{ "metadata": { "name": "MCMC_surface_brightness" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Model fitting with MCMC in Python: #\n", "\n", "This notebook illustrates how to use the pymc module to fit a two-component model \n", "to observations of the radial surface brightness profile of M31, as originally \n", "measured by [Kent et al., 1987](http://adsabs.harvard.edu/abs/1987AJ.....94..306K).\n", "\n", "Running this code requires the following modules and files to be installed and present:\n", "\n", "- [PyLab](http://www.scipy.org/PyLab), Scipy/Numpy etc\n", "- [pymc](http://pypi.python.org/pypi/pymc/)\n", "- SB_model.py\n", "- m31_SB_profile.txt\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Imports ###\n", "Import pylab using the IPy Notebook magic inline function (%inline), and import our model \n", "(defined in the file 'SB_model.py') as well as the pymc MCMC fitter and plotting function. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "import SB_model\n", "from pymc import MCMC, Matplot" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'.\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Create the MCMC fitter ###\n", "Here we construct the MCMC object out of our model. Remember that the model \n", "is just a set of interconnected random variables --- the hard work is\n", "all handled by this MCMC object." ] }, { "cell_type": "code", "collapsed": false, "input": [ "M = MCMC(SB_model)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Accessing variables ###\n", "Now that we have our MCMC object, which we called 'M', we can access the model's \n", "variables and their values. For non-observed variables (like SB), a call to .value \n", "returns the variable's current value, while the values of observed variables don't change, \n", "of course. Here we plot our observations in red, and a realization of our model generated \n", "from our priors on the parameters --- i.e. our model before we begin fitting it." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(M.r.value, M.SB.value, c='gray', label='model')\n", "plt.scatter(M.r.value, M.mags.value, c='r', label='observations')\n", "\n", "plt.gca().invert_yaxis()\n", "plt.xlabel('radius (\")')\n", "plt.ylabel('Surface Brightness (mag)')\n", "plt.legend(loc='best')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "output_type": "display_data", "png": 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hRYsWdOjQgccff5yAgABj1SmEEMKIKgyHESNGoNfrGTNmDA8++CD+/v4opYiKiiIiIoLp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\nY2el8zO3bduWnj17MnToUDw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} ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fitting the model ###\n", "To do this, we sample from the posterior distribution built up by the Markov Chain. \n", "The first keyword, *iter*, is the number of samples to draw from our posterior. \n", "This is a tradeoff between quality and execution time, since more samples is pretty \n", "much always better.\n", "\n", "Of course, we only want to sample after the Markov Chain has found the equilibrium \n", "distribution, i.e. after our sampling has converged to the true posterior. That's \n", "where the *burn* keyword comes in: the first *burn* samples will be thrown away. \n", "We want to ensure that *burn* is large enough so that our Markov Chain converges \n", "to the true distribution after that many samples.\n", "\n", "MCMC sampling is oftentimes inherently auto-correlated (the current value of \n", "sampled parameters influences the next sample), so *thinning* can be helpful. \n", "A sample is collected only every *thin* steps of the Markov Chain. This gets \n", "our sampling closer to the independently-distributed ideal." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# reasonable values for this model\n", "# this will take a few seconds to run, so be patient!\n", "M.sample(iter=5e4, burn=1000, thin=100)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 50000 of 50000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing the Posterior ###\n", "The pymc Matplot module is a great way to get a quick snapshot of \n", "the posterior. For each parameter, it produces three plots: \n", "\n", "- A trace, which shows the value of the parameter over time as the Markov Chain walks around. \n", " This should be very noisy --- if the trace has a lot of clear structure, you probably need \n", " to increase the number of samples you *burn*.\n", "- An autocorrelation plot. High autocorrelation values indicate that you probably should \n", " increase the *thinning* parameter, and sample the space more randomly.\n", "- A histogram, which will approximate the posterior PDF of that parameter. \n", " This plot is the holy grail of this endeavor --- it shows you the mean (or best-fit) \n", " value for each parameter, as well as the 95% confidence interval." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# plot function takes the model (or a single parameter) as an argument:\n", "Matplot.plot(M)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting r_e_B\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " r_e_D\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " M_e_B\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " M_e_D\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " n\n" ] }, { "output_type": "display_data", "png": 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ndQV5u7Wv1BAktZcG83//21tskWAaNMhXbJHbJBcPlUOKRmIrPl4XAUZiSxUU\nNDFC7V/fvtbOFk0wkKHPSz4HOVtyGJGuV7lta9boi3cTt90GjBmjPzYLI9J55Wrv1Dar2luys2X2\n40F2tgYOFM/Nni2cybNn9dm1DMMwjC8mWUyCkpISDBgwADNnzsSuXbswduxYFBYWAgBWrFiBlStX\nYuzYsVi6dCkSEhJQUVGBLEkppKamotyg4mZBQYHnfnZ2NrKzs4PuQGurKAJ69Ki5swUAa9cCL79s\nfIzmZvE3ezbw058aiy352EOG6EvN+JuNKDtb8vI7UVG+QolEmDww9ujhfzaiWRiRwk0ytO1HH3m/\nHxRGlAvAGjlbdstAkLMli+HYWNGmuDixbmH//kK0NDWJ41IhWLOcLXlpIlkoqrq/udlbNFIYUUYV\nW3V1Yhv1nGbO1tmz4j2jayc9XQh26jvgLdIoZ0t2tugakdt2+jQwfTpw3336c+pnKDtbchhRdi0p\nhGrn85JztmjChab55n6R2CJ38+BBcdvQID5LOYxYXFyM4uJi/ydnuiSU/9LVQzMMAzjjerUUWy0t\nLfjiiy/wxBNP4OWXX8aDDz6IN998E7Nnz8aiRYtQU1ODRx55BAsWLMDKlSsNj+Ey+Ekti6320tqq\nL29jJbaGDzcvuCgPpg0NekirVy+xtMo33wCjRhnvGxMj8rVGjBCPaeA3ytmSHQgjsUUiTB7wzcKI\n8uBo5mzRrEn1+WHDROmBVav052WxRULEqM6W3bCUGkYksQWI2/p6Uei0slIv7PnDHwIbNpi7MbKz\nJX/WtL0cKpXFFs1GlFHdKnK2VLF18cXGYTWqDUalFcaNA370I+Dxx83Fllpni64zf0nxqtiSnS05\njCiHbIN1tuj6o2MTcoI8/R+R4KWJBEeO6NurP6K6evIq401XHrQYRsUJ16tlGDE1NRX9+vXDnXfe\nie7du2Pq1KnYsmULEhMT4XK5EB8fj7lz53pChSkpKSiV4jtlZWVISUkJawfkgUoVW3fdpa+daJaL\nAngLCDWM+MEHwOefmy9JEhur/8IH9IFPdbbILaDnzMKIlBdD+MvZsnK2jEpekEMBGOdsqWFENUHe\nrtiSw4hUOV19T6KidGdQdk7ofKrIaGvT30O57dQmOYzYq5cQO7fdJj4fO2HEXr18xVafPsZhRMoz\nk9sut1NuF2AcRuzTBygo8BXEqjBSP381QV6tLxaoswV4u7dG5UTo84uK0sUW/Z80NQnhzDAMwxhj\nKbaSk5OQ/KjNAAAgAElEQVQxdOhQfP7552hra8N7772HSZMm4cT5gjotLS14/fXXMeK8rTNlyhSs\nW7cOTU1NKCkpwZEjRzBGTjYJIRMmiFsrsTVypF5fSl5gWMVMbMmujpXYkmch0rHUnC3Z2aIQjVkY\nUR7w4+KCz9nyJ7bMcrZCFUakwfncOXGfRITcn0DEFqALE2pvVJSvs0Vi69w54P33xXP+EuTNnC0K\nFaqoYkueOGA3jAjoTtF//Afw+9/rfZKxCiMaOVutrfq57YpjcrYAXwF/8qSxs0WlUZqbWWwxDMNY\n4Xc2YlFREebNm4fLL78c5eXluOeee7Bw4UJkZGQgKysLzc3NeOGFFwAA6enpmDVrFjIzM/H9738f\nq1evNgwjhoKtW8WtldiSsVofUR6Qqqp0sSUPimaFUdXZazRIWRU1jYoyFlsURpTfMqMiktRmO2KL\nBkS5fWqCNmAcRlQT5DXNWGxVVurrSBJyqLSx0VuMyDlWqtiSK+Kr/erVS19Lktres6e3yABE+3v2\ntK7MbpYgrwodWtJIhWqD2XW2KPleXa6HnCK5RIk/sSV/5mZhRHqO1m30F0aUnS11VYLEROGUkRhW\nnS2akAD4LyDMOAMn1C1iGMIJ16tlzhYAXH755fj73//u9dyaNWtMt583bx7mzZvX/pbZRHVJzKCS\nA0bIg+LXX+slIuQB1MrZMjqWVc4WDaZ2nC0zMUWzL63CiHFxIueIBlxN8w7nGTlbCQneBVBlZ4uE\nmtqejz4SpRjImaF9o6LEuRobjcUIYOxs0flUkTFggBBbqan659Gjh57LJde3iovznrxgJbaefFLM\nRM3J8RU6ZhMgyNmqrdXbLoeJNU2fZdnWJkKGahgREK+fPavndAH2woh07Kgo47Ie6vqQVrS1+Yot\n1S2kz1AOI1J7a2t1Z+vcOZG79tpr/s/LdF2ckAPDMIQTrlfHV5CXUQdKGbthxOpqXXjQYHLttWKA\nN8JMbBlVkFfraNlJkI+OBp5+Wp/pRlBRUn/Oljwln2pCGeVskbM1dKi+LI7qbJGbRq4iYSRESTjG\nxIgwq7yN7GyRcySLrc2bRfK+Krb69NGXySFkYSAXbKUyE4QstmJjvd2qX/1KlKIwytkKxtlyuXS3\niJLgSWzREjsEOUWy2LLjbLW0iPO4XMbOlprHZkVzsy6kAO/3lI5z9qweRqRQLr0v6gQEOazOMAzD\nRIjYopmAVtgNIwLev/AB4dhYzUaUUQWdUUgsUGcLADZt8j5uXZ0QB1ZrI6pi69Qp/zlbl18O/Otf\nepvJ2aIQYkyMWEBZxih0RGHEmBjRVrlCvZWzFRMjXJH77zcWW+TSye8btU92tki4EXKF+rg442vh\n4ovtO1stLeYJ8uRmycsQ9enjLbLlbcnZonOrzpZZzpbqbJ0vh4fWVvu5dYB3vhZgLLYaGnzfU/l9\nOXnSu30MwzCMTkR8LT72mP9tqFijWbK5ui1gPDgaHVeGQlpqKEwOI/pztuTBlrZdsUKUmCAox0jN\nr6E2NDSIAZQKgvbpo4stq5ytlBSx75kzesjR5RI1lIqLjUO1RmJLDiPW15vXxTIKIwLCTbRytuQ8\nMhIfqrMlu2Byu7t1M3arkpJ8P2t/zhaVfoiJ0d9DEltGzhbgK7boPHadLTWMSK/LeYxqkV+rnC1y\n1ghZbFHfGxp0Z4uQ3xfZ+Q1TmibTgTghB4ZhCCdcrxEhtoYP9x8ucbnMyz/4c7bMFrAGfMVHUZFx\nkrcs9MycLaPSD3S/ogJ49VX9ebnieVMT8Mkn+msJCWJZoIsu0sXWoEEiRCq7MHJFfRJDsbGiOv6Y\nMSIPi0KBjz8uSmnYFVtyGFEVWzIktiiURYP5xRf7isjevX3FFs0EPH7cewFptRK6y+Xd73PngK++\n8j5+UpKxs2W39MPcucCuXcbOFgljwDeMCIj3xyxnyyyMSMLcqHCtnLTuD7m2HGAsts6e9Q41yq8B\nQH6+fg2ys+V8nLDWHMMQTrheI+JrcdAge9vRWocq7XG2VCG2fbuYxm/kbBFyBXFZEFDozSiMKLcL\n0MOIMTHAO++Iopoqjz4KPPCAuJ+SIpwtOUFezrORp/3n5QGHD+uP5TwdI+FJ7ZIHfXk2Yn29dxhR\nhvpL5SFkd0cVEb166WJLFq4xMSLXbOlS8Rw5Wyokort3FyG3d9/1ft1IbMXF2Sv9QM5WZqa32DJy\nrvw5W3bCiEYJ8gS5fPLn6282opnYshtGpNm1cp8YhmEYQUR8Lfbvb287Wn5HxUxsGTkRKgMGiDUP\nia+/Bi65xLccgZ3ZiEbOlpnYkp2t82XPfLj0UiA5WdwfNMg3Z0t2PuRJAbQPPab1H9U2ENQv2TW0\nCiMC3oN/XJzYRq7FZeTY9Ozpm7M1Zoxx3pzczhtv1M8jH0t1ztrrbBFyGFG+tqzCiLSUkfwcYeVs\n0bnkHxEURlSr5lvhz9kyCiOqLjF9diy2GIZhvHH81+KUKfa/3Pv0EaGjvXu9nzcLI6pr2BnRuzfw\n6af648pKIbbUwpxyBXl/CfJGOVtyu9ra9OKr0dHms7/kdez69fMuUwB4iy25j0lJ3segUCWgH++b\nb/Tp/tRHecD3F0aUPzMqoaA6KlbOFr1vzz7rKwBlsTV4MPDxx95t1zT9XPJnH6iz1b27EBxVVeYJ\n8rLrZBVGlF0jO6Uf1DCivC6hURjRKFdRxq6zZRZGpHYZtZ9xHk7IgWEYwgnXq986W12dJUvsbxsf\nD0yeLO7Lg2B7nC0jBg+2drbsln74+mvvUBeJrYYGMdCTmJGRw5K0HA4gtqfwEp1fHozpOU0Tbp38\nvJGzJRdbpYFcnokpz0Y0CiOqSxKdOeN9HiOxRdvRe/Xww2IBaPU9oJAk9ZswSgKnAqiHDoltqV3Z\n2cCkSebOVkuLEJuNjcAbbwATJ3r3jaq433UXcOut4nmrMKLsGgUTRpTFFn3O8ufrr5K8P2eLSlaY\nJcjL7WZny/l09fwXhpFxwvXq+K/FQL7YKaySmOj9vD9nK1CxlZjoK0SCKWo6eLBxGJFCiEZtq67W\n78vH6tZNHN/M2aLtyPWRjyGLIFmAUt/kwpeEHEasq7MOI5KIkh20piZjsSU7W2bOo5yzJYs82QEj\nQdHYKLahJTzpfZg6VUwK8JezJR+PkJ2tHj2Am2/23sZIbKn5ajLy+5CTYxxGVMWWGkY0KgVxyy36\nfX/OltpG9TW53V1FbDU2NuLaa6/FqFGjkJWV5VnpoqCgAKmpqXC73XC73diyZYtnn8LCQmRkZGD0\n6NHYvn17ZzWdYZgIw/HOViBCiMSFWpdLHTTUQdwqjGiEPBNOnjVn19kyGozpuIC12JIFj1xGgoSM\nnCBvJrYAkUC+apV5GFFOYA80jHjPPd6DO+U+qc6WGj4zE1tWYURZbJGIlsOIao0pWQjTPmY5W2pt\nKoKEaHOz9/n9OVv+6mxddRXw9tuiwG1zsx5ybmvzrnNlFEY0EowffKDflz8PuXab3He7zlZXCSNe\ndNFF2Lp1K3r06IFz584hMzMTd9xxB1wuF/Lz85Gfn++1/YEDB7Bq1Srs3r0b5eXlmDRpEg4fPoyo\nrqIeGYZxLH6/Rerr65GXlwe324309HR8/vnnqK2tRU5ODjIyMpCbm4s6Keu8o38ZBuo6Ab6Jw0aD\nqXzsQM8hD1bBOFvyYCW/TgKirk4v26AKQXlQjY4WpR/+9jddAMjOlvw+UJvouAsW6MegBZTlNtgN\nIxrNRly3Tgg5Qu6LvzCinCBv5mzJYstOGNFKbFklyKtOmXyMhgYxS9RoG6OcLVnImI3t8rays6Vp\nYvbo/feL2afHj4s2y2LLX5FTu86W7JSa5Wx1JW3S43zH6urq0NLSgm7nP2zNoFbMxo0bMXXqVMTG\nxiItLQ1Dhw7Fzp07O7S9XQUn5MAwDOGE69Xv1+KcOXNw0003Yc+ePdi/fz+GDx+Op59+Gtdddx32\n79+PrKwsPPPMMwC8fxmuX78eM2fORJu/zNz2diCAL3ZaJ04dJMzyWewkyBthVGcrmJwtwHiQlAtW\nqkJQFVsuFzBhgnfhT6N+RUWJ5P4rrhCP5dmJ0dG+OVtyGNHI2fI3G1HGSGwZhRETEoDTp/Xj2xFb\nl1+uP0/PDRniG0YkVIFtFUa0EltvvQXs3+9fbBnlbPkTW3KCPDmMhw6JmZkTJgDbtont5EXI1T7M\nnev92F/OFj0v1wVTj9kVc7ba2towcuRIJCUl4aGHHsIll1wCAFixYgXS09Nx//334/T5i6qiogKp\nUnXW1NRUlMuVhC8gnFC3iGEIJ1yvljLizJkz+OSTT1BUVCQ2jolBfHw8Nm3ahG3nv9Hz8vKQnZ2N\nJUuWmP4yzMrKClsHAnGdKLlaHkBoGRojgk2Qlwcrdd06wH/ph/x8XfTI+8nCzaxtct/UEhIktmRh\n8NZbwA9+4FvyQa67ZZSzZcfZksOIctK9Cg30soNm5GwlJoo1DOk9MAsjUs7WqVPegiMuToiMX/9a\nFIg9e9Y3n0zOoaJjB+Ns0XllN02t36aeT06Qf+01YNo073PKYqu52XttxCNHgBkz9PcH8C5aqwqj\nl17yfqyKLXk9TPn81Aaj5a+6orMVFRWFffv24dixY5g8eTKuv/56zJ49G4sWLUJNTQ0eeeQRLFiw\nACtXrjTc32USEy0oKPDcz87ORnZ2dhhazzBMZ1BcXIzi4uKQHtNSbJWUlGDAgAGYOXMmdu3ahbFj\nx2L58uWoqqpC0vn6AElJSaiqqgIgfhnKwsrsl2Eov6gCEUI04MuDJzkERgZcKMKIRmsjmjlbJFBG\njxZ/1D75dXrOzNVRB0f5/rJl4r7salBBWHWAlJ0tszCipok/O7MRzRbyBuw7W0lJoswCoK/bSPvJ\n0NqI/fp5Px8bK57r0UO8/t//LUKaV16pb2OUs2XH2ZLfv6goPUQrfwYU0jQLI8pi5b77gNxc4Kc/\nNd5WDSPW1Ymw4Tff6NvLAirYMKLqbMlhxNpa72PIOVvh+LJqD2lpaZg8eTK2bduGhx9+GAAQHx+P\nuXPn4r777gMApKSkoLS01LNPWVkZUmjmhIL8HcYwTGSh6pJQhCgtxVZLSwu++OILPPHEE3j55Zfx\n4IMP4s033/TaxuVymf76o9dVQvlFFYgQeu01sX7c4sX6czRoGi3jE2yCvOwMGFWQN3K2mptFiEwV\nPYE6W7IwUAWA3D71eSuxZRRGJFdFFlsUpqU2yrMRzSrIA97OllWCfGKicKva2qydLU0zryCvilS1\nbXZztlSHUHUUKWQs10Cj89gt/eByAX/5i76t7GzRmpD0Q4Heb/k9kwVUsKUfzJyt7t29hZ3cl6io\n8HxZBcqpU6cQExODhIQEVFdXY8uWLSgsLMSJEyeQnJyMlpYWvP766xhxfsbMlClTMG3aNOTn56O8\nvBxHjhzBmDFjOrzdXQH6vLp6aIZhAGdcr5YyIjU1Ff369cOdd94JAJg6dSrWrFmD5ORkzxdWZWUl\nEs/XUgjkl2GoCCRk0auXcHLkgdFKbAUTFqEBXQ0j/vrX+jZGztbDDwO7d1uLJ3lmYzDOFhGo2IqJ\nMV6uhwZ3EhZyCEsOI9bUhCZnKzZWOEbV1dY5W7St0XNG+/ibjWjH2ZKvH8qpArwFqJGzZSS26P3U\nNG+xpjqtNNu0rU13EuUSEPLkgIYGcTyz30V2nS16L/r3B0pKvI/R1XK2KisrkZeXh9bWViQnJyM/\nPx8TJ07EjBkzsHfvXsTFxWHcuHGekhDp6emYNWsWMjMzERMTg9WrV1v+kIxkuvKgxTAqTrheLcVW\ncnIyhg4dis8//xzXXHMN3nvvPUycOBGDBw9GUVERHn30URQVFSEnJwdA5/wyDDTEp07lVwdNmWCm\nsnfr5j1YkUCSByYjZ+vAAe/XCKMwol1ny0xsGQ326nkp18jlEo4Mhe/k94qS5Kld8rJB6mzEQMWW\nUc4WIPLKKiqCE1tGzhZgbzaiKlTU60YtuUH9kMUWOVtqLh3d0n114oG6rfyZkctF4tYsjPjppyJP\na+5c40XbqZQIYD0bkT5juY9yv9X+dSYjRozAl19+6fP8mjVrTPeZN28e5s2bF85mMQxzAeI3QFZU\nVIQZM2bg1KlTGDFiBJ577jm0tbVh+vTpyMjIwJAhQ7B27VoAnfPLMFCxpU5ZtxJbwUBiSw0jysgD\n7PvvC1eLtlf7YxRGlJ0tuwnyZmFEsxlw9LG1topBm+pbqXlKra16H0mQ0X5yGNFKbNGyP9266QLB\nTGzddJMoqUBiDvBOQr/6amDXrsDEllUYkWZ0ygKX2mfmbMnOptFi3/K/hJwgT/dlsdW9u+4qmokt\n2dmSZ1/26iVy/+6+G/jFL3Tn0Wh5J3kigZmzFR3tLbbUbbtanS2GYZiugl+xdfnll+Pvf/+7z/Mb\nNmww3L6jfxkG+is6Ls57YAyH2DJKkJeRB/T/+R9g4UJ9QFX7o85WpFuzfDKapUbLqxD+wohmorWl\nRQz4VN/KzNnq1s3X2aIworowtMpDD4mK7T16AOvXi7ysUaOMxdbkycBvfytEhTwzjs553XW+7SSC\nCSMCeijRSmylp3sfo7lZFCF9/HHv46gYhRFlsdXaKso6DBtmHUYkcfv974tZiWvWANdeKyYAHD3q\nfX411woIztmiY9K2Xc3ZYoLHCTkwDEM44Xq9oCrIA8GFEQPBjrOlDuhLl+qvqf259FJxO2KE8WxE\nozAiFf80ClcB9nK2iJYWIYLo3EY5W21tIhdOdrbk2YjyWoVGxMUBAweK+4mJIh/IKEEeEDPu6uq8\nw4hyyNMqtBhMGBHQQ4lyDpR83SxbJupbycdoaRF9Mir9IGMURqQwHwlZtWSEVRhRPk90NPDd74pr\n6K67hIgFvOuhEWZiq6lJzOCsrhbHe/hhsZj7jh2+fepqOVtM8HTlQYthVJxwvTrya1HOOQlGbJ06\nBZSVicfyoBmK8MevfmWcsyVj1Wb1tQcfFCG87Gz/sxE1TfTHKhFbfd4sjEiQs0WYOVsDBnivyyiH\nERsbA/ucKNfLaBZg796i5ICR2JL7YeZsGYkpo6KmshgzSpJvaRHHGzgQuOEG3/ZTaQYZu86WLNRb\nW30L2MpiS02QN+p7XJxwvEhsGSX8m4URm5tFva9Ro4TovucecY3T/4pR+QsWWwzDMN448mvRqECo\nXWjgHDxYPJbFVnsHiZwc4Ec/Mp6NKEPnsZoBSbhcYpCTk+llZ4uOT6FDWWzJ4rG9zhahDq5tbeK8\n/fp5h6fkMOK5c4GL4thYY5HWq5e5swWYl4MAALdbOD1A4M6W+llRWLGiArjmGu/XKIwYiNgyytmi\nmZ6qsyWLLnK2SNya9b1/f2+xddVVwu0irJytnj2BPXuMrxsjZ4tzthiGYbxxZBhRFlvBJMjLqGJL\ndqKMZm2Z8e233kU2jYqZEtRmo3CO2UBFLhIdk45BLgUJH3WBZPWc1D7CSmxlZooE608+0Z8zS5BP\nSBD9ofdTno2ont8OcXG62JLfw/aILbmYayBii4SKXMVEDtupBOJsWYURW1q8Q6NmzhaJLasQav/+\n+mLVLS2iz5MmARs3iufMxBY5eEZ9BMSPiz17fNvFOBsn5MAwDOGE69WRYksOgwT6K1odOGSxde+9\nvlWx7UIz6gDd2ZILfsrQYCSXCyCMBBjtIztbNKCqYqupybiAqNlsRKsBctcucavWYCLkMGJ0NHDx\nxUJ0JiaKtsbGBr/kEblJ6n69e/uKLatcKDPszkYERPX7sjJg5Ej9OTlsp0JiS22D3TCiLLbk580S\n5AH/zlavXvosRHLl5PbJYUTZmVWLtxJ03jlzgMsu836OxZbz6cqDFsOoOOF6ddzX4g9/KNa1CxZ5\nIKCwGw1Ot9wCvP22/nqw4RB1lpiKlbNlNC2f9pHdMjoG5TWRGGtuNhZbZs6WHefJLGdLdraiooTY\nolCiHEZUz2kH2dlS29LYKPppJLbsrnseiLNFYktGFjcqwYQRjWYj0jHMnC1Z3MhOmrwmonxued1J\nWQgD3u+B6mwZfXZG75PaLoZhGEbgOGfrrbf0AqDtZe/e0CfIExRKtHK2jMQWzT5UkcOI8gBIrkIg\nYUSjAdLKjTDL2ZKdragooG9fvYK5PBtRPacduncXsxvV/aKiRHvOnDEOI9oN/bZXbFmFEaOjjcWW\nlQNnlLNFglJe/NvsVhZbCxaIEKGMkdgya79aXNZKbMmvsbPFMAxjjCO/Fs3cn0D47neB5cu9xZbV\n+n2BQqEYK2dLDSOeOQMMGWJ8PDmMKDtbV16p19QisRWqMCIhO1vqvrLYkp0teTai3Ge7UCFVo/16\n9Qqt2PIXRhw4EKis9N4/mDCiLFqNzqc6WySgrMKIgBA58vl69tTrjRFyfTkS6/Qe7N3rvW1Cgnh/\n5W1VSFgFKtwZZ/DUU091ynqWDBMMTrheHedsAd7FM4Pl7ruBI0d0sbV7t3dOTnuhUAzVSTJaIFoV\nW0ZhJkINI6oDYDgS5Amr2Yjk3rlcelkGwDeMGIzYUttK9O7tLbbkNsm5R1YE4mz16OHrQtoRW+rr\nN94ols1Rt6XzGYURjXK2VAeWPgerz9AqjHjlld7b9u8PHD4s7vtLkJfPyc5W5OCEHBiGIZxwvTry\na7GxUS+CGQzl5WKm3blz+sAzenTggsAKCiO2tvo6TWbOllWVdTWMaBRes0qQ95ezZTVAUmiwZ0/j\nMKKm6Q6MXP1cdmUCzdkisWXmbH37rbGzdfHF9o4vH9dIbKliTC394C9ny0hsuVzA2LG+21J7zJwt\nf4LYLEdMxiqMqO43YIBeJoJzthiGYdqPX7GVlpaGjIwMuN1uz6LSBQUFSE1NhdvthtvtxpYtWzzb\nFxYWIiMjA6NHj8b27dvD1vARI4Lfd9AgfQBtbrZ2lIKFwoi0lI0MDUo//7nvPmaoYUQjZ4sS5EeN\nEsveGJ1TPY/RoKmSmQnceacYoK0S5FX3rb05W2q7CQpX0jHltc7lWaFWmIURjSYMGIktf6Uf/Ikf\n9XxWOVtm9asoZEprN1q9x1ZiSz2uXJMrkDAiO1sMwzDG+PUbXC4XiouL0bdvX6/n8vPzkZ+f77Xt\ngQMHsGrVKuzevRvl5eWYNGkSDh8+jKgwfPtefrlYVzBYZLEVyrURCQojtraai61p04AXX/QNLRkh\nCxkrZ4vCiLm5vvvLbVPbYvUR3XCD+BswwLz0g5GzFYowolG7+vYVYT16beJEXXjYdbYCXRvRSGwF\nmrNlti2dz6z0A2EmJO18hrGxuvgnAWXmRFFNrv/7P+Af//DN/1LbHUg7GGfghLpFDEM44Xq1FdzR\nDLKOjZ7buHEjpk6ditjYWKSlpWHo0KHYuXMnsrKy2t9ShQED2rc/ia36euOp8u1Fno2oiq1gwpWy\nkDFytuQEeX91pwIVW/IxjCrIk/CQ3bf2zka0ytnq18/8mMGILdnZMnJnzJwtf2LLjog3EluE6o6Z\nXfN2PkOXS88dpGvEbHsKI772GvD5597FYK3Oyc5W5NCVBy2GUXHC9WrL2ZowYQKioqIwZ84c/OQn\nPwEArFixAitXrsTYsWOxdOlSJCQkoKKiwktYpaamory83OeYBQUFnvvZ2dnIzs4OuOFXXBHwLl50\n6yZypqzEVntyT+TZiCS2JkwAPvoouMFIFjL+nC2rhGYg8JwteT9/YURZEMpiK5Q5W2SyGr12+eX2\njm/mbBHyZ9+tm+86jXbqbBkdV0UOW6r9UT/nxETv1+UwonwsMyiU6E9s9ekD1NToAjOYnK3i4mIU\nFxdbN4hhGOYCwe8QuGPHDgwcOBAHDx7E5MmTMXz4cMyePRuLFi1CTU0NHnnkESxYsAArV6403N9l\noFhksRUsV19tXFbBLuRW1NXZn8EWCEbO1v33C7EVrLMl50OpeWb+xFY4nC05jOhy+TpboQgjGjlV\nVs7W7bd7r9FoRqBiK5CcrehoIWoCCSPGxIhz7tolrm0gtM4Wtfl3vxPXu5XYos/VSmz5y9lSf0R1\n9WnZDMMw4cTvEDvw/LS/K664Arm5udi5cycSExPhcrkQHx+PuXPnYufOnQCAlJQUlJaWevYtKytD\nirygXAjp37994Qo7YcScHOAHPwju+EY5W3Qrt9tuXajoaODLL0Wukpmz1doqBnmrNfjU+4GKLXng\n3bdPLO5sZzZioGKLRFt8vO9rVs4WYC+UaBZGJOyIrUBnI5ptCxgnqwfqbPk739mzwMKFwF//6p2z\npULCmcpdcJ2tCw8n1C1iGMIJ16uls9XQ0IDW1lb07t0bJ0+exObNm1FYWIgTJ04gOTkZLS0teP31\n1zHi/NTAKVOmYNq0acjPz0d5eTmOHDnimcEYatrrRsnOllkZiZEjgTffDO74RrMRyRUKxtmKigJ2\n7ACef95/na1Awoh2ZiPK+xkd2yhnq72zEU+fFrdGodz+/YM7poxZ6QfCn9iyCiPGxAjRG8hsRKNw\nrizY/vhHIWytsBv2PnwY+M53rNsXE6MXD7YSW/I5OWcrcnBCDgzDEE64Xi3FVlVVFXLPT2vr168f\n5s+fj1tuuQUzZszA3r17ERcXh3HjxuGFF14AAKSnp2PWrFnIzMxETEwMVq9ebRhGDAXtPWxHJcg3\nN+shMXKcghmMaDA+d87Y2Qo2QT6QnC01jEiYlX6Qq5QHmrOliq1339VfmzhR3NpNhvdHuMKIwThb\nqtii53/0I//HssupU9ZhRGqPldgycmS5zhbDMIwxlkPgZZddhr3qWh4A1qxZY7rPvHnzMG/evPa3\nzIRLLwVCIWI7ImerpUWcg8QcDerB5mwBwNatYkkfdQ3FjsjZksWTjOxsqes3ButsqQLo9tv1+z16\n2A+/miGHDtUw4ttve7udgZZ+IGcr0NIP8mPAf62uYN8DEltWosif2DJa85OdLYZhGGMc97XY1qY7\nG+0h3M4WhRGbmvTjt8fZon0++0yElNozGzHYqt9mzhaF1NRaYO0RW3/4A1BSEj6XpEcPvXCnKuxy\nci95vd8AACAASURBVPzPRrQSW4E4W2qFfVVsWb1vJLaCEV1WOVv0en29d9uMzi3DOVuRgxNyYBiG\ncML16ri1EZubAw9JGdFRsxFlZ4vEVnucLfn4MoEkyMv7mlUnN8IsZ4sKjBotKRSs2EpIEH/hDElR\n2/yVaAg0Zys62n4FeX9hRDvOVjBiKxBny+gzNzpnINcS07VxQg4MwxBOuF4d9xvUbrFIf9BU+9On\nneFsGeVoyQQbRgyEuDhjYVJT41v6gXK2VOcmUHr3Dm4/O9D7ZFdsyQLDKmcrkAR5f2FEOyI1WLHl\nz9mymo3IzhbDMIx9HPe1GCpnCxCDaHV1eHO2Qh1GlI8v4y9B3mw2ImHHjSgqAq65xvf5mhpjZ6s9\nYUTilVfEsjHhoFs34I47/H8e0dF6OQfCThjRTp/9zUa0OgYJ20DEljxhwV+CfKBhRM7ZYhiGMcZR\nX4t1daLqe6jWMuzWTRTADHcYkY5vFEYMpM6W1eP2Olt22vHd7xoP/iS2oqKEeP35z0MnthISgGHD\ngtvXH9HRwDvv2NtWDiWq9a1UYmLshxEJI1fI3zEqK+0fn6BaXXacrUBnI3IYMXJwQg4MwxBOuF4d\nlbNFIaVQOlsdGUYkERTMYOTP2QpEbLWnPpXML34BFBYCZ87o7SsvF/XAhg1rX85WV4PEVq9e1vla\nQGAJ8uqsPrvOVo8eQtgCgTlbl1wCVFTYK/1gFUa0mo3IYsv5OCEHhmEIJ1yvjnK2iFA5WzTlP5zO\nVlOT76LKtNxMIMghLMC6gnwwYcRgePZZ4LrrdLFFVcfPnvWtsxUpYguwztcCAgsjqth1tr7zHf2+\nXbE1YQJAVVlkgWyEv9IPDMMwjH0cKbZClRNCidFGs/fai1GdLRq0LrnEd3tagsaM5mbf48vIzlYg\nsxHbS/fuYlCmnK2zZ8VjNYzo9AGbFnEGrPO1gMAS5I3WuCSsnK3HHgNmzPB/fJm//Q24915x/+hR\nsULCokXG28bE6CIu2LAzwzAMI3DkEBiqMEU4BYBRGJEGTiOxRTWfzFDFVqgqyLcXKvjpcom/xkbx\nRxMZgl0bsathtO6j1bZ2c7b69hVhPUK+tq2OMXWq+AMCFz4PPgjcdZcQymZpDu3J8eMwovOh/Bcn\nhGcYxgnXqyPFVqgIVTjSCKM6WzRopaXp21FI0d8ApRbVDFVRUyIpyfr8ZsTGij5GReliCxCTGSIp\nZ8to3UczAnG2AO9q9YHMRgyW3/3O/zaywLKbs8VEDl150GIYFSdcr36Hg7S0NGRkZMDtdnsWla6t\nrUVOTg4yMjKQm5uLuro6z/aFhYXIyMjA6NGjsX379pA1lAa6UBJOZ8uo9ENMDLBvH3DZZfp2r70G\nHDvm/3iqs6UKqvbMRtQ0MesvGMjZojAiia3a2sjK2VKdLX85W/62MSOQ2YhEOEJ64XJCGYZhLkT8\nfpW7XC4UFxdjz5492LlzJwDg6aefxnXXXYf9+/cjKysLzzzzDADgwIEDWLVqFXbv3o3169dj5syZ\naAvRT2BamDiUdEYYMSPDe7v4eN91Do1QxZZaiJOcl2DrbAVLbKwQWHKCPCDKQURSzpbsbNnJ2aJ9\ngjkPYdfZCofY8udscc4WwzCMfWwNB5ryzbpp0ybk5eUBAPLy8rBhwwYAwMaNGzF16lTExsYiLS0N\nQ4cO9Qi09vLttyE5jBfhdrYojEjCqD3nU8OIRonVbW2BL9fTXi5EZ8tO6Qeg/WIr0FpdocTf9WL1\nG4pztpyPE+oWMQzhhOvV77DrcrkwYcIEREVFYc6cOfjJT36CqqoqJJ1P8klKSkJVVRUAoKKiAllZ\nWZ59U1NTUV5e7nPMgoICz/3s7GxkZ2f7bWhtrd9NAqajnK1u3drvBIwc6f1YFVSdlSAfG6vnJ8nO\nFoXR2uPydCVUZ8tfGJH2CeY8hN3lesJxHcvntbs2okxxcTGKi4tD2iam43BCDgzDEE64Xv1+Te/Y\nsQMDBw7EwYMHMXnyZAwfPtzrdZfLBZfFT1mj12SxZReq+RNKOiJn69y50JSWmDwZWLYMyM8Xj43C\niHYS5IcODa3LJC9BJDtbgD4bkZLnnUwgsxHb4+YFshC1er5QEhMj6tA1NgYXRlR/RHX1X50MwzDh\nxO9X+cDzU6WuuOIK5ObmYufOnUhKSsKJEycAAJWVlUg8vwZISkoKSktLPfuWlZUhJSUlJA2tr/ee\nxRcKVq4EPvootMck5KKmoarjJQ9wRmFEyusyGuTpuUOHQit85Kr4UVG+YksOJToZErOAvdIPtE8w\n5yE629lSS5bIcM4WwzCMfSyHg4aGBtSej9+dPHkSmzdvxogRIzBlyhQUFRUBAIqKipCTkwMAmDJl\nCtatW4empiaUlJTgyJEjnhmM7aW+XoTSQvklf+mlwPjxoTuejBpGDAX+xJbVupFGa++FAtXZknN5\nSGg5PV8L0MOIR48Cf/5z10qQD0cJk5gYfTkrTpC/8HBCDgzDEE64Xi1/E1dVVSE3NxcA0K9fP8yf\nPx+33HILxo4di+nTpyMjIwNDhgzB2rVrAQDp6emYNWsWMjMzERMTg9WrV1uGGAOhvj48axiGC1qM\n2Gz5nPZiFEZsbDR30WJigDVrQt8O6hvlbKnnjBSxRULy8ceBN94wLkwrbyvfBoIqtuxcO+G4vqKj\nxbUUH2/8OoutyMYJOTAMQzjherUUW5dddhn27t3r83zv3r09MxBV5s2bh3m0AFsIaWhwlti66CJR\n/sDfgr+BYOVsRUeL/DCzgdflAqZPD007ZFRnS21TpIgtcrZoHc1wO1t9+gixRet3WhGunC0rR5Yr\nyDMMw9jHMXPEnOZsDRoElJSEdt1FWtAaMHa2rMRWuJCdLVVURaKzZUdshSJnKyHBfumHcDlbwYot\nhmEYxhtHiS1ZbHR1Bg8G/vnP0Iqtn/wEINPQKGerM8SW7GwZhRETE4E//rFj2xQOyNkiwR8usUWu\nUEJC5+ZsURjRDBZbkY0TcmAYhnDC9eqYeWINDbqr4AQGDxbJ1KFKjgfEoDp6tLhvJLbq6jpekMqz\nEUkYuFxiMI6JEfe/972ObVM4IGfLaoYeEYrSDxdfbN/Z6mphRMb5OCEHhmEIJ1yvXdbZUtdCdFoY\ncfBg4NSp0DpbMuogHBUlCr92tNgycrb69BG3kRA+JMjZohwqqwrqoXC24uM739myEltcQZ5hGMY+\nXVJs/e1v4pe1/OvZaWHEiy8Wt6EWW2aDXHS0EFsdLUiNcrZoBlskiS1ytlpaxOOaGvNt25MgL4ut\nzszZYmeLYRgmdHRJsXXsmLiVl1V02mxEOaQWSlTHj6AwYke/R0bOVny86H8kORzyQt+Atdhqj7MF\niCWPLrrIvrMVrqKmnLN14eKEHBiGIZxwvXbJnK1//lPc3nor8MEHwDXXOC+MSFiFW0J5vH79gM8/\nB5KTQ3s+fxg5WwkJkVE1XkZeDgnwrpSv0t7Fty+6SF8RgJ0tpjNwQg4MwxBOuF67pLN19CjQty9w\n5gxQVAS8+abzwohER4mtCROE2OpKzlYkoYYRrcRGe50t2tfucj1drfRDV3E0Gxsbce2112LUqFHI\nysrCCy+8AACora1FTk4OMjIykJubi7q6Os8+hYWFyMjIwOjRo7F9+/bOajrDMBFGlxRblZXAqFHi\n/uHDwJNPsrPl73i0KlJn5WzJsxH79o1MZ0sOI1oRKrFldyFqLv1gzEUXXYStW7di79692LZtG1au\nXIkjR47g6aefxnXXXYf9+/cjKysLzzzzDADgwIEDWLVqFXbv3o3169dj5syZaAv1PzDDMBckXVJs\n1dXpi07X14t8LaflbBEdJbYGDBC3diqOhxKjCvL9+kWe2CJny47Yam8YEQjM2eLSD+b0OG+H19XV\nobW1Fd26dcOmTZuQl5cHAMjLy/OshrFx40ZMnToVsbGxSEtLw9ChQ7FTThy9gHBCDgzDEE64Xm2J\nrdbWVrjdbtx5550AgIKCAqSmpsLtdsPtdmPLli2ebYOx4WtqvJPha2uB3r3F/dJSIbg4jGh9PBpw\nrXKJwoHR2oj9+0ee2LoQna1IEFttbW0YOXIkkpKSMHfuXFxyySWoqqpCUlISACApKQlVVVUAgIqK\nCqSmpnr2TU1NRXl5eae0u7N58sknHZEHwzCAM65XW0Pi8uXLkZ6ejtraWgCAy+VCfn4+8vPzvbaT\nbfjy8nJMmjQJhw8fRpSfEeOXvwQKC/Uv8Lo6EYoCgLIyoHt3MXizswVcdZX161L6SYdANbUaG/XP\nrF+/yM/ZsoKEZnsmKwSyIkC4EuStcELOFgBERUVh3759OHbsGCZPnozrr7/e63WXywWXRYPNXiso\nKPDcz87ORnZ2diiayzBMF6C4uBjFxcUhPaZfsVVWVobNmzfj8ccfx7JlywAAmqZBM/i2NbPhs7Ky\nLM9RX+/9uLYWeOghYN8+YP16EUKMimKxBQDjx1sPdB0ttq68EpgzR8wYrawUz0ViGDEYZ4tC4cGe\nr6nJnpD6/vfFOpyhhBYRN8MpzhaRlpaGyZMnY9u2bUhKSsKJEyeQnJyMyspKJCYmAgBSUlJQWlrq\n2aesrAwpKSmGx5PFFsMwkYX6AyoUIUq/Q+L8+fPx/PPPo0YqLORyubBixQqsXLkSY8eOxdKlS5GQ\nkICKigovYWVmw6u/Cltasj2PW1tFnaGEBOCmm4TYAjpnKZpQ0NH5tR29NiIAvPiiuP33v8XtFVcA\nixZ1fDvCSXS0mKzx3nv+tz17Vtz27x/8+cjZsiNac3PFXyiZPNnanfR3XYfjl2GgnDp1CjExMUhI\nSEB1dTW2bNmCwsJCTJkyBUVFRXj00UdRVFSEnJwcAMCUKVMwbdo05Ofno7y8HEeOHMEYmnlygUGD\nS1cPzTAM4Izr1fKr/N1330ViYiLcbrfXF+fs2bOxaNEi1NTU4JFHHsGCBQuwcuVKw2MY2fDqr8JX\nXtHv06xDIyerM4REe+lIsXXkiHCVOgt5Xb8HHui8doSDqCjgV7+yty39LmlPOC0QZyscKNE2Hx58\nULiaZoTjl2GgVFZWIi8vD62trUhOTkZ+fj4mTpyIMWPGYPr06cjIyMCQIUOwdu1aAEB6ejpmzZqF\nzMxMxMTEYPXq1ZYhxkimKw9aDKPihOvVUmx9+umn2LRpEzZv3ozGxkbU1NRgxowZWLNmDQAgPj4e\nc+fOxX333QcgMBseEINSaal3aOabb/QFp50YNlTpyHDL0KEddy4jyAlxogPpj0By0HJzgf3723c+\nEq5dNRz7wAPmgrqr6JMRI0bgyy+/9Hm+d+/enhmIKvPmzcO8efPC3TSGYS4wLDPXFy9ejNLSUpSU\nlGDdunWYMGEC1qxZg8rzyTktLS14/fXXMWLECADChl+3bh2amppQUlLi14a/4QaR8E1Jx+fOAZdd\nBpw4IR737Cm+uDu6nEEoMVteJxIhgRCJYiuQmYUxMcD5f4l2n8+Jbi7DMAzjje3fzZqmeSz1hQsX\nYt++fYiLi8O4ceM8lZkDteH/8Q9g0CDd2Zo50/v1nj1F/Sg1gd5JXEg1EamvkSgQ2lPGIRjo36ar\nOltmrFsH3HFHZ7eCaS9OyIFhGMIJ16tLM5pWGM4TulyemYwuFzB8uJi19de/iqrxEycCS5eK8Nve\nvSJUsXu32NZpwsXlEiHR8xUzIp5PPgHGjXPeTDU7zJ4N/O533s+Fs59PPilyxH73O5Ef5XTk/3un\nE0l9YS4MyPTg6zY4QvE/32kV5M+dE7cxMXoYsa5ODCwkqkaOBD78UL/vNG6/Hbjrrs5uRcdBn2kk\nIjtbHRHW7uo5WwzDMIx9Ou2r/ORJcdvQoIcR6+qEE0QhFJdLlID44Q+Be+/tnHa2h3ff7ewWdCyR\nLLbkBPmePcNfqZ9zthiGYSKHThVblI+lii2VN97o2LYxwXHDDcB//mdntyI8yM7WpZcC1dUdcz52\ntpjOwAk5MAxDOOF67VSxlZYGHDyoF4F0auFSRhAfDyxe3NmtCA+ys/XrXwPDhoX3fOxsMZ1JVx60\nGEbFCddrp+VsnTolHIKGBlFbi4i0NfWYyECeVOtyAdJ6xWGBFoFmZ4thGMb5dJrYOnkSGDhQDCYV\nFecb02mtYRhr5JmwHZGbRkn4LLYYhmGcT6eKrQEDRJiEcrY4ZMJ0Vag47fjxokRJuCGxxf8TTGfw\n1FNPdcoSSwwTDE64Xjvld7OmiUWLR4/2ntXFAwvTVSFn66OPOuZ8HEZkOhMn5MAwDOGE67VTnK3f\n/EYsPt2/v/dyNiy2mK5KRy+7xM4WwzBM5NApYmvfPnHbv7/37MO4uM5oDcP4p7PEFjtbDMMwzseW\n2GptbYXb7cadd94JAKitrUVOTg4yMjKQm5uLuro6z7aFhYXIyMjA6NGjsX37dsPj0fI1AwYAK1YA\nEyaIx7fd1o6eMEwYYWeLuZBwQg4MwxBOuF5trY24bNky7N69G7W1tdi0aRMWLlyI/v37Y+HChXju\nuefw7bffYsmSJThw4ACmTZuGL774AuXl5Zg0aRIOHz6MKGmaocvlQlychoMHge98Rz9HcTFwzTWi\nOjfDdDV+/GPg1Vc7bt3H7duBG28U64KOHt0x5wwnkbSeYCT1hbkw4LUR20eHrI1YVlaGzZs344EH\nHvCcbNOmTcjLywMA5OXlYcOGDQCAjRs3YurUqYiNjUVaWhqGDh2KnTt3+hxz3z5voQUA2dkstJiu\nCztbDMMwTLD4zQiZP38+nn/+edTU1Hieq6qqQlJSEgAgKSkJVVVVAICKigpkZWV5tktNTUV5ebnP\nMdetK/Dcz87ORnZ2drDtZ5gOgXO2AqO4uBjFxcWd3QyGYZgugeVX+bvvvovExES43W7TL06Xy+Wx\nKM1eVykoKAiokQzT2bCzFRjqj6iunk/BeOOEteYYhnDC9Woptj799FNs2rQJmzdvRmNjI2pqajB9\n+nQkJSXhxIkTSE5ORmVlJRITEwEAKSkpKC0t9exfVlaGlJSU8PaAYTqAjhZbXGeL6Uy68qDFMCpO\nuF4tc7YWL16M0tJSlJSUYN26dZgwYQLWrl2LKVOmoKioCABQVFSEnJwcAMCUKVOwbt06NDU1oaSk\nBEeOHMGYMWPC3wuGCTPsbDEMwzDBEtDvZgoJ/vKXv8T06dORkZGBIUOGYO3atQCA9PR0zJo1C5mZ\nmYiJicHq1astQ4wM4xQ4Z4thGIYJFlulH0J6Qp42zTiQKVOAd97puNIPTU0ilFhdDfTt2zHnDCeR\n9H8fSX0xwwk5MIx9Ir30Q7iv11D8z7PYYhgb3H47sHlzx4ktTQOiooBvvgEuvrhjzhlOIun/PpL6\nwlwYRLrYCjcdUmeLYZiODyNS9J3CiQzDMIxz4YwQhrFBR4stoONcNIZhGCa8sLPFMDa4/npg4MDO\nbgXDdAxOWGuOYQgnXK+cs8UwTNiJpP/7SOoLc2HAOVvtg3O2GIZhGIZhujgsthiGYRiGYcIIiy2G\nYRjGCyfkwDAM4YTrlXO2GIYJO5H0fx9JfWEuDDhnq31wzlYnU1xc3NlNCBmR0pdI6QcQWX1hGIa5\nkLEUW42Njbj22msxatQoZGVl4YUXXgAAFBQUIDU1FW63G263G1u2bPHsU1hYiIyMDIwePRrbt28P\nb+s7mUgaDCOlL5HSDyCy+sIwDHMhY1nU9KKLLsLWrVvRo0cPnDt3DpmZmbjjjjvgcrmQn5+P/Px8\nr+0PHDiAVatWYffu3SgvL8ekSZNw+PBhREWxgcYwDOMUeG1Exkk44Xr1W0G+R48eAIC6ujq0tLSg\nW7duAIxjvxs3bsTUqVMRGxuLtLQ0DB06FDt37kRWVlaIm80wDMOEi648aDGMihOuV7+WU1tbG0aO\nHImkpCQ89NBDuOSSSwAAK1asQHp6Ou6//36cPn0aAFBRUYHU1FTPvqmpqSgvL/c5psvlioi/p556\nqtPbwH2JzH5EWl9CxYwZM7zSFhiGYZyAX7EVFRWFffv24ejRo3jppZewZ88ezJ49GyUlJfjss88Q\nHR2NBQsWmO6vftFqmsZ//Md/F+BfKHjllVdw8uRJ3HPPPVi+fDkaGxtDclyGYZhwYjuZKi0tDZMn\nT8a2bduQmJgIl8uF+Ph4zJ07Fzt37gQApKSkoLS01LNPWVkZUlJSQt9qhmEuSKqrq/Gvf/0L8fHx\nSExMxKxZszq7SRGJE+oWMQzhhOvVss7WqVOnEBMTg4SEBFRXV2PcuHEoLCzElVdeieTkZLS0tODx\nxx9HaWkpXn/9dRw4cADTpk3Dzp07PQnyR48eDWkYgWGYC5cFCxZgzpw5GDJkCABgx44duP766zu0\nDS4X19linAWNwXzdBkco/uctE+QrKyuRl5eH1tZWJCcnIz8/HxMnTsSMGTOwd+9exMXFYdy4cZ6S\nEOnp6Zg1axYyMzMRExOD1atXs9BiGCZkZGdne4TWe++9h9tvv72TW8QwDGMDrQPZtm2b5na7tREj\nRmiFhYUdeeqgmDVrlpaYmKhdddVVnudqamq0u+66SxsxYoSWk5Oj1dbWel5bvny5NmLECM3tdmuf\nfPJJZzTZkK+//lrLzs7W0tPTtZtuukl79dVXNU1zZl/Onj2rjRkzRhs5cqR27bXXasuWLdM0zZl9\nIVpaWrRRo0Zpd9xxh6ZpzuzLpZdeqo0YMUIbNWqUds0112iaFp5+5Ofne+4/8sgjoetAAHTw1ybD\ntBsAfN22g1C8dx327re0tGhDhgzRSkpKtKamJm3kyJHagQMHOur0QfHxxx9rX375pZfYeuSRR7Tn\nnntO0zRNW7Jkifboo49qmqZpX331lTZy5EitqalJKykp0YYMGaK1trZ2SrtVKisrtT179miapmkn\nT57UkpKStAMHDjiyL5qmafX19ZqmaVpjY6N25ZVXaocPH3ZsXzRN05YuXapNmzZNu/POOzVNc+Y1\nlpaWplVXV3s9F45+/PznP9f+8pe/aOvXr9fmz58f2k7Y5EIYtAoKCrSCgoLObgYTIiJdbIX7enWU\n2Pr000+1W2+91fP42Wef1Z599tmOOn3QlJSUeImtYcOGaSdOnNA0TYiYYcOGaZqmaYsXL9aWLFni\n2e7WW2/VPvvss45trE3uuOMO7YMPPnB8X06dOqUNHz5cO378uGP7Ulpaqk2cOFH76KOPPM6WE/uS\nlpamnTp1yuu5cPTj7Nmz2l/+8hftrbfe0s6ePRui1gdGJA9aTGQS6WIr3ITiveuw0u7l5eUYPHiw\n57FZDa6uTlVVFZKSkgAASUlJqKqqAmC/xlhnc/ToUXz11VfIyspybF/k2m9z587FJZdc4ti+zJ8/\nH88//7zXKgtO7IvL5cKECRPgdrvxyiuvAAhPP8rLy1FaWor//d//xa9//esQ94JhGCY8+K0gHyoi\nMVHeX8HGrtbnuro63HvvvXjhhRfQq1cvr9ec1Beq/Xbs2DFMnjzZZzaaU/ry7rvvIjExEW6323Qd\nRKf0ZceOHRg4cCAOHjyIyZP/f3v3HhdVnfcB/AMymBce8AYkQ5GSiXJXESt01NotMxXtAlumomWt\n+azW0r0V3TZpe3wMqXbdVdJu6uPmE7he6rEc0FIwRCE1JcUcBlAQjYtyG37PH+6cdbg1yMw5c4bP\n+/Xy9Zo5czi/72/8nZnvnPM9vzMFw4cPt3jdVv1YtWoV5s+f32r8EhE5MtmSrZZzcBkMBotft2rh\n4+ODsrIy+Pr6orS0FN7e3gAcf46xxsZGzJo1C48//jimT58OQL19Mbt+7jc19uXbb79FRkYGdu7c\nibq6OlRVVWH27Nmq7MvNN98MAAgKCkJsbCxycnLs0g8fHx+EhITA3d3d9p0giRruNUdkporxaoPT\nmVZpbGwUQ4YMEUVFRaK+vl4VBfJCtK7ZSkxMlOpNVq5c2arot76+Xpw5c0YMGTJENDc3KxJzS83N\nzWL27NmtCorV2Jfy8nJx6dIlIcS1mq0RI0aIPXv2qLIv19Pr9VLNltr6UltbK6qqqoQQQly4cEHc\ncccd4osvvrBLPx544AFx3333iYceekg89NBD9unQL5DxY5PIJsCarS6xxXsn67uv1+tFeHi4CA4O\nFikpKXI2fUPi4uLEzTffLNzd3YVWqxVpaWkdXs7+zjvviODgYBEeHi6ysrIUjNzSvn37hIuLiwgL\nCxPh4eEiPDxc7Nq1S5V9yc/PFxERESI0NFT86le/EuvWrRNCdDzNgKP25Xp6vV66GlFtfTlz5owI\nCwsTYWFhYtKkSeKvf/2rEMI+/TCZTCI/P18Ice3igo60N+XJsmXLhJ+fn7Qv7Ny5U/oba6ak4JcW\nqQ2Tra6xxXvX4QzyRESOJDExETU1NfjLX/6C3/72t3j//ffbXbesrAxlZWUIDw9HRUUFgoODsXfv\nXvzP//wPPDw88Nxzz1msb74DxqFDh6Q7YJw6dcri4gWAM8iT+nAG+a6xxT4v29WIRERd1bt3b6k+\n7KabbupwXV9fX4SHhwMABg4ciDFjxkhXPbb1wZmeno74+HhoNBoEBAQgMDBQuu9rd6OGe80Rmalh\nvMpWIE9E1FVarRafffYZnnrqKdx+++1W/515ypNx48bhm2++QWpqKtavX49x48Zh1apV8PLyQklJ\nCaKjoy3aam9KiqSkJOmxTqeDTqe70S45JIcuNCZqwdbjVa/Xt3uF+I3iaUQiUpWKigqYTCZpDq9f\nUlNTA51Oh9dffx3Tp0/HhQsXMGjQIFRVVSExMREmkwnr16/H4sWLER0djcceewwAsGDBAkyZMgUz\nZ8602B5PI5La8DRi19j9RtRERI4kPj4eAFBdXQ03Nzd8/vnnHa7f1pQn5ikoPD09sWjRIjz++OMA\nHHtqDSJSN9ZsEZFqbNq0CZs2bcJnn32GyMjIDtcVQmD+/PkYOXIklixZIi0vLS0FADQ1NeHTTz9F\nSEgIAGDatGnYvHkzGhoaUFRUhMLCQkRFRdmvMw5MDTUwRGZqGK88jUhEqnHs2DG4uLigtrYWOaZ7\n9wAAIABJREFUH3zwQYdXI+7fvx/jx49HaGiodBrlzTffxKZNm3DkyBG4u7tj/PjxePHFF6VTkikp\nKVi3bh3c3NywZs0axMTEtNouTyOS2vA0YtfYYp9nskVEqmH+9erp6YmpU6ciMDBQ9hiYbJHaMNnq\nGiZbRNSt7Nixo9WyBx54QNYYmGyR2jDZ6hoWyBNRt/L+++9jzJgxAIBDhw7hkUceUTgi56SKe80R\n/YsaxiuPbBGRavznf/4n1qxZ0+qxnHhki9SGR7a6hke2iKhbue2225CQkAAACA0NVTgaIiLr8MgW\nEalKeXk5vLy80NzcjJ49e8rePo9skdrwyFbX8N6IRNStrFixAi+88AI0Gg0WL16sdDhOSw3zFhGZ\nqWG88jQiEalGY2MjAgICAAAeHh7KBuPEHLnQmKglNYxXHtkiItXw8vJCQUEBVqxYAY1Go3Q4RERW\nYc0WEamCEALfffcd3NzcYDKZMHr0aEXiYM0WqQ1rtrqGNVtE1G24uLggIyMDERERiiVa3YUaamCI\nzNQwXmU/smXOsImoe+nqR016ejr+/Oc/44cffsCkSZMAAFu3brVFaJ3CI1ukNjyy1TWqPbIlhOi2\n/5YtW6Z4DOw7+y73P1vYvXs3vvnmGzzyyCPYunWrIokWEdGN4GlEIlKFc+fOYceOHTh37hx27tyJ\nnTt3Kh0SEZFVOPUDEanCww8/jIqKCjzyyCMoLy9XOhynpoZ7zRGZqWG8KlKzJXOTDkWv10On0ykd\nhiLYd53SYSjGmfZ7Z+oLdQ+s2eoaW+zzTLaIyO6cab93pr5Q98Bkq2tUWyBPRERE1F0w2SIiIgtq\nmLeIyEwN45WnEYnI7pxpv3emvlD3wNOIXSP7acSEhAT4+PggJCSk3XVefvllhIaGIjo6Gj/88EOX\ngiMiIiJSu04lW/PmzcPu3bvbfX3nzp04evQo8vPzkZKSgrlz53Y1PiIiIiJV61SyFRMTg379+rX7\nekZGBubMmQMAGDt2LC5fvozz5893LcIu8PDwwMSJE6HT6fDRRx8pFgcRkZqooQaGyEwN49Wmk5oa\njUb4+/tLz7VaLYqLi+Hj42OxXlJSkvRYp9N1OP+QEOKG76c4fPhw7N27F0IIjBs3DrNnz76h7XSk\nubkZrq7/zlm7Ei+Rs9Dr9dDr9UqHQTfIkSeHJGpJDePV5jPItywiayvxuD7ZasuGDRuwe/dulJWV\n4cUXX8T9999v8fpPP/2E2bNno7a2FpMmTcLbb7/d4faqq6vR2NjYavnHH3+M9evXAwCef/55TJ06\nFZWVlYiPj8fly5cxbNgwfPTRR9i6dSuSkpLg6uqKlJQUTJo0CTqdDiEhIfj+++8xd+5c7Nq1q914\n6Zq0tDR4eXlh5syZSodCdtbyR5Sj/+okIrInm0794OfnB4PBID0vLi6Gn5/fDW3r6tWr0Ov1bSYu\nf/nLX5CSkoLc3FyUlZW1e+uOkydPYuLEiRg6dGib9WOzZs3C3r17kZGRgZSUFADApk2bMHPmTGRn\nZ0unHt977z3k5ORg7969WLVqFYBrSaROp5OOnHUUL11z4sQJnD59WukwiIiIZGXTZGvatGn48MMP\nAQAHDx6El5dXq1OI1jAnMu3JysrCc889h4kTJ+LEiRP47rvv2lzvjjvuwN69e1FSUoIdO3a0ujry\nwIEDmDFjBqZOnSptIzMz0yJhqq6uhkajQZ8+fTBw4EBcunRJem3y5MlWxUtEpCZqqIEhMlPDeO3U\nacT4+HhkZmaioqIC/v7+WL58uXR6buHChZgyZQqysrIQEhKCPn364IMPPrjhwNzd3dt9bfz48YiP\nj0dYWBgAwGQydbgtjUYDT09PVFVVWSz/4x//iM8++ww9evSQas10Oh12796Np556CkIIeHh4oKGh\nATU1Nbh69Sr69+/fZowdxUtEpCZqqIEhMlPDeO1UsrVp06ZfXCc5ORnJyck3HJBZR0XmixcvxvLl\ny3H69Gm4uroiLS3NojDfzHwa0WQyISIiAlFRURavx8XFYdq0afD395f+Pj4+Ho8++ijWr18v1Wy9\n9NJLiI2Nhbu7O1599dVOx0tERETdF2eQJ9kkJibC29sbiYmJSodCMnOm/d6Z+kLdA2eQ7xpb7PM2\nvxrR1l555RUcOHBAen7vvffilVdesVjn1KlTWLhwocWyTz75BIMHD5YlRiIiZ2Kuf1HD6RkiNYxX\nHtki2fDIVvflTPu9M/WFugce2eoa2e+NSERERESdw2SLiIiIyI6YbBERkQU1zFtEZKaG8erwBfJE\nRCQvRy40JmpJDeOVR7aIiIiI7IjJFhEREZEdMdkiIiILaqiBITJTw3hlzRYREVlQQw0MkZkaxiuP\nbBERERHZEZMtIiIiIjtiskVERBbUUANDZKaG8cqaLSIisqCGGhgiMzWMVx7ZIiIiIrKjTiVbWVlZ\niIyMRGhoKFJTU1u9fvXqVcyZMwcRERGYMGEC0tPTbRYoERERkRpZfRrRZDIhISEBe/bsgZ+fH8aM\nGYN77rkHQUFB0jobN25Enz59kJeXh59++gmTJk3CtGnT4OLiYpfgiYjI9sz1L2o4PUOkhvFqdbKV\nk5ODwMBABAQEAADi4uKQnp5ukWx5enqiuroajY2NqKysRO/evZloERGpjCN/aRG1pIbxavVpRKPR\nCH9/f+m5VquF0Wi0WCc+Ph4mkwkDBw7E3XffjU8++cR2kRIRdYLBYMDEiRMxcuRI6HQ6bNiwAQBQ\nXV2NGTNmIDQ0FLGxsaipqZH+Zs2aNQgNDUVkZCT279+vUORE5GysPrJlzRGqd999F25ubigtLUVB\nQQEeeOAB/PTTT3B1tczpkpKSpMc6nQ46nc7qgInI8en1euj1ekVj0Gg0WL16NcLDw1FRUYHg4GCM\nHTsWH3zwAe688058/vnneOutt/DGG28gOTkZx48fR1paGnJzc2E0GnHPPffg1KlTrT6/iIg6y+pk\ny8/PDwaDQXpuMBig1Wot1snKysL8+fPRu3dvjB07FoMHD8apU6cwfPhwi/WuT7aIyPm0/BGlxBw4\nvr6+8PX1BQAMHDgQY8aMgdFoREZGBjIzMwEAc+bMgU6nQ3JyMtLT0xEfHw+NRoOAgAAEBgYiJycH\n0dHRsseuNDXUwBCZqWG8Wp1sjR49GoWFhTh79iwGDx6MLVu2YNOmTRbrTJ48Gdu3b8e9996Ls2fP\norKyslWiRUQktx9//BHHjh1DdHQ0zp8/Dx8fHwCAj48Pzp8/DwAoKSmxSKzaKpUwc/aj8478pUXU\nkq3Hqz2OzFudbLm5uSEtLQ2xsbFoamrCk08+iaCgIKxduxYAsHDhQsTFxeH48eMYPXo0Bg0ahJSU\nFJsGS0TUWTU1NYiLi8Pq1avRt29fi9dcXFw6LJFo7zUenSdyXvY4Mt+pGeQnTJiAvLw8i2ULFy6U\nHnt6ejLBIiKH0djYiFmzZuHxxx/H9OnTAVw7mlVWVgZfX1+UlpbC29sbQOtSieLiYvj5+SkSNxE5\nF1Z+EpFTEkJg/vz5GDlyJJYsWSItnzZtGjZu3Ajg2tyAM2bMkJZv3rwZDQ0NKCoqQmFhIaKiohSJ\nXWlquNcckZkaxquLEELI2qCLC2RukhxEYmIivL29kZiYqHQoJDMl9vv9+/dj/PjxCA0NlU4Hrly5\nEnfddRdmz56NM2fOYOjQofjoo4+k04spKSlYt24d3NzcsGbNGsTExDhEX4i6wjz+OW5vjC32eSZb\nJBsmW92XM+33ztQX6h6YbHWNLfZ5nkYkIiIisiMmW0REZEENNTBEZmoYr526GpGIiJwf59kiNVHD\neOWRLSIiIiI7YrJFREREZEdMtoiIyIIaamCIzNQwXlmzRUREFtRQA0NkpobxyiNbRERERHbEZIuI\niIjIjphskSyOHj2KxsZGXL16FcePH1c6HCLqgBpqYIjM1DBeebsekkV4eDjCwsKg0WhgMBjwxRdf\nKB0SyciZ9ntn6gt1D7xdT9fwdj1EREREDo7JFhEREZEdMdkiIiILaqiBITJTw3jtVM1WVlYWlixZ\ngqamJjz55JNYvHhxq3UOHTqEpUuXorq6Gv369YNer7dskPUO3RJrtro3Z9rvnakv1D2wZqtrbLHP\nWz2pqclkQkJCAvbs2QM/Pz+MGTMG99xzD4KCgqR1Ll++jLlz5+KLL76AVqtFRUVFl4IjIiIiUjur\nTyPm5OQgMDAQAQEB0Gg0iIuLQ3p6usU6n376KWbNmgWtVgsAGDhwoG2jJSIiIlIZq49sGY1G+Pv7\nS8+1Wi2ys7Mt1iksLERjYyNiYmJQU1OD3//+93jsscdabSspKUl6rNPpoNPpOh85ETksvV7fqoSA\n1MNc/6KG26AQqWG8Wp1smc/5dqSxsRF6vR579uzBlStXcO+992LmzJno1auXxXrXJ1tE5Hxa/ohy\n9OJVsuTIX1pELalhvFp9GtHPzw8Gg0F6bjAYpNOFZv7+/rj//vvh6+uLIUOGYPTo0cjKyrJdtERE\nREQqY3WyNXr0aBQWFuLs2bNoaGjAli1bMG3aNIt1pk+fjszMTFy5cgWVlZXIy8vDXXfdZfOgiYiI\niNTC6tOIbm5uSEtLQ2xsrDT1Q1BQENauXQsAWLhwIYYPH4558+Zh9OjRqKurw+9//3v07dvXbsET\nEZHtqaEGhshMDeOV90YkWXCere7NmfZ7Z+oLdQ+cZ6treG9EIiIiIgfHZIuIiIjIjphsERGRBTXc\na47ITA3jlTVbJAvWbHVvzrTfO1NfqHtgzVbXsGaLHF5NTQ3eeOMNi2VCCLzyyisKRURERCQvJltk\nV1evXkVKSkqr5cnJyQpEQ0REJD8mW0REZEENNTBEZmoYr6zZIrsqLy/HiBEj4OfnJ9VsnTt3Dnv2\n7EFzc7PS4ZFMnGm/d6a+UPfAmq2uYc0WERERkYNjskVERERkR0y2iIjIghpqYIjM1DBeWbNFdsWa\nLQKca793pr5Q98Cara5hzRYRERGRg2OyRURERGRHTLaIiMiCGmpgiMzUMF7dlA6AnFdNTQ0uXLjQ\n7uslJSXo168fevXqJWNURPRLli1bpnQIRFZTw3jt1JGtrKwsREZGIjQ0FKmpqe2ud+jQIbi5uWHb\ntm1dDpDUa/v27XjttdfafX327Nn49ttvZYyIiIhIflYf2TKZTEhISMCePXvg5+eHMWPG4J577kFQ\nUFCr9V588UXcd999vPKBiIiIuj2rj2zl5OQgMDAQAQEB0Gg0iIuLQ3p6eqv1UlNT8dBDD2HQoEE2\nDZSIiOShhhoYIjM1jFerj2wZjUb4+/tLz7VaLbKzs1utk56ejq+//hqHDh2S5vZoKSkpSXqs0+mg\n0+k6FzUROTS9Xg+9Xq90GHSD1FADQ2SmhvFqdbLVXuJ0vSVLliA5OVmaAKy904jXJ1tE5Hxa/ohy\n9F+dRET2ZHWy5efnB4PBID03GAzQarUW6+Tm5iIuLg4AUFFRgV27dkGj0WDatGk2CpeIiIhIXaxO\ntkaPHo3CwkKcPXsWgwcPxpYtW7Bp0yaLdc6cOSM9njdvHh588EEmWkREKmM+EqmG0zNEahivVidb\nbm5uSEtLQ2xsLJqamvDkk08iKCgIa9euBQAsXLjQbkESEZF8HPlLi6glNYzXTk1qOmHCBOTl5Vks\nay/J+uCDD248KiIiG0hISMCOHTvg7e2NgoICANdqRtetWyddMf3mm2/i/vvvBwCsWbMG69atg5ub\nG9asWYO7775bsdiJyHnwdj1E5LTmzZuH3bt3WyxzcXHBc889h7y8POTl5UmJ1vHjx5GWlobc3Fxs\n27YNc+fORXNzsxJhE5GTYbJFRE4rJiYG/fr1a7W8rSul09PTER8fD41Gg4CAAAQGBiInJ0eOMB2O\nGuYtIjJTw3jlvRGJqNtJTU3F+vXrMW7cOKxatQpeXl4oKSlBdHS0tI5Wq4XRaGzz7519rkA11MAQ\nmdl6vNpjnkAmW0TUrTzzzDP4wx/+gKqqKiQmJuL555/H+vXr21zXmomZici52GOeQJ5GJLtITU2V\nCpI7kpWVhY8++kiGiIiu8fb2houLCzw9PbFo0SLpVGHLuQSLi4vh5+enVJhE5ESYbJFd5OXl4eLF\ni7+4ntFoxPHjx2WIiOia0tJSAEBTUxM+/fRThISEAACmTZuGzZs3o6GhAUVFRSgsLERUVJSSoSpG\nDTUwRGZqGK88jUhETis+Ph6ZmZmoqKiAv78/li9fDr1ejyNHjsDd3R3jx4/H6tWrAQAjRozAvHnz\nMGrUKLi5uWHDhg1W3abMGbFmi9REDeOVyRYROa2Wd7kArs291Z7f/e53+N3vfmfPkIioG+JpRCIi\nIiI7YrJFREQW1FADQ2SmhvHK04hERGRBDTUwRGZqGK88skU2N3/+fNTV1Vm9/qVLl/D888/bMSIi\nIiLlMNkim/vyyy9hMpmsXr+urg6ZmZl2jIiIiEg5TLaIiMiCGmpgiMzUMF5Zs0VERBbUUANDZKaG\n8cojW0RERER21KlkKysrC5GRkQgNDUVqamqr1z/55BOEhYUhLCwMv/nNb/D999/bLFByfCdPnsTI\nkSNv+O8HDRqES5cu2TAiIiIi5VmdbJlMJiQkJGDbtm3Izc3F+vXrceLECYt1hgwZgqysLBw9ehS/\n/vWvsWDBApsHTI6tqalJkb8lIttRQw0MkZkaxqvVNVs5OTkIDAxEQEAAACAuLg7p6ekICgqS1hk3\nbpz0+IEHHsCrr75qu0jJoe3duxeHDx/u8nY2bNiA8ePHY9SoUTaIiohuhBpqYIjM1DBerT6yZTQa\n4e/vLz3XarUwGo3trv+3v/0N06dP71p0pBrHjh2zSbKVmZmJM2fO2CAiIiIix2D1kS0XFxerN7p3\n7158/PHH+Pbbb9t8PSkpSXqs0+mg0+ms3jYROT69Xg+9Xq90GEREDsHqZMvPzw8Gg0F6bjAYoNVq\nW62Xn5+Pp556Crt27YKXl1eb27o+2SL1y8/PR01Njc22V1lZiR9++AHDhw+32TZJXi1/RDl6PQVZ\nMv9/qeH0DJEaxqvVydbo0aNRWFiIs2fPYvDgwdiyZQs2bdpksc65c+cwa9YsfPzxxwgMDLR5sOSY\nXn/9dfj4+Nhse4cPH0Zubi7+9re/2WybRGQ9R/7SImpJDePV6potNzc3pKWlITY2FqNGjUJCQgKC\ngoKwdu1arF27FgCwYsUKVFZW4umnn0ZERASioqLsFjgpKz8/HwkJCXZvZ8aMGSguLrZ7O0RERPbS\nqRnkJ0yYgLy8PItlCxculB6vW7cO69ats01k5NBqamrwww8/2L2dgoIC1NfX270dIiIie+EM8tQl\nf/7zn9Hc3Gzz7dbX1+Pdd9+1+XaJ6JepYd4iIjM1jFfeG5G6ZPny5Zg4caLNt1tfX49Vq1bB1ZW/\nB4jkpoYaGCIzNYxXfpNRp/3Xf/0XPv74Y9naS05OxsaNG2Vrj4iIyJaYbFGn1dbWoq6uTtb2rl69\nKlt7REREtsRki4iILKihBobITA3jlTVbRERkQQ01MERmahivPLJFnbJ69WpUVlbK3q7BYMDf//53\n2dslIiLqKiZb1Cnbtm1DdXW17O1WVFRg9+7dsrdLRETUVUy2iIjIghpqYIjM1DBeWbOlgB9++AGD\nBg3CgAEDlA6FZFBWVoba2loMHTpU6VCIrKKGGhgiMzWMVx7Zktnu3bvx0ksvISsrS+lQOkUIgQsX\nLigeQ3l5uaIx3Ij09HT86U9/wt69e5UOhYiIFMBky06amprwpz/9qdXyhx56CCaTSYGIrPOPf/wD\nS5cuBQDs27cPNTU1AK7N6H7LLbcoGRqampoQGBgoPb948SJycnIAALNnz4Zer1cosl929epVLFiw\nwGJZXV0d3nrrLYUiIiIiuTDZsgOTyYTa2lqsWLFC6VCsVlFRgeLiYpSXl8NoNGLixIlYuHAhzp07\nhx07diAuLk7pECUxMTE4dOgQ8vPz8eKLLyIsLAwXLlyQYlfiaskbUVdXh5UrV6Kurs6hE3DqftRQ\nA0NkpobxypotGztw4AAOHz6M7du3Kx2KVQoKCvDYY4/hwoULuPvuuzFgwAAIIXDy5El4eXkBAJqb\nm9HQ0KBwpP9WX18PIYT0/NixY/D19cWXX36J7du348iRIzh//jwKCgrg7e2tYKTWiYmJwaJFixAe\nHo7w8HClwyFSRQ0MkZkaxqsiydZ7772HRYsWKdG03W3ZsgVXrlyxWHbq1ClUVlZa3HLmq6++wsGD\nBx3iNNL1iUtLR44cccgjRcePH0djY2O7r3fUJzklJCSgV69e0vPdu3fD09MTgwcPhqenp7Rcr9ej\ntLSUyRYRkRNS5DTiwYMHlWjW7k6dOtXm6aAtW7Zg7dq1eOWVV6RlDQ0NMBqNiIyMlDPETtu1axeO\nHj2qdBit6PV6ZGdnKx1Gh/z9/XHx4kU0NTVJy377299izZo1bc4ZVl9fjzNnzsgZIhERyUCRZKu5\nuRnHjh1Tomm7io2NxeXLly2WHT9+HPX19W2uL4SQCtCVcOTIERw+fFix9u0tMzMTJ0+eVKz9qqqq\ndl+rqanB6dOnLZYVFxe3KqJ3Bo6YrFPH1FADQ2SmhvHaqdOIWVlZWLJkCZqamvDkk09i8eLFrdZ5\n+eWXsWPHDvTu3RsbNmzA8OHDW61TX1+PyZMno6ys7MYjV4mnn34at99+u9JhtOnrr7/GkSNHlA7D\nbjZv3oyGhgbccccdSofSysmTJ1U3/ceN4qlR9VFDDQyRmRrGq9VHtkwmExISErBt2zbk5uZi/fr1\nOHHihMU6O3fuxNGjR5Gfn4+UlBTMnTvX1vE6lPz8fJSUlCgdBjmpoqIiRY/MERGRbVidbOXk5CAw\nMBABAQHQaDSIi4tDenq6xToZGRmYM2cOAGDs2LG4fPkyzp8/b9uIHcjbb7+Nr776Ck1NTSguLr7h\n7SQnJ+PSpUs2jIyUZDAY8O67797w3//0008QQuCzzz7jzbeJiJyAi7Dysq1//OMf+OKLL6QP/48/\n/hjZ2dlITU2V1nnwwQfx8ssv48477wQA3HPPPXjrrbcwatSofzfo4gLg+kN+un/9IyLnof/XP7Pl\nDnOFaFe5uLg4TV/aY65/UcPpGfpl1753HecqbVuz93i1xT5vdc2W+T/rl7QMqK2/Kyt7Bo2NjejR\nowf279+P/v2/wpgxYxAREYHIyEj4+/ujubkZRUVFOHXqFKKjozFgwABcvXoVBQUFaGpqQlhYGPr2\n7YvKykrk5OTA398ft99+O3r06IGysjLs378fd999N26++WY0Njbixx9/RHFxMaKiouDl5YXa2loc\nOXIE7u7uCA4ORq9evVBRUYHs7GwMGzYMQ4YMAXCtaPnw4cO46667MGjQIDQ0NODEiRO4fPkyPvzw\nQwwYMAAuLi5oaGhAjx494Or674OF9fX16Nmzp8V709jYCHd3d2mZyWSCEAL//d//jZCQENx9992Y\nOXMm/Pz8MGzYsFb98fX1RVNTE06fPo1z584hKioK/fv3R01NDY4ePYoePXogNDRU6o/5iOSQIUPg\n4uICo9GI7777DnfddRceeeQRREVFobm5GSaTCRqNRoqrqakJLi4ucHNzQ3NzM1xdXVFXV2d1f9zc\n/j20zP/X1r435oFtjqFHjx7Seg0NDdBoNBbjquW2ru/Pl19+iX379uHIkSPo27cvRo4cCXd3d5SX\nl+PAgQMICQnBrbfeCuDaEaXvv/8e48aNw6BBg1BXV4djx46htrYWkZGR8PDwwKVLl5Cbmwtvb28M\nGzYM7u7uKCsrwzfffIPs7Gx8+umnuHLlCubPn9/ue6PRaKT95Jf6c+bMGSQlJeH8+fMYM2YMvLy8\nUFVVhSNHjqB3794YOXIkevbsiYqKChw4cAAjR45EQECA1J+CggKMGzcO3t7eqKurw4kTJ1BVVSX1\n5+eff0Zubi4GDhyIO+64A+7u7jh//jy++eYbjBkzBlqtFs3NzTh9+jROnz6N6Oho9O/fH1euXEFB\nQQGam5sRFhaG3r17o7KyEocOHUJOTg6+/PJnaDRRGDVqFOrr63HrrY5dvEqWmGSRmqhhvFqdbPn5\n+cFgMEjPDQYDtFpth+sUFxfDz8+v1bZ8fHykxw8//DCAa1865m0OGzYMAHD+/HkUFxfj4sWL0Gg0\nqKmpQWlpKRobG3HLLbegubkZFy9ehNFohEajgbe3N9zc3HDhwgUYDAaUl5ejT58+aGhoQFlZmTS7\nuKurK6qqqlBSUoKePXvCz88PjY2N0izqnp6eUhJ1/bZ69uyJuro6lJWV4eLFi+jXr59FX7rC1dUV\nN910E/r16wej0YgePXrA29sbGo0G5eXlMBgMuHDhAnr37o2mpiapPxcvXoSbmxt+/vlnlJSUwM3N\nDf7+/mhsbMTFixdRXFwMDw8PDBgwAK6urlJ/rly5gp49e9osfkfl6uqKq1evoqSkBB4eHhg8eDB6\n9eolvTc+Pj7S5K3m8VZRUYGePXviypUrKC0tRU1NDW677TYIIVBZWQmj0Yjm5mb4+PhIiY7BYICP\njw80Gg3c3Nzg6+trk/jLyspQVlaGkpISDB06FK6urrh06RJKSkrQp08f+Pn5SYl1cXExBg4ciH79\n+lmM3WHDhuGmm26S+vPzzz+36k9TUxN8fX3Rs2dPabzdeuut+I//+A+YTKZW+2JVVRVKS0thMpmg\n0+nQ1NSEyspKFBcXo1evXpg+fbpN+k9EziEl5T28+eZqu21/4MB+KCjItvhR70isTrZGjx6NwsJC\nnD17FoMHD8aWLVuwadMmi3WmTZuGd999F3FxcTh48CC8vLw69WV+6623YuPGjRg0aBAKCgrw1Vdf\nWd8TO9NqtYiJiUHPnj2Rl5eHtLQ09OvXz2bbf/vttwFcu98fAEyePBlVVVVobm62WRvX27x5s8WR\nLGf12GOPYcKECYiOjrbL9j08PHDnnXdiz549AIBnn33WptsPCAjA6tWr8eijj2LevHkQcZj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FW3mWeFRUlNss8dzcXFRXV2PMmDG2TOgHON/IjvA1tQ62E2QHD/q3vaKYO2Sy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KuPPVsiW7Dj3xBcjheH7PxM/rzBnmoBHWxKq5OFcDp0+fxurVq712/ICAAEyd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mzpexvIWV82U81tjmsjJ75SUAEVbNzTXPRVI5X/feC/z2t+L19u3A/v3AlVea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xceK65LwbEgL+OFZ//atYAPqJJ4ydOMCcY0XCil6fOBH4/HMgJ0cIDLkfyMJP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} ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Making inferences about model parameters ###\n", "The *stats()* function provides an interface to the statistics of our posterior, \n", "in the form of a dictionary. For example, let's find the predicted ratio between \n", "effective sizes of the disk and the bulge, and let's also explore how confidently \n", "we can determine the effective surface brightness of the disk.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print 'R_effective (bulge) / R_effective (disk) =', \\\n", " M.stats()['r_e_B']['mean'] / M.stats()['r_e_D']['mean']\n", "print 'Effective surface brightness of the bulge: \\n', \\\n", " ' Best-fit value:', M.stats()['M_e_B']['mean'], \\\n", " '\\n 95% Confidence interval:', M.stats()['M_e_B']['quantiles'][2.5], \\\n", " 'to', M.stats()['M_e_B']['quantiles'][97.5]" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "R_effective (bulge) / R_effective (disk) = " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "0.201445991003\n", "Effective surface brightness of the bulge: \n", " Best-fit value: 20.7427508071 \n", " 95% Confidence interval: " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "20.2909794208 to 21.0286373194\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing specific realizations of our model ###\n", "The *trace()* method presents the values of a variable for all of the saved \n", "Markov Chain steps. Let's plot up several of these traces, and see how \n", "the model changes with different parameter values." ] }, { "cell_type": "code", "collapsed": false, "input": [ "for i in range(50):\n", " plt.plot(M.r.value, M.trace('SB')[i], c='gray', alpha=.25)\n", "\n", "plt.scatter(M.r.value, M.mags.value, c='r') \n", "plt.gca().invert_yaxis()\n", "plt.xlabel('radius (\")')\n", "plt.ylabel('Surface Brightness (mag)')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "output_type": "display_data", "png": 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8SEVFBaNGjeq0IgKKknDocg0NDUy/9FIqa2sxJSQwevRoHG43PU2mn8YlQB13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\nGqeTpR4P1954I4MGDVJbDh6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} ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing the best-fit model and its components ###\n", "Now that we have our best-fit, let's see how it decomposes into the components, \n", "the bulge and the disk. In other words, we can finally take our results and \n", "explore what they imply about the physical system we observed!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# our best-fit parameters\n", "r_e_B = M.stats()['r_e_B']['mean']\n", "r_e_D = M.stats()['r_e_D']['mean']\n", "M_e_B = M.stats()['M_e_B']['mean']\n", "M_e_D = M.stats()['M_e_D']['mean']\n", "n = M.stats()['n']['mean']\n", "r = M.r.value\n", "\n", "from SB_model import sersic\n", "# the sersic profile defined in SB_model.py expects brightnesses\n", "# in flux units, not magnitudes, so we have to convert M_e_B and\n", "# M_e_D before feeding them in.\n", "plt.plot(r, M.stats()['SB']['mean'], c='k')\n", "plt.plot(r, -2.5*np.log10(sersic( r, r_e_B, n, 10**(-.4*M_e_B) )), 'g:', label='bulge')\n", "plt.plot(r, -2.5*np.log10(sersic( r, r_e_D, 1., 10**(-.4*M_e_D) )), 'g--', label='disk')\n", "plt.scatter(M.r.value, M.mags.value, c='r', label='obs')\n", "\n", "plt.gca().invert_yaxis()\n", "plt.axis( [0, 6000, 26, 14] )\n", "plt.ylabel('Surface Brightness (mag)')\n", "plt.xlabel('Radius (\")')\n", "plt.legend(loc='best')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "output_type": "display_data", "png": 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nzuX999+nV69eWFlV2399VWlpaRw8eJDw8HDOnDmDj48PAD4+Ppw5c+aqn4mJ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\nADKZDO3tIytnXr16FQqFQnjfnYx3jwcEBLhk9oa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