{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Here we show issues resulting from the data analysis and interpretation in DOI: 10.1126/science.1249168." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### All code available at http://github.com/rgerkin/trillion
Below we refer to the paper above, along with the associated data and methods, as trillion. This is designed for execution in Python 3.4. Figures appearing in the paper are based on this code, with prettification in Illustrator. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Table of Contents\n", "1. [Preliminaries](#preliminaries)\n", "2. [Data loading](#loading)\n", "3. [Figures](#Figures)\n", "
i. Fig 1 (schematic produced in Illustrator)\n", "
ii. [Fig 2](#Fig2)\n", "
iii. Fig 3 (schematic produced in Illustrator)\n", "
iv. [Fig 4](#Fig4)\n", "
v. [Fig 5](#Fig5)\n", "4. Tables\n", "
i. Table 1 (text produced in LaTeX)\n", "
ii. [Table 2](#Table2)\n", "5. [Supplemental Info](#Supplement)\n", "
i. [Fig S1](#FigS1)\n", "
ii. [Fig S2](#FigS2)\n", "
iii. [Fig S3](#FigS3)\n", "
iv. [Fig S4](#FigS4)\n", "
v. [Fig S5](#FigS5)\n", "
v. [Fig S6](#FigS6)\n", "
vi. [More on the bounds](#gamma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Preliminaries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] } ], "source": [ "# Preliminaries. \n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Load the code. \n", "import trillion\n", "# Set to True to get more information from each function call. \n", "trillion.verbose = False" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Default figure size. \n", "plt.rcParams['figure.figsize'] = 8, 6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### We load the raw data used in trillion and provided in the published supplemental information. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Load the mixture components using the authors' supplemental information (Bushdid-tableS1.csv). \n", "components = trillion.load_components()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Load the odorants, tests, and test results using the authors's supplemental information (Bushdid-tableS2.csv).\n", "odorants,tests,results = trillion.load_odorants_tests_results(components)\n", "r = results # Rename for convenience." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Set default values for all the parameters:\n", "C = 128\n", "N = 30\n", "S = 26\n", "T = 20\n", "alpha = 0.05\n", "multiple_correction = None # Other options are 'fdr' and 'bonferroni'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figures from our paper (Gerkin and Castro, 2015). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Figure 1 (not shown here) is a schematic produced in Illustrator." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Table 1 (not shown here) is a list of definitions. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 2: Color maps for the estimated number of discriminable stimuli as sample size and significance criterion are varied. See Fig. S8 and S9 for other parameter combinations. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CT6yqlwJU1a3AzwZ6knlyTFiSNCn2AH6U5Pgk307y4SQ7dBmQSViS1FMDv4PD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\nSVJHTMKSJHXEJCxJUkdMwpI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O99mr/ueoopYk3ZUd2mXG6aM82WQ9HHC9jXLU9J7AAcATk5zXLnsDhwFPSfJd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\nJH9A83CL3apqTZItgXt0HJa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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure 2\n", "def plot_(fig):\n", " n_reps = trillion.N_TESTS if fig=='a' else trillion.N_SUBJECTS\n", " n_replicates_list = np.ceil(n_reps*2.0**np.arange(3.5,-2.5,-0.5))\n", " alphas,reps,z_ = trillion.num_odors_vs_alpha_and_replicates(r,fig=fig,n_replicates_list=n_replicates_list)\n", " z_ = z_.transpose() # Rotate. \n", " vmin = np.log10(trillion.disc(N,C,N))\n", " vmax = np.log10(trillion.disc(N,C,0))\n", " fig, ax = plt.subplots()\n", " plt.pcolor(np.log10(z_), vmin=vmin, vmax=vmax)\n", " plt.xticks(np.arange(0,len(alphas))+0.5)\n", " ax.set_xticklabels(alphas,rotation=45)\n", " plt.yticks(np.arange(0,len(reps))+0.5)\n", " ax.set_yticklabels(reps)\n", " plt.ylabel(r\"$\\alpha$\")\n", " plt.xlabel(\"$%s$\" % 'T' if fig=='a' else 'S')\n", " bar = plt.colorbar()\n", " bar.set_label(\"Log$_{10}$ of $\\hatz$\")\n", "\n", "plot_('a')\n", "plot_('b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Table 2: Selected values from the color map in Figure 2. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z\talpha\tT\n", "2.02e+12\t0.05\t20\n", "4.56e+03\t0.05\t5\n", "6.08e+09\t0.05\t10\n", "1.54e+29\t0.05\t185\n", "8.94e+03\t0.001\t20\n", "1.79e+04\t0.01\t15\n", "\n", "z\talpha\tS\n", "3.81e+13\t0.025\t26\n", "4.56e+03\t0.025\t7\n", "1.54e+29\t0.025\t135\n", "1.54e+29\t0.05\t110\n", "3.47e+07\t0.001\t26\n", "2.98e+05\t0.01\t15\n", "\n" ] } ], "source": [ "# Table 2\n", "params_list = {'a':[(0.05,T),\n", " (0.05,5),\n", " (0.05,10),\n", " (0.05,185),\n", " (0.001,T),\n", " (0.01,15)],\n", " 'b':[(0.025,S),\n", " (0.025,7),\n", " (0.025,135),\n", " (0.05,110),\n", " (0.001,S),\n", " (0.01,15)]}\n", "for fig in ['a','b']:\n", " print(u'z\\talpha\\t%s' % ('T' if fig=='a' else 'S')) \n", " for alpha_,n_replicates in params_list[fig]:\n", " z = trillion.num_odors(results,fig=fig,alpha=alpha_,C=C,N=30,n_replicates=n_replicates)\n", " print('%.3g\\t%.2g\\t%d' % (z,alpha_,n_replicates))\n", " print('\\r')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Figure 3 (not shown here) is a schematic produced in Illustrator." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 4: How many discriminable stimuli do we estimate if we vary the size of the molecular library $C$, and consider same performance, best performance, or worst possible performance? " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fmRsAItIC6MeRlQDLOo1mDDAcGF/sPasCI4A2wBZgqYjMUNXPAk/ZgesFAHfX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\nMHDgQEpLS3n44Yf9DoU1a6B1a7ec7+zZfkcTBV9/7ZL5LFg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute (using pooling across tests; change 'fig' to 'b' to do pooling across subjects). \n", "C_list,z_same = trillion.num_odors_vs_C(r,fig='a')\n", "z_worst = [trillion.disc(N,_,N) for _ in C_list]\n", "z_best = [trillion.disc(N,_,0) for _ in C_list] \n", "\n", "def plot_(C_list,z_list,color,label):\n", " plt.scatter(C_list,z_list,color=color,s=40)\n", " plt.plot(C_list,z_list,color=color,label=label)\n", " \n", "plot_(C_list,z_same,'b','same performance')\n", "plot_(C_list,z_worst,'r','worst possible')\n", "plot_(C_list,z_best,'k','best possible')\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.xlim(C_list[0]/2,C_list[-1]*2)\n", "plt.ylim(1,1e85)\n", "plt.xlabel(\"Number of components (C) \\n in the molecular library\")\n", "plt.ylabel(r'Minimum allowable number of discriminable stimuli $\\hat{z}$')\n", "\n", "\n", "# Add dashed lines indicating estimate in the original paper. \n", "z_same_C = z_same[list(C_list).index(128)]\n", "plt.plot([C,C],[1,z_same_C],color='k',linestyle='--')\n", "plt.plot([C_list[0],C],[z_same_C,z_same_C],color='k',linestyle='--')\n", "\n", "# Save data. \n", "def savetxt(kind,x,y):\n", " np.savetxt('z_vs_C_%s.csv' % kind, np.vstack((x,y)).transpose(), delimiter=\",\")\n", "savetxt('same',C_list,z_same)\n", "savetxt('worst',C_list,z_worst)\n", "savetxt('best',C_list,z_best)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 5: Alternative versions of Figure 4c from the original paper, comparing $\\gamma$=1 vs $\\gamma$=2. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2m5nhnEuJ9BkaR0SCFY6E2f+B/VmzbQ2zrpzFIfvFWA9iE97ezx14CTIO+vmP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\npox7+vIBdgH5hRChwFlUuusB22hNQtl+ejtVp1cl2hZNKnMqmpmakZ3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rJa24Y7lDw/0N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\nfs60NdOYm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,(ax1,ax2,ax3) = plt.subplots(1,3,figsize=(12,5))\n", "_ = trillion.fig4x(results,'a',alpha=alpha,gamma=2,axes=ax1,xlabel=False)\n", "for color,N_ in [('blue',10),('magenta',20),('green',30)]:\n", " z_min = trillion.disc(N_,128,N_)\n", " ax1.plot([0,100],[z_min,z_min],'--',color=color)\n", "ax1.text(55, 3e4, 'Minimum possible', fontsize=9)\n", "_ = trillion.fig4x(results,'a',alpha=alpha,gamma=1,axes=ax2,ylabel=False)\n", "_,z_high = trillion.fig4x(results,'a',alpha=alpha,gamma=2,axes=ax3,Ns=[30],xlabel=False,ylabel=False,lines=False)[0]\n", "_,z_low = trillion.fig4x(results,'a',alpha=alpha,gamma=1,axes=ax3,Ns=[30],xlabel=False,ylabel=False,lines=False)[0]\n", "d = trillion.fig3x(results,fig='a',plot=False)\n", "x = np.linspace(0,100,1000)\n", "y1 = [trillion.disc(30,128,30*(100-xi)/100) for xi in x]\n", "y2 = [trillion.disc_prime(30,128,30*(100-xi)/100) for xi in x]\n", "ax3.fill_between(x, y1, y2, facecolor='gray', interpolate=True)\n", "ax3.plot([d,d],[z_low,z_high],'-',color='k',linewidth=3)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Supplemental Information" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure S1: Regeneration of trillion's Fig. 3a and Fig. 4c using their raw data and reconstituted methods (see Fig. S7 for reproduction of their 3b and 4d, and Fig. S10 for reproduction of their 2b and 2c)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mixture overlap at which 50% of subjects can significantly discriminate is 51.47%\n" ] }, { "data": { "image/png": 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DOYWFhVx9+dVkzMygX24/AJ5q8JQmtolUs0ovuxotVMRFKu+///0vAwYM4Jtv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\nk09zPyWB4DUgj1MbnMr9U++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U/F3wDJDl7o8X+5aubdXbvgmYmdUjMFH7rfLeFNXLrprZ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\njFIRFxERiVEq4iIiIjFKRVxERCRG/T/Oe7MlSglRKAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S1A: Regenerate Fig. 3a from Bushdid et al. using their data and methods.\n", "overlap = trillion.fig3x(results,fig='a',alpha=alpha)\n", "print('Mixture overlap at which 50%% of subjects can significantly discriminate is %.2f%%' % overlap)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated number of discriminable stimuli for N=10 is 1e+08\n", "Estimated number of discriminable stimuli for N=20 is 1.27e+11\n", "Estimated number of discriminable stimuli for N=30 is 2.02e+12\n" ] }, { "data": { "image/png": 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W8Wd5HVpgDuNmIJ4E0oHauLL8y7wMqnDJNZEQkVP8Ll8FPhaRQbh6hJq4XRyv\nHOXeb+L6hoE7+uRIiYQCpxxhPLeYRuOamB4nIuuBAao6XET6ATNw2z+HqeryQO9pjDGF1Z6De7ht\n2m18uPRDAHrV68XrV79OqaKlPI4sQMtwtRDf+67/i1uIL53rO0wY5NrZ8ihHh/9DICeDisj9qvrC\nEcbvVdWXAnlOJFlnS2NMrFuyaQmdxndi1V+rKFW0FG+3epuu53X1OqzAZOB2YzwGHMT9aJsENPUy\nqIItmM6WAbXIDpaI7FHVskcY/7vddjSxRMIYE6tUlXd/fJc7pt/BwYyDnFPlHMZ1HMcZlQvIcUir\ngR649oIAvXFJRUR6JseuSLTIzhcRaYIre4n3vfZXG1d7YYwxJgJ2H9zNLVNvIflnd0JA3/P7Mrjl\nYEoWLQAViZnAG8CDwAGgOu68jKu9DMpA4H0kagGP41p5+O8DUlU92lEnSbg6iOK4Oom/34drTNU/\nT9EaY4zJl0V/LqLT+E6s2b6GMsXKMLT1ULrU7eJ1WIFJxXUymu27vhF3/GIlrwIy/gI9/XMhrrXH\nOFy/sL+p6hcBvH+UqhaQxTdb2jDGxA5V5a3v3+LuGXdzKOMQ51U9j7Edx3LacQXguMtM3KzDvcBe\n4HhgKHCtl0HFprDXSIjILqCSqmbk6yFuWSNVVX8Tkeq4utoM4GFV3ZSfe4aTJRLGmFiwK20Xfab0\nYfyy8QDcesGtvHzlywVjKWMhcAfwre+6PfAWLpkwIRdMIhHQoV3AVNy2y/x6E7fDF1xZTBHc8sY7\nQdzTGGNMLn744wfOf+d8xi8bT9liZUlun8xbrd+K/iRiE64FYgNcElEN+Ag3H25JRFQKdEaiMu68\ntFXAFr8Pqar2CuD9u1W1nIgUxdVG1MJt2vlTVY/LV+RhZDMSxpiCSlUZsnAI9828j0MZh6hfrT5j\nO47l1Eqneh3a0R0CBgNP4dodFgXuxh289a89fybUIrFrIwn3v3k5rkZCcbsxAv1uu1tEquEObv1F\nVfeISHHcXxVjjDEhsDNtJ70n92bC8gkA3P6f23npypcoUaSEx5EdwzRc0rDad90aN3ddx7OITB4E\nmkhcAZyoqvndrvk6bsWrOHCXb6whLjExxhgTpIUbF9J5fGdSd6ZSrng5hrUZRoezAjrs2DsrcQnE\ndN/16bg+yi09i8jkQ6BLG/OBm1R1bb4fJHI6kKGqa3zXpwHFVXVpfu8ZLra0YYwpKFSVwd8O5oGZ\nD3A48zBNyNJFAAAgAElEQVQXVL+AMR3GULtSba9Dy90u3BLGYFz1XDngf0A/bJ7aI5FY2pgFzBCR\n4bgaB/AtbahqUiA3UNWVOa5XBRylMcaYf9l+YDu9JvVi0spJAPS/qD8vNH+B4kWKexxZLjKB94GH\ncdV2AvQBngGqeBeWCU6gMxIpvpf/+mRVvSLEMXnOZiSMMdHumw3f0Hl8Z9btWkf54uVJapvEdWde\n53VYuVuA286ZdcDWpbimUhd4FpHxE/VnbRQ0lkgYY6JVpmby8oKXefjLh0nPTOfCEy5kTIcxnFzx\nZK9DO7I/cG2tP/BdnwC8ANyAm5EwUSHsSxsikmu/CVUN6JRQY4wxwfljzx/0mdyH6WtcdeJdDe5i\nUPNBFIsv5nFkR5AGvIJbttiHK7W/F7esUeYo7zMFTqA1Eum5jCsQH6JYjDHGHIGqMvrn0fT7tB87\n0nZQsURFhrcdTtsz2nod2r8pMBm4B/jNN9YOeAk4xaugTDgFmkjk/N9fDZdXTgn0QSLSArgeqKKq\nrUXkP0A5VZ0V6D2MMaaw2bpvK7dNu42Pl38MwFWnXsV7bd7jhLIneBzZESzDbfCf6bs+G7eds5ln\nEZkIyHeNhIiUB747xumfWZ/bH/fX6z3c+RrlROQc4B1VvTRfAYSR1UgYY6LBxBUTuXnKzWzdv5Uy\nxcrwypWv0Lt+b0SirLhgJ2775hDcKUoVgCeB2wj8x1XjKU+KLUWkBvCTqlYM4HN/A5qq6loR2aGq\nFUUkHtiqqlF3EKwlEsYYL+04sIM7P7uTUT+NAiAxIZHhbYeTUCHB28ByygCGAf8HbMOd3nQzrkdE\nZQ/jMnkWiWLLUTmGSgGNgQ8DfE4ZYH2OsWK48zaMMcb4zFgzg96Te7Nxz0ZKFinJc82eo99F/YjL\nvebdG3OBO4FFvuvGuAZT9TyLyHgk0EmnX8k+XwNcDe7bqjoz97f8w1zgIeBpv7H+wOwA32+MMTFt\nz8E93D/zfob+MBSAi0+6mBHtRnDaccdcPY6s9cADQLLvugbwItAR285ZSEWkj4SInIArzKyM20W8\nFne+W2tV/TPsAeSRLW0YYyJpTuocek7qydqdaykaV5Qnr3iS+y69jyJxUVRgcACXMDzre10C1x/i\nAdwctSnQIlIjISJX4iatSmcN4VpkDwjw/XHAhbgjxNcBC6O1B4UlEsaYSDhw+ACPfPkIg78djKLU\nq1aPke1GUrdqXa9Dy6bAx8B9wO++sY64plK1vArKhFokaiSGAJ1wSxH7s4Y5yjHiItI0l49vw+Wv\nib7Aw7b9U0ROxpUBlVfVjr6xRFwp0M9AsqrOCdfzjTEmNws3LqTbJ91Y+ddK4iWeRy57hEcbPxpd\nzaWW4uogshahz8XVQSR6FZCJRoHOm90InKuqOQsmj2YYR0k0/IStr6vvtNI+IjLObzgTt6xSHNgQ\nrmcbY8yRHMo4xJNznuTZec+SqZmcWflMRrQbwYUnXuh1aNn+AgYAb+O+YlbCVbj1xbZzmn8J9K/E\nVtzBrwFT1YQ8RxMAEUkCWgFbVLWu33hLXOuTeOA9VR2Uyy3mqupXIlIFeBm4KRxxGmNMTks2LaHb\nxG78tPknBOHeS+7lqSueomTRkl6H5qQDQ3FJxHbcV9N+wBO4ZMKYIwg0kXgJ+EBEngM2+X9AVX87\n8lvCZjjwOjAya8DXk2IIrn/aRuA7EZmsqstzvtmv+GEnblbCGGPCKj0znefnP8//Uv7H4czDnFLx\nFN5v+z6X1brM69CyzcYtYyz1XTfBLWOc41lEpoAINJF4y/ff1jnGAzprQ0SKA4/izns7AXceXDLw\ntKqmBRiDe6DqXBFJyDF8EbBGVVN9z0sG2orIZmAgUF9EHlTVQSJyLXAlrvfa63l5tjHG5NWKbSvo\nPrE7CzcuBOC2/9zG882fp0yxKDm5KhVXSPmx7zoBN1fbDtvOaQISUCKhqsF2QnkLOA3XO2IdUBNX\nBHki0DPIe+O7j3/9xgaggapuB271/0RV/QT45Fg3TExMJCEhgYSEBBITE0lMTAxBmMaYwiJTM3nt\n29d4+MuHSUtP46RyJ5HUJonmtZt7HZqzDxiE232RhiuBfwR3QmcJD+MyEZGSkkJKSgqpqamkpqYG\nda9I9ZHYDtRW1R1+Y5WAXwNpsX2E+yUAU7JqJESkPdBSVfv6rm/CJRL98xmvbf80xuTb2h1r6Tmp\nJ3N+d5vCup/XnVdbvkqFEhU8jgw3jzwGuJ/scvMuuKTiJK+CMl4L+/bPEPgTl+/u8BsriVviCIWN\nuP5qWWpgOzKMMRGmqrz747vcM+Me9h3eR5XSVXin9TvRc9z3j7jjE+f6rs8HXgMaehaRiQFhSyRy\n9JEYBUz39aNYj1va+C9+BZNB+h6o45up+APojKvHMMaYiNi4eyO9J/dmxq8zAOhwVgfeavUWlUtF\nwelVPwOPAxN818fjqsd6EkCVmzFHF7alDRFJ5Z99JHI2sMrqjJmnPhIiMhq4HDgO2AIMUNXhInIV\n2ds/h6nqs0HEbksbxpiAqCofLv2Q/tP7szNtJxVLVOTNVm/S+ezO3h/3vRK3dTMZ99W3BO5HuEdx\n5ebG+HhyjHgss0TCGBOILfu2cOvUW/lkhavfblWnFe9e8y7Vy1b3NrDfgCdxc8GZuLOWbwYexu2b\nMyaHsNRIiEjOLpb+p3/+PaaqNQN5kIhUxW3TrOx/H1VNCixUY4yJDqrKmF/G0H96f7bt30bZYmV5\nteWr9KzX09tZiHW4DpTDcc2ligC9cTMQAX2lNoVNejrMmBHcPY5WI9HV7/WFQHdce5Ks7Zv9CbDG\nQUTaAR8Aq3HtTX72/XceYImEMabA+HX7r9z+6e18/uvnADQ5uQlJbZKoVcHDE6z+wNU8vAscAuJw\nX7EHAKd4F5aJXqtWwfDhMGIE/BnkGdwBLW2IyC/Alaq6wW/sJOAzVT1m3zPf+59Q1bEiskNVK4pI\nT+AcVb03iPjDwpY2jDE5Hco4xAvzX+DpuU+Tlp5GhRIVeL7Z8/Q+vzdxEmyrnXzagtu2+SauF4QA\n1+MKK0/3JiQTvfbuhfHjISkJ5s7NHq9TB1avDnONhK8PxCmqutNvrAKwNpA+ECKyW1XL+V7vwHVt\njwM2qerx+Qk8nCyRMMb4++r3r7h16q0s3+a67t907k281OIlqpSu4k1AfwEv4nrz7vONXYcrrLSW\n1saPKnzzjUsekpNdMgFQujR06gS9ekHDhhAXF/4+EpOBSSLyDNnbNx/2jQdii4hUU9VNuIasl+CO\nE/cojTfGmGPbtn8bD8x8gOGLhwNQp1Id3mr1Fk1PaepNQDuBV3y/9vjGWuMKK+t7E5KJTps3w6hR\nLoFY7nfq1KWXuuShUycoWzY0zwo0kbgNN1n2Fq7m909gLC7/DcR7QCNgPO6fwCxc8eZLeQnWGGMi\nQVUZsWQE931+H38d+Iti8cV4uNHDPNToIUoU8aB/9F5c46gXcMkEQAtcAtEg8uGY6JSeDtOnw7Bh\nMG2auwaoWhW6dYOePeHMM0P/XE+2f4pILaC0qi6L+MMDYEsbxhReK7at4Napt/7d3vqKhCt4q9Vb\nnF7Zg6KD/bj6h0G4OVxwXXSeAqLo4FDjrRUrXOHkyJGwyXc+d3w8tGoFvXvDVVdB0aJHv0dE+kiI\nSAtcGU8VVW0tIv8ByqnqrPw8OJpZImFM4XPg8AEGzh3IoPmDOJx5mMqlKvNyi5e56dybIr+lMw14\nB3gW8H1j4BJcAtEEO5XTsHcvjB3rli7mz88eP/10lzx07QrVqgV+v7CftSEi/XEd2t8DOviG03CT\nbZcG8P7iQA+gHuB/dq6qarc8xGuMMSE389eZ3DbtNn7d8SsAfer3YVDzQVQqWSmygRzCbYh/huzT\ngi7AJRAtsQSikFOFr792ycOYMbDPV2hbpgx07uxqHy65BCKd9wa6a+M3oKmqrvXbvhkPbFXVY/5L\nE5Fk4FxgCnCA7OZWqqqB1llEjM1IGFM4bN67mXs+v4ePln4EwNnHn83brd+mUc1GkQ0kHdeF8klc\nOTpAXVwC0QZLIAq5TZvcskVSEqxcmT3eqJFLHjp2dMlEMCJx+mcZ3G4Nf8WAgwG+vyVwsv8x4sYY\n45VMzeTdH97lwS8eZNfBXZQsUpIBlw/gnkvuoVh8scgFkoE7B+MJXLs+gDN81x2wfW2F2OHD8Omn\nrnDy008hI8ONV6sG3bu7wsnTo6RXSKCJxFzgIVzz1Sz9gdkBvv93oHge4jLGmLD4afNP3Dr1VhZs\nWABAy1Nb8sbVb3BKxQi2gMzEncT5OJBVcn6q7/oG7ETOQmz5cjfzMHIkbNnixooUgXbtXO1Dy5bu\nOpoEurRxAm5ZojJu++da3C7m1qp6zOaaInIv0BFXU7HJ/2PRWKxpSxvGxJ59h/bxxJwneHnBy2Ro\nBtXLVGdwy8F0OKtD5IopFfeVdACwxDdWy3fdjcB/tDMxZc8eV/OQlAQLFmSPn3mmSx5uuslt4Qyn\nSO3aiMOduVELd97GQlXNDPC9qb6X/3pYXo8RjwRLJIyJLVNXTaXfp/34fdfvCMJ/L/wvTzd5mvIl\nykcmAAVm4BKG73xjJwL/hztUK4KrKSY6qMK8eS55GDsW9u9342XLwvXXu9qHBg0iVzgZ9kRCRCap\natsjjE9Q1evy8+BoZomEMbFhw+4N3PnZnUxYPgGA+tXqM7T1UC488cLIBTEbd/rm177rqri+wLcA\nHvS2Mt7644/swsnVq7PHGzd2yUOHDq59daRFIpHYo6r/aqaZtYMjl/c0VtWvfK+b5HZvW9owxoRa\nRmYGQxYO4dHZj7L30F5KFy3N002ept9F/SgSF6H1g/nAY2RXkh0HPAjcDnjwjcJ459Ah12kyKckV\nTmb65vKrV4cePVzhZJ06noYYvl0bIvKU72UxEXmSf25COoXsjUpH8ibZx8ckcYRlDZ+oW9owxhRc\n3//xPbdMvYUf//wRgGvPuJbBLQdTo3yNyASwELeEMcN3XQG4F7gTCNHZBqZgWLYsu3By61Y35l84\n2aJF9BVO5sexfgtZ//LE7zW4pGAdrsb4iPyPF1fVhHzGZ4wxAdl9cDePznqUN757g0zNpGb5mgy5\nagjXnH5NZAJYjEsgpviuy+La+N2DSyZMobB7tyucHDYMvv02e/zss7MLJ4+PujOvgxPo0sbNqvpO\nBOKJCra0YUzBoap8vPxj7vzsTv7Y8wfxEs/dF9/N44mPU6ZYkF16AvEL8D/ckYQApXCb4+/HLWeY\nmKcKc+e65GHcODhwwI2XKwc33OBqHy68MPIdJ/MiIrs2fA8qi9sC+vfDVPW3AN5XAbgDd9BtzhbZ\nLQIOIEIskTCmYPhp80/cPeNuZq11pVYNTmzA0NZDOa/aeeF/+DJcK+vRuDna4rhzkh/CFVSamLdx\nI4wY4Q7MWrMme/zyy93sQ/v2UKqUd/HlRSTO2jgL+BDI+a9TCax1yjhcj7ZPcGd0+L/fGGPyZMu+\nLTw26zHeW/QemZpJpZKVeKbJM9x8wc3ESRjbQSrwFe4472m+saJAX+AR3JZOE9MOHYIpU1ztw2ef\nZRdOnniiK5zs0QNOPdXLCCMv0DKPt4AU4ApcM6qTgYHAgqO8x99FuFNDA22pbYwx/3Iw/SCDvx3M\n0189zZ5DeygSV4T+F/VnwOUDwnvAVjquE+WLZPeBKAH0xO3EqBW+R5vo8PPPLnkYNQq2+Y50L1oU\nrrvOLV20aOGO7i6MAq2R2Akcr6qHRWSXqpYXkdLAz4E0lBKR6cBDqrrkWJ8bDWxpw5jooqp8suIT\n7p95P7/tcKuprU9rzYvNX+T0ymE8cGAfMBx4GfcjFLi6h37Af4EYK5oz/7RrFyQnu9qH777LHq9b\n1y1d3HgjVK7sXXyhFIlDuw7geq8dBraKSC1gO4GXEvUApovIAmAz2TUWqqpPBh5u3ojIybjeceVV\ntaNvrC3QCigHDFPVmeF6vjEmeIv+XMTdM+5mzu9zAHdC58tXvkyL2mEsr9oCDAHewH2lA6iN28bZ\nHVdQaWJSZibMmeNmH8aPhzTfYnz58tCli5t9uOCC6C6cjLRAE4l5uLMy3sfVJk/HnfwZaDOpgbjV\nw6q4b+ARoaprgT4iMs5vbBIwyVcA+iJwxEQiYr33jTEBOW7QcTx1xVP0vaBv+JpKrcLNPowgu5qr\nAW4HRjvsMK0Ytn59duHkb35bCJo0ccnDtdcWnMLJSMvTrg0AEYkHuuB2X4xU1X0BvGcPcLqq/pGv\nKP95ryTcjMIWVa3rN94SeBX3T/09VR3k97FxWTMSfmMvAh+o6uIjPMOWNozxSFp6Gq8seIWB8way\n99BeisYV5fCAw+w4sIMKJcLUkOFrXAHlJLJLwK/BJRCN+GcrPhMzDh6EyZPd7MOMGW4bJ8BJJ7lu\nkz16wCkRPBTWSxHb/plfIvIT0FRVt4bgXpcBe3FJTF3fWDywEmgGbMSVQ92gqst9Hx/nt7QhwHPA\n56r6ZS7PsETCmAhTVcYvG8/9M+/n912/A9D29La80PwFTqt8GiH/N5kJTMYlEFnnYBQDuuKWMM4M\n7eNM9PjpJ5c8fPAB/PWXGytWzHWc7NULmjUrfIWTkdj+GWwfiJG45YTXcTUS/jfI01kbqjpXRBJy\nDF8ErFHVVF+8yUBbEdmMW1apLyIP+mYp+gNNgXIicqqqDs3L840xoff9H99z94y7mbduHgB1q9Tl\nlStfoekpTUP/sDTcV6SXcEsZ4DpP3o776lAt9I803tu5E0aPdoWTP/yQPX7uudmFk8dZA7F8CXSh\nMdg+EP18/x14hI+F4qyNE4H1ftcbgAaquh241f8TVfU14LVj3TAxMZGEhAQSEhJITEwkMTExBGEa\nY/xt3L2RR2Y9wsglIwE4vtTxPN3kaXrX7018XIh/JPwLdwLQEFwxJbhtm3fjjvKOQBNME1mZmZCS\n4pKHCROyCycrVHCFk717Q/36hbNwMiUlhZSUFFJTU0lNTQ3qXoEmEkH1gYjAWRshX4dISUkJ9S2N\nMT77D+/npa9f4rn5z7H/8H6KxRfjzgZ38n+X/R/lS5QP7cPW4gook4D9vrHzcfUPHQj8q6ApMNat\ng/ffd4WT/t8jmzVzSxft2kHJkl5FFx1y/oAczAaDQP8JfQ2cAQTcByLCx4hv5J+HitXAzUoYY6KI\nqjL659E8+MWDbNjt/oled+Z1PN/seWpXqh3ah32Pq38Yj6uHAGiJSyCuwAooY0xaGkya5GofZs7M\nLpysWTO7cDIhwcsIY1egDamq4rZ8BtwHQkR+zjoBVERSyWXWIJCGVke4dwIwxa/Ysgiu2LIp8Afu\nIN+/iy3zcX8rtjQmxL7Z8A13z7ibbzZ8A0C9avV45cpXSExIPOZ7fYVgx35IJvAZLoFI8Y0Vwe0z\nuw+oe+S3mYJr8eLswskdO9xY8eJuu2avXtC0KcSFsWt6rIhEQ6o894HwP0YcqK2qGXmM7YhEZDRw\nOXCciKwHBqjqcBHpB8zAbf8clt8kwhgTWut3reehLx/io6UfAVC1dFUGNh1I9/O6h64O4iDwEa4z\nzDLfWFngFuBO4KTQPMZEhx074KOPXO3DokXZ4/Xru+ShSxeoFMaO6eafAp2RyHcfCN9swR6gQkE5\na8NmJIwJ3r5D+3h+/vO88PULHEg/QPH44txzyT083OhhyhYvm6d75TojsRMYCgwG/vSNnQjchTtI\nK8TlFsY7mZnw5Zdu9uGTT1wPCICKFd2Oi169XCJh8icSMxJrce2x80xV00VkNe748Y35uYcxpuDI\n1Ew++OkDHv7yYf7Y43726HR2JwY1G0RChYTQPGQdLnl4B9dVBtyyxX3A9bh+ECYmpKZmF06uW+fG\nRNwhWb16Qdu2UKKElxGaQBOJYPtAfABMEZHXcNs0//7RIkTFlsaYKDBv3TzunnE33//xPQAXVL+A\nV1u+SqOajULzgCW4+ocxuBM5wVVG3QdciRVQxgBV+PFHd1T35Mn/XLpISHCFk927Qy07cTVqBLq0\nkUoQxZK+93Oke+Sn2DLcbGnDmLxZvGkxj856lGmrpwFQvUx1nm36LF3P60qcBFnppiBxgjbX7JNx\n4oFOuATi/OBub7yXlgazZrnEYepU2Og3d12qlJt16N0brrjCCifDJepbZBc0lkgYE5iV21byeMrj\njPllDACli5bmnkvu4YGGD1CmWJAdng4DY4EXQRYLikJpoA+uBiIhuNsbb23eDNOmuZmHzz+H/fuz\nP3bCCdCmDVxzjTs0y5Yuwi/qEwnfkkayqn7tN3Yp0ElV7wp7AHkkIpZFGHM05XF7p+rhet6m4064\nmQcc8xi//NFn1PWptWr8AkkVfvkle8ni22+zez0AnH++SxzatCm83Sa9FJZEQkRWqOoZvtfrj/hJ\nro9EzQAC3Aac6L9rQ0RKAOtV9fi8hx1eNiNhzJFt3ruZgXMH8vYPb3Mo4xDxEk+v+r14rPFj1Chf\n49g3OJo/cM3r3wZ2+cbOAO4D6RNgHwkTVQ4dgrlzXeIwZQqsXZv9seLF3WxDmzbQurU7cdN4J1y7\nNvr6ve6ay+cE+i87E/dzi784rDTKmAJhx4EdvPD1Cwz+djD7D+9HELrU7cL/Lv8fdY6rk/8bKzAH\neAuYQHYB5WW4DpStcF8p+gQVvomg7dth+nSXOEyfDrt3Z3/s+ONd0nDNNdC8OZSx801iQq6JhKrO\n9bs8XlXH5fwcEekQ4HPmAU+LyP2qmuk79vsJYO4x3meM8dDeQ3t57dvXeH7+8+w66KYJ2pzehqeu\neIpzq56b/xvvBEbgZh9W+MbigPa4BKJBMFGbSFu9OnvJYt48yPBrP3j22dlLFhddVPiO5y4MAm5I\npar/6iAjIjtUtWIA768BTAWqA78DNXHtY65R1dyWTTxjSxumsEtLT2Po90MZOG8gW/a5ozKbntyU\nZ5o8Q4OTgvgu/x0ueRgNHPCNVcfNf/Yl1w6UAbfINhGRkQELFmQvWaxYkf2xIkWgcePsYslTTvEu\nThO4sDWkEpFTcMsP4nvtrzbZXwqOSlXXi8j5uFNEa+B6SSwMVdtsY0xopGemM2LxCJ6Y8wTrd7sc\n/+KTLuaZJs/Q5ORcz947un1AMm754ge/8WbAbcA1QNFgojaRsGcPzJjhEodp0+Cvv7I/VqECXH21\nSxxatnTXpvA46oyEiGTm+kHXmOp/qjo05FF5zGYkTGGTqZmM/WUsA2YPYPX21QCcW/VcnmnyDK3q\ntMrfEcPLcLMPI8kunqwE9MSdgZGH0gqbkfDGunXZSxYpKa54Mkvt2m7WoU0baNgQiloyWKCFbUZC\nVeN8D/hKVRvn5wG+9zcBUlX1NxGpDgwCMoCHVXVTfu9rjAmOqjJ11VQenf0oP23+CYA6lerwROIT\ndD6nc96bSR3CFU2+BXzlN34JbvahA1AyFJGbcMjMhB9+yF6yWLIk+2NxcS5hyFqyOOMM26JpnHz1\nkfAtc2SqamqAn78CaKGq63yndyqQBlRW1TZ5DiDMbEbCFAaz187mkVmP/H2sd41yNXj88sfpXq87\nReIC7Z7vk4o7PCsJ2OIbKw3chEsgzgsuVpuRCJ/9+91hWFOmuF+b/H60K1MGrrzSJQ5XX+12XZjY\nFPaGVL5v/q+r6tci0hN4E5cM3KGq7wXw/t2qWk5EiuKWRGrhDv79U1WPy0/g4WSJhIll3274lv+b\n9X98ufZLAI4vdTz/d9n/cct/bqFEkTy0EMwApuNmH6aTvRm8Li55uBEoF5qYLZEIrU2bXCvqyZPh\niy/ggF+1W40a2bssEhNdvwcT+yJx+mczoLvv9b2+653AJOCYiQSwW0SqAWcDv6jqHhEpjpVYGRMx\nSzcv5bHZjzFp5SQAyhcvzwMNH+COBnfkrZ31JmAY7uRN32mMFMOdfXErcCnWISbKqMLSpdlLFgsX\n/vPj//lP9pLFeefZkoXJm0ATiaKqekhETgQqqup8ABGpGuD7XwcWAsVxXfIBGgLL8xKsMSbv1mxf\nw+MpjzN66WgUpVTRUtzZ4E7uv/R+KpY85u5tR4EU3OzDJ2Q3jqqNK5zsCVQOeegmCAcPwpw52cWS\nWUdwgzu7olkzlzi0bu3OtjAmvwJd2pgDfIY7JkdU9WYROQn4RlUDamwqIqcD6ar6q+/6NKC4qi7N\nb/DhYksbJhas37Wep756iqRFSWRoBsXii3HrBbfy8GUPU61MtcBusoPsxlErfWNxQBvc8kUz/t2z\nNgxsaSMwf/0Fn37qEocZM9yWzSxVq/6zq2SpUt7FaaJPJJY2egNP4WqyH/CNXQJ8eJSgGqvqV77X\nTfzG7RR5Y8Jow+4NvDD/BYb+MJSDGQeJkzh61evFgMsHUKtCgP/8vsPNPiST3S3mBFzTqD7k2jjK\nRN7KldlLFvPnu50XWc491yUO11wDF15oR3Cb8Ajb6Z8i8rOqnuN7nUou53Ko6slhCSAINiNhCqI1\n29cwaN4gRiwZweHMwwB0PrszTyQ+wemVTz/2DfbhOk6+zT8bRzXH1T542DjKZiSypae7hCEreVi9\nOvtjRYu6Asmsg7ASEryK0hQ0Ydu1ISKvqeodfte9VXWY3/XHqto+Pw+OZpZImIJk6ealPDvvWcb8\nMoZMzUQQOp3diUcueySw8zBC2DgqXAp7IrFrF3z2mUscPv0UduzI/lilStCqlZt1uPJKKBeinTKm\ncAlnIvGPMzZynq2R2xkcBZ0lEqYgWLhxIc/MfYbJKycDUCSuCN3O7caDjR7ktONOO/qbj9U4qiOQ\nh52g4VYYE4m1a7MLJefMcTMRWU4/PXuL5iWXuPMtjAlGJGok8kxEnsItZ2QFlvVVQPxeo6oDwhWD\nMbFGVUlJTWHgvIF88dsXAJQoUoK+5/flvkvvo2b5mke/QSr/bhxVBtc46laCbhxl8i8z023LzFqy\n+Pnn7I/Fxf3zIKzTjpEnGhNJ4cxja5CdMJTAHRD8He70z1rAhcDHYXz+v4jIWcDjwF/Al6oa0ecb\nk/QwlscAACAASURBVF+qyrTV0xg4dyALNiwAoGyxsvz3wv9y18V3UbXMUXZiR7BxlMmbfftg5kyX\nOEydClu2ZH+sbFm46iqXOFx1FRwXda37jHGOlUjE++24EKBIjutcT5ZX1R5Zr0UkGbjB/xu3iFyH\na2ETSS1xHTrnicgkIpzIGJNXGZkZfLz8YwbOHciSze7gg0olK3FXg7vod1G/o/eBOFrjqNtwyxjW\neCjiNm7M7ir55Zeu30OWhITsJYvGjaFYMc/CNCZgx6qRSOWfuy0kx3VAuy5EZDeukVWG31hR4C9V\nDepnIRFJAloBW1S1rt94S+BVXLLznqoOEpHjcTMS+4FLVbVRLve0GgnjqcMZh/ngpw94bv5zrPpr\nFQDVy1Tnvkvv4+YLbs69E+UhXMeXkbi+s/6No24FelAgG0cV5BoJVVi8OHvJ4ge/HTEicNFF2UsW\n55xjXSWNN8J+1kawRORHYISqDvYbuwPooarnB3nvy4C9wMisREJE4nHtc5oBG3FLKjeo6nK/j3+s\nqu1yuaclEsYTBw4fYNiiYbzw9Qus2+WmEU6ucDIPNnyQHvV6ULzIEQ4+UNx2zZG47ZvbfOPxuMZR\ntxKxxlHhUtASibQ0mD3bJQ9Tp8KGDdkfK1kSWrRwiUOrVlAtwN5gxoRTVBZb5tAbmCgiD+C+sZ+I\n+1npumBvrKpzRSQhx/BFwJqs00l9SyttRWQ/8AjuXMLng322MaGy++Bu3vruLV7+5mW27HML5Wcd\nfxYPN3qY68+5/sinca7HtYQbyT+bzZ+NOxnnRlwTKRMRW7bAtGlu1uHzz139Q5YTTnB9Hdq0gSZN\nXDJhTKyISCKhqotEpA5wMe5L25/A16p6OEyPPJH/b+/O46SqzvyPfx6azYV9B8FGBJRVUEERtI1K\njBBJDMQhE4iYoJmJE83MZJLRmUwmsyTxl0kwZpwYFBMwYETFBTUGlMaFHVcW2aQVaEA2kR26+/n9\ncW51VfUGFlXdXd3f9+vVL6rvvXXr1EWpb517znnCP7MxW4Gh7v4hYWb8SeXl5ZGbm0tubi55eXnk\n5eVloJlS3+05vIdfL/01v172az45+gkAF3e6mHtG3MOYC8bQwMp0IxwkTNucDrxC/EZjO0JwmAhc\nhMY+VAN3WLMmPkVzyZKwLeaii+K3LAYP1qqSUrvk5+eTn59PQUEBBQUFp3Wuapt97O7HSZ6xntGX\nO90T5Ofnp6EZIhUrPFDILxf/kt+u+C2HToSvrleeeyV3D7+bkT1GYok3youBBYTw8CRhhA+EEnhj\nCOFhJKqlm2HusGlTuGWRnx9+Cgvj+xs3Dr0NsUJY3U4yE1ekJpX9gmynMTinri5jso0w/TSmK6FX\nQqRGbd63mXvfuJdpb0/jePFxAK4//3ruGXEPw7uVGfu7hhAeHiX8Fx0znBAexgEtq6PV9ZN7WBQq\nFhwWLAgzLhK1awc33BB6Hq67LkzZFKlv6mqQWAH0jMZOFAI3A+NrskFSv63ZtYafvf4zZr43k2Iv\nxjC+cuFXuHvE3QzulDDeeBdhwOR0kutddCeEhwmEGRiSEQUFycFhy5bk/W3ahFoWeXlw9dXQp49m\nWYhkfZAws1nAVUAbM9sC/MjdHzGzO4CXCGPXH47N2BCpTku3LuXeRfcyZ+0cHCfHcpg4cCI/vOKH\nXNjuwnDQUWAuITy8SHzKZgvCmg8TgSvQuIcM+Oij5ODw4YfJ+1u3hquuigeHvn011kGkrGqZ/plt\nNP1TTkdRSRFPrnmSKUunsGTrEgCa5DTh1kG38v1h36d7q+5hFM9iQnj4E/BJ9OQcwrJpEwnVNjW6\nH0jf9M+tW5ODw+bNyftbtkwODv37KzhI/ZAN0z9F6rx9R/Yx9c2p/GbZb9jyaegTb9m0JbcNvo27\nLruLTs06wWbgfkKA2JTw5EGE8DAeqGK1a/lsCguTg8OmTcn7W7QIK0jGgsOAAZBT6Xq9IlIRBQmR\n07Ru9zruW3off3jnDxw+EaZU9G7TmzuH3snEgRM568hZ8DghPCTOW+pEKJY1gVD3Qk7b9u3xGRUL\nFsCGDcn7mzVLDg4XXaTgIHK6FCREUuDuzP9gPlOWTuGFDS+Ubh/ZYyR3Db2Lz+d+ngbzG4SFoZ4m\njIOAcKviJkLvwzVUUa1GTsXOncnBYd265P1nnw0jRsSDw6BBKrktkm76X0rkMzhy4gh/fO+PTFky\nhdW7VgOhjPeEARO4c+id9N3eF35LWHFyZ8IT8wih4iZUafM07NqVHBzWlhlCfdZZMHx4PDgMHgyN\ntL6GSEYpSIicgsIDhTyw/AF+u+K37DmyBwhFtO4Ycge3nXMbbZ9qC/8CvJvwpF6EnoevA+dWf5vr\ngt27YeHC8LhfP1i9Onn/GWckB4dLLlFwEKlumrVRATPTRZGgE2Fh937Eb0MUQqPFjfjSmi8xqXgS\nIxlJTrRzD3uYxSxmMINlLKuhRtdVTtOmcMUV8eBw6aUqtS2SDrW++me20fTP+q24pJhn1j3DlCVT\neO2j1wBoYA34cu8v870zvsewZ4Zhsw0ORE9oBIwm9D7cAOiD7ZTt2wevvhq/VfHuu8n1Kpo0gWHD\nYMEC49VXnSFDwjYRSS8FiTRTkKif9h/dz8NvPcz9y+6n4JMCAJo3ac7kbpO5Y+0d5D6aCwUJTxhK\nCA83A22qu7XZaf/+5ODw9tvJwaFxY7j88niPw9Ch0LRp9pURF8k2WkdC5DRs3LuR+5fez7S3p3Hw\n+EEAepzVgzsP3Mktf7yFZqsSCih0I0zXnAD0ronWZpdPP4XXXw+hYcECeOstKCmJ72/UKISFq68O\n4eHyy1ViWyTbKEhIveTuLPxwIb9a8iueW/ccHhWMvbrkau569S5GLRxFjkeDIloDXyaU6b4K0EqH\nlTpwAN54I74I1MqVUFwc39+wIVx2WTw4DBsGZ55ZU60VkXRQkJB65VjRMWatmsWUJVN4Z+c7ADT2\nxnxt09e4a95dDNw5MBzYljBVcxwhPGgmQIUOHUoODsuXJweHnJzk4HDFFWGKpojUHRojUQGNkah7\nCg8UMnXlVB5Y8QAfH/oYgPZH2vO3S/6Wb6/4Nh0OdQhLU98EjAWuRDG7AocPw6JF8eCwbBkUFcX3\n5+TAxRfHg8Pw4WFRqNOlMRIimaUxEiIVKC4p5i+b/sKDKx5k7oa5FHv4qjxgxwC+t+R7jH9vPE3a\nN4FJhPAwHK00WcaRI7B4cTw4LF0KJ07E9zdoENZuSAwOzbXglki9oh6JCqhHIrsVHihk2pvTeGjJ\nQ3x4NNSFbljckDHrxvCdZd8h70QeNtZCeBiGxjwkOHoUliyJB4clS+D48fh+s7DMdCw4jBgRCl9l\nmnokRDJL0z/TTEEi+xSXFDNv4zwenPcgz+16jmILvQ/d93Vn8srJTNo1iY6jOobwMBSFh8ixY6GX\nIRYcFi8O22LMYODAeHC48spQaru6KUiIZJaCRJopSGSP7fu2M+2ZaUz9YCof5iT3Pty29TauHXYt\nDcY1gEuBlP4XqVuOHw/jGmLrOCxaFHohEg0YkBwcWreuiZYmU5AQySwFiTRTkKjdSo6XMO/peTz4\n5oM82+RZihuE3ofcfblM3jyZSRdOotPYTnAx9T48nDgRZlLEgsMbb4RxD4n69YsHh6uugja1cHEt\nBQmRzFKQSDMFiVroBOx4cQfTFkxjqk2loEUBADklOYzZOobbOt3GdTddR4NBDep1eNi3LwSHpUvD\nQlCvvx5mWiTq0yc5OLRrVyNN/UwUJEQyS7M2pG46BiXzSpj//HwePPggz3Z/lqKWYa5h7sFcJp85\nmUmjJtHp0k71MjwcPw7vvBNCw7Jl4c/168sfd8EFycGhQ4dqb6qI1GEKElK7HAX+Ajvm7OCRrY8w\nte9UNnfcDITehy/zZW4bfhsjPzeSBlZ/Rky6w6ZNyaHhrbeSZ1RAKGg1eDAMGRIWgsrLg44da6TJ\nIlJP6NZGBXRro5odAV6CktklzH93Pr/r8zue6f0MRTmh9+FczmVyv8ncOvJWOjXrVLNtrSa7d4fA\nEAsNy5bB3r3lj7vgghAahg4NP/37182y2rq1IZJZGiORZgoS1eAw8CIwG3Ys2MEjvR5h6sVT2dwq\n6n0ghy+e80Vuv+p2rjvvOnIa1N2Voo4eDb0LsdCwdCl88EH549q3jweGoUPDQlA1MRWzJihIiGSW\ngkSaKUhkyE5CeJgLJS+W8HLHl3nwkgeTeh+6ndmNyUMnc+ugW+ncrHONNjcTSkrCOIbE0PDOO8nL\nTEOogHnxxfHQMGQIdOsW1nWojxQkRDJLQeIUmZkB/wk0A1a4+/RKjlOQSAcH3gLmAs8Dy2FLsy08\nOuBRHhr8EB+0Dl+7cyyH0b1Gc/vFtzOyx8g61fuwc2dyaFi+HPbvTz7GLMykSAwN/fqFSpkSKEiI\nZJZmbZy6LwFdgN3A1hpuS910EJhPCA7PA9vhQOMDPNnnSaZ/Yzr55+bjFj4QurXoxrcGfYtbB91K\nl+ZdarDR6XH4MLz5Zjw0LFsGH35Y/rjOnZNDwyWXQLNm1d9eEZF0yPogYWbTgFHAx+7eP2H79cAU\nQhmmh9z950Av4A13n2pms4FXaqLNdc4HhNAwF8gHjkNRgyLmnzef6V+fztPnPc2RBmEVpCY5Tbix\n943cctEtfL7H57O296G4GN5/Pzk0vPdecgltCJUvL7kkHhqGDoUu2Z+ZRERKZX2QAB4B7gdKb1OY\nWQ7wG+BaYBuw3MyeJfRCxCbMlVRzO+uOE8AbxHsd1obNjvNOx3eYfv10ZubOZCc7S58yotsIJg6c\nyNg+Y2nZNPtGCBYWJoeGFSvgwIHkYxo0CHUpEkPDhReG0toiInVV1gcJd3/NzHLLbB4CbHT3AgAz\newwYA9wH3G9mIwjfneVU7aZ0oCQvAQn3+bd13sbMMTOZfs50Vp1YVbq9Z+ueTBgwga8P+DrdW3Wv\n5gan7sABWLkyec2GbdvKH9etW3JoGDwYzjqr+tsrIlKTsj5IVKILsCXh963AUHc/AnzrVE6Ql5dH\nbm4uubm55OXlkZeXl4Fm1mIOvEt8oOSSaFvkYL+DzBk9hxmdZjB/33wchxPQ+ozWjO83ngkDJjCk\nyxCslk8zKCqC1auTQ8OaNWF2RaLmzUNgiIWGIUO00JOIZK/8/Hzy8/MpKCigoKDgtM5VV4PEaQ/v\nzs/PT0Mzssxh4GXitywSh6M2huK8Yl4Z+QrT201nztY5HDpxCPZB45zGfLHXF5kwYAJf6PkFGufU\nzhWR3GHLluTQsHJl+VoUDRvCoEHJCz316hVuXYiI1AVlvyCfzpe+uhoktgFdE37vimZpVKyAeHBY\nQFiiOqYjMAreu+Y9pjefzsx1Myk8UBhmZgDDug5j4oCJfLXvV2l1RqtqbvjJ7d8fplsmTr/cubP8\nceedlxwaLroorOMgIiInV1eDxAqgZzR2ohC4GRhfkw2qNYqAxcRnWawus38IMAq2X7udmT6TGe/N\n4J3175Tu7tGqR+m4hx6te1Rbs0/m+PEwayKxt+H998sf16pVcmi49NLsqH4pIlJbZX2QMLNZwFVA\nGzPbAvzI3R8xszsIwwJzgIfdfW1NtrNG7QX+TAgOfwb2JexrBowERsOhaw/x9N6nmfHuDObNn0eJ\nh4ECrZq24ua+NzNx4EQuO+eyGh/34A6bNyeHhjffhGPHko9r3Dj0LiSu2XD++fV3dUgRkUyoVytb\nnqqsX9nSgVXEex0WkzzZtScwGhgFxVcUk1+Yz4x3Z/Dk2ic5eDzct2jUoBGje41mwoAJ3NDzBpo0\nbFK97yHB3r3lC1jt3l3+uJ49k0PDwIGhGqZkP61sKZJZWiI7zbIySBwhjHGIzbL4KGFfQ+BKSsOD\n93SWFy5n9urZzFo1i20H4nMbLz/nciYMmMBX+36VNme2qcY3EBw7Bm+/nTyuYePG8se1bZscGi69\nFFq3rvbmSjVRkBDJLAWJNMuKIOHA+4RZFi9Ffx5J2N8euIGw5ud1UNK8hKVblzJ7zWyeXPskH+2P\nJ43uLbuXjnvo2aZn9b0Fhw0bkkPD22/DiRPJxzVtGtZoSFyzITdXtyjqEwUJkcxSrY36YgshMLxM\nWNy7sMz+wYTgMBq4BEqshEVbFvHE4id4cu2TbP00PnGlS7MujO0zlnF9xjGs67CMj3soLg49C+++\nG6pdLl8efvbtSz7OLKwGmRga+veHRo0y2jwREUmReiQqUGt6JPYSblfEwsP6MvvbA58jLAT+BaAz\nFJcU88aWN5i9OvQ8bD+4vfTwrs27loaHoecMpYFlZmGEvXtDYEj8WbUKjhwpf2zHjsmh4ZJLoEWL\njDRLsph6JEQyS7c20qzGgsRh4DXiweEtkpfWOhvIA66JfvoBBkUlRbz24WvMXjObp9Y+xc5D8cUS\nzm1xLuP6jGNsn7FpX2myqAjWrw89DImhYWslK3Z07QoDBoSf2K2Kc87RLQo5OQUJkczSrY1sdQJY\nTjw4LIq2xTQGLiceHC4Foi7+opIi8jfn88SaJ3hq7VPsOryr9GnntTqPsReOZVzfcVzc6eK0hIdd\nu+JBIRYc1qwpP+USwmJO/fvHQ0Psp1XtW7NKREROk4JEdSohTMuMBYeFlK4SCYABFxMPDsOBM+O7\nTxSfYMGmBcxePZs5789hz5E9pfvOb31+ac/DoI6DUg4Px4+HhZzKhoYdOyo+Pjc3TLNMDAw9eqji\npYhIfaEgkWmbiQeHl4FdZfb3Jh4c8oAyUxiPFx/n5Q9e5ok1T/D0uqfZe2Rv6b5ebXoxrs84xvUZ\nx4AOAz5TeHAPy0WXvS2xdm35WRMAZ58dehkSQ0O/fhrPICJS3ylIpNvHhBkVseCwucz+zsSDwzXA\nOeVPcazoGPM/mM/sNbN5Zt0zfHL0k9J9F7a9sLTnoV/7fqcUHo4eDQGhbGjYVTbUEMYrnH9+PCzE\ngkNuropWiYhIeQoSp+tT4FXiweG9MvtbAlcTDw69CbcwyjhadJS/bPoLT6x5gmfXPcv+Y/tL9/Vr\n3690zEOfdn0qbYo7bNtW/rbEunVh+mVZLVok35IYOBD69g29DyIiIqdCQeKzOkZYcjoWHJYBiR/S\nTYERxIPDIEK1jwrsPrybFze8yNwNc3lxw4scOH6gdN+ADgNKex4uaHtBuecePgyrV5cPDWXXZYDQ\nk3DBBeVDQ9eumjEhIiKnR0HiZIoJ0zBjweF1kleQzCF5ZsXlQCX1HdydVR+vYu76uczdMJfFWxbj\nCfM7B3UcxLg+4/hKn6/Qq02v6Dnw4Yflb0ts2AAlJeVfo3X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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S1B: Regenerate Fig. 4c from Bushdid et al. using their data and methods.\n", "_ = trillion.fig4x(results,'a',alpha=alpha)\n", "for (N_,z_) in _:\n", " print('Estimated number of discriminable stimuli for N=%d is %.3g' % (N_,z_))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure S2 shows the relationship between a threshold and a function of the data and that threshold." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Pgsd3dS7biTHT+ez2XA4e29X53C1z2eFRn/nACmAw0ANYBAwLa3MGMCf48/HA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\nc82Wpuh+4u3sacgmu/cg1uf8MkPhd1x0zI7o2W9azjSqqkT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S2\n", "from scipy.optimize import leastsq\n", "# Used to generate noisy data. \n", "def sigmoid(x,steepness,linearity,noise):\n", " sig = 1/(1+np.exp((-1*(x-0.5))*steepness))\n", " y = linearity*x + ((1-linearity)*sig) + noise*np.random.randn()\n", " return y\n", "\n", "fig,ax = plt.subplots(3,2)\n", "for axis_num,(steepness,linearity) in enumerate([(40,0.2),(20,0.5),(1,1)]):\n", " # Generate noisy data. \n", " noise = 0.1\n", " left = ax[axis_num,0]\n", " x = np.linspace(0,1,100)\n", " y = np.array([sigmoid(xi,steepness,linearity,noise) for xi in x])\n", " \n", " # Left panel: scatter plot. \n", " left.scatter(x,y,color='k')\n", " left.plot([0,1],[0.5,0.5],color='r',linestyle='--')\n", " left.plot([0.5,0.5],[0,0.5],color='b',linestyle='--')\n", " \n", " # Left panel: compute and plot fit. \n", " thresholds = np.linspace(0.15,0.85,100)\n", " fitfunc = lambda p, x: sigmoid(x,*p) # Target function\n", " errfunc = lambda p, x, y: fitfunc(p, x) - y # Distance to the target function\n", " p0 = [20,0.5,0.1] # Initial guess for the parameters\n", " p1, success = leastsq(errfunc, p0[:], args=(x, y)) \n", " y_fit = np.array([sigmoid(xi,p1[0],p1[1],0) for xi in x])\n", " left.plot(x,y_fit,color='g')\n", " \n", " # Right panel: compute d for each threshold. \n", " d = [sum(y_fit Figure S3 shows a result similar to Fig. 3a from Bushdid et al. (and to our Fig. S1a), but using the fraction discriminated instead of the fraction signifiantly discriminable. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mixture overlap at which 50% of discriminations were successful is 63.75%\n" ] }, { "data": { "image/png": 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EJDs6bImb2fjgoRMdB2/N3f2dzJXVvjC3xFPxwQcfUFNTEwvturo6zj///Fgr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\nojsdXW9JkJkNBf7U3R+D6Jo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Hypothetical reproduction of Fig. 3a from Bushdid et al. using their data and methods, but with fraction discriminated \n", "# rather than fraction significantly discriminated. An analogous reproduction of Fig. 3b would be identical since without \n", "# a thresholding step due to hypothesis testing, it doesn't matter whether we average across subjects or tests first. \n", "overlap = trillion.fig3x(results,alpha=None,threshold=50.0)\n", "print('Mixture overlap at which 50%% of discriminations were successful is %.2f%%' % overlap)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure S4 shows the relationship between the threshold in Figure S3 and the calculation of a discriminability limen $d$ and the estimated number of discriminable olfactory stimuli $z$, using the equations used in the paper. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KUJbqWkPKuyJ6jIvACKzb2e0RaFy9tVsyKL0d5R70nh2yYQbynGiohHFTw18j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\nf+5q9+OhIyJrK25vdndz1FfKOmtLISYOFm30P9/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1l/DXetS6zbhqS2H1VdEFHrmnxSG1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\n16urq3n4e/9GUnElrZ2hnh7PPvssK1eaq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CUi9bilb8rKraCITyxpoKkWMtOgql4+V6N/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\nzMGKshxZ0OavEHFp3on4O8G62+X6rr5YruWJD4V9WGZTHmsgb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0BZFfz7v4NXMmhVmeas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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S4. Note that this is again avoids a hypothesis testing step, i.e. it computes fraction \n", "# discriminable directly instead of computing fraction significantly discriminable, in an effort to avoid the\n", "# strong effects of the number of subjects, the number of tests, and the significance threshold $\\alpha$ on the result. \n", "# It is the result of computing Fig. S3 under a number of different thresholds. \n", "\n", "# Set up figure. \n", "fig, ax1 = plt.subplots()\n", "ax2 = ax1.twinx()\n", "\n", "thresholds = np.linspace(100,33.3,50)\n", "for subject_num in range(trillion.N_SUBJECTS+1):\n", " # Compute. \n", " results_subject = [result for result in results if subject_num==0 or result.subject_id==subject_num]\n", " overlaps = [trillion.fig3x(results_subject,alpha=None,threshold=threshold,plot=False) for threshold in thresholds]\n", " d = [(100-overlap)/100 for overlap in overlaps] # Convert from percent overlap to fraction distinct components.\n", " z_ = [trillion.disc(N,C,N*d_) for d_ in d]\n", "\n", " # Plot.\n", " if subject_num:\n", " #ax1.plot(thresholds,z_,color='lightgrey',linewidth=0.5)\n", " ax2.plot(thresholds,overlaps,color='lightsalmon',linewidth=0.5)\n", " data_ = np.vstack((data_,overlaps,z_))\n", " else:\n", " ax1.plot(thresholds,z_,color='k',linewidth=5)\n", " ax2.plot(thresholds,overlaps,color='r',linewidth=5)\n", " data_ = np.vstack((thresholds,overlaps,z_))\n", " \n", "# Scale, label, and colorize. \n", "ax1.set_xlim(100,33.3)\n", "ax1.set_yscale('log')\n", "ax1.set_ylim(trillion.disc(N,C,N),trillion.disc(N,C,0))\n", "ax1.set_xlabel('Threshold for discrimination (% correct)')\n", "ax1.set_ylabel('Number of discriminable stimuli (z)')\n", "ax2.set_ylabel(r'% mixture overlap $d$')\n", "ax2.spines['right'].set_color('red')\n", "ax2.yaxis.label.set_color('red')\n", "ax2.tick_params(axis='y', colors='red')\n", "\n", "np.savetxt('z_and_d_vs_threshold.csv',data_.transpose(),delimiter=',')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure S5: Dependence of z on the number of subjects, the number of tests, $\\alpha$, or the decision to correct for multiple comparisons. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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M+TNtGnTuXGxyB//Y+xNPPGHJ3cScEhN8ILmjqieFPxxjjIkhJYy/L1iwgNmz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\nVidNmsTAgQM197qIZLVkvoNPO3cfXs/6hcDCFo4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S5a: z vs. S, Z vs T. \n", "\n", "# Compute and plot. \n", "(n_tests,z_tests) = trillion.num_odors_vs_replicates(results,fig='a',n_replicates_list=trillion.N_TESTS_LIST)\n", "(n_subjects,z_subjects) = trillion.num_odors_vs_replicates(results,fig='b',n_replicates_list=trillion.N_TESTS_LIST)\n", "plt.xlabel(\"Number of replicates\")\n", "plt.legend(loc=7)\n", "\n", "# Add dashed lines indicating the minimum and maximum possible values under the framework. \n", "z_max = trillion.disc(N,C,0)\n", "z_min = trillion.disc(N,C,N)\n", "plt.plot([5,250],[z_min,z_min],color='k',linestyle='--')\n", "plt.plot([5,250],[z_max,z_max],color='k',linestyle='--')\n", "\n", "# Save data. \n", "def savetxt(fig,x,y):\n", " np.savetxt('z_vs_%s.csv' % ('tests' if fig=='a' else 'subjects'), np.vstack((x,y)).transpose(), delimiter=\",\")\n", "savetxt('a',n_tests,z_tests)\n", "savetxt('b',n_subjects,z_subjects)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BXApMAW4EHlXVt50M6g8R0eHDh1sffDAcPAjJyd517GfN8m5cY04qOTmZt98u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\nJAea0kR/BPgoWOwAfJzycQd3z5sbK5XgRQRINtV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S5b. z vs. alpha, corrected and uncorrected. \n", "\n", "# Compute and plot. \n", "(alphas,z_uncorrected) = trillion.num_odors_vs_alpha(results,fig='a',alphas=trillion.ALPHAS_LIST,multiple_correction=None)\n", "(alphas,z_corrected) = trillion.num_odors_vs_alpha(results,fig='a',alphas=trillion.ALPHAS_LIST,multiple_correction='fdr')\n", "plt.ylim(1e3,1e13)\n", "plt.legend()\n", "\n", "# Add dashed lines indicating the minimum possible values under the framework, and alpha=0.05. \n", "z_min = trillion.disc(N,C,N)\n", "plt.plot([0.5,0.0001],[z_min,z_min],color='k',linestyle='-.')\n", "plt.plot([0.05,0.05],[1e3,1e13],color='k',linestyle='--')\n", "\n", "# Save data. \n", "def savetxt(corrected,x,y):\n", " np.savetxt('z_vs_alpha_%scorrected.csv' % ('un' if not corrected else ''), np.vstack((x,y)).transpose(), delimiter=\",\")\n", "savetxt(False,alphas,z_uncorrected)\n", "savetxt(True,alphas,z_corrected)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure S6: The fraction discriminated at which significance is reached. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Z8AjOZL8G4CJVnR/f1wd4GBiD8+HiIlX9dzpxGJMLnlXQy0Kyb9ImOneyC8X5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\nsmW88MIL5OTk8MILL7Bs2TI6dIjWJLPhiXSA3q3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S6. \n", "from scipy.optimize import fsolve\n", "fig,(ax1,ax2) = plt.subplots(2,1,sharex=True)\n", "\n", "num_tests = [5,20,80,320] # Consider four differently size studies (the original paper used 20 tests per class.)\n", "for T_ in [5,20,80,320]:\n", " # The cumulative distribution function for chance (1/3 expected correct) performance\n", " # for observed fraction discriminated fnd_. \n", " def func(fnd_):\n", " return sum([trillion.get_n_combos(T_,k)*((1/3)**k)*((2/3)**(T_-k)) \n", " for k in range(0,1+np.round(fnd_*T_).astype('int'))])\n", " \n", " # Plot. \n", " tau = np.linspace(0, 1, 201)\n", " cdf = [func(_) for _ in tau]\n", " for i,ax in enumerate([ax1,ax2]):\n", " ax.plot(tau,cdf,label='T = %d' % T_ if i else None)\n", " \n", " # Save data. \n", " np.savetxt('T%d.csv' % T_,np.vstack((tau, [func(_) for _ in tau])).transpose(),delimiter=',')\n", "\n", "# Break y-axis: \n", "ax1.set_ylim(0.95,1) # outliers only\n", "ax2.set_ylim(0,0.9) # most of the data\n", "ax1.spines['bottom'].set_visible(False)\n", "ax2.spines['top'].set_visible(False)\n", "diag = .015 # how big to make the diagonal lines in axes coordinates\n", "# arguments to pass plot, just so we don't keep repeating them\n", "kwargs = dict(transform=ax1.transAxes, color='k', clip_on=False)\n", "ax.plot((-diag,+diag),(-diag,+diag), **kwargs) # top-left diagonal\n", "ax.plot((1-diag,1+diag),(-diag,+diag), **kwargs) # top-right diagonal\n", "kwargs.update(transform=ax2.transAxes) # switch to the bottom axes\n", "ax2.plot((-diag,+diag),(1-diag,1+diag), **kwargs) # bottom-left diagonal\n", "ax2.plot((1-diag,1+diag),(1-diag,1+diag), **kwargs) # bottom-right diagonal\n", " \n", "# Plot dashed lines to indicate crossing points for alpha=0.05, \n", "# i.e. for what fraction discriminated significance is acheived. \n", "ax1.plot([0,1],[1-alpha/2,1-alpha/2],color='k',linewidth=3, linestyle='--', label=r\"1 - $\\alpha$/2\")\n", "for ax in [ax1,ax2]:\n", " ax.plot([0.378,0.378],[0,1],color='c',linestyle='--')\n", " ax.plot([0.43,0.43],[0,1],color='r',linestyle='--')\n", " ax.plot([0.525,0.525],[0,1],color='g',linestyle='--')\n", " ax.plot([0.695,0.695],[0,1],color='b',linestyle='--')\n", " ax.set_ylabel(\"Cumulative probability\")\n", "ax2.set_xlabel(\"Fraction discriminated\")\n", "ax1.legend(loc=4)\n", "ax2.legend(loc=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Fig. S7: regeneration of the trillion's Fig. 3b using their raw data and reconstituted methods:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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f/cWzOXTwUAAVnb7c3FyysrLYu3cvCxcupHfv3qd+UZTKysoYdt0wdmzYwa2F\ntwLwaNKjpH47lWW/XqYgF6kjNVpPPBLWZnYu0Kx2SxMJzuGPD8OMCrbPODnY483+/fuZPn06q1at\nYvr06dx+++00aRLVBIxRW7duHTs27ODPhX+mWfi//k2FN5G2Po1169bRv3//Wv08ETl9p/xV2swG\nmNlfgd3Aq8C7wO9jXJeIVODo0aMsXLiQjh070rRpU/Lz8xk9enStBzjA6qdXc2vhrccCHKAZzbi1\n8FaeW/5crX+eiFSDu1d5A7YD5wBbw4//C3j8VK+LxS1U7vHuvfdeJ7TO+XG3e++996R9tb/2Lw9w\nep68bzzWP336dF+7dq23b9/e27Vr5zt27Ih5PSNuGOF96Vvh/p0v7hxXx0f7a//6sn9lP6u8klyM\nZkz8TXfvambbgK+7e6mZbfcATmzTmLjUJjOrsDudGRBP/87y8vLIysrivffeY8GCBWRnZzNz5syY\nf+7atWu5Z/A9ZBdmH2uNF1FEWlIas56Zpe50kTpS0/XEPzKzs4E/AcvN7MfAJ7VZoIic7MCBA9x1\n11307NmTPn36kJubS9++feskwAH69etH6rdTSUtKY0n4T1pSGqnfTqVfv351UoOIVC2alngSUEQo\n8IcCLYDl7v6v2Jd3Ui1qiUutidez00tKSnjkkUe47777uO6667jvvvs455xzAqklcolZZAz82qHX\n6hIzkTpW7Rnb4o1CXOq79evXM3bsWFq1asXChQtJTU09aZ8ZM2YwY8aMui9ORAJRo0vMRCT2CgoK\nGDduHPn5+cyfP58BAwaExuxFRKqglrhIgD766CPuv/9+li1bxqRJk7jrrrs488wzgy5LROJIjU5s\nM7Mx0WwTkeiVlJTws5/9jJSUFAoLC8nLy2PChAkKcBE5LdGcnTKigm0ja7kOkQbj5Zdf5utf/zrP\nPvssGzZs4NFHH+Xcc8+N+vUaDxeRiErHxM1sMDAEaGtma8s9dTZQ52emiyS6Xbt2MX78eHJzc/nR\nj37EwIEDNe4tIjVS6Zi4mf070BaYA0wCIj9tDgPb3L2kTio8viaNiUvCOXToELNmzeLxxx9n/Pjx\nZGZm0qyZliEQkehU6+x0d38PeI/QUqQicppKS0tZunQp06ZNOzZZS6tWrYIuS0TqkWhObPtPM3vD\nzD4xs2IzKzOzxFinUSQgr776KpdddhlPPPEEzz//PI8//nitBbjGxEUkIprrxH8KfBd4FrgM+D5w\nUSyLEkkFp9E/AAAd3ElEQVRUu3fvZsKECbzxxhs89NBD3HDDDRr3FpGYiWruRHf/K9DY3UvdfSlw\ndWzLEkkshw8fZurUqVx22WVceuml5Ofnc+ONN8YkwNUSF5GIaFrihWZ2JrDNzB4CPuTzk9xEGrSy\nsjKWLVvG1KlTueqqq9i+fTutW7cOuiwRaSCiaYl/P7zfaOBT4N+AQbEsSiQRvP7666SlpfHoo4/y\n3HPPsWzZsjoJcLXERSTilC1xd383fPczKl59WaRB2bNnD5MmTeK1115jzpw5DBkyROPeIhKIaJYi\n/RZwL3ABn4e+u/uFsS2twlp0nbgEprCwkLlz57JkyRJGjx7NxIkTSUpKCrosEannarqK2S+BTOAt\noLQ2CxNJBGVlZaxYsYIpU6bQo0cPtm7dSps2bYIuS0QkqhA/6O6/j3klInEoOzubMWPGUFpaysqV\nK+nevXvQJWk9cRE5pqq507uG7/7RzOYBq4Ejkefd/a0Y1yYSmA8++IDJkyfzyiuv8OCDDzJs2DAa\nNYrqikwRkTpT1dzpG4FKB6Dd/b9iVFOlNCYusfbpp5/yox/9iMWLF3P77bczZcoUmjdvHnRZItKA\nVXfu9PTwiy9097+f8IZ1flKbSCy5OytXrmTSpEmkpaXx5ptvcsEFFwRdlohIlaLpH/xNBdt+XduF\niAQlJyeHHj168NBDD/HUU0/x7LPPxnWAazxcRCKqGhPvAHQEks0sg9AsbQ60ALSOoiS8vXv3MnXq\nVF588UVmzZrFiBEjaNy4cdBliYhEraqz09sD/YEvhr9GHAZuiWVRIrFUVFTEggULmD9/PjfffDMF\nBQW0aNEi6LKippa4iERUNSb+O+B3Ztbd3TfXYU0iMeHurFq1igkTJtC5c2e2bNlCu3btgi5LRKTa\nTjkmrgCX+mDr1q2kp6dz33338ctf/pLnnnsuYQNcLXERiQjswlcza2xmW81sbfhxSzN7ycz+YmYb\nzCw5qNqk/ti3bx+33HILffr0YciQIbz11lv06tUr6LJERGpFkLNXjAHy+Pxa9MnAS+7eHng5/Fik\nWo4cOcK8efO4+OKLadGiBfn5+dx22200aRLNJIXxTS1xEYk4ZYibWaaZfdFCfhluPX+7Jh9qZv8G\n9AUe4/O1yQcAT4bvPwkMrMlnSMPk7vz2t7/l4osvZtOmTWzevJn58+eTnKyOHRGpf6Jpid/k7h8D\nvYGWwDBgTg0/dyEwASgrt+08d98Xvr8POK+GnyENTG5uLldddRV33303Dz/8MGvXrqV9+/ZBl1Xr\n1BIXkYho+hYjLeV+wFPu/k5N1k42s2uAf7j7VjNLr2gfd3czq3B+1fI/wNLT00lPr/AtpAHZv38/\n9957L7/5zW+YPn06t99+e73oNheRhmnjxo1s3Lgxqn2jWU/8CeBrwIVAJ0LB/0d371rV66p4vwcJ\nteZLCE0a04LQ4irfANLd/UMzaxX+jJQTXqu50+WYo0ePsmTJEh588EGGDBnCvffeS8uWLYMuS0Sk\nVlU1d3o0Id4YuBT4u7sfNLMvA63dfXstFNYTGO/u/c3sIeBf7j7XzCYDye4++YT9FeKCu/PCCy8w\nduxYLrzwQhYsWECHDh2CLktEJCaqCvFoxsQduBi4K/w4idqddjWSynOA/zazvwC9qPm4u9RDeXl5\n9OnTh3HjxrFo0SJ+//vfN7gA15i4iEREE+IPA92AIeHHn4S31Zi7v+ruA8L3D7j7Ve7e3t17u/vB\n2vgMqR8OHDjAnXfeSc+ePbn66qvJzc2lT58+QZclIhKoaEI8zd1/CHwGobAFmsa0KpGw4uJifvKT\nn5CSkkJZWRk7d+4kMzOTpk0b7j9BtcRFJCKaU3iPhsfFATCzr3D8pWEiMbF+/XqysrJo3bo1r7zy\nCpdccknQJYmIxJVoWuI/AZ4Dzg2fWf46MDumVUmDVlBQwDXXXMPo0aOZO3cuGzZsUICXo5a4iERU\nGeJm1gjYDUwiFNz/B3zH3Z+tg9qkgfnoo4/IysriW9/6Funp6ezYsYP+/ftTk3kJRETqs2guMXvb\n3TvXUT1V0iVm9VNJSQm/+MUvmDFjBgMHDuT+++/n3HPPDbosEZG4UNUlZtGMif/BzK4DVilBpba9\n/PLLZGVl8eUvf5kNGzZw6aWXBl2SiEjCiGZM/HbgWUInuB0O3w7FuC6p53bt2sXAgQO55ZZbmDFj\nBq+88ooCPEoaExeRiFOGuLs3d/dG7t7U3c8O31rURXH1SXFxMUOHDmXo0KEUFxcHXU5gDh06xMSJ\nE+nWrRvdunUjLy+PjIwMjXuLiFRDNGPiV1S03d03xaSiqmtJyB79SIAXFhYCkJSUxPLlyxvUtc6l\npaUsXbqUadOm0adPHx544AFatWoVdFkiInGvpnOnP8/nU6M2Ay4H3nT3XrVaZRQSMcTLB/iqVasA\nGDRoUIMK8k2bNjFmzBiSkpJYvHgxXbtWa+0cEZEGqUZzp7v7Ne7eP3z7b+ASQFOiRuHEAG/WrBnN\nmjVj1apVFBYW1vuu9d27d3P99dczbNgwJk+ezJ/+9CcFeC3QmLiIRERzYtuJ3gca1ooT1TRixIjj\nAjyifJCPGDEiuAJj5PDhw0ydOpXLLruMSy+9lPz8fG688UaNe4uI1LJTXmJmZj8p97AR0Bl4M2YV\nScIqKytj2bJl3H333Vx55ZVs376d1q1bB11WvaOWuIhERDMmPrzcwxLgXXd/PaZVVV5LQo2JV9Sd\nDlBUVFTvxsVfe+21YwuTLFq0iLS0tKBLEhGpF2q6nviX3P3J8G25u79uZmNqucZ6qWnTpixfvpyk\npCQGDRpEUVFRvQvwPXv28N3vfpfBgweTlZXF5s2bFeAxppa4iEREE+LDK9g2srYLqa9ODPL6EuCF\nhYVMnz6dLl26kJKSQn5+PkOHDtW4t4hIHaq0O93MBgNDgB7An8o9dTZQ6u5Xxr68k2pKqO708oqL\ni4+dxPbEE08kbICXlZWxYsUKpkyZQo8ePZg7dy7nn39+0GWJiNRb1bpO3Mz+HWgLzCG0ilnkDQ4D\n29y9JAa1VimRQ7w+yM7OZsyYMZSWlrJ48WK6d+8edEkiIvVetcbE3f09d98IjHL3V919Y/j2JvCt\nGNUqcej9999n2LBhZGRkcMcdd5Cdna0AD5DGxEUkIpox8ZVmNslCvhC+5GxOrAuT4H366afcd999\nXHrppbRp04aCggKGDx9Oo0bVmV5ARERqWzSXmCUBc4HLgObACmCOu5fFvryTalF3eh1wd1auXMmk\nSZNIS0tj7ty5tG3bNuiyREQapJquJ14CfAacRWju9L8HEeBSN3JycsjMzKSwsJCnnnqKK66ocP0b\nERGJA9H0i24Bigi1xHsAQ8zs1zGtSurc3r17GTFiBP3792fkyJHk5OQowOOUxsRFJCKaEL/Z3ae5\ne7G773X3AcDaWBcmdaOoqIjZs2eTmprKeeedR0FBAaNGjaJx48ZBlyYiIqdQ1SVmLdz9kJm1rOh5\ndz8Q08oqrklj4rXE3Vm1ahUTJkygS5cuzJs3j3bt2sXs88rKyli3bh2rn14NQMb3MujXr59OkhMR\nOYXqXie+zt37mdm7fL6eeIS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Fig. S7a: Regenerate Fig. 3b from Bushdid et al. using their data and methods.\n", "overlap = trillion.fig3x(results,fig='b',alpha=0.025)\n", "# Note that a different value of alpha is required to match Fig. 3b than Fig. 3a. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated number of discriminable stimuli for N=10 is 3.43e+08\n", "Estimated number of discriminable stimuli for N=20 is 1.17e+12\n", "Estimated number of discriminable stimuli for N=30 is 3.81e+13\n" ] }, { "data": { "image/png": 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t6NO8Di0wB3EzEE8A6UBdXFn+JV4GVbTkmUiIyAl+l68AH4jIYFw9Qm3cLo6X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\nqk+Rsf/vRnUm/jlT1zvJayXW7bjHzCZn+PrDzez9NM/tEtUJSXt67Em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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S7b: Regenerate Fig. 4c from Bushdid et al. using their data and methods.\n", "_ = trillion.fig4x(results,'b',alpha=alpha)\n", "for (N_,z_) in _:\n", " print('Estimated number of discriminable stimuli for N=%d is %.3g' % (N_,z_))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Fig. S8: If we vary $S$ (or $T$) and $C$ simultaneously:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sCLxW0kPA14FxwLhquNOLwMcAImKqpEuBqaT+c5+JiBrcE5mZWZ11ojf1/gO8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\nxsAfJb0zIv5R/Z3MBVaONC/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TG84fLxGfmZktfSJi/0FWbbOY758HTBhkXQCXL0lcxaqmI+LpPLsMMBxY0MIuSaSrjp0K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\nPChpLeChvPyNwCU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Note the saturated dark red area represents the maximum possible number of discriminable stimuli, i.e. all stimuli. \n", "# Similarly, the dark blue area represents the minimum possible number of discriminable stimuli. \n", "def plot_(fig):\n", " n_reps = trillion.N_TESTS if fig=='a' else trillion.N_SUBJECTS\n", " n_replicates_list = np.ceil(n_reps*2.0**np.arange(3.5,-2.5,-0.5))\n", " reps,Cs,z_ = trillion.num_odors_vs_replicates_and_C(r,fig=fig,n_replicates_list=n_replicates_list,Cs=trillion.C_LIST[:8])\n", " vmin = np.log10(trillion.disc(N,C,N))\n", " vmax = np.log10(trillion.disc(N,C,0))\n", " f, ax = plt.subplots()\n", " plt.pcolor(np.log10(z_), vmin=vmin, vmax=vmax)\n", " plt.xticks(np.arange(0,len(Cs))+0.5)\n", " ax.set_xticklabels(Cs.astype('int'),rotation=45)\n", " plt.yticks(np.arange(0,len(reps))+0.5)\n", " ax.set_yticklabels(reps.astype('int'))\n", " plt.xlabel(r\"$C$\")\n", " plt.ylabel(\"$%s$\" % 'T' if fig=='a' else 'S')\n", " bar = plt.colorbar()\n", " bar.set_label(\"Log$_{10}$ of $\\hatz$\")\n", " \n", "plot_('a')\n", "plot_('b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Fig. S9: If we vary $\\alpha$ and $C$ simultaneously:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Note the saturated dark red area represents the maximum possible number of discriminable stimuli, i.e. all stimuli. \n", "# Similarly, the dark blue area represents the minimum possible number of discriminable stimuli. \n", "def plot_(fig):\n", " n_reps = trillion.N_TESTS if fig=='a' else trillion.N_SUBJECTS\n", " n_replicates_list = np.ceil(n_reps*2.0**np.arange(3.5,-2.5,-0.5))\n", " alphas,Cs,z_ = trillion.num_odors_vs_alpha_and_C(r,fig=fig,alphas=trillion.ALPHAS_LIST,Cs=trillion.C_LIST[:8])\n", " vmin = np.log10(trillion.disc(N,C,N))\n", " vmax = np.log10(trillion.disc(N,C,0))\n", " f, ax = plt.subplots()\n", " plt.pcolor(np.log10(z_), vmin=vmin, vmax=vmax)\n", " plt.xticks(np.arange(0,len(Cs))+0.5)\n", " ax.set_xticklabels(Cs.astype('int'),rotation=45)\n", " plt.yticks(np.arange(0,len(alphas))+0.5)\n", " ax.set_yticklabels(alphas)\n", " plt.xlabel(r\"$C$\")\n", " plt.ylabel(r\"$\\alpha$\")\n", " bar = plt.colorbar()\n", " bar.set_label(\"Log$_{10}$ of $\\hatz$\")\n", " \n", "plot_('a') # Pooling across tests as in Fig. 3a from the original paper. \n", "plot_('b') # Pooling across subjects as in Fig. 3a from the original paper. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Figure S10: Reproduction of the raw data from the original paper, using the supplemental materials. " ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S10a: Across mixtures (tests). Reproduction of Fig. 2b from the original paper. \n", "trillion.fig2x(results,fig='b')" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kjirkAAAgKSQ5AAAgSiQ5AAAgSiQ5AAAgSiQ5AAAgSiQ5AAAgSiQ5AAAgSiQ5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\naGbXmdl5PdvdklWEflJW0fu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Figure S10b: Across mixtures (tests). Reproduction of Fig. 2c from the original paper. \n", "trillion.fig2x(results,fig='c')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### More details on why the estimate provided is an upper bound" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The minimum possible number of discrimable stimuli occurs when olfactory resolution is as bad as possible.
This occurs when $d$, the discriminability limen, is equal to $N$, the number of components.
This means that even when substitute every component, discrimination is still hard or impossible. \n", "\n", "However, using equation 1 from our paper (implemented from the original paper), where the final parameter $d$ is set to $N$:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z = 4561\n" ] } ], "source": [ "d = N\n", "print('z = %d' % trillion.disc(N,C,d))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We still get thousands of discriminable stimuli.
This can be confirmed by looking at the minimum value in Figure 4C and 4D in the original paper.
How is this possible?
Shouldn't the worst possible resolution mean that everything smells the same, i.e. anosmia, so that there should be only $z=1$ discriminable stimuli?

\n", "Maybe $d=N$ means that mixtures are just discriminable when all components are replaced.
But there are only $C/N \\sim 4$ ways to replace all the components, not $\\sim4500$.
So maybe it means that $d=N$ is perfectly discriminable, and $d=N-1$ is barely discriminable, and there are $\\sim4500$ ways to replace all but 1 component.
In that case, we should just be able to plug in N+1 into our formula: " ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z = 2024\n" ] } ], "source": [ "d = N+1\n", "print('z = %d' % trillion.disc(N,C,d))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This doesn't seem to work; we're still left with $\\sim 2000$ discriminable stimuli.
\n", "Let's take it up a notch. " ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z = 8\n" ] } ], "source": [ "d = N+10\n", "print('z = %d' % trillion.disc(N,C,d))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is already well out of bounds of the way $N$ and $d$ were originally described.
We shouldn't be able to make $d$ bigger than $N$, much less 10 components bigger.
And yet we still have $>1$ discriminable stimuli. " ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z = 1\n" ] } ], "source": [ "d = 2*N\n", "print('z = %d' % trillion.disc(N,C,d))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now we finally get to 1 discriminable stimulus, i.e. anosmia, when we set $d$ to twice $N$.
\n", "This strongly suggests that there is a mistake in the equation by which the original paper produced the estimate $z$.
\n", "In fact, it suggests that the mistake is an anomalous factor of 2 in one of the equations.

\n", "\n", "Equation 2 (also implemented from the original paper), is used to compute the denominator in equation 1.
It is supposed to give the size of the ball within which pairs of stimuli cannot be discriminated.
\n", "Let's see what this equation produces: " ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# of stimuli inside the ball = 1.54e+29\n" ] } ], "source": [ "D = N\n", "print('# of stimuli inside the ball = %.3g' % trillion.ball(N,C,D))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the ball has a large enough 'radius', i.e. if olfactory resoution
is bad enough, then it should encompass every possible stimulus. " ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# of possible stimuli = 1.54e+29\n" ] } ], "source": [ "print('# of possible stimuli = %.3g' % trillion.get_n_combos(C,N))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Good, this means that the ball with radius N, the one that allows
total replacement of stimuli, covers all possible stimuli.

\n", "But is this ball that gets used when we calculate the number of discriminable stimuli for worst possible olfactory acuity?
\n", "In order to get common sense outcomes, the denominator of equation 1 (the number of stimuli in the ball)
should match the numerator of equation 1 (the total number of stimuli) when olfactory acuity is
as bad as possible, resulting in a number of discriminable stimuli of $1/1=1$\n", "\n", "But instead we get: " ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z = 4561\n" ] } ], "source": [ "d = N\n", "print('z = %d' % trillion.disc(N,C,d))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "which is not 1. \n", "\n", "This is because the denominator of equation 1 doesn't use:\n", "
ball(N,C,d)
\n", "instead it uses
ball(N,C,d/2)\n", "\n", "Let's confirm: " ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# of possible stimuli = 1.54e+29\n", "# of stimuli inside the ball with half the radius = 3.38e+25\n", "The ratio is 4561\n" ] } ], "source": [ "print('# of possible stimuli = %.3g' % trillion.get_n_combos(C,N))\n", "D = N\n", "print('# of stimuli inside the ball with half the radius = %.3g' % trillion.ball(N,C,int(D/2)))\n", "print('The ratio is %d' % (trillion.get_n_combos(C,N)/trillion.ball(N,C,int(D/2))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So now see the source of the problem.
\n", "By introducing an anomalous factor of 2 into the formula,
\n", "we generate numbers that do not make sense for worst case performance,
\n", "and seem likely to not make sense for any level of performance. \n", "\n", "We'll call this factor $\\gamma$, such that the original paper (and this one) use $\\gamma=2$,
\n", "which we would like to then compare to a $\\gamma=1$ scenario. \n", "\n", "See Fig. 5 for this result. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We notice three things when we change $\\gamma$ from 2 to 1:

\n", "1) The minimum number of discriminable stimuli is now 1, which makes sense.
\n", "2) The maximum number of discriminable stimuli is unchanged, and is equal to the total number of stimuli, which also makes sense.

\n", "and most importantly...

\n", "3) The number of discriminable stimuli estimated from the data is now
several orders of magnitude lower, and in the folk wisdom range.

And this argument (that gamma was chosen incorrectly) is completely independent of and can be combined with, the arguments from the rest of our paper. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The authors originally argued that the sphere-packing framework provided a lower bound for the number of discriminable stimuli.
\n", "Next, we'll show that in the event that we ignore statistical issues and take the reported $d$ as a true measure of human olfactory resolution,
\n", "the sphere-packing framework as originally shown by the authors actually gives an upper bound.
\n", "In fact, we will show that $\\gamma=1$ and $\\gamma=2$, respectively, are the lower and upper bounds of this computational problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before continuing, we'd also like to note that all of this is predicated on the stimulus dimensions being independent, which they certainly are not.
That further constratins the usefulness of this approach, but the math that follows is nonetheless interesting. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The general problem of determing how many ways you can substitute $d$ components from a set of $N$, with a total of $C$ to choose from, is known in coding theory as the problem of \"constant weight codes\".
\n", "In this literature, the \"largest\" constant weight code for values of $N$, $D$, and $C$ (which annoyingly have different letters in the math literature) is the one with the most \"words\". This is equivalent to the largest olfactory mixture set -- the one with the largest number of mutually discriminable mixtures. This is the one we want to solve the problem of how many mutually discriminable mixtures there are (given $N$, $C$, and a data-determined $d$).
We will call $z$ the size of the largest such code, because it is the same $z$ that we have been trying to compute all along
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There has been a great deal of research on determing $z$.
\n", "Once any of these numbers gets especially large, especially C, \n", "it is essentially impossible to directly compute $z$.
\n", "There a few theorems that propose lower and upper bounds for $z$ (more on this later),
\n", "but in some cases people have enumerated all the codes (for a given $N$, $C$, and $d$), and then $z$ is just the largest of these.
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the web (http://www.win.tue.nl/~aeb/codes/Andw.html) there is a page that gives the size $z$ of these codes for smallish values of $N$, $C$, and $d$.
\n", "So we can directly compare these known, proven values, against our sphere-packing estimates using $\\gamma=1$ and $\\gamma=2$. Note on that page that $N$ is called $w$, $C$ is called $n$, and $d$ corresponds to floor(($d$-1)/2).
\n", "For example:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "def cwc(x_cwc,y_cwc,N,d): # Note that d = floor((d-1)/2). \n", " plt.plot(x_cwc,y_cwc,linewidth=4,label='Exact values')\n", " y_disc = np.array([trillion.disc(N,_,d) for _ in x_cwc])\n", " y_disc_prime = np.array([trillion.disc_prime(N,_,d) for _ in x_cwc])\n", " plt.plot(x_cwc,y_disc,label='$\\gamma=2$',linestyle='--')\n", " plt.plot(x_cwc,y_disc_prime,label='$\\gamma=1$',linestyle='--')\n", " plt.plot(x_cwc,[trillion.disc_prime(N,_,d*np.sqrt(2)/2) for _ in x_cwc],label='$\\gamma=\\sqrt{2}$')\n", " plt.plot(x_cwc,[trillion.disc_prime(N,_,d*0.75) for _ in x_cwc],label='$\\gamma=4/3$')\n", " plt.yscale('log')\n", " plt.xlabel('C')\n", " plt.ylabel('z')\n", " plt.legend(loc=2)\n", " plt.title('N = %d, d = %d' % (N,d))" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SjMGtB+PT3MfW4TgkacE3Em+99Rbbt2/HaGw84zmFEPbHqqz8kvoLm+M3syVhC8PbDmfW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\nsL62DktUIbWkRE/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D+tvqvxHRJoLFNy+meZMrr+h2NsklJSxJT2dxWhqnS0u5PSiIxVdf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\nZVUGt2xbRcQ3DUh5o+5J5y5iF4+UWkuL1xrT9K7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+P//9VBkZcMst8NlnngMDUyH1PMKX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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C_list = np.arange(6,65)\n", "z_list = [4,7,8,12,13,17,20,26,28,35]\n", "z_list += [37,44,48,57,60,70,73,83,88,100]\n", "z_list += [104,117,121,134,140,155,160,176,181,197]\n", "z_list += [204,222,228,247,253,272,280,301,308,330]\n", "z_list += [337,359,368,392,400,425,433,458,468,495]\n", "z_list += [504,532,541,569,580,610,620,651,661]\n", "\n", "cwc(C_list,z_list,3,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above shows exact values of $z$ from the literature in blue, with predicted values from equation 1 using various values of $\\gamma$ in other colors.
\n", "Here and further on, values of $\\gamma$ near $\\frac{4}{3}$ or $\\sqrt{2}$ are reasonably good fits, but as far as we know there is no systematic best fit.
\n", "However, here and in all other cases we could find, $\\gamma=1$ is lower than all published values (i.e. a lower bound) and \\$gamma=2 is higher than all published values (i.e. a higher bound).
\n", "This further confirms that the equation (using $\\gamma=1$) in the original paper (and our own) is too generous: it is certainly not a lower bound. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the results for a few other values of $N$:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7Vt9pzdqWfLV2dtVEX5VBdtpNbr13nqrCwL7FixczZ84cAgMDWbVqFXv27CE+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\nIuJC/x8T+HUSlfoZqgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_cwc = [14,18,30,35,51,65,91,105,140,157]\n", "y_cwc += [198,228,285,315,385,419,498,550,650,702]\n", "y_cwc += [819,877,1005,1085,1240,1320,1496,1583,1773,1887]\n", "y_cwc += [2109,2223,2470,2593,2856,3010,3311,3465,3795,3959]\n", "y_cwc += [4308,4508,4900,5100,5525,5737,6183,6435,6930,7182]\n", "y_cwc += [7714,7979,8535,8845,9455,9765,10416]\n", "x_cwc = np.arange(8,65)\n", "\n", "cwc(x_cwc,y_cwc,4,1)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IKnaxkt2sWbNqToK3txb8tb744gsmTZp026/buXMnvXv3vvR9KorC2bNnCQsLq+wQbYo9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\nwJpr1xAYFkj3t+phtvyGDe69voiI+BS/Cvj0vekMmjWIjF8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LiIj4IAW8iIiID1LAi4iI\n+CAFvIiIiA8KaugKlGeMaQq8BhQCCdbaDxu4SiIiIl7J03rwY4B/WGtvBi5t6MqIiIh4K7cHvDFm\nljEmyxiTfET5MGPMWmNMujHmAVdxB2Cb6+dSd9fN1+kwnqpTW1WN2qnq1FZVo3Zyn/rowc8GhpUv\nMMYEAq+4yqOAq40xkcB2ILwe6+bT9Ben6tRWVaN2qjq1VdWondzH7SFqrV0K5BxRPBDYYK3dbK0t\nBuYDo4CPgbHGmNeAhe6um4iIiK9qqEl25Yfiwem5/85amw/c2DBVEhER8R31ch68MaYTsMha28f1\neCwwzFo72fV4PE7A317F6+kweBER8SvVPQ++oXrwmRy+147r5+1VfXN1f0kRERF/01AT2RKBbsaY\nTsaYEOBKdM9dRESkztTHMrl5wI9Ad2PMNmPMDdbaEuCPwL+BNcDfrbVp7q6LiIiIv6iXe/C1YYyZ\nBVwCZJe7h98K+DvQEdgMjLPW/tpglfQAxphw4H3gZMACb1lrX1JbVWSMaQx8BzQCQoDPrLV/Vjsd\nnWtJayKw3Vo7Uu10dMaYzUAuzv4dxdbagWqryowxLYCZQC+c/0/dAKSjdqrAGNMDZ3XZIZ2BR4E5\nVKOtvGGteaV19MCDwDfW2u7AYtdjf1cM3G2t7QX8HrjNtbeA2qoca20BMMRa2w+IBoYYY85C7XQs\nd+KMsh3qCaidjs4Cg621Mdbaga4ytVVlLwJfWmsjcf7+rUXtVIm1dp3rz1IM0B/IBz6hum1lrfX4\nf4BOQHK5x2uBdq6fTwHWNnQdPe0f4FNgqNrquG3UBFiG05tQO1Vun9OA/wBDcFbB6O/esdsqA2h9\nRJnaqmJ7nARsOkq52un47XYhsLQmbeUNPfijaWetzXL9nAW0a8jKeBrXssQY4H+orSoxxgQYY1bh\ntMcSa20qaqejeQG4DygrV6Z2OjoL/McYk2iMmewqU1tVFAHsNsbMNsasMMa87TpgTO10fFcB81w/\nV6utvDXgf2OdrzKePZGgHhljmgH/BO601uaVf05t5bDWlllniP404BxjzJAjnvf7djLGjMCZ97IS\nOOqyVLVTBYOsM5w6HOf22Nnln1RbAc6y7FjgNWttLHCAI4aY1U4VuVaZjQQ+OvK5qrSVtwZ8ljHm\nFABjTHsgu4Hr4xGMMcE44f6BtfZTV7Ha6histfuAL3DucamdKjoTuNQYk4HTezjPGPMBaqejstbu\ndP17N8690oGorY60HWey5jLX4wU4gb9L7XRMw4Hlrj9XUM0/U94a8AuB61w/X4dzv9mvGWMM8A6w\nxlo7o9xTaqtyjDFtXDN5McaEAhcAK1E7VWCtfchaG26tjcAZIvzWWjsBtVMlxpgmxpjmrp+b4twz\nTUZtVYG1dhewzRjT3VU0FEgFFqF2OparOTw8D9X8M+UNy+TmAecCbXDuOTwGfAb8AzgdLasAwDUT\n/HsgicPDNn8GfkZt9RtjTB/gPZwvtwE4ox3TXUua1E5HYYw5F7jXWnup2qkyY0wETq8dnGHoudba\nqWqryowxfXGWyYUAG3GWyQWidqrE9WVxCxBx6HZrdf9MeXzAi4iISPV56xC9iIiIHIcCXkRExAcp\n4EVERHyQAl5ERMQHKeBFRER8kAJeRETEByngReSEjDGnGGPmG2M2uPZb/8IY062h6yUixxbU0BUQ\nEc/m2iXxE2C2tfYqV1k0zkEX6Q1ZNxE5NgW8iJzIEKDIWvvWoQJrbVID1kdEqkBD9CJyIr2B5Q1d\nCRGpHgW8iJyI9rMW8UIKeBE5kVScI3VFxIso4EXkuKy13wKNjDGTD5UZY6JdJxiKiIdSwItIVYwG\nhrqWyaUATwM7G7hOInIcOi5WRETEB6kHLyIi4oMU8CIiIj5IAS8iIuKDFPAiIiI+SAEvIiLigxTw\nIiIiPkgBLyIi4oMU8CIiIj7o/wFtTgF/eq1BZAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_cwc = [36,66,80,123,169,242,322,441,544,692]\n", "y_cwc += [874,1113,1386,1771,1895,2334,2670,3276,3718,4423]\n", "y_cwc += [5148,6138,6758,7656,8976,10472,10948,12473,13471,15010]\n", "y_cwc += [17119,19258,21320,23478,25564,28413,31878,35673,36809,40560]\n", "y_cwc += [43372,46612,51420,56251,59293,64449,69931,75550,79866,87261]\n", "y_cwc += [93206,100527,105472,113553,121902]\n", "x_cwc = np.arange(10,65)\n", "\n", "cwc(x_cwc,y_cwc,5,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now what about for other values of $d$?
\n", "The exact values are harder to come by. In many cases, however, there are proofs of very narrow upper and lower bounds,\n", "
which for convenience I have averaged together to approximate exact values.
\n", "Note that the reported lower and upper bounds are well within the crude $\\gamma=1$ and $\\gamma=2$ bounds shown here. " ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Pf/M0vWf3Zvup7UaHI4RoIMnJySQlJdXqWOmiF8KDlJSX8NYPb/Hi5hcZ02UM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\n7ZMnm6S4JrbsFUKI9uRWy+QWLVp0wqVq28orrzQI7gEV8L9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_cwc = [2,2,2,3,3,3,4,4,5,7]\n", "y_cwc += [7,8,9,10,13,14,16,20,25,31]\n", "y_cwc += [31,31.5,33.5,35,37,40,41.5,42,45.5,51]\n", "y_cwc += [55.5,56,56.5,58.5,62,66.5,72,72.5,73.5,80.5]\n", "y_cwc += [82,84,88.5,89,96,99.5,100.5,102,107.5,116.5]\n", "y_cwc += [119,126,127]\n", "x_cwc = np.arange(12,65)\n", "\n", "cwc(x_cwc,y_cwc,6,4)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hhKhNC14CXrgF+W6FEA1ZbQLey1nFCCHcW4mthBf2vMDiw4v1LkUIUQsS8EKI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\na0xgDw6W9KxCuAgJ8G5m0ReH4XkLrI2Afw3g2l+oJvtW2Kp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_cwc = [2,2,2,2,2,3,3,3,3,3]\n", "y_cwc += [4,4,4,4,5,5,5,6,6,7]\n", "y_cwc += [9,9,9,10,10,11,12,12,13,15]\n", "y_cwc += [17,18,19,21,25,26,28,32,36,42]\n", "y_cwc += [49,57,58,59,60,61,62,63,72,73]\n", "y_cwc += [74,75,76,77,78,87,90,91,92,93]\n", "y_cwc += [95]\n", "x_cwc = np.arange(16,77)\n", "\n", "cwc(x_cwc,y_cwc,8,6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In no case that we could find are the exact values (or any reported bounds) either less than predicted by equation 1 with $\\gamma=1$ or greater than predicted with $\\gamma=2$. At best they are equal, for example in the case of D=N, when both the exact value and that predicted using $\\gamma$=1 are equal to 1. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do these bounds (the sphere-packing equation 1 with $\\gamma=1$ or $\\gamma=2$) have any mathematical justification,
\n", "or are they just conveniently small and large numbers, respectively?
\n", "In fact, there are two well-known bounds from coding theory (that can be found in any textbook on the subject) that look almost exactly like equation 1, one with $\\gamma=1$ and one with $\\gamma=2$.\n", "\n", "The first of these is called the Hamming bound (http://en.wikipedia.org/wiki/Hamming_bound).
\n", "The Hamming bound is well known to be an upper bound.
\n", "The second is only slightly more obscure and is called the Gilbert-Varshamov (or GSV) bound (http://en.wikipedia.org/wiki/Gilbert%E2%80%93Varshamov_bound).
\n", "It is just like the Hamming Bound, except with a difference of factor of 2 in upper limit of the summations.\n", "\n", "And a factor of 2 in the upper limit of the summation is exactly what distinguishes $\\gamma=2$ from $\\gamma=1$ in equation 1!
\n", "However, the form of the Hamming and GSV bounds isn't quite the same as that of equation 1.
\n", "This is because those bounds are for codes of arbitrary weight, i.e. where N is allowed to vary.
\n", "In that scenario, the size of the space is not ${C \\choose N}$ but simply $2^{C}$, accounting for the discrepancy in the numerator.
\n", "With this small change, equation 1 with $\\gamma=1$ matches the GSV bound precisely,
\n", "and equation 1 with $\\gamma=2$ matches the Hamming bounds precisely.\n", "\n", "Further support for the corresponding modifications to the such bounds can be found in:
\n", "V.I. LEVENSHTEIN,Upper bound estimates for fixed-weight codes, Probl. Inform. Transmission, 7, (1971), 281–287.
\n", "as discussed in:
\n", "\"Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes\", JIANG T and VARDY A (eq. 44)
\n", "Further support for the corresponding modifications to the GSV bounds can be found in:
\n", "V.I. LEVENSHTEIN,Upper bound estimates for fixed-weight codes, Probl. Inform. Transmission, 7, (1971), 281–287.
\n", "as discussed in:
\n", "\"Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes\", JIANG T and VARDY A (eq. 44)\n", "\n", "The most likely explanation for this mistake is that, in the literature on codes, the Hamming distance represents the number of \"bit flips\", i.e. the number of changes from 0 to 1 or 1 to 0 across the digits of a word.
\n", "This means that a difference of D=1, i.e. the substituion of one mixture component for another, represents a Hamming distance of 2, correspond to one addition (0 to 1) plus one deletion (1 to 0).
\n", "In the literature discussing these bounds, the upper limit on the summation in the denominator is often expressed as the Hamming distance divided by 2, especially for constant weight codes where the Hamming distance is necessarily an even number.\n", "\n", "We believe that the authors of the original paper took this division by 2 to apply to D itself, when in fact D *already represents* division of the Hamming distance by 2, so an *extra* division by 2 changes the equation completely.
\n", "In fact, that extra division by 2 turned an equation for lower bound (that they thought they were using) into an equation of an upper bound (which they were actually using).\n", "\n", "In conclusion, the constant-weight version of the Hamming bound is exactly what was used in the original paper -- however there it was falsely advertised as a lower bound.
That is obviously a very big difference, especially since these are very conservative bounds.
I can conservatively say that $10^{15}$ is an upper bound on the number of humans on Earth, and not to br wrong. But if I call that a lower bound, then I would be terribly mistaken.

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