Lab-4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 4- Model Building\n",
    "\n",
    "In this lab, we will attempt to follow the first paper on Deep Learning in High Energy physics [P. Baldi, et al](https://arxiv.org/pdf/1402.4735.pdf). This paper demonstrates that Deep Neural Networks can learn from rad data the features that are typically used by physicists for searches for exotics particles. The authors provide the data they used for this paper. They considered two benchmark scenarios. We will focus on the SUSY benchmark. The physics behind this sample will be discussed in class.\n",
    "\n",
    "The data is provided as a comma separated file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000000000000000000e+00,9.728614687919616699e-01,6.538545489311218262e-01,1.176224589347839355e+00,1.157156467437744141e+00,-1.739873170852661133e+00,-8.743090629577636719e-01,5.677649974822998047e-01,-1.750000417232513428e-01,8.100607395172119141e-01,-2.525521218776702881e-01,1.921887040138244629e+00,8.896374106407165527e-01,4.107718467712402344e-01,1.145620822906494141e+00,1.932632088661193848e+00,9.944640994071960449e-01,1.367815494537353516e+00,4.071449860930442810e-02\r\n",
      "1.000000000000000000e+00,1.667973041534423828e+00,6.419061869382858276e-02,-1.225171446800231934e+00,5.061022043228149414e-01,-3.389389812946319580e-01,1.672542810440063477e+00,3.475464344024658203e+00,-1.219136357307434082e+00,1.295456290245056152e-02,3.775173664093017578e+00,1.045977115631103516e+00,5.680512785911560059e-01,4.819284379482269287e-01,0.000000000000000000e+00,4.484102725982666016e-01,2.053557634353637695e-01,1.321893453598022461e+00,3.775840103626251221e-01\r\n",
      "1.000000000000000000e+00,4.448399245738983154e-01,-1.342980116605758667e-01,-7.099716067314147949e-01,4.517189264297485352e-01,-1.613871216773986816e+00,-7.686609029769897461e-01,1.219918131828308105e+00,5.040258169174194336e-01,1.831247568130493164e+00,-4.313853085041046143e-01,5.262832045555114746e-01,9.415140151977539062e-01,1.587535023689270020e+00,2.024308204650878906e+00,6.034975647926330566e-01,1.562373995780944824e+00,1.135454416275024414e+00,1.809100061655044556e-01\r\n",
      "1.000000000000000000e+00,3.812560737133026123e-01,-9.761453866958618164e-01,6.931523084640502930e-01,4.489588439464569092e-01,8.917528986930847168e-01,-6.773284673690795898e-01,2.033060073852539062e+00,1.533040523529052734e+00,3.046259880065917969e+00,-1.005284786224365234e+00,5.693860650062561035e-01,1.015211343765258789e+00,1.582216739654541016e+00,1.551914215087890625e+00,7.612152099609375000e-01,1.715463757514953613e+00,1.492256760597229004e+00,9.071890264749526978e-02\r\n",
      "1.000000000000000000e+00,1.309996485710144043e+00,-6.900894641876220703e-01,-6.762592792510986328e-01,1.589282631874084473e+00,-6.933256387710571289e-01,6.229069828987121582e-01,1.087561845779418945e+00,-3.817416727542877197e-01,5.892043709754943848e-01,1.365478992462158203e+00,1.179295063018798828e+00,9.682182073593139648e-01,7.285631299018859863e-01,0.000000000000000000e+00,1.083157896995544434e+00,4.342924803495407104e-02,1.154853701591491699e+00,9.485860168933868408e-02\r\n"
     ]
    }
   ],
   "source": [
    "filename=\"/data/afarbin/DLClass/SUSY/SUSY.csv\"\n",
    "# print out the first 5 lines using unix head command\n",
    "!head -5  \"/data/afarbin/DLClass/SUSY/SUSY.csv\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row represents a LHC collision event. Each column contains some observable from that event. The variable names are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "VarNames=[\"signal\", \"l_1_pT\", \"l_1_eta\",\"l_1_phi\", \"l_2_pT\", \"l_2_eta\", \"l_2_phi\", \"MET\", \"MET_phi\", \"MET_rel\", \"axial_MET\", \"M_R\", \"M_TR_2\", \"R\", \"MT2\", \"S_R\", \"M_Delta_R\", \"dPhi_r_b\", \"cos_theta_r1\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some of these variables represent the \"raw\" kinematics of the observed final state particles, while others are \"features\" that are derived from these raw quantities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "RawNames=[\"l_1_pT\", \"l_1_eta\",\"l_1_phi\", \"l_2_pT\", \"l_2_eta\", \"l_2_phi\"]\n",
    "FeatureNames=[ \"MET\", \"MET_phi\", \"MET_rel\", \"axial_MET\", \"M_R\", \"M_TR_2\", \"R\", \"MT2\", \"S_R\", \"M_Delta_R\", \"dPhi_r_b\", \"cos_theta_r1\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use pandas to read in the file, and matplotlib to make plots. The following ensures pandas is installed and sets everything up:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
      "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can read the data into a pandas dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(filename, dtype='float64', names=VarNames)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see the data in Jupyter by just evaluating the dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>signal</th>\n",
       "      <th>l_1_pT</th>\n",
       "      <th>l_1_eta</th>\n",
       "      <th>l_1_phi</th>\n",
       "      <th>l_2_pT</th>\n",
       "      <th>l_2_eta</th>\n",
       "      <th>l_2_phi</th>\n",
       "      <th>MET</th>\n",
       "      <th>MET_phi</th>\n",
       "      <th>MET_rel</th>\n",
       "      <th>axial_MET</th>\n",
       "      <th>M_R</th>\n",
       "      <th>M_TR_2</th>\n",
       "      <th>R</th>\n",
       "      <th>MT2</th>\n",
       "      <th>S_R</th>\n",
       "      <th>M_Delta_R</th>\n",
       "      <th>dPhi_r_b</th>\n",
       "      <th>cos_theta_r1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.972861</td>\n",
       "      <td>0.653855</td>\n",
       "      <td>1.176225</td>\n",
       "      <td>1.157156</td>\n",
       "      <td>-1.739873</td>\n",
       "      <td>-0.874309</td>\n",
       "      <td>0.567765</td>\n",
       "      <td>-0.175000</td>\n",
       "      <td>0.810061</td>\n",
       "      <td>-0.252552</td>\n",
       "      <td>1.921887</td>\n",
       "      <td>0.889637</td>\n",
       "      <td>0.410772</td>\n",
       "      <td>1.145621</td>\n",
       "      <td>1.932632</td>\n",
       "      <td>0.994464</td>\n",
       "      <td>1.367815</td>\n",
       "      <td>0.040714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.667973</td>\n",
       "      <td>0.064191</td>\n",
       "      <td>-1.225171</td>\n",
       "      <td>0.506102</td>\n",
       "      <td>-0.338939</td>\n",
       "      <td>1.672543</td>\n",
       "      <td>3.475464</td>\n",
       "      <td>-1.219136</td>\n",
       "      <td>0.012955</td>\n",
       "      <td>3.775174</td>\n",
       "      <td>1.045977</td>\n",
       "      <td>0.568051</td>\n",
       "      <td>0.481928</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.448410</td>\n",
       "      <td>0.205356</td>\n",
       "      <td>1.321893</td>\n",
       "      <td>0.377584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.444840</td>\n",
       "      <td>-0.134298</td>\n",
       "      <td>-0.709972</td>\n",
       "      <td>0.451719</td>\n",
       "      <td>-1.613871</td>\n",
       "      <td>-0.768661</td>\n",
       "      <td>1.219918</td>\n",
       "      <td>0.504026</td>\n",
       "      <td>1.831248</td>\n",
       "      <td>-0.431385</td>\n",
       "      <td>0.526283</td>\n",
       "      <td>0.941514</td>\n",
       "      <td>1.587535</td>\n",
       "      <td>2.024308</td>\n",
       "      <td>0.603498</td>\n",
       "      <td>1.562374</td>\n",
       "      <td>1.135454</td>\n",
       "      <td>0.180910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.381256</td>\n",
       "      <td>-0.976145</td>\n",
       "      <td>0.693152</td>\n",
       "      <td>0.448959</td>\n",
       "      <td>0.891753</td>\n",
       "      <td>-0.677328</td>\n",
       "      <td>2.033060</td>\n",
       "      <td>1.533041</td>\n",
       "      <td>3.046260</td>\n",
       "      <td>-1.005285</td>\n",
       "      <td>0.569386</td>\n",
       "      <td>1.015211</td>\n",
       "      <td>1.582217</td>\n",
       "      <td>1.551914</td>\n",
       "      <td>0.761215</td>\n",
       "      <td>1.715464</td>\n",
       "      <td>1.492257</td>\n",
       "      <td>0.090719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.309996</td>\n",
       "      <td>-0.690089</td>\n",
       "      <td>-0.676259</td>\n",
       "      <td>1.589283</td>\n",
       "      <td>-0.693326</td>\n",
       "      <td>0.622907</td>\n",
       "      <td>1.087562</td>\n",
       "      <td>-0.381742</td>\n",
       "      <td>0.589204</td>\n",
       "      <td>1.365479</td>\n",
       "      <td>1.179295</td>\n",
       "      <td>0.968218</td>\n",
       "      <td>0.728563</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.083158</td>\n",
       "      <td>0.043429</td>\n",
       "      <td>1.154854</td>\n",
       "      <td>0.094859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.456398</td>\n",
       "      <td>1.099371</td>\n",
       "      <td>1.512453</td>\n",
       "      <td>0.751772</td>\n",
       "      <td>0.638967</td>\n",
       "      <td>-0.742216</td>\n",
       "      <td>0.322601</td>\n",
       "      <td>1.321054</td>\n",
       "      <td>0.169502</td>\n",
       "      <td>0.359941</td>\n",
       "      <td>0.489256</td>\n",
       "      <td>0.416168</td>\n",
       "      <td>0.754829</td>\n",
       "      <td>0.303750</td>\n",
       "      <td>0.461067</td>\n",
       "      <td>0.345541</td>\n",
       "      <td>0.733242</td>\n",
       "      <td>0.186044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.437818</td>\n",
       "      <td>-1.119883</td>\n",
       "      <td>-1.336823</td>\n",
       "      <td>0.502320</td>\n",
       "      <td>-1.717515</td>\n",
       "      <td>1.017067</td>\n",
       "      <td>0.215619</td>\n",
       "      <td>-0.461200</td>\n",
       "      <td>0.323671</td>\n",
       "      <td>0.173626</td>\n",
       "      <td>0.411898</td>\n",
       "      <td>0.370525</td>\n",
       "      <td>0.798260</td>\n",
       "      <td>0.671369</td>\n",
       "      <td>0.385910</td>\n",
       "      <td>0.515522</td>\n",
       "      <td>0.479110</td>\n",
       "      <td>0.029058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.571656</td>\n",
       "      <td>0.205696</td>\n",
       "      <td>0.425950</td>\n",
       "      <td>0.578514</td>\n",
       "      <td>0.927399</td>\n",
       "      <td>-1.101478</td>\n",
       "      <td>0.116555</td>\n",
       "      <td>1.549753</td>\n",
       "      <td>0.174421</td>\n",
       "      <td>0.223450</td>\n",
       "      <td>0.523164</td>\n",
       "      <td>0.289889</td>\n",
       "      <td>0.491710</td>\n",
       "      <td>0.334593</td>\n",
       "      <td>0.514246</td>\n",
       "      <td>0.268207</td>\n",
       "      <td>0.315795</td>\n",
       "      <td>0.125728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.112812</td>\n",
       "      <td>0.742983</td>\n",
       "      <td>-0.330539</td>\n",
       "      <td>0.805253</td>\n",
       "      <td>-0.028887</td>\n",
       "      <td>-1.446679</td>\n",
       "      <td>2.299946</td>\n",
       "      <td>1.450429</td>\n",
       "      <td>2.989110</td>\n",
       "      <td>-1.894770</td>\n",
       "      <td>1.445125</td>\n",
       "      <td>2.548166</td>\n",
       "      <td>1.564721</td>\n",
       "      <td>2.393632</td>\n",
       "      <td>1.554566</td>\n",
       "      <td>2.148468</td>\n",
       "      <td>1.179117</td>\n",
       "      <td>0.688057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.001869</td>\n",
       "      <td>-0.471788</td>\n",
       "      <td>0.555614</td>\n",
       "      <td>1.233368</td>\n",
       "      <td>1.255548</td>\n",
       "      <td>-1.052491</td>\n",
       "      <td>0.437615</td>\n",
       "      <td>-1.333052</td>\n",
       "      <td>0.326858</td>\n",
       "      <td>-0.111678</td>\n",
       "      <td>1.435708</td>\n",
       "      <td>0.755201</td>\n",
       "      <td>0.466779</td>\n",
       "      <td>0.454541</td>\n",
       "      <td>1.446331</td>\n",
       "      <td>0.592259</td>\n",
       "      <td>1.325197</td>\n",
       "      <td>0.083014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.840115</td>\n",
       "      <td>0.958249</td>\n",
       "      <td>-0.585658</td>\n",
       "      <td>1.317930</td>\n",
       "      <td>-1.063730</td>\n",
       "      <td>1.246235</td>\n",
       "      <td>0.261865</td>\n",
       "      <td>-0.027341</td>\n",
       "      <td>0.330517</td>\n",
       "      <td>0.183190</td>\n",
       "      <td>1.557298</td>\n",
       "      <td>0.531022</td>\n",
       "      <td>0.302592</td>\n",
       "      <td>0.426702</td>\n",
       "      <td>1.564376</td>\n",
       "      <td>0.338552</td>\n",
       "      <td>1.137456</td>\n",
       "      <td>0.011040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.263320</td>\n",
       "      <td>0.733208</td>\n",
       "      <td>0.331149</td>\n",
       "      <td>1.511739</td>\n",
       "      <td>0.371084</td>\n",
       "      <td>-1.585176</td>\n",
       "      <td>0.572889</td>\n",
       "      <td>-1.054526</td>\n",
       "      <td>0.698872</td>\n",
       "      <td>-0.259238</td>\n",
       "      <td>1.155319</td>\n",
       "      <td>0.983545</td>\n",
       "      <td>0.755454</td>\n",
       "      <td>0.926953</td>\n",
       "      <td>1.168115</td>\n",
       "      <td>0.709708</td>\n",
       "      <td>1.578325</td>\n",
       "      <td>0.184405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.698336</td>\n",
       "      <td>1.689431</td>\n",
       "      <td>-1.134670</td>\n",
       "      <td>0.966594</td>\n",
       "      <td>1.503367</td>\n",
       "      <td>0.880949</td>\n",
       "      <td>0.242573</td>\n",
       "      <td>-0.228654</td>\n",
       "      <td>0.364132</td>\n",
       "      <td>0.109350</td>\n",
       "      <td>0.668554</td>\n",
       "      <td>0.489941</td>\n",
       "      <td>0.650313</td>\n",
       "      <td>0.683634</td>\n",
       "      <td>0.664825</td>\n",
       "      <td>0.510385</td>\n",
       "      <td>0.584092</td>\n",
       "      <td>0.031694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.578286</td>\n",
       "      <td>-0.689652</td>\n",
       "      <td>-0.390094</td>\n",
       "      <td>0.480061</td>\n",
       "      <td>-0.632219</td>\n",
       "      <td>1.212005</td>\n",
       "      <td>0.640473</td>\n",
       "      <td>-1.622401</td>\n",
       "      <td>0.872160</td>\n",
       "      <td>-0.186169</td>\n",
       "      <td>0.451853</td>\n",
       "      <td>0.669288</td>\n",
       "      <td>1.314412</td>\n",
       "      <td>0.559444</td>\n",
       "      <td>0.491753</td>\n",
       "      <td>0.559017</td>\n",
       "      <td>1.286520</td>\n",
       "      <td>0.400292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.798202</td>\n",
       "      <td>0.099358</td>\n",
       "      <td>-1.095839</td>\n",
       "      <td>0.531147</td>\n",
       "      <td>-0.962327</td>\n",
       "      <td>1.500362</td>\n",
       "      <td>1.273941</td>\n",
       "      <td>0.675408</td>\n",
       "      <td>1.803743</td>\n",
       "      <td>-0.845941</td>\n",
       "      <td>0.685836</td>\n",
       "      <td>1.234757</td>\n",
       "      <td>1.597630</td>\n",
       "      <td>1.864630</td>\n",
       "      <td>0.775854</td>\n",
       "      <td>1.556949</td>\n",
       "      <td>1.245781</td>\n",
       "      <td>0.538010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.452214</td>\n",
       "      <td>-0.004851</td>\n",
       "      <td>-1.374135</td>\n",
       "      <td>0.455546</td>\n",
       "      <td>0.271702</td>\n",
       "      <td>1.643006</td>\n",
       "      <td>0.835887</td>\n",
       "      <td>-0.254897</td>\n",
       "      <td>1.254769</td>\n",
       "      <td>-0.252735</td>\n",
       "      <td>0.383118</td>\n",
       "      <td>0.788506</td>\n",
       "      <td>1.826371</td>\n",
       "      <td>1.687989</td>\n",
       "      <td>0.412063</td>\n",
       "      <td>1.258978</td>\n",
       "      <td>1.000029</td>\n",
       "      <td>0.237916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.865126</td>\n",
       "      <td>-1.109674</td>\n",
       "      <td>1.378841</td>\n",
       "      <td>1.225827</td>\n",
       "      <td>-1.599314</td>\n",
       "      <td>-0.335546</td>\n",
       "      <td>0.452621</td>\n",
       "      <td>1.396529</td>\n",
       "      <td>0.014348</td>\n",
       "      <td>0.761019</td>\n",
       "      <td>0.873992</td>\n",
       "      <td>0.646078</td>\n",
       "      <td>0.655985</td>\n",
       "      <td>0.027587</td>\n",
       "      <td>0.879327</td>\n",
       "      <td>0.099123</td>\n",
       "      <td>1.526896</td>\n",
       "      <td>0.103202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.679042</td>\n",
       "      <td>-0.116113</td>\n",
       "      <td>-1.449247</td>\n",
       "      <td>0.725930</td>\n",
       "      <td>0.832636</td>\n",
       "      <td>-1.068640</td>\n",
       "      <td>0.734276</td>\n",
       "      <td>0.616541</td>\n",
       "      <td>1.102238</td>\n",
       "      <td>-0.383189</td>\n",
       "      <td>0.674581</td>\n",
       "      <td>0.989127</td>\n",
       "      <td>1.301167</td>\n",
       "      <td>2.113569</td>\n",
       "      <td>0.622589</td>\n",
       "      <td>1.583448</td>\n",
       "      <td>0.462588</td>\n",
       "      <td>0.192226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.696711</td>\n",
       "      <td>1.532483</td>\n",
       "      <td>0.451737</td>\n",
       "      <td>0.953612</td>\n",
       "      <td>1.085324</td>\n",
       "      <td>-1.261485</td>\n",
       "      <td>0.021957</td>\n",
       "      <td>0.769306</td>\n",
       "      <td>0.017608</td>\n",
       "      <td>0.332876</td>\n",
       "      <td>0.681880</td>\n",
       "      <td>0.127229</td>\n",
       "      <td>0.165574</td>\n",
       "      <td>0.041008</td>\n",
       "      <td>0.681533</td>\n",
       "      <td>0.039989</td>\n",
       "      <td>0.126778</td>\n",
       "      <td>0.040972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.006098</td>\n",
       "      <td>-0.218872</td>\n",
       "      <td>1.273336</td>\n",
       "      <td>1.621487</td>\n",
       "      <td>0.076018</td>\n",
       "      <td>0.586132</td>\n",
       "      <td>0.561284</td>\n",
       "      <td>0.170752</td>\n",
       "      <td>0.582976</td>\n",
       "      <td>0.411129</td>\n",
       "      <td>1.046204</td>\n",
       "      <td>0.777395</td>\n",
       "      <td>0.659388</td>\n",
       "      <td>1.177816</td>\n",
       "      <td>0.740323</td>\n",
       "      <td>1.207057</td>\n",
       "      <td>0.418392</td>\n",
       "      <td>0.219343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.837867</td>\n",
       "      <td>1.134530</td>\n",
       "      <td>-0.911252</td>\n",
       "      <td>0.616626</td>\n",
       "      <td>1.000158</td>\n",
       "      <td>1.292737</td>\n",
       "      <td>1.272458</td>\n",
       "      <td>-0.676616</td>\n",
       "      <td>0.764920</td>\n",
       "      <td>1.165517</td>\n",
       "      <td>0.631193</td>\n",
       "      <td>0.786714</td>\n",
       "      <td>1.106040</td>\n",
       "      <td>0.815495</td>\n",
       "      <td>0.588254</td>\n",
       "      <td>0.607716</td>\n",
       "      <td>1.156936</td>\n",
       "      <td>0.310599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.641748</td>\n",
       "      <td>-1.829807</td>\n",
       "      <td>0.150152</td>\n",
       "      <td>2.702642</td>\n",
       "      <td>-0.129722</td>\n",
       "      <td>-1.380814</td>\n",
       "      <td>0.194475</td>\n",
       "      <td>-1.478649</td>\n",
       "      <td>0.055107</td>\n",
       "      <td>0.303612</td>\n",
       "      <td>2.638832</td>\n",
       "      <td>0.636117</td>\n",
       "      <td>0.213914</td>\n",
       "      <td>0.230072</td>\n",
       "      <td>2.635528</td>\n",
       "      <td>0.546993</td>\n",
       "      <td>0.354201</td>\n",
       "      <td>0.016105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.466649</td>\n",
       "      <td>0.115517</td>\n",
       "      <td>-1.036161</td>\n",
       "      <td>0.877247</td>\n",
       "      <td>0.690861</td>\n",
       "      <td>1.130069</td>\n",
       "      <td>0.890722</td>\n",
       "      <td>0.426515</td>\n",
       "      <td>1.283212</td>\n",
       "      <td>-0.563880</td>\n",
       "      <td>1.090046</td>\n",
       "      <td>1.327570</td>\n",
       "      <td>1.080762</td>\n",
       "      <td>1.588076</td>\n",
       "      <td>1.069615</td>\n",
       "      <td>1.258800</td>\n",
       "      <td>0.443045</td>\n",
       "      <td>0.415406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.641595</td>\n",
       "      <td>-1.044596</td>\n",
       "      <td>0.543058</td>\n",
       "      <td>0.744842</td>\n",
       "      <td>-0.308126</td>\n",
       "      <td>-0.956825</td>\n",
       "      <td>1.249039</td>\n",
       "      <td>-1.477087</td>\n",
       "      <td>0.731511</td>\n",
       "      <td>-0.847167</td>\n",
       "      <td>1.160934</td>\n",
       "      <td>1.601837</td>\n",
       "      <td>1.224409</td>\n",
       "      <td>1.256747</td>\n",
       "      <td>1.179161</td>\n",
       "      <td>1.215011</td>\n",
       "      <td>0.937398</td>\n",
       "      <td>0.513443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.361442</td>\n",
       "      <td>-0.506247</td>\n",
       "      <td>-0.646164</td>\n",
       "      <td>1.047869</td>\n",
       "      <td>1.136730</td>\n",
       "      <td>0.698665</td>\n",
       "      <td>1.657924</td>\n",
       "      <td>-0.061501</td>\n",
       "      <td>2.154410</td>\n",
       "      <td>1.672853</td>\n",
       "      <td>1.525310</td>\n",
       "      <td>1.117499</td>\n",
       "      <td>0.650136</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.472982</td>\n",
       "      <td>0.969957</td>\n",
       "      <td>1.209303</td>\n",
       "      <td>0.039710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.297482</td>\n",
       "      <td>-0.254912</td>\n",
       "      <td>1.116834</td>\n",
       "      <td>0.979169</td>\n",
       "      <td>-0.135346</td>\n",
       "      <td>-0.697154</td>\n",
       "      <td>1.027495</td>\n",
       "      <td>-0.166322</td>\n",
       "      <td>1.254201</td>\n",
       "      <td>-0.479649</td>\n",
       "      <td>0.985066</td>\n",
       "      <td>1.259747</td>\n",
       "      <td>1.134837</td>\n",
       "      <td>0.760780</td>\n",
       "      <td>1.022235</td>\n",
       "      <td>0.810835</td>\n",
       "      <td>1.115006</td>\n",
       "      <td>0.394822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.378505</td>\n",
       "      <td>-1.082134</td>\n",
       "      <td>1.008099</td>\n",
       "      <td>0.611425</td>\n",
       "      <td>-1.285566</td>\n",
       "      <td>-0.065581</td>\n",
       "      <td>0.916273</td>\n",
       "      <td>-0.886186</td>\n",
       "      <td>1.371866</td>\n",
       "      <td>-0.421905</td>\n",
       "      <td>0.391697</td>\n",
       "      <td>0.790429</td>\n",
       "      <td>1.790726</td>\n",
       "      <td>1.388440</td>\n",
       "      <td>0.473287</td>\n",
       "      <td>1.068429</td>\n",
       "      <td>1.305904</td>\n",
       "      <td>0.347194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.675933</td>\n",
       "      <td>0.126536</td>\n",
       "      <td>0.956136</td>\n",
       "      <td>0.686048</td>\n",
       "      <td>-0.199500</td>\n",
       "      <td>-1.708110</td>\n",
       "      <td>0.924259</td>\n",
       "      <td>-0.693053</td>\n",
       "      <td>1.387424</td>\n",
       "      <td>-0.549809</td>\n",
       "      <td>0.577165</td>\n",
       "      <td>1.042057</td>\n",
       "      <td>1.602167</td>\n",
       "      <td>1.921268</td>\n",
       "      <td>0.612655</td>\n",
       "      <td>1.435927</td>\n",
       "      <td>1.072373</td>\n",
       "      <td>0.474427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.463987</td>\n",
       "      <td>0.011333</td>\n",
       "      <td>0.369054</td>\n",
       "      <td>0.553187</td>\n",
       "      <td>0.389280</td>\n",
       "      <td>0.301573</td>\n",
       "      <td>1.657913</td>\n",
       "      <td>1.520308</td>\n",
       "      <td>2.488732</td>\n",
       "      <td>-0.559999</td>\n",
       "      <td>0.425258</td>\n",
       "      <td>1.126461</td>\n",
       "      <td>2.350607</td>\n",
       "      <td>2.460358</td>\n",
       "      <td>0.565242</td>\n",
       "      <td>1.836446</td>\n",
       "      <td>1.168629</td>\n",
       "      <td>0.602618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.164915</td>\n",
       "      <td>-1.216874</td>\n",
       "      <td>1.387384</td>\n",
       "      <td>1.289362</td>\n",
       "      <td>0.853503</td>\n",
       "      <td>-0.864189</td>\n",
       "      <td>0.552337</td>\n",
       "      <td>0.371583</td>\n",
       "      <td>0.829126</td>\n",
       "      <td>-0.149219</td>\n",
       "      <td>1.863999</td>\n",
       "      <td>0.975417</td>\n",
       "      <td>0.464368</td>\n",
       "      <td>1.686075</td>\n",
       "      <td>1.846609</td>\n",
       "      <td>1.296029</td>\n",
       "      <td>0.454520</td>\n",
       "      <td>0.027528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999970</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.772051</td>\n",
       "      <td>0.081051</td>\n",
       "      <td>0.665382</td>\n",
       "      <td>0.995895</td>\n",
       "      <td>0.564401</td>\n",
       "      <td>-1.218781</td>\n",
       "      <td>0.545470</td>\n",
       "      <td>-0.938474</td>\n",
       "      <td>0.389197</td>\n",
       "      <td>-0.179175</td>\n",
       "      <td>0.743884</td>\n",
       "      <td>0.742403</td>\n",
       "      <td>0.885624</td>\n",
       "      <td>0.465971</td>\n",
       "      <td>0.766907</td>\n",
       "      <td>0.393374</td>\n",
       "      <td>1.380740</td>\n",
       "      <td>0.246574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999971</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.306894</td>\n",
       "      <td>0.609032</td>\n",
       "      <td>0.864028</td>\n",
       "      <td>0.438315</td>\n",
       "      <td>1.402401</td>\n",
       "      <td>-1.173018</td>\n",
       "      <td>0.267329</td>\n",
       "      <td>-1.031219</td>\n",
       "      <td>0.097099</td>\n",
       "      <td>0.248908</td>\n",
       "      <td>0.332664</td>\n",
       "      <td>0.320653</td>\n",
       "      <td>0.855355</td>\n",
       "      <td>0.143922</td>\n",
       "      <td>0.337387</td>\n",
       "      <td>0.191113</td>\n",
       "      <td>1.094609</td>\n",
       "      <td>0.235031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999972</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.555719</td>\n",
       "      <td>-1.809759</td>\n",
       "      <td>-0.517869</td>\n",
       "      <td>0.468845</td>\n",
       "      <td>-1.798199</td>\n",
       "      <td>0.126298</td>\n",
       "      <td>0.611404</td>\n",
       "      <td>1.140576</td>\n",
       "      <td>0.917792</td>\n",
       "      <td>-0.217717</td>\n",
       "      <td>0.436476</td>\n",
       "      <td>0.750250</td>\n",
       "      <td>1.525324</td>\n",
       "      <td>1.361695</td>\n",
       "      <td>0.420984</td>\n",
       "      <td>1.014244</td>\n",
       "      <td>0.752499</td>\n",
       "      <td>0.621426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999973</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.411936</td>\n",
       "      <td>1.639347</td>\n",
       "      <td>0.155845</td>\n",
       "      <td>0.654584</td>\n",
       "      <td>-0.201792</td>\n",
       "      <td>0.927203</td>\n",
       "      <td>0.428966</td>\n",
       "      <td>1.456556</td>\n",
       "      <td>0.522951</td>\n",
       "      <td>0.273558</td>\n",
       "      <td>0.697551</td>\n",
       "      <td>0.483795</td>\n",
       "      <td>0.615466</td>\n",
       "      <td>0.778334</td>\n",
       "      <td>0.657248</td>\n",
       "      <td>0.686104</td>\n",
       "      <td>0.675997</td>\n",
       "      <td>0.088808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999974</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.579771</td>\n",
       "      <td>0.669194</td>\n",
       "      <td>0.916361</td>\n",
       "      <td>0.481992</td>\n",
       "      <td>0.383977</td>\n",
       "      <td>-0.449522</td>\n",
       "      <td>0.547135</td>\n",
       "      <td>1.628749</td>\n",
       "      <td>0.786687</td>\n",
       "      <td>0.222415</td>\n",
       "      <td>0.458597</td>\n",
       "      <td>0.568793</td>\n",
       "      <td>1.100624</td>\n",
       "      <td>0.861468</td>\n",
       "      <td>0.458086</td>\n",
       "      <td>0.675585</td>\n",
       "      <td>0.998140</td>\n",
       "      <td>0.031265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999975</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.630982</td>\n",
       "      <td>0.345205</td>\n",
       "      <td>-1.239799</td>\n",
       "      <td>0.897030</td>\n",
       "      <td>-0.087721</td>\n",
       "      <td>-0.006848</td>\n",
       "      <td>0.525165</td>\n",
       "      <td>1.174039</td>\n",
       "      <td>0.788337</td>\n",
       "      <td>-0.191744</td>\n",
       "      <td>0.629268</td>\n",
       "      <td>0.743672</td>\n",
       "      <td>1.048725</td>\n",
       "      <td>1.280769</td>\n",
       "      <td>0.638197</td>\n",
       "      <td>0.954547</td>\n",
       "      <td>1.012330</td>\n",
       "      <td>0.030134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999976</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.632756</td>\n",
       "      <td>-0.972319</td>\n",
       "      <td>-0.034061</td>\n",
       "      <td>0.770231</td>\n",
       "      <td>-0.980846</td>\n",
       "      <td>-0.999496</td>\n",
       "      <td>1.130503</td>\n",
       "      <td>1.031468</td>\n",
       "      <td>1.697023</td>\n",
       "      <td>-0.658722</td>\n",
       "      <td>0.570481</td>\n",
       "      <td>1.103604</td>\n",
       "      <td>1.716675</td>\n",
       "      <td>2.145489</td>\n",
       "      <td>0.653565</td>\n",
       "      <td>1.627295</td>\n",
       "      <td>1.224264</td>\n",
       "      <td>0.017822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999977</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.821894</td>\n",
       "      <td>0.721731</td>\n",
       "      <td>0.232942</td>\n",
       "      <td>0.984021</td>\n",
       "      <td>1.408234</td>\n",
       "      <td>-1.499447</td>\n",
       "      <td>0.451208</td>\n",
       "      <td>0.585650</td>\n",
       "      <td>0.397412</td>\n",
       "      <td>0.681289</td>\n",
       "      <td>0.801412</td>\n",
       "      <td>0.589269</td>\n",
       "      <td>0.652491</td>\n",
       "      <td>0.061916</td>\n",
       "      <td>0.799578</td>\n",
       "      <td>0.264371</td>\n",
       "      <td>1.269593</td>\n",
       "      <td>0.049163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999978</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.689959</td>\n",
       "      <td>0.000985</td>\n",
       "      <td>-0.889892</td>\n",
       "      <td>1.559262</td>\n",
       "      <td>-0.177674</td>\n",
       "      <td>0.773766</td>\n",
       "      <td>2.579031</td>\n",
       "      <td>0.598344</td>\n",
       "      <td>1.251830</td>\n",
       "      <td>-1.805566</td>\n",
       "      <td>1.376108</td>\n",
       "      <td>2.305554</td>\n",
       "      <td>1.486756</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.584048</td>\n",
       "      <td>0.694180</td>\n",
       "      <td>1.416985</td>\n",
       "      <td>0.542614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999979</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.588275</td>\n",
       "      <td>-1.153023</td>\n",
       "      <td>0.681203</td>\n",
       "      <td>0.895145</td>\n",
       "      <td>0.302639</td>\n",
       "      <td>-1.565196</td>\n",
       "      <td>0.407740</td>\n",
       "      <td>-0.442062</td>\n",
       "      <td>0.612068</td>\n",
       "      <td>-0.091711</td>\n",
       "      <td>0.820799</td>\n",
       "      <td>0.647016</td>\n",
       "      <td>0.699510</td>\n",
       "      <td>1.120962</td>\n",
       "      <td>0.819772</td>\n",
       "      <td>0.835719</td>\n",
       "      <td>0.363649</td>\n",
       "      <td>0.017190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999980</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.759629</td>\n",
       "      <td>-1.099936</td>\n",
       "      <td>1.018840</td>\n",
       "      <td>1.023628</td>\n",
       "      <td>-1.524405</td>\n",
       "      <td>-0.539747</td>\n",
       "      <td>0.440853</td>\n",
       "      <td>0.375886</td>\n",
       "      <td>0.610924</td>\n",
       "      <td>0.729659</td>\n",
       "      <td>0.741773</td>\n",
       "      <td>0.559601</td>\n",
       "      <td>0.669459</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.734658</td>\n",
       "      <td>0.222678</td>\n",
       "      <td>1.333323</td>\n",
       "      <td>0.012691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999981</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.980560</td>\n",
       "      <td>0.244252</td>\n",
       "      <td>1.370602</td>\n",
       "      <td>1.504819</td>\n",
       "      <td>0.681870</td>\n",
       "      <td>-0.753009</td>\n",
       "      <td>0.881322</td>\n",
       "      <td>0.730479</td>\n",
       "      <td>1.218523</td>\n",
       "      <td>-0.249648</td>\n",
       "      <td>1.016021</td>\n",
       "      <td>1.130732</td>\n",
       "      <td>0.987583</td>\n",
       "      <td>1.625787</td>\n",
       "      <td>1.036363</td>\n",
       "      <td>1.218644</td>\n",
       "      <td>1.046883</td>\n",
       "      <td>0.135561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999982</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.991963</td>\n",
       "      <td>0.114058</td>\n",
       "      <td>-1.284302</td>\n",
       "      <td>1.091986</td>\n",
       "      <td>0.883251</td>\n",
       "      <td>0.534301</td>\n",
       "      <td>0.704755</td>\n",
       "      <td>0.564092</td>\n",
       "      <td>0.044870</td>\n",
       "      <td>-0.316144</td>\n",
       "      <td>0.949935</td>\n",
       "      <td>0.936588</td>\n",
       "      <td>0.874928</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.979003</td>\n",
       "      <td>0.420024</td>\n",
       "      <td>1.343193</td>\n",
       "      <td>0.272565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999983</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.399545</td>\n",
       "      <td>0.889210</td>\n",
       "      <td>0.889816</td>\n",
       "      <td>0.566762</td>\n",
       "      <td>0.529097</td>\n",
       "      <td>-0.452789</td>\n",
       "      <td>0.895946</td>\n",
       "      <td>-0.489040</td>\n",
       "      <td>0.104523</td>\n",
       "      <td>-0.296892</td>\n",
       "      <td>0.920684</td>\n",
       "      <td>1.197951</td>\n",
       "      <td>1.154634</td>\n",
       "      <td>0.105272</td>\n",
       "      <td>0.866587</td>\n",
       "      <td>0.362570</td>\n",
       "      <td>0.694904</td>\n",
       "      <td>0.592398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999984</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.108980</td>\n",
       "      <td>0.561875</td>\n",
       "      <td>-1.306236</td>\n",
       "      <td>0.913503</td>\n",
       "      <td>1.112271</td>\n",
       "      <td>0.970117</td>\n",
       "      <td>2.291246</td>\n",
       "      <td>0.902578</td>\n",
       "      <td>0.458420</td>\n",
       "      <td>-0.745272</td>\n",
       "      <td>1.440563</td>\n",
       "      <td>2.256679</td>\n",
       "      <td>1.390125</td>\n",
       "      <td>0.365905</td>\n",
       "      <td>1.452357</td>\n",
       "      <td>1.035867</td>\n",
       "      <td>0.959336</td>\n",
       "      <td>0.660579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999985</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.620572</td>\n",
       "      <td>-1.481400</td>\n",
       "      <td>0.798580</td>\n",
       "      <td>0.582676</td>\n",
       "      <td>-0.993491</td>\n",
       "      <td>1.097208</td>\n",
       "      <td>0.998735</td>\n",
       "      <td>-0.805931</td>\n",
       "      <td>1.499224</td>\n",
       "      <td>-0.686666</td>\n",
       "      <td>0.523753</td>\n",
       "      <td>1.096319</td>\n",
       "      <td>1.857497</td>\n",
       "      <td>2.295498</td>\n",
       "      <td>0.568390</td>\n",
       "      <td>1.713308</td>\n",
       "      <td>1.503671</td>\n",
       "      <td>0.622427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999986</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.951119</td>\n",
       "      <td>-1.025120</td>\n",
       "      <td>0.735755</td>\n",
       "      <td>1.072442</td>\n",
       "      <td>-1.268414</td>\n",
       "      <td>-1.365378</td>\n",
       "      <td>0.496042</td>\n",
       "      <td>-1.378751</td>\n",
       "      <td>0.027446</td>\n",
       "      <td>0.241199</td>\n",
       "      <td>0.841212</td>\n",
       "      <td>0.726010</td>\n",
       "      <td>0.765865</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.816827</td>\n",
       "      <td>0.300119</td>\n",
       "      <td>0.758559</td>\n",
       "      <td>0.259673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999987</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.499972</td>\n",
       "      <td>-0.472138</td>\n",
       "      <td>0.035389</td>\n",
       "      <td>0.617406</td>\n",
       "      <td>0.037837</td>\n",
       "      <td>1.096518</td>\n",
       "      <td>0.547123</td>\n",
       "      <td>-1.299799</td>\n",
       "      <td>0.821299</td>\n",
       "      <td>-0.233039</td>\n",
       "      <td>0.473948</td>\n",
       "      <td>0.690110</td>\n",
       "      <td>1.292122</td>\n",
       "      <td>1.258712</td>\n",
       "      <td>0.491017</td>\n",
       "      <td>0.941776</td>\n",
       "      <td>1.498757</td>\n",
       "      <td>0.193106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999988</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.039801</td>\n",
       "      <td>0.851302</td>\n",
       "      <td>0.125229</td>\n",
       "      <td>0.934144</td>\n",
       "      <td>0.551678</td>\n",
       "      <td>-0.811299</td>\n",
       "      <td>1.602762</td>\n",
       "      <td>-0.852513</td>\n",
       "      <td>0.209035</td>\n",
       "      <td>0.412390</td>\n",
       "      <td>1.370954</td>\n",
       "      <td>1.584090</td>\n",
       "      <td>1.025354</td>\n",
       "      <td>0.202440</td>\n",
       "      <td>1.102830</td>\n",
       "      <td>0.605197</td>\n",
       "      <td>0.739403</td>\n",
       "      <td>0.612186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999989</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.413233</td>\n",
       "      <td>-0.329456</td>\n",
       "      <td>-1.490198</td>\n",
       "      <td>0.479811</td>\n",
       "      <td>-1.487803</td>\n",
       "      <td>-0.729794</td>\n",
       "      <td>0.850578</td>\n",
       "      <td>0.334140</td>\n",
       "      <td>1.276822</td>\n",
       "      <td>-0.474693</td>\n",
       "      <td>0.457745</td>\n",
       "      <td>0.804949</td>\n",
       "      <td>1.560490</td>\n",
       "      <td>1.552907</td>\n",
       "      <td>0.521348</td>\n",
       "      <td>1.203032</td>\n",
       "      <td>1.293182</td>\n",
       "      <td>0.292971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999990</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.482755</td>\n",
       "      <td>1.204410</td>\n",
       "      <td>0.299445</td>\n",
       "      <td>0.780271</td>\n",
       "      <td>1.958697</td>\n",
       "      <td>0.938929</td>\n",
       "      <td>0.887801</td>\n",
       "      <td>-1.404129</td>\n",
       "      <td>1.332697</td>\n",
       "      <td>-0.456543</td>\n",
       "      <td>0.551233</td>\n",
       "      <td>0.957969</td>\n",
       "      <td>1.542171</td>\n",
       "      <td>1.982478</td>\n",
       "      <td>0.579808</td>\n",
       "      <td>1.481396</td>\n",
       "      <td>1.006600</td>\n",
       "      <td>0.189843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999991</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.031701</td>\n",
       "      <td>0.648011</td>\n",
       "      <td>-1.616710</td>\n",
       "      <td>0.532912</td>\n",
       "      <td>1.663047</td>\n",
       "      <td>-1.243807</td>\n",
       "      <td>0.706740</td>\n",
       "      <td>0.189915</td>\n",
       "      <td>0.433557</td>\n",
       "      <td>-0.393302</td>\n",
       "      <td>0.809631</td>\n",
       "      <td>1.087218</td>\n",
       "      <td>1.191645</td>\n",
       "      <td>1.972363</td>\n",
       "      <td>0.698013</td>\n",
       "      <td>1.564201</td>\n",
       "      <td>0.035361</td>\n",
       "      <td>0.504437</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999992</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.085361</td>\n",
       "      <td>0.861342</td>\n",
       "      <td>-1.356951</td>\n",
       "      <td>0.483685</td>\n",
       "      <td>0.059381</td>\n",
       "      <td>0.292341</td>\n",
       "      <td>0.340940</td>\n",
       "      <td>0.761038</td>\n",
       "      <td>0.380255</td>\n",
       "      <td>0.038984</td>\n",
       "      <td>0.774140</td>\n",
       "      <td>0.660777</td>\n",
       "      <td>0.757443</td>\n",
       "      <td>0.331105</td>\n",
       "      <td>0.715807</td>\n",
       "      <td>0.447304</td>\n",
       "      <td>0.320159</td>\n",
       "      <td>0.371521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999993</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.339252</td>\n",
       "      <td>-1.753881</td>\n",
       "      <td>0.667430</td>\n",
       "      <td>1.279321</td>\n",
       "      <td>-0.125801</td>\n",
       "      <td>-1.025262</td>\n",
       "      <td>0.996305</td>\n",
       "      <td>-1.425422</td>\n",
       "      <td>1.005658</td>\n",
       "      <td>-0.529824</td>\n",
       "      <td>1.616218</td>\n",
       "      <td>1.278956</td>\n",
       "      <td>0.702218</td>\n",
       "      <td>0.541788</td>\n",
       "      <td>1.649413</td>\n",
       "      <td>1.139551</td>\n",
       "      <td>1.256152</td>\n",
       "      <td>0.159157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999994</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.726624</td>\n",
       "      <td>0.098401</td>\n",
       "      <td>-0.917547</td>\n",
       "      <td>0.477953</td>\n",
       "      <td>-0.297608</td>\n",
       "      <td>1.398104</td>\n",
       "      <td>0.372883</td>\n",
       "      <td>0.774908</td>\n",
       "      <td>0.508651</td>\n",
       "      <td>-0.040399</td>\n",
       "      <td>0.541026</td>\n",
       "      <td>0.617639</td>\n",
       "      <td>1.013056</td>\n",
       "      <td>0.745807</td>\n",
       "      <td>0.507010</td>\n",
       "      <td>0.598500</td>\n",
       "      <td>0.311856</td>\n",
       "      <td>0.428370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999995</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.853325</td>\n",
       "      <td>-0.961783</td>\n",
       "      <td>-1.487277</td>\n",
       "      <td>0.678190</td>\n",
       "      <td>0.493580</td>\n",
       "      <td>1.647969</td>\n",
       "      <td>1.843867</td>\n",
       "      <td>0.276954</td>\n",
       "      <td>1.025105</td>\n",
       "      <td>-1.486535</td>\n",
       "      <td>0.892879</td>\n",
       "      <td>1.684429</td>\n",
       "      <td>1.674084</td>\n",
       "      <td>3.366298</td>\n",
       "      <td>1.046707</td>\n",
       "      <td>2.646649</td>\n",
       "      <td>1.389226</td>\n",
       "      <td>0.364599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999996</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.951581</td>\n",
       "      <td>0.139370</td>\n",
       "      <td>1.436884</td>\n",
       "      <td>0.880440</td>\n",
       "      <td>-0.351948</td>\n",
       "      <td>-0.740852</td>\n",
       "      <td>0.290863</td>\n",
       "      <td>-0.732360</td>\n",
       "      <td>0.001360</td>\n",
       "      <td>0.257738</td>\n",
       "      <td>0.802871</td>\n",
       "      <td>0.545319</td>\n",
       "      <td>0.602730</td>\n",
       "      <td>0.002998</td>\n",
       "      <td>0.748959</td>\n",
       "      <td>0.401166</td>\n",
       "      <td>0.443471</td>\n",
       "      <td>0.239953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999997</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.840389</td>\n",
       "      <td>1.419162</td>\n",
       "      <td>-1.218766</td>\n",
       "      <td>1.195631</td>\n",
       "      <td>1.695645</td>\n",
       "      <td>0.663756</td>\n",
       "      <td>0.490888</td>\n",
       "      <td>-0.509186</td>\n",
       "      <td>0.704289</td>\n",
       "      <td>0.045744</td>\n",
       "      <td>0.825015</td>\n",
       "      <td>0.723530</td>\n",
       "      <td>0.778236</td>\n",
       "      <td>0.752942</td>\n",
       "      <td>0.838953</td>\n",
       "      <td>0.614048</td>\n",
       "      <td>1.210595</td>\n",
       "      <td>0.026692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999998</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.784218</td>\n",
       "      <td>-0.833565</td>\n",
       "      <td>-0.560091</td>\n",
       "      <td>0.953342</td>\n",
       "      <td>-0.688969</td>\n",
       "      <td>-1.428233</td>\n",
       "      <td>2.660703</td>\n",
       "      <td>-0.861344</td>\n",
       "      <td>2.116892</td>\n",
       "      <td>2.906151</td>\n",
       "      <td>1.232334</td>\n",
       "      <td>0.952444</td>\n",
       "      <td>0.685846</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.781874</td>\n",
       "      <td>0.676003</td>\n",
       "      <td>1.197807</td>\n",
       "      <td>0.093689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999999</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.761500</td>\n",
       "      <td>0.680454</td>\n",
       "      <td>-1.186213</td>\n",
       "      <td>1.043521</td>\n",
       "      <td>-0.316755</td>\n",
       "      <td>0.246879</td>\n",
       "      <td>1.120280</td>\n",
       "      <td>0.998479</td>\n",
       "      <td>1.640881</td>\n",
       "      <td>-0.797688</td>\n",
       "      <td>0.854212</td>\n",
       "      <td>1.121858</td>\n",
       "      <td>1.165438</td>\n",
       "      <td>1.498351</td>\n",
       "      <td>0.931580</td>\n",
       "      <td>1.293524</td>\n",
       "      <td>1.539167</td>\n",
       "      <td>0.187496</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5000000 rows × 19 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         signal    l_1_pT   l_1_eta   l_1_phi    l_2_pT   l_2_eta   l_2_phi  \\\n",
       "0           0.0  0.972861  0.653855  1.176225  1.157156 -1.739873 -0.874309   \n",
       "1           1.0  1.667973  0.064191 -1.225171  0.506102 -0.338939  1.672543   \n",
       "2           1.0  0.444840 -0.134298 -0.709972  0.451719 -1.613871 -0.768661   \n",
       "3           1.0  0.381256 -0.976145  0.693152  0.448959  0.891753 -0.677328   \n",
       "4           1.0  1.309996 -0.690089 -0.676259  1.589283 -0.693326  0.622907   \n",
       "5           0.0  0.456398  1.099371  1.512453  0.751772  0.638967 -0.742216   \n",
       "6           0.0  0.437818 -1.119883 -1.336823  0.502320 -1.717515  1.017067   \n",
       "7           0.0  0.571656  0.205696  0.425950  0.578514  0.927399 -1.101478   \n",
       "8           1.0  2.112812  0.742983 -0.330539  0.805253 -0.028887 -1.446679   \n",
       "9           0.0  1.001869 -0.471788  0.555614  1.233368  1.255548 -1.052491   \n",
       "10          0.0  0.840115  0.958249 -0.585658  1.317930 -1.063730  1.246235   \n",
       "11          0.0  1.263320  0.733208  0.331149  1.511739  0.371084 -1.585176   \n",
       "12          0.0  0.698336  1.689431 -1.134670  0.966594  1.503367  0.880949   \n",
       "13          0.0  0.578286 -0.689652 -0.390094  0.480061 -0.632219  1.212005   \n",
       "14          1.0  0.798202  0.099358 -1.095839  0.531147 -0.962327  1.500362   \n",
       "15          1.0  0.452214 -0.004851 -1.374135  0.455546  0.271702  1.643006   \n",
       "16          0.0  0.865126 -1.109674  1.378841  1.225827 -1.599314 -0.335546   \n",
       "17          0.0  0.679042 -0.116113 -1.449247  0.725930  0.832636 -1.068640   \n",
       "18          0.0  0.696711  1.532483  0.451737  0.953612  1.085324 -1.261485   \n",
       "19          1.0  1.006098 -0.218872  1.273336  1.621487  0.076018  0.586132   \n",
       "20          1.0  0.837867  1.134530 -0.911252  0.616626  1.000158  1.292737   \n",
       "21          0.0  1.641748 -1.829807  0.150152  2.702642 -0.129722 -1.380814   \n",
       "22          0.0  1.466649  0.115517 -1.036161  0.877247  0.690861  1.130069   \n",
       "23          1.0  1.641595 -1.044596  0.543058  0.744842 -0.308126 -0.956825   \n",
       "24          1.0  1.361442 -0.506247 -0.646164  1.047869  1.136730  0.698665   \n",
       "25          0.0  1.297482 -0.254912  1.116834  0.979169 -0.135346 -0.697154   \n",
       "26          0.0  0.378505 -1.082134  1.008099  0.611425 -1.285566 -0.065581   \n",
       "27          0.0  0.675933  0.126536  0.956136  0.686048 -0.199500 -1.708110   \n",
       "28          0.0  0.463987  0.011333  0.369054  0.553187  0.389280  0.301573   \n",
       "29          0.0  1.164915 -1.216874  1.387384  1.289362  0.853503 -0.864189   \n",
       "...         ...       ...       ...       ...       ...       ...       ...   \n",
       "4999970     0.0  0.772051  0.081051  0.665382  0.995895  0.564401 -1.218781   \n",
       "4999971     0.0  0.306894  0.609032  0.864028  0.438315  1.402401 -1.173018   \n",
       "4999972     0.0  0.555719 -1.809759 -0.517869  0.468845 -1.798199  0.126298   \n",
       "4999973     0.0  0.411936  1.639347  0.155845  0.654584 -0.201792  0.927203   \n",
       "4999974     0.0  0.579771  0.669194  0.916361  0.481992  0.383977 -0.449522   \n",
       "4999975     1.0  0.630982  0.345205 -1.239799  0.897030 -0.087721 -0.006848   \n",
       "4999976     0.0  0.632756 -0.972319 -0.034061  0.770231 -0.980846 -0.999496   \n",
       "4999977     0.0  0.821894  0.721731  0.232942  0.984021  1.408234 -1.499447   \n",
       "4999978     1.0  1.689959  0.000985 -0.889892  1.559262 -0.177674  0.773766   \n",
       "4999979     0.0  0.588275 -1.153023  0.681203  0.895145  0.302639 -1.565196   \n",
       "4999980     0.0  0.759629 -1.099936  1.018840  1.023628 -1.524405 -0.539747   \n",
       "4999981     0.0  0.980560  0.244252  1.370602  1.504819  0.681870 -0.753009   \n",
       "4999982     0.0  0.991963  0.114058 -1.284302  1.091986  0.883251  0.534301   \n",
       "4999983     0.0  1.399545  0.889210  0.889816  0.566762  0.529097 -0.452789   \n",
       "4999984     1.0  2.108980  0.561875 -1.306236  0.913503  1.112271  0.970117   \n",
       "4999985     0.0  0.620572 -1.481400  0.798580  0.582676 -0.993491  1.097208   \n",
       "4999986     1.0  0.951119 -1.025120  0.735755  1.072442 -1.268414 -1.365378   \n",
       "4999987     0.0  0.499972 -0.472138  0.035389  0.617406  0.037837  1.096518   \n",
       "4999988     1.0  2.039801  0.851302  0.125229  0.934144  0.551678 -0.811299   \n",
       "4999989     0.0  0.413233 -0.329456 -1.490198  0.479811 -1.487803 -0.729794   \n",
       "4999990     0.0  0.482755  1.204410  0.299445  0.780271  1.958697  0.938929   \n",
       "4999991     1.0  1.031701  0.648011 -1.616710  0.532912  1.663047 -1.243807   \n",
       "4999992     0.0  1.085361  0.861342 -1.356951  0.483685  0.059381  0.292341   \n",
       "4999993     0.0  1.339252 -1.753881  0.667430  1.279321 -0.125801 -1.025262   \n",
       "4999994     0.0  0.726624  0.098401 -0.917547  0.477953 -0.297608  1.398104   \n",
       "4999995     1.0  0.853325 -0.961783 -1.487277  0.678190  0.493580  1.647969   \n",
       "4999996     0.0  0.951581  0.139370  1.436884  0.880440 -0.351948 -0.740852   \n",
       "4999997     0.0  0.840389  1.419162 -1.218766  1.195631  1.695645  0.663756   \n",
       "4999998     1.0  1.784218 -0.833565 -0.560091  0.953342 -0.688969 -1.428233   \n",
       "4999999     0.0  0.761500  0.680454 -1.186213  1.043521 -0.316755  0.246879   \n",
       "\n",
       "              MET   MET_phi   MET_rel  axial_MET       M_R    M_TR_2  \\\n",
       "0        0.567765 -0.175000  0.810061  -0.252552  1.921887  0.889637   \n",
       "1        3.475464 -1.219136  0.012955   3.775174  1.045977  0.568051   \n",
       "2        1.219918  0.504026  1.831248  -0.431385  0.526283  0.941514   \n",
       "3        2.033060  1.533041  3.046260  -1.005285  0.569386  1.015211   \n",
       "4        1.087562 -0.381742  0.589204   1.365479  1.179295  0.968218   \n",
       "5        0.322601  1.321054  0.169502   0.359941  0.489256  0.416168   \n",
       "6        0.215619 -0.461200  0.323671   0.173626  0.411898  0.370525   \n",
       "7        0.116555  1.549753  0.174421   0.223450  0.523164  0.289889   \n",
       "8        2.299946  1.450429  2.989110  -1.894770  1.445125  2.548166   \n",
       "9        0.437615 -1.333052  0.326858  -0.111678  1.435708  0.755201   \n",
       "10       0.261865 -0.027341  0.330517   0.183190  1.557298  0.531022   \n",
       "11       0.572889 -1.054526  0.698872  -0.259238  1.155319  0.983545   \n",
       "12       0.242573 -0.228654  0.364132   0.109350  0.668554  0.489941   \n",
       "13       0.640473 -1.622401  0.872160  -0.186169  0.451853  0.669288   \n",
       "14       1.273941  0.675408  1.803743  -0.845941  0.685836  1.234757   \n",
       "15       0.835887 -0.254897  1.254769  -0.252735  0.383118  0.788506   \n",
       "16       0.452621  1.396529  0.014348   0.761019  0.873992  0.646078   \n",
       "17       0.734276  0.616541  1.102238  -0.383189  0.674581  0.989127   \n",
       "18       0.021957  0.769306  0.017608   0.332876  0.681880  0.127229   \n",
       "19       0.561284  0.170752  0.582976   0.411129  1.046204  0.777395   \n",
       "20       1.272458 -0.676616  0.764920   1.165517  0.631193  0.786714   \n",
       "21       0.194475 -1.478649  0.055107   0.303612  2.638832  0.636117   \n",
       "22       0.890722  0.426515  1.283212  -0.563880  1.090046  1.327570   \n",
       "23       1.249039 -1.477087  0.731511  -0.847167  1.160934  1.601837   \n",
       "24       1.657924 -0.061501  2.154410   1.672853  1.525310  1.117499   \n",
       "25       1.027495 -0.166322  1.254201  -0.479649  0.985066  1.259747   \n",
       "26       0.916273 -0.886186  1.371866  -0.421905  0.391697  0.790429   \n",
       "27       0.924259 -0.693053  1.387424  -0.549809  0.577165  1.042057   \n",
       "28       1.657913  1.520308  2.488732  -0.559999  0.425258  1.126461   \n",
       "29       0.552337  0.371583  0.829126  -0.149219  1.863999  0.975417   \n",
       "...           ...       ...       ...        ...       ...       ...   \n",
       "4999970  0.545470 -0.938474  0.389197  -0.179175  0.743884  0.742403   \n",
       "4999971  0.267329 -1.031219  0.097099   0.248908  0.332664  0.320653   \n",
       "4999972  0.611404  1.140576  0.917792  -0.217717  0.436476  0.750250   \n",
       "4999973  0.428966  1.456556  0.522951   0.273558  0.697551  0.483795   \n",
       "4999974  0.547135  1.628749  0.786687   0.222415  0.458597  0.568793   \n",
       "4999975  0.525165  1.174039  0.788337  -0.191744  0.629268  0.743672   \n",
       "4999976  1.130503  1.031468  1.697023  -0.658722  0.570481  1.103604   \n",
       "4999977  0.451208  0.585650  0.397412   0.681289  0.801412  0.589269   \n",
       "4999978  2.579031  0.598344  1.251830  -1.805566  1.376108  2.305554   \n",
       "4999979  0.407740 -0.442062  0.612068  -0.091711  0.820799  0.647016   \n",
       "4999980  0.440853  0.375886  0.610924   0.729659  0.741773  0.559601   \n",
       "4999981  0.881322  0.730479  1.218523  -0.249648  1.016021  1.130732   \n",
       "4999982  0.704755  0.564092  0.044870  -0.316144  0.949935  0.936588   \n",
       "4999983  0.895946 -0.489040  0.104523  -0.296892  0.920684  1.197951   \n",
       "4999984  2.291246  0.902578  0.458420  -0.745272  1.440563  2.256679   \n",
       "4999985  0.998735 -0.805931  1.499224  -0.686666  0.523753  1.096319   \n",
       "4999986  0.496042 -1.378751  0.027446   0.241199  0.841212  0.726010   \n",
       "4999987  0.547123 -1.299799  0.821299  -0.233039  0.473948  0.690110   \n",
       "4999988  1.602762 -0.852513  0.209035   0.412390  1.370954  1.584090   \n",
       "4999989  0.850578  0.334140  1.276822  -0.474693  0.457745  0.804949   \n",
       "4999990  0.887801 -1.404129  1.332697  -0.456543  0.551233  0.957969   \n",
       "4999991  0.706740  0.189915  0.433557  -0.393302  0.809631  1.087218   \n",
       "4999992  0.340940  0.761038  0.380255   0.038984  0.774140  0.660777   \n",
       "4999993  0.996305 -1.425422  1.005658  -0.529824  1.616218  1.278956   \n",
       "4999994  0.372883  0.774908  0.508651  -0.040399  0.541026  0.617639   \n",
       "4999995  1.843867  0.276954  1.025105  -1.486535  0.892879  1.684429   \n",
       "4999996  0.290863 -0.732360  0.001360   0.257738  0.802871  0.545319   \n",
       "4999997  0.490888 -0.509186  0.704289   0.045744  0.825015  0.723530   \n",
       "4999998  2.660703 -0.861344  2.116892   2.906151  1.232334  0.952444   \n",
       "4999999  1.120280  0.998479  1.640881  -0.797688  0.854212  1.121858   \n",
       "\n",
       "                R       MT2       S_R  M_Delta_R  dPhi_r_b  cos_theta_r1  \n",
       "0        0.410772  1.145621  1.932632   0.994464  1.367815      0.040714  \n",
       "1        0.481928  0.000000  0.448410   0.205356  1.321893      0.377584  \n",
       "2        1.587535  2.024308  0.603498   1.562374  1.135454      0.180910  \n",
       "3        1.582217  1.551914  0.761215   1.715464  1.492257      0.090719  \n",
       "4        0.728563  0.000000  1.083158   0.043429  1.154854      0.094859  \n",
       "5        0.754829  0.303750  0.461067   0.345541  0.733242      0.186044  \n",
       "6        0.798260  0.671369  0.385910   0.515522  0.479110      0.029058  \n",
       "7        0.491710  0.334593  0.514246   0.268207  0.315795      0.125728  \n",
       "8        1.564721  2.393632  1.554566   2.148468  1.179117      0.688057  \n",
       "9        0.466779  0.454541  1.446331   0.592259  1.325197      0.083014  \n",
       "10       0.302592  0.426702  1.564376   0.338552  1.137456      0.011040  \n",
       "11       0.755454  0.926953  1.168115   0.709708  1.578325      0.184405  \n",
       "12       0.650313  0.683634  0.664825   0.510385  0.584092      0.031694  \n",
       "13       1.314412  0.559444  0.491753   0.559017  1.286520      0.400292  \n",
       "14       1.597630  1.864630  0.775854   1.556949  1.245781      0.538010  \n",
       "15       1.826371  1.687989  0.412063   1.258978  1.000029      0.237916  \n",
       "16       0.655985  0.027587  0.879327   0.099123  1.526896      0.103202  \n",
       "17       1.301167  2.113569  0.622589   1.583448  0.462588      0.192226  \n",
       "18       0.165574  0.041008  0.681533   0.039989  0.126778      0.040972  \n",
       "19       0.659388  1.177816  0.740323   1.207057  0.418392      0.219343  \n",
       "20       1.106040  0.815495  0.588254   0.607716  1.156936      0.310599  \n",
       "21       0.213914  0.230072  2.635528   0.546993  0.354201      0.016105  \n",
       "22       1.080762  1.588076  1.069615   1.258800  0.443045      0.415406  \n",
       "23       1.224409  1.256747  1.179161   1.215011  0.937398      0.513443  \n",
       "24       0.650136  0.000000  1.472982   0.969957  1.209303      0.039710  \n",
       "25       1.134837  0.760780  1.022235   0.810835  1.115006      0.394822  \n",
       "26       1.790726  1.388440  0.473287   1.068429  1.305904      0.347194  \n",
       "27       1.602167  1.921268  0.612655   1.435927  1.072373      0.474427  \n",
       "28       2.350607  2.460358  0.565242   1.836446  1.168629      0.602618  \n",
       "29       0.464368  1.686075  1.846609   1.296029  0.454520      0.027528  \n",
       "...           ...       ...       ...        ...       ...           ...  \n",
       "4999970  0.885624  0.465971  0.766907   0.393374  1.380740      0.246574  \n",
       "4999971  0.855355  0.143922  0.337387   0.191113  1.094609      0.235031  \n",
       "4999972  1.525324  1.361695  0.420984   1.014244  0.752499      0.621426  \n",
       "4999973  0.615466  0.778334  0.657248   0.686104  0.675997      0.088808  \n",
       "4999974  1.100624  0.861468  0.458086   0.675585  0.998140      0.031265  \n",
       "4999975  1.048725  1.280769  0.638197   0.954547  1.012330      0.030134  \n",
       "4999976  1.716675  2.145489  0.653565   1.627295  1.224264      0.017822  \n",
       "4999977  0.652491  0.061916  0.799578   0.264371  1.269593      0.049163  \n",
       "4999978  1.486756  0.000000  1.584048   0.694180  1.416985      0.542614  \n",
       "4999979  0.699510  1.120962  0.819772   0.835719  0.363649      0.017190  \n",
       "4999980  0.669459  0.000000  0.734658   0.222678  1.333323      0.012691  \n",
       "4999981  0.987583  1.625787  1.036363   1.218644  1.046883      0.135561  \n",
       "4999982  0.874928  0.000000  0.979003   0.420024  1.343193      0.272565  \n",
       "4999983  1.154634  0.105272  0.866587   0.362570  0.694904      0.592398  \n",
       "4999984  1.390125  0.365905  1.452357   1.035867  0.959336      0.660579  \n",
       "4999985  1.857497  2.295498  0.568390   1.713308  1.503671      0.622427  \n",
       "4999986  0.765865  0.000000  0.816827   0.300119  0.758559      0.259673  \n",
       "4999987  1.292122  1.258712  0.491017   0.941776  1.498757      0.193106  \n",
       "4999988  1.025354  0.202440  1.102830   0.605197  0.739403      0.612186  \n",
       "4999989  1.560490  1.552907  0.521348   1.203032  1.293182      0.292971  \n",
       "4999990  1.542171  1.982478  0.579808   1.481396  1.006600      0.189843  \n",
       "4999991  1.191645  1.972363  0.698013   1.564201  0.035361      0.504437  \n",
       "4999992  0.757443  0.331105  0.715807   0.447304  0.320159      0.371521  \n",
       "4999993  0.702218  0.541788  1.649413   1.139551  1.256152      0.159157  \n",
       "4999994  1.013056  0.745807  0.507010   0.598500  0.311856      0.428370  \n",
       "4999995  1.674084  3.366298  1.046707   2.646649  1.389226      0.364599  \n",
       "4999996  0.602730  0.002998  0.748959   0.401166  0.443471      0.239953  \n",
       "4999997  0.778236  0.752942  0.838953   0.614048  1.210595      0.026692  \n",
       "4999998  0.685846  0.000000  0.781874   0.676003  1.197807      0.093689  \n",
       "4999999  1.165438  1.498351  0.931580   1.293524  1.539167      0.187496  \n",
       "\n",
       "[5000000 rows x 19 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first column stores the \"truth\" label of whether an event was signal or background. Pandas makes it easy to create dataframes that store only the signal or background events:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_sig=df[df.signal==1]\n",
    "df_bkg=df[df.signal==0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following example plots the signal and background distributions of every variable. Note that we use VarNames[1:] to skip the first variable, which was the true label."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l_1_pT\n"
     ]
    },
    {
     "data": {
      "image/png": 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h8ODBNGvWjDlz5pCfn88VV1xR6uZwUnMKMCIiIrVkwIABzJs3j5tuuokvvviCrl27MnXq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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a98fd9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l_1_eta\n"
     ]
    },
    {
     "data": {
      "image/png": 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EygJVgOBsyjTy93mUKnYOHLDjZJw4AQcPOh2NyoM6deoUyC98pZyQlxqNTUBL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a98fde50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l_1_phi\n"
     ]
    },
    {
     "data": {
      "image/png": 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DD+SLL77YrWWU0ilVCInc7yMDOBPYaGZBS0Sec26zmf0Of0ntTOBn4EhgLDDX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\nihARERGJQkWIiIiIRKEiRERERKL4BY577dPGc8bcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a9734f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l_2_pT\n"
     ]
    },
    {
     "data": {
      "image/png": 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M2rTkY9QKObgwJ5dJKgLmzZs3j6Kiour2DRsgbbYPgF13hTrWTJmZNZvy8nKKi4vJ/HOq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a9665790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l_2_eta\n"
     ]
    },
    {
     "data": {
      "image/png": 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pFQBNNJTKz268ERYu9G4PHhzUy/3zDzRseHZOU6aMrW1YsQKmT7ePQ8qUgaef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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a9564ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l_2_phi\n"
     ]
    },
    {
     "data": {
      "image/png": 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I3zUxf5smlGkCbHTO7TSz9cCefMokto7EGT9+PJ0q8/VtIiKVVE5ODps3byY1\nNXXvuMaNG9OiRQt27NiR52v69u3Lk08+yZNPPsnw4cMBf8XMI488UuK7mSYnJ2Nm7N69e28IWbly\nJW+88UaJ5lfV5HVgvmjRIjp3Tuz+ue+KHUIiAeRsoJdzblURXnI8vnUiCCvzgTvNrHFMv5AzgGwg\nK6ZMYvfkMyLjcc7tMrNMoA/wZqReFhmeUNx1EhGRsrdp0yYOPvhgzjvvPI477jjq1q3Le++9xyef\nfMK4cePyfM3AgQM58cQTufnmm1m2bBlHHXUUb775Jr/88gtQstuqDxgwgHHjxtG3b18uvvhi1q5d\ny6RJkzjiiCP47LPP9mkdpXiKFUIi9/tIA34DbDGzoCUi2zm33cwOw19SOx34CTgOGAfMds59Hik7\nE/gSeMHMbgeaA/cAE51zuyJlHgOuM7O/Ak/jw8V5+NaXwDjguUgYCS7RTQGeLc46iYhUJllZhZep\nqMtPSUlh2LBhzJw5k6lTp5KTk0ObNm149NFHufrqq/eWiw0WSUlJTJ8+nRtuuIHnn3+epKQkzjnn\nHEaOHMkpp5ySq8NqfqEkdnzv3r15+umnuf/++xkxYgSHHnooY8eOZcWKFblCSOJ9S6SUOeeK/ABy\n8KdBEh+XRaYfDPwLWIe/XHYp/l4idRPm0xJ/H5DN+NMnfwWSEsr0AjKBbcAy4Hd51GcosDJSZj5w\nQgF17wS4zMxMV96ef945cG7HjnJftIhUMpmZmS6vbdW33zqXkuK3JWE/UlJ8fcI0depUl5SU5ObN\nmxduRaqI/D53idOBTq4YuaGwR7FaQpxzBV5N45z7Dn9VTGHz+R8woJAys8l9/5HEMpPwHWRFRKq0\nVq18K0RV/xXdvOzYsSPuvh45OTk8/PDDpKamqo9fJaffjhERqSRatSrfnX9FMXz4cLZu3Uq3bt3Y\nsWMHU6ZMYcGCBdx3331x4UQqH4UQERGp0E499VTGjRvHO++8w/bt22nTpg0TJ07k2muvDbtqso8U\nQkREpELTvZyqrn29bbuIiIhIiSiEiIiISCgUQkRERCQUCiEiIiISCnVMFRGpgLLCvjWq7FfC+rwp\nhIiIVCCNGzcmJSWFSy+9NOyqyH4mJSWFxo0bl+syFUJERCqQVq1akZWVxfqKcGtUqVB+/BH69YOH\nH4aTTy79+Tdu3JhW5Xw3PIUQEZEKplWrVuW+M5CK7/vv/d82baCq3K1eIUREysc778Bzz8WPu/tu\n6NAhnPrV8P6iAAAgAElEQVTI/mfnTnjxRdi9Ozru5JPhmGPCq9N+TiGkKnAOnnoKvvkmOq5ZM7j+\neiitn6DeuBHWro0O16gBrVuXzryldHzxBXz7bXS4USPo2jW8+iT60598e/LRR/vhf/8b6tSBZ54J\nt16l5X//g3PPhezs6LiOHeGll6CaNrUVwoQJcOut0e2ic9CyJaxaFW699mP6ZlQW69fD5s3R4dRU\nv5MBWLoUrroKDjoIatWCXbv8l2r37mjCP+AAOOGE6OtfeQU+/TQ6XL8+3HwzVK/uhzdvjv+5zgED\n/E4u1htvwG9+459v2QI//BCdVq0aHHpo/uuzfTusXBk/rm3b0gtNhdmwwW+QcnKi4/r1C3en/csv\nsHVrdLhuXf8+F8WPP/r3d/v2+PHz51esIDJgADz6qH9+yimlO+8tW2DKFL9jCZx6aun94tumTT5I\nxb5HJ58Mgwb55x99BB9/DDfc4EP6smXw6qvwyCP+Z2fBHyjEhpQmTeDgg0unfvuDPXvgk0/ix7Vv\n778rRbFli99OfvedH/7rX2Hs2Pj5v/hi/PfohBOgc8wPum/d6suB/95de63/bATbruOOg4kTITm5\neOsW+M9/ovUD/xk56aSSzasSUAgpD7t2AjXgppsgeY//wK5c6TeWwQf32GPhgQeiH9wff4yGjtWr\n/Q5y06boPBs2hM8/hxYtol+I117zO5yff/ZfzFtuiZY380eeXbr4nd1FF/kPd926fke8cqUPDRde\n6Ot1wgk+3MS6/37o1s0/79fPb2QDZ54Jc+fGlz/wQOjVyz9PSoK//AUOP9wP/+53vr6x/vQnuOYa\n//yf/4TXX4+fftttRd+hOhc9gQp+5zRiBNSu7YeDHUnLlv7vL7/Ayy/Hr1N5+u9//Une2PcYfJ0P\nPNA/b90aLr4479dv3eo3nK+8Aj16+M9Px47w008lr9O2bT6sBapV85+ZwObN8UeQyck+SJbUrl3x\nLTngP5NF3ZjffTeMH597/OjR0ef9+8fvUIrjpZfgwQf9dwhg3Tp44gm49NL4Ot57r2/hmTbNPwKL\nF/vX7toVHVe/vv/MBe9xebvoIpg504cm8Acx06b5zw5EA115HRzMm5f7Pbzuuuh2ZORI//+N9dvf\n5t5WBBYv9q8PtpH/+1/By3/6abj6ar+9Ar9trFs3+r3MzITu3XOH/YsugpQU/3147DH/mQu+K2+9\nFd+KfNhh8KtfRYc//xzWrPHPf/rJbxtjPyPg9x3HHQc/1wbOL3gdKhmFkPLw8SfAyX7HmrzHfyGS\nk32zdHKyT70PPeR3/A0b+p3/zTfHz6N2bb/Trl/fT7/uOr+jadEi9/IaNfJlNm70w6tXw4knRls2\ngqP/xx7zX+CtW/1Gc9s2/8jJidbhzDN92ZSU+O7Yic3LX38NV17pv0AAU6dCVlb0y/vhh36H//e/\n++Fly/yyb7rJD991F4wZ4x+x+vXzf2fM8PPs27fQfzcAs2fn3lAA3Hdf9PkZZ8BRR/nnf/yjDyGx\ntm6N/q9++gnuuSf+XPKJJ0Lij2rFbqxTUqIb98KsWuX/V089Bc2b+/fqttv8cI0a0ffuySejrVsH\nHeTLJMXcc/CAA/zrS2On0auXP7IPmPkNav/+fviss/z7Guupp+CKK/zzbdviN/p5vR+xbrwRJk2K\nH3fbbf5oFfy8Ek/dXHQRHHmkf75pk9/Jz5vnh999138mH3/cD2dn+5aJzz/Pe/nO+dfu3OmHN2zw\nn7vAl1/6z/3ChX74pZd8AGnWzP9vtm/370VSPveAXL3a71xmzICmTf0O7aqr/Dxij+Tbt49+v1q1\n8i0tRXk/d++Gyy7zO95AgwZ+nQ86yH+Wzz47+v8Bf8DStq2vA/jv30svRcPH4MHw2Wf+ebBusY/q\n1X3wLer3cu5cmDw5flzPntCunX9+++3w1VfRoPjpp/6zH4S5b76B44+H55+P1nfZsviwnJoaDYXp\n6X4e50d23EcdFW29zcvWrf57u2WLH37iCd/SEfjiC/8+x55iO+oofxAJ/vsxa1a0/Lx5uZdnBitW\n+IOK4OAjNnSkpvoDxhYt/Ge2Z08YNy4ysQVwvq/Hme3zX49KRCGkPLjIjmzhQqibx07piy/8Di3Y\ngQdef92HDvAbkeAos0GDwpeZmhptyi9sA5ac7L94l1/uH4GuXeG00wpfVuDQQ6NHLMHfQLCzj9Wi\nhT+qAB8w5s+Pn/6rX/kjM4A5c/zpk6Lq3993eIxtOenSJXoKqzDTp8Ovfx1/ugaipxA++sh3shw2\nLP95dOgAixZFN1bffx/duG3b5lu+gh1zcKTUu7c/UoL4z8OWLb4VZPly/7/Yvt0Hv549S36t3pNP\nwoIF0eGlS+Nb5z75BIYM8f8HgAsu8DviIIT897/w+99HPzPnnefHBdLS/Cm7WBddFH1eo4YPfm+9\n5Yezs33o/cMf/PAf/uC/A0F9gjDSvLn/u2EDfPBBdBk7d/qywf97wID4I9Dbbstdn1jPPONDS6IT\nT4w+jz04uPBCvxOPPU16/PHR1rZAEO537PDDxxzjT8EcdZT/zK9e7adv2eLf09mz/f9m1y6/A+7Y\nMdoy8d578X2/mjSBc87xz3/+2e90f/1r3+K4c6cPdR9+6HfCu3bB22/758FOPiXF72SD/1l6uj9Q\nCA4WwIf1887z34Xg4Zz/O2aMfw/yCyGffgr/93/R4Rde8J/dIDgG36NYN94YbQ255hofBGK3eQMG\nRIP44Yf7+cd+r5OSojv+zz/3ge/pp/OuH/j1CFoiggO3WM5Fv7fBe3jeeUU7wAhet3KlDx1z5/qW\nyv79/bZty5ZoMA22kfXq+YMJ8HX//vvodihzDXTDf16qCIWQiqB9e/9Biz1SrFs3//OcwZHWOef4\nD3LwuvyOwIKN+I03wqhR0aP5YHzNmj6xx/b5qFs3uvPJz2uvRXc6eX15E82e7XcEEN9/BHwL0Fln\n5f/anj39oyxt2+Y38uCPHuvV861Fgc6d4Ygj/HPn/JH2tm3xfRCC53Pm+Iv5L7/cb+C/+CK+VSHQ\ntatfTs2aMHx4/v0X6tSJ34FmZfmWtHnz/Kmk2J1trD/9yZ+f3rXLt8QFISO2zkFQc84HwyD4Hnus\nP4UW7ABq1PDzmjrVD69b5+sbhKCUFP//mjLFD69Y4UPH0KF+2Cx6Og/8ziWxGX3wYL/hBf+60aOj\np+1at/bN8UHoGT7c1yeoL/gdZkF++MGHB/A7/CVLoqFhxw6//nPmRMs3bZr/97BaNV+H/AQHAbHv\nafXq/r0Gv9ynnsr/9Z995pvgL7nE12HNmujpr+Tk6CkG8O9N8J4OHw6nn+6P6p9+2ofB2Ba7iy6K\nBpdEc+bE99WqUaPgq5cefjh+eNo036ciEHwWDjkkWu8nn/QtMuA/l19/HT+P2FN6DzyQ+0Do1FOj\nz0eN8iExWPevv/ahK2hZaNvWh+f8NG7svz9BsIX496t+fT/v2M9A3br5b2sDU6b41y5ZEj++Wzcf\n3GK3f5df7kNcfgeLycnRlp0q2MHZXOzGqAozs05AZmZmJp3K+QLrF4bM5bLHu7Nj005q5NUSUlzO\n+S9/7Pnzli19h7i8PshB+dhm6EaN/AY+2CAW1113xTdVV6/uN6jt82kivPfe+CMeM99BMfbcaJhe\nfDF3S9SvfgXvv1+y+a1d63eoQThzzm/wbropugFr2bLgzrsFWb/eHw3Gho969XzLS5s2fnljxkSb\n0gMnn+zLgd9JXnhh0U/dvPoqZGREh6tX98sIzn3PmRNt1QC/nrfcUnb9HbZs8Zf9xurVKxpiEn35\npW/JCHbezvnvQWww6tXLt2aUlhkzfAtF4Igj4ltWCpKT41t/VqyIjmvRwvd9CXZKs2bF99064ID4\n9/Tjj+MPLurV8wGktPp4HHGEb6UJguHQof7/GpxeMfPf/Yp6Uwvn/P8wOAUH/nsVXPnnnP9Mx3ZG\nPuaY/C/pXbrUv7+xB2WHH+47mwbfu33w/SerObhLc2bc8wln3nVC4S8oRYsWLaKzb0Hr7JxbVFrz\nVQgpB6UeQqRsfPdd/NFlkya5m9Yrkk2b4k8F1K5dtFN1IqXlnHOiLWOBJ5/0p+n2Vzt2xG9HqleP\nXnW4j6piCKl6bTsiJVXZLpWsV69Ujq5ESuwf/4i/lD8pyXfU3Z+VtHV5P6UQIiIiJVOjRt5X6IkU\nUSG9a0RERETKhkKIiIiIhEIhREREREKhECIiIiKhUAgRERGRUCiEiIiISCgUQkRERCQUCiEiIiIS\nCoUQERERCYVCiIiIiIRCIURERERCoRAiIiIioVAIERERkVAohIiIiEgoFEJEREQkFAohIiIiEgqF\nEBEREQmFQoiIiIiEolghxMzuMLOFZrbRzNaa2VQzOzKhTE0ze8TM1pvZJjN7zcyaJJRpaWbvmNkW\nM1tjZmPNLCmhTG8zyzSz7Wb2tZkNyqM+w8xshZltM7MFZtalOOsjIiIi4SluS0gP4GHgJOA0oDow\n08xqx5R5EOgPnAv0BFoAU4KJkbAxHagGdAUGAYOBMTFlDgHeBt4HjgMeAiab2ekxZS4EHgBGAscD\ni4EMM2tczHUSERGREFQrTmHn3Fmxw2Y2GPgR6AzMNbNU4ArgIufc7EiZy4EsMzvRObcQ6AscBZzq\nnFsPLDGzu4H7zWyUc243cC2w3Dl3W2RRS82sOzACeC8ybgTwuHPu+chyhuDDzxXA2OKsl4iIiJS/\nfe0T0gBwwM+R4c74YPN+UMA5txRYBXSLjOoKLIkEkEAGUB9oH1NmVsKyMoJ5mFn1yLJil+Mir+mG\niIiIVHglDiFmZvhTL3Odc19GRjcDdjrnNiYUXxuZFpRZm8d0ilAm1cxqAo2B5HzKNENEREQqvGKd\njkkwCTga6F6EsoZvMSlMQWWsiGWKshwREREJWYlCiJlNBM4CejjnfoiZtAaoYWapCa0hTYi2WqwB\nEq9iaRozLfjbNKFME2Cjc26nma0H9uRTJrF1JM6IESOoX79+3Li0tDTS0tIKepmIiMh+IT09nfT0\n9Lhx2dnZZbKsYoeQSAA5G+jlnFuVMDkT2A30AaZGyh8JtALmRcrMB+40s8Yx/ULOALKBrJgy/RLm\nfUZkPM65XWaWGVnOm5HlWGR4QkH1Hz9+PJ06dSry+oqIiOxP8jowX7RoEZ07dy71ZRUrhJjZJCAN\n+A2wxcyClohs59x259xGM3sKGGdmG4BN+FDwkXPu40jZmcCXwAtmdjvQHLgHmOic2xUp8xhwnZn9\nFXgaHy7Ow7e+BMYBz0XCyEL81TIpwLPFWScREREJR3FbQobg+1z8K2H85cDzkecj8KdKXgNqAu8C\nw4KCzrkcMxsAPIpvHdmCDw4jY8qsNLP++KBxPfAdcKVzblZMmVcj9wQZgz8t8ynQ1zm3rpjrJCIi\nIiEo7n1CCr2axjm3AxgeeeRX5n/AgELmMxt/GW5BZSbhO8iKiIhIJaPfjhEREZFQKISIiIhIKBRC\nREREJBQKISIiIhIKhRAREREJhUKIiIiIhEIhREREREKhECIiIiKhUAgRERGRUCiEiIiISCgUQkRE\nRCQUCiEiIiISCoUQERERCYVCiIiIiIRCIURERERCoRAiIiIioVAIERERkVAohIiIiEgoFEJEREQk\nFAohIiIiEgqFEBEREQmFQoiIiIiEQiFEREREQqEQIiIiIqFQCBEREZFQKISIiIhIKBRCREREJBQK\nISIiIhIKhRAREREJhUKIiIiIhEIhREREREKhECIiIiKhUAgRERGRUCiEiIiISCgUQkRERCQUCiEi\nIiISCoUQERERCYVCiIiIiIRCIURERERCoRAiIiIioVAIERERkVAUO4SYWQ8ze9PMvjezHDP7TcL0\nZyLjYx/TE8o0NLOXzCzbzDaY2WQzq5NQ5lgzm2Nm28zsWzO7NY+6nG9mWZEyi82sX3HXR0RERMJR\nkpaQOsCnwDDA5VNmBtAUaBZ5pCVMfxloB/QB+gM9gceDiWZWD8gAVgCdgFuBUWb2+5gy3SLzeRLo\nCEwDppnZ0SVYJxERESln1Yr7Aufcu8C7AGZm+RTb4Zxbl9cEMzsK6At0ds79JzJuOPCOmd3inFsD\nXApUB650zu0GsszseOAmYHJkVjcAM5xz4yLDI83sDOA6YGhx10tERETKV1n1CeltZmvN7Cszm2Rm\njWKmdQM2BAEkYha+VeWkyHBXYE4kgAQygLZmVj9mPrMSlpsRGS8iIiIVXFmEkBnAZcCvgNuAXsD0\nmFaTZsCPsS9wzu0Bfo5MC8qsTZjv2phpBZVphoiIiFR4xT4dUxjn3Ksxg1+Y2RLgG6A38EEBLzXy\n72MSTC9KmYKmM2LECOrXrx83Li0tjbS0xG4rIiIi+5/09HTS09PjxmVnZ5fJsko9hCRyzq0ws/VA\nG3wIWQM0iS1jZslAw8g0In+bJsyqCT5grC2kTGLrSJzx48fTqVOnYq6FiIjI/iGvA/NFixbRuXPn\nUl9Wmd8nxMwOBg4AVkdGzQcaRDqaBvrgWzEWxpTpGQkngTOApc657JgyfRIWd3pkvIiIiFRwJblP\nSB0zO87MOkZGHRYZbhmZNtbMTjKz1mbWB3/p7Nf4TqM4576KPH/SzLqY2SnAw0B65MoY8Jfe7gSe\nNrOjzexC4HrggZiqPAT0M7ObzKytmY0COgMTi7tOIiIiUv5K0hJyAvAfIBN/euQBYBEwGtgDHAu8\nASzF38PjY6Cnc25XzDwuBr7CX93yNjAHuCaY6JzbiL+M9xDgE+BvwCjn3FMxZebj7z9yNf6+JecA\nZzvnvizBOomIiEg5K8l9QmZTcHg5swjz+AV/L5CCyizBX1lTUJkpwJTCliciIiIVj347RkREREKh\nECIiIiKhUAgRERGRUCiEiIiISCgUQkRERCQUCiEiIiISCoUQERERCYVCiIiIiIRCIURERERCoRAi\nIiIioVAIERERkVAohIiIiEgoFEJEREQkFAohIiIiEgqFEBEREQmFQoiIiIiEQiFEREREQqEQIiIi\nIqFQCBEREZFQKISIiIhIKBRCREREJBQKISIiIhIKhRAREREJhUKIiIiIhEIhREREREKhECIiIiKh\nUAgRERGRUCiEiIiISCgUQkRERCQUCiEiIiISCoUQERERCYVCiIiIiIRCIURERERCoRAiIiIioVAI\nERERkVAohIiIiEgoFEJEREQkFAohIiIiEgqFEBEREQmFQoiIiIiEQiFEREREQlHsEGJmPczsTTP7\n3sxyzOw3eZQZY2Y/mNlWM3vPzNokTG9oZi+ZWbaZbTCzyWZWJ6HMsWY2x8y2mdm3ZnZrHss538yy\nImUWm1m/4q6PiIiIhKMkLSF1gE+BYYBLnGhmtwPXAdcAJwJbgAwzqxFT7GWgHdAH6A/0BB6PmUc9\nIANYAXQCbgVGmdnvY8p0i8znSaAjMA2YZmZHl2CdREREpJxVK+4LnHPvAu8CmJnlUeQG4B7n3FuR\nMpcBa4GBwKtm1g7oC3R2zv0nUmY48I6Z3eKcWwNcClQHrnTO7QayzOx44CZgcsxyZjjnxkWGR5rZ\nGfgANLS46yUiIiLlq1T7hJjZoUAz4P1gnHNuI/BvoFtkVFdgQxBAImbhW1VOiikzJxJAAhlAWzOr\nHxnuFnkdCWW6ISIiIhVeaXdMbYYPE2sTxq+NTAvK/Bg70Tm3B/g5oUxe86AIZZohIiIiFV6xT8eU\nkJFH/5FilrEililwOSNGjKB+/fpx49LS0khLSyukeiIiIlVfeno66enpceOys7PLZFmlHULW4INA\nU+JbKZoA/4kp0yT2RWaWDDSMTAvKNE2YdxPiW1nyK5PYOhJn/PjxdOrUqbD1EBER2S/ldWC+aNEi\nOnfuXOrLKtXTMc65Ffhw0CcYZ2ap+L4e8yKj5gMNIh1NA33w4WVhTJmekXASOANY6pzLjinTh3in\nR8aLiIhIBVeS+4TUMbPjzKxjZNRhkeGWkeEHgbvM7Ndm1gF4HvgOeAPAOfcVvgPpk2bWxcxOAR4G\n0iNXxoC/9HYn8LSZHW1mFwLXAw/EVOUhoJ+Z3WRmbc1sFNAZmFjcdRIREZHyV5LTMScAH+BPjTii\nweA54Arn3FgzS8Hf96MB8CHQzzm3M2YeF+PDwiwgB3gNf8kt4K+oMbO+kTKfAOuBUc65p2LKzDez\nNODeyGMZcLZz7ssSrJOIiIiUs5LcJ2Q2hbSgOOdGAaMKmP4L/l4gBc1jCdCrkDJTgCkFlREREZGK\nSb8dIyIiIqFQCBEREZFQKISIiIhIKBRCREREJBQKISIiIhIKhRAREREJhUKIiIiIhEIhREREREKh\nECIiIiKhUAgRERGRUCiEiIiISCgUQkRERCQUCiEiIiISCoUQERERCYVCiIiIiIRCIURERERCoRAi\nIiIioVAIERERkVAohIiIiEgoFEJEREQkFAohIiIiEgqFEBEREQmFQoiIiIiEQiFEREREQqEQIiIi\nIqFQCBEREZFQKISIiIhIKBRCREREJBQKISIiIhIKhRAREREJhUKIiIiIhEIhREREREKhECIiIiKh\nUAgRERGRUCiEiIiISCgUQkRERCQUCiEiIiISCoUQERERCYVCiIiIiIRCIURERERCUeohxMxGmllO\nwuPLmOk1zewRM1tvZpvM7DUza5Iwj5Zm9o6ZbTGzNWY21sySEsr0NrNMM9tuZl+b2aDSXhcREREp\nO2XVEvI50BRoFnl0j5n2INAfOBfoCbQApgQTI2FjOlAN6AoMAgYDY2LKHAK8DbwPHAc8BEw2s9PL\nZnVERESktFUro/nuds6tSxxpZqnAFcBFzrnZkXGXA1lmdqJzbiHQFzgKONU5tx5YYmZ3A/eb2Sjn\n3G7gWmC5c+62yKyXmll3YATwXhmtk4iIiJSismoJOcLMvjezb8zsRTNrGRnfGR983g8KOueWAquA\nbpFRXYElkQASyADqA+1jysxKWGZGzDxERESkgiuLELIAf/qkLzAEOBSYY2Z18KdmdjrnNia8Zm1k\nGpG/a/OYThHKpJpZzX1dARERESl7pX46xjmXETP4uZktBL4FLgC25/MyA1xRZl/ANCtCGREREakg\nyqpPyF7OuWwz+xpogz+FUsPMUhNaQ5oQbdlYA3RJmE3TmGnB36YJZZoAG51zOwuqz4gRI6hfv37c\nuLS0NNLS0oqyOiIiIlVaeno66enpceOys7PLZFllHkLMrC5wOPAckAnsBvoAUyPTjwRaAfMiL5kP\n3GlmjWP6hZwBZANZMWX6JSzqjMj4Ao0fP55OnTqVeH1ERESqsrwOzBctWkTnzp1LfVllcZ+Qv5lZ\nTzNrbWYn48PGbuAfkdaPp4Bxkft8dAaeAT5yzn0cmcVM4EvgBTM71sz6AvcAE51zuyJlHgMON7O/\nmllbMxsKnAeMK+31ERERkbJRFi0hBwMvAwcA64C5QFfn3E+R6SOAPcBrQE3gXWBY8GLnXI6ZDQAe\nxbeObAGeBUbGlFlpZv3xoeN64DvgSudc4hUzIiIiUkGVRcfUAjtXOOd2AMMjj/zK/A8YUMh8ZuMv\n+RUREZFKSL8dIyIiIqFQCBEREZFQKISIiIhIKBRCREREJBQKISIiIhIKhRAREREJhUKIiIiIhEIh\nREREREKhECIiIiKhUAgRERGRUCiEiIiISCgUQkRERCQUCiEiIiISCoUQERERCYVCiIiIiIRCIURE\nRERCoRAiIiIioVAIERERkVAohIiIiEgoFEJEREQkFAohIiIiEgqFEBEREQmFQoiIiIiEQiFERERE\nQqEQIiIiIqFQCBEREZFQKISIiIhIKBRCREREJBQKISIiIhIKhRAREREJhUKIiIiIhEIhREREREKh\nECIiIiKhUAgRERGRUCiEiIiISCgUQkRERCQUCiEiIiISCoUQERERCYVCiIiIiIRCIURERERCoRBS\nRaWnp4ddhXKh9axatJ5Vi9ZTClPpQ4iZDTOzFWa2zcwWmFmXsOtUEewvXwqtZ9Wi9axatJ5SmEod\nQszsQuABYCRwPLAYyDCzxqFWTERERApVqUMIMAJ43Dn3vHPuK2AIsBW4ItxqiYiISGEqbQgxs+pA\nZ+D9YJxzzgGzgG5h1UtERESKplrYFdgHjYFkYG3C+LVA2zzK1wLIysoq42rltnLdUiCF/3y6i+op\n1ctlmdnZ2SxatKhclhUmrWfVovWsWrSepevHr9YBq/nvD1+xaFH5tiHE7DtrleZ8zTceVD5m1hz4\nHujmnPt3zPixQHfn3MkJ5S8GXirfWoqIiFQplzjnXi6tmVXmlpD1wB6gacL4JuRuHQHIAC4BVgLb\ny7RmIiIiVUst4BD8vrTUVNqWEAAzWwD82zl3Q2TYgFXABOfc30KtnIiIiBSoMreEAIwDnjOzTGAh\n/mqZFODZMCslIiIihavUIcQ592rkniBj8KdlPgX6OufWhVszERERKUylPh0jIiIilVelvU+IiIiI\nVG4KISIiIhKKKhtCzKy1mU02s+VmttXMlpnZqMidVgt6XU0ze8TM1pvZJjN7zcyalFe9S8LM7jSz\nj8xsi5n9XMTXPGNmOQmP6WVd131RkvWMvG6Mmf0Q+Ry8Z2ZtyrKepcHMGprZS2aWbWYbIp/lOoW8\n5l8J7+ceM5tUXnUuiuL+4KSZnW9mWZHyi82sX3nVdV8UZz3NbFDM+xW8d1vLs74lYWY9zOxNM/s+\nUuffFOE1vc0s08y2m9nXZjaoPOq6L4q7nmbWK49t656KvB8xszvMbKGZbTSztWY21cyOLMLr9vn7\nWWVDCHAUYMBVwNH4K2eGAPcW8roHgf7AuUBPoAUwpeyqWSqqA68CjxbzdTPwHXqbRR5ppVyv0lbs\n9TSz24HrgGuAE4Et+B85rFEmNSw9LwPtgD74z2NP4PFCXuOAJ4i+p82B28qwjsVS3B+cNLNu+P/D\nk0BHYBowzcyOLp8al0wJf1gzm+j3sBnQuqzrWQrq4C8GGIb/7BXIzA4B3sb/1MZxwEPAZDM7veyq\nWMQknuQAAAZkSURBVCqKtZ4RDjiC6PvZ3Dn3Y9lUr1T0AB4GTgJOw29rZ5pZ7fxeUGrfT+fcfvMA\nbgH+W8D0VGAH8NuYcW2BHODEsOtfhPUbBPxcxLLPAK+HXedyWM8fgBEJ7/E24IKw16OAOh8V+cwd\nHzOuL7AbaFbA6z4AxoVd/wLqtwB4KGbYgO+A2/Ip/w/gzYRx84FJYa9LKa9nkT/PFfUR+bz+ppAy\nfwU+SxiXDkwPu/6lvJ698DfSTA27vvuwno0j69q9gDKl8v2syi0heWkAFNSM3xl/2XLsj+Itxd8A\nrSr+KF7vSNPbV2Y2ycwahV2h0mRmh+KPQmLfz43Av6nY72c3YINz7j8x42bhj65OKuS1l5jZOjNb\nYmZ/KehIpjxZyX5wsltkeqyMAsqHroTrCVDXzFaa2Sozq/CtPSXUlUr2fu4DAz6NnAaeaWYnF/qK\niqUBfntT0P6yVL6flfo+IcUR6QdwHXBTAcWaATsjO6pYayPTqpIZ+NNMK4DDgfuA6WbWLbLRrAqa\n4b9Ief3IYUV+P5sBcU23zrk9kX4wBdX7JeBbfOvPscBY4EjgvDKqZ3EU9wcnwa9rZXvvSrKeS4Er\ngM+A+sCtwDwza++c+76sKhqC/N7PVDOr6ZzbEUKdysJq/OnfT4Ca+C4B/zKzE51zn4ZasyIwM8N3\nS5jrnPuygKKl8v2sdCHEzO4Dbi+giAPaOee+jnnNQfid7ivOuadLsliKfi6wVJRkPYvDOfdqzOAX\nZrYE+AbojW/WLxdlvZ75LZZyfj+h6Ota0CwooN7Ouckxg1+Y2Rpglpkd6pxbUazKlp/ivhehvHel\nIN96O+cW4E/h+IJm84Es4Gp8v5KqzCJ/K+N7mqfItip2e7XAzA7H90us8B1xgUn4fpSnlOC1xf5+\nVroQAvwd35+hIMuDJ2bWAvgnPtVdU8jr1gA1zCw1oTUkvx/FK0vFWs995dz/t3c3ITZGcRzHv4e8\nZCSSmch4nYy8zohkYUZdL6WwUHbY27CyQlbs5SUbGpSFhaKk1KSkCU1TNugqsmBqZppCyBjH4n9m\neu7tztyXnnvPxe9TT83c51zz/Obc89z/88w5rn/nnBsEWqhhEUJ1c/Zjg6KJ3P5rBPoKPqO6Ss3a\njx3jOOfcVGAe5b0On2H5W7A7XjGV+4GTYL+HctrXg0py5vDe/3LO9WH99i+ZqD8/e+9/RjieWnpO\nZW/qNeWcuwjsBbZ77z8VaZ7K+PzrihDv/RAwVErbcAekG3iB3e4spheb/JcB7oZ/YxWwBJtwUzPl\n5EyDc24xMB+7lVgz1cwZCqt+rD9fAjjn5mDzKi5V42cWOZ6SsoYr4bnOufbEvJAMVlA8K+NHtmNX\nJTXt00K89yPOPuMpA9yD8du+GeDCBE/rKbB/FzUei+WoMGcO59wUYB1Q10vmK9AD5C/h3E0d92eK\n2qiDcTiZUIAcADq99x9KeEo64zP2LNwqzu5dCGSBR9gy26axLdFmEXbbc3PiscvYVeMObILZU+BJ\n7DxFsjZjS97OYEv9NoatIdHmNXAgfN2AzRfYii0FzGB/v3wFTIudJ62c4fuT2Bv/PmA9towsC0yP\nnadI1gehT7ZgV1BvgJsTvXaBFcApYFPo0/3AW6A7dpbEMR/CViYdwVYAXQ19syDsvwGcS7TfBvzE\n5nG1AmeBH8Ca2FlSznkaO3kvxwrH29hS8tWxsxTJ2RDGXxu2kuJE+L457D8PdCXaLwO+YqtkWoFj\noX93xs6Scs7jYfytBNZi8ytGgB2xs0yS8TIwjC3VbUpsMxNtuqoxPqOHr+Iv9Sh2WzS5/QZGE22W\nhsc7Eo/NwNZLDwJfgDtAY+w8RbJeL5A1P9cocCR8PRN4iN1O+4H9CeDK2EmyXrdycyYeO4tN1vyG\nzd5uiZ2lhKxzgVtYsTWMrcWfldif89oFFgOPgYGQ8004Oc6OnSUv1zHgPfYm3UPuBUA3cC2v/UGs\nsPyO3c3aEztD2jmxTwN/F9p+BO4DG2JnKCFj59g5NW+7FvZfJ68IDs/pDVmzwOHYOdLOiU0szmKF\n5AC2UqojxrGXkbFQvpxzabXGpz7ATkRERKL43/6fEBEREakTKkJEREQkChUhIiIiEoWKEBEREYlC\nRYiIiIhEoSJEREREolARIiIiIlGoCBEREZEoVISIiIhIFCpCREREJAoVISIiIhLFHz86/LKzYBTn\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a9524190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MET\n"
     ]
    },
    {
     "data": {
      "image/png": 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pbp1q+O47ePZZyMqC99+Hf/0r2RmJiEh96dOnD9999x2///3vue666/jkk0+45ZZbmDJl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\nZu+s+zgAAAAPSURBVFYrLk7MzMysVv4DtcG1Ag96kMsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a93d1490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MET_phi\n"
     ]
    },
    {
     "data": {
      "image/png": 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CO++8w7Zt2+JaQ1asWFHi7b/88svUqVOHjIwMqlePHgYfe+yxEq+zKpk2bRrT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a93be250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MET_rel\n"
     ]
    },
    {
     "data": {
      "image/png": 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9fAwMqyRmIcFy4YpiZhNMzC3v+A5gQriJiIhII6Bn64iIiEikqDgRERGRSFFx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\nDCeSJKkUw4kkSSrFcCJJkkr5BE6gZAcu1E/8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff67804b050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "axial_MET\n"
     ]
    },
    {
     "data": {
      "image/png": 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WI488kvHjx/PFF19ErjixKE6ESRYzywTy8/PzyczMTHY6IpH1wS+fIHPiMPLzg4eCcvXV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\nKBURnARBEARBUCr+BYZaF/MOCaPWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a93e5b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M_R\n"
     ]
    },
    {
     "data": {
      "image/png": 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sH0ExckUyuaT43kVERKQBpHpa52fAXDN72sxWmFlZwmpGB6Ad8Fqszd3XAP8A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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff678071bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M_TR_2\n"
     ]
    },
    {
     "data": {
      "image/png": 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EREQSi0ZQ4uAcvPceDBsGffp4bUlJkJUVbF4iIiKJRgVKNfTtCyNGBJ2FiIhI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\n8/8BU7NwRSa6DF0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff67801ac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R\n"
     ]
    },
    {
     "data": {
      "image/png": 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NTEgN6oZXOHweEtMlUKQE9QC+cc5lh8R0I6/ugfbi5iIiIiI+K806I7XN7GQz\nax9oahnYbxrYHwvcbWYXmFk74EXgR2AagHNuJd5E02fM7FQzOwN4DMgIPEkD3iO7e4HnzOx4M/sL\nMBR4NCSVcUBPM7vVzNqYWTqQAkwIiSk0FxEREfFfaW7TnAJ8iHfLxJFbILwAXOOcG2Vm8XjrhtQF\nFgA9nXN7Q/roi1c0zAVygMl4j+EC3lMvZpYaiFkEbALSnXPPhsQsNLM04IHAtgro7Zz7OiSmOLmI\niIiIj0qzzsg8ihhRcc6lA+mFHN+Kt5ZIYX2sAM4qImYKMOVQchERERF/6d00IiIi4isVIyIiIuIr\nFSMiIiLiKxUjIiIi4isVIyIiIuIrFSMiIiLiKxUjIiIi4isVIyIiIuKrsnprr5SBX36BHTsgJgaO\nPtrvbERERIpHIyMVXEYGdOwITZtCw4bQsiU0bw4XXghTp8I33/idoYiISOE0MlJB7dsHOTnwxBOw\naROkpkJCApx3HgwZAtOne1vduvDbb95oiYiISHmkYqQC2rABkpPh55+9/Ztugscfzz2+YgVkZ8Mr\nr8DNN8Of/ww1aniFyzHH+JOziIhIQVSMlCcTJsAXX+Tuf/IJHHHEQWHr1nmFyAMPeLdnLroo7/Fq\n1bzTBgyAr7+G33+HN9+EyZNh+PDofoSDmHkJnHJKblt8PLzwArRoUcbJiIhIeaRipLz49Vfv/krr\n1lCvntdWty4MHFjgKRdcAO3aFdxlQgI8+aT3/axZEcy1JK6+Gtauhd27c9uefhree88b0hERkSpP\nxUh54Zz39dFHvSqjsqhbF8aOzdv23HP+5CIiIuWSpjVWIT/+CIsWwebNfmciIiKSS8VIBfLSS9Ck\niffEDED16sU/t0ULb0rKqadC9+7RyU9ERKQ0dJumApk2zZv7OXCgt57IcccV/9w5c7ypG8895z1l\nIyIiUl6oGKlgWrWCe+4p+Xl163pbkyaRz0lERORQ6DaNiIiI+ErFSBW0bRv07g1XXumtzioiIuIn\nFSMVwOrVsGCBtxTJoerb13tyeP9+ePVVbx6KiIiInzRnpJz79Vc4+WRvEVOAwYMPrb+mTWHKFO+9\nNrGxh56fiIjIoVIxUs79/ru3Pf88dOqkd8uIiEjlo2KkgmjaFNq08TsLERGRyNOckSru5Ze9Wz8f\nfuh3JiIiUlWpGKmizGDQIG9p+Ndf974XERHxg4qRKsrMWx5+2TK46qrc9/SJiIiUNRUjIiIi4isV\nIyIiIuKX3kDVAAAgAElEQVQrFSPl1IcfwoknQo8e3n6M/kuJiEglpUd7y6k334RffoF+/aBRIzjr\nLL8zEhERiQ4VI+VY06YwerTfWUTJa6/Bl1/m7l9wAfTs6V8+IiLim4gP/ptZjJndZ2arzWynmf3P\nzO7OJ+5eM1sfiJljZq3Cjtczs1fMLNvMtpjZJDOrHRZzkpnNN7NdZrbWzG7P5zqXmVlWIGa5melv\nvDDx8bByJcTFQZMmsGZNlC94882wYwf85z/eNnUqDBwY5YuKiEh5FY2ZCHcANwA3AccBfwf+bmYH\n3qpiZsOBwYG404AdQKaZxYX08yrQFugG9AK6AE+F9FEHyATWAMnA7UC6mV0XEtMp0M8zQHvgbeBt\nMzs+sh+5YvvHP2DiRBg5En7+Gb76KsoXfOQRWLw4d7v+ej1bLCJShUWjGOkETHPOzXLOrXPOvQXM\nxis6gm4G7nPOTXfOfQlcBTQB+gCYWVsgFbjWObfIOfcpMAS4wswaBfroB1QPxGQ5594AxgO3hl3n\nPefcaOfcN865EcASvEJIAuLjvYGJq6/2OxMREamKolGMfAp0M7PWAGZ2MnAGMDOw3wJoBLwfPME5\ntw34D14hA9AR2OKcWxrS71zAAaeHxMx3zu0LickE2phZYmC/U+A8wmI6ISIiIuVCNCawPgQkACvN\nbD9ewXOXc+61wPFGeEXFxrDzNgaOBWN+CT3onNtvZpvDYlbn00fwWHbga2HXEREREZ9Foxj5C9AX\nuAL4Gm+uxjgzW++ce6mQ8wyvSClMUTFWzJhCrzNs2DASExPztKWlpZGWllZEeiIiIpVfRkYGGRkZ\nedqys7NL3V80ipFRwP85594M7H9lZs2BfwAvARvwCoKG5B21SAKCt2U2BPYPMLNYoF7gWDCmYdi1\nk8g76lJQTPhoSR5jxowhOTm5sJBKbfRoeOMNb15p585+ZyMiIuVNfv9AX7JkCSkpKaXqLxpzRuI5\neOQhJ3gt59wavCKhW/CgmSXgzQX5NNC0EKhrZh1C+uiGV8R8HhLTJVCkBPUAvnHOZYfEdCOv7oH2\ncmc/MfS4pyP16sGzz0KNGmV7/QYNvLf37tsHs2bB3Qc9kC0iIhJ50RgZmQ7cZWY/AF/hPXY7DJgU\nEjMWuNvM/gd8D9wH/AhMA3DOrTSzTOAZM7sRiAMeAzKcc8GRkVeBe4DnzOxhoB0wFO8JmqBxwDwz\nuxV4F0gDUoDrI/2hI2E3NZmzrAF9+0KHDt46YGUpNtZ7ky94b/Jdu7Zsry8iIlVTNIqRwXjFxeN4\nt0TWAxMDbQA450aZWTzeuiF1gQVAT+fc3pB++gIT8J6GyQEmE1JoOOe2mVlqIGYRsAlId849GxKz\n0MzSgAcC2yqgt3Pu60h/6Ei64AK44gq/sxARESkbES9GnHM78Nb6uLWIuHQgvZDjW/HWEimsjxVA\noW9tcc5NAaYUFiMiIiL+0btgRURExFcqRkRERMRXKkakQKtWweDB8PDDkJPjdzYiIlJZqRiRfPXr\nBw0bwty5cMcd3vvsREREokHFiOSrRw9YuhTeDCxdp5fqiohItKgYEREREV+pGBERERFfqRgRERER\nX0VjBVYpjqVL4dZbcx9T2bu38HifbdoEP/8MjRqBWYQ7j42Fn36CFi1y2xISYNo0aN48whcTEZHy\nRsWIX158EZYsgQsvxDn4Ymsztl96hbfofTmSkADVq0OvXt5+ejqMGBHhi9xyi1eU7dvn7f/xBzzy\nCHz6qYoREZEqQMWIn446Cl56ieefg2uv9ZpiYqBpU3/TCnX00fDf/3oDF//8J6xYEYWLJCbCyJG5\n+7t2ecWIiIhUCZozUg6sXQtJSd5AycqVcMYZfmeU18knw3nnQYMGfmciIiKVkUZGyom4OOjQwe8s\nREREyp5GRkRERMRXKkZERETEVypGRERExFcqRkRERMRXKkak2KpVg3ff9R497t7dewJXRETkUKkY\nkWIbNw6GD4ezz4a5c2HDBr8zEhGRykDFiBTbMcd4K7D27+93JiIiUpmoGBERERFfqRgRERERX6kY\nEREREV9pOXgfzf79T8y/G+bN8zsTERER/6gY8dGlP46h2hOQkAB9+/qdTcn94x/eC3f/8Q9o3tzv\nbEREpKJSMeKjfS6W+9Nh6FC/MymZU06BCy+ENWtgxQpv/ZHHH/c7KxERqahUjEiJJSbCtGne9ykp\n4Jy/+YiISMWmYkTKrxkzYP363P3zzoPjj/cvHxERiQoVI1L+xMVBaiq89563AezcCa+9BosW+Zub\niIhEnB7tlfInNhZmzYItW3K3gQNhzx6/MxMRkShQMSIiIiK+UjEihyQ2Fl55BVq39h5P3r/f74xE\nRKSiUTEih2TiRLjxRmjbFjIyYPduvzMSEZGKJirFiJk1MbOXzGyTme00s+VmlhwWc6+ZrQ8cn2Nm\nrcKO1zOzV8ws28y2mNkkM6sdFnOSmc03s11mttbMbs8nl8vMLCsQs9zMekbjM1dVKSnw0EMVc9E2\nEREpHyJejJhZXeATYA+QCrQF/gZsCYkZDgwGbgBOA3YAmWYWF9LVq4FzuwG9gC7AUyF91AEygTVA\nMnA7kG5m14XEdAr08wzQHngbeNvM9HyoiIhIORGNR3vvANY5564LaVsbFnMzcJ9zbjqAmV0FbAT6\nAG+YWVu8QibFObc0EDMEeNfMbnPObQD6AdWBa51z+4AsM+sA3ApMCrnOe8650YH9EWbWA68Quimi\nn1pERERKJRq3aS4AFpnZG2a20cyWhI1WtAAaAe8H25xz24D/AJ0CTR2BLcFCJGAu4IDTQ2LmBwqR\noEygjZklBvY7Bc4jLKYTIiIiUi5EoxhpCdwIfAP0AJ4ExptZv8DxRnhFxcaw8zYGjgVjfgk96Jzb\nD2wOi8mvD4oR0wgREREpF6JxmyYG+Nw598/A/nIzOwGvQHm5kPMMr0gpTFExVswYvU1FRESknIhG\nMfIzkBXWlgVcHPh+A15B0JC8oxZJwNKQmKTQDswsFqgXOBaMaRh2nSTyjroUFBM+WpLHsGHDSExM\nzNOWlpZGWlpaYacJcPPNUKsW3HMPNGjgdzYiIhINGRkZZGRk5GnLzs4udX/RKEY+AdqEtbUhMInV\nObfGzDbgPSXzBYCZJeDNBQm+iH4hUNfMOoTMG+mGV8R8HhJzv5nFBm7hgHdb6BvnXHZITDdgfEgu\n3QPtBRozZgzJycmFhZTaV1/BJZfArvX/ZJerRbVK8nags86Cs8+GpUvhiy/giCMgPd3vrEREJBry\n+wf6kiVLSElJKVV/0fircAzwiZn9A3gDr8i4Drg+JGYscLeZ/Q/4HrgP+BGYBuCcW2lmmcAzZnYj\nEAc8BmQEnqQB75Hde4DnzOxhoB0wFO8JmqBxwDwzuxV4F0gDUsJyKVMffQSrVsFdp/6XWmu+5ppr\nhvmVSkQ1bgwffOB937QpON0IExGRYop4MeKcW2RmFwEPAf/EWwfkZufcayExo8wsHm/dkLrAAqCn\nc25vSFd9gQl4T8PkAJMJKTScc9vMLDUQswjYBKQ7554NiVloZmnAA4FtFdDbOfd1pD93SVSrBvd2\nmgXbZ0PNylGMiIiIlFZUbhI452YCM4uISQfSCzm+FW8tkcL6WAGcVUTMFGBKYTEiIiLiH72bRkRE\nRHylYkSiIifHe4Ov5o6IiEhRVIxIxB12GNx/vzc3pkcPv7MREZHyrpI8WCrlyTvvwMcfw5w58Pbb\nEeo0Jga+/Rbats1tq18fpkyBpKSCzxMRkXJPxYhEXOvW3rZ9ewSLkTvugOrVvfs/AL//Dk89Bf/9\nL/TqFaGLiIiIH1SMSMXQsCGMGpW7//PPXjEiIiIVnoqRsuCctxzpwoXwwwXwxw3e7YU6dfzOTERE\nxHeawFoW9u6Fe++FrVuhVjyYQceO8MADfmcmIiLiO42MlKUhQ2Db/4NbgTfe8DsbERGRckEjIxJV\nu3dDair06QPr1/udjYiIlEcqRiRq0tKgXz9ISPAe95061e+MRESkPNJtGomaBg3gxRe972vU8DcX\nEREpv1SMlJGPOYOZb7Zn8R6/MxERESlfVIyUkf68wOb3j+LwRtC/v9/ZiIiIlB8qRsrIfmIZfM43\n3DftJL9TERERKVdUjEiZmTMHduyA7t2hQwe/sxERkfJCT9NImejdG+bPh3vugSuu8DsbEREpT1SM\nSJl44w3YvBluvx32aBKviIiEUDEiIiIivlIxIiIiIr7SBFap2O69F556Knf/hhugVy//8hERkRLT\nyIhUTA0bwp13el+Dli6Fhx7yLycRESkVjYxIxRQTAw88kLdtwAD47jtf0hERkdLTyIiUuV9+gUsv\nheuug+3b/c5GRET8pmJEytRVV8Gf/wxbt8Kzz8KsWX5nJCIiftNtGilTrVvDjBmwbRskJvqdjYiI\nlAcaGRERERFfqRgRERERX6kYEREREV+pGBERERFfaQJrlO3YAft2QI7qPhERkXzpb8go+uILSEqC\nug1r8APNqFd7r98plRsxMd52zTVQv763qruIiFRNKkai6JtvYOdOeGHSH0ylDzenrvQ7pXLjsMNg\n5ky4+2445hiYPt3vjERExC9RL0bM7B9mlmNmo0PaapjZ42a2ycy2m9lkM0sKO6+pmb1rZjvMbIOZ\njTKzmLCYrma22Mx2m9m3ZtY/n+sPMrM1ZrbLzD4zs1Oj92nz1+fCHPowjdgYV9aXLtdSU2H4cGjf\n3u9MRETET1EtRgJ/8V8PLA87NBboBVwCdAGaAFNCzosBZuLNaekI9AcGAPeGxDQHZgDvAycD44BJ\nZtY9JOYvwKPACKBDII9MM6sfsQ8pIiIihyRqxYiZHQa8DFwHbA1pTwCuAYY55+Y555YCVwNnmNlp\ngbBU4DjgSufcCudcJvBPYJCZBSfd3gisds793Tn3jXPucWAyMCwkjWHAU865F51zK4GBwM7A9aUc\n2bsX1q/3lok/JNu2wcKFudu330YkPxERiZ5ojow8Dkx3zn0Q1n4K3ojH+8EG59w3wDqgU6CpI7DC\nObcp5LxMIBE4ISRmbljfmcE+zKw6kBJ2HRc4pxNSbjRo4E32PfJIOPpoWL26lB21auV19Kc/5W7t\n2nmTd0REpNyKSjFiZlcA7YF/5HO4IbDXObctrH0j0CjwfaPAfvhxihGTYGY1gPpAbAExjZByY8QI\neO89mDTJG9hYt66UHd15J3z1Ve42fbo35PLrrxHNV0REIivi64yY2VF4c0K6O+f+KMmpQHFmeBYW\nY8WM0UzScqR6dTj3XPjf/w6xo5gYOP74vPsiIlLuRWPRsxSgAbDYzILFQSzQxcwGA+cCNcwsIWx0\nJIncUYwNQPhTLw1DjgW/NgyLSQK2Oef2mtkmYH8BMeGjJXkMGzaMxLBXyqalpZGWllbYaSIiIlVC\nRkYGGRkZedqys7NL3V80ipG5QLuwtn8DWcBDwE/AH0A3YCqAmR0LNAM+DcQvBO40s/oh80Z6ANmB\nfoIxPcOu0yPQjnPuDzNbHLjOO4HrWGB/fGEfYMyYMSQnJxfv04qIiFQx+f0DfcmSJaSkpJSqv4gX\nI865HcDXoW1mtgP4zTmXFdh/FhhtZluA7XjFwSfOuf8GTpkd6OMlMxsONAbuAyaE3Pp5EhhsZg8D\nz+EVGZcC54VcejTwQqAo+Rzv6Zp4vOJIREREyoGyejdN+ByNYXi3UCYDNYBZwKADwc7lmNn5wES8\n0ZIdeAXEiJCY782sF17BMRT4EbjWOTc3JOaNwJoi9+LdrlkGpDrnNKNRRESknCiTYsQ59+ew/T3A\nkMBW0Dk/AOcX0e88vDkqhcU8ATxR7GQjYft2GDMGvmgD/AUeeqhML1/RjRjhPe57yy1w5pl+ZyMi\nItGmxw2iYfx4GDkSPvrI23/9dTjhBG/dCylQ8+YwdCjUqgXz58ODD/qdkYiIlIWyuk1TtezbB40b\nw5iJcDnw9deQ4HdS5V+1ajBunPf9RRd5S4SIiEjlp5ERERER8ZWKEREREfGVihEpt37+GaZMgf/+\nt+hYERGpuFSMRIFzuZuUTkoKLF0Kl17qzftdu9bvjEREJFpUjETB3zJ7ELP+R/7yF6hRA2Jj/c6o\n4rnrLtiyBTIzvfnAO3aUopO4OO9raiokJuZuEyZENFcRETk0epomChasa0aXuM+46omOnHgi1K7t\nd0YVjxnUrQt16hxCJy1bwttvw3ff5bY99xzMmgWDBx9yjiIiEhkqRqLkuGr/49prO/qdhvTunXd/\nwQL4oyQvkxYRkWjTbRoRERHxlYoRqRCGDoWLL4Zly/zOREREIk3FiJRrHTrA9dd7c1E//DB3hVYR\nEak8NGdEyrWaNeHpp73v9dI8EZHKSSMjIiIi4isVIyIiIuIrFSMiIiLiKxUjUmHUqAGvvAKHHw5/\n/jPs3et3RiIiEgmawCoVxlNPwVtvwVdfwYsvQnY2NGjgd1YiInKoNDIiFUarVvD3v3vrjRySXbvg\nhx9yt61bI5KfiIiUjkZGpGpJSvLeV9OsWW5b/frw5ZfQsKF/eYmIVGEqRqRqGTMm79DKypVwyy3w\n668qRkREfKJiRKqW+HhITc3dr1vXv1xERATQnBGpgGICf2rPPBNOOgkWLvQ3HxEROTQqRiJk/354\n4AEYPBjWbtW/tqOpZ0+4/37o1QvWrYOpU/3OSEREDoVu00TIxx/D3XdD27ZwVMI20vZNA/r5nVal\nVK0a3HWX9/2MGf7mIiIih04jIxHinPf1nXdgycCn6VpD9w5ERESKQ8WIVHgvvwydOsHw4X5nIiIi\npaFiRCq0ceO8OSSxsTBqlN/ZiIhIaagYkQqtZ0949lkYMMDvTEREpLQ0gVUEYOlS72U3QaedBtWr\n+5ePiEgVomJEqraGDeGww+Cqq/K233677vuIiJQRFSNSqUyZAjVqeGuQmBXjhObN4dtv874sr39/\n+OmnaKUoIiJhVIxEwv79sGcfUAN274Y//vA7oyrnhBMgLg4uvdTbnzQJrr22mCc3buxtQbVrRzw/\nEREpmIqRSPjzn2G+AR9BuxOB77zVz6TMdOoEmzbBvn3eYMeWLX5nJCIixRXxp2nM7B9m9rmZbTOz\njWY21cyODYupYWaPm9kmM9tuZpPNLCkspqmZvWtmO8xsg5mNMrOYsJiuZrbYzHab2bdm1j+ffAaZ\n2Roz22Vmn5nZqZH+zPznP9Aj8PK1R0fDK69oaVAf1KkD9erlvrtGREQqhmj82u4MPAacDpwDVAdm\nm1mtkJixQC/gEqAL0ASYEjwYKDpm4o3cdAT6AwOAe0NimgMzgPeBk4FxwCQz6x4S8xfgUWAE0AFY\nDmSaWf3IfdyA447zvl54IfTtCy1bRvwSUnwrVsBbb8H33/udiYiIFCXixYhz7jzn3EvOuSzn3Aq8\nIqIZkAJgZgnANcAw59w859xS4GrgDDM7LdBNKnAccKVzboVzLhP4JzDIzIK3lm4EVjvn/u6c+8Y5\n9zgwGRgWks4w4Cnn3IvOuZXAQGBn4PpSSSUnw4svwiWXwLnn+p2NiIgUpSwGtOsCDtgc2E/BG/F4\nPxjgnPsGWAd0CjR1BFY45zaF9JMJJAInhMTMDbtWZrAPM6seuFbodVzgnE5IpTVrFvz2m/cyvc2b\ni44XERF/RbUYMTPDuyXzsXPu60BzI2Cvc25bWPjGwLFgzMZ8jlOMmAQzqwHUB2ILiGmEVFrVq8Ph\nh0N8vN+ZiIhIcUT7aZongOOBM4sRa3gjKEUpLMaKGVPodYYNG0ZiYmKetrS0NNLS0oqRnpQnu3fD\nq696k1vPP7+Ya4/ExMD06bnzgMB7dvjVV71FTEREqriMjAwyMjLytGWHrmJdQlErRsxsAnAe0Nk5\ntz7k0AYgzswSwkZHksgdxdgAhD/10jDkWPBrw7CYJGCbc26vmW0C9hcQEz5akseYMWNITk4uLOSA\nt96Ch/YuYNtrrYBi/mUnZSIlBXbuhCuv9PbfegsuuqgYJ44d6006Cfr+e5g8GX75BZo2jUaqIiIV\nSn7/QF+yZAkpKSml6i8qxUigEOkNnOWcWxd2eDGwD+gGTA3EH4s3yfXTQMxC4E4zqx8yb6QHkA1k\nhcT0DOu7R6Ad59wfZrY4cJ13AtexwP74CHxMwHtJ2y8uidTWP/HX4fX0EE05kpoKv/8Oe/dCYiJs\nC78xWJB27eCRR3L3Z8/2ihEREYmKiBcjZvYEkAZcCOwws+DIRLZzbrdzbpuZPQuMNrMtwHa84uAT\n59x/A7Gzga+Bl8xsONAYuA+Y4JwLLm/6JDDYzB4GnsMrMi7FG40JGg28EChKPsd7uiYe+HckP3OH\nmGU8dcUPMPjESHYrEVCzJsTG+p2FiIgUJhojIwPx5mR8FNZ+NRAc+x6GdwtlMlADmAUMCgY653LM\n7HxgIt5oyQ68AmJESMz3ZtYLr+AYCvwIXOucmxsS80ZgTZF78W7XLANSnXO/RuizioiIyCGKeDHi\nnCvyCR3n3B5gSGArKOYH4Pwi+plHYP2SQmKewJtIK1VcejpMmAADBsCgQUVFi4hIWdHC2VLpVa8O\nzz8PPXp4T9dMnOh3RiIiEkovypMqYcAAb7vlFpgbvlRecc2fD0mBVyiZQdeuUE3/C4mIHCr9JhUp\nSrNm3gpq/frlbR85Eu65x5+cREQqERUjUuWsXw9DhkCDBnDnncUY3DjuOFi71lu0JOi882BjocvV\niIhIMakYkSrl8sth3jx4/33IyoLTTivmy/Tqh73oOS4uKvmJiFRFKkakSvnTn2DpUm905MgjwRXn\nBQQiIhJVeppGqrRXXvGmfnz7rd+ZiIhUXRoZkSrpiCO85eI/+gimTIFPPvFWfRcRkbKnYkSqpBo1\nYNYs7/srr4Sffy5FJ1Onwldf5e6fcgqMGuW99VdERIpNvzVL6YsvYOZM70WuUvFt2eJNbF25spgn\nPPggdOvmvcW3aVPYvx8efdR7M5+IiJSIRkZK4Ycf4NRTvbfBAvSM/QpI8DUnKb1jj4VXX/XWMIuL\n856yKfLty6mp3hb0xhvw8cfRTFNEpNLSyEhJ5eSw/c1Z7N0L79zyAevHvcnI3Pf3SQX0z396E1jf\nftsrMDdv9jsjEZGqRSMjJfX88/C3R4FzqT/2LhrzmTcBoUMHvzOTUoqJgdatYccOvzMREamaVIyU\n1PbtULMW7AbmzYeOzntPSfXqfmcmhyg21vt60UVQsyY89BBcckkJO5kxw1s6PtjheefldiwiIvlS\nMVIaZt7X6tVBC3FWGiee6L3Rd80aeP11bxpIsYuRY4+FWrW8R3NCPfII3HZbxHMVEalMVIyIBJjB\nwIHe90uWeINg337rrUlyxBFFnNy+PWzYkDurGbxHfTUBRUSkSJrAKpKPJk3gvfegTRs4/njYurUY\nJyUkeO+wCW66PSMiUiwqRkTyMXEizJ8P//qXt5bMtm2l7Mi5gzcREclDxYhIPuLjoXNnaNfO2//x\nR1i3roSdHHaYNws2JiZ3O+usiOcqIlLRac6ISCHq1/fmkpxxhrf/xBNw443FPHnKFG94JWjePHjp\npYjnKCJS0akYESlEcjIsWgS//eZNbv3kE28V+KQkqFu3iJNbtfK2oP37VYyIiORDxUgJOAff/ZrI\n2pymfqciZSg52fvapg288oq3tWjhPWlTraT/BzkHP/2Uu1+tGjRsGLFcRUQqIs0ZKYGHH4bW/3c1\n5+2ZSvXqxXjcUyqVV1/17rTcfbe3Fsm+fSXsoEED7+tRR+VujRvD9OkRz1VEpCJRMVIC33wDJzbe\nxIc1e7JsmbfOlVQddetCly5w0kneftOmcOSRJXg/Xp8+XjUzc2buVrs2fP111HIWEakIdJumhBJr\n7qFr7AI43u9MxC8XXwwTJniP+/7f/8EHH8CZZxbz5C5d8u7HxXkdhA6zdO2aO2NWRKQKUDEiUkKx\nsTBokPf944/DY495y8efey48+mgJO7vkEpg2DZYt8/Z37IBx47zFTUREqgjdphE5BM8/D//v/3mP\nAD/1FOTkeFuxPf00bNyYu6Wnw+7d3uzY4FbiBU5ERCoWjYwUZcIEeOcd7/uv/gab64NW+ZaA7t29\n7ZlnvCVFYmO99+V99BGcdlopOmzSxHspTps2uW1mMHs2nHNOpNIWESlXVIwU5f77vacgjj8e4mrA\nYbXhwbF+ZyXlzDXXeHNRd++G66/3lhPZvBk6dCjhk7tpaXDMMbBnT27b2Wd769MHb+WAV5i0bx+x\n/EVE/GRO78o4wMySgcWLFy8mObi4RKNGMGQI3HUXV18Nq1aV4OkJqZLat4fly73vTz3Ve+FeXBzU\nqVPKDi++GD78MHd/1y44+mjv8S4RkXJiyZIlpKSkAKQ455aU5FyNjBTD6yvasvxOWLzYezGrSGE+\n/dQbFXnmGbj3Xm8+SXw8fPZZ7rtuSuStt/Lu///27jxG6vqM4/j7M+se7tKyHhRsEYWilFqlCo1Y\nRdvg0WALZWsUb0VraSQSlcRgRbDRxqhFI62RtE3VWmmppmlNqoi1TSPKufWiHJVSpKBUjowVjwr7\n9I/nN87sirpHmO925nkl3+z8vju/mWd+md155nvecAPMmQPnnFOs69vXR892O+MJIYR0Ihn5GNvb\nDmDSr1vo39+b4a+4InVEobdrbPRy440wciTk83DRRV769/f3UEtLD57gwgs9M96xw4/37IEFC2DI\nEJ/SU3DEEf6mDSGEXi5m03yMtuwSzZsH69fD1KmJAyqj+fPnpw6hV+judaipgfHj4YIL4JZbfCjI\nwoU+m7epyXOF117rxgMPG+Z9P4sWeXn8cV/JdcYMH6RSKC0t8OKLxbJxY7deR0G8H4riWri4DkVx\nLXqmKpIRSVdK2iDpbUlLJH0pdUz/D+KPy/X0Okhw/fXw8MOwc6cvIzJ9Orz8Mowa5fvc3HyzH2/b\n1o0nqKuD1lbf0a9Qrr3WZ+Acc0yxHH64Z0KzZxfLmjWdfpp4PxTFtXBxHYriWvRMxXfTSDoH+CFw\nBVJGqgkAAAe/SURBVLAMuBpYKOlIM+vOv/4Quq25Ga66ym8PGuQDou+4A2bO9AJ+3K9fsQWlUwYM\n8FJw7LFw9tm+MR/47JypU3309dKlXrd5M9x0kz9RQb9+XldXV6zr29czqhBC2EcqPhnBk495ZvYA\ngKQpwJnAZOC2vZ5x7rmsy32O616dxlv5O8sWaKgul13mP2fP9sGtmzd7l8706V5/8cU+M6epyacL\n19XBWWdBbW0nHjyX++BCJy+80P54yRJ/8jff9OMtW+CRR+Dee9vfr6nJl6hfvhzOPNN3Gm5pab9l\n8YQJ0KdP5154CCF0UNHJiKRaYCTwg0KdmZmkJ4ETPvTEo4/mp+u/wxO7TuTUIeu4dPS7jB1bv+8D\nDlWpocE/6wEmTfIVXJ99FubP93FKixbB4sX++/POg/p6X1ht3DivGzrUGy+OOsqXw2loKG4Q/JFG\nj/bxJqWWL2+/4utzz/l4E/AEJ5/3YAoLAZYaPtx/7tnj9x0zpn0Ly2GHwYEHFo8POMC7jgpyOd99\nsrQVpq7OB9+EECpaRScjwMH4eqlbO9RvBYZ98O40AFy6biLbth/EQYesYtZvAFaxbt0+jbNXyufz\ntLZ2aap4RUpxHfr08dYQ8PEkbW0+pmTFCp9Es2qVLzOydq0vtFa6z16pxkYf77rffl5qa72ho7nZ\nbxfq6uv9Z01NDbncYGpqPCeoqRlM7riJ5HLw97VXc/uEO9HXd3tAhZxhyxZU0uqit3fBpn+hR994\nP7HQ61thd+E+xbWNlN3WXur8NvDJvsXz2tpQnz7QuD9ISPIkRqCcAPnPulrYr9YfoKaGfg1vMrh5\np8eTy3lpbCzelopJ0PuPWXJcqMuO86tW0XrNNcXfld6nvr7YavRh3Vul9Z253dPzOnP/bpyX37CB\n1rlzP/7cnsT6fyK/cSOt8+alDqP7Bg70gfA9sHr16sLNhq6eW9GLnkk6BNgMnGBmS0vqbwNOMrMv\nd7j/ecAvyxtlCCGEUFHON7OHunJCpbeMbAP2AB0X5P4UH2wtAVgInA/8E3hnn0YWQgghVJYG4HD8\ns7RLKrplBEDSEmCpmU3LjgW8AtxtZrcnDS6EEEIIFd8yAjAHuF/SSopTexuB+1IGFUIIIQRX8cmI\nmS2QdDDwfby75jngDDN7PW1kIYQQQoAq6KYJIYQQQu9WFcvBhxBCCKH3imQkhBBCCElFMlIiNtQD\nSWMk/V7SZkltksanjikFSTMkLZP0hqStkn4r6cjUcZWbpCmSnpeUz8ozkr6WOq7UsvdHm6Q5qWMp\nN0mzstdeWv6WOq4UJH1a0i8kbZP0Vva3clzquMot+9zs+J5okzS3s48RyUimZEO9WcCxwPP4hnoH\nJw2s/JrwQb5XUrpUZvUZA8wFjgdOBWqBJyTtnzSq8tsEXIdvqzASeAr4naThSaNKKPuS8m38f0S1\negmfEDAgKyelDaf8JDUDi4F3gTOA4cC1wM6UcSUyiuJ7YQBwGv75saCzDxADWDMfsh7JJnw9kr1v\nqFfhJLUB3zSzvWxEUl2ypPTfwMlm9nTqeFKStB2YbmY/Tx1LuUnqA6wEvgvMBP5qZtekjaq8JM0C\nJphZ1bUAlJJ0K7669ympY+ltJN0FjDOzTrcmR8sI7TbU+2OhzjxL++gN9UI1acYz/R2pA0lFUk7S\nJHydnmdTx5PIj4FHzeyp1IEkdkTWlbte0oOSDk0dUALfAFZIWpB15bZKujx1UKlln6fnAz/rynmR\njLiP2lBvQPnDCb1J1kp2F/C0mVVd37ikL0j6D94cfQ8w0czWJA6r7LJE7IvAjNSxJLYEuATvmpgC\nDAb+IqkpZVAJDMFbyNYCpwP3AndLuiBpVOlNBPoC93flpIpf9KyHRHWPmwjuHuDzwImpA0lkDTAC\nbx36FvCApJOrKSGRNBBPSE8zs/dSx5OSmZXuO/KSpGXARuBsoJq67nLAMjObmR0/L+koPEF5MF1Y\nyU0GHjOz17pyUrSMuK5uqBeqhKQfAeOAr5jZq6njScHMdpvZP8ys1cy+hw/cnJY6rjIbCfQDVkp6\nT9J7wCnANEn/zVrPqpKZ5YF1wNDUsZTZq8DqDnWrgUEJYukVJA3CB/z/pKvnRjICZN90VgJjC3XZ\nP5exwDOp4gppZYnIBOCrZvZK6nh6kRxQnzqIMnsSOBrvphmRlRX4N+ARVsUzAbJBvZ/FP5yryWJg\nWIe6YXgrUbWajH+B/0NXT4xumqLYUA/I+n2H4l1UAEMkjQB2mNmmdJGVl6R7gHOB8cAuSYVWs7yZ\nvZMusvKSdAvwGD6z7BP4wLRT8D7yqmFmu4B244Uk7QK2m1nHb8cVTdLtwKP4h+5ngJuA3cD8lHEl\ncCewWNIMfArr8cDl+LTvqpN9gb8EuM/M2rp6fiQjmdhQ732jgD/hY2UMX3sFfDDS5FRBJTAFf/1/\n7lB/KfBA2aNJpz/+eg8B8sALwOkxmwSo3vFkA4GHgIOA14GngdFmtj1pVGVmZiskTQRuxad5bwCm\nmdmv0kaWzKnAoXRz3FCsMxJCCCGEpGLMSAghhBCSimQkhBBCCElFMhJCCCGEpCIZCSGEEEJSkYyE\nEEIIIalIRkIIIYSQVCQjIYQQQkgqkpEQQgghJBXJSAghhBCSimQkhBBCCElFMhJCCCGEpP4HMUsA\nkdMryjYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a98ae890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MT2\n"
     ]
    },
    {
     "data": {
      "image/png": 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iIiISLbUuTsJC4PvAmoRNdwPDgUuA84AuwNNx+6UAS4FmQH9gAjARmBkX0x1Y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\no73/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff677fddb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S_R\n"
     ]
    },
    {
     "data": {
      "image/png": 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QHLjU3TcBZWZ2LPALYGLcPK+6+9jweLSZDSAoRq5OJpcUf3YRERFpBKle1vkJ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\nmZWKixMzMzMrlf8AJt7gjUp++cYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a93a18d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M_Delta_R\n"
     ]
    },
    {
     "data": {
      "image/png": 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JsGxZdNuf/gSzZvlTj4iISAwooBzL7Nnelapnn13YNnEiNGniX00iIiIJTgGl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\nnlVN7LoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a94b4510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dPhi_r_b\n"
     ]
    },
    {
     "data": {
      "image/png": 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hKcqUhIiIlGDbtsHpp8P69bHlzZsHE49INCUhIiIl2M6dPgF57DFo3z5Sfvzx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\nfD7sAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a9584350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cos_theta_r1\n"
     ]
    },
    {
     "data": {
      "image/png": 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ci4D+zrkvI3LK05ek8+OP8OWX4XZWlt9aX0REpKYx57Y397TmMLNsoKCgoCBh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\nRev/AeHrg/5ufS7HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6a95e5b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for var in VarNames[1:]:\n",
    "    print var\n",
    "    plt.figure()\n",
    "    plt.hist(df_sig[var],bins=100,histtype=\"step\", color=\"red\",label=\"background\",stacked=True)\n",
    "    plt.hist(df_bkg[var],bins=100,histtype=\"step\", color=\"blue\", label=\"signal\",stacked=True)\n",
    "    plt.legend(loc='upper right')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building a classifier with Scikit-Learn\n",
    "\n",
    "[Scikit-learn](http://scikit-learn.org) is a rich python library for data science, including machine learning. For example, we can build a Fisher Discriminant (aka Linear Discriminant Analysis, or LDA). The [LDA Documentation](http://scikit-learn.org/stable/modules/lda_qda.html#dimensionality-reduction-using-linear-discriminant-analysis) does as great job explaining this classifier. Here's how we instanciate the classifier: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sklearn.discriminant_analysis as DA\n",
    "Fisher=DA.LinearDiscriminantAnalysis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets separate the data into inputs (X) vs outputs (Y) and training vs testing samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_Train=4000000\n",
    "\n",
    "Train_Sample=df[:N_Train]\n",
    "Test_Sample=df[N_Train:]\n",
    "\n",
    "X_Train=Train_Sample[VarNames[1:]]\n",
    "y_Train=Train_Sample[\"signal\"]\n",
    "\n",
    "X_Test=Test_Sample[VarNames[1:]]\n",
    "y_Test=Test_Sample[\"signal\"]\n",
    "\n",
    "Test_sig=Test_Sample[Test_Sample.signal==1]\n",
    "Test_bkg=Test_Sample[Test_Sample.signal==0]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can train the classifier as follow:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearDiscriminantAnalysis(n_components=None, priors=None, shrinkage=None,\n",
       "              solver='svd', store_covariance=False, tol=0.0001)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fisher.fit(X_Train,y_Train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the output, comparing signal and background:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5wTk3E5hZSp9RwKg9LF+Pv5fJntaxEDi9lD5Tgal76iMSabfdBg8E9x/8179g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\nzIRZs8KtSUQqP405EZF9Nm8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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fae59eb1910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.hist(Fisher.decision_function(Test_sig[VarNames[1:]]),bins=100,histtype=\"step\", color=\"blue\", label=\"signal\",stacked=True)\n",
    "plt.hist(Fisher.decision_function(Test_bkg[VarNames[1:]]),bins=100,histtype=\"step\", color=\"red\", label=\"background\",stacked=True)\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can make a ROC curve and evaluate the AUC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hVyIiIpK0Kh1A3H1L9GW7aqql5tuYC1Pvgv7/A83UHUZERKQ8lZ2I7FJgvLtv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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fae5178e0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve, auc\n",
    "fpr, tpr, _ = roc_curve(y_Test, Fisher.decision_function(X_Test))\n",
    "\n",
    "roc_auc = auc(fpr, tpr)\n",
    "\n",
    "plt.plot(fpr,tpr,color='darkorange',label='ROC curve (area = %0.2f)' % roc_auc)\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4.1\n",
    "\n",
    "Train the Fisher performance of using the raw, features, and raw+features as input. Compare the performance one a single plot. Add cells to this notebook as needed. Or start new notebooks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_Train_Raw=Train_Sample[RawNames]\n",
    "X_Test_Raw=Test_Sample[RawNames]\n",
    "\n",
    "X_Train_Features=Train_Sample[FeatureNames]\n",
    "X_Test_Features=Test_Sample[FeatureNames]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nIrsRmOCcOxD8vljOuefCkkzKJnujN9FYcmu4/A2Iq+J3IhERkWKVtgVkFN7i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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fae4e7adc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zopYocvdd8QxWJxV+D9P/AP0u1Eq3IiIiVah2AeLuO6IPO9VSlrov7yHYsTFY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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fae4e702b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def TrainFisher(X_Train,X_Test,y_Train):\n",
    "    Fisher=DA.LinearDiscriminantAnalysis()\n",
    "    Fisher.fit(X_Train,y_Train)\n",
    "\n",
    "    fpr, tpr, _ = roc_curve(y_Test, Fisher.decision_function(X_Test))\n",
    "    roc_auc = auc(fpr, tpr)\n",
    "\n",
    "    plt.plot(fpr,tpr,color='darkorange',label='ROC curve (area = %0.2f)' % roc_auc)\n",
    "    plt.legend(loc=\"lower right\")\n",
    "    plt.xlabel('False Positive Rate')\n",
    "    plt.ylabel('True Positive Rate')\n",
    "    plt.show()\n",
    "    \n",
    "    return Fisher\n",
    "\n",
    "RawFisher=TrainFisher(X_Train_Raw,X_Test_Raw,y_Train)\n",
    "FeatureFisher=TrainFisher(X_Train_Features,X_Test_Features,y_Train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4.2\n",
    "\n",
    "Select 3 different classifiers from the techniques listed [here](http://scikit-learn.org/stable/supervised_learning.html#supervised-learning). Note that you can use the multi-layer peceptron to build a deep network, though training may be prohibitively slow, so avoid this technique. Perform the comparison in exercise 1 for each classifier. Compare your conclusions for your selected techniques to the paper.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4.3\n",
    "\n",
    "The following function calculates the significance of the observation of the signal given the number of expected Signal and Background events, using the simple formula $\\sigma_S= \\frac{N_S}{\\sqrt{N_S+N_B}}$. Read through the code carefully."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jsKYohYqIiEjpiiokmFlVoDPwj+w255wDFgNHGoY1BvjeOTezKEWKiIhI6Yv2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\nB6sNL2D4au1dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff669329210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff669608050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max significance at  -5.92031800082  of 3.1622618489\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-5.9203180008157137, 3.1622618488986629, 0)"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def PlotSignificance(N_S,N_B, N_S_min=1):\n",
    "    plt.figure()\n",
    "    eff_sig,bins_sig,p_sig=plt.hist(Fisher.decision_function(Test_sig[VarNames[1:]]),bins=100,histtype=\"step\", color=\"blue\", label=\"signal\",cumulative=-1,stacked=True,normed=True)\n",
    "    eff_bkg,bins_bkg,p_bkg=plt.hist(Fisher.decision_function(Test_bkg[VarNames[1:]]),bins=100,histtype=\"step\", color=\"red\", label=\"background\",cumulative=-1,stacked=True,normed=True)\n",
    "    plt.legend(loc='upper right')\n",
    "    plt.show()\n",
    "    \n",
    "    good_bins = np.where(eff_sig*N_S>=N_S_min)\n",
    "\n",
    "    print len(good_bins[0])\n",
    "    if len(good_bins[0])<1:\n",
    "        print \"Insufficient Signal.\"\n",
    "        return 0,0,0\n",
    "    \n",
    "    significance=(N_S*eff_sig)/np.sqrt((N_B*eff_bkg)+(N_S*eff_sig))\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(bins_sig[:-1],significance)\n",
    "    \n",
    "    max_sign=np.max(significance[good_bins])\n",
    "    max_signI=np.argmax(significance[good_bins])\n",
    "    \n",
    "    plt.show()\n",
    "    print \"Max significance at \", bins_sig[max_signI], \" of\", max_sign\n",
    "    return bins_sig[max_signI],max_sign, max_signI\n",
    "    \n",
    "PlotSignificance(1000000,1e11)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Answer the following questions:\n",
    "   * What are we computing when making a normalized cummulative plot? \n",
    "   * Assume that the experiment produces 1 signal event for every $10^{11}$ background events. For each of your classifiers, how many signal events need to be produced to be able to make a $5\\sigma$ discovery claim?\n",
    "  "
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    "## Honors problems:\n",
    "\n",
    "### Exercise 4.4\n",
    "\n",
    "Read the paper and attempt to reproduce the results, as closely as possible, using scikit-learn. \n",
    "Try using the [multi-layer peceptron](http://scikitlearn.org/stable/modules/neural_networks_supervised.html#multi-layer-perceptron) to build a deep network. Or if you are capable, try it using [Keras Scikit-learn interface](https://keras.io/scikit-learn-api/). \n",
    "                                                "
   ]
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