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     "source": [
      "[![Py4Life](https://raw.githubusercontent.com/Py4Life/TAU2015/gh-pages/img/Py4Life-logo-small.png)](http://py4life.github.io/TAU2015/)\n",
      "## Lecture 10 - 27.5.2015\n",
      "### Last update: 10.5.2015\n",
      "### Tel-Aviv University / 0411-3122 / Spring 2015"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from IPython.display import HTML, YouTubeVideo\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import pandas as pd\n",
      "import urllib.request\n",
      "import os.path\n",
      "import zipfile\n",
      "from scipy.integrate import odeint\n",
      "from scipy.optimize import curve_fit\n",
      "from scipy.integrate import odeint\n",
      "from scipy.stats import linregress\n",
      "import seaborn as sns\n",
      "sns.set_style('ticks')\n",
      "sns.set_context('talk')\n",
      "sns.set_palette(\"Set1\", 8, .75)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Population growth dynamics\n",
      "\n",
      "Our focus todays will be on modeling population growth. \n",
      "We will start with human populations and use data from the [World Bank](http://www.worldbank.org/) on the [population size of countries](http://data.worldbank.org/indicator/SP.POP.TOTL) around the world from 1960 until 2013.\n",
      "\n",
      "## Data preparation"
     ]
    },
    {
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     "collapsed": false,
     "input": [
      "HTML('<blockquote class=\"twitter-tweet\" lang=\"he\"><p>In Data Science, 80% of time spent prepare data, 20% of time spent complain about need for prepare data.</p>&mdash; Big Data Borat (@BigDataBorat) <a href=\"https://twitter.com/BigDataBorat/status/306596352991830016\">\u05e4\u05d1\u05e8\u05d5\u05d0\u05e8 27, 2013</a></blockquote><script async src=\"//platform.twitter.com/widgets.js\" charset=\"utf-8\"></script>')"
     ],
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     "metadata": {},
     "outputs": [
      {
       "html": [
        "<blockquote class=\"twitter-tweet\" lang=\"he\"><p>In Data Science, 80% of time spent prepare data, 20% of time spent complain about need for prepare data.</p>&mdash; Big Data Borat (@BigDataBorat) <a href=\"https://twitter.com/BigDataBorat/status/306596352991830016\">\u05e4\u05d1\u05e8\u05d5\u05d0\u05e8 27, 2013</a></blockquote><script async src=\"//platform.twitter.com/widgets.js\" charset=\"utf-8\"></script>"
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        "<IPython.core.display.HTML object>"
       ]
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     "metadata": {},
     "source": [
      "So let's prepare the data from *scratch*.\n",
      "\n",
      "Start by retrieving the data as a zip file (if not already downloaded). Follow the link to the World Bank page on [Population, total](http://data.worldbank.org/indicator/SP.POP.TOTL), click `DOWNLOAD DATA`, choose `CSV`, a zip file will be downloaded.  \n",
      "\n",
      "Even better, click the `CSV` button with the right button and click `Copy link address` in the context menu. This link can be used to get the file directly from Python using `urllib`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fname = 'world_growth.zip'\n",
      "if not os.path.exists(fname):\n",
      "    urllib.request.urlretrieve('http://api.worldbank.org/v2/en/indicator/sp.pop.totl?downloadformat=csv', fname)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Open the file using the `zipfile` module and read it using _pandas_, skipping the first two rows and dropping the last two columns that have `NaN` values:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with zipfile.ZipFile('world_growth.zip') as z:\n",
      "    f = z.open('sp.pop.totl_Indicator_en_csv_v2.csv')\n",
      "    df = pd.read_csv(f, skiprows=2)\n",
      "df.drop('2014', axis=1, inplace=True)\n",
      "df.drop('Unnamed: 59', axis=1, inplace=True)\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {
      "scrolled": true
     },
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Country Name</th>\n",
        "      <th>Country Code</th>\n",
        "      <th>Indicator Name</th>\n",
        "      <th>Indicator Code</th>\n",
        "      <th>1960</th>\n",
        "      <th>1961</th>\n",
        "      <th>1962</th>\n",
        "      <th>1963</th>\n",
        "      <th>1964</th>\n",
        "      <th>1965</th>\n",
        "      <th>...</th>\n",
        "      <th>2004</th>\n",
        "      <th>2005</th>\n",
        "      <th>2006</th>\n",
        "      <th>2007</th>\n",
        "      <th>2008</th>\n",
        "      <th>2009</th>\n",
        "      <th>2010</th>\n",
        "      <th>2011</th>\n",
        "      <th>2012</th>\n",
        "      <th>2013</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>       Aruba</td>\n",
        "      <td> ABW</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td>   54208</td>\n",
        "      <td>   55435</td>\n",
        "      <td>   56226</td>\n",
        "      <td>   56697</td>\n",
        "      <td>   57029</td>\n",
        "      <td>   57360</td>\n",
        "      <td>...</td>\n",
        "      <td>    98742</td>\n",
        "      <td>   100031</td>\n",
        "      <td>   100830</td>\n",
        "      <td>   101219</td>\n",
        "      <td>   101344</td>\n",
        "      <td>   101418</td>\n",
        "      <td>   101597</td>\n",
        "      <td>   101932</td>\n",
        "      <td>   102384</td>\n",
        "      <td>   102911</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>     Andorra</td>\n",
        "      <td> AND</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td>   13414</td>\n",
        "      <td>   14376</td>\n",
        "      <td>   15376</td>\n",
        "      <td>   16410</td>\n",
        "      <td>   17470</td>\n",
        "      <td>   18551</td>\n",
        "      <td>...</td>\n",
        "      <td>    79060</td>\n",
        "      <td>    81223</td>\n",
        "      <td>    81877</td>\n",
        "      <td>    81292</td>\n",
        "      <td>    79969</td>\n",
        "      <td>    78659</td>\n",
        "      <td>    77907</td>\n",
        "      <td>    77865</td>\n",
        "      <td>    78360</td>\n",
        "      <td>    79218</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> Afghanistan</td>\n",
        "      <td> AFG</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 8774440</td>\n",
        "      <td> 8953544</td>\n",
        "      <td> 9141783</td>\n",
        "      <td> 9339507</td>\n",
        "      <td> 9547131</td>\n",
        "      <td> 9765015</td>\n",
        "      <td>...</td>\n",
        "      <td> 24018682</td>\n",
        "      <td> 24860855</td>\n",
        "      <td> 25631282</td>\n",
        "      <td> 26349243</td>\n",
        "      <td> 27032197</td>\n",
        "      <td> 27708187</td>\n",
        "      <td> 28397812</td>\n",
        "      <td> 29105480</td>\n",
        "      <td> 29824536</td>\n",
        "      <td> 30551674</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>      Angola</td>\n",
        "      <td> AGO</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 4965988</td>\n",
        "      <td> 5056688</td>\n",
        "      <td> 5150076</td>\n",
        "      <td> 5245015</td>\n",
        "      <td> 5339893</td>\n",
        "      <td> 5433841</td>\n",
        "      <td>...</td>\n",
        "      <td> 15976715</td>\n",
        "      <td> 16544376</td>\n",
        "      <td> 17122409</td>\n",
        "      <td> 17712824</td>\n",
        "      <td> 18314441</td>\n",
        "      <td> 18926650</td>\n",
        "      <td> 19549124</td>\n",
        "      <td> 20180490</td>\n",
        "      <td> 20820525</td>\n",
        "      <td> 21471618</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>     Albania</td>\n",
        "      <td> ALB</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1608800</td>\n",
        "      <td> 1659800</td>\n",
        "      <td> 1711319</td>\n",
        "      <td> 1762621</td>\n",
        "      <td> 1814135</td>\n",
        "      <td> 1864791</td>\n",
        "      <td>...</td>\n",
        "      <td>  3026939</td>\n",
        "      <td>  3011487</td>\n",
        "      <td>  2992547</td>\n",
        "      <td>  2970017</td>\n",
        "      <td>  2947314</td>\n",
        "      <td>  2927519</td>\n",
        "      <td>  2913021</td>\n",
        "      <td>  2904780</td>\n",
        "      <td>  2900489</td>\n",
        "      <td>  2897366</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 58 columns</p>\n",
        "</div>"
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       "text": [
        "  Country Name Country Code     Indicator Name Indicator Code     1960  \\\n",
        "0        Aruba          ABW  Population, total    SP.POP.TOTL    54208   \n",
        "1      Andorra          AND  Population, total    SP.POP.TOTL    13414   \n",
        "2  Afghanistan          AFG  Population, total    SP.POP.TOTL  8774440   \n",
        "3       Angola          AGO  Population, total    SP.POP.TOTL  4965988   \n",
        "4      Albania          ALB  Population, total    SP.POP.TOTL  1608800   \n",
        "\n",
        "      1961     1962     1963     1964     1965    ...         2004      2005  \\\n",
        "0    55435    56226    56697    57029    57360    ...        98742    100031   \n",
        "1    14376    15376    16410    17470    18551    ...        79060     81223   \n",
        "2  8953544  9141783  9339507  9547131  9765015    ...     24018682  24860855   \n",
        "3  5056688  5150076  5245015  5339893  5433841    ...     15976715  16544376   \n",
        "4  1659800  1711319  1762621  1814135  1864791    ...      3026939   3011487   \n",
        "\n",
        "       2006      2007      2008      2009      2010      2011      2012  \\\n",
        "0    100830    101219    101344    101418    101597    101932    102384   \n",
        "1     81877     81292     79969     78659     77907     77865     78360   \n",
        "2  25631282  26349243  27032197  27708187  28397812  29105480  29824536   \n",
        "3  17122409  17712824  18314441  18926650  19549124  20180490  20820525   \n",
        "4   2992547   2970017   2947314   2927519   2913021   2904780   2900489   \n",
        "\n",
        "       2013  \n",
        "0    102911  \n",
        "1     79218  \n",
        "2  30551674  \n",
        "3  21471618  \n",
        "4   2897366  \n",
        "\n",
        "[5 rows x 58 columns]"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.tail()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Country Name</th>\n",
        "      <th>Country Code</th>\n",
        "      <th>Indicator Name</th>\n",
        "      <th>Indicator Code</th>\n",
        "      <th>1960</th>\n",
        "      <th>1961</th>\n",
        "      <th>1962</th>\n",
        "      <th>1963</th>\n",
        "      <th>1964</th>\n",
        "      <th>1965</th>\n",
        "      <th>...</th>\n",
        "      <th>2004</th>\n",
        "      <th>2005</th>\n",
        "      <th>2006</th>\n",
        "      <th>2007</th>\n",
        "      <th>2008</th>\n",
        "      <th>2009</th>\n",
        "      <th>2010</th>\n",
        "      <th>2011</th>\n",
        "      <th>2012</th>\n",
        "      <th>2013</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>243</th>\n",
        "      <td>      Yemen, Rep.</td>\n",
        "      <td> YEM</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td>  5099785</td>\n",
        "      <td>  5184477</td>\n",
        "      <td>  5276093</td>\n",
        "      <td>  5372934</td>\n",
        "      <td>  5472775</td>\n",
        "      <td>  5573959</td>\n",
        "      <td>...</td>\n",
        "      <td> 19612696</td>\n",
        "      <td> 20139661</td>\n",
        "      <td> 20661714</td>\n",
        "      <td> 21182162</td>\n",
        "      <td> 21703571</td>\n",
        "      <td> 22229625</td>\n",
        "      <td> 22763008</td>\n",
        "      <td> 23304206</td>\n",
        "      <td> 23852409</td>\n",
        "      <td> 24407381</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>244</th>\n",
        "      <td>     South Africa</td>\n",
        "      <td> ZAF</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 17396000</td>\n",
        "      <td> 17949962</td>\n",
        "      <td> 18459442</td>\n",
        "      <td> 18936138</td>\n",
        "      <td> 19390554</td>\n",
        "      <td> 19832000</td>\n",
        "      <td>...</td>\n",
        "      <td> 46727694</td>\n",
        "      <td> 47349013</td>\n",
        "      <td> 47991699</td>\n",
        "      <td> 48656506</td>\n",
        "      <td> 49344228</td>\n",
        "      <td> 50055701</td>\n",
        "      <td> 50791808</td>\n",
        "      <td> 51553479</td>\n",
        "      <td> 52341695</td>\n",
        "      <td> 53157490</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>245</th>\n",
        "      <td> Congo, Dem. Rep.</td>\n",
        "      <td> COD</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 15248246</td>\n",
        "      <td> 15637715</td>\n",
        "      <td> 16041247</td>\n",
        "      <td> 16461914</td>\n",
        "      <td> 16903899</td>\n",
        "      <td> 17369859</td>\n",
        "      <td>...</td>\n",
        "      <td> 52487293</td>\n",
        "      <td> 54028003</td>\n",
        "      <td> 55590838</td>\n",
        "      <td> 57187942</td>\n",
        "      <td> 58819038</td>\n",
        "      <td> 60486276</td>\n",
        "      <td> 62191161</td>\n",
        "      <td> 63931512</td>\n",
        "      <td> 65705093</td>\n",
        "      <td> 67513677</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>246</th>\n",
        "      <td>           Zambia</td>\n",
        "      <td> ZMB</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td>  3082627</td>\n",
        "      <td>  3173662</td>\n",
        "      <td>  3269151</td>\n",
        "      <td>  3368961</td>\n",
        "      <td>  3472843</td>\n",
        "      <td>  3580708</td>\n",
        "      <td>...</td>\n",
        "      <td> 11174650</td>\n",
        "      <td> 11470022</td>\n",
        "      <td> 11781612</td>\n",
        "      <td> 12109620</td>\n",
        "      <td> 12456527</td>\n",
        "      <td> 12825031</td>\n",
        "      <td> 13216985</td>\n",
        "      <td> 13633796</td>\n",
        "      <td> 14075099</td>\n",
        "      <td> 14538640</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>247</th>\n",
        "      <td>         Zimbabwe</td>\n",
        "      <td> ZWE</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td>  3752390</td>\n",
        "      <td>  3876638</td>\n",
        "      <td>  4006261</td>\n",
        "      <td>  4140802</td>\n",
        "      <td>  4279559</td>\n",
        "      <td>  4422129</td>\n",
        "      <td>...</td>\n",
        "      <td> 12693047</td>\n",
        "      <td> 12710589</td>\n",
        "      <td> 12724308</td>\n",
        "      <td> 12740160</td>\n",
        "      <td> 12784041</td>\n",
        "      <td> 12888918</td>\n",
        "      <td> 13076978</td>\n",
        "      <td> 13358738</td>\n",
        "      <td> 13724317</td>\n",
        "      <td> 14149648</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 58 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
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       "prompt_number": 12,
       "text": [
        "         Country Name Country Code     Indicator Name Indicator Code  \\\n",
        "243       Yemen, Rep.          YEM  Population, total    SP.POP.TOTL   \n",
        "244      South Africa          ZAF  Population, total    SP.POP.TOTL   \n",
        "245  Congo, Dem. Rep.          COD  Population, total    SP.POP.TOTL   \n",
        "246            Zambia          ZMB  Population, total    SP.POP.TOTL   \n",
        "247          Zimbabwe          ZWE  Population, total    SP.POP.TOTL   \n",
        "\n",
        "         1960      1961      1962      1963      1964      1965    ...     \\\n",
        "243   5099785   5184477   5276093   5372934   5472775   5573959    ...      \n",
        "244  17396000  17949962  18459442  18936138  19390554  19832000    ...      \n",
        "245  15248246  15637715  16041247  16461914  16903899  17369859    ...      \n",
        "246   3082627   3173662   3269151   3368961   3472843   3580708    ...      \n",
        "247   3752390   3876638   4006261   4140802   4279559   4422129    ...      \n",
        "\n",
        "         2004      2005      2006      2007      2008      2009      2010  \\\n",
        "243  19612696  20139661  20661714  21182162  21703571  22229625  22763008   \n",
        "244  46727694  47349013  47991699  48656506  49344228  50055701  50791808   \n",
        "245  52487293  54028003  55590838  57187942  58819038  60486276  62191161   \n",
        "246  11174650  11470022  11781612  12109620  12456527  12825031  13216985   \n",
        "247  12693047  12710589  12724308  12740160  12784041  12888918  13076978   \n",
        "\n",
        "         2011      2012      2013  \n",
        "243  23304206  23852409  24407381  \n",
        "244  51553479  52341695  53157490  \n",
        "245  63931512  65705093  67513677  \n",
        "246  13633796  14075099  14538640  \n",
        "247  13358738  13724317  14149648  \n",
        "\n",
        "[5 rows x 58 columns]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now want to **tidy our data** - transform the dataset to a **DataFrame** format:\n",
      "\n",
      "> Tidy datasets are easy to manipulate, model and visualize, and have a specific structure: each variable is a column, each observation is a row, and each type of observational unit is a table - [Hadley Wickham (2014), _Tidy Data_, J. Stat. Soft.](http://www.jstatsoft.org/v59/i10)\n",
      "\n",
      "\n",
      "This means that every row in the table has exactly one measurement population size with all the relevant variables: country name and year. Read more on [tidy data](http://www.jstatsoft.org/v59/i10).\n",
      "\n",
      "We do this using  _pandas_ `melt` function: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(df.shape)\n",
      "df = pd.melt(df, id_vars=('Country Name','Country Code','Indicator Name', 'Indicator Code'), var_name='Year', value_name='Population')\n",
      "print(df.shape)\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(248, 58)\n",
        "(13392, 6)\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Country Name</th>\n",
        "      <th>Country Code</th>\n",
        "      <th>Indicator Name</th>\n",
        "      <th>Indicator Code</th>\n",
        "      <th>Year</th>\n",
        "      <th>Population</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>       Aruba</td>\n",
        "      <td> ABW</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td>   54208</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>     Andorra</td>\n",
        "      <td> AND</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td>   13414</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> Afghanistan</td>\n",
        "      <td> AFG</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td> 8774440</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>      Angola</td>\n",
        "      <td> AGO</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td> 4965988</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>     Albania</td>\n",
        "      <td> ALB</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td> 1608800</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "  Country Name Country Code     Indicator Name Indicator Code  Year  \\\n",
        "0        Aruba          ABW  Population, total    SP.POP.TOTL  1960   \n",
        "1      Andorra          AND  Population, total    SP.POP.TOTL  1960   \n",
        "2  Afghanistan          AFG  Population, total    SP.POP.TOTL  1960   \n",
        "3       Angola          AGO  Population, total    SP.POP.TOTL  1960   \n",
        "4      Albania          ALB  Population, total    SP.POP.TOTL  1960   \n",
        "\n",
        "   Population  \n",
        "0       54208  \n",
        "1       13414  \n",
        "2     8774440  \n",
        "3     4965988  \n",
        "4     1608800  "
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.tail()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Country Name</th>\n",
        "      <th>Country Code</th>\n",
        "      <th>Indicator Name</th>\n",
        "      <th>Indicator Code</th>\n",
        "      <th>Year</th>\n",
        "      <th>Population</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>13387</th>\n",
        "      <td>      Yemen, Rep.</td>\n",
        "      <td> YEM</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 2013</td>\n",
        "      <td> 24407381</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13388</th>\n",
        "      <td>     South Africa</td>\n",
        "      <td> ZAF</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 2013</td>\n",
        "      <td> 53157490</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13389</th>\n",
        "      <td> Congo, Dem. Rep.</td>\n",
        "      <td> COD</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 2013</td>\n",
        "      <td> 67513677</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13390</th>\n",
        "      <td>           Zambia</td>\n",
        "      <td> ZMB</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 2013</td>\n",
        "      <td> 14538640</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13391</th>\n",
        "      <td>         Zimbabwe</td>\n",
        "      <td> ZWE</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 2013</td>\n",
        "      <td> 14149648</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "           Country Name Country Code     Indicator Name Indicator Code  Year  \\\n",
        "13387       Yemen, Rep.          YEM  Population, total    SP.POP.TOTL  2013   \n",
        "13388      South Africa          ZAF  Population, total    SP.POP.TOTL  2013   \n",
        "13389  Congo, Dem. Rep.          COD  Population, total    SP.POP.TOTL  2013   \n",
        "13390            Zambia          ZMB  Population, total    SP.POP.TOTL  2013   \n",
        "13391          Zimbabwe          ZWE  Population, total    SP.POP.TOTL  2013   \n",
        "\n",
        "       Population  \n",
        "13387    24407381  \n",
        "13388    53157490  \n",
        "13389    67513677  \n",
        "13390    14538640  \n",
        "13391    14149648  "
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We get rid of rows that have `NA` values:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.dropna(axis=0, inplace=True)\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Country Name</th>\n",
        "      <th>Country Code</th>\n",
        "      <th>Indicator Name</th>\n",
        "      <th>Indicator Code</th>\n",
        "      <th>Year</th>\n",
        "      <th>Population</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>       Aruba</td>\n",
        "      <td> ABW</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td>   54208</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>     Andorra</td>\n",
        "      <td> AND</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td>   13414</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> Afghanistan</td>\n",
        "      <td> AFG</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td> 8774440</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>      Angola</td>\n",
        "      <td> AGO</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td> 4965988</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>     Albania</td>\n",
        "      <td> ALB</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td> 1608800</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "  Country Name Country Code     Indicator Name Indicator Code  Year  \\\n",
        "0        Aruba          ABW  Population, total    SP.POP.TOTL  1960   \n",
        "1      Andorra          AND  Population, total    SP.POP.TOTL  1960   \n",
        "2  Afghanistan          AFG  Population, total    SP.POP.TOTL  1960   \n",
        "3       Angola          AGO  Population, total    SP.POP.TOTL  1960   \n",
        "4      Albania          ALB  Population, total    SP.POP.TOTL  1960   \n",
        "\n",
        "   Population  \n",
        "0       54208  \n",
        "1       13414  \n",
        "2     8774440  \n",
        "3     4965988  \n",
        "4     1608800  "
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that for some reason the `Year` variable has a type `O` (object?) instead of `int`, so we change that:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(df.Year.dtype, df.Population.dtype)\n",
      "df.Year = df.Year.astype(int)\n",
      "print(df.Year.dtype, df.Population.dtype)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "object float64\n",
        "int32 float64\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Data exploration with plots\n",
      "\n",
      "Let's start with the three biggest population in the dataset - the entire world, China and India.\n",
      "We will plot their population size over time:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "world = df[df['Country Name'] == 'World']\n",
      "china = df[df['Country Name'] == 'China']\n",
      "india = df[df['Country Name'] == 'India']\n",
      "\n",
      "plt.plot(world.Year, world.Population, label='World')\n",
      "plt.plot(china.Year, china.Population, label='China')\n",
      "plt.plot(india.Year, india.Population, label='India')\n",
      "plt.legend(loc='upper left')\n",
      "plt.xlabel('Year')\n",
      "plt.ylabel('Population');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uj0dFSxZr7A2flPe00xzuEAAGHmERAI4hEomo6dAhfXjf71X/xN543Z2Xq5K1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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7bb2cb0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Alternatively we can also plot using the `DataFrame.plot` method:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ax = world.plot('Year', 'Population')\n",
      "china.plot('Year', 'Population', ax=ax)\n",
      "india.plot('Year', 'Population', ax=ax)\n",
      "ax.legend(['World', 'China', 'India'], loc='upper left')\n",
      "ax.set_ylabel('Population');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ERGzR3dyMt7oG76rVtL/xRkwt/+abKFm6lKJ5c3Fq0WORi6KwJyIicRPu7qZl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\nOOv0WRuPxwzGfbqDLt1hl86wS3fQoTvsTh/5fX/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       "text": [
        "<matplotlib.figure.Figure at 0x7bb2350>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Exponential growth model\n",
      "\n",
      "According to [Malthus](http://en.wikipedia.org/wiki/Thomas_Robert_Malthus) (but that was a long time ago, so don't count on it!), populations grow exponentialy ([how to solve this](https://www.youtube.com/watch?v=mhO9eL9Nuz0)):\n",
      "\n",
      "$$\n",
      "\\frac{dN(t)}{dt} = r N(t) \\Rightarrow \\\\\n",
      "N(t) = N(0) e^{rt} \\Rightarrow \\\\\n",
      "\\log{N(t)} = \\log{N(0)} + rt\n",
      "$$\n",
      "\n",
      "where $N(t)$ is the population size at time $t$ and $r$ is the growth rate.\n",
      "\n",
      "That means that that logarithm of the population should be a linear function of time."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"Exponential growth\")\n",
      "YouTubeVideo(\"https://www.youtube.com/watch?v=c6pcRR5Uy6w\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exponential growth\n"
       ]
      },
      {
       "html": [
        "\n",
        "        <iframe\n",
        "            width=\"400\"\n",
        "            height=\"300\"\n",
        "            src=\"https://www.youtube.com/embed/https://www.youtube.com/watch?v=c6pcRR5Uy6w\"\n",
        "            frameborder=\"0\"\n",
        "            allowfullscreen\n",
        "        ></iframe>\n",
        "        "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "<IPython.lib.display.YouTubeVideo at 0x3ac4890>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's check if the world population growth is according to the exponential model. \n",
      "First define a new column for the log of the population size:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df['LogPopulation'] = np.log(df.Population)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![G8 flags](https://images1-focus-opensocial.googleusercontent.com/gadgets/proxy?url=http://environmentalgovernance.org/wp-content/uploads/2012/06/g8logo.jpg&container=focus&resize_w=150&refresh=2592000)\n",
      "\n",
      "Let's concentrate on the [G8 countires](http://en.wikipedia.org/wiki/G8) (well, not exactly, but good enough for the purpose of this presentation):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G8_countries = ('France', 'Germany', 'Italy', 'Japan', 'United Kingdom', 'United States', 'Canada', 'European Union') # 'Russian Federation' was suspended in 2014\n",
      "G8 = df[df['Country Name'].isin(G8_countries)]\n",
      "G8.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Country Name</th>\n",
        "      <th>Country Code</th>\n",
        "      <th>Indicator Name</th>\n",
        "      <th>Indicator Code</th>\n",
        "      <th>Year</th>\n",
        "      <th>Population</th>\n",
        "      <th>LogPopulation</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>33</th>\n",
        "      <td>         Canada</td>\n",
        "      <td> CAN</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td>  17909009</td>\n",
        "      <td> 16.700814</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>52</th>\n",
        "      <td>        Germany</td>\n",
        "      <td> DEU</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td>  72814900</td>\n",
        "      <td> 18.103431</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>69</th>\n",
        "      <td> European Union</td>\n",
        "      <td> EUU</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td> 409331746</td>\n",
        "      <td> 19.830037</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>73</th>\n",
        "      <td>         France</td>\n",
        "      <td> FRA</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td>  46647521</td>\n",
        "      <td> 17.658130</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>77</th>\n",
        "      <td> United Kingdom</td>\n",
        "      <td> GBR</td>\n",
        "      <td> Population, total</td>\n",
        "      <td> SP.POP.TOTL</td>\n",
        "      <td> 1960</td>\n",
        "      <td>  52400000</td>\n",
        "      <td> 17.774417</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "      Country Name Country Code     Indicator Name Indicator Code  Year  \\\n",
        "33          Canada          CAN  Population, total    SP.POP.TOTL  1960   \n",
        "52         Germany          DEU  Population, total    SP.POP.TOTL  1960   \n",
        "69  European Union          EUU  Population, total    SP.POP.TOTL  1960   \n",
        "73          France          FRA  Population, total    SP.POP.TOTL  1960   \n",
        "77  United Kingdom          GBR  Population, total    SP.POP.TOTL  1960   \n",
        "\n",
        "    Population  LogPopulation  \n",
        "33    17909009      16.700814  \n",
        "52    72814900      18.103431  \n",
        "69   409331746      19.830037  \n",
        "73    46647521      17.658130  \n",
        "77    52400000      17.774417  "
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we do a _hack_ to sort the countires names based on the largest population in 2013 so that the next plot will have a legend that is ordered by country size. \n",
      "\n",
      "We start by splitting the data frame according to country name and extracting the max size for each country so that we will have a `pandas.Series` with the country as index and the max population size as the value. We then sort by the value (the population max size) and extract the index (the country). We will use this sorted list for ordering the colors in the next plot."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G8_countries = G8.groupby('Country Name').Population.max()\n",
      "G8_countries.sort(ascending=False)\n",
      "G8_countries = G8_countries.index\n",
      "print(G8_countries.tolist())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "['European Union', 'United States', 'Japan', 'Germany', 'France', 'United Kingdom', 'Italy', 'Canada']\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now plot the log of the population sizes. Note that only the first 3 arguments are neccessary and the rest are are just used to make a more aesthetic and professional looking plot."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sns.lmplot(x='Year', y='LogPopulation', data=G8, hue='Country Name', \n",
      "           size=7, aspect=1.5, line_kws={'alpha':0.5}, hue_order=G8_countries);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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at29l+rnnCQpFmvfcQnztWswFqls9H/kw7tg4ke4u7JaW6utomaGIiIjINUkh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       "text": [
        "<matplotlib.figure.Figure at 0x7d645f0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is interesting. While some countries fit very well to the Malthusian model (United States, France, United Kingdom), some countries don't fit as well: Japan seems to have stopped growing during the 1980's, and, European Union, Italy and Canada also seem to decelerate their growth. But this can be due to these countires being \"developed\". What about some \"developing\" countries?\n",
      "\n",
      "## Predictions using linear regression\n",
      "\n",
      "Let's focus on the four largest countries, only one of the is \"developed\", but as we saw above it fits the Malthusian model.\n",
      "We will use _SciPy_'s [`linregress`](http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.stats.linregress.html) function to perform linear regression. This will allow us to **extrapolate** - to predict what will be the population of these countries if the rate at which they grow remain constant under the Malthusian model. \n",
      "\n",
      "Note that the linear regression of $y$ as a function of $x$ is $y = a x + b$, where $a$ is the slope of the regression and $b$ is the interception. \n",
      "But then we have to exponentiate both sides of the equation as we want actual population size and not log population - so we get $e^y = e^{ax+b}$.\n",
      "\n",
      "Let's extrapolate to the end of the century:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "years = np.linspace(df.Year.min(), 2100)\n",
      "for country_name in ('India','China','United States', 'Brazil'):\n",
      "    country_df = df[df['Country Name'] == country_name]\n",
      "    slope, intercept, r_value, p_value, std_err = linregress(country_df.Year, country_df.LogPopulation)\n",
      "    print(\"Coefficient of correlation for %s: %.4f\" % ( country_name, r_value), end=\", \")\n",
      "    print(\"P-value for %s: %.2g\" % ( country_name, p_value))\n",
      "    population = np.exp(intercept + slope * years)\n",
      "    plt.plot(years, population, label=country_name) # prediction\n",
      "    plt.scatter(country_df.Year, country_df.Population, marker='.') #data\n",
      "plt.xlabel('Year')\n",
      "plt.ylabel('Population')\n",
      "plt.yscale('log')\n",
      "plt.ylim(5e7,1e10)\n",
      "plt.legend(loc='upper left')\n",
      "plt.axvline(x=2032, color='gray', linestyle='--')\n",
      "plt.axvline(x=2056, color='gray', linestyle='--');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Coefficient of correlation for India: 0.9968, P-value for India: 1.1e-58\n",
        "Coefficient of correlation for China: 0.9764, P-value for China: 2.9e-36\n",
        "Coefficient of correlation for United States: 0.9993, P-value for United States: 3.2e-76\n",
        "Coefficient of correlation for Brazil: 0.9889, P-value for Brazil: 9.1e-45\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sWhrh48eh8mp/P3bLq+vYciiPzBwz+45bcTgVV59GrWJgLy0pRj0jk+IJC2yf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\n9mF3fvB6eHpgOG8+eauyCI4JdnOEYrKM91+hWuA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RypYK+of7x8zz8/QjLTKNtKh0DFFp\nzA1JRKeVTk3T3biSUFVVXznk6z3OGpoGoE5V1bGbMcS0tyQznp4BMxkJ4SzKiCclJvgrT0tarVYu\nuOCPVFdn8sADhfz0p9nExDzBbbeddQqjnjjPPbeJu+60cknCo9yd08mj81TXY96JiUSvu4HQVSvR\n6qf+7SwhxMxkt9tpNDZRWFDMvt11rnG9t56MC9LIWZlFUGSgGyMcy2K1UNO+11WjU21VGRwZHDMv\n0CvwkJPrBuJD4tFqpu4KrjgxJ7R2rarqALBrgmOZEqRjksN5WQmcl/X1vcv/+c+tjIxYWLPmfFpb\nw+noWEZV1T+49dZvcOmli05BpBPHZGrloYfe4NorzkL3yUc8O7eMBO9mzM780y8jg+hvryN4yRI0\nU/h2lhBiZrNarFR/VsPujUW01o6uA/mH+pGzMovMCw14+Xm5McJRw9Zh9rZVu1Y6q1pVhq3DY+YF\n+4S4Tq6nRRqIDYqd1mWiZqgJ75h0zN9hRVGegKNUcx37/XZVVW+fiGCmEudq775t27YRFxfn7nCm\npB07drFyZRc2mzevvw5arQc7dxr5+c+vwXsadgFau+aPaHdEsi7uaYIZ/ck88OyFRK9bR8BpC+RD\nUbid9EA/MTPhfTMPmCl7z8ied0ro6xi9ZR2RGE5efjapC1PQebj3FvXQyBBVbVWOPZ0mI9Vt1Vhs\nljHzwv3CXfU5DVHpRAVEyefrFNXQ0MDSpUsBkk5lxyQD40xCJy4cMVU89th/2Lq1nnvvvYDTThst\ngNDX18cvf/kKubkJLFw4j8DAL7HZ9EREnMVpp2WwYsX0uv3+yCNv8XFBNT/I6eaOxvfwjHMWbtZq\nCVl6ITHr1uGbNt+9QQohZrWe1h72vFNC2fsVjAyNuMYT8+ayYHU2sYY5bkvgDvZdP7jSua99bN91\ngKiA6MNWOiP8I45yNTHbHDMJVVX1/FMYh5hiHn20gYqK2/HyeoJzzlF56qkmLrrIB7DwyCPXExPz\nGuXlC/nii4ux2WzEx8e7O+TjZm5sZOCZf3GnZh/6rc7k08ODsG9cTMwN1+M9DV+TEGLmOFBtorCg\nmOrPaly9zXV6HYbFCrkXZRMaG3LKY+oz91HRUkGFM+ms7TxW3/U4V8JpiEojxHf6rTyLySf1DMRR\nXXihDh+fx7n00jReeqmCsrLb8fV9nF/8IpPExOeIj2/D39+f4GlWkshsNvNfK+9jYXcNC/X1LNU5\nuoZYPb2IvfZqIq+9Bs/wcDdHKYSYrWw2G/t21VFYUERT5WjnH59Ab7JXZJK1LAPfQJ9TFs/BvusH\nDxIdre+6Bg0JIQmuwvBpkWkEek+tA1Fiahpv7/iv3B86E/eEznaPPXaL6+u4uFB8fJ7gyisNXHbZ\nEvLzz0Kv10/pWnNHqqnZh7amhp7XXuOHfbtBB9jAIyyUqGuvJeKKNXj4S99gIYR7jAyNUL69kj2b\niuk2jdbFDIkNIS8/m7RzU/HwnPx1I1ffdWfSeay+60mhSc6VznTmR86XvuvihIz3T/SR+0M9gTQc\n/5QXTnRQYmpZvDiXxYtzXb/28poapy7Hw26z8eFjz1L35H/I8G5yjXd7+qPccTOxay5HOw0PUQkh\nZob+zn6KNpdSuq2coT6zazw+I5a81TnMzY5Hc5S6zBPl8L7rRky9pjFzdBodyeHJGCLTMUQZSI1Q\npO+6mBDjrRN6/pFjiqL4AM8BWyY2JCFOXl93Ny/98HcsaKnE/0ATGc48U5Mwl6RbbyHkwgvQeMhu\nFDH9zNYe6Cdrqr1vbfvbKSwoonJHNTarY1uQVqdFOXseefnZRCRO/LYgu93Ogd4Djv2cX9N3fV7E\nPOd+TgPzpO+6mCQn/K+wqqqDiqL8FvgP8LeJC0mIE2cdGqL9zbcoe3g9pw+P9rnvj01k6PzlrPjB\nzVIGRAjhFna7nf3FDewuKKK+ZLQjnZevJ5nLMshZkYF/6MTd1rbb7TR2NzpbYFZgNBnpOkrfdS+d\nl6vvelqUQfqui1PmZJeCfAE58ibcztLdzXv3PYTXzu342c0EOMdLdNFc+bcH8M/Kcmt8QojZyzJi\nRd1RReGmYtrrO1zjgZGB5F2UheG8NDy9T777ms1uY3/n/sNWOnvNvWPmSd91MVWM92DSVUcMaYBY\n4HbggwmOSYhxGzaZML3yKq2vv0HooKPAvBUNkd+4GJYv49oFedOycL4QYvob7B2iZGsZxZtLGege\nbYARo0SRl59D8umJJ3XA02qzUttRi9FU7ui73lrJwNf2XTcwN2Su9F0XU8J4f/T5+xG/tgMtwFbg\nJxMakRDjMFhby4EXXqTlrbfROc/MWXR6PrAoBFx2Pnfcu87NEQohZqvO5i72bCrGuF3FMuzoFqTR\naEg5I4m81TnEpEad0HUP7btubDGitlQyZBkaM+/QvuuGKANxwdJ3XUxN4z2YNGv+9Erv+Kmtr7QM\n9ZHHsO3eBXY7OqDLEkR1fDI3v/ggC6dZ3VIhxMxgt9tpqmhmd0Ex+3bXuurJ6L08yLjAQM6qLIIi\nj6925rB1mOrWKud+znKqWquO2nc9xNl3/WCdzjmB7uugJGa0Ce8dL5tAjuB8Yzc4e8df4uZwBI4P\n957PPuPAc8/T++Uu17gtOIT6tDMp6A7jgT9ch4ckoGIWmAk90N1hst43q8VK9ec1FBYU01LT6hr3\nC/Ujd2UmmRem4+U3vrJ2x9t3/WBHIum7Lk6Ru05l7/jDKIpyEfAjIN05VA78WVXVgokMSIiD7FYr\nne+9R+Mzz2KuqnaN1w6H8Wr7Bdzy67NZk7+YNW6MUQgxO5kHzJS9X8Ged0roax+txBE+N4wFq3NI\nXZiCzuOr910ODA9Q2VrpaoF5rL7r0QHRjk5EUWnSd13MKOM9mHQH8DCwAXjIOXwO8KaiKD9SVfWR\nSYpPzEI2s5n2jQUcePElzPX1rnGjOZrzfvcdBgKi+e6whRUrznZjlEKI2ai3rZc975RQ+r6RkcER\n13hibgJ5q3OISz/2rfBecy+VLZXOlc6Kr+277ljplL7rYuYa70roz4GfqKr6l0PGHlYU5S7gZ4Ak\noeKkWfv6aNnwOi2vvMpIe7tr3Jxq4Pe7E+iO0HPNqlUk6E++lIkQQhwP094Wdm8sovrzGuw2R+Ko\n0+tIW6SQl59NaGzImO/pHuzC2FLhWums79o/Zo6j7/pc10Ei6bsuZpPxJqGhwNtHGS8Afjdx4YjZ\naKS9HdPf/0HLa69h63OUF7GhYXPHcr4I8eHNV+/hjZERPDw8ZN+TEOKUsdvs1OyupbCgmKaKZte4\nd4A32cszyF6eiW+Qj2u8vb+dihZn33WTkaaepjHX1Gq0JIYmYYhKk77rYtYbbxK6GVgOVB8xvhRH\nmSYhjpu5oZEDL71E21v/wT7sOPFptnlQHz+fiOuu4pMXarn00rkA6GX1UwhxioyYRzBuV9mzqZiu\nA92u8ZA5weTlZ5O2SEGn19Ha18qXez93lEwyldPS1zLmWjqtjpSwFFcLTCVyPj56nzHzhJiNxrWs\npCjK94BfAW8CnziHz8ZxevxXgOtIoKqq/5zQCN3EeTp+37Zt24iLi3N3ODPKgKpy4PkX6NiyFWzO\nnsl+fmzsi+cvxQ/wjbVv8dxzd7g5SiHEbNPfNUDx5lJKtpYz1DdafzMufQ65+dl4J+upbK10KOTA\nQQAAIABJREFUFYdvH2gfc42DfdcNUekYIg3Mi0jFy2N8p+OFmIoaGhpYunQpQJK7Tsf/n/P/33b+\nd6gj94POiCRUTCy73U5fYSHNz71Az86drvF2ix8vH7iWjFs1rLnqQrRvbOMHP7jRfYEKIWad9voO\nCguKqNhRhc3i/MFYpyX2tBg8cmGftoatNZvoKjt633UlUnGtdKaEz0Ovkzs3QoyHFKsXk8pus9H9\n0cc0P/88/cUlrvE2rR/KHd/mzkdqMPmOcOOSs0hPTyE9PcWN0QohZgu73U59aQO7Nxazv3i0CofW\nS4MlzUxldAU7te9B/eHf56P3YX5kmqtGZ1JYEh5aKbktxImQvzliUtgsFjreeZcDL7zAUM0+13hP\ncAS/23Ub23tD+CTTh48/W8vIyIj0dxdCnBKWESvqzioKC4ppr+9wjQ/7mmmau5+WuAPYPEZrdfp7\n+ruSTkNUOnND5p5Uv3chxKjjLVb/C0aL1ZcC/6uq6juTEZiYnqyDg7T9+01ML73MsMnkGv+i18AO\n/2Aef/03RN32PN8NbSIv72a0Wi063VcXdBZCiJPV193HR2/voObDOqx9Ntd4b3A3zYkNdES1gdZO\noHeQqz6nISqduOA46bsuxCQZb7H6G4G/4djv+Ypz+DzgbUVRblJV9fnJCU9MF5auLlr++Rot//gn\nlm7HaVI7MJKRw/v6JP77mWvIzv4HgYGBvPzyne4NVggx4w1bhqluq6KkopT67U3oqjzRWR0/8Nqx\n0xHVRnNSPfoYHYZoA4aoS0mLMkjfdSFOoeMpVv8zVVX/dMjYekVRvnQ+NmOSUEVR1gBrAD93xzId\nDB8wceDll2l749/YhhynSTUeHnxiS+KPxQ+ghG5i06ZbSLrwXRYtusHN0Qox/Unv+KMbGhlCba2k\nwlSB0VSOqaqVyJoYQkzheOKDVW+hc57j7kxoVigXZC/GEJVGpL/0XRdinB5WFKUf2KCq6oaJuOB4\nk9Ak4N9HGX+LGVas3vnGbnCWaLrEzeFMWYP79nHghRfpKNiE3erYP2VGx6a+LObfsZSWVguBQ++w\nYkUkOp2O667Ld3PEQoiZZGB4gMqWCkdh+BYj+9r3YbXaCDWFM2dfPGndMaOT/SDqjDB6mh0lldae\nv1aSdyGO313uKtHUDJwL7D1i/GznY2KW6Csp4cDzL9D1wYeuMbOnN3HXX8fqh4Ypq72Zu/a+xF/+\ncgu//rUbAxVCzCi95l4qTBVUmMoxtlRQ11nr6ruuteiIrI8hpi4Or8HRQ44h8cGcfvEClLNT6O7p\npuoR1V3hCyGOYrxJ6JPA44qizAM+co4tAX4I/HYyAhNTh91up+fTTznw3Av07trlGrcGh/Bw2XLe\nbFvG8z9q5Tf/z4tPPnmF++9f68ZohRAzQfdgl6MTUYujBWZ9V/2YOV6D3igmA357g2B4dDwxN4G8\n/GziMmLlVrsQU9h4k9A/AwPAT4B7nWONwM9VVX10MgIT7me3WOh8732an3ueQXV0BaHeGsSOgBRu\nf+Ju9lz6T+KDNpOTcxWpqYlcdtkSN0YshJiu2vvbXbfWjSYjzcfou54UmsQ8FDxLfWgr6cRudayG\n6vQ60halkntRNmFxcqtdiOngK5NQRVFCgReAVYAW+BRYDdSqqtoz+eEJd+nds4faX/0ac0PD6GBK\nKh94JXH3i/cSFb2Be8JD2LPnRwB4enq6KVIhxHRjt9tp6WtxJZxGk5HWY/Zdn4chysD8iDS8m3wp\ne9dIo7EZGATAO8Cb7OUZZC/PwDfI9xS/EiHEyfi6ldAHgDOA+4Ah4A7gD6qqrpzswIR7HXjueVcC\nqnrN4aGi+/D1/JBNm/6LSq9nyc6eQ0hIiJujFGL2CQ0N5f7773d3GMfFbrfT3NOM0VRORYvj9HrH\nQMeYeXqdntTwVNKiDK6+61qrloqPVApfKqaruds1NyQmmNz8bAyLFTw8v/6m3nR834SY6b7ub+5F\nwHdUVX0LQFGUd4ASRVE8VFW1THp0wm0ebQjGZyiHjLVns6cN6ivqWBYPQUFB/PWvt7k7PCHEFGaz\n22jsasTYUu64xW4y0j3UPWael4cXSoSCISqdtMi0w/quD3QPUPhGMcVbyhjqG3J9T2z6HBbk55CY\nm4BGK/s9hZjOvi4JjQW+PPgLVVXLFUUxA3OA/ZMZmHCvLeXhGI33cXXR47z66u385CcHiIyUilVC\niLFsNhv7u+pct9YrWiroM/eOmeej9yEtMs210pl4lL7r7Q0dFBYUU7mjCuuIo/ybVqcldWEKefnZ\nRCZFnJLXJISYfF+XhOqAI1c8reP4PjHN3XtvGps2PcF9912MRqMhJibm679JCDErWGwWajtqnauc\n5VS2VDIwMjBmnr+nvyPhjDKQFmk4Zt91u91OfWkjhQVF1BWNnoL39PEkc6mBnJVZBIT5T+prEkKc\neuNJJl9RFGUERxdGDeANPKMoyqDzcbuqqlKJfIa57rqlXHfdUneHIYSYAkasI+xt30uFc6VTba3E\nbDGPmXew7/rBpPPr+q5bLVbUndUUbiqmra7dNR4Q7k/uRdlknJ+Gp48cehRipvq6JPQFRpPPg14+\nYo59QiMSQgjhVsOWYaraqhwHiUwVVLWpjFhHxswL9Q0lLdKZdB5H3/WhviFKtpVT/G4p/V2jK6hR\nKZHkrc5m3hnJaHXHTl6FEDPDVyahqqreeIriEEIIMQ6T0Tv+YN/1g3s697ZXY7VZx8yL8I90rXIa\nogxE+kceVzH4LlM3ezaVUP5hBRazc6eXBlJOTyIvP5sYJXrSistPxvsmhDg5srdTCCFmmSP7rte0\n12Cz28bMiwmMcSac6Rii0gjzCz+h52tWD7B7YxF7v9znunfm4eVB+nlp5K7KIjg66GRejhBimpIk\nVAghZrieoR4qWyocezpbjNR11GE/yk6q+OD4w26vB/sEn/Bz2qw29n6xj8KCYg5Um1zjfsG+ZK/M\nJGtpOt7+3l9xBSHETCdJqBBCzDBdg12uQ0RGUzkN3Q1j5mjQMDd0LoZIR8I5PzKNQO/Ak37u4cFh\nyj+oYM87JfS0jpZpCosPZcHqHJRz5qHz0J308wghpj9JQoUQYppr7287pEankeae5jFzDvZdd9xa\nN6BEzsfP02/CYuht76N4cykl28oZHhh2jc/NiScvP4f4zNhJ2+8phJieJAk9gqIoa4A1wMR9Ogsh\nxASx20dvo7+y62Wq+qqO2nfdQ+tBSngKhsh00qLSUCLm462f+NvfLbVtFG4sourTvdisjn2lWg8t\naYsU8vKzCYuTA0BCzBAPK4rSD2xQVXXDRFxQfiw9BkVREoF927ZtIy4uzt3hCCFmqUP7rh9c6Tx2\n33XFtZ8zNTwVT4/JqbFpt9mpLdpP4cYiGsqbXOPe/t5kLUsne0UmfsG+k/LcQohTq6GhgaVLlwIk\nqapaO5HXlpVQIYSYQo6v7/p8Z3H4dJLDkl191yeLZdhCxUcqhZuK6Wzqco0HRweRl59N2mIFvdfk\nxiCEmDkkCRVCCDey2WzUddZR0fLVfdd99b7MP9h3PcpAUmgSOu2pOeAz0D1I8ZZSSraWMdgz5Bqf\nkxbDgtU5JOXNRaOVG2tCiOMjSagQQpxCFpuF2vZ9GFscq5zH7LvuFYDhkKQzIfjofdcnU0djJ4UF\nRVR8XIV1xFG8XqPVkHpWCnmrs4lKjjyl8QghZhZJQoUQYhKNWEfY21ZNRUsFRlM5aqt61L7rQa6+\n647T63OCYr+y7/pksdvtNJQ3UbixiNo9+13jeh89mRemk7syk4DwgFMelxBi5pEkVAghJpDZYqa6\ntcq10lnVVnXMvusHE05DlIHogBi3ljCyWqxUfbqX3RuLaKtrd40HhPuTszKLjAsMePlOzkEnIcTs\nJEmoEEKchMGRQdRWFaOpnAqTkb3te4/adz3SP9J1a90QmU6Ef8QJJZ0T3QPd3G+mZFs5RZtL6e/o\nH403OYIFq3OYd2YyWt2pX5GdaNI7XoipR5JQIYQ4Dv3D/a6+60aTkdqOfcfouz6HtMi0k+67Plm6\nW3rYs6mY8g8qGDFbHIMaSF6QSN7qHObMj5bi8kKISSVJqBBCfIWDfdcPJp37O7+i77pzT2daZNpJ\n9V2fTM1VJgo3FrH3i32uwvcenh4YlijkXZRNcMzUjFsIMfNIEiqEEIfoHOikosVIhani2H3XNRrm\nhhzsu+7oSBTgNXUP69hsNmq+rGX3xiIOVJlc475BPuSszCRzaQY+ARPfTUkIIb6KJKFCiFmtrb+N\nCucqp9FUzoHeA2PmaDVaksOSHd2IIg3Mj0zD13PqdwQaHhrB+GEFhZtK6GnpcY2HxoWwID8H5dxU\nPPSnptaoEEIcSZJQIcSsYbfbaekzuToRGU1GWvtbx8w7tO+6IcpAaoQyKX3XJ0tfRx9F75ZSuq0c\n88CwazwhK468/BwSsuNkv6cQwu0kCRVCzFh2u52mniZXwnmsvuueOk9SI1JJi3ScXp83iX3XT1Zo\naCj333//UR9rrW2jsKAY9ZNqbFbHYSmtTsv8c1PJy88mPCHsVIY6pXzV+yaEcA9JQoUQM4bNbqOh\nq8FRLqmlYtx911PCUvDQTc+PQ7vNTl3RfnYXFNNQ1uga9/b3ImtZBtnLM/AL8XNjhEIIcXTT81NX\nCCEY7btuNJVjNBmpbKmgb7hvzDx39l2fLJZhCxU7qigsKKazsdM1HhQVSF5+NobF89F7690YoRBC\nfDVJQoUQ04bFZmFf+z4qWoyupHNwZHDMvKnQd32yDPQMUrK1jOLNZQz2jL72OWkx5OVnk7Rg5rxW\nIcTMJkmoEGLKOth3vexAGdt2b6df38mIfWwLzMGuQELx4ZoVq93ad30ydTR2smdTMcaPVKwjjo5M\nGq2GeWcms2B1DlEpkW6OUAghjo8koUKIKaO9q52dxp0M+QzyQfFOOqwmNB7OwvAecLBGfH97EC0V\niXxziS9vPddK1Z5MHnoomOXzV7gt9slgt9tpKG+isKCY2sI617jeR0/G+QZyV2URGDF165MKIcRX\nkSRUCOE2gyODPPjUMxwYbiAyzYMqUzUanTPT1IDG+QnlZfVD/TQOXXc/Lzz8PR64t4AYrYYfX/Ud\nvn/ZCN3d3URHR7vvhUwwq8VK1ad7KSwoprW2zTXuH+ZP6vnJvFe6hZaaBjJ1aW6McnqR3vFCTD2S\nhAohTgmTyYR3gDc7jZ+y/p+b8I3rRRs8gD3QkXT2tIHGeVZIO+BLgv9cij6AFacbuOu7V1GYU0xC\nQixhYWH89anbXdf18PDAx8fHDa9o4pn7zZS+Z6To3RL6Ovpd45FJEeStzmbemcl093TzXukWN0Yp\nhBATQ5JQIcSkqKtr5IW/b2LxJSn8670t1PZ0EBDbhUYDfpmOOQc7sA+YfFmoGEgOTqHy03Z++v3r\n8fb2hrWj18vLyz7lr+FU6W7poeidEso+qGBkyLnnVQNJCxLJy88mNi1GissLIWYcSUKPoCjKGmAN\nIIX1hBgHu92RSmo0Gn75P09T3V7Hkssi+LBkF/o5Qxi/3AqBEBjomK9Bg6XDF8/+YO5cexVK+Hx8\nPHzw8vJyTFjiphfiBs1VJgoLitj7+T7X+6jT60hfMp/c/GxCYoLdHKEQQrg8rChKP7BBVdUNE3FB\nSUKP4HxjNyiKkghc4uZwhJhyrFYrL7ywkTPPNDCiG+L7//MC/vF9JJ+uoSO5A49k2Nmgog9xfoNN\nQ2JoIq2VVs7LOovLL7hoWvRdnyw2m42aL2spLCiiWTW5xn0CfchZkUnWsnR8AmfG9gIhxIxyl6qq\ntRN5QUlChRBf6733drF+/edctnYun1Tu5ou9nrzd9y+8goeJy3fM6TA7/m+zaIj1j+O0pFy8B3xY\nedZK/Lz84Bvui38qGB4awfhhJXveKabb1OMaD40NIS8/m/nnpuLhKR/JQojZQzYZHYNzJXTftm3b\niIuLc3c4QpwSIyMjWK1WvL29uenmxyir7efKWwLYUVGOLciCb2jn2G+yafEaCObicy4kPTqdlPB5\neOqmZt91d+jr7Kfo3VJKt5Vj7je7xuMzY8lbncPc7HjZ7ymEmLIaGhpYunQpQJKshAohJlR1dTVB\nQUFotBouuuoveEZZWHalDz2nVZN83gi7zOCdNDrf28ObSH002XFZnJ58OsnTuO/6ZGqta6OwoBh1\nZzU2qw0ArU7L/HPnkXtRNhFzw90coRBCuJf8yyHELDM8PMyrr77LsuWn8/aHH7L+n3VEZ9QQbRgi\n9UbHSl1VH+j9HfO9dd6kx2RgiDKQFmkgMTRx2vddnyx2u5264noKNxZRX9roGvfy8yJraTrZKzPx\nD5Ezj0IIAZKECjErqGotL760hcu/fRoPv/gatT1ebBp5Fa2XDcPljjlmx2IdWoueBUm5pEelY4hK\nJz44XnqRfw3LsIXKHVUUFhTT0Ti6ZSEoKpDcVdmknzcfvbfejREKIcTUI0moEDPUX595mz37yjjv\nm4m8+u5W9Alm/vDxNkiCOYfM87R5E+s7l/Ozz8UQlU5sUKzsURynwZ5BSraWU7S5lMGeQdd4jBLN\ngtU5JJ02VxJ4IYQ4BklChZghegd6+dGvH4XQHqLTdajUoFNs/Lu8EJ/40XlhvmEEWsI4O+0MTks6\nneiAaEk6j1NnUxeFm4oxbq/EOmIFHHVS552VTF5+NtHzotwcoRBCTH2ShAoxTQ0MD7Bt94c8/9ZW\nApMGMHt1Yc9wFDzf2wk6591ff20QeXNzCLGHcmHuhUQGRLox6unLbrfTWNFM4cYi9u2uc43rvfVk\nXJBG7qosAiMCJz0O6YF+YuR9E2LqkSRUiGmiz9xHZUsFb368hQpTDR5hfYAdTwMMHTJvuMOLC3PP\nJDs+h5SQFGJCYtwV8oxgtVip/qyGwoJiWva1usb9Q/3IXZVFxgUGvPy83BihEEJMT5KECjFF9Qz1\nUGEyYjQZ2V72CQO6bg7eNfcIG51nbvPFdzCI7629mrTINIJ8pNXjRDAPmCl7z8ied0vpa+9zjUck\nhrNgdQ7zzkpG5yFVAoQQ4kRJEirEFNE50InRZMTYUo7xgJGmntESP3g4O0vYwc8aQkOxH6clz+Xn\nt3wbfy9/d4U8I/W09rLnnRLKPjAyMjjiGk/Mm8uC1dnEGubIHlohhJgAkoQK4Satfa1UtBjZvW83\ntT37MPWZxsyxWbQE2oMZaPSldlcgP7hxEVd880I3RDvzHag2UVhQTPXnNdhtjr21Or0Ow2KF3Iuy\nCY0NcXOEQggxs0gSKsQpYLfbMfWaMJrK+VT9HKOpAot+aMw867CerrpQLl2s8NZzTXTX+fHqSzeQ\nmCitYyeDzWZj3646CguKaKo84Br3CfQme0UmWcsy8A30cWOEQggxc8k9pWOQ3vHiZNjtdva17qOq\nXUVtreTTql3YPYfHzrNqMVUY8Ojp5p7bLuF/f/4lCXE+rF9/q9zynUQj5hGM2yspLCim29TjGg+J\nDSEvP5u0c1Px8JSf0YUQQnrHCzHF2ew2alpqePJfr+Iba6NxcD8Dlv7RCZ6O/2msOoZNflR9prAk\nU8sv7riOP5a8xZU3fJOFWVmct3GJe17ALNHf2U/xljJKtpYx1Gd2jcdnxJK3Ooe52fFotJL8CyHE\nqSBJqBDHyWazMTA4QMuQiZc3vUVRfTV+cb2MMAyBQO/o3OF+L5SIWGp3W2mp8Ocvv74aJTWRuro6\n5s2bh0aj4U9/usVtr2W2aNvfTmFBMZU7q7BZHP1JtTotytnzyMvPJiIx3M0RCiHE7CNJqBDj8N4H\nn1HfXUdQsp6XNm5EGzaIh7ejU45nHBw8Q23u8WakxZNbr/4m29+oIdQzgrtvvRrWHH691NTUU/sC\nZiG73c7+4gZ2FxRRX9LgGvfy9SRzWQY5KzLwD5XKAkII4S6ShApxFB1dHfz0gScJSbHgGTXA3o79\n6DytsAc8Y0fn6W0+dFQHkBWbwB3XXktnfScJCQkEBgaSn+6++Gczy4gVdUcVhZuKaa/vcI0HRgaS\nd1EWhvPS8PTWuzFCIYQQIEmomOXsdjtmsxl08Pirf+fdz8uZk9mL2acLsu0MAvSBzrmn018XSIg9\nmo5qDT+5aS1KbOphB4hig2KP+jxi8g32DlGytYzizaUMdA+6xqNTo1iwOofk0xPRarVujFAIIcSh\nJAkVs059fSP1zU34xnrw4FMv0Os5QGB8D2jshJ0F5kPmWro9uTD3bEIIJ9pzDuedea7b4hZH19Xc\nReGmYozbVSzDFgA0Gg0pZySRl59NjBLt5ggnlvRAPzHyvgkx9UgSKmY8m83Gbx96Hl34INEGT978\neCd+0YNoKu1o5jnOEh1k7fYlzjeONResZH5kGmF+Yce8rnAfu91OU0UzuwuK2be7Fhy15dF7eZB+\nfhq5q7IJigr8ymsIIYRwL0lCxYwyMjKCXq/n/R2f8adnNxGXNYQ1uJO+mB40WjtlNeA/xznZDiEe\n4fTt9+KqZctYlHEOQT5Bbo1ffDWb1Ub1ZzXsLiiipabVNe4X4kvOyiwyL0zH29/LjREKIYQYL0lC\nxbRWXr6Xzz8v4+I153DPn9ajtnUSn9OFxbufwPPgYBlyDWC3QUJwAhG6GHTdfty85loCvAPcGb4Y\nJ/OAmbL3Kyh6t4Tetj7XePjcMBasziF1YQo6D50bIxRCCHG8JAkV04rNZuPuu59jwN7Lmu9k8ODT\nb+AVA5v//QqkQEwKWJxz7TYNngOBXHTW+SQEJDhurwfJ7fXppLetlz3vlFD6vpGRwRHXeGJuAnmr\nc4hLnyOdpYQQYpqSJFRMeWVl1dz1y9eYkzlAQq6GqtgD+IX38PQXnxCeOzpPp9Fh7/TnzHk5XJC7\nmNTwVLz13u4LXJwwU00LhRuLqfpsL3abY8OnTq8jbVEquRdlExYnh0qEEGK6kyWEY5De8e5htzsS\njkef+ydvflRK8un9DHi1YTtK33W9Vk9SSDLB1jBWnLGMeRHz8DxYS0lMO3abnZrdtRQWFNNU0ewa\n9w7wJnt5BtnLM/EN8nFjhEIIMftI73gxY9XV1WMytRM5L5h7/9+TtFl7iUzrxeJhJvIC6Dt0skVH\nTkIWhigDhqh0kkKT8NDJH+HpbsQ8gnG7yp5NxXQd6HaNh8QEk5efTdpiBQ/PY/8+Dw0N0dPTQ2Rk\n5KkIVwghxASRf8HFKWW1WvntAy/hG21jbp4vz7z5Pv7xA3hWDsN8CGV0T6fN7EGELppVZ12AIcpA\nYogUG59J+rsGKN5cSsnWcob6hlzjcelzyFudQ2JOAhrt2Js1drud//u/DWg0Gm699RssWfIH6urm\n8dBDoaxbt/JUvgQhhBAnQZLQIyiKsgZHp28/d8cyU5SUVvI/D79Oyhl2evUmWqO70PuYKayA0Pmj\n8zzxZsTkz8ozzub87EXEBcej1UjSOdO013dQWFBExY4qbBYbAFqdltSFKeTlZxOZFAE4DqFVqVUk\nJyezZ4/Kj3+8lfnz9VxyiYG7705Go7ESH/8BJlM0LS2rKS9/zZ0vSwghZrqHFUXpBzaoqrphIi4o\nSegRnG/sBuee0EvcHM60NGwd5sEnn+PTyhqSFpjpsJvwXGKj3vm43vmnLsgriCjPOHwHg7nuosuI\nDYqVk84zlN1up760gd0bi9lfXO8a9/T1JGtpOtkrMgkI82fLli8o+L83uO++K/nFL/7Biy+msnr1\nRsLCfNi+/U5U9RVuuSWE2Nj30WjsZGZexiOP+PLFFxu45561bnyFQggx490le0LFlDM0MkRVq8qD\nf32Bfu8e/Ob0YwuwEnQ6dBwyTzPoxaKMs0gKSiI9OoP4sHhJOmc4y4iVqk+qKSwopm1/u2vcL9SX\nzOXpZJxv4L++8xSdz+zg+efXctddOzAa76Cz8yna20cYGDiPlpYifvWr5dTUPEJ6uh+nn57Dnj1J\nAAQGBpKamsgllyxy10sUQghxgiQJFcdtYHiAytZKShqKeXvndnShA2i0dkgGH8DmnGfp9iEpKIGL\nz12KISqdcL9wd4YtTqGhviFKtpZTvLmU/q4B13hQXBC+KcH88NfNBH+wmSeeGOT118/Cal3A00+/\nSnz8IO3tG8jMjOZb31rM//3fc9x00xWkpCTw7rvfd10nMHD2tuSUHugnRt43IaYeSULF1+o191Jh\nqqCixUjR/iIaexs5uFXT45C8Um/2Z6Den+tWXcj5OYsI8ZUP+dmm60A3ezYVU769EovZMjqutfPs\nu8sJiX+dtVHQ1JzPwOBO5syZw9q1BbS3f8att17PL34RTHd3N2FhjqYCv/vdze56KUIIISaZJKHi\nqFr7WtlY/jZGk5H6rv2HPabROlpgzgmcQ2OxDUtrAI/++g6iQ6PdFK1wJ7vdTnPlAQo3FVP9xT5X\n8eERm52dVVnoYgtJTPOnoauFhHQrP/jBVQwNvUpiYhQpKSk8//ydh13vYAIqhBBiZpMkVBzVk9vX\nU95e5vq1zapluM2Xcw2ZbHq5k2ivIP74zA/RXCZ7Omcrm9VG6fZy3ly/nSCdY2lcA3QN+GIJH8CE\nnV3tZdx8WQT33HM111xThKLciU6n4557vuXe4IUQQridJKHiqLY8M4g9Pp2UyD4i9bG89pQHy87X\n8uOf3MaPV7s7OuFOn31Swt8e+JC0YA/0NlwJqD7Ik7LOPnYfMPOXXy7lzDMzsdlsrtquCxbkftVl\nhRBCzDKShIqjGmkK4LM3VnPa9z/nwT/fzO9/ZJNC8bPYK69s4+VnVVYvCMRc30NWoIfrBFrriIUG\nq4VH/3o9fv+/vfuOr7K8/z/+OtkkJCQETJC9PgwhITjAhQooS62LaqvUaq3Fil/9qUVra8HRSv22\ntopQFOvEgaP6QwGhAlYcrSIQNpcsWSEiMwRIQnK+f5yTeEyDSMZZeT8fDx7Jua77vrk+n8edK5/c\nM+Xbj9fVPiMiIkejc6lH0djfHb9nzx4WLVrJoEFnqJBopCZMeI2PPipk7M39efvJRbQ2DJjPAAAc\ndElEQVRKiCE2xld5lnu9FDeJ4ab7R5LZRjegiYhEK707XoIuIyOD88/XsxcbE6/Xy69//Rx79hzi\nL49cy3uvfU2P9LYseX4RbZIAKvDGeeh3UV9yLjiJ5GbJoR6yiIhEMBWhIo1YaWkp48e/SOfOWfTp\n04pH/9KZvm2TmDpmGhd38wAFAKS3akbe8Fy6n9WV+MT40A5aRESigopQkUbm4MGD/O1vb/KDH5zF\n9On/4qGHLqFN1jwmjyvg/ks2kRgbAyW+ZVv3aEXe8Fw65rXHE6Ord0REpP6oCBVpBA4ePMiyZSs5\n9dS+3HzzMzz77NVMnz6Ve+88lRsGTqdnSy8bF3pIjI3BE+PB+ncmb3guJ3RqGeqhi4hIlFIRKhKl\njhw5QklJCSkpKVx22UT++c+B3HjjVDLSE+ne6jMGt0li41tr6J0F4CGhSQK9BvYgd2hvUjObhnr4\nIiIS5VSEikShkpISzjnnjxQUZPPooz04cMCDh87E7f0Pp7TPpMO56wHftZ2pLZrSZ1gOPc/pTmJy\nQmgHLsekd6DXjvImEn5UhIpEiW3bdjBy5HPEx3t55pkfsmlTZwoLL2bRv19l/I39WNn5NTxlcXy9\neRcAWZ1PIG9EDl1O7URMrB7DJSIiwaUiVCSCLV26lrvumkufPml07dqMTz75CR7P16xbt40/jGtG\nweKXyNgRy6rNq30PBfZA51M6kjc8h1aWjcejm41ERCQ0VISKRJiPP17GlCkf8bOf9eP55//D3Lm3\nsGrV31m5ciAff/wC6bGxlK7oQPHn20j1ejnCEeIS4+g5oBt9huWQnt0s1CGIiIioCBWJBIsXr+a9\n9z7n1ltHcu+9HzB//hi+/PJx/vCHs3FuIr17xVO4aidD25zIjnWFbFi0CYCU9GRyhvSi96CeJDVN\nCm0QIiIiAVSEioSpvXv3UlpaSsuWLbn66pmsWXMDW7c+R79+zdi4cQqnndaUU/v2YOI9Hpa+u5zZ\nj/2zat3Mts3pOyKXrqd3IS4+NoRRiIiI1ExFqEgYKigo4OyzX+LQoWZMn34yaWmHSEpaTHZ2Gvfc\ncxW/vr2I/LkrePqWaZQeLK1ar11OW/qOyKFtrza63jNKNW/enHHjxoV6GBFHeRMJPypCRcLEmjUb\nufHGt2jd2sPYsQMpLOxFSUkH1q//gvfeu40tW7bQIjmHOZPm8cW/11NRXgFATFwM3c8y8oblkNlW\nj50REZHIoCJUJIQKC3cyYcKbjBzZnzff/DcLF/4PqalzmTChGZMnb2f37mWMuuZyvszfwupZ69i2\n6oOqdZOaJtF7cE9yLuhFSnpyCKMQERE5fipCRYLM6/VSVFREWloat9zyCq+99ks++GAiM2ZcxerV\nE2nXrgnt2g3lR1e2Zs1Cx4t3vcqe7Xur1k/Pbkbe8By6n23EJ8aHMBIREZHaUxEqEmRXXvkXFi7M\nYvToGHr0aE5m5pu0bVtG69bZvPPObRzcd4j/vLGIZf9cyeGiw1Xrndi9FX1H5NIxrz2eGF3vKSIi\nkU1FqEgQ/OlPr7N27Vc88sgo1q+PZceOH7F8+SRef/0Wbr75KzIzL2X3tj0smZXPmg+/oLysHABP\njIeu/TqTNyKHrE4nhDgKERGR+qMiVKSBHD58mJiYGHbt2sVDD3nYvft6MjOn8cgjZ/Pqq09y992X\n4/V6KdlZxsxn57Bp6eaqdeObxNNrYE/6DOlFaovUEEYh4UbvQK8d5U0k/KgIFWkA+flrueKKWSQk\nHGbOnFHk5Kxmx47NDB06gHPO6ctZZ+biPlnPy5Nf5+svd1Wtl9qiKblDenPSeT1ITE4IYQQiIiIN\nS0WoSD0pLi7mgQdeZtCgHLZu3cGGDZcSH7+VrVsLWbDgt76jnsWlLJqxhPy5KyjeXVy17gmdWtJ3\neC5d+nUiJjYmhFGIiIgEh4pQkXoyduwLTJ58Lf/4x1RWrryJL798hbS0JvTvfwX7vtrP0tnLWPX+\nGspKjvhW8EDHvh3oOzyHE7u30sPlRUSkUVERKlIHU6bM5KWXtnD11W3p0aMVLVq8Q3b2PuLi4hg/\nfhQFXxQy669zWf/ZRrxeLwBxCXH0GGD0GZZDRqv0EEcgIiISGipCRY5TWVkZ+/fvJzMzk5df3sLC\nhaOJiZnC+++P5oordpCefhHrP9vI4pn57PiisGq95GZNyLmgF70H9aRJWpMQRiAiIhJ6KkJFjoPX\n62Xw4AmsXduZceNSufbaDsTGTmHUqI6UHi6jMH8n786ez/6v9letk9m2OXnDcrAzuxIXHxvC0Us0\n0DvQa0d5Ewk/KkJFvoc5cz6huPgQF188gG3b0iksvIzly59l8uTR/PCSA+TPWcEzY16g5GBp1Trt\nerchb3gu7XLa6HpPERGRalSEihzDsmWrueqqHZSWZvHiiwt59NGTef/9F7j5umHMnTwf98k6Ksor\nAIiJjaHbmV3JG55Di3aZIR65iIhI+FIRKlKDoqIibr/9BcxO4NJLT6ZJk53ExJSRltaBThlZlKTv\nYsaDs6uWT0xJpPfgnuRe0IuUjJQQjlxERCQyqAgVqcGDD07nqaeuJzNzJqNGNeGD9wezcdFmts3e\nyIpti6uWa5aVRt7wHHqc3Y34pPgQjlhERCSyqAgV8Xv55fk89thaLrigGUOH5jFjxt9of+IhNnzQ\nhpXzV3No/+GqZU/slk3e8Fw6ntyemBg9XF5EROR4qQiVRs3r9VJUVERaWhqvvLKWf//7Jg4fnsKt\nN3bi8TsOsGahY9FbSwDwxHjoclon8obnkN0lK8Qjl8ZK70CvHeVNJPyoCJVGbeTIR/jooyzGjIln\n9Og8Uo78jf7tk5j2q+lVy8QnxXPSeT3oM7QXaS3TQjhaERGR6KEiVBqdVavWsWXLDoYMOYv16+P4\nqvAqti+bQqfiWPo388DeEgCaNk+hz9DenDSwB4nJiSEetYiISHRRESqNyu7duxk2bDaFhf34y5/e\n5O5rO7P1s6eI98axc9PXALTs0IK+I3Lp0q8TsXF6uLyIiEhDUBEqUa+8vJwHHniRjIymjBp1LmmJ\ncFrvLZT952sKy71U3tPesW978kbk0rp7Kz1cXkREpIGpCJWoN3XqW9x//3l0yV5Byz3z+Pmp8eDd\nCeUQGx9LzwHd6DMsh4wT00M9VBERkUYjag73mNmfgdPxFdaPOuderOP2OgAb582bR5s2bephhBJM\nixev4be/fY/+/TLp3601819cwYmp3zxKqUlaE3Iv6EXvwT1pktYkhCMVEREJX1u3bmXQoEEAHZ1z\nm+pz21FxJNTMegB5zrkzzCwZWA7UqQiVyDbxr+9zYN25kPQha9buqypAm7fOIG9ELt3O6EJcQlTs\n/iIiIhEpWn4L7wUSzCwOaAbsCvF4JATuuecFZs8o5qpzEzk5Jpa8Uz6s6mvbqzV5I3Jpn9NW13uK\niIiEgagoQp1zBWb2CeCAFODGEA9JgqSoqIiCggKaJ2VyeGURo06KI253CRVATGwM3c7sQp9hObRs\n3yLUQxUREZEAYVOEmtlVwM1ADpDsnIuv1h8LTACuBZKAucAvnHO7zOxMoCvQGUgHPjSzWc65smDG\nIMFVXl7ONRdOol1CNl1bHqZDSgxQQWxiLHlDcsgZ0oumGSmhHqaIiIjUIGyKUGA38DiQDDxZQ//d\nwMXAaf5lnwZeAIbjOwW/2znnNbMDQDwQC6gIjUKvvvJP9m3YQ9KeCga1Tgd873RvlpVGn6E59Dyn\nG/FJ8d+9EREREQmpsClCnXNzAczs3KMsciMwvvLOLDMbC6wzs7bAHOAqM/sQSAAec84dbvBBS1Ad\n2n+I2c/O44v3C0hNKueQv708OYbhPzuXrv26EBMT853bEIl0egd67ShvIuEnbIrQ72Jm6UBb4PPK\nNufcBjPbD+Q657YAP6nD9jOBzGrNrWu7PalfW77YylMPvE3zCg+eCkhNggovtLBMBo8aQHaXrFAP\nUUREJNp1NLOEam27nHO1vhk8IopQINX/dV+19r1AWj1s/xZgXD1sR+qJ1+tl+5oCFs9axobPN5Hp\nf6RtXGIcHU9rR8cz2tM9t1uIRykiItJozK+h7T5gfG03GClFaJH/a7Nq7enA/nrY/kTgpWptrak5\n4dKAyo+Us+7TDSx46WNKd/tOuHuAA6Veviw5yJ8n/4Km6U1DO0gREZHGZyCwrVpbnR6JGRFFqHNu\nr5ltBk4GlgGYWWd8R0GX1cP2d1EtkWZWWtftyvdXcrCElQvWsPTd5RzYdaCqfddhLz+6fRBd+nUi\nLj4idlcREZFotDFq35hkZjH4bipK8H9OBDwBNxg9CdxlZguAPcDDwLvOuc2hGK/Uj/07i1j67nJW\nvr+askPfPMwg4YQU5iw7wCkDM+h+loVwhCIiItIQwqYIxXdj0dP+773AIcBrZh39heYEIAP4DEjE\n95zQa0IxUKm7wvVfsXhmPus+3YC3wgvAkQov/9nQk8T2q3j+r6MYHeIxioSj5s2bM26cLmE/Xsqb\nSPgJmyLUOfcs8Ox39FcAv/L/kwhUUVHBxs+/ZMmsfLav3VHVfrDMS+cz2rIzppySwyu5c+w5IRyl\niIiIBEPYFKESvcoOl7F64VqWzFrGvsJv7iNr2jKFafMS+HDNUO456R+MH38dv7w1hAMVERGRoFER\nWo2ZXQ5cju8d9FIHxXuKyZ+7ghXzVnH4QElV+5Z9FazaW8QLE3/I163n0W3jy4wdW+vHvIqIiEjD\ne9TMioE3nHNv1McGVYRW40/sG2bWAd9rQuU4fb15F0tmLWPtx19QcaQCAE+MBzujC2v37eBP9wyi\nSZMVbC8oYOzYkSEerYiIiHwPt0bt3fES2bxeL5uXb2XJzHw2L99a1Z6YnEBpRgKPv15Gp12f8vbb\nv6LwwDRatkyjV6/BIRyxiIiIhJKKUKmTI2XluI++YMnsZezasruqPa1lKn2G5dDz3O6M/uVU3KYb\nIWEycXFx/P73Pw3dgEUinN6BXjvKm0j4UREqtXKo6DAr5q0kf+5KDu49WNWe3TWLviNymThtPvfd\n9DHXXLOMhx++kuTkp7jggpNDOGIREREJJypC5bjsLdjLkneXs/pfazlSegQAj8dD51M7kjc8h1aW\nDcDiO2axadMYPv30cVq0yOTxx/XUTxEREfmGilA5Jq/Xy/a1O1gyM58Nizf5XiUAxCfG0fPc7vQZ\nmkPaCalcf/0k1qyp4OGHB3Dffafz3HNTGDPmvJCOXURERMKTilA5qoryCtZ9uoElM/Mp3LCzqj0l\nI5ncIb3pNbAnSU0TASguLmbOnFQKCn7CtGlTeOKJmxg4UKffRUREpGYqQqVGW1Zu470nFlD09YGq\nthbtM+k7Ipeu/TsTGxdLeXk5Y8Y8wZEjFUyceAPXXx9Lfv7j3HHHRSEcuYiIiEQCT6gHEG6qPaz+\n4nnz5tGmTZsQjyr4ZvzvbDYt+RKADn3akTcilzY9T8Tj+WaXmTFjPpdc0gqvtwnTpq3i6quHh2q4\nIiIi0gC2bt3KoEGDAGYAelh9Q9LD6n3O+nF/TuyWTce+7cls882jTMrLy5k06XVOPrkbZ5yRS//+\nT1Je7mHgwOtCOFoRERFpYHpYvQRH89YZNG+d8V/tDz74Ivfddz7t27/JsmWj+PjjX4dgdCIiIhLp\nYkI9AAl/Xq+X7du3U15eTnZ2BsnJ+TRtupf4+PhQD01EREQilI6EyjHdccfTPPtsC84/fwPTp/8/\nBgxYQ1bWaSQlJYV6aCIiIhKhdCRUjmnDhgPs2XMRW7b4Pvfo0V2vvBMREZE60ZFQqdHttz/NRx8d\n5q67ejFp0pV06jSVa6/V3e8ioaZ3oNeO8iYSfnQkVGo0a1YJn376S155ZSWtW2fzyCO/IDe3W6iH\nJSIiIlFCR0KlRjfckMWCBZO57bazQj0UERERiUIqQqVGd955GXfeGepRiIiISLRSEVpNtTcmiYiI\niAg8amZ6Y1JD0huTRERERP6L3pgkItKYNW/enHHjxoV6GBFHeRMJP7o7XkRERESCTkWoiIiIiASd\nilARERERCToVoSIiIiISdCpCRURERCTodHe8iEgE0TvQa0d5Ewk/OhIqIiIiIkGnIlREREREgk5F\nqIiIiIgEna4JrUbvjhcRERH5L3p3fEPTu+NFRERE/oveHS8i0pjpHei1o7yJhB9dEyoiIiIiQaci\nVERERESCTkWoiIiIiASdilARERERCToVoSIiIiISdLo7XkQkgugd6LWjvImEHx0JFREREZGgUxEq\nIiIiIkGnIlREREREgk5FqIiIiIgEnW5MOoYdO3aEeggiIlX27dvHgQMHACgoKODgwYMhHlFkUN5E\naqch6yBPg205QpnZ5cDlQApwOtAytCMSERERCamdwCdAMfCGc+6N+tioitCjMDMD1gIDgY0hHk4o\ndATm03jjB+WgsccPykFjjx+Ug8YePygHlfF3c865+tywTscf2zbn3KZQDyLYzCzB/22jjB+Ug8Ye\nPygHjT1+UA4ae/ygHATEX+90Y5KIiIiIBJ2KUBEREREJOhWhIiIiIhJ0KkKPbhdwn/9rY9TY4wfl\noLHHD8pBY48flIPGHj8oB409fhERERERERERERERERERERERERERERERERERERERERERERERERER\nEREREREREREREREREYlonlAPoKGZ2VXAzUAOkOyciw/oiwF+A1wHtASWADc755bXsJ1hwEzg7865\nnwe0nwBMAQYDh4GngV8757wNFtRxqGv8ZpYCPARcAaQCW4AfO+eW+vujPf6RwL1Ae2AP8Ixz7r6A\n/rCOH8DM/giMANoCB/Dtx3c55/YELPMTYByQDSwHfumcWxzQfwowGTgJKADGOedeDOgP2zzUNX4z\n649vHzgZSALWAQ845/5/wPphGz/Uzz4QsFzEzYX19DMQ6XNhfeQgYufDY8VvZrnABKAPkAWc7Zz7\nqNo2InYehLrnoCHmwsbw7vjdwOPAbTX03QFcDQwEmgMLgTlm1jRwITNrBjwKfAhUT+SLQAXQGugH\nXAr8qh7HX1e1jt/MPMBbQDvgVOdcKjAc2B6wjWiOvwcwDbjHOdcMGAL8wsxuCNhGuMcPcARfnM2B\nXKAN8Gxlp5mdhW9i/QWQDrwBzDKzVH9/M2A28Jq/fzQwxT8hVQrnPNQpfiADeBno6ZxLBx4AXvb/\nQqoUzvFD3XNQuVykzoV1/RmIhrmwrjmI9PnwO+MHSoDXgQv9n7+1f0fBPAh1zAHRMReGhpmda2Zl\n1do+NbNbAj7HmVmJmY2qttzfzexXZvaMmU0NaO9oZhVm1jGg7Xoz29CQsdRGbeI3syFmVmxm6UfZ\nZrTHf4WZba+2zktm9pj/+4iJP5CZDTWzfQGfnzOz56ots8l/VAQzu87MNlbrf97MnvZ/H1F5ON74\nj7KNT8zsNv/3ERU/1D4H0TAXQq1+BqJmLqxUixxE1XxYPf5qfRVmdka1tqiaB+H4c3CU5eo0FzaG\nI6HHEpgDj/9fbmWDmQ3Bdyr3z/z35Qu5wD7nXOCOuQToYNWOpoax74r/PGAjcL+ZFZrZOjP7vZnF\n+fujPf4PgDgzu8TMYsysFzAAmOHvj9T4BwFLAz7nAJ9XW2apvx18cS6p1r+Eb/IUaXn4vvHnUgMz\ny8Z3Oi7f3xRp8UMtchBlc+Hxxh+Nc+Hx5iDa5sPq8R9LtM2DcPw5+Jb6mAsbexH6DnCzmXUxsyTg\nQSAWSAMwszR8pyducM5V4Ds0HXh4OhWo/lfEXv/XtIYceD35zviBFkBPfNd1tAWGAiOBsf7+qI7f\nOfcVcBO+U1AlwDLgeefce/71Iy5+M7sc3+m2WwOajxZHWkD//mP0R0Qeahl/4Pop+E5TvuOcW3CM\n9alpG6FWmxxE01x4nPFXXo4QVXNhbfaBaJoPjxL/sTQlSuZBqHUOAtevl7mwsRehE4A3gbnAl/iu\nY1gNfO3v/xMw3TlXWeVXHimrVAQ0q7bN9IC+cHes+IuAcuA3zrlS59w6YBLwg4D+qI3ffDdgTAIG\n+m9o6gScZ2b3+9ePqPjNd1PBk8BFlTdT+NUURwbfTLhHi/NY/ZV9YaEW8X9rMjXftXGzgR1A4Gnq\niIgf6pSDqJgL6/gzEBVzYW33gWiZD78j/mOJinkQ6pSDyvXrbS5s1EWofzK5yznXyTmXhe80Uyfg\nff8i5wOjzWynme0ErgSuCbi+IR9oFnj9A9AX2OicC6udribfI/7KnTPwl40HX7EG0R//CGCBc+5T\n//KbgJeAi/z9ERO/mV2H747FC51z/6rWnY/vbsfKZT1AHt+cYlmK727JQH35Zv8I+zzUMX7MLBOY\nB2wFRjrnjlRbP6zjhzrnIOLnwnr4GYAInwvrmIOInw+PEf+x5BPh8yDUOQf1PhdGfRHqv3YlCUjw\nf070f8bMssysg//7tvjuEvvYOTfXv3o/oBe+6xz64Lv25Q3gDAD/dQ/vAQ+bWaqZdcJ3euaJ4ER3\nbHWM/w1gJ3CfmcX7d6zRwD+gUcS/GBhoZn0DlrkGWASRET+Amf0P8L/ABc65T2pYZCpwmZkNNLNE\nfHcyxuM7Soz/a4qZ3enP32DgEnx/SYd9Huoav/+6p38Bq4Br/Kejq4R7/FAv+0B/IngurIf4o2Eu\nrGsOIno+/B7xY2ZJZtbE/zHR/7myToroeRDqnoOGmAsbw3NCf4rvOVXgu4bJ4//aEd+zIV/G9yiB\nIuBV4G7n3MGjbOsZoMw5d2NAW0t8f1Wcj+86mb875+5ukGBqoa7xm1lvfKdg+uI7Tf008GDlztcI\n4r8XuBbfM9P2A7OA2yv/qgv3+MF3lyNQBpQGNHudc2kBy4wCxgOt8F3rdZNzbklA/yn49oPe+B5L\n8zvn3EsB/WGbh7rGb2bj8D078SDfvg7y9865Cf5lwjZ+qJ99oNr2ImourKefgUifC+sjBxE7Hx4r\nfv8Bicoj+5W/KwB+6px73r9MxM6DUPccRMNcKCIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIi\nIiIiIiIiIiIiIiIiIiIiIiJhIOrfmCQiEg7MbAaQDZzunCsPaO8HfAhc6px7J1TjExEJtqh/d7yI\nSJj4GdAOuLeywcySgReAp+q7ADWzWDPTgQYRCVuaoEREgsTMRgBvAmc65z4zs0nAQKAf8BBwKZAK\nrAR+45ybF7DuVOA84ESgAHgFuM85V+rvHw9cCTyI7/3OHYHOzrnNwYlOROT46EioiEiQOOdmAn8H\nXjCzHwA3ANcAbwNd8RWhOcB0YJaZ9QLwH9EsBH4EdAduBa4F7qn2X7QFrgd+DJwE7GzgkEREai0u\n1AMQEWlkbgeWAG8AvwPSgFOALOfcAf8yfzGzwcBoYIxzzgv8NmAbm83sj8AtwPiA9iTgGudcQcOG\nICJSdypCRUSCyDl3yMz+DEzEdwr+TnzFY4GZBS6aCASejv85viOn7YEUfPN39UuqtqsAFZFIoSJU\nRCT4ygCvc85rZjHALqB/DcsdAjCzkfiK1rHAQmA/cDkwodryxQ02YhGReqYiVEQktD4HWgBxzjl3\nlGUGAIucc49VNphZx2AMTkSkoagIFREJIefce2a2AHjLzMbiuzO+BXAusM459yawBrjOzC4EVgMX\nAleEaMgiIvVCd8eLiISGN+D7C4F3gMfxFZxvAacDm/z9TwDTgOeAxfge6fS7atvwVvssIiIiIiIi\nIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiEl7+D6Dm5XxODO8NAAAA\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8212db0>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From our prediction, India will pass China around 2032 and Brazil will pass United States around 2056. \n",
      "\n",
      "From the results of `linregress` we can estimate confidence intervals on the intercept and slope -- look for it online. We can also [calculate the coefficient of determination](http://stackoverflow.com/a/895063/1063612) ($R^2$)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Logistic growth model\n",
      "\n",
      "The Malthusian/exponential growth model can't always be correct: many times growth decelerates and effectively stops when reaching a certain size _K_ (carrying capacity, maximum yield, maximum population density etc.). \n",
      "This is true for fish body size (Schnute 1981), microbial population size in a constant volume (Zwietering 1990), and natural animal populations. \n",
      "In these cases it is common to use the [**logistic growth model**](http://en.wikipedia.org/wiki/Logistic_function#In_ecology:_modeling_population_growth) in which the size of the population inhibits growth, leading to a maximum population size after which growth stops:\n",
      "\n",
      "$$\n",
      "\\frac{dN}{dt} = r N \\Big( 1 - \\frac{N}{K} \\Big)\n",
      "$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"Logistic growth\")\n",
      "YouTubeVideo(\"https://www.youtube.com/watch?v=rXlyYFXyfIM\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Logistic growth\n"
       ]
      },
      {
       "html": [
        "\n",
        "        <iframe\n",
        "            width=\"400\"\n",
        "            height=\"300\"\n",
        "            src=\"https://www.youtube.com/embed/https://www.youtube.com/watch?v=rXlyYFXyfIM\"\n",
        "            frameborder=\"0\"\n",
        "            allowfullscreen\n",
        "        ></iframe>\n",
        "        "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "<IPython.lib.display.YouTubeVideo at 0x8379090>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's start by plotting the solution to this _ordinary differential equation_ (ODE).\n",
      "We need to define the ODE as a function of _N_, _t_ and whatever other parameters are needed. It is important that _N_ comes before _t_:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def logistic_ode(N, t, r, K):\n",
      "    return r * N * (1 - N / K)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Integrating ODEs is really easy with Python. After defining the ODE function we can define a new function that given $t$, $r$, $K$ and $N_0$ (initial population size) calculates $N(t)$ by integration. For this we use _SciPy_'s `odeint` (ODE integration)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def integrate_logistic(t, N0, r, K):\n",
      "    N = odeint(logistic_ode, N0, t, args=(r, K))\n",
      "    return N\n",
      "\n",
      "t = np.linspace(0,10)\n",
      "N = integrate_logistic(t, N0=1, r=1, K=10)\n",
      "plt.plot(t, N)\n",
      "plt.xlabel('Time')\n",
      "plt.ylabel('Population')\n",
      "sns.despine();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GRsTJJEnvsyhK6ncdDQ28c8KJNMx5DYDxR/yI0iOP8MpmSUozFkVJ/ap9xQrennk8TW92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\nivJcCtwchuFjq43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8eB3bzgY27XHbva+CasMlOjpYPPsGAIbttBNFu+4ScSJJkvRJ0maP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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f65c6b9b5c0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Incredibly, there is a solution to the [logistic equation](http://en.wikipedia.org/wiki/Logistic_function) that doesn't require numerical integration:\n",
      "\n",
      "$$\n",
      "\\frac{dN}{dt} = r N(t)(1 - N/K) \\Rightarrow \\\\\n",
      "N(t) = \\frac{K N_0 e^{rt}}{K + N_0(e^{rt}-1)}\n",
      "$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def logistic(t, N0, r, K):\n",
      "    return K * N0 * np.exp(r*t) / ( K + N0 * (np.exp(r*t) - 1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = np.linspace(0,10)\n",
      "N_integration = integrate_logistic(t, 1, 1, 10)\n",
      "N_solution = logistic(t, 1, 1, 10)\n",
      "plt.plot(t, N_integration, label='ODE')\n",
      "plt.plot(t, N_solution, 'o', label='Solution')\n",
      "plt.legend(loc='upper left');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mtGTyFLZ9+imxNm0Y8JPriBnsJEkJZriTmsn6uXNZ8difAej77W/RcdCgiCuS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\nqiIMw65x3rfFW3zHnaz53/8F4NxxR3D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       "text": [
        "<matplotlib.figure.Figure at 0x7f65afbca978>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Fitting a logistic model \n",
      "\n",
      "So we have a standard growth model, but how do we find the right model (_i.e._ parameters: `N0`, `r`, `K`) for our data? To do this we need to **fit the logistic model** to our data. \n",
      "\n",
      "We will use a _SciPy_ function called [`curve_fit`](http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.optimize.curve_fit.html) that accepts a model (a function of `t` and some other arguments/parameters that returns `N`), data (`t` and `N`), initial guesses of the model parameters, and some other optional arguments. It evaluates the model with the initial guesses and calculates the _fit_ of the result -- in standrad fitting this is done by the sum of the square of the differences between the model and the data. It then makes another guess of the model parameters, evaluates the model result and calculates the distance, and again and again. It stops when it reaches a minimal distance, and that's why this operation is called **least squares**. This operation isn't perfect, and when there are even just 3 or 4 model parameters there might be more than one minimum or the function might not find a minimum in a reasonable time.\n",
      "\n",
      "## Simulated data\n",
      "\n",
      "Before we try to work with real data we want to [try it with simulated data](http://stackoverflow.com/a/16241965/1063612) and see that we know what we are doing. \n",
      "To simulate data we generate data from the logistic function and add some normally distributed noise:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "simulated = logistic(t, N0=1.5, r=0.75, K=8.5) +  np.random.normal(loc=0, scale=0.7, size=t.shape)\n",
      "plt.scatter(t, simulated)\n",
      "sns.despine()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GKCws5LbbvmDx4l8A+zJjxiCuuur5uGNJkjKMxU6qAQoKCsjPz91k3dq1DWJK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\nkAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f65afbdc6a0>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can call `curve_fit` and give it the simulated data and get back an estimate of the model parameters. As you can see, although there is a lot of noise, we get a pretty good estimate of the parameters."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "params, cov = curve_fit(f=logistic, xdata=t, ydata=simulated, p0=(1,1,10))\n",
      "N0,r,K = params\n",
      "plt.scatter(t, simulated)\n",
      "plt.plot(t, logistic(t, N0, r, K), '-')\n",
      "sns.despine()\n",
      "print('N0=%.3f, r=%.3f, K=%.3f' % (N0,r,K))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "N0=1.452, r=0.742, K=8.576\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZUpeXl8ell07lzDN3cdppqUyc+JrVkeq9gQOfpX//TsyceQ8331zEwoUfW5Yl\nMDBQpU58ioqdSD3RvHkAkF01HR//K4mJp/bEhNGjF/Gf/9xDWto9rF07iJEj11NQUODlpLWjOC2N\nTbffyd7nFoLbTXDrVnRYuICE/v2wBwVZHe+Yxo59na+/HkZR0V/Yv/8m5s4NYdeuXVbHqrfcbjef\nfOKgrCwFgOzsS3n99d0WpxLxHbrGTqSemDDhFjZunM3337ckJCSPQYOa06pVq1Paxu7dAL8fXdiz\nx2Dfvn2kpKR4N6wXmW43Ga+9TvrTz1QNNNzkxj60HDgAR2ioxelOLDfXDvz+WKWcnAQyM7NO+b+d\nVLDZbNjthz+P1273WJRGxPeo2InUE0FBQbz33iiKiooICgqq1hhRp58eynvv7cbjqbiGtW3bn0hI\nON/bUb2mdHc62yZOpGDNWgCCmjYlcfxDRHXrZnGyk3fNNW356KMvyMnpDrg566z/0qnTYKtj1Vt2\nu51bb41m+vQvyc/vTMuWSxk4UI90E/mNbp4QaUA8Hg/Dhz/Pd9+ZREQU8/jjPTjnnI5Wxzqqg8s+\nY/ujk/EUFQEQe3VvWo0YTkA9HGj41Vc/44MPthMaWsYTT/ShWbMmVkeq97766gfWrEmjZ8+udOiQ\nbHUckVpRnZsnVOxExKd4SkvZNWs2mf95B4CAmBjajBtLTPdLLE4mGRmZ3Hrry+zYEU2zZnk888zf\n6NAhyepYIn6rOsVOp2JFxGeU7N7N1jFjKdq0CYDIc84hafIkguLiLE4mAPfe+wrLlg0FHPz6q0nf\nvjP58svhVscSkUOo2ImIJdLT97By5S+cdVYK7dq1Jfvz/7J94iMVjwSz2Wh+5x20uOdubHrepM/Y\nuzcC+O1pHjb27o22Mo6IHIU+MUWkzi1Z8i333edk587uNI39ged6zaL5hu8BCGjUiKRJE4k+33dv\n6mioEhMLWbWqFAgGPLRpk2N1JBE5goqdiNS56dNXs3Nnf5oF7eXx+I9ovmE9ABGdzyR58qMENW1q\ncUI5moUL78Q0n2b79nCaNSvg2Wf/ZXUkETmCip2I1LmysiDOj/qWSUkPER2QB0DTW/9Fy373Y9ep\nV58VFRXF228PsTqGiByHPkFFpE6Zpsl9xmZSihbisJnkuiL4tn03Hhw00OpoIiL1noqdiNQZT3k5\nO5+YQvufvgAbHAhtzJYeNzDuwbuPunxpaSkej4fQevCECRERX6BiJyJ1ojw7m7RRo6ueItHoL905\na+IEeoaP3Y2aAAAgAElEQVSFHXX5ESNe4M03wTQdXHVVPgsW9KcaQzqJiDQoKnYiUuuKNm9my7AR\nlO3dC0Dzu+6kRd97sdntR13+k0++Zv780yku7grAyy9v5dxzP+Duu6+ts8wiIvXR0T9VRUS8JPuL\nL9l0592U7d2LLTiYpEcn0fL++45Z6gDWrdtBcfGfqqbLy5NwOvfXRVwRkXpNxU5EaoVpmux98SXS\nRo7CU1xMYFwcHRY8S+yVPU+47l//egEJCe9XTTdp8jHXXtu1NuOKiPgFnYoVEa/zlJez/ZFHObhk\nCQBhnTqSMn0aQU2anNT6HToks3Dhfp58cj6maef22w0uvLBzbUYWEfELKnYi4lXuwkLSRo0h77vv\nAIi54goSxz+EIyTklLbTs+d59Ox5Xm1EFBHxWyp2IuI15QcPsnnwEIo2bgKoeN7r/ffpblYRkTqi\nYiciXlGyezebBwyidPdusNloPXIETW7sY3UsEZEGRcVORGqsaNOvOAcNxnXwILbAQJImTaTx5Zdb\nHUtEpMHRXbEiUiN533/Ppr734Tp4EEd4OO3mzqk3pW7DhjQuuWQGnTo9R+/e0zl4MNvqSCIiNaIj\ndiJSbQeXfca2h8djulwExsbS7sk5hLU3rI510u655z2++WY4YGPjxnL69p3P228PtjqWiEi1qdiJ\nSLVkvPEmu2bMBNMkuHUrjLlPEtyypdWxTpppmuzd2wj47caOQPbsOfrjzURE6gudihWRU2KaJnsW\nPMeu6TPANAnr1IkOzy+sV6UOwGaz0apVNmBWzimhTZtiKyOJiNSYjtiJyEkzTZP0+U+z78WXAIg6\n71zaTp2CI6x+Hul6+eWbuf/+2ezfH0HbtoUsWHC31ZFERGpExU5EToppmux+ci4Z/34FgEYXX0zy\nE49hDwqyOFn1JSYmsGTJUKtjiIh4jYqdiJyQaZrsmjGT/W+8CUDMpZeSNHkS9sBAi5OJiMihVOxE\n5LhMj4edU6aS+c67ADTu0YOkRyZgC9DHh4iIr9Ens4gck+l2s2PyY2R98CEAsb2uInH8w9gcDouT\niYjI0ajYichRmS4X2x+ZxIFPlgAQd+1faTP2AZU6EREfpmInIn/gcbnY/vAEDi5bBkD832+g9aiR\n2OwaIUlExJep2InIYUyXi23jHiQ79XMAmtx8E62GDcVms51gTRERsZqKnYhUMT0etk2cVFXqmv7r\nnyQMGqhSJyJST+i8iogAFUOa7Hh8CgeXVFxT1/SW/1OpExGpZ1TsRKRinLqZs8h67z0A4m/4GwlD\nBqvUiYjUMyp2IsKep59h/+tvABDbuxetR49SqRMRqYe8co2dYRiXA48CfwJKgLecTmd/b2xbRGrX\n3hdfYu8LLwIQc/llJD704HHvfjVNkylT3uR//8sjNracmTP/SXR0dF3FFRGR46hxsTMMozvwNnAX\n8CFgo6LgiYiPy3j9DdKfmg9A9EUXkjTpEb74+iceeeQbiotDuOgiG9Om3XXY0btJk17j0Ue7UV7e\nDihl+/aZpKY+YNFPICIih/LGEbvHgaedTue7h8xb44Xtikgtynz/fXbNmAlAZLeutJ3yBHmFhfTt\n+wObNw8EYPXqbTRr9jYjRtxYtd7KlYWVpQ4gmPXrk8jLyyMqKqqufwQRETlCjYqdYRjhQFdghWEY\nPwKtgXXACKfT+eMJ1o0FYo+Y3bImeUTk5BxYspQdkx8HIOLMM0mZMR17cDCbf17H5s1dqpYrL09i\n7drlh60bFVUCePjtEt3o6CzCw8PrKrqIiBxHTW+eiKncxk3AbUALYBnwiWEYJ7roZiDw6xGvz2uY\nR0ROIOerr9k2YSKYJmGdOpIyZxaO0FAAkpLa0Lr1L1XL2mwZpKSEHLb+zJl/p2vXaURFLSU5+VnG\njWuPQ48ZExHxCTW67a2yvGUDjzqdzocPmX8Q+D+n07n0OOse64jd56mpqSQkJNQkmogcRcFPP/Nr\nv/6YpaWEpqTQ/tmnCTjixoe33/6Cxx//haKiEM4/v5iFC/v/obi5XC727NlDbGzsUY/WLVjwMfPm\nbae8PJDLLvMwd25f3WUrInKKbNX44KzRqVin05lrGMb2Q+cZhmEDzMrX8dY9ABw4Yt2ymuQRkWMr\n3rqVzUOHYZaWEtS8Oe3mzvlDqQPo06c7ffp0P+62AgICaN269VHf27x5Kw8+WEpmZsWN8Wlp22jf\n/l0GDryhxj+DiIgcnzfGsZsP3GEYRkfDMAKAkVQMefKNF7YtIl5QlpGBc+Ag3Hl5BERHY8x9kqD4\n+FrZ1+rVTjIzD79Ob/36A8dZQ0REvKXGxc7pdE4HXqDi+rhMoCdwldPpzK/ptkWk5lx5eTgHDqY8\nYz/2kBBS5swiJLFNre3vggtOIyHh66rpsLCfOP/8VrW2PxER+Z1XBih2Op3jgfHe2JaIeI+npIQt\nw4ZTsnUrOBy0nfIEEaedVqv7bNUqgblzWzNr1lOUlQXRq1cYt912S63uU0REKnil2ImI7zFdLraO\ne5CCtT8BkPjQOKIvvKBO9n3ddX/muuv+XCf7EhGR3+lZsSJ+yDRNdkyZRs6XXwHQckB/4q6+2uJU\nIiJS21TsRPzQngXPkfXeewA0uekfNLvtVosTiYhIXVCxE/Ezme+8y97nFgIQc8UVtBo2VGPIiYg0\nECp2In4kd+U37JgyFYDIrl1Imjgem11/zUVEGgp94ov4iSKnk7QHxoLHQ2hKCinTpmIPCrI6loiI\n1CEVOxEfkp6ezooV/yM3N/eU1ivLzGTz0GF4iooIjI0lZfZMHBERtZRSRER8lYqdiI+YN+8Dzjln\nJX/+cxjnn7+I1as3ntR67uJitgwdXjEAcXAwKbNmENysWS2nFRERX6RiJ+ID3G43c+bsIiPjRuAM\nNm4cyPjxy0+4nul2s23cQxRt2gQ2G0mTJxHeqVPtBxYREZ+kYifiA8rLyykujjxsXmlpyAnX2zV7\nDjlfVYxVlzBkMDHdu9dGPBERqSdU7ER8QEhICN26ZQDZAISFreGKK6KPu87+t95m/+tvABD/9xto\n+n8313ZMERHxcXqkmIiPeOONwUyY8Crp6eVcfHECd9114zGXzVmxkp3TZwAQdcH5tB4xXGPViYiI\nip2IrwgKCuKxx+444XJFTidbx46rGNakXQptH5uMLUB/lUVERKdiReqVssxMNg+pHNYkLo52s2Zp\nWBMREamiYidST3hKStgyfCTl+/djDwkhZdYMgpo1tTqWiIj4EBU7kXrANE22PzqZog0bAEh6ZCLh\nHTv+YbnU1B8477w5dOr0HDffPIvS0tK6jioiIhbShTki9cC+lxdxcOmnALS4ry8xl/7lD8uUlpYy\ncOA3bNw4GICNG3Np2nQRs2ffU6dZRUTEOjpiJ+Ljcr76mvSn5gMQc8UVNL/rzqMut2/fPtLT2x8y\nJ5rt22s/n4iI+A4VOxEfVrwlja0PPgSmSVjHDiSOf+iYw5o0b96cNm0OfQxZJu3b66C8iEhDok99\nER9VnpPD5mGVd8DGxpIyfRqOkGM/jSIoKIiFCy9nzJg55OWFcdZZZUye3LcOE4uIiNVU7ER8kKe8\nnLRRYyjbsxdbUBBtZ0wjqOmJ74Dt1u00Pv/8tDpIKCIivkinYkV8jGma7Jw6nYLVqwFIfHAcEaep\nrImIyImp2In4mMy33ibrvfcAaHbbrcT2usriRCIiUl+o2In4kLzvv2fnzFkARP/5Ilr2u9/iRCIi\nUp+o2In4iNL0dNIeGAtuNyHJySRPegSbw2F1LBERqUdU7ER8gLu4mC0jRuLOzcMRFUXKzOl6BqyI\niJwyFTsRi5mmyfZHJlG8eQvY7SQ/NpmQhASrY4mISD2kYidisX2L/k32Z8sBSBjQn+jzzrU4kYiI\n1FcqdiIWyv3226rHhTXu0YOm//qnxYlERKQ+U7ETsUjJ7t1sHfsgeDyEGu1o8/CDx3xcmIiIyMlQ\nsROxgLuoiLThI3Hn5xMQHX3Cx4WJiIicDBU7kTpmmibbJz5CcVpaxc0Sj08muEULq2OJiIgfULET\nqWP7XnqZ7NTPAUgYNJCobt0sTiQiIv5CxU6kDuWu/Ib0+U8D0PiqK2l6y/9ZnEhERPyJip1IHSnZ\ntYutDz4EpklY+/a0GTdWN0uIiIhXqdiJ1AF3cTFpI0ZV3CzRqBFtp0/VzRIiIuJ1KnYitcw0TXZM\nmnz4zRLNm1sdS0RE/JCKnUgt2//6GxxctgyAhIEDiOra1eJEIiLir1TsRGpR/o+r2TXnSQBiLr+M\npv+8xeJEIiLiz1TsRGpJWUYGaQ+MBbebkOQkEh/SkyVERKR2qdiJ1AJPWRlpox/AdfAgjvBwUqZO\nxREebnUsERHxcyp2IrVg1/QZFK5bB0DixAmEJLaxOJGIiDQEKnYiXpb5/mIy330PgOZ33UlM90ss\nTiQiIg2Fip2IFxWu38DOqdMAiDr/PFrce4/FiUREpCFRsRPxkvLsbNJGjcYsKyOoZQuSH52EzeGw\nOpaIiDQgKnYiXmC6XGwdO46yjAxswcGkTJ1KQHS01bFERKSBUbET8YL0+U+Tv+oHABLHPkBYe8Pi\nRCIi0hCp2InUUHbq5+xb9G8A4vv0IbZ3L4sTiYhIQ6ViJ1IDxdu2sW3iIwCEn3EGrYYNsTiRiIg0\nZCp2ItXkLiwkbeRoPEVFBMQ2pu2Ux7EHBlodS0REGjAVO5FqME2T7RMnUbJ9OzgctH38MYLi462O\nJSIiDZyKnUg1ZPz7FbI//xyAVoMHEXn22RYnEhERgQCrA4jUtgMHDvLYY+/gcpkMHNiTlJSaPd4r\nb9Uqds97CoDGPXrQ5OabvBFTRESkxlTsxK/l5eVxxRULWLNmOBDAkiXz+PTT60hKalWt7ZXty2Dr\nA+PA4yEkOZk2D47FZrN5N7SIiEg16VSs+LU330xlzZo7gUDAxubNA5g/f2m1tuUpKyNt9BhcOTk4\nwsNJmT4VR1iYV/OKiIjUhIqd+LWoqFBstvxD5hQTGlq9x3ztmj6DwvXrAUh6ZCIhrVt7IaGIiIj3\neK3YGYZhNwzjG8MwPIZhtPDWdkVq4u9/v4Jevd7CZlsPbOWCC2YxevQ/Tnk7WYs/IPPd9wBofucd\nNLrkYi8nFRERqTlvXmM3FCgETC9uU6RGHA4HixePYunSrykpKad37+GEhISc0jYKN2xgx5SpAESd\ndy4t+t5bG1FFRERqzCvFzjAMA7gfuAFY441tiniLw+Ggd+/u1Vq3PDubtJGjMcvKCGrRnORHJ2Fz\nVO9UroiISG2r8alYwzDswAvAcCC3xolEfITpcrF13IOUZWRgCw4mZepUAho1sjqWiIjIMXnjiN1g\nYI/T6VxsGEbiya5kGEYsEHvE7JZeyCPiFenznyb/+1UAJI59gLAO7S1OJCIicnw1KnaGYaQAw4Au\nR7x1MgN7DQTG12T/IrXl4PLl7Fv0bwCa3NiH2N69arzNsWNf4pNPSgkIcNGvXzJ33nlVjbcpIiJy\nqBqNrGoYxu3AM8Bv40nYgRggGxjndDqfOc66xzpi93lqaioJCQk1iSZSbcVbt7LxtjvwFBcTceaZ\nGM/Mxx4YWKNtvvDCx/Tvn0RJSScA4uPf46uvTqdDhxRvRBYRET9kq8YI+DU9FfsmsOyQ6VbAt8AV\nwK/HW9HpdB4ADhw6zzCMshrmEakRV0EBW0aMwlNcTGBcHMlTHq9xqQNYs2YPJSW9q6YzMy/g22+/\nU7ETERGvqlGxczqdxUDxb9OGYQRRMdzJPqfTWVjDbCJ1yvR42D5+AqU7d2ILCKDtlCcIiovzyra7\ndm1FaOgvFBefDkCzZiu48MKzvLJtERGR33j1WbFOp3M7oLEgpF7a99LL5Hz5FQCthg8j4swzvLbt\nW2+9ki1bFvHxx98SGFhO//7tMIxkr21fREQEaniNnbdV3lW7TdfYSV3L/eZbNg8eAqZJ7NW9SRz/\nMNW4tEFERMRrqnONnZ4VKw1eya5dbB33IJgmYe3b02bMaJU6ERGpl1TspEFzFxWxZfhI3Pn5BERH\n03baFOyn+MgxERERX+HVa+xE6hPTNNk+4RFKtm4Fh4PkJx4juEWLoy5bWFjICy98jN1u4847ryY0\nNLSO04qIiJyYip00WPtefInszz8HoNXgQUR17XrU5QoKCrj88if57rv7AA+vvz6Tzz4bpnInIiI+\nR6dixVJbt+5k1qzXWbJkRZ3uN2fFCtKfrhg/u/FVV9Hk5puOueyTT77Ld98NAhoDcaxc2Y9nn11c\nN0FFREROgYqd1Cq3201h4dGHNPzqq9Vcemkqw4Zdzd/+FsKQIc/VSaaSHTvY9uDDFTdLdOhA4rgH\njnuzhMvl4fCD2wGV80RERHyLip3Umuee+4SOHZ+hXbv36d17CsXFxYe9P2vWd+zYcQcQSUlJF95+\nO4T8/Pyjb8xL3JVPlnAXFBAQE0Pb6VNPeLPEoEHX0bnzbKAUKKFLl7n07XtNreYUERGpDl1jJ7Xi\nwIEDPPJIFrt39wdg794CHnjgFWbPvqdqGY/n8N8r3O4g3G53rWUyPR62jZ9AybZtFTdLPP4Ywc2a\nnXC9Ro0a8fnnfZkz5zVsNhg6dACRkZG1llNERKS6VOykVuzbt4+MjEOfgxpBRsbhy9xxR0e++24x\nGRl/xeHYzRVX7KFRo0a1lmnv8y/8/mSJoUOI6nLOSa8bExPDhAl31FY0ERERr1Cxk1qRnJxMp05P\n89NP5wM2QkLWc8EF8Yctc911F9OkyU+8++5CEhNj6NdvcK3lyfnyK/Y8uwCA2Kt70+QfNx7+fk4O\nW7akkZSUSGxsbK3lEBERqU0+Nby+HinmXzZt2sqYMR9TXBxC9+6RPPDAse88rU3FW7ey8Y678BQW\nEtapIx2eW4A9OLjq/c8++55+/daSlnYObdr8xKxZ7bjuuj9bklVEROQ31XmkmIqd+DVXTg4bb7uD\n0vR0Aho3ptOilwlq1vSwZf7857msWDGwarpr17l8//3AIzclIiJSp/SsWJFDeFwu0sY8QGl6OrbA\nQFKmTf1DqQMoLj58oOGiIg08LCIi9ZOKnfitXTNmkv/DjwC0GfcAEWeecdTlLrzQQ0DATgDs9r2c\nd15JtfbncrnIyMio1Tt7RUREjkc3T4hf2v+f/5D59n8AaPrPW4i7+upjLjt79j20aPEWv/zyKYYR\nyrhx95/y/lJTf2Dw4JXs3ZtEmza/smjRdZx2Wrtq5xcREakOXWMnfifvhx9w9h8IbjdRF1xAu1kz\nsDkctbrPbt1ms2rVkMopkx495vDpp0OOu46IiMjx6Bo7afBKdu8mbfQYcLsJSUoi+bFHa73UAeTk\nhB8yZSMnJ6zW9ykiInIkFTvxG+6CArYMG447Nw9HVBQpM6cTEBFRJ/v+059ygd+eiZtF586uOtmv\niIjIoXSNnfgF0+1m60MPU7K14nFhbZ94jJBWreps/6++2o9hwxaRnh5A+/Y2Hn/8nhOvJCIi4mUq\nduIX0p+aT+7XKwBoPXwYUd261en+w8LCeOaZ++p0nyIiIkfSqVip97I++ph9i/4NQPwNfyO+z98t\nTiQiImINFTup1/J/XM2ORycDEHnOObQaOYJq3EQkIiLiF1TspN4q2b6DLSNHYbpcBLduTdupT2AP\n0NUFIiLScKnYSb1Unp3N5sFDcOflERAdTbs5swiIjrY6loiIiKVU7KTe8ZSWsmX4yKpnwLadMb1O\n74AVERHxVSp2Uq+YHg/bJjxC4c8/A5A4/mEiO59pcSoRERHfoGIn9cqeZ54l+7PPAGhxX19ir+xp\ncSIRERHfoWIn9UbWBx+y94UXAYi9ujfN77rT4kQiIiK+RcVO6oW8VavYMfkxoGJYkzbjxmpYExER\nkSOo2InPK962jbSRozHdbkLatKHttCnYAwOtjiUiIuJzVOzEp5VlZVUMa1JQQEBMDO3mzCYgKsrq\nWCIiIj5JxU58lquggM2DBlO2Zy+24GBSpk8jOKGl1bFERER8loqd+CRPWRlpw0dS7NwMdjvJkx8l\n4swzrI4lIiLi01TsxOeYbjfbHh5P/o8/AtDmgTHEdL/E4lQiIiK+T8VOfIppmuyaMZPs5akAtOh7\nL/HXX2dxKhERkfpBxU58yr4XX2L/W28DEH/D32h+910WJxIREak/VOzEZ2Qt/oD0+U8D0Ogvf6H1\nqJEaq05EROQUqNiJT8j5+mu2P/Y4ABFnn0Xyo49gczgsTiUiIlK/qNiJ5Qp+/pmtY8aC201oSgop\nM6ZjDw62OpaIiEi9o2InlireupXNQ4fhKS0lqFkz2s2dQ0BkpNWxRERE6iUVO7FMya5dOPsNwJ2b\nR0B0NO3mPUlQfLzVsUREROotFTuxROnevTjv7095Vhb28HBS5swmNDHR6lgiIiL1moqd1LmyrCyc\n/QZQtm8f9uBg2s2eScRpf7I6loiISL2nYid1qjw7G2e//pTu2oUtMJC2M6YTedZZVscSERHxCyp2\nUmdc+flsHjCIkq3bsDkctH3icaLPO9fqWCIiIn5DxU7qhLuwkM2DBlP0669gt5M06REaXXKx1bFE\nRET8ioqd1Dp3SQlbho2g8Jd1ACQ+/CCNe1xhcSoRERH/o2IntcpTVkbayFHk//gjAK1HjyLu6qst\nTiUiIuKfVOyk1njKytj6wFjyvv0fAAmDB9Gkz98tTiUiIuK/AqwOIP7JU1pK2ugx5K5YCUCLe++h\n2b/+aXEqERER/6ZiJ0dVWFjIAw+8yoEDNi69tCV33dXrpNd1l5SQNmIkef/7DoDm99xN83vurq2o\nIiIiUknFroHKycnhzTc/Jy4ukuuvvwy7/fez8qZpcu21c0hNHQKEsXjxDxQVvc/AgdedcLvu4mK2\nDB1G/g8V19S17Hc/ze+8o7Z+DBERETmErrFrgPbs2cfFFz/HffddzD/+0Zp//GMGpmlWvZ+Zmcna\ntR2BMAAKC7uwbFnmCbfrLixk88BBVaUuYcjgGpe6115bTpcu8zjjjAUMGvTsYTlFRETkcDpi1wBN\nnryYX34ZBjhwu+N4771L+O67HznvvC4AREZGEhGRxYEDv63hITS05LjbdOXns3nQ4KohTVqNGE7T\nm/5Ro5y7d+9m5MhM9uwZAMCmTdto2/ZdBg++4ff9ulyMHv0S69aZxMeXMG/ev2jUqFGN9isiIlJf\nqdg1QG63jUMP1rrdoZSUFFRNh4aGMnRoPFOmvE5mZhKnn76CKVOOXdJcubk4BwykaOMmANo8MIb4\nG/5W45xr125mz54uVdPl5UmsW7f8sGWGDXuBuXOvA5oAZezfP5tly0bVeN8iIiL1kU7FNkADBvyF\n5OTnABPIp3v3D7jwwi6HLTN48HWsWXMpq1eHs3Jlf5KSWh11W+XZ2fx6f7+KUmezkfjwQ14pdQDn\nnNOBhIT/VU0HBTk566z4w5b56ScbFaUOIIhff43F7XZ7Zf8iIiL1TY2O2BmGMQXoDbQCCoCPgdFO\npzPbC9mklpx2Wjs+/tjB888vJDIykJEjhxEYGPiH5Zo2bUrTpk2PuZ2yrCyc/QZQsnVrxWPCJown\nttdVXsvZvHlznnyyDdOmzaOsLJhLL7Vz//13HrZMTEwR4OG331FiYvJwOBxeyyAiIlKf2GqysmEY\nk4G3gHVADLAIKHc6nddWc3uJwLbU1FQSEhJqEk1qWcmOHTgHDqJsz15wOEie9IgljwnbsSOdm276\nN9u2JREXt5cZM86nZ89z6zyHiIiIt9lstlPuaTUqdkcyDONK4E2n0xldzfUTUbHzeQXr1rNlyFBc\nOTnYgoNJnvwoMd0vsSyPaZrk5eURGRl52LAtIiIi9Vl1ip23b564DFh7MgsahhELxB4xu6WX84iX\n5a78hrTRY/CUlOCIjCRl1gwiO3e2NJPNZiM6ulq/S4iIiPgVrxU7wzBuAPoCF5/kKgOB8d7av9S+\nrI8+ZsekRzHdbgKbNsF4cg6hbdtaHUtEREQqeaXYGYbRB3gGuMbpdJ7UETtgLvDaEfNaAp97I5N4\nj2ma7Fv0b9LnzgMgJCkJY+7/t3f3QVbV9x3H3wvLUxXkyVSeggJ+M5oR26IOmaaMkgRMStPOOJnG\noTZaBVqVRCQJODYSEgeIEHW047RWEzOaUtuaxiRSQ0dtJ7H+kUAiccb6FeRJU41BUILyILv949y1\nuGUJu/dmz97D+zWzs+zZe8985jeXPZ/7O79z7h0MPK3rCyskSVLvq7vYRcQVwBpgTmY+dbzPy8xd\nwK4jt0XEwXrzqLHa29rYedvt/GLtPwJw0tSpnHnbV2n11KckSX1Ovbc7+TRwEzArMzc0JpL6iraD\nB9n2xS/x2vr1AAyfMYNJK26m3+DBJSeTJElHU++M3e3AIeA/IqJjW3tmDqtzvyrZ23v2sGXJDezd\nUPT10X/yx0xcuoSWVj+sRJKkvqquo3Rmem+JCnrrhRfYvGgxB156CYAxV13J2AXz6cFV15IkqRc5\n/aJ32fPDJ3nhxr+mbd8+WgYMYOKNNzB6zpyyY0mSpONgsRNQXPn6ygPf5MU77oT2dlpHjmTKmls4\neerUsqNJkqTjZLETbQcPsn3FSnZ97xEAhkQw5dY1DDrttJKTSZKk7rDYneAO7drF5s8tYd+mTQCM\nmDmT05cvo/+QISUnkyRJ3WWxO4G9+Vyy+frFHHzlFQDGzLuKsfOuosXPW5UkqSlZ7E5Qux5Zx/aV\nq2jbv5+WQYM4Y9lNjJz1kbJjSZKkOljsTjBt+/ezY/UafvnwdwAYcOqpTPnqak46++ySk0mSpHpZ\n7E4g+7dtZ8vSG3hr82YAhl5wAZO+vJwBo0aVnEySJDWCxe4EsevR77N9xUra3nwTWloYO38eY/7i\nClr69+/xPrdvf4m1ax/nve8dzaWXXuwNjCVJKpnFruLaDhxg56238epD3wKgddRIJt38ZYadf35d\n+3366ee45JIn2LLlclpbd7Ju3e3cf/91ljtJkkrk5Y8Vtn/nTp694sp3St3Q86bx/m8+UHepA1i9\n+kii3AEAAAj0SURBVAm2bFkADObtt8/k4YfPYuvWrXXvV5Ik9ZwzdhW1d+NGnl+0mLZ9+6Clpfi8\n16uurOvU67u11L4K7e2ttLW1NWjfkiSpJ5yxq6hXH/oWbfv20TpiBGfeeQfjFsxvYKmDa6/9ABMn\n3ge00dLyP8yevZHJkyc3bP+SJKn7nLGrqLF/uYAhEYz62EcZeOqpDd//9OlTWbfuJB544GuMGTOM\nq69e7Po6SZJK1qeOxBFxOrD1scceY/z48WXHkSRJKk1LD2ZMPBUrSZJUERY7SZKkirDYSZIkVYTF\nTpIkqSIsdpIkSRVhsZMkSaoIi50kSVJFWOwkSZIqwmInSZJUERY7SZKkirDYSZIkVYTFTpIkqSIs\ndpIkSRVhsZMkSaqI1rIDqPHa29u5997v8uyzrzBr1jnMnj297EiSJKkXOGNXQQsX/h3XXHM2t946\nj0svfZN77nmk7EiSJKkXWOwq5vDhw6xb15+DB6cAsHv3TNaufbHkVJIkqTdY7CqmpaWFfv0Ov2tb\n558lSVI1Wewqpl+/flx22VCGDv1P4A3GjXuQhQvPKTuWJEnqBV48UUHLls3loot+zMaN65g9+3zO\nOmty2ZEkSVIvsNhV1IwZ5zFjxnllx5AkSb3IU7GSJEkVYbGTJEmqCIudJElSRVjsJEmSKsJiJ0mS\nVBEWO0mSpIqw2EmSJFWExU6SJKkiLHaSJEkVYbGTJEmqCIudJElSRVjsJEmSKsJiJ0mSVBEWO0mS\npIqw2EmSJFWExU6SJKkiLHaSJEkVYbGTJEmqCIudJElSRVjsJEmSKqK13h1ERH9gFfApYDCwHliQ\nmbvq3bckSZKOXyNm7JYCHwcuAMbXtt3fgP1KkiSpGxpR7OYDqzJzW2a+AXweuDgiJjRg35IkSTpO\ndRW7iBgOTAA2dGzLzBeAN4Bz64smSZKk7qh3jd3Q2vfXO23fAww71hMjYhQwqtPmcQAvv/xynbEk\nSZKaW0QMz8w93XlOvcVub+37KZ22D6eYtTuWhcCyo2x/fe7cuZ33J0mSdKL5dkRc0p0LUusqdpm5\nJyJ2ANOATQARMZlitm7Tr3n6ncA/dNp2OvB9YCawtZ5s4gzgcRzLRnAsG8exbBzHsnEcy8ZxLBun\nYyxHAb1T7GruBpZExBPAbuAW4NHM3HGsJ9Xa57uCRkTHP1/KzG0NyHbCioiBtX86lnVyLBvHsWwc\nx7JxHMvGcSwb54ix7JZGFLtVwAjgR8AgivvY/VkD9itJkqRuqLvYZWYb8LnalyRJkkriR4pJkiRV\nRF8rdruA5XRjkaC65Fg2jmPZOI5l4ziWjeNYNo5j2TiOpSRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJ\nkiRJkiRJkiRJkiRJ0gmlpewARxMRA4E7gYuA04DdwIPAFzLzQJnZmkFE9AdWAZ8CBgPrgQWZ6ceS\ndENEfAX4Q2AC8CvgEWBJZu4uNViTi4h+wA+B6cD4zPx5yZGaUkR8GLgZeD+wH/inzLym3FTNJyJG\nAbcDHwEGAj8BFmXmplKD9XER8UngGmAq8FuZOaDT7/8cWEZxDP8ZcHVmbuz1oE3gWGNZG8cFwFnA\nYeBHwOcz85mu9tfXPiu2QyvwKjAHOAX4A2AmcEuZoZrIUuDjwAXA+Nq2+8uL07TeBuYCI4FzKcby\nvjIDVcQiYB/QXnaQZhURFwL/TPE3cSQwDrinzExN7A7gPcD7gN8Gfgx8r9REzeE14G+A6zr/IiI+\nCNxFUUiGAw8B6yJiaK8mbB5djiVwMnATxf/xccBGYH1EDOm9eL8hEbEgIp4uO0cziIjtEXHFET9P\nioi2iJhQZq5mFxEXR8TrZedoZlHYHBHn1l6TY8vO1Iwi4qmIWFF2jiqIiJ9FxLwjfn5f7bU5ssxc\nzSIiLoyIQ522fSMivtFp27ba7JO6cLSxPMpjBtden7/T1WP66ozd0XwY+GnZIfq6iBhOcepwQ8e2\nzHwBeINi1kk99yF8DfZY7RTs14DFgAW5hyLiJOB8YEBEbIiIVyPiiYiYVna2JvVt4E8jYnREDAbm\nAz/IzNdKztXMpnLEMajmp3gMaoQPUZzxeL6rB7T2XpZCRNwHHKu135yZN3V6znUUp2PP+w1Gq4qO\nqe7OB849wLBezlIZEXEJxWmFGWVnaWKfAX6emQ9HxOllh2liIyjelH8S+CjwHPBZilNdkZmW5u5Z\nBXwH+AXFGqYdwMdKTdT8huIxqOEiIqi9Oc7MfV09rowZu2uA0cf4WnnkgyNiEbAEmJmZL/Zu1Ka0\nt/b9lE7bh1PM2qmbIuITwN3AH2WmM3Y9EBFTgOuBhZ1+1Scv4OrjOv6Pfz0zn8nMQ5m5EhgAfKDE\nXM3q34H/pigdQ4AVwA8i4j2lpmpue/n/x6AROFPfYxFxNvA4sDoz7z7WY3t9xq7WMrtsmkeKiC8A\n84AZmdnltKP+T2buiYgdwDRgE0BETKb4o+VVXt1UW6u4BpiTmU+VnaeJfRA4FXimeNP5zpvKTRFx\nY2b+bWnJmkxmvh4R247cFhEtFBejeEFKN0TEaIqrsy/PzF/VNt9buyJ+OsVMnrrvaYpjEPDO6/N3\ngX8pLVETi4jfA/4NWJ6Zd/26x/d6sTteEbEa+ARwYW2NmI7f3cCSiHiC4lYxtwCPZuaOcmM1l4j4\nNMXVSLMys/N6EXXPgxS33ekwAXiK4hYTz5WSqLndBXwmItZSrLW5nuKWJ/9Vaqomk5m/jIidwLUR\nsRQ4SLFU6GR8I3xMtTWzA2tfRMQgoCUz9wN/Dzxau4DiSYplGAOAfy0pbp92rLGMiN+nuEr7s5l5\n7/Hsr0+eBomIicBW4ADFLSc6bMvMc8pJ1TxqL5KvAJcDgygOqPNdDNw9EdEGHKL4Y9+hPTNdJ1Kn\n2hq7LcAE72PXMxGxnGKh/2CKWyB477UeiIhzKd78TqOY7Hge+FJmfrfUYH1cRFxOsd4Lipnijlnj\nMzJzR0RcBnwRGENRkv8qM39SQtQ+7xhjOQn4OsXa7rc6Pe3izHyytzJKkiRJkiRJkiRJkiRJkiRJ\nkiRJkiRJkiRJkiRJkiRJkqQ+7n8B3R2U9WecKa0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f65c6afabe0>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can also get confidence intervals for the parameter values from the `cov` return value. But if you need to work with confidence interals you might prefer to work with the package [lmfit](http://lmfit.github.io/lmfit-py/) which is easier to use if you need more than the basics."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Real data - bacterial growth curves\n",
      "\n",
      "We will use growth curves of _E. coli_ bacteria. [This data](https://github.com/Py4Life/TAU2015/blob/master/Yoav_311214c_only_OD.csv) was generated by growing bacteria in a 96-well microtiter plate.\n",
      "\n",
      "![96-well plate](http://www.ddw-online.com/library/sid32/microplates.jpg)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "if not os.path.exists('Yoav_311214c_only_OD.csv'):\n",
      "    urllib.request.urlretrieve('https://raw.githubusercontent.com/Py4Life/TAU2015/master/Yoav_311214c_only_OD.csv', 'Yoav_311214c_only_OD.csv')\n",
      "df = pd.read_csv('Yoav_311214c_only_OD.csv')\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Cycle Nr.</th>\n",
        "      <th>Time [s]</th>\n",
        "      <th>Temp. [\u00b0C]</th>\n",
        "      <th>A1</th>\n",
        "      <th>A2</th>\n",
        "      <th>A3</th>\n",
        "      <th>A4</th>\n",
        "      <th>A5</th>\n",
        "      <th>A6</th>\n",
        "      <th>A7</th>\n",
        "      <th>...</th>\n",
        "      <th>H4</th>\n",
        "      <th>H5</th>\n",
        "      <th>H6</th>\n",
        "      <th>H7</th>\n",
        "      <th>H8</th>\n",
        "      <th>H9</th>\n",
        "      <th>H10</th>\n",
        "      <th>H11</th>\n",
        "      <th>H12</th>\n",
        "      <th>Time</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1</td>\n",
        "      <td>    0.0</td>\n",
        "      <td> 37.2</td>\n",
        "      <td> 0.1128</td>\n",
        "      <td> 0.1118</td>\n",
        "      <td> 0.1186</td>\n",
        "      <td> 0.1213</td>\n",
        "      <td> 0.1131</td>\n",
        "      <td> 0.1111</td>\n",
        "      <td> 0.1178</td>\n",
        "      <td>...</td>\n",
        "      <td> 0.1240</td>\n",
        "      <td> 0.1352</td>\n",
        "      <td> 0.1266</td>\n",
        "      <td> 0.1147</td>\n",
        "      <td> 0.1157</td>\n",
        "      <td> 0.1084</td>\n",
        "      <td> 0.1177</td>\n",
        "      <td> 0.1217</td>\n",
        "      <td> 0.1110</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 2</td>\n",
        "      <td> 1136.9</td>\n",
        "      <td> 37.4</td>\n",
        "      <td> 0.1164</td>\n",
        "      <td> 0.1151</td>\n",
        "      <td> 0.1189</td>\n",
        "      <td> 0.1209</td>\n",
        "      <td> 0.1173</td>\n",
        "      <td> 0.1144</td>\n",
        "      <td> 0.1221</td>\n",
        "      <td>...</td>\n",
        "      <td> 0.1229</td>\n",
        "      <td> 0.1386</td>\n",
        "      <td> 0.1289</td>\n",
        "      <td> 0.1154</td>\n",
        "      <td> 0.1211</td>\n",
        "      <td> 0.1103</td>\n",
        "      <td> 0.1216</td>\n",
        "      <td> 0.1208</td>\n",
        "      <td> 0.1130</td>\n",
        "      <td> 0.315806</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 3</td>\n",
        "      <td> 2273.7</td>\n",
        "      <td> 37.3</td>\n",
        "      <td> 0.1221</td>\n",
        "      <td> 0.1260</td>\n",
        "      <td> 0.1242</td>\n",
        "      <td> 0.1251</td>\n",
        "      <td> 0.1247</td>\n",
        "      <td> 0.1222</td>\n",
        "      <td> 0.1312</td>\n",
        "      <td>...</td>\n",
        "      <td> 0.1350</td>\n",
        "      <td> 0.1431</td>\n",
        "      <td> 0.1373</td>\n",
        "      <td> 0.1219</td>\n",
        "      <td> 0.1258</td>\n",
        "      <td> 0.1175</td>\n",
        "      <td> 0.1276</td>\n",
        "      <td> 0.1408</td>\n",
        "      <td> 0.1080</td>\n",
        "      <td> 0.631583</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 4</td>\n",
        "      <td> 3410.5</td>\n",
        "      <td> 37.3</td>\n",
        "      <td> 0.1315</td>\n",
        "      <td> 0.1405</td>\n",
        "      <td> 0.1335</td>\n",
        "      <td> 0.1338</td>\n",
        "      <td> 0.1342</td>\n",
        "      <td> 0.1321</td>\n",
        "      <td> 0.1469</td>\n",
        "      <td>...</td>\n",
        "      <td> 0.1586</td>\n",
        "      <td> 0.1493</td>\n",
        "      <td> 0.1455</td>\n",
        "      <td> 0.1362</td>\n",
        "      <td> 0.1349</td>\n",
        "      <td> 0.1263</td>\n",
        "      <td> 0.1374</td>\n",
        "      <td> 0.1777</td>\n",
        "      <td> 0.1104</td>\n",
        "      <td> 0.947361</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 5</td>\n",
        "      <td> 4547.4</td>\n",
        "      <td> 36.9</td>\n",
        "      <td> 0.1451</td>\n",
        "      <td> 0.1464</td>\n",
        "      <td> 0.1467</td>\n",
        "      <td> 0.1470</td>\n",
        "      <td> 0.1486</td>\n",
        "      <td> 0.1465</td>\n",
        "      <td> 0.1584</td>\n",
        "      <td>...</td>\n",
        "      <td> 0.1500</td>\n",
        "      <td> 0.1622</td>\n",
        "      <td> 0.1593</td>\n",
        "      <td> 0.1481</td>\n",
        "      <td> 0.1477</td>\n",
        "      <td> 0.1385</td>\n",
        "      <td> 0.1554</td>\n",
        "      <td> 0.1537</td>\n",
        "      <td> 0.1089</td>\n",
        "      <td> 1.263167</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 100 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "   Cycle Nr.  Time [s]  Temp. [\u00b0C]      A1      A2      A3      A4      A5  \\\n",
        "0          1       0.0        37.2  0.1128  0.1118  0.1186  0.1213  0.1131   \n",
        "1          2    1136.9        37.4  0.1164  0.1151  0.1189  0.1209  0.1173   \n",
        "2          3    2273.7        37.3  0.1221  0.1260  0.1242  0.1251  0.1247   \n",
        "3          4    3410.5        37.3  0.1315  0.1405  0.1335  0.1338  0.1342   \n",
        "4          5    4547.4        36.9  0.1451  0.1464  0.1467  0.1470  0.1486   \n",
        "\n",
        "       A6      A7   ...        H4      H5      H6      H7      H8      H9  \\\n",
        "0  0.1111  0.1178   ...    0.1240  0.1352  0.1266  0.1147  0.1157  0.1084   \n",
        "1  0.1144  0.1221   ...    0.1229  0.1386  0.1289  0.1154  0.1211  0.1103   \n",
        "2  0.1222  0.1312   ...    0.1350  0.1431  0.1373  0.1219  0.1258  0.1175   \n",
        "3  0.1321  0.1469   ...    0.1586  0.1493  0.1455  0.1362  0.1349  0.1263   \n",
        "4  0.1465  0.1584   ...    0.1500  0.1622  0.1593  0.1481  0.1477  0.1385   \n",
        "\n",
        "      H10     H11     H12      Time  \n",
        "0  0.1177  0.1217  0.1110  0.000000  \n",
        "1  0.1216  0.1208  0.1130  0.315806  \n",
        "2  0.1276  0.1408  0.1080  0.631583  \n",
        "3  0.1374  0.1777  0.1104  0.947361  \n",
        "4  0.1554  0.1537  0.1089  1.263167  \n",
        "\n",
        "[5 rows x 100 columns]"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We don't need the `Time [s]` column (we got `Time` in hours) and we don't need `Temp. [\u00b0C]`, so we drop these columns.\n",
      "\n",
      "Then we [melt](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.melt.html) the data. That means that we transform our data from a matrix format (one row per timepoint, one column per well + columns for other variables such as time) into a data frame format (one row for each measurement, with one column for each measurement variable). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = df.drop(axis=1, labels=['Time [s]', 'Temp. [\u00b0C]'])\n",
      "df = pd.melt(df, id_vars=('Time','Cycle Nr.'), var_name='Well', value_name='OD')\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Time</th>\n",
        "      <th>Cycle Nr.</th>\n",
        "      <th>Well</th>\n",
        "      <th>OD</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 1</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1128</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 0.315806</td>\n",
        "      <td> 2</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1164</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0.631583</td>\n",
        "      <td> 3</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1221</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 0.947361</td>\n",
        "      <td> 4</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1315</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1.263167</td>\n",
        "      <td> 5</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1451</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "       Time  Cycle Nr. Well      OD\n",
        "0  0.000000          1   A1  0.1128\n",
        "1  0.315806          2   A1  0.1164\n",
        "2  0.631583          3   A1  0.1221\n",
        "3  0.947361          4   A1  0.1315\n",
        "4  1.263167          5   A1  0.1451"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's add a column for the plate row (A - H) and the plate columns (1 - 12). We will use a [list comprehension](http://python-3-patterns-idioms-test.readthedocs.org/en/latest/Comprehensions.html) for that:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def well2row(well):\n",
      "    return well[0]\n",
      "def well2col(well):\n",
      "    return int(well[1:])\n",
      "df['Row'] = [well2row(x) for x in df.Well]\n",
      "df['Col'] = [well2col(x) for x in df.Well]\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Time</th>\n",
        "      <th>Cycle Nr.</th>\n",
        "      <th>Well</th>\n",
        "      <th>OD</th>\n",
        "      <th>Row</th>\n",
        "      <th>Col</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 1</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1128</td>\n",
        "      <td> A</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 0.315806</td>\n",
        "      <td> 2</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1164</td>\n",
        "      <td> A</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0.631583</td>\n",
        "      <td> 3</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1221</td>\n",
        "      <td> A</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 0.947361</td>\n",
        "      <td> 4</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1315</td>\n",
        "      <td> A</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1.263167</td>\n",
        "      <td> 5</td>\n",
        "      <td> A1</td>\n",
        "      <td> 0.1451</td>\n",
        "      <td> A</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "       Time  Cycle Nr. Well      OD Row  Col\n",
        "0  0.000000          1   A1  0.1128   A    1\n",
        "1  0.315806          2   A1  0.1164   A    1\n",
        "2  0.631583          3   A1  0.1221   A    1\n",
        "3  0.947361          4   A1  0.1315   A    1\n",
        "4  1.263167          5   A1  0.1451   A    1"
       ]
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     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally the data is **prepared** and we are ready to explore it.\n",
      "Let's start by plotting the OD over time curve of every well - just to make sure we know what we have in our hands.\n",
      "\n",
      "We use `seaborn.FacetGrid` which allows us to easily-ish make faceted plots. We need to specific the DataFrame columns on which we want to facet (these are the `Col` and `Row` we just created) and we can specify a bunch of styling options too. `FacetGrid` will break the data into smaller data sets according to our instructions. We can also specify which column controls the `hue` (color) of the plots.\n",
      "\n",
      "Then we can `map` a function to each of the facets. We give the function and then the columns that should be used as the function arguments."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g = sns.FacetGrid(df, col='Col', row='Row', hue='Well', sharex=True, sharey=True, size=0.75,\n",
      "                      aspect=12./8, despine=True, margin_titles=True)\n",
      "g.map(plt.plot, 'Time', 'OD')\n",
      "plt.locator_params(nbins=4) # 4 ticks is enough\n",
      "g.set_axis_labels('','')    # remove facets axis labels\n",
      "g.fig.text(0.5, 0, 'Time', size='x-large') # xlabel\n",
      "g.fig.text(-0.01, 0.5, 'OD', size='x-large', rotation='vertical') # ylabel\n",
      "g.fig.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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s4L4Yk7n9Qa31nwqpqFxp/3OdEVJX32pC2B0H55jD8Jx8VMGJHCzLglDAzDsv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\ni7N7UAi2BSyot5lTa9M022beLIfyqDUuzrNlmbn6hwmkB1CC0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JZfedEt97KiWX7lRbfc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\nCCGEEEIIIYQQQgghhBBCCCGEEFXg/wP90w8BuYSqqQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f65a62c8198>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You might notice that the curves in G12 and H12 are constant - these are the blank/control wells. Let's get rid of them:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "df = df[(df.Well != 'G12') & (df.Well != 'H12')]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": null
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to fit a logistic curve to the data we need to calculate the average curve. This is easy (once you learn how to do it) in _pandas_. The idea is: we _split_ the data by one or more columns. Rows with the same values in these columns will be _grouped_ together. We then _apply_ an aggregation to these groups, meaning we make a single row out of each group. We then _combine_ the rows back together into a single data frame.\n",
      "\n",
      "This strategy is known as _split-apply_combine_ and it is a very powerful strategy to work with data frames. One of it's powers is that it easily extends to parallel computing because the _apply_ part can be done in parallel over the different groups.\n",
      "\n",
      "Using [_pandas_](http://pandas.pydata.org/pandas-docs/stable/groupby.html) we will split using the `groupby` method; we will aggregate using `mean` (for general aggregations use `aggregate`); we will then resetthe indices (which were lost during the aggregation) with `reset_index`.\n",
      "\n",
      "We want the mean OD value for each time point so we group by `Time` and aggregate with `mean`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "grouped = df.groupby('Time')\n",
      "aggregated = grouped.OD.mean().reset_index()\n",
      "aggregated.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>Time</th>\n",
        "      <th>OD</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.115260</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 0.315806</td>\n",
        "      <td> 0.118860</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0.631583</td>\n",
        "      <td> 0.125469</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 0.947361</td>\n",
        "      <td> 0.135600</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1.263167</td>\n",
        "      <td> 0.149310</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "       Time        OD\n",
        "0  0.000000  0.115260\n",
        "1  0.315806  0.118860\n",
        "2  0.631583  0.125469\n",
        "3  0.947361  0.135600\n",
        "4  1.263167  0.149310"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's plot:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = aggregated.Time\n",
      "N = aggregated.OD\n",
      "\n",
      "plt.scatter(t, N)\n",
      "plt.xlabel('Time')\n",
      "plt.ylabel('Mean OD')\n",
      "plt.axvline(x=10, color='gray')\n",
      "sns.despine()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mAt4kV5IkKY9SjTyGEFoCBwGdyQS4qcAzMcZFVdxfP+CqGOP07OsOBqaEEDrF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\n8H3gn8CWMcYv8lyOJFWrenl7QknaVCG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       "text": [
        "<matplotlib.figure.Figure at 0x7f65a6d05a90>"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You might notice that after about 10 hours the population size starts to decrease. This is an artifact of the experiments, due to the wells starting to dry out. Let's drop this data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = N[t<10]\n",
      "t = t[t<10]\n",
      "\n",
      "plt.scatter(t, N)\n",
      "plt.xlabel('Time')\n",
      "plt.ylabel('Mean OD')\n",
      "sns.despine()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Rc0+E6XIiYhjwfF1dHbW1tXmXI3Vqjz32NJ/85HO88canAejX7xF+8pNlHH30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\nkiRJkiRJkiRJkiRJkiRJkiRJUmf3//G5m6pKrUHgAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f65a603e1d0>"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, finally, to the fitting (80% is data preparation!):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "popt, cov = curve_fit(logistic, t, N, (1., N.max(), N.min()))\n",
      "N0, r, K = popt\n",
      "print('N0=%.3f, r=%.6f, K=%.3f' % (N0, r, K))\n",
      "\n",
      "plt.scatter(t, N)\n",
      "plt.plot(t, logistic(t, N0, r, K))\n",
      "plt.xlabel('Time')\n",
      "plt.ylabel('OD')\n",
      "sns.despine();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "N0=0.081, r=0.601459, K=0.601\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PMAXoB4QBnwIDLcvKrmG/+4C5wBjLsibVelARaRRyf/yRlMfHgG0T0bUrSTOm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\n5/ai45MT9PhAERGRAFBxlMPi9Xq55pr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SFw9VS1JzDAHOy8z/BYiIm4FrgamZ+Xit7SZg\nQbf7XApck5mLaz8/FxGzgP+JiFmZ+Vrzypckg6MkNcu2rtBY83Ltdnld2/iIGFZbJ3kUcHREzO7W\npw3oBA4HDI6SmsrgKEnN0VH3cydAZnbUt/HWMqI24ArgGz083ks9tEnSLmVwlKTd1zLg3Zn5XNWF\nSBIYHCVpdzYPWBoRq4ElwBvAbwInZ+bMSiuTNCi5q1qSdk5nyfae+u2wLTMfAD5EsZP6YeAxikPX\nHqaWJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJKnV/T8ngIzXsLSBxgAAAABJRU5E\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f65a6cdfba8>"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can see that the fit is so-so. It's not that bad but it's not perfect, especially at the begining. This is because the logistic model probably isn't the best choice (although it's a common, simple choice)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Other functions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The [Gompertz model](http://en.wikipedia.org/wiki/Gompertz_function) is a different growth model. Let's try it:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def gompertz(t, N0, r, K):\n",
      "    return K * np.exp( np.log(N0/K) * np.exp(-r*t) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "popt, cov = curve_fit(gompertz, t, N, (r, N.max(), N.min()))\n",
      "N0gomp, rgomp, Kgomp = popt\n",
      "print('N0=%.3f, r=%.6f, K=%.3f' % (N0gomp, rgomp,Kgomp))\n",
      "\n",
      "plt.scatter(t, N, label='data')\n",
      "plt.plot(t, logistic(t, N0, r, K), '-', label='logistic')\n",
      "plt.plot(t, gompertz(t, N0gomp, rgomp, Kgomp), '--', label='gompertz')\n",
      "plt.legend(loc='upper left');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "N0=0.065, r=0.371695, K=0.641\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EzkRhT0REzpvly39i2bIbgRDAwuPAVax+aBLHcpNwZP5+mtbD35/Qq64krH9/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\nYkYpJ04gwLb33mfDjMfx5wQHb+uc0ZFWI0cQ07gxRcV+prz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       "text": [
        "<matplotlib.figure.Figure at 0x7f65a60a6470>"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Not much better...\n",
      "\n",
      "Let's try the [Richards model](http://en.wikipedia.org/wiki/Generalised_logistic_function), a generalized logsitic model:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def richards(t, N0, r, K, nu):\n",
      "    Q = -1 + (K/N0)**nu\n",
      "    return K / ( 1 + Q * np.exp(-r * nu * t) )**(1/nu)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The difference between the logistic and the Richards model is in the deceleration of growth: $1-(K/N)^{\\nu}$. When $\\nu=1$ Richards model is just the logistic model; when $\\nu>1$ growth decelerates later in the growth; when $\\nu<1$ it decelerates earlier."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(t, logistic(t, N0, r, K), '--', lw=5, label='logistic')\n",
      "plt.plot(t, richards(t, N0, r, K, 0.5), label='richards, nu=0')\n",
      "plt.plot(t, richards(t, N0, r, K, 1), label='richards, nu=1')\n",
      "plt.plot(t, richards(t, N0, r, K, 2), label='richards, nu=2')\n",
      "plt.legend(loc='upper left')\n",
      "sns.despine()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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R0cRMefxKfBRtgiR7QghxDdiq7ZzYfZLj27PI2nWy0dGxoTEhRJvb1yV4UYTF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f65a6040c18>"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's try to fit the data with Richards model:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "popt, cov = curve_fit(richards, t, N, (r, N.max(), N.min(), 1))\n",
      "N0rich, rrich, Krich, nurich = popt\n",
      "print('N0=%.3f, r=%.6f, K=%.3f, nu=%.3f' % (N0rich, rrich, Krich, nurich))\n",
      "\n",
      "plt.scatter(t, N, label='data')\n",
      "plt.plot(t, logistic(t, N0, r, K), '--', label='logistic')\n",
      "plt.plot(t, richards(t, N0rich, rrich, Krich, nurich), '--', label='richards')\n",
      "plt.legend(loc='upper left')\n",
      "sns.despine()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "N0=0.098, r=0.369301, K=0.580, nu=2.682\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dFsh7D/8DXx8nGxctBTKAUAAMI4XIyGAAApo2BcAVF0e9YUOJuPQSDIfmBkSq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\nJEmSJEmSJEmSJEmSJEmSJEmSlHL/H7CGz/UUHA4FAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f65a6b4f390>"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Richards model indeed provides a better fit to the data. We can measure this fit using [AIC](http://en.wikipedia.org/wiki/Akaike_information_criterion) (the lower the better):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = len(t)\n",
      "print(\"Logistic AIC:\", n * np.log(((logistic(t, N0, r, K)-N)**2).sum()/n) + 2*3)\n",
      "print(\"Richards AIC:\", n * np.log(((richards(t, N0rich, rrich, Krich, nurich)-N)**2).sum()/n) + 2*4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Logistic AIC: -281.123079061\n",
        "Richards AIC: -322.617475464\n"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# References\n",
      "\n",
      "- Schnute, J., 1981. A Versatile Growth Model with Statistically Stable Parameters. Can. J. Fish. Aquat. Sci. 38, 1128\u20131140.\n",
      "- Zwietering, M.H., Jongenburger, I., Rombouts, F.M., van \u2019t Riet, K., 1990. Modeling of the bacterial growth curve. Appl. Environ. Microbiol. 56, 1875\u201381."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Fin\n",
      "This notebook is part of the _Python Programming for Life Sciences Graduate Students_ course given in Tel-Aviv University, Spring 2015.\n",
      "\n",
      "The notebook was written using [Python](http://pytho.org/) 3.4.1 and [IPython](http://ipython.org/) 3.1.0 (download from [PyZo](http://www.pyzo.org/downloads.html)).\n",
      "\n",
      "The code is available at https://github.com/Py4Life/TAU2015/blob/master/lecture10.ipynb.\n",
      "\n",
      "The notebook can be viewed online at http://nbviewer.ipython.org/github/Py4Life/TAU2015/blob/master/lecture10.ipynb.\n",
      "\n",
      "This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.\n",
      "\n",
      "![Python logo](https://www.python.org/static/community_logos/python-logo.png)"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}