zA7BuOemrRrB717l16npRSku9M54T7BxiMbQ7Yfyoa7Z6sc7iyvivO6fTDme8Gjvd6mcXJjcgIqtu+wwEM9YdUoWHpHHB3rbaPw4p3FZOHfy2rgLMPieZw1ikKwgNRG8NsoSP9bgBy/RMrwQLkdGIb61euI0ii5AJW73QhV3dk0d7sT5V1noXRNOqPaqnVElcZ/jPLmnZSmgMdsKpnGs0ZzulBuj1xK6RdCPIgKYJqBD6WUxbWK0RiQdjSNkV+NZMORDQBIg6yJqRvhh+0wtK3K7Z6zFY44JZPW3kdAqlzs2nGw6X6om5BncNNRDYr7oRolm1m1vxXTN2WT4YXXB0Hj3IKfoASzScWSTcLYYFuj3P4TrPDQeSo1ESDZDkHpR+R3aw+gUuneLnRUKkqDpTAdMK5A9RLa+m0Dqjo02spX3kQLh27sKJkAjab6EJMYuZTyOyKbK2pKQaY3k74f9uWk56ShAS/McTd8tC50W54RH3I2fHmjWtALNcIBlNbKT0gp6NrQzKfXSOZsg74fwhEn9G0K/x0CLWrASa+KyTeO0tch2iJpfJizaxISFcf+Fyos0rXIa1OU1Lt2U1ibJS8BSwgTymA/itJ0yUTF8u3AWShZAI2m+qArO4tASknQHUT6K35tdtrGaeQEciKMuFmYsZltJNuTsZvthkVD/ZrD3/rCvd3h8+tUvnRRcsZCSKxmP0PbBhh/GWx9EF4eAF8Ph1YpKo5cL0F59jlhNjWasBYU1SRuH3AjUnZh+d7lzNo8i8PZReWP3YJRV/viEAJ8QVh1oAb7M79AiU3tQEkC/BXVK3Mj0ArVO1M/OGpKhhCCWwoJ4/n9furWrcuQXFXVw4cPM2TIEM4991w6dOjA4MFKx37Xrl2cUwmS1lprJQq+P324vnMRzAqCAFsnG/GXxSOsFSNwv+PEDpy+yLxqkzDxUM+H6NO0D+3qtOPeOfeybO8yAjKAzQxzb4YejVRM3B80XoSMhhAFud4P5ybfWArd2h1WFYs/7k6mYZKTTK/AbvJjjxJilkQz5vXZdXI3F398MYedhzEJEzn+HMb0HsNLA14yENEfixK52oSx/kh0rCboVO8EHv+VeP3vYLfcj0pTHIu6oeRJAaxFtbzbiaqk1Jw2VEEieUJCAhs3bsTtdhMXF8ePP/5I48YFWdbPPPMMl1xyCQ/npiOvX78+dvMrAdojN8B/0E/2jGyCGcH8dpY5G3Nwfl18AYuUkjlb53D5p5fTe1Jvxq8YX4QWSgE9G/c0VA00m8z0bdaXjUc28pe5f8FhceQbvgd6wHmNIcmuvPDoBTjFYxahRjwPIWDe9kuAWiTZHNii3CikVEY/cvE0Dribq6YOZefJnWTnZJPpzcQT8PDWyreYvcVoXTwBtYb+X1SGS8kRQol81XBIzGIMSlVxLmqdoLCei0TdJP5XqvE1pwBVpGM7ePBgvv1WZTtNnTqVm266Kf+9gwcP0qRQb4POnStXP14bcgM8yzyR2Wx+8G3zKQ+9CJ5a+BTDZwzn++3fs2LfCp5c8CR9JvWJSAkMZ2jbodSNj1Q4zPHncMvMW3h56css2LmA+Tvm55f339VVaYgUJtYdsSwmuKXzAuAoQmRHHV+iBLaeWADpbghKM+rXy09QjuO7m/+gV5PQz87pc/LWr29FOzNwByoFsTkqLdGGWk+PR4VebASC0X+FLeYcVIPjXRh79nla5RpN8QwfPpzPP/8cj8fD+vXrQ9QNH3jgAe666y769+/PSy+9xIEDByp1btqQhxF0B/HtiJKTbIFgZnRDfjDrIK8vfz0kROLyu/gz/U+mbigo4w8EAyzevZjvtn2XX05vMVlokhzZrShIEKffmX8jKBxDj2pUC1WtlRSjsdw+OOk+B4upeGVCk4AuDeDbbdD0dZUaqR5nfJiEh8bJku9vVjnohTnhPlHMyL1R4Y91wFZU5soKVKz7IPszLyXLW9S17kUtsBo9SiSiOthrNMXTuXNndu3axdSpU/Nj4HkMGjSIHTt2MGrUKDZv3kzXrl2pzAp2HSMvhJSSrClZhYsVQ/FD4EiAYHYQaytrRLz8l72/YDfb8QZCKwudPidzts1BCMETC57gUPYhTJhwWBxIJM/1f44Ve1ewZM+SUs13yjp49qLITJG8BhEl8c6N9lNGUWA130CDpKtRHX2KJycAzWqo/p3CoAbVbIIRneCtlepnh0UVMRWPANoU+rlAn7tx8hx6TuzMots2kRRW+CmlGSH6oapZu6Jap+V9uTZUL9DrSnRtGg3AlVdeyWOPPcaiRYs4fvx4yHu1atVixIgRjBgxgiFDhrB48WK6d+9eKfPSHnkh/Dv9Ki5uhACC4PrBhfNrJydfP4lvV6jnXie+jmHqoFmYOe46zv3f3s+hbLWoEiSIy680yv/641/5cvOXpZ7v+JWqV6aRN1qcEVfCWCpv3OhYIc7DYpqG6hlZsgVHuxk2HoH6CUSVvm2SlPfveJrVaMaDPR8s0djRMJvMLLj1F77d2ickPq+MeCLwd9SX9wNqwbMRqiR/FEoqwKjsX6Mx5s477+TZZ5+lU6fQZh8LFy7E5VJrYVlZWWzfvp1mzcJbHlYc2pAXInAsEL2/gaRgfSz3lf15NjKnwBJe0OwCajhqIMJyN2wmG+sPrw9RMowF3oDyyo2MsRFSqn3dPhi3DP46rxc+g/tWTkDgysnL966DEqUyouA6s3Pgv6vgmAtWH7RjFpESs4FgPA7LZQxuM5jXLn6NNfesIdkeJVG9FKQ4Uhje6RcSbLNRoZjmCDECWAO0zN0rDpWOuB9VJfoOxYt2aTShNGnShIceeihi++rVq0lNTaVz58707t2bu+++mx49egCwZcuWEAnc6dOnx3xe5ZaxLQunqoytb7uP7BnZkQ6oIKo0taWphcSRiQizMmpbj29lyGdDOJB1ALPJjJSSlwe+zJh5YyI0yGNB36bw/c2QWALHUkqYvQUe/h72ZAgSbYksvqMZZ9f6g/hcuxsMQlYO3DErlS+H/ZZ7ZGdUFWVhTEBLpMwi3Q0vLnbx1q9O2tVpz6Sht3NekycRovD1mlFl9YsJVyUsP5ko77omKj+8YlJENVVDhJzrGaJjW9kyttUGSysLpmRT6KciKNLu+Pf72fHVDnp+0BPbCzb6Te7HqG6jWHLHEl4e8DJJ9iQemvtQyY24Jwl8JX/c/2UvzN+Zt7ioCASNwy1ePyzYCbsz1KJpVk4WqRP+4J+/wOFspWv+ww7oNQm+3baeFxe/yI/bv0DKzQZnDgIZCHGY2vGHeeOyLI48dpTO9drRts5fw4w4qA/xaWJvxN9GxbpvQMndnk3ZGjRrThu0jm0E2iMPI+gO4vrehS/NBxIsrS3YOthwfeeKKrDnxk2zYDMCuXGZeGs8N3W8iSm/T8EvS2jA9/WAWZPgeFsQEs7+Bq4cBXEniz3UJODmTnBnV/XgsGwPPNYnMk7t9kGX92HrccNhIrCb7dR0WNk9Jhubof1tQp4UvZSSzv/tTNPkNKZeFzBoZgEwgtjmbS9FSeEWztNXTwoqrVB75tUBI8/0TKA0HrnOWgnDFGci8ZpEuEYZJyEEUkp8W33KuBtgl3bqUY+DHATA5XMxed1kglFbiIVxsil8vAByCsnmbhlK6yUf0GvsDRzIgkW7ojceC0r4ZL165dG6FlzRRhULBaXytj9YHd2Im4Qq8x/TC1IcsPYQPDTXy8r9XhbuhIEtVdFRAXEUbk788+6f2XVyF81qFJWqWHQufel5m8JaK4ogSkRrNUqQS6Op/mhDXggpJb5tPnI25CDMAlsXG9YWVoQQJFyXQNYHWQQOGxuq18RrjJQFqnpFGfH7U+9n6sapnPDk5lD/NhoCBTmEQgSZNPFehg+fhk+YQAQ55oKLPoK9mUYTB3b3g5MtoOFqqP8HI2YqhcSbOynxq8nrVFglGm8MCi0w6tkYFtyqwiy3fQ2LblPNi80mE3azlcPOtoyY+T0n3DO5vsP1pDhSCMogP+8yrhBV1Zojok+gTBzF+PZmwqjNm0ZTXdGGPBcpJc4vnfi2+cCXG0PemMWX9i851OgQd6fcTa0GtQwNuUmYuFheTBJJZJEFgEBEVTFsW7stXw77kis+u0KV7x/tAIGCWMSdd07ixhunExfnIU/1PN4KM2+EnhPDBsuqB5OWg7M+ICFogWZLkbdczuwtfmZvKdg1wZqAL+gjJ5BDlwbw5PnQvi6sOwTXt1faKoVxWODJC2DETOjwHyXO1TIlyIbDfv44mpafL781fSv1E+qDBKcf7poNH16ltQ8dWQAAIABJREFUyv6tZvAH7djMFwNXl+IbKQnXoBY5wyUQfEB456ZMIA1oCFReWphGUxmccYud0i/xrveS/WU2rvkuAseVYfbv9ucbcVCG2C7tDPPcwH077iNhTQI5v0fPpw4SJCm3c3u8NZ6r2xkbLbMw065OO1rVbMXEoRNxWBzQdBlYCozRAw/8h4SEUONkMcE59ZRueD7H2sBb2+FkS/AlgC9R3RB2DkS8vRmTu2bIGE6fk+Y1mnNJK8HSO+Da9mrM4R2N877NJujaoODnxbthyu+w5lAgpOjJ4/dwzHWMhkkNsZvtTPsDOr0Hr/4imLQmHn/gC5QIlhlldB9HLVDWRoVnyloBdxfQgoKWbCL336+gCn7yeDH3fINQbdwGoQy7RlM9OKMMucyRZH6Yies7F74/fHhXesmckEnO1pwQI14YE2biiMOEKSI/vDABESCbbJLtyTzW+zHeufwdLmx2Yf77AoFJmDAJEzfOuJG277Tl3d/exSRM0P0DsGVDbqZHQoKxOFdAFqriDJrgo0XKgBeaV82a6Xz22U14Drcn56WTLLwVzqpFfgTiz/Q/eXewCqGYc799S5REkkAQ1pcwy8vpc9Kxbkfu73E/teJqcTg7gbSjwxjcZivxtispyOEcBIxHxbHTgSmoMvmy5NjHA78C/0RlrFyHyl55BhXKaQn8Lfd9N6ohswel36KbS2hKx9dff40Qgs2bC7K4tm7dyuDBg2nTpg3dunXjxhtv5PDhwyxatIgaNWrQpUsXOnfuzMUXX8yRI0cqbG5nVNaKe5kbz8+eyL4FVjDVNRE8UMLFSSNMIBIFyfcks8Ot0hHdfjcevydfQ9xisoR4snaznQRrAlk5WfhO1Id5/4atQ3jx+WcZ++h4HPbQO8v+TGj6BsiABb59B9bcTWg6n+T338+lbdvN2HOPDQQEJzOSad1qBxk5QeIHvELG7NejxLFD8fotXPyxg6V7s4vd1yIsPNDzAd687M2wdzahDGdtVEXlUEJ7dILSPHkHuK34SRXJ/wH/ITTUEq0IwA4cQBcFnfqEZ280GNeAw87Y5ZHXT6jPoceKT0EcNmwYBw4cYMCAATz33HN4PB46derE66+/ztChQwFYtGgRderU4dixY4wbN445c+YA8MQTT2Cz2XjuuedKPC+dRx4F3yafcfMZH2U34iKAucE6zPXWI50BvCu9jJ03lmxvNv39/fk//o+r5dVYpCVCg8Ub8JLuSadj3Y5YZTLsHAgiyGv/fJrdu5uTna1CBl6/yhMf+VWuSfr8S1h3G+E52f36LaZly535RhzAbJY47D5uvfVTcNfBM/8ZcnKiScMmAzVQxq8zdssCbuvyBvHWUKUrkftfYWwWG6NTC1eASuBOVObIWOBuVL9Noy8gGyVbWx5cwLtExsujOSoW9ILo6UksjXhJx8vOzmbp0qVMmjSJzz//HIDPPvuM3r175xtxgIsuuiiikYSUkqysLGrWDA11xpIzarEz1k0hLM1+IeH6O8DiUUub3mRc8z9j1Y5VLGYxjUQjEkjAiZMXeIFBchB7c/OuC7Pl+BZa/ryDbZ5aSCnI9EGXc9dz082fcvG1H7IraQUTVsPuDb3hq4/hRGuMcqTbtt2CyRR5Q0pIcNGpk8pNDHprMHHiXYwePQmrubDH///tnXl8VNXZx7/P7DNZIEBYI/smWxIgaCAKSFXoqwLyCmJVKLa0itrWtlq1LdaqiHXFDam1uEZEBX2tCwoIlLQCyq7UgoAo+5KQddbz/nFnss1kI5Nlwvl+PvNJ7p075z4nN/ObM899FhfwJ4w2aGUtIm5Iv4Dcklz+vPbPeP1eTGJiZtpM1u1fx39P/heLyYLVbGXxxMX0a9ev3HhvBB+VXSaRroELI5GnPhyhbusSB2Xp+xpN9bzzzjuMHz+evn370rZtWz7//HN27NhRbVGsdevWkZaWxokTJ4iLi+OBBx5oMPvOKiG3D7fjO+SrMrGnLojrOPHTr0ZsZW4CsRfiuuwK5u65h+7F3bGLkaGZQAJO5WSBLGCymhw2VnGJn6+3JIMqE7mSEid//9tP+fvL0+CuVnCiN7y8wrihWQU7dgxEqXChLCiIY9Omsm9jv/ndffS/6BMuGXAAQ9DcGBUOQzUkysYQEX4z8jf84rxfcLTwKO1c7bBbjHntPrmbAk8Bg9oPwmKq/K+0iHAXSggzZUVtBOPGZH191p2pOgHIGnzOE/zpxHDlRDvLVNNSyc7OLu3+c/XVV5OdnV3DK+CCCy4oda3Mnz+f22+/nYULFzaIffUSchH5C4bT04ORF/1jpVTNqYhNhHWAFdu3NjybPcZ72EvV37xrwDboTZDwUMSA+Jjex4lve8U0e4tYGKlGYseOCxc3y82MZzwnOMFT8hwrJAAqgrCEVs3/+hX4qkvdV2zbMZzt2weTnr4Zh8Nw4/h8ZvLz43nttR+VHul1O7n01e954NIbufPCazBKxFbf7sxqttIlsUuFfb3b9K7mFe4q9scBgzBKygIMxeipWd+vnXbgTuB+KrpXXMCbGNUPV2NEudwOjKzn+TRnCydPnmTVqlVs374dEcHv9yMizJ07lzVr1tRqjCuuuIIpUxquZHJ9feQfA4OUUkMwqv7fWX+TGg4RIW5CHIk3JWIbZKtXBrfEHQNLeKaiWfyYXVXnwCeSyBpZw43cyLlyLlmSxd8sCzm3/17MlkpuEUsJDHnZ+P3oQFDVtz2zmu1cfPHH/PWvPyE3txVFRU6WLZtERsYmCgqCcYvWAjj/cbAVc8+aZziQ15GG6Vl5LWVhgeWxAeswwv9OYcSBD4jSOe8EHsPoKOTAKNK1ApgQ3L8FWI4WcU1dePPNN7nuuuvYv38/+/bt48CBA/To0YPevXuTk5NT2v4NYO3atezYsSNsjH/+85/06tWrwWysl5ArpVYoVVpM5N8YxTeaPaYEE56dHmqbQR8J374s8MSFPxEw49s/Kvx45WOjrGfOrseZ8Oi5dLmnI0MfS+SdnVbiJI6llydBq71gO23ElNvyocNWGLYQPr4fipNAqvMJCQUFUFTk4tZbnyIpKZe4uCKmTn2T779PARSY3DDmHrjo91CUhNo1kceyt+KLflFGjBudGRgRKWCsmF0YtVYsGO6Nqt1EZ4YAszFauxVj/EuGXwuNpi5kZ2czeXJFl+iUKVN4/fXXee+993jyySfp06cPAwYM4JlnniE52WjZGPKRp6am8vLLL/PII480mI3R9JHPApZEcbwGI3A8cMYulRC+vaPxfT8cS8pGxGZ8lVceF97dF+M/nFbhWKUUeeSxfc8/eeit+RR5jT/7vlNmbno7DrMUMnpAPqPm/IS139jgZG9I3gmbfgbPfBUcJRRGV3WveosFTCbBEzFvScAUgIFvwGe3wMoH8Zo9PPuOk9fugY8+gtTU+v1NKmIDVmI0Pv4YaI8RXhgTn/WaZkyHuA5RDz+sjtWrV4ftK1+T/MMPPwwfs0MH8vLy6m9cLalRyEXkE4y0uMrcrZR6J3jM3RhxZVWWthOR2RjLpUbtnBHRFpdEjoKrEyYKst/Alvoq9tRslDLj2Xw9nu1XhR3pw8d99tF8sHxTqYiHKPYK937sZPUAE8dMR6D3V8AKWDEPdk6lomiHxNwf/L3iFyq3J4AKlD+2En4rfDkFVt8HPif4nJS4oaQQLrkEDh4Ec1Tv/5mBy4IPjSY61Cbm+2yjRiFXSv2guudFZCbGO3Wcqia7SCm1CCOUgeHDhzd+FlI5TAkmY+a162BWNQErns0z8WyeWeUhSine4A3aWI9yLC/yJ/+3uSb2spevCK6+D6ZBzu1E9nwFBVz8wSiXkGArVKDidpiYKzOsuh984TVmi4th7VoYO7bKqcQgCtiG4YsfTvRdORpN86BePnIRGY8RAnCFUqpyJkazRhyNU6vah4+daidf+nwkt4r8dbBrWy85I3KMxBuvA15cSfWXRkBZCF+tV96O8DqfM+LYInC6RZUf2YtxE3UUMBHoADRM6JdG09TUN2rlKSAB+FhEtohIzLxTrD2tjdJ3wCpW+kt/Pi6GGyf9AZetcmy1Yu8JK3+afDuOZ/diWrEgKNINReRJezxw4YUNeNpGJVTT5WuMWPbTGCGJvwb+1YR2aTQNQ70UQylVXSBxs8Z5oRPPdk/VzZajRIkqYbPaTAB4vNff+N+pfj55/14Ongzd9BP8fsO1UfxdeyyHfwJK1Segps64XDBvHiS08rFm33rcfjdZXbPCUvNjh8+BQ4SHJRVjrD0yG90ijaYhOasyO8sTKApUsTitOiqkrigUxVLMm+pNAPIC8FLvxTBtEyzaWKEGeQifr3Hbk5lM8MknYO66gU6P/A9un9tIegj4eWHiC0wdOLVR7YkOJ4n8ZVMB+kaZpuVxVhXNKo9vv6+KEMSqquXVHUFoTWvuTb63Ygr74VSjAUQ1r2wM7HaYMQPShhdzycuXcLzoOPmefE67T1PoLWTm8pnsPrm7UWyJLiOIfCfbieEv12jqTuUytoFAgFtvvZVBgwYxePBgMjIy2Lt3L0888QS//OUvS1/3s5/9jB/8oCxm5Mknn6wQvhgNzlohF5dUo5fRE1JBmHliJj/hJ2UVA5O+qVBXpakYORIWLIB//PcfBFS4M8cX8LF4y+LGN6zetMZoJlHeNeTEyPi8oUks0kSTjpTd3I/GI1J0dTjZ2dlkZWWV1llZsmQJBw8eZNu2bWzfvp1ly5bRunVrRo0aRU5OTunrtm7dSl5eHn6/4cfNyclh5MjoZhefVUIeKAjgO+jDf9KP/5g/CrHktUMQ/sgfWSALjB3n/Aucp4jWyv9MsFhg1SqIj4fcklz8KvxmgTfg5XjR8SawLhr8GngPox3cKAxh34hR60UT20S3jG1txotUxvbQoUN06tQJk8mQ0ZSUFJKSkkhLS+Prr7+muLiYvLw8nE4naWlpbN++HTCEfNSo6GYcnxU+cuVVFC4P9uM0U1YEz3iWhnZlLN9h5d6PEzmQOwdTwiQCrfcEV+QhIW/81bmtXCe0i3pcFHFFHm+L5/K+l4ftjx3GBh8aTf2IVMZ26tSpZGVlsW7dOsaNG8e1115Leno6FouF9PR0Nm7cSHFxMeeddx59+vQhJyeH5ORklFKcc845UbXvrFiRF71fhHe314hQCblOSxfDUnlHVFm+w8qcZXHsO2XGr4TA6RT49kIoaQuYMJkEp7PGYaJO+Rr3PZN6MidjDnHWstVqnDWOzJRMJvSZ0PjGaTTNjOzsbK6++mqgrIxtSkoK//nPf5g3bx4mk4lx48axcuVKAEaOHElOTg45OTlkZmaSmZlZuh1ttwq09BV54beoo5vx7MwCf2N/Zhkr/Xs/dlLsrbziLtsOBCDgVSy7rYjrn3GSX1Jmpwikp8MXX0TXMosFpk83zv3RR5CTAz07/YXFl05gyZ6FFHoL+dHgHzFt0DSjp6hGcxZTVRnbv/zlL9jtdiZMmMCECRPo0KEDy5cvZ9y4cYwaNYqFCxdSUlLCnDlzSE5O5ssvvyQ5OVkLea1RAdhwI+x9CRXoAoF1GGVNqyOa7o2y1f23uTULoc2sKDyk2Pzb05z/ZCLHc03Exxtiu25dFM3C+HBo3x5uuQWysmD7digoAJdLsFjGsXLlOIaHdQTUaM5eQmVsn3vuudJ9o0ePZt26dfTu3ZvOnTsTCATYtm0bQ4YMASAzM5OZM2fSpUsX2rdvD0BycjLvvPMOS5cujbqNLVPIdz8P+16BQAmi9iCmkyh/50Y6eVDETUcBIaVVIt/mVl+Jyh8Q2rgCXPJMAkUlxgdKURH89a8NYJ0yUvHnzIEtW4xEpND5AKZNg927DcHXaDSGW+WOO+6osG/KlCnMmDGDNm3a4HYbTVRGjBjBzTffDEBSUhLJyckMHDiw9DWZmZmsX7+e1OiWGQVAqqlz1WAMHz5cbdq0qeYDz5R/DIa8suLunoIJFB79KygHjXtbwMvSrQ5++W5CBPeKgdWkGNzJz9heXp5a78DtbxwFFTFEvTIuF2zdCr1jNmdX09II7ybfkehGrnSgOSaKhc8bRORzpVTYd+aW6QD1Vqz+ZIv/AFv868GtUE3vxsDKVak+Zg43mjOHo+iWFGDpdQW8+6Wt0UQcIot4aL+pZf5XaFoMhyl7H0fj0fxEvK60zLdsykQwlbVFKzz6MJ78H2NMt3Kp18qPaCP0bx/AaY00tnB+Nx9JLkW8vUkr+5bStSv00M3lNZqYomUK+aDfg6MDmJ14i8bgyb+Wqm9mhuLIK5eBjR6Z3XwEImRyxlkVF/T04vXDD/t7MNX4QdIwYm82G4lBbdrAm29q/7hGE2u0TCF3tIcf7oAh9+H23AFU1bQ4vMtOQ9C7XYCrhnhwlVuVO21ekhID/PY9Fz3nteb+lS4CNX6QNIzC+v0waxYcOACDBjXIKTQaTQPSYoQ8UBygZFMJRauL8O7xoiwJ4OxIoDiRxs+cVBglVMuE+/GJRTwxsZDMbm6GdvuKuyfO5YL+yzldYqLQ0/RL4MWLwVFThKZGo2mWtIjwQ9/3PvJfyTe00wduqxtzwncktLkZYQHQn8YVcwF8mBwrCbgvABWHCExJzeXSITnctMzJn5fNBcy0dga4oIeXf+61cqq4YT5XrVZj1R2opsh5cTHs2QN9+jSICRqNpgGJ+RW5UoqCNwuM1PtQESwv+E+1wX1qKhbnWsIbDETVgir2W3C0Xogr+ddYHOuwONbhSv4NV7/chRXbLsXts+P2WcgtNvHJ1zZevaaAXm39WK3RjxrxeqsX8RCJidE9r0bTkjhy5AjXXHMNPXv2ZNiwYWRmZrJs2TLS09PZsmULAD6fj/j4eF555ZXS1w0bNowvvviCxYsXk5ycTHp6On369OHSSy+tUCWxPsTOivzEJvj6SSg+CJ0vg143gDWewPEAqjiCmCoX7vxrSOg8iZIT92JUy4o21d98dJ+6k7gON2JPeAOAXQf7sXl/Gh6/reJxPnh8rYN7xxfxqSuBFSsMf3VtxDdaZGVBh8i9oTWaZsW1HR8l90jllolnTusOcbxy+LZqj1FKMWnSJGbMmMFrr70GwP79+3n33XdLy9ampaWxdetW+vbtS05ODtdeey2FhYXs2bOH1NRUtm3bxrRp03jqqacAWL16NVdeeSWrV68OixevK7GxIv/mJfhkNOx9BQ5/AlvvhA+HGvHi1XhMhAAm8ymcbf9A5FV5baNAqjquukgXwe8ezulvP8Xv6QXAt8e7YjN7w44MIKzcbWXWknjMZsXHH0P//kY0SUNjsUBqKrz+es3HajTNgWiKeG3HW7VqFTabjZ///Oel+7p168Ytt9xSWiALjBK1P//5z0tX6Bs2bGDYsGGYI7yZx44dy+zZs1m0aFG959D8hdxXDJvmgL+IUjH2F0PRAfj6GUxtTZjiI0xDCrElvgSAvdXzmO2fA+5yB4QEtSHjt81AAvmHXkUpIa3bFtw+e8Qj/Upw+4QXXoCbb4ZFi4w0epst4uH1pnt3eP99+PxzI1U/WA5Co9FEYOfOnQwdOjTic+UbSeTk5HDhhRdit9vJz8+vsdrh0KFDSzsO1YeoCLmI/FpElIi0i8Z4FTi1hYhm+kvgwNuICHH/G4c4ACkAPCAFWBzrsQeFXAQSOk/G3moRYjqGmE4hloMh62thRH1ulArK15uSU7fTNjGPPl2+pboPD49HWLHC6Gi/YIHR3b4hePRRmDABgjV+NBpNHZgzZw6pqalkZGTQrVs3PB4Phw8fZteuXfTr14+MjAw+++yzGptIRKtESr195CJyDnAJ8G39zYmArTWoKlr52NsCYOloodVsN5437kR52mBx/huzfWOFxBYxFeFqNxdXu7kE/HHk7dtL40WymCjJvYmH989kz9F+tXpFQ/rHO3WCyZMbbnyNpqUxcOBA3nrrrdLtp59+muPHjzM8WCp05MiRLF26lE6dOiEinH/++axfv54NGzaQmZlZ5bibN2+ut38corMifwy4nYbyUbQ6F+J7QuW62OY46FfWwFQS2mJv/X84kp7E4tgYMTtRKSg+eQd5+/5D9G5+1nba8Tzx936lVQabCqcTfvWrprVBo4k1LrroIkpKSnj22WdL9xWVezOPHDmSxx9/vFS0MzMzeemll+jYsSOtWrWKOOaaNWtYtGgRP/3pT+ttX72EXEQmAt8rpbbW25LqGPMexPcGSzxYE8HkgAF3QOdy3WtMVhh4F5hdVQ7jPn09Jbk3YzTljdZqvJbjmIvJzY3SKc8Am82obDhuHJRr8K3RaGqBiLB8+XLWrFlDjx49GDFiBDNmzGD+/PmA4Sf/5ptvSoW8U6dO+P3+MP/4kiVLSEtLo2/fvjzwwAO89dZbUVmR1+haEZFPiNxm+m7gLgy3So2IyGxgNkDXrl3rYCIQ1w0u2wUnN0HJMWh3XqlbpQLn3g6WVrDzPig5Yoi6L5/Qqtmd+0tQjdF8N0IvTp+J9D6FbNoVf8ajJiYaMeaBALjdxqMmTCaw241vI4GA0azCWlXFAo0mBmjdIS7q4Ye1oVOnTqWNlyuTkZER5u/et29fhe2ZM2cyc+bMMzGxRs64HrmIDAZWAqHvFynAQWCEUqraupANXo88xCej4eja0s1T3+wHldDAJw05t8O/7Gw6fJpJi7tRUnJmPvDnn4frr4fPPjNCE202yMw0En5qi9MJ27bpeuOa2CFSXe6zgUapR66U2q6Uaq+U6q6U6g58BwytScQblY6XVti02L/gzOPJqztGYXR29mO2b6SqP+vwjk4++wymToWePSPHicfHwx/+YESthPz8Tic89hjccIOxms7KMgR82DCYN69uNVJ8Pnjxxdofr9Fomj+xk9l5Jjg6YLg3DBF2tvsj+d+9DzgxxFZh5PX7gvuqozpfuCIhZRRm2x5E/OTt/4KAr3vYUSbnIQYNak92trGdnQ2zZ5e5S5KS4IMPINQdKuRCcTgil5bNz4errzbCCP/2N2O8kyfLXCdeb7j7xeuFU6dqmKpGo4kpopYQFFyZH4/WeFEhUAJS5hA2WfYj5jKfeZk41+fzTCGW3VjsXyPiB8DR9g8glcJTpBjXmIrfBqZPh6NH4Z13YNUq2L+/TMTBEHinM1zECwqM3prJyYaL5OKLYcwYOHgQdu2CnBzYvDmy+MfFweWX12O6Go2m2dGyV+QdxlHeJeI+PQsVaEXF0EMr9Y2cNNt2Vti2x/8Dk9xA8am78Hu6Y3YexDnGgnVY0LXlK4Sj/wSzA2fyKMaMqdtluOoqWL26bLV98KCxMl+71nC3hPjFL+Cpp6AweF8oLs4Q/IsvPsOJajSaZknLFvJW/Y1wRc8JALxFPwAVyYXixxD3MwtJ9BVNwFN4Cba4FcYYYsE6qBPWjGFgiQPKRensew0++ymYLMbnh9kOo9+DdiNqda79++HTT8NdJsXF8NBDsGRJ2b4HHzRE+4UXjOenT4crr9Q9OTWalkbLf0uby2qbmCzfYYh22EGceVy5AA6Kjj1c1tBYzJA8Miji5Tj9tSHi/iKj4JfvNLiPwepLjZIDteDAASOcsDJKwe7d4fvHjYNXX4W33zZW8o1RiEujaUkopcjKyuKDDz4o3bd06VLGjx+P2WwmLS2NQYMGcfnll5MbTBbZt28fgxqx3VbLXpEDtE41St8CjlbP4S28DFTlpKH6Jwcpf3tUoA1iPmn45j+/FbpeZZQYCPHN3yFgxAoqBWu+Gs2yTZOId3m5rt1a+o+tOSR/4MDI8eM2mxHpotG0dHIfzUUVRi+RXOKE1re1rvp5ERYuXMhVV13F2LFj8fl83HXXXXz44YekpqaWVjqcMWMGTz/9NHfffXfUbKstLVvIT/8XjnxaumlxbMbZ7jaKjz1L9OusmBAxnNHeogtwn76RwN9PYR1ixzHMgdgE3CdAeVEKrnv2JZZvmkyR24XZ7OOxD0w8/oQRxVIdSUmG7/vJJylN9zeZDP/3r38d5SlpNM2QaIp4bccLrbjnz59PYWEh119/Pb169apwTGZmJtu2bYuqbbWlZQv51wtAVcyWsce/T/ExH1U3ZD4TFCbrXsTkpiT3RopP3mX44gtN+D8twbPZQ+JPEpEul8H+bFZ8MZLlmyZT6DayPH1+Gz6/IdBTpkDbCEmr5Zk3D/r1g4cfhhMnDPfJffdBSkoUp6TRaCowd+5chg4dis1mo3JCo9/vZ+XKldxwww1NYlvLFvK8L8MrJ0oBJsu3BHy9Ir+mShRlMemVV/N+nG3vRvkTKD75+4o3VH0QyAvg3uLGMfx/oF0mb2y4hkJ3eE0YqxVWrDBuSlaHCPz4x8ZDo9E0DnFxcUybNo34+HjswRtVxcXFpKWl8f3333PuuedycROFhLXsm53tRoKp4p1BEXAl3wYUUrewQw/W+Fexxb8KFGM0CQ2AFGFLWILV9Qk+93CQCAXEfeDd5QWTGca8j6PL+Zgk8rkbqpGERqOpPyaTCVO5sC+n08mWLVvYv38/SimefvrpJrGrRa/IAyk3U7LegS8/C7EcxtHqaayudVhd60joPIn8gx9Rs6/cD1KCK/km7An/B4CjzWN48qegVBy2uA8w2zcggnGjU0UOC5H44HlMFq6/uR+L3yaspG0gAOPH12/OGo2m8XG5XCxYsIBJkyZx0003Nfr5W+yKPFAU4PRLdty5N+L3DMFXdAkFh1+jJG8WAGbH58FwxMqocj89ONv+ntbd+5aKOIDZuhdnm4dxtf0TFseG0gxKs20rJsthjJT/cljBMaKsIMp558Fddxmp9y6XUV8lLg6WLTN+ajSa2CM9PZ0hQ4aQHarB0YiccfXD+tAY1Q+LVhXh/rc7PGxcCmndvS9iKsZTeAmFR14A5cD4TAseLHlYnZ/haPMAFvtO6oLfew4Fh5YS8HUBCYA5AefFThzDwitbHThg1FYJpc0nJp7RVDWaFk3lKoCNHX7YVNSl+mGLda14d3sj5/5lONmxAAAI4klEQVRIAL9vCBbnTmyJ6zGZr6T45G8IeHthtm/B6lqF+/T1+EoyKTr2OM4292N1fVrr85qtB0g853z8/mGocx/GkjraCD2MwDnn1BxuqNFoKtIcRbepabFCboo3ETgSoWStuJCBs6BzCnS6FMunl5HgmAqAt2gcBYdfLE0Y8ruHUXD4FeI6zAqm39cCRwekTQaWgXdBctW9+jQajSZatFgfueN8R3iouAnMnWyYM2ZDlx8aUSSdxxP6MxQd/3N41qdyUXz8/uDraxFS4iuErCVaxDUaTaPRYoXc2tOK8yKnIeZ2wALmzmbip1ZqtdbzeqMXKBDw9ok4VsDXE9VlEvS/zWglVy0mOLKq3vZrNBpNbWmxrhUwIkXs6Xb8R/xInGBOihAaaEuC8Rtg/XTEfBTl7xR2iNjdyOhlxoYlAXbcC4EqGmYKoM6gj5tGo9GcIS12RR5CrIIlxRJZxEMk9oNhT+BIWgBSqamrFOIYlle2PfB30GcOSBWfgQE/dBxXf8M1Go2mlrR4Ia81hz7CnvgczjbzwJQHUgJyGkfSw9hPX0ppjVoxwbBHYMoJ6DIZTMG2cSYHmJ0w8uXw8rUajSamCZWrDT0efPBBAN577z3S09NJTU1lwIABPPfccwDcc889uFwujh49WjpGfHx8xLGjQYt2rdQJWxtEzDhaP4O91XMofxJiPmW0b3Pb4fi/jBrjpccnwui34cRGOPghWOOh6zRwdW66OWg0ZwNvd4SSI9Ebz9EBrqy+Z3woFb88Xq+X2bNns2HDBlJSUnC73ezbt6/0+Xbt2vHII48wf/786NlaBXpFHqJ7WaUqET8my/HSHpyICXK3R35d2wwY/Afo/yst4hpNYxBNEa/HePn5+fh8PtoGy5Xa7Xb69etX+vysWbNYsmQJJ0+ejIqZ1aGFPISzE/SqogSlmCEhckSLRqNp+YSqHIYeS5YsoU2bNlxxxRV069aN6dOn8+qrrxIIlAU6xMfHM2vWLJ544okGt6/eQi4it4jILhHZKSIPRcOoJiN9vhHFUr6QlljB1RU6jGkqqzQaTRMTcq2EHtOmTQPg+eefZ+XKlYwYMYKHH36YWbNmVXjdrbfeyosvvkh+fn6D2lcvH7mIjAUmAqlKKbeItI+OWY1MwTewcx4cy4GkoUYnn7xtgBlSroCMhYZ7RaPRaCoxePBgBg8ezHXXXUePHj1YvHhx6XOtW7fmmmuuafDytvW92Xkj8KBSyg2glDpaw/HNj7xd8NEI8BcbTShOf2VEn2QthS4TjexPjUajqURBQQGbNm1izJgxAGzZsoVu3bqFHXfbbbeRkZGBz+cLey5a1HeZ2Re4QEQ+E5E1IpJR1YEiMltENonIpmPHjtXztFFkyx3gKyjXSUgZXe433apX4RqNBgj3kf/ud79DKcVDDz1Ev379SEtLY+7cuRVW4yHatWvH5MmTcUfqmh4laixjKyKfAB0jPHU3cD+wGrgVyACWAD1VDYM2RhnbWvNmW/BEuKtsssOkA+BIbnybNBpNKWHlXJsg/LApiGoZW6XUD6p6TkRuBN4OCvcGEQkA7YBmtOSuAXtyZCEHsCY0ri0ajaZmmqHoNjX19R0sB8YCiEhfwAYcr69Rjcq5vwVzpUxMkwO6/wjM4c0gNBqNprlRXyF/AegpIjuA14EZNblVmh29ZhnJPGYnWBMNEe9yOQx/qqkt02g0mlpRr6gVpZQHuDZKtjQNIpD6ZxjwW8jfDc4u4OzQ1FZpNJpyKKUQqalResuhruthHZYRwpoIbYZqEddomhkOh4MTJ07UWdxiFaUUJ06cwOGovWtXF83SaDTNmpSUFL777juaVdhyA+NwOEhJSan18VrINRpNs8ZqtdKjR4+mNqNZo10rGo1GE+NoIddoNJoYRwu5RqPRxDg1pug3yElFjgH7G/3E9aMdsZbsVJFYtx9ifw6xbj/E/hxi3f5uSqmwuiFNIuSxiIhsilTjIFaIdfsh9ucQ6/ZD7M8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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "x = np.dot(matrix, pca.components_[0])\n",
    "y = np.dot(matrix, pca.components_[1])\n",
    "populations = list(set(dataset['population']))\n",
    "colors_list = ['blue', 'red', 'green', 'yellow', 'indigo', 'violet', 'orange']\n",
    "colors = {key: value for key, value in zip(populations, colors_list)}\n",
    "scatter = plt.scatter(x, y, c=dataset['population'].map(colors))\n",
    "handles=[mpatches.Patch(color=c, label=l) for c, l in zip(colors_list, populations)]\n",
    "plt.legend(handles=handles)\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "Opazimo določene vzorce. Populaciji GWD in MSL sta si blizu in sta nekoliko ločeni od ostalih. Populaciji YRI in ESN se skoraj popolnoma prekrivata, populaciji ACB in ASW pa sta najbolj razpršeni. Vse te opazke imajo preprosto razlago, če pogledamo geografsko pripadnost danih populacij. Populacija GWD je iz območja Gambije, MSL pa iz Sierra Leone, torej sta geografsko nekoliko bolj zahodno od ostalih. Populaciji YRI in ESN sta obe iz območja Nigerije, zato se praktično prekrivata. Člani populacije ACB ljudje so z območja Barbadosa z afriškimi koreninami, člani populacije ASW pa ljudje z ameriškega jugovzhoda, prav tako z afriškimi koreninami. Zaradi mešanja z ostalimi narodnostmi v Ameriki ter na Karibih sta populaciji ACB in ASW torej razumljivo najbolj razpršeni."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "Drugi graf prikazuje projekcijo na prostor, ki ga napenjata prva in tretja glavna komponenta. Vidimo lahko, da so podatki glede na y-os ločeni v dva približno enako velika sklopa. Najbolj verjetna razlaga je, da gre za sklopa moških in ženskih osebkov, torej y-os, oziroma tretja glavna komponenta, vsebuje podatek o spolu. To je pričakovano, saj vemo, da se moški in ženski genomi med seboj močno razlikujejo in so eden izmed glavnih povzročiteljev variance med genomi osebkov. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = np.dot(matrix, pca.components_[2])\n",
    "scatter = plt.scatter(x, z, c=dataset['population'].map(colors))\n",
    "plt.legend(handles=handles)\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "Tretji graf prikazuje absolutno vrednost tretje glavne komponente na posameznem mestu v sekvenci. Vidimo, da so vrednosti skoraj povsod blizu 0. Bistveno večje vrednosti se pojavijo šele proti koncu, v približno zadnjih 10% sekvence. Glede na našo prejšnjo ugotovitev, da tretja glavna komponenta ujame raliko med spoloma, sklepamo, da se ta razlika izraža kot mutacija na zadnjem delu sekvence. Razlaga za to je preprosta: celotna sekvenca človeškega genoma je sestavljena iz 24 delov, ki se imenujejo kromosomi. Vemo, da se zadnja dva kromosoma razlikujeta glede na spol: ženski osebki imajo dva X kromosoma, moški pa kromosom X in Y. Če predpostavimo, da je bila naša sekvenca vzorčena v približno istem zaporedju, nam zadnjih del sekvence predstavja ravno varianco na tih dveh kromosomih, torej ni nič čudnega, da ima komponenta, ki ujame informacijo o spolu, neničelne vrednosti le na tem delu sekvence."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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