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@Saurabh7
Created March 23, 2014 14:28
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{
"metadata": {
"name": "MKL"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Multiple Kernel Learning"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<em>Multiple kernel learning</em> is about using a combined kernel i.e. a kernel consisting of a linear combination of arbitrary kernels over different domains. The coefficients or weights of the linear combination can be learned as well. We will see how to construct a combined kernel, determine kernel weights and use them for predictions."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# import all shogun classes\n",
"from modshogun import *\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Introduction:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Kernel based methods such as support vector machines (SVMs) employ a so-called kernel function $k(x_{i},x_{j})$ which intuitively computes the similarity between two examples $x_{i}$ and $x_{j}$. </br>\n",
"Selecting the kernel function\n",
"$k()$ and its parameters is an important issue in training. Kernels designed by humans usually capture one aspect of data. Choosing one kernel means to select exactly one such aspect. Which means combining such ascpects is often better than selecting.\n",
"</br>So in a svm, defined as:\n",
"$$f({\\bf x})=sign\\left(\\sum_{i=0}^{N-1} \\alpha_i k({\\bf x}, {\\bf x_i})+b\\right)$$</brr>\n",
"\n",
"\n",
"One could make a combination of kernels like:\n",
"$${\\bf k}(x_i,x_j)=\\sum_{k=0}^{K} \\beta_k {\\bf k_k}(x_i, x_j)$$\n",
"where $\\beta_k > 0$ and $\\sum_{k=0}^{K} \\beta_k = 1$\n"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Prediction using MKL in shogun:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Shogun provides an easy way to make combination of kernels using the [CombinedKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CCombinedKernel.html) class, to which can append any [Kernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CKernel.html) from the many options shogun provides."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"kernel = CombinedKernel()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To see the preiction capabilities, lets generate some data using the [GMM](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGMM.html) class. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"num=30;\n",
"dist=1.0;\n",
"\n",
"gmm=GMM(4)\n",
"gmm.set_nth_mean(array([-dist,dist]),0)\n",
"gmm.set_nth_mean(array([2*dist,-1.5*dist]),1)\n",
"gmm.set_nth_mean(array([-dist,-3*dist]),2)\n",
"gmm.set_nth_mean(array([2*dist,dist]),3)\n",
"gmm.set_nth_cov(array([[1.0,0.0],[0.0,1.0]]),0)\n",
"gmm.set_nth_cov(array([[1.0,0.0],[0.0,1.0]]),1)\n",
"gmm.set_nth_cov(array([[1.0,0.0],[0.0,1.0]]),2)\n",
"gmm.set_nth_cov(array([[1.0,0.0],[0.0,1.0]]),3)\n",
"gmm.set_coef(array([1.0,0.0,0.0,0.0]))\n",
"xntr=array([gmm.sample() for i in xrange(num)]).T\n",
"xnte=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,1.0,0.0,0.0]))\n",
"xntr1=array([gmm.sample() for i in xrange(num)]).T\n",
"xnte1=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,0.0,1.0,0.0]))\n",
"xptr=array([gmm.sample() for i in xrange(num)]).T\n",
"xpte=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,0.0,0.0,1.0]))\n",
"xptr1=array([gmm.sample() for i in xrange(num)]).T\n",
"xpte1=array([gmm.sample() for i in xrange(5000)]).T\n",
"traindata=concatenate((xntr,xntr1,xptr,xptr1), axis=1)\n",
"trainlab=concatenate((-ones(2*num), ones(2*num)))\n",
"\n",
"testdata=concatenate((xnte,xnte1,xpte,xpte1), axis=1)\n",
"testlab=concatenate((-ones(10000), ones(10000)))\n",
"\n",
"feats_train=RealFeatures(traindata) #convert to shogun features\n",
"labels=BinaryLabels(trainlab) #generate labels for data"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"_=jet()\n",
"_=scatter(traindata[0,:], traindata[1,:], c=trainlab, s=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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kSiE6evTHzJhxFmjs+kBAp9vOtGkDGDJkSKrnZ7PZCA0NxWq1UqJECXLlcmX3\nhq1bt9KjxzsYDL1JHC4CYEOr3US7dpVYu9a5J8qxY8eYPHk6gYHbsVjMFC1ago8+GsY777zjsian\nIAgEBwc/9aSpUaMGe/bsYd68JTx8+BBfX1+GDx9E79690emcGSmylqNHj9KuZUv6GgxJrlAksAjR\nUNYAMVeiA9FGvVehoF2vXixYsiSR+6EgCFSvWJHrV6/SEeffIhuiSJsQA3n84WkyquOIG6OvAe2c\nHGsC/kJ0QWyIeHM5q1Zz2cODDVu30rRp0zRdhxeJioqidPHijLBYXGaHEYCZgFGl4m5UFLlzpyTH\nzctB8ip5xVGrVYi5qN0jCJYkRRcUCjnu6lk+d7TLSDhBELh06RJRUVHky5ePatWqJRIGpVJJxYoV\nUzA/gTFjPsdgaENS0QZQYjR2ZPv237h8+bLTPuvUqcOqVctScD4igYGBDBs2mvv3nyAIxXA4LBiN\nF5HLvXE4mgP1iIh4yOjR0xk3bgJBQTtfepGQevXqMW3WLMaMGEFtk4kaDgeexGf0Q/xrxgFz4/9t\nA3wBvVKZRLRBFIjBw4czefRoKrkQigfx/QwgcdHiQohuhBUQ/cGbkDQxsCa+zUagJeKzXWGzmbJm\nM13at+fspUvpym6YgK+vL6VLl2bX5ct0wPnm6UlEu30RlYrt27fTq1evdI/7MpBMJa8AnTu3w9Mz\nOTe3R9hs96ldu3aidxs3boi3961kjrUD/1KvXr0kn6xatYry5atRt25zunQZQsOGbShRohzTp0/n\nxx9/okKF6hQuXBJ///r89ddfGAyut7XOnTtHREQkUM7NXDywWmswZ868ZOacPOvXr6d79z7cuFEb\nvf594uLaYzR2BT7F4agB7EGUnQro9W9y/34dmjZtycOHD9M9dnp5d8AA9hw6RMG33mIaMBHRzAEw\nBHgL+AQYiWju6AfI5XKXgT67t22jjpsn46OIK3hXBfLKIZpqTrr4vDiikD5fRrgMUMliYfbMmS7H\nTS316tcnFPEm8nz1Uj3iXzMIeBPwtNt5/Phxho2b1UjC/QrQr18/xMK4t120EFCrD9K/f388PRMX\nM+jYsSMeHk/ij3fFWcqVK0316tUTvTtx4ncMGDCK0FB/4uKG8fhxH+LihhIeXoaPPhrL11+v4urV\n2ty715HTp0szatQ0ypSpSGio85tMWFgYSmVhkvta2mw+XLmSPn9sg8HA228PiK/KU47E6zMVomdN\ndeBZulXD6yXxAAAgAElEQVRBqElcXBHmz/8rXWNnFDVr1mTJihUUL1yYAYi25SeIppIZwDogCjFj\nSzhQzk2u8yePHzv1VAFx1X4O0RTijteAsy4+kyE6hr6YVLemxcLC+fOdHJE2SpcrRzkPD7wRzTO/\nAX8gBgzFAQMRn+UeKZWpDizLTkjC/Qrg5eXF8uVL0GrXIP7Ent9Zf4JavY2SJU38738/JDlWqVSy\ndOkCtNr1iH4Dz6+6HMBpvLz2s2jR3ETHhYSEMGnSDAyGfvA05xyI65yDQF/s9i5ACcSfSgX0+reI\njKxBkyYt0euTppHV6XQIQkryZZvw9k5fDowVK1YgkxXH9RoSRItsKM+nvDUaazJr1p/pGjsBm83G\ntWvXuHLlitMN15QybNQoNisUbERc2faLfxUHNiGuPo/rdIz69FOXffiVLk20i9W4FfGbkNwVz4tr\nd0QB0bb9Yg2kvEBMBq58+/Tty2W5nKaIm6tvIkZ4fgR0BPIgbqDehxztYSQJ9ytCx44dCQzciL9/\nBDrdb+TOvZbcuZej1c6lX7/XCAk55HJTsF27dmzcuIrixYPx8pqHWr0DjeYfdLrZVKlykwMH9lCj\nRo1Ex0yePB2TqTZJf85HENMblXQ6liDUJjY2D8uWJbVDN2zYELs9CtFa6xpv78v06tXdbZvkCAzc\njV6fXF1JDaL8RTz3XgGiou66aJ8y9Ho9E776iiI+PjT296dFnToUKlCAUSNGEBkZmer+Im7dQutw\nMBTxyuePf9UDhiJezScajVt77vvDhnFGp8Ph5DMPxNtycr7bT3BdMiIMcUPtxWjPJ0DuDExEVaJE\nCTp16sRWjQZZ/HiFeeZvZQK26nR8PHZsiqKJsyuSV8kryOXLl7l27RpqtZoGDRq49KZ4EUEQ2Ldv\nH2fOnEEul9OwYUOXlUxy5cpHbOy7wPO78nZgEqJl1d2PMZTKlS9w/vwJgoOD2bFjBxaLhUqVKhEc\nHML8+fswmbrifHvpEr6+B4iIuJmqwgsPHjxg4cJFhIScwsNDwaVLlzhxwhcxSNwdKxBjCBM2JKPJ\nl28NMTFpE+/Hjx/TtH595GFhNDSZnqZjfQQc9fDgVt68HAoJoUSJEinur1ihQgwxmZKUeE4gFpij\n0XD73j2XXhSCINC8YUOsJ0/SxmJJcuVXIHr5u4uf3YIY4PJidc04xORWTRCv5PPs8fCgxuDB/Prb\nb256Th1Go5HOb7zB1ePH8dfrKUW8Z41Mxkmdjm69ezP7zz9Tndgrq5G8Sv5jVKxYMUVeHC8ik8lS\nXMzZYjGT1G/chJilIrkVVAEiIm5ToUI17tyJwWgsi8PhgZfXRgQhAl/f/Ny/vwajsQmi3wKAAbn8\nJJ6eJ9m2bUeKRVsQBCZNmsI333yLXF4Bg6EI4ECligZOxc/VVWEFG6J1+Jn7pFJ5nrfeSvtqf+jA\ngWivX6ftC+KYBwiwWjkSE8NbnTsTcjq5UBqRtWvXUlahcCnaILrtlVEoWLNmDQMHDnTaRiaTsXH7\ndtq1asWiq1epqddTBNH3+5JaTThwWxCoaLHg4+T4m4geLcUQ08oWjT/2HBCMeHt8UbTvAGc8PJiX\nwSUPtVot23ftYvv27cyYNIll588jl8lo0qQJaz/5hEaNGmV70U4OSbhfUaKioggNDUWlUlG1alU0\nGk2G9l+8eElCQ++QOI2qB6JF1Br/b1fE8eRJLE+eNEIQ3iRhZS2avaMRhLU0blyOkyc3YDaDXO6B\nxfKQjh078f33R1JVrHjKlGl8990MTKbBPP90YLHUQdzMXY6YRsnZxt1ZnhkexLmpVKcYPfr3FI//\nPJGRkWzZupURTla0CdSz25l97RonTpxIUd3GO3fukMuNp04CuQ0G7t51/5SQJ08eDoaEsH37dmZN\nnUrgtWtoNBo6devGsuHDOXDgACOHDKG2yUTNeBfEx8AppZIQQSAPcNduZy2iaCviXxbEv3Acoo07\nFjitUHBCrWbhsmWUK+fOiyhtKBQKOnToQIcOznIe5nwk4c7BGI1GVq5cye7d+3E4HDRsWIfatWsz\nceJP7NmzG42mIIJgQxCeMHjwQCZOnJBhie1Hjx7G2LFzMBieFzwV4mbkBcQs0c6RyU4hCEVdtCmA\nwdCLAwfmcuPGNR4+fIjFYqFEiRLkyeMsdZBrnjx5woQJEzEa3yOxSSeBYkAnxCDvF5OhXgX+QVyN\ni2tHne4gs2f/mqanGRB9xssplbi7hcqBSiYTGzdsSJFw58qVC5NaDclsbprUareBTwm4E7wSJUpQ\nrVo1pk2axOy1azFZLHjrdLz99tv0rlmTMcOH04ukuxsngJ0yGYcUCgRBwEOppFfPnswYO5YqVZJL\niyXhDMnGnUNZs2YNAwYMBoqh15cAZGg0tzCZLiIm7+zMM1NGDBrNAcqUkREcvD9DxFuv11O1qj+3\nb5fEbm/EM9ELRUwcOhDnJpM7iBbPITgPshHRarfy1VfdGDjwPZ48eYKvr2+KhOd5fv/9dz75ZA4G\nQ1c3rQRgKmKISnlE88glxPVhS2ArKpWCpk2b880342jUqFGq5vA8s2fPZuknnxBgdO85cwioPHIk\n01OQevTWrVtUrVCBkSYTKhdtLMCvajUXrl7Fz89VBu3UIQgCNpsNDw8P7HY7JYoU4fWoKBdb0qK/\n0qEiRbhw7RparTZDTRX3799n2bJlhIbeIHdub7p06UydOnWSPzCb4047Ja+SHMiWLVvo3/999Pqe\n8XUi6wC1MZm6IRahugecf+6I/JhMnQkNlTNmzNgMmYOXlxcHD+6lTJl7eHsvRKziHgo8QaWSI5PN\nQbRw2uKPMCKTBaNWL0erLYg70QYBo1HOTz9Nw8+vDP7+jfH1LUKXLm9x6tSpFM/x5MmzGAzucrCA\neMMpg3iTeYAo2M2AD4GyaDQeREZGsHPn1nSJNoCfnx/RKbDNP9BoKOnG5/rFPlu3asVelcpp/KsA\n7FWrad2qVYaJNoiiklAC7p9//kFlNLoUbRAdRm1PnhAcHJxhom232xkxYjR+fqUZN24Zv/12mZ9/\nPkDz5u2pVq0WN27cyJBxsiOScOcwHA4HQ4aMwGjsiPPEUPmA3oipgJ4Pg5dhNjdj6dKlxMY6z6CX\nWooVK8alS2dYvXoOXbt6UbfuLTp0ULJ69V9s2LCUunWj8PCYiqfnLFSqX+nUyYspU37Ew8PdVpoA\n7ARCiY1thdk8Br3+A8zmkWzapKdx45Zs3bo1RfMTUwEkny1ObFMGsahXAOLKWw7E4ONTKNUmGlcE\nBATwSKHAncOfAbgsCPTt2zfF/f61dCmGMmVYp9Vym2dpWG8D67Ra4kqXZoET98uM4sSJExR34pf/\nPDKgpNnMiRMnMmzcAQMGs2DBdkymYRiNHYCGOBwtMRg+4OLFgtSt2yhZu35ORRLuHEZQUBBPnjgA\ndz7IPoiBJRdfeD8XHh5FOXjwYIbNRy6XExAQwLp1Kzh6dB+bN6+lU6dOdOrUiaNH9xMVdYeLF0/w\n4MF9NmxYzVtvvYXZfAucJiYF0UxxDbG4VkWefUU1CEJ9DIY36dmzb4r8ndu0aYWX17/JtLIg+kEk\ndb/Tas8wbNigJO+nFQ8PD76eOJFNOh3OZM4CbNDpGDhwID4+znw3nJMnTx4OHTtGvwkTCPT1Zapa\nzVS1mkBfX/p+/TWHjx3LsJuPM2QyGUIKVtFCfNuM4OTJk6xduyk+HfGLMZ9yHI56PHpUmokTv8+Q\n8bIbknDnMC5cuIDNVozk64+UQIwPexF1uqL0UkuePHnw8/N7GmpfsGBBAgLaolCEuDgiGNG27CqU\noxgORwX+/HOui8+f0b59ezQaI88ySbsazw+S1Ew5j0Zzi0GDnLvPpZXhI0cycMwY5mq17PXwIBwx\nvOeQXM6fOh0NunZl6owZqe7X09OTsZ99xs27dwmLiCAsIoKbd+/y2eefJ0lzkNHUr1+fMJ3Obaoy\nAbiuUlG/fv1U958QX/DLL78wffp0jhw5wrRpMzGb/cGlZR9strosWbLUbX6cnIok3DkMpVKJTJaS\nx38bSf+8Duz2O5ROof00s5g5cxp58lxELg8msSnDgJiY1JVftYjRWIWlS1clO45CoWDdupXodFsQ\nvYyfH8uMXL4POIharUH0136EmL97I/nyHWDv3h0UKJD+mpjPI5PJmPjdd4ScPk31QYM4Vr48R8qW\npXCvXmzft4+FS5emKrDoReRyOfnz5yd//vwuszlmNC1btkSZO7fb+kOXgFy+vqneJwgKCqJ8yZL0\n7dCBNZ9/zurPPqPb66+zYdXf2O2ubu4J5Eah8EqSg/5VQHIHzGGIwTFfIoqQq6IAAuJP5cVcDNco\nXrxIkvD1rMbPz49jxw7Tu/c7nD07E0GogMOhxMPjFnFxCpJfT+jQ61Nmp2/SpAl79+7ggw9Gc+lS\nEEplScCO1XqD5s1b8OOPwWzduo3585fw+PEjfHx8GTZsIO+8806mmhfKly/Pr7NnZ1r/WYlcLmfB\nsmV0eeMN2hoMVODZ82DCN/EfnY5tS5emylSyZ88eunfsyBsGQ6I0YILFwkVgPduxURDcFCsTBEeW\n3cCyEskdMAdSt25jjh/PjSDUddHiImISy+E8+7pHotWuYP365RlS5zGjuHz5Mrt27Xrqq9237zuY\nzSNwbSoBuEjdunc5enR/qsa6dOkS586dQ6FQUL9+fYoWfbFUm0R62L9/P4P690cfE0MpiwVBJuOG\nUkmeggWZv2QJDRs2THFfDoeDkkWK0DwykjIu2pwHNpEPCyNxbjqMInfuVdy/f+epB0xOQgp5f8VY\ntmwBdes24skTOw5HbZ5FKdoRqw4GIpdXx+H4F7FqzDXgKvPnz8lWog1Jw/OXL1/D+vWncTgauDzG\n2/sso0d/7fLzK1euMHfufEJDw8iTJze9enWnTZs2VKpU6aUXQXiVadq0KVdu3ODgwYNPvUfq1q1L\ngwYNUr0puWPHDhQGg9N41gSqAIHEYiGCpKtuAbX6CB988H6OFO3kkFbcOZTQ0FAGDx5OcPARPDxK\nI5MpsFqvU7VqVT799EN27tzL6dPnUKnUdO7cloED3yNfvnwve9rJcu7cOerXbxJf+Dip37FCcYji\nxcO4fPlckuxuRqOR3r37888/O7HZqmOzFQAMeHldIl8+DwIDN+do4RYEgQcPHmC328mfP3+a62eG\nhoaycuVKoqOiKFSkCL17985QH++M4JtvvmHvxIlJEla9yCbgJA2BNs+9a0Kl2kfJkrEcP344xUnW\nshvutDPdwh0YGMjo0aOx2+0MGjSIzz5LXElcEu7MJSwsjGPHjuFwOKhZsyYVKrjf2MsJ7Nixg27d\neuJwlMNorIzo7hWNl9dZfHwE9u3bRfHixRMdY7PZaNkygJCQKMzmLiR+mBSQyc6QJ89hzpw5nuTY\n7I7VamXu3LlMmjSdu3cjkMuVqNUqhg0bwscff0T+/PkxGo1s2LCB69evo9PpeOONN5J8Fx49ekTf\nHj04eOAAVe12PK1WnqhUXJDJaN++PX8tWfK0pubdu3f5Y/ZsFs2fT8yjR+T29qZv//4MHzkyS0T+\nmwkTCPr2W1ok0267QsFZlRalshA2WwEUCjM22zXat+/AvHm/Z+o+RWaTacJtt9upUKECu3btomjR\notSpU4fly5cnWtVIwi2RFqKjo5k//y8WLVpObGwsxYoVY9SooXTr1i1R3czIyEimTJnG7Nl/YDCY\nELfDfBBL2tbgedunUrmb996rypw5OWdT0Gw28/rrb3DixG0MhgaImUBkwH3U6mPky3ePd9/tz8yZ\ns5DJihIXlw8PDyty+WX8/WuyatVSihYtitFopFGdOmiuXaOVxZLotmYBtms05HrtNXbt20dISAgd\n27alvNVKdZOJvIh5s8+qVFzw8GDF2rWZbnLbtGkTY/r14203wWICMNfLi6WbNmE0Grl58yaenp4E\nBARQsOCLmb9zHpkm3EeOHGHixIkEBgYC8PPPPwPw+eefp2hwCYn0EBoaSoMGTXnypAQWS23EMHoH\nYkDNPsTEUt155qXyGK12HjExkWi1ybmSZQ9GjBjFX38FYTR2wZm3jUx2EDiMILxH4jQCNpTKYPLn\nv8yZM8dZs2YNs8eO5S2Dwek2ngNY6unJ2KlTGffpp7wRG0tZJ+3CgTU6HSGnTqUqS2NqsdlsFC9U\niHYxMU5Co0SuAMdLlODKjRs5Pk2rMzJtczIiIiLRY2exYsU4evRoknbffPPN03+nNN+zhIQ7HA4H\nbdq058GDWvEbtAnIEWtIlgL+Riyj1jT+s9woFDoiIiIoW9aZLGUv9Ho9f/21AKNxEK5cJAWhEXCc\npJGoSmy2xjx4YGD8+Ans3xlIAxeiTXzvteLi+OmbbyhvsTgVbRDrAdW0WJg+dSqz58xJw1mlDKVS\nyZ8LFvBOz550MRoTibeAeGvertOxbsGCV0a0g4KCCAoKSlHbdAl3Si/Y88ItIZER7Nq1i+hoMw6H\nq9SnSqAdYuncRog+7wIOhyWRqSU7s2vXLpTKYjhPSZuADDE97kWc+TNbrfVYunQuFnMcvZMZrzSw\n/t69JN7/L/Kazca8JUsyVbhBLMe3eNUqBr/7LjqLheKxsQjATS8vHF5erF22jBYtkrOC5xxeXNRO\nnDjRZdt0CXfRokUJDw9/+v/w8HCKFXPtDC8hkVEsWbKc2NhKuA/990EUvXBE2/Btcuf2zjHf0ceP\nH+NwpCRc3QtwlUwpNx4e+bCY48RcIS98+vx7CfUm8yYzWi4gzmTCYsn8m2CHDh0Iv3ePbdu2ceL4\ncWRyOQ0aNOD1119/JQNrUkq6hLt27dpcu3aNsLAwihQpwsqVK1m+fHlGzU1CwiUxMQ9JWjPcGV6I\nZgQHWu0hxoz5MMf84IsUKYJcHpOCltHgpniZTCajQqlSXL1+nYqIOSPPIBY4iEQ0k/gh1vlRKxTE\n2u1uiz3EAWoPjyzzj1YqlU8Tl0mIpOsbrFQqmTVrFgEBAVSuXJmePXvmaD9ZiZxDyZJ+KBTuq8GL\n68kYQECr3YC/f0E+/HBkFswuY2jRogUeHgZcr6ZBlOGzQHUXnz/Ban3AR59/ToinJ3pgIXAZaA2M\nA8YiGlv+BfL7+nImmVwpp+Vy3uze/ZWxLedEpAAciRzJyZMnadIkAINhGK7XH2HIZKvQapUMHjyI\n//3vxyRBO9mdmTNn8fnn/8Ng6E3SJww7sBrR2NHT6fFK5Q7eeacqf/zxGx0CAjgaFEQFh4O2JDWb\nWIFVWi0RVit9bTacJQS4DyzT6Qg6fPil57x51ZEq4Ei8crz22mvUqeOPSvUPOE0oGotavYUxY4Zx\n//5dpk+fmuNEG2DEiOEMH94PnW4+CsVBROl8AJzCy2sRfn42tNon8e89jx2F4iD589/i++8nolQq\n+WnKFGwyGW1wvjPgAbQzGpErlazUatmvUJDgRR0HHJTJWOjhwQcffkj16q5W+BJZgSTcEjmWjRtX\nU62aHC+vJYhl0h4C91Eo9qPV/sX48R8xZcrkp9GAORGZTMakST9x8OAuevUqRqFCW/DxWUvLlmZW\nrfqD69cv8803o/H0XISX12pksj2oVP+g1c6kbl0rx48foVChQgCsWb0af5nMZU5JEOsnFfXw4MfJ\nkyn99tvMVqn4FrEq537yYRYqM3PWUvz8yrBr164suAISzpBMJRI5GpvNxubNm5ky5VeuXLmCh4cH\nbdu2YcyYD6lWrdrLnl6WYTQaWbdu3dOQ9/bt2yepRj/43Xe5u2gRyZXR3erpydBff6VKlSq0aNEG\no7E1UJVn6zwBCEWn28r69Stp06aN684k0kym5ipJz+ASEhLOefjwIevWrSMyMpJ8+fLRpUuXpyvn\ntDJ+3Dj2T55MK5vNbbvl3t78vHgxH374KeHhNRFF2xnX8fXdzZ07N9Oc8ErCNZJwS0jkEKxWK2M+\n/JCFCxdSVqHA22RC7+HBVYeDzp078+eCBWkuRXbx4kUa167NCKPRpbkkBljs6UmeAoW5efMe8DHu\nfOW9vRexfPlM2rdvn6Y5SbhG2pyUkMgBOBwOenTrxp7Fi/nAZKJLXByt7HY6m0yMtFg4s3o11SpU\nRJ9MRXVXVK5cmTr167NLpXK6nWsFtmu12AUZN2/GIVa7d+/yFxvrR3Bw0jQXEpmLJNwSEtmEbdu2\ncWLvXroZDEkc/zTAm4A1IoLatethtVrTNMaKtWsxly/PCk9PriGKtQmx/MYiT0+URYpiNFdFrL+Z\nEvOHDOdePRKZiSTcEok4cuQI3bv3wsenKAUKFKZFiwC2bduGw+FI/uBszpMnT5g1axYVK9Ygb15f\nihcvy7hx47l9+/bLnhoAMyZPplZcnMtwZhnQAoEbV65SuLAf77//ARcvXkzVGHnz5uXQsWN8OmMG\nZytUYLJSyQyViieNGzN90SJu3Y3Cbi+M6DN+neREWa3+l1q1EueLMRgMzJs3j2rVapMvXyGKFy/L\nJ5+MfSWL9r4sJBu3BCBWVxk27EMWL16J0fgaglAeccV1Ay+vU9SrV5ktW9aj0bgLhs6+XL58maZN\nWxEX54PBUAMxwDsOtfocCsVFVq5cSocOHV7qHPN6ezNIr8fLTRsB+BYQ8EKhqIVKdYahQwcxdeqk\nVEcyPn78mMWLF/PPP0HYbDYqVizD3LlL4vN+3wbuAC2Aii56uIVavRq9/sHTyvRhYWE0btyCR488\niYuriZgvxohKdR6F4hwLFvxJz57Og4UkEiNtTkoky08//Y8ffphDXFxPSJKpwo5Gs5HOnauzYsWS\nlzG9dBEbG0uZMhWJjq6DIPg7aRGBTreaI0f2vdTAkpQLtwyBvIjRkho0mpWMHfs+EydOSPFYS5Ys\nYciQ4chkZTAYSgNy1OpbmM2nENPiCkB9YBXQOf69528MN4EVdOnSlvXr1wFi0Ydy5SoTEVEBh6Oe\nk1H/RalcQ9269fD19aVjxwB69eqVo/3sMxNJuCXcYjab8fEpQmxsHxIn438eCxrNTK5evZDjSn/N\nnj2bsWP/JC6uq8s2cvlh3nyzACtXLsvCmSWmVePG5D50CHeB5NeBFeTFggbRnBGOGPNopG7dhnzz\nzRe0a9fO7Tjr1q2jX7/BGI29AN8XPo1FzGYSC3yEmIZqc/wYCeL9L6BHrZaxe/cWGjVqBMDff//N\nkCHfote/mEBWAPYg5g2vhJgr3YaX17/AbZYvX/LSn3ayI5JwS7hl48aNvP32Z8TGus/YrFYHMmFC\nJ7744ossmlnGUKXKa1y8WBUo46aVAZVqJo8fP3hp5qBNmzYxuHt3hthsTrcFBeAvPAinJaIQNkRc\nFWsBG3ARne4gn3wynIkTv3Y6hsPhoHjx0ty50wIx1a0zHgG/IyaueiP+veuI5hMBKAzEUr78DS5f\nPvfURNOwYQuOHPFBrL/+PHsQxb4vYv3Q57mNVruGrVvXpTi3tsFgYP369YSFhT0NNsrMajwvC8kd\nUMItd+/exWZLvqiq2ZybW7fuZMGMMpbIyHuIwdzu0KFQqHn06FFWTMkpHTp0oHytWiwDDC98ZgbW\noeAeBRB/tkUQ7c8JJdiUQHUMhv5Mnfrb03KCL7Jv3z5iYx3gsiAYQB7EogxXgQ2IeVDKAM2A2shk\nt8mbN4TNm9clsqvfuXMHce/gefRAMFAL8engxTMrhtHYhpEjP3YzHxFBEPjpp//h61uEoUN/4uuv\n/+GLL1ZRo0ZdmjRpGT/+f4N05eOWeDXIkycPSuWLP6ikKBQG8ufPeVWzvb1zERMTh/sSAVZsNhPe\n3q7zWrvi5s2b3Lp1C51OR40aNZ5u1KUWuVzOrn37KFeyNNPu3aUsSnyw8hAllwEZZbFSF1gJ9HfR\nixdxcY344YfJtG2btJbNlStXsNmKkpx/NpRGLg9HobiH1fon4r6HHA8PE7179+a775YmqfaeK1du\nRKFO4AawCdHMkuB8uB5xs7MNz1bfFblxYw9nz551u8fw2Wfj+O23ZRgM75BwIzabAVoTHHyYOnUa\ncvr0MXx8fJI5t5yPtOKWoG3btlitN0j8o3sRO2r1RXr0eCurppVh9O/fG43mfDKtztOwYZNURSXu\n37+fZg0aUL1iRQZ27EiXFi0oVrAgP/7wA7ZkwspdoVaruXjtCvUaNeW6SssBynCe17DRDisKYDnQ\nHJwmXU2gCsHBh5wG6qhUKuTylPiA2xg2bCgLF07jt9+mMXv2Txw7toPo6HssWjQ/iWgDDBjQB50u\nwT3xCrAGeB0x+rIn0A/4EFADCwBjfFs5CkVxLl265HI2V69eZdas3zEYepH06UmJzdaU+/cLM2HC\ndyk4t5yPJNwS5MmTh379+qHV7uRZAavEKJUHqV69cqIVkdVqzdD9i+joaH768Uf8K1WiTPHiNKtf\nn7///huzuKxKMx98MASF4jJwy0WLWHS6w4wfPxYQReKjjz7m9dc70LnzWyxZsgSTKXEx3jVr1tCl\nXTvyBwfzoclE38ePGRQbS5cHD1j84490atcuzeLt5eXFgQN72bt3Oz17NkCnuw4cRTRvaHHtnpeA\nEqVS41S4W7Rogd2esPp1hYCX1zW6du1Mnz59GDZsGB988AG1a9cmV65cLo8aMOBdFIobiKK9EegD\nVCaxzOgQa4GWAp5lF5TJrG7LoP3662/YbDVwV/XIaq3P4sWLMRiSf3rM6UibkxKAmF2uVau2nDkT\nicFQD/GHJQPuotGEULBgLEePHgTgt5kzmTN7NtGPHiGXy2ndrBkff/EFrVu3TvP4O3bsoGe3bpRz\nOKhsNOKJWJDrjJcX9vz52b1/v9NVXmr679q1B2ZzHez2moglzSzA+XjR/oSPP/6Id98dxPr1m7Db\na2C1FgLMeHldRaGIYuPGtTRr1ozo6GhK+/nRx2iksJOx7MBKnY4h337LmI+Tt90mx927d6lduwHR\n0QWxWMKBlogeHq6IQ63+jcePHzjNQd6qVVv27TNjt5dAFPC8iP7WCZzHz+80YWFXU+0bfuDAAVq1\nClxa+isAACAASURBVMBqLQK87aalHpgFjAYcaDSzuXXrukszR/XqdTh3riquN1RFcuWaz4EDW16J\nfOHS5qREsmi1WoKCdjJp0khKlgzGw+N/qFSTyZ9/I+PGdePEiWCOHz9O1QoV+GfKFLo/fMhXgsBY\nux2PPXvo16ULX4wdm6axz507R4+uXekWF0d7o5FSiE5qlYHeej1lbt+mVdOm6Vp5t2nThmPHDtOr\nVzHU6tloNFNRKqfQooWZTZtW8MUXn/H22++xYcMJTKbhWK0t42fgj17fk8eP2/PGG505deoU8+fN\noyI4FW0Qw5aaGgzMmDIlQyJOC/+/vTsPi6psHzj+HZiBWVBRcdfcMdFEUkNTUzPENLc0zeW1NFMT\nLbX0rdfqtcXMpZ+5pS+aWZm5mxuZK+6K+75gLrGIO8IwM8x2fn8cxAVmBhAYkOdzXV1XModz7kG5\n5znPuZ/7qVCB48cPMWxYS7y87iE/7HPMw+Mo3bv3yDRpGwwGqlZ9BpttD7AZiAJ+BX4EzqNQHMDH\nZyt//LEsR1uT1ahRA5VKA7hqqesDlAfiUKn20rHja0Vibjq3iBG3kIEkSSQlJWG321GpVEydPJkf\nZs4k6d49QiWJ5zP5HgOwSKtl6vz59O7tvKzwcX3eeIPbq1bxopMkt8THh0/nzqVv377ZezOZsFgs\n3Lt3D51Oh0YjV2WcOnWKF154CaNxGPLDtMwc4uWXrRjvXqfm0aPUcnINCfhBp2P3kSO5Wqp2584d\n6tSpz+3bjZCkxpkc8Q863SqiovYQEBDwyCtGo5EWLdpw5kwqJlMrHjystXN/eqNevWdZtuy3DN+b\nFUlJSdSvH0RMjBFojuN2sPf9iqenFxUqmDhy5IDTxB0W9j7z5h1P+0B1JBGtdgE3b157Khb1iBG3\nkC0KhYISJUrg5eXFyy1asGrKFBomJlLRQdIGeebyZYOBb/7732x9UBsMBtasW0dDFyPTBno9c77/\nPutvwgmVSoWfn1960gaYNWsOZnNDHCdtgED27t1DUnIyrjZBUwBqT0+MRqOLI7OnVKlS7N27g3Ll\njuPjswK5ZO828A9qdQQ63SpWrVqaaeL9+utvOHPGgMnUhUcrbDyQF8YM4NKlvylXrlyOYgsPn8et\nW8WRuwrGuDjaCsTSoUMdDhzYzbFjx1iyZAnbt2/P9NnABx8MR6k8TsZywgdUqgO89Vb/pyJpuyIS\nt+DQhx98gP38eV43mYgBMlss/rCawLW4OC5evJjla9y8eRONp2eGZRmPKwvExcVl+bzZdeLEWWy2\nii6OUuHtXYGy5ctzzcU0ggm4azbnySrT2rVr8/ff55g+fRSBgRcpV+4PatU6wLhxnbl06XymO9KY\nzWZmz56LydQSx6WA5QB/fvxxQY7i+v772RiNjYDnkXeed/ahdYLGjRvTqNHzBAQE0qPHMAYPnkzX\nru9QvnwVpk37/pEBgL+/P2FhQ9FqlyBvUfcwK0rlLvz84hwuPHraiDpuIVNJSUksXryYwSYTCuRf\nQcf1BDIFUEKl4vbt29Su7ezh2QPFihXDaLViw3kTUQPgk8MNBLLC29sL+WGlc5Jkpkfv3nxz7BiN\n9XqHI5+jCgXtQ0MpVcrVwp+c0Wq1DBw4kIEDB2bp+DNnzmC3e5NxifujjEZ/Vq1az9ixY7IVj91u\nJz7+KnKZogfyx/xioDcZV0v+jVa7g+LFg5k8+VcMhl48+nA0gU8//Z7o6EvMnj09fa598uSJ+PqW\nYOLESSgUlUlJKYVKZcHD4yyNGj3PsmX7isw8uRhxC5navn07VVQq7i9H0ZFxnPM4O3DHbM7WrXap\nUqWoHxDAeRfHnVKreaNfvyyfN7tef70jOl20i6NuY7ffY8CAAfg3bEiEt3emxZOXgP0aDZ9/JdcU\nF4SWuGazGQ+PrOxyr8Jsdv0B9jiFQoGHhwfyFAjI9dvPADOQe50cRX4Q+hOwhLFjR3HgwFkMhp48\nmrQBymMw9OaXX5axY8eOR64xbtwn3LgRz5w5H/Pll+2YOPENjh07wO7d26hY0dUd09NDJG4hUwaD\nAfVDt6oNgCMuvucCUKtWLapXr56ta4399FN26XQOb6zjgPMeHgweMiRb582Onj17YrVGIyeYzOZR\nJby9dzF48CA0Gg1rIiIo2bQp/9Pp2OvhwUXkfeaX+/iwvnhxpv/wA999Nx2tthienp74+PgydOhw\noqNdfTjkjerVq2My3UCexHHM0zOeBg0e7zXimkKhoHnz1sD9BTgK5OQdhryE/gogtx5o1y6U9es3\nk5ISjONnCmoMhsZMnpzxuYZWq6Vfv358+umnjB49mjp16mQ73sJOVJUImdq7dy89Q0MZpNejQB5N\nz0GevWyWyfFJwK9aLfMWL6ZLly7ZupYkSXw0ahRL5s+nZUoKdZBHFCbgmELBfo2GX5cuzZMOcklJ\nSXz++Rf8+OMCbDYtRqMZuTNebeReIKWBRNTqHfj7e7Jv3470h1+SJBEVFcXcWbP4+8IFfHx86NG3\nLyqVF0OHjiA1tRE2WyBQDEhEqTyGl9cxVq1aSmhoaK6/F1dee+11IiIMSFJmf4MAVrTaueza9RfP\nP+/oMbRjERER9Oz5Likpb0Gmj2+N6HQLWbt2MSEh7bDbP8H5bG0yOt189Hr39Y9xJ9EdUMg2SZLk\n1YtxcelLHhKRK37LAU2Q65hNwCkPD46o1fxn/Hg+HJO9udGHrVixgilff82Zc+fQKpXcS02lVLFi\n2CQJrUZD+9deY8TIkTkqVctMYmIiwcEtuHpVTWpqcx4spTYCB4Hd6HTlkKR7DBw4gG+/neBySfyp\nU6cIDm6ZtjQ7s13ZY9DpVnDq1DGqVauWK+8jq06fPk1wcAtSUjqScQGPBY1mDaGhz7J69fIcnV+S\nJAYNGsqSJZswGNohN8ICuTgyDp1uEwMGdGPatKl4eXkjSZ/hvGeKEY1mNgZDco7iKexE4hZyZOnS\npYwYOJA+BkN68VgqcBw4jFyEpgCqVK7MlOnTef3113PlutHR0bzRpQvJMTEE6fVURn5seFap5JhK\nxadffPFEHxD39e37FitWnMdsbk/mCeQUfn57uHxZHk1nxb/+NZDff/8Hm62lw2O8vLYwfHhTvvtu\nSs4CfwL79++nY8euWCy+JCf7A2pUqusolcd57bWO/PrrgkwX7mSVJEl8//10Jk6cgsmkRKEogSQl\notXC559/wnvvDUWhUFCxYjWuXXsFcFZ1c5569c5x6pSrSbqnk0jcQo7NmjmT/4wdS31Jwj81FSXy\nbOVh5F+5UOC4QsEhnY6NW7fywgsv5PhaycnJLFq0iM/HjsWq11MBaIg8Nrz/MOYe8JtWy8yffqJn\nz545vtadO3eoVKkqJtMwMlY93CdRrNjPLF8+N0tTG5IkodH4kJr6HuCsy+ANSpdeza1b7mlDajab\n+eOPP1i6dBV6vYHatavTqVMH6tWrR6VKlXK0YvJxNpuN/fv3c/v2bcqUKUNwcHDaw0vZlClT+e9/\nF2E0OtrcQkKnW8Ls2Z/w1ltvPXE8hVGeJe4xY8awfv16vLy8qFmzJj/99BMlSpTI8sWFwiEmJoZe\n3btz5tAhikkSZYDGPNqf7jywvXRprsbHO20W5MiePXvo0rEjFcxmnjMa0SL3KjmM3PujDw9S4d/A\nwerVOfP33zlOMitXrmTgwC9ISuru4si9vPtuTcLDf3B5TovFgre3GklyVUucipfX96SmurcZ0oUL\nFxg//mtWr16NUumD1WqkfPnyfPzxKN59991HEm1uS0pKokGDxsTFVcFqfby23I6X1xb8/U0cPLin\n0O5z+qTybOVku3btOH36NMePH8ff35+JEyc+yencIjU1lcWLF9O8cWMq+vlRo1Il3h82jAsXLrg7\ntALDz8+Ps2fP8pYkMQh5B8LHm4rWAYqnjeSy68KFC3Rq355X792jh9FIHeTRfBDwDvI6vN+QEzhA\nDeDujRscP348h+9IXv5tt2flA8ablBQ5wer1eubOnUvjxs2pWTOA5s1ffqR7oVKpRK3WIj+qdSYR\nX9/HNxzIX/v376dRo6YsXRqPyfQeev1QTKaRXLkSzOjRk+nWrSc2m831iXKoePHi7Nu3g+ee06PT\nzcXDYxdwDE/PSLTa2QQHa9i5c0uRTdquPFHiDgkJSf9UDg4OJjY2NleCyi83btygcYMGfDlkCJUP\nH6bX7duExsdzfP58XmjYkP/NmePuEAuEAwcOUNrDw+UeMnWSk1m1dGm2z//t118TZDRm2vtDgdx9\nWg2cfehrfkrlE+14UrNmTeAa8oMzx7y9b1C3bm0OHjxIlSo1+OijuRw+XI1Ll1qyd68fQ4d+Rc2a\nz/J32ui/d+8+eHoedXHO4wwc6GgjhCdjt9vZtGkTXbq8QcOGwbz0UggLFix4pNWp0Wjk1Vc7o9e/\nit3ekgetUhVADQyGPmzZcpzvv5+eJzHeV6FCBQ4f3s/WrWsYOjSAbt28GT48iL17t7Jz5xZKlnS2\n8UXRlmsrJxcsWOCwudD48ePT/79169a0bt06ty6bY3a7nVfbtqX0pUu0tlofuVErb7HQ0GJh3Icf\nUqVqVTp06ODwPEWBwWBAnYUpCTWgT3I12nyUyWRi2fLlvOdkdKdArmI5zIO2RSmSlGFa7j673c7W\nrVs5deoUnp6etGrVisDAR7fgbdq0KaVKadHrLyOP4TNjBE4TGjqTtm3bk5zcjkd7YVckObkeKSkH\nadGiDRcunGbMmFEsWdIUg6EWmW92cAmV6ixhYdn/gHPl5s2btG37Kpcv30Svb4Dcf8TA0aPT+PDD\nj9m4cR3BwcEsXboUq7Us8r1MZpQYDG2YPHkaI0d+gKenszWtWRcbG8vNmzcpXbp0eotehUJBcHAw\nwcGZ7QpftERGRhIZGZmlY13OcYeEhJCQkJDh69988w2dOnUCYMKECRw5coSVK1dmvEABnePevHkz\n77z+OgPT6pQzcwa4EhjIgWPH8jO0AufMmTO81KQJYQaD01u07UolDYcO5fuZMwH5YV1ycjJ2u50S\nJUpkOh8dGxtLYJ06vO+i+f0t5AXU7yMv41hdqhSx169n2CZs7dq1jBgyBPR6qpjN2BQKoj09qV6r\nFj///vsjpYSrV6+mb993MRp7k3F3+1S02hW89VZ7lEpP5s49jMXS1mF8Ot1qJk16l7CwMNavX0+v\nXv2wWAKxWBogNwtIxMvrGF5eZ1m/fjWtWrVy+n6zy2Kx0LDhC0RHF0vroPf4z/oCxYr9yZEjUQwZ\n8j7btmlx3npVwscnnF27ImjYsOETxbZ+/Xo+++wrzp07h5dXSczmRGrXrs0XX/yHbt0cPZwUnOVO\nlyPuzZs3O3194cKFREREsHXr1pxF5yY/zpnDc06SNsjztpsuXODSpUvUqOFoVPb0CwgI4Jnq1Tl/\n+jR1HRxjBU6oVPzw3nukpqYyf/58pk+Zwj9xcXh6eFCyRAnCRo5k+IgRj+zrqNVqMVmt2HE+b2cC\nvNKus1Wr5YPRozMk7RUrVjC4f386G41U40HqagccO3mSl5o1Y9f+/dStK7+Lbt26MXPmXYYP/wCF\nIgCjsRbgiVIZg0p1nJ49uzNjxv/h6+uHxfK2059RSkog338/h7CwMF577TVOnDjM9OmzWLRoMcnJ\niZQoUZqBA99ixIgludJ46ubNm6xbt47ExEQqVKiAzWbjn3/0WCxdyLy00R+D4RoTJkwiKSmJjB9U\nj1Pg6emT6S462TFlyneMHz8Jg6ENEIrJ5AnYOXnyPP36DeXjj8/w2WfjnugaRdETVZVs3LiRDz/8\nkB07duDnl/k/hII64m7euDE1Dx+mpovjFpUowcING2jevHm+xFVQ/fXXX/Tu1o3eRmOGNkVWYK1a\nTe127fjl998JbdOGm6dO0dRgSE+gcUCUWo25UiV27t//yL+XJg0aUPPkSYcfCgARyAvRU3Q6GoWE\nsGTFikdu4U0mExXLluWN5GQcdayIUigwNGvG9j17Hvn6zZs3CQ+fx/r1m7FarTRu3JD33x9G3bp1\n0ev1lCzph9X6iYufkB4fn/kkJ7vq6PJkUlJSGDx4GCtXrkSp9Mdi0eLllYjBcAm7vSPOe2Ano9GE\n06FDR1atSkSSmjo51oZaPYOzZ7O+UMhms3H27FlMJhPVqlXjypUrtGoVmra5b2bTWslotT+zadMf\nRf73KzN5VlUyYsQI9Ho9ISEhBAUFMWzYsCc5Xb7yLVmSFBfHSECy1epwLrUoCQ0NZUZ4OL9qNESo\n1VwErgJ7FQrCdTqqtm7Nr0uW8MGwYaScOEEvgyF98zOQZ3u7mkyUiYmhd/dHS/A+/M9/2KPT4Wh/\nm+vIHURsNWvy39mzWbpyZYZ51+XLl1NBkhwmbYDnJYmjR45kaDtbpkwZxo37D/v2befgwV3MmTMz\nfVSuVquRJBuuOwca0ypK8k5qaiqtWoWwatVpUlOHk5LSBbM5BL3+Dex2NZmv1HxYMRQKL958szta\n7XGcP5g9Q/369bOUtC0WC998M5Hy5Z+hWbMQXnnlDSpXrk6nTj0wGuuQedKW4zEaX2DSpGkuryE8\n6okeTrqrYU5u6PP223y9fz8NnNwK/gNofX2pVy/7TXeeRv369SMkJIT58+YRsXo1ptRUAurXZ83I\nkQQHB3Pnzh2WLFnCsNTUTEcECuAls5lZBw9y7tw5nn1WftDXq1cvIrds4bclS2iVkkKNtGMtwClg\nh0bDnJkzeeeddxzGtjsykqoubuuVQE2VigMHDlCrlrP9ax76HqWSli1fJjLyFDjcRgKUylN07563\n87Xz5s3j7NlETKaeZJwO8QaHH3332bFaTbRq1Yp69Wpy7NhfmM2hmZzrBhrNNiZNWuEyJrPZTLt2\nHYmKisVofI0Hy9xTSUg4AuxEnnSslun3S9Jz/PVX3lavPI2KbHfAHj16cE+t5rSD183Adq2WMePG\n5cpKsqdFuXLlGPfpp+w5fJjDp07x65IlNG3alHPnzhHati3lU1OdboqgBAIsFlaseJAUFAoFc+bN\nY/zMmRyqUYOZWi0Lihdnurc3KS+9xLpNm5wmbQDJbnf6vCL9WpDtqbv//OcjtNr94PAe7TYq1TFG\njhyerfNmhyRJTJkyPW0j58zeaW3k/oTORFOrlj9lypRh48a11K8PPj4Lke9nEoCreHv/hUaziHnz\nZvLyy862CZNNmDCRqKg4jMae8Mj9jjdyO7I3gOU43lXeG4sltUC0vi1Mimzi9vb2JmLzZraXKMFW\nlYr7/cdsyNUkv+p0vNyjB0OHDnVjlIXD4cOHaR4cjP74cbJSeauzWrl769YjX1MoFAwYMIDTFy8S\ndeIEa3bs4OLVq2zesYMWLVq4PGdwixbEuOgnYgMuWa00atQoC1E+EBISwsiRQ9Bqf0WuJr+fZCzA\nMTSaRcyaNS39DiIvJCcnc+1aLFDVwRGNkLvI3HTwuhlv7x189NEIAEqWLElU1G6WLv2BV16xULXq\nNurUOcyYMSFER5/J0t6eFouFGTNmYzS2wXEqqYE8UXbKwes38POrmKerNJ9GRXoHnIYNG3L4xAmm\nTprEgoULwW4n1WolsF49pnzyCT179hSjbRdsNhtdO3akXXIydlz37Aa45+1NpbQ63scpFIq0xTHZ\n8+abbzL6/fe5Sca2/PedAOoGBKTPX2fHhAlf0rhxEF988S3nzkXg5VUcs/kewcFN+eKLVXm+NkEe\nkTr7t+gLvAosRO4gE4D86y0hT/ptxGZLZeTIj6hYsSKhoaF4enrSoUOHHK9TOHr0KDabBle76shl\nh2fIbPM7tfoIYWGDc3T9okw0mUpjtVq5e/cuarX6kXI1wbn169fzQZ8+9E9OxgJMA94FhyNvEzBb\nreb8pUtUqFAhV2P5acECxo4YQXeDgYfPLCGnjc06Hdt27SIoyNXumc7Fx8eTmJhImTJl8m2rLEmS\nqFixKgkJoUBlJ0f+hbf36bRl+KWRa3GUQFPkUfk/aLWr2LhxHS1bOu5gmBU7duygS5fB3LvXx8WR\n0cAB4NEdjBSK45QsuZdz504WmS3HsuOJ6riLCqVSKf7x5MDaVavwT5b7JauQ08Mq5F/Rx5uD2oAN\nGg09evTI9aQNMGDgQDyVSkaPGIGfJFEhORmbQsElnQ5N6dL8tWzZEydtgIoVK+b7NlkKhYJRo0Yw\nfvwijMZKZD76tqLT/ZO29Vh/5I8sb+Sa7fvHV8VgaEdY2ChOnDj0RDFVrVqV1NTryAWhzlJJPErl\nHazWk8h3Bvfw8TmNTpfEtm3b8vT37vr169y7d48yZco8VUvoxYhbeCL9evUiedmy9HoLCdiA3MHv\nBUjfzeYSsFuhoGZgIJF79qTvIpMX7rctPXXyJJ5KJa1ataJVq1aFftpLr9fTqFEzrlzxxWxuzaPJ\n0ohGs55nnlFw9ao3JlMnJ2eyo9X+wP7923juOWerJ11r2vQlDhzwAwIdHGFDq53LuHEj2bQpkuvX\nb1KmjB9DhrxNjx49nqj3tzOrV69Om9Y6g5dXMczmJFq2bMVXX31G06bO6tcLDtGPW8gzX335JX9+\n8w2hqQ9K0ezAH8g3yB5p/5VB3jknXqejWmAgGzZtcrmbjJDRnTt36NmzH3v27MFmC8Bi0aJWJwHn\n6N27N3p9CsuXJyNPizhWrNhawsPH8Oabbz5RPLt27SI0tHMmVSUgL+JZT8uWFdi0acMTXSc7Pvnk\nU2bM+BGDoRVyPxZP5DqxE2i1e1iwYA69evXKt3hySkyVCHnCbDZT/7nnmGi38xwPfm0PIy+aGUHG\nLQrsKSlsOHKEfr16sXr9+vwM96lQqlQptmyJ4OLFi6xcuZI7dxKpVKkCvXr1oly5crz11iDA9R6N\nCoU1Q8uAnGjZsiWLF/9E375vAbUxGOoA3igU8Wi1x2natCGrVy974utk1Z9//smMGfPTVms+/K/P\nC2iMwVCFAQMGExwcnO9bx+UmMeIWss1sNvP1l1/yw8yZ8uYGJhPXzWb8gFbAOuBNwNEsthWYpdFw\n4Ngx/P0ddagTsuPEiRNcuXKFqKgopk9fhl7vrJzPhLf3LK5ciaZ8eVerLbPmzp07LFjwE8uWrcFk\nMlK3bh1GjgyjadOm+TpF1bz5y+zd64vjqRt567gRI5oxderkfIsrJ8RUiZBrzGYzHV55hYRDh2ht\nNKaX3tmAc8Aa5MdPrpofbFGpeOnDD5lQCDffKEgiIiIYPfoTYmOvoVRWQJKMJCVdQX660JXMbqqV\nyu20b1+adesydvMszAwGAyVKlMRqHYvzyYRrVKy4ibi4S/kVWo6IqRIh1/zfd98Rf+gQbxiNjyy5\n8ATqAXeAmCycp6TFQuzVq3kSY1Hx888/8957ozEaQ5GT9P2/kbvAn0A4MAh5mgDAhFK5j9Kl/yY8\n/Pf8DziPpaSkoFR6Y7W6SmtajEZXnYoKNrFcScgym83GzGnTaPlY0n5YWeTtB1xJ8fCgpIOOkoJr\nCQkJvPfeiLRe4vdrd+4rCfRGoSiGUvk9xYqtoXjxlajVs+jQwY8jRw7kSTmmu/n6+qJQSLjeOu4m\nFSs6q4Uv+MSIuwhJSEjgwoULqFQqGjZsiEajydb3X7hwAZvR6LQDXw3kOu5E5CmTzEjAaY2Grx3s\nmCS4Fh4+D0kKwPE6UQWSFIJOt4I5c8bg7e3Niy++mGtz2gWRSqWid+8+/PzzUWw2xxtV6HTH+OCD\n9/MxstwnRtxFwOnTp+n86qv4V6/OoM6d6du+PRXKlGHkiBFpTfWzxmQyoVIoiAVikVdBPk6FPP5b\np1DgaDOyfZ6eVKpevdDU0xZEf/wRgcnk6sFueWw2JYGBgbz++utPddK+75NPxqDRHEVeSZCRh8cB\nSpRIpk8fV6s9CzYx4n7KRUVF0b5tW4JTUhguSXib5HR7F9g9bx4vbtrEnqgolz3HExISmDZlCgnJ\nyWxAXod3B3leuzXwcJOA8sAZPz9+NxhompJCzbTjrwMHvb25UaoUuyMiCv2CGHeSV0e6/vX18PBK\nO7ZoqFWrFn/+uY6OHbtgtVbFYKgH+AC38fE5ia9vKjt3bi/0awhEVclTzGq1UrVSJV66cYPM+tZJ\nwEYvL+r16sWPv/zi8DyxsbE0a9yYqrdv09RqTU/SemAfct+3AchTIzZgnk7Hkg0biI6OZtq33/L3\n1auoPD3RarUMDQvj/ZEjKV26dO6+2SKmd+9/sWzZDez2F50cZcDbezYJCbH4+jqauHo6JSYm8vPP\nP/Pjj7+RlHSPChUqMGLEYLp3755nqzVzmygHLKLWrFnDR//6F/3SeolkRg/MVauJuXYt/ZfbaDSS\nmJhIiRIl0Gq1tGneHOWBA7Sw2TAjl/0lI+/qXge5694F4F/AerWacs2bE7F5c/rffXJyMlarFV9f\nX9G+M5fs37+fV17pSkrKuzgaeXt47KZbNz9WrHj6KkiKgjzbukwo2NatXk1tJ0kb5JvIql5e7Ny5\nk0OHDvFG166U9vUloGZNSvv60urFFzl86BDBNhvbkbv/nUJO+FeBWcgt+G8AM9RqqrRpw8q1a9On\nQRQKBcWLF6dUqVIiaeei4OBgWrUKRqNZS+abFJxDpzvChAnj8zkyIT+IOe58ZrfbOXToELdv36Zs\n2bI8//zzeTbXm6LXp1fwOuMlSWzbto2fw8NpZjLxgSShRu7usGbfPmoAG4FbwFAe3UHQBGxCfijZ\n7513mDVrlvx1k4k1a9Zw9epVdDodHTt2LNRLjAsahULBypVL6dv3bf78czYWSwOs1rKAiWLFzqNW\npxAR8Rd16tTJ99ju3LmD0WjEz8+v0ExLFDZiCJRPJEli9qxZVKtYke6vvMKY3r3p1Lo1tZ55hp9+\n+ilPrvls/frccPGLIwGxVis//u9/9DYaCU5L2iAv26iA3DTqEtCHjNu+qoFOyI1DL0ZHI0kSUydP\npmKZMnz57rusGzeOX8aMIbBuXTq2a8fNm452aBGyS61Ws3LlEo4c2cfw4Y1p395Mz54lWLjwU6U/\nrQAAFYpJREFUW+LirtC4ceMsnefatWt8/vl4goKaUa9eI/r06U9UVFS2YpEkid9++43n69WjSoUK\nNPD3p0zJkgweOJBLlwr2CsXCSMxx5wNJkggbMoSI334jxGDgfjfl+3uTbNLp6B8WxjeTJuXqdWNj\nYwmoXZswkyk9GT/uArClRAme1et52ZaxgO808oi6GXKvbUf+Adb7+jJg0CAW//ADXQ0GHn78aAF2\nqVTEV6xI1NGjedobOSoqiulTp7Jr505sNhsNGzbk/Y8+IiQkREzXPGb+/B8ZMWIUUC+tvFCJh0cs\nGs0x2rZtwbJli12OmiVJ4p3+/dm6ejXNU1KojTwiTAKOeHpyQqtl49atNGnSJO/f0FNEPJx0sw0b\nNvBur168nZKSYXMBkPcoWaDV8semTTRv3jxXrz186FA2//or3Q2GDNe+DizRaJA8Pemn15PZOkYr\nMAUYDDirA5GAySoVKk9PhphMOCq22uDtzUvDhjH1//4v2+/FFUmSGDliBIt/+onnTSb87XY8gCvA\nUR8fGrz4IivXrhW372n++OMP+vQZhNHYh4x/u1Y0mj/o3DmQJUsWOT3PnDlzmPzRR/QxGDKdmjsH\nbCtZkitxcdle9FWUiYeTbjbt228JdpC0QW4+2dho5PspU3L92tNnz6ZVr178oNGwXakkGnm727Va\nLYs0GmbNn4/ZYsHRNrtK5PlrV7PwCsBus1HfYnGYtAGapqayYP78tK21cteUSZNY89NPvGMw8KLd\njh9QCngeeFuv52xkJHVr1KC4Vovay4u6NWowa9Ys9Hp9rsdS0EmSxIcffoLR2J7MP5KVGI1dWLNm\nHRcvXnR6nqnffEMbB0kb4FmgjMXCsmX51971aScSdx6TJInIvXsJcHFcPUli85YtuX59T09Pwhcs\n4MDRozQYPJj4Zs2489JL9PniC67GxdGnTx/K+flx28k5qgCOf3VlcYCHQkGdTKZbHlYaUEtSrs17\npqamsmTJEv49dizj//tfAg2GTKeFdgC3zWbqxMczxGjkQ4uF4MuXCf/3vwmqX5/4+PhciaewOHLk\nCNev3wVqOTlKhc3WgPDwHx0ecebMGfR375L51s8P1NXrWZxHz3KKIlFVksdsNhuSJKFycZwXYLFa\n8yyOOnXqMGP27Exfe2foUNZMmEAlU2aL2KEJco/tIMj0fUjAAbWakj4+KG7dchlLblXR/Prrr4wc\nPpyyaftLNkHeknY30AG5b4oHcAz5LmMIj7bWrw5UNxjYFRdHq2bNCF+4kMDAQEqVKpUr8RVkV65c\nwdOzPK7upSyWMpw/7/hjOykpiWJKpcs7Mh0Qc+9etuMUMidG3HlMqVRSsWxZXI3nYoEaz7gat+SN\nwUOGcEWt5rSD1+2AydOTlWo1hsdeswBbvbywVqlC6KuvctnT0+m17gIpdnu2SgMvXrzImNGjeS0k\nhB6dO/Pzzz8zLzyc0UOH0jMpiTeTk2kF1EYe0d8DlgATkfuD7wA6knE3nvtaWK3c/ucf+nfqRNVK\nlejfu/dTPwKXl3xn/kH9KBPFizuaSINKlSpxy2x22JfmvltAlapVsxGh4IwYceeDYe+/z4qvvnI4\nopWAIzodw0ePzt/A0pQpU4ZN27cT+vLLXExNpYHBgC9yVcApjYa/lUo2rFnDyqVLmb1wIc96eqI2\nGIjx8OCWJOGr0/F29+60a9+ebitW8ILRiKNHUAdUKt4eMCBLD6ksFgtDBw1i5bJlBNpslLNYsACT\ntm0jOiWFwchtZEHeLi0SaAl0Qd7bPAU4glwZ4yxFKYBg4HpKCr2B/cuX02TbNvYfOkSVKlVcxlkY\ntWzZEqv1GvLHnOM+NcWKnadnz/ccvv7MM89Qv149zh46RH0Hx0jASR8f5oeFPUnIwkNEVUk+uHv3\nLg3r1aPejRu8YLM9clspAbuUSuKqVOHwyZNubX5z7949Fi5cyII5c7h56xa+JUrQf9AgBr37Ln5p\nvbNv3brFe0OHsn7NGuoCtaxWFMDVtBF7YGAg8SdP0s1goPhD57YB+5RKLpQpw6HjxylTxlE70gcG\n9u/PvpUref2xB1/HkFdv9kv7cyywFLlfSmaTHPHAIuTKGEcdO84hJ/n7PeN2e3pib9aMrbt2uYyz\nsAoLe58FC3ZhMnUh8ymT05Qvv4/Y2Ct4OrmT2rJlCz07d6av0ZihMkkCtqtUpDz7LFHHjolyzGzI\n03LA7777jjFjxnDr1q1M5wZF4pZdvXqVDq+8gj4hgXp6PcWBRIWCUzod5apVY/2mTYWiuf2P8+Yx\nbuRIeqeNyh92D1ii1dKwRQt279pFDQ8PSqakYFapOKtU8lxgIItXrKBSpUour3P+/HmaBgUxzGjM\nUK3wJ3ICbpb255VAZeRRsyN/Ie/S84qD16OQE3zXtD9bgZlqNYdOnqRWLWcP8Aovg8FAy5ZtOXtW\nj9HYArmvI4ABD4/D+PgcIzJyM0FBQS7PtfCnn/ggLIwGNht1zWbUwDXguI8PmsqV2bxjB2XLlnV1\nGuEhebZ1WUxMDJs3b6aqmLtyqWrVqpw8f54tW7bw64IF3Lx+nfKVKvHJu+/y0ksvFYoWp2azmY/H\njKFHJkkb5Bvu7gYDi/buJfryZdavX5++5H1ep04EBLiqrXngfz/8QAOrNdMSs/uLl0Cefz+LPIft\nTEPkee/MEreEPNp++DUlUEehYPPmzU9t4tZqtezZs52JEycxc+YPWCweaW1g79ClSxe+/np/lt/7\n2wMG0LpNG36YNYs1K1ZgMpmoVr06X48aRdeuXfHyykrzBSGrnihxjx49msmTJ9OlS5fciuep5uHh\nQbt27WjXrp27Q8mRDRs2UMpux1k7fj+gIrB161beeeedHF/rzPHjVLRk1jxJHl0fBl5EHhkrwOHK\n0PuK4Xieez9y8q752NdVNhsmB88lnhZqtZovvvgvn302jgsXLmA2m6levbrL/uyZqVatGpOnTmXy\n1Kl5EKnwsBwn7jVr1lC5cmUaNGjg8tjx48en/3/r1q1p3bp1Ti8ruFF0dDRlja53lCyj1xMdHf1E\n1/JWq3HU/r8uctOrGOQkfn95dXEHxwNynbpCwRFJoh5yWWM8cvlgHNCfjLO88SoV/v6udpl5OiiV\nymzdEQm5LzIyksjIyCwd6zRxh4SEkJCQkOHrEyZMYOLEiWzatCn9a87msR9O3ELh5e3tjdXTE1zU\nm1uVyideVt6hWzdm795Ng5SMu3F7Ije2WgK8DjRAHoG3cXK+ExoNb/bqRfzVq0zduROLzYYvco16\nB8hQBRMPxBkMWRqYCEJueHxQ+8UXXzg8NkcPJ0+dOkXbtm3RauXK2NjYWCpVqkRUVFSGBxDi4eTT\n48yZM7Ro3JjhRiOOagzswA9aLX/t2sXzzz+f42vp9Xoqly/PGykpZLYftwQsUqm44+WFlySRaDDQ\nB8jsacsZYLuvL2eio/Hz80OSJIYNHcrS8HAG8ui2ayDXmv8ClPbwoOOwYXw/c2aO34cg5FSeN5mq\nXr06hw8fFlUlRUCLF17A5/Bhmtntmb5+UKEgoX59Dp048cTX2rBhA33feIO2RiP1IP3D4h6w09sb\na82a7Nq/n0OHDrFixQp+nj+f+kCg2Uwx5D0xT2g0/OPtzV/btj1SHdGjc2dOrlvHP0B95PltCblb\n4jmgLfJi8IU6Hddv3xaNqYR8l+eJu0aNGhw6dEgk7iLg8uXLvNikCc8mJvKCzZa+GtEIHPTw4GTx\n4uyJiqJ27dq5cr3du3fz8ahRnD59mkpeXpiB6xYLb731Ft9MnoyPz4NVffHx8fxvzhx+W7iQxKQk\nypQuzaBhwxgwcGCGf5t1qlXj5atX0QJHkUvXFMhz5g0hvVHWbJ2OAydPUr169Vx5P4KQVaKtq5Cr\nYmJiGDNyJOs3bKCyWo0CiE1NpX1oKJOnTcuTJBcdHc3Fixfx9vYmODj4iRcqBdSsSYtLl3BWUS4B\nMzQajp8//9SuoBQKLpG4hTxx69YtTqRNidSvX79QLbAY8d57nJw/nzZOHrTGAn+VK8eV+Hix4k/I\ndyJxC8Jjzp8/T3BQEIOMxgwPJ0EebS/XaHh7/HjGjB2b3+EJgthIQRAeV6dOHT76+GMWa7XEPfZa\nMrBWrca3Xj1GvP++O8ITBKfEiFso0n6cN4//jhuH0mSijN2O0cODf6xW+vbty3fTp6eXvGbH5cuX\n+WHmTDasWUNqair+deowfPRo2rdv77RZkyA8TEyVCIITNpuNnTt3EhMTQ7FixWjbti3Fiztbh+lY\n+Ny5jBk9mkCbjWfNZlTIKzOP+fhQOSCAiM2bc3xuoWgRiVsQ8sG6desY0KsXfY3GDO1l7cBGb2+K\nBQezZccOd4QnFDIicQtCPmhYty4B585Rx8HrdmCuTsf67dtp0qRJfoYmFELi4aQg5LHTp08T988/\nOFt25AE0MBqZN2dOfoUlPKVE4haEXBAbG0tZlcrlL5Sf3c7VXNrhXii6ROIWhFxQrFgx9A76tzzM\nABTPQa9rQXiYSNyCkAuaNGmCSankuovjzhYrxpv9++dLTMLTSyRuQcgFKpWK90eNYptWi6NF9KcA\ng0ZD586d8zM04SkkqkoEIZdYrVa6d+7M6R07aG4wUB2542AScNjTk1M6HVt37iQwMNDNkQqFgSgH\nFIR8YrPZmD9/PtMmTeLatWt4e3pistvp06cPH3/6KdWqVXN3iEIhIRK3IOQzSZJISEggNTWV8uXL\no1a72s5YEB4lErcgCEIhIxbgCIIgPEVE4hYEQShkROIWBEEoZETiFgRBKGSU7g5AEEDev3LRokVc\nio7Gp3hxOnXuTNOmTVEoFO4OTRAKHFFVIriVzWbj3x99xP/mzuVZhYLSRiMmhYJzWi3lqlRh5bp1\n1KpVy91hCkK+E+WAQoE15J132LZkCd0MBnQPfV0CDnt4cNDXl4PHjlGlShV3hSgIbiHKAYUC6eTJ\nkyz//XfeeCxpg7xUvLHdjv+9e3z5+efuCE8QCiyRuAW3mT19OkEWC95OjnnBZmPp0qUkJyfnW1yC\nUNCJxC24zaEDB6hqddRLT1YMKKlScUlsPiAI6UTiFtzG09MT11sPgE2S8PAQ/1QF4T7x2yC4TZuQ\nEC56eTk95jZgBPz9/fMlJkEoDJ4occ+cOZO6detSv359/v3vf+dWTEIR8d7w4Zzw8CDJwesSsNfb\nm3cGD8bb29lMuCAULTlegLN9+3bWrl3LiRMnUKlU3Lx5MzfjEoqAqlWr8tn48fzfl1/S2WCg4kOv\nmYCdXl4YKldm3GefuStEQSiQclzH3bNnT4YOHcrLL7/s/AKijltwYcH8+Yz7+GO0ZjNlrVZSPT2J\ntljo0KEDc3/8kZIlS7o7REHId3myACcoKIguXbqwceNG1Go1U6dOpXHjxtm6uCDcZ7Va2bJlC1eu\nXEGr1dKuXTvKly/v7rAEwW2c5U6nUyUhISEkJCRk+PqECROwWq3cvXuX/fv3c/DgQXr27OmwZGv8\n+PHp/9+6dWtat26d9eiFIkGpVNK+fXt3hyEIbhMZGUlkZGSWjs3xiPvVV1/l448/plWrVgDUqlWL\nAwcOULp06UcvIEbcgiAI2ZYnS967du3Ktm3bALhw4QJmszlD0hYEQRByX46rSgYOHMjAgQN57rnn\n8PLy4pdffsnNuARBEAQHRHdAQRCEAkh0BxQEQXiKiMQtCIJQyIjELQiCUMiIxC0IglDIiMQtCIJQ\nyIjELQiCUMiIxC0IglDIiMQtCIJQyIjELQiCUMiIxC0IglDIiMQtCIJQyIjELQiCUMiIxC0IglDI\niMQtCIJQyIjELQiCUMiIxC0IglDIiMQtCIJQyIjELQiCUMiIxC0IglDIiMQtCIJQyIjELQiCUMiI\nxC0IglDIiMQtCIJQyIjELQiCUMiIxC0IglDIiMQtCIJQyIjELQiCUMiIxC0IglDI5DhxR0VF8cIL\nLxAUFESTJk04ePBgbsaV6yIjI90dQoEhfhYPiJ/FA+Jn8UBB/1nkOHGPHTuWr776iqNHj/Lll18y\nduzY3Iwr1xX0v4j8JH4WD4ifxQPiZ/FAQf9Z5DhxV6hQgXv37gGQmJhIpUqVci0oQRAEwTFlTr/x\n22+/pUWLFnz00UfY7Xb27duXm3EJgiAIDigkSZIcvRgSEkJCQkKGr0+YMIEZM2YQFhZGt27dWL58\nOeHh4WzevDnjBRSK3I1YEAShiHCUnp0mbmeKFy9OUlJS+sl9fX3Tp04EQRCEvJPjOe5atWqxY8cO\nALZt24a/v3+uBSUIgiA4luM57vDwcMLCwkhNTUWj0RAeHp6bcQmCIAgO5HjE3bhxYw4cOMCxY8fY\nt28fQUFBuRlXnvnuu+/w8PDgzp077g7FbcaMGUPdunUJDAzk9ddfL5JTXBs3buTZZ5+ldu3aTJo0\nyd3huE1MTAxt2rShXr161K9fnxkzZrg7JLez2WwEBQXRqVMnd4fiUJFaORkTE8PmzZupWrWqu0Nx\nq3bt2nH69GmOHz+Ov78/EydOdHdI+cpmszF8+HA2btzImTNn+P333zl79qy7w3ILlUrFtGnTOH36\nNPv372f27NlF9mdx3/Tp0wkICCjQhRVFKnGPHj2ayZMnuzsMtwsJCcHDQ/6rDw4OJjY21s0R5a+o\nqChq1apFtWrVUKlUvPnmm6xZs8bdYblF+fLladiwIQA+Pj7UrVuX+Ph4N0flPrGxsURERDBo0CCH\nFR0FQZFJ3GvWrKFy5co0aNDA3aEUKAsWLKBDhw7uDiNfxcXFUaVKlfQ/V65cmbi4ODdGVDBcuXKF\no0ePEhwc7O5Q3GbUqFFMmTIlfWBTUOX44WRB5KzufOLEiWzatCn9awX50zQ3OPpZfPPNN+lzdxMm\nTMDLy4s+ffrkd3huVZBvgd1Fr9fTo0cPpk+fjo+Pj7vDcYv169dTtmxZgoKCCvyS96cqcWe2AAjg\n1KlTXL58mcDAQEC+HWrUqBFRUVGULVs2P0PMN45+FvctXLiQiIgItm7dmk8RFRyVKlUiJiYm/c8x\nMTFUrlzZjRG5l8VioXv37vTr14+uXbu6Oxy32bt3L2vXriUiIgKTyURSUhL9+/fnl19+cXdoGUlF\nULVq1aTbt2+7Owy3+fPPP6WAgADp5s2b7g7FLSwWi1SjRg3p8uXLUmpqqhQYGCidOXPG3WG5hd1u\nl/71r39JI0eOdHcoBUpkZKT02muvuTsMhwr2RE4eKeq3yiNGjECv1xMSEkJQUBDDhg1zd0j5SqlU\nMmvWLEJDQwkICKBXr17UrVvX3WG5xZ49e1i0aBHbt28nKCiIoKAgNm7c6O6wCoSCnCdyvORdEARB\ncI8iOeIWBEEozETiFgRBKGRE4hYEQShkROIWBEEoZETiFgRBKGRE4hYEQShk/h/1G5ho+1YlFQAA\nAABJRU5ErkJggg==\n"
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Just to help us visualize lets use two gaussian kernels ([CGaussianKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGaussianKernel.html)) with considerably different widths. After appending them to the Combined kernel, to generate the optimal weights (i.e $\\beta$s in the above equation), training of [MKL](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLClassification.html) is required. This generates the wieghts as seen in this example."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"width0=0.5\n",
"kernel0=GaussianKernel(feats_train, feats_train, width0)\n",
"\n",
"width1=25\n",
"kernel1=GaussianKernel(feats_train, feats_train, width1)\n",
"\n",
"kernel.append_kernel(kernel0) #combine kernels\n",
"kernel.append_kernel(kernel1)\n",
"kernel.init(feats_train, feats_train)\n",
"\n",
"mkl = MKLClassification()\n",
"mkl.set_mkl_norm(1)\n",
"mkl.set_C(1, 1)\n",
"mkl.set_kernel(kernel)\n",
"mkl.set_labels(labels)\n",
"\n",
"mkl.train() #train to get weights\n",
"\n",
"w=kernel.get_subkernel_weights()\n",
"print w"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0.95364778 0.04635222]\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The weights generated can be intuitively understood too. We will see that on plotting individual subkernels outputs and and outputs of the MKL classification. To apply on test features, we can reinitialize the kernel with `kernel.init` now passing test features. After that its just a matter of doing `mkl.apply` to generate outputs. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"size=100\n",
"x1=linspace(-5, 5, size)\n",
"x2=linspace(-5, 5, size)\n",
"x, y=meshgrid(x1, x2)\n",
"grid=RealFeatures(array((ravel(x), ravel(y)))) # generate X-Y grid test data\n",
"\n",
"kernel0t=GaussianKernel(feats_train, grid, width0)\n",
"kernel1t=GaussianKernel(feats_train, grid, width1)\n",
"\n",
"kernelt=CombinedKernel()\n",
"kernelt.append_kernel(kernel0t)\n",
"kernelt.append_kernel(kernel1t)\n",
"kernelt.init(feats_train, grid) #initailize with test grid\n",
"\n",
"mkl.set_kernel(kernelt)\n",
"grid_out=mkl.apply() #prediction\n",
"\n",
"z=grid_out.get_values().reshape((size, size))\n",
"\n",
"figure(figsize=(10,5))\n",
"title(\"Classification using MKL\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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uPNAzziP80N8JTzpVabl2p4pvbVhRQ8d9dss0djI9wCq/yOQQd6j1E9BESSaQ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\ncP8A3xjkcI93Ti4AAAAASUVORK5CYII=\n"
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Training with a single kernel appended to a combined kernel makes no sense and is just like normal single kernel based classification. To justify the weights, lets train and compare two subkernels with the MKL classification output."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"z=grid_out.get_labels().reshape((size, size))\n",
"\n",
"figure(figsize=(20,5)) # MKL\n",
"subplot(131, title=\"Multiple Kernels combined\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n",
"comb_ker0=CombinedKernel()\n",
"comb_ker0.append_kernel(kernel0)\n",
"comb_ker0.init(feats_train, feats_train)\n",
"mkl.set_kernel(comb_ker0)\n",
"mkl.train()\n",
"comb_ker0t=CombinedKernel()\n",
"comb_ker0t.append_kernel(kernel0)\n",
"comb_ker0t.init(feats_train, grid)\n",
"mkl.set_kernel(comb_ker0t)\n",
"out0=mkl.apply()\n",
"\n",
"z=out0.get_labels().reshape((size, size)) #subkernel 1\n",
"subplot(132, title=\"Kernel 1\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n",
"comb_ker1=CombinedKernel()\n",
"comb_ker1.append_kernel(kernel1)\n",
"comb_ker1.init(feats_train, feats_train)\n",
"mkl.set_kernel(comb_ker1)\n",
"mkl.train()\n",
"comb_ker1t=CombinedKernel()\n",
"comb_ker1t.append_kernel(kernel1)\n",
"comb_ker1t.init(feats_train, grid)\n",
"mkl.set_kernel(comb_ker1t)\n",
"out1=mkl.apply()\n",
"\n",
"z=out1.get_labels().reshape((size, size)) #subkernel 2\n",
"subplot(133, title=\"kernel 2\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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+tAYuBPoBsMhqLCLR4Wj9SUSEmBmjKiISqzzAKcB3gXtKrMVihfKESAJpCUCp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\n"
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see the multiple kernel output seems just about right. Kernel 1 gives a sort of overfiting output while the kernel 2 seems not so accurate. The kernel weights are hence so adjusted to get a refined output. We can have a look at the errors by these subkernels to have more food for thought. Most of the times, the MKL error is lesser as it incorporates aspects of both kernels. One is strict while other is lenient, MKL finds a balance between those."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"kernelt.init(feats_train, RealFeatures(testdata))\n",
"mkl.set_kernel(kernelt)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :MKL\" % (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n",
"\n",
"\n",
"comb_ker0t.init(feats_train,RealFeatures(testdata)) \n",
"mkl.set_kernel(comb_ker0t)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :Subkernel1\"% (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n",
"\n",
"comb_ker1t.init(feats_train, RealFeatures(testdata))\n",
"mkl.set_kernel(comb_ker1t)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :subkernel2\" % (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Test error is 12.82% :MKL\n",
"Test error is 27.76% :Subkernel1"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Test error is 15.97% :subkernel2"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"MKL for knowledge discovery:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MKL can recover information about the problem at hand.Lets us see this with a binary classification problem. The task is to separate two concentric classes shaped like circles. By varying the distance between the boundary of the circles we can control the separability of the problem. Starting with an almost non-separable scenario , the data quickly becomes separable as the distance between the circles increases."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def circle(x, radius, neg):\n",
" y=sqrt(square(radius)-square(x))\n",
" if neg:\n",
" return[x, -y]\n",
" else:\n",
" return [x,y]\n",
" \n",
"def get_circle(radius):\n",
" neg=False\n",
" range0=linspace(-radius,radius,100)\n",
" pos_a=array([circle(i, radius, neg) for i in range0]).T\n",
" neg=True\n",
" neg_a=array([circle(i, radius, neg) for i in range0]).T\n",
" c=concatenate((neg_a,pos_a), axis=1)\n",
" return c\n",
"\n",
"def get_data(r1, r2):\n",
" c1=get_circle(r1)\n",
" c2=get_circle(r2)\n",
" c=concatenate((c1, c2), axis=1)\n",
" feats_tr=RealFeatures(c)\n",
" return c, feats_tr\n",
"\n",
"l=concatenate((-ones(200),ones(200)))\n",
"lab=BinaryLabels(l)\n",
"\n",
"c, feats_tr=get_data(2,4) #get 2 circles with radius 2 and 4\n",
"c1, feats_tr1=get_data(2,3)\n",
"_=gray()\n",
"figure(figsize=(10,5))\n",
"subplot(121)\n",
"p=scatter(c[0,:], c[1,:], c=lab)\n",
"subplot(122)\n",
"q=scatter(c1[0,:], c1[1,:], c=lab)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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UrFkz9ke7npw8eZLU1NRIV1eX1q9fTwMHDqSysjLy8vIiT09P6tu3L/H5fDp3\n7hzXUcUaa6A4IBKJaOjQoWRvb0/NmjUjon8O9xgbG9OAAQPI0tKSpkyZwnFKprbNnj2bjIyMyMLC\nour7Zs2aUVhYGLm7u1Pfvn0b3F420lT30jSW2pKRkUGenp6kpKREp06doqZNm5JAIKDJkyeTubk5\ndejQgbS1tWnjxo3scF09q6iooFGjRhGfz6eOHTtWbbopFApp8+bNpKurS0pKSjRixAgqLS3lOq5Y\nYg1UPSspKaFJkyaRvr4+ZWVlEZ/Pr9ofaNOmTaSqqkpHjx7lNiRTZ06fPl21uFxVVZVycnJIJBLR\n1q1bSUdHh8aMGdOgNrmTprqXprHUhlu3bpGFhQWNGTOGrKysSCAQkI+PD/Xt25e2b99Obm5u5Orq\nyq6ewLHY2FgyMjIid3d3mj59Op08eZLMzMzo9u3b9PjxY2rRogX5+vpSZmYm11HFTnVrnl1MuBYI\nBAJ06NABQqEQJSUlSE5ORlxcHH788UcIBALIyMhg79696NixI9dRmTp04cIF9OnTB0KhEO/evcOM\nGTMQGxuLoKAgXLx4Ea9evcKFCxcaxDYV0lT30jSW77V3716EhISgtLQUOTk5sLGxwYIFC9CnTx8E\nBwfj1KlTmDBhAmbNmgV5eXmu4zZ4b9++xYQJE3D+/Hn4+/vD1tYWgYGBaN26NVq0aAE5OTkkJiYi\nLi4O9vb2XMcVG+xiwvWkuLiYfv75Z7KxsaH379+TkZER/fHHH/T69WtasGABWVpaNqiZh4autLSU\nbG1tadasWaSkpES5ublE9M/p3cbGxjR8+HAqLCzkOGXdk6a6l6ax/FsVFRUUFhZGysrKdO3aNVJR\nUaH09HS6ffs22draEo/HIyMjI7p8+TLXUZnP+OOPP0hJSYmGDBlCkydPpkmTJhER0datW6lp06Zk\nbGxMu3bt4jil+KhuzbMZqO9QXl4OHx8fyMj8sx/ppUuXcO/ePYwaNQq3b9+Gs7Mzdu3aBQsLC46T\nMvUpIyMDgYGBuHLlCoqLi7Fs2TJERkZi5MiRSEpKQmpqKi5dugRlZWWuo9YZaap7aRrLv0FECA4O\nxtOnT5GYmIiysjKsXbsW69atQ/fu3XHlyhUYGxsjOjq66r2QET95eXlo3bo1AGDmzJlQVFTEnDlz\nsHnzZgiFQowYMQLz58/H8OHDOU7KPTYDVccqKytp2rRp5OzsTO/evSNTU1NasWIFpaSk0JgxY8jL\ny6vBLRx4KZZEAAAgAElEQVRmPtapUycaPnw4KSkpVa0zuHXrFllZWVFISIhU78kiTXUvTWOpqbdv\n31Lr1q2rZpy8vb1p5syZVFZWRuvXr6dGjRrRsmXLGuSZppLo/fv3NHToULKzs6OOHTvSwYMHKT8/\nn3x9fUlDQ4OUlJRo1KhRDf7fs7o1zz4u/AsCgQDdunXDsWPHwOfzoampibi4OMTFxcHLywv5+fk4\nfPgweDwe11EZDu3fvx8ikQiVlZXg8/k4ePAgOnfuDB8fHyQnJ8PPzw8VFRVcx2SYzyooKED//v3h\n5OQEbW1tvHv3Dnv27MH169fRqFEjzJkzB5GRkZg2bRpkZWW5jstUg4aGBnbu3Il+/frhxo0bePfu\nHaZPnw5zc3Pk5ubi4cOHuHTpEiZNmgSBQMB1XLHHDuH9C1u3bsXmzZtx5MgRODs7Y968eWjTpg1W\nrVqFV69e4fTp01xHZMRIr169oKqqinPnzuHo0aNwc3NDaWkpvLy8EBgYiAkTJnAdsdZJU91L01iq\nKy0tDd7e3vjw4QMSExORkJCAFStWYNKkSXj06BFiYmJw8+ZN6OjocB2V+ZcuX76Mnj17onHjxti7\ndy8UFRXRuXNn2NvbIzMzEyYmJjh+/DgUFRW5jlrvqlvzbAaqhn755ReEhISgSZMmMDQ0xNmzZ7F3\n7154eHigsrIS+/bt4zoiI2Z27doFRUVF5Obmonnz5nj27BmaN2+O3NxchIeHY9KkSQ3uDzQjvnJy\ncjBw4EAEBQXByckJsbGxGDNmDFasWIGIiAg8efIESUlJrHmScG3atMHp06ehpKSEs2fPYvz48Viw\nYAFiY2Oxd+9evHr1CqNHj0Z5eTnXUcUWm4GqgdOnTyM0NBQ7duxAQEAADh8+DCcnJ/z666+4ceMG\nzp8/z3VERoz5+/vDysoKycnJ6Nu3LyZNmoSCggK0bdsW8+fPR8+ePbmOWGukqe6laSzf8vLlS3h6\nekJWVhZ//fUXdHR00LFjR5ibmyM7Oxvm5uYNdlZCWr18+RI+Pj7Iz89HcnIy7t69i1GjRqFHjx54\n8OABZGVlce7cuQb1b17dmmcNVDVdvXoVQUFB6NChA37//XfExMRgzJgxyM7Oho+PDyIjI6Gvr891\nTEaM5ebmIjAwEPHx8cjIyIC2tjaWL1+OP/74A4qKiti0aRO8vLy4jlkrpKXuAekay9fk5+ejV69e\n8PLyQkFBAd68eYNdu3bh9evX8Pf3h6+vL1atWgU5OTmuozK1rLCwED169EDz5s0RExODXbt2oW3b\ntrh+/TqGDh2KDh06YO3atQ1mrRtroGrRw4cP4eXlhSFDhuDs2bO4du0aGjdujL/++gvLly/H7du3\nuY7ISBB3d3eMGDECr169wqlTp7B8+XJkZGQgNDQUsbGxaNGiBdcRv5s01P1/SdNYviQnJwetW7cG\nEWHZsmXo3LkzBg4ciPPnz6OyshLDhg3Dhg0bGswf0Ibo7du36N27N5KSkpCTk4OjR48iLCwM3bp1\nw61bt2BgYIAjR440iN8B1kDVEpFIhJCQECgoKGDlypUICQnBgQMHoKmpicLCQpw4cQItW7bkOiYj\nQe7fv48uXbqgqKgIFy9ehIODA4qLizFmzBjIy8tjy5YtEr+fjqTX/f+SprF8jkAgQGBgIDQ0NNCs\nWTPs3r0bR44cgYyMDLp3746AgADMnj2b65hMPSAidO3aFWZmZti9ezeSkpJga2uLR48ewd/fHxMn\nTsTEiRO5jlnn2CLyWiAQCNC3b1/s2bMH7969A4/Hw7p167BhwwYUFBTg4cOHrHliasze3h7379+H\ntrY2CgsLkZaWhpYtWyIlJQWxsbEICAhg2xsw9aK8vBxdunTBhQsX0KJFC4wfPx4+Pj6wtraGqakp\nPD09ERYWxnVMpp7weDz89ddfePnyJUpKSmBjY4OoqCh4eXnBysoKS5cuxaxZs7iOKT6+b7upb6uH\np6gzGzduJF9fX3r58iUZGRnRlClTaNOmTWRpaUkbNmzgOh4j4bZt20ZmZmbk7OxM8+fPJ6J/Nmj1\n9/enVatWcZzu+0hy3f9f0jSW/2v16tXk5+dHkZGRZGtrS8+fP6e8vDzy8/OjGTNmcB2P4VDr1q1p\n+vTppKamRvfu3SMiopycHNLX16fk5GSO09Wt6tY8m4H6goyMDERGRsLPzw9mZma4evUq3r17h/Dw\ncCxfvhxjxozhOiIj4YYPH45169YhKysLPXr0AADcvXsXlZWViIqKwosXLzhOKP0yMjLg4+MDe3t7\nODg4YO3atVxHqjcRERGYOXMm2rVrh8GDByMwMBCOjo7Q19eHqakp5s+fz3XEekNEKCsrQ3Z2Np4+\nfYq7d+8iJSUF9+7dw4sXL5CTk9PgNpY8cOAAEhMTwePxYG9vj8TERPzwww8oKipChw4dEB8fz3VE\nzrE1UJ+RlpYGDw8PODg4IDc3FxcuXICqqirCw8Nx7949HDlyhOuIjBQZNGgQDAwMEBAQgH79+mHM\nmDEoKipCVFQUEhMTYW1tzXXEGpOUus/OzkZ2djZatmyJoqIiODs748iRI7C1ta16jKSMpSYSEhIQ\nFBSEGTNmYMOGDTh//jy0tLQwZcoUZGZm4sCBA1xHrHXl5eW4desWLl++jAsXLuDhw4d48+YNSktL\nIRQKq/1z5OTkoKqqCiMjIzRv3hzt27dH69atYWNjI3ULrAUCASwtLbFgwQJMmzYNO3fuROfOnREf\nH48ff/wRjx49gpaWFtcxax27Ft53mDZtGk2bNo2EQiEFBweTuro66enpUYsWLejVq1dcx2OkzJs3\nb8jFxYX4fD799ddfVbfPmTOHxo8fz2Gyf08S656IqEePHhQbG/vRbZI6li/JzMwkV1dXCgkJIZFI\nRLNmzSJlZWVSUVGhNm3aUE5ODtcRa0VOTg5t2rSJOnToQKqqqgSgTr94PB5pa2tT37596ciRI1Rc\nXMz1S1Arbt68SXp6emRubk5ERO/evaOQkBAyMjKi4cOHU2lpKccJa191a541UP9HUlISOTg40OrV\nq6tui4mJITs7O6qsrOQwGSPNBAIBtWrViuLj44mIKC4ujtq0aUO2trZ06dIljtPVnKTVPRHRixcv\nyNTUlD58+PDR7ZI4li959+4dmZubU/fu3alVq1ZUUVFBREQHDhwgKysrib4Aukgkotu3b9Po0aNJ\nXV29zhum6nwZGxtTeHg4ZWdnc/3yfJesrCzS0NCgJ0+ekJOTE40ePZqOHDlCvXr1om7dukn0783n\nVLfm2Y5o/+PGjRvo2rUr+vXrhyVLlqBFixbQ0tLCwoULMWjQILaBHFNnZGVl8eOPP2Lq1KkYOXIk\n5s6di99++w1CoRC9evXCoUOH4OnpyXVMqVVUVIS+ffsiIiICqqqqn9z/66+/Vv23t7c3vL296y9c\nLTp48CDs7Oxw6NAh9OvXD46OjtDV1cXdu3cRHR0tkRdAT0tLw6+//or9+/ejpKSE6zgfyczMxG+/\n/YbffvsNenp6GD9+PMaPHw8NDQ2uo9WIgYEB5s2bB3d3d+jo6GDTpk3g8XhwdXWFnZ0dnj17JpFL\nDf4rISEBCQkJNf8/1nEjJ1Gf3kaMGFF19tOePXvIysqK+Hw+/frrryQUCjlOx0g7kUhEixYtIj09\nPYqMjKy6fcOGDTRo0CAOk9WcJNV9RUUFderU6aNZ5/8lSWP5mq1bt5KysjK1b9+eiIiEQiHFxMSQ\nnJwcPX/+nON0NSMUCunAgQPUpEkTzmeZavrF4/HI09OTrl+/LnEzN9u3b6fmzZuTSCSidevWkbq6\nOhkZGZGenh5du3aN63i1pro1zxaR/8f9+/cRGBiIn376CePGjQMAHD9+HKtXr0ZcXBzH6ZiGpFu3\nbggMDET//v3x4MEDTJ06FWlpaYiKipKYXcolpe6JCMOGDYO2tjZWr1792cdIyli+5unTp2jTpg1O\nnDiBfv36YejQoXB1dcWaNWtgZWWFzZs3cx2xWiorK7FkyRIsWrQIZWVl3/Wz5OTkoKWlBWNjY5ib\nm8PIyAiGhobQ0NCAsrIygH8WUZeWluLdu3d4/fo10tPT8fLlS2RlZaGwsBAikei7MhgYGCAiIgL9\n+vX7rp9TX8rLy+Hu7o6mTZsiISEB169fh5mZGY4cOYIJEyYgPT1dImcx/y+2iLwGkpOTic/n09Ch\nQ0lLS4t2795Nhw8fJgsLi48W9TJMfYiOjiYTExNauXIlaWho0KxZs2ju3LnE5/Pp6tWrXMerFkmo\neyKixMRE4vF41KJFC2rZsiW1bNmSTp069dFjJGUsXyISiSgsLKxq5ik9PZ1++ukn4vP5NGPGDIlY\n21lcXEyzZs0ieXn5fzXro6ysTJ6enrRw4UK6detWrY25uLiYLly4QKGhoeTg4EBycnL/Kp+GhgZF\nRkaSQCColVx1KS8vjzp27Ehdu3YlIqKysjLatm0bKSoq0tmzZzlOVzuqW/OsgSKiQYMGUUREBBER\nnTlzhhwdHcnCwoJ2797NcTKmoTp48CBZWlrSihUrqm77448/qHfv3hymqj5JqPvqkvSxjBs3jqyt\nrUlLS6vqLOKrV6+SpqYmlZWVcZzu60QiEa1evZoUFRVr1JDIyMiQs7MzrVu3jnJzc+s187Nnz2jm\nzJlkZmZW40ZKT0/vk7NAxdH169fJxMSEMjMzqW3btuTj40Pjx48nfX19qZh0YA1UNZWXl5Ovry/t\n2bOn6raDBw9St27dOEzFMET9+vWrWgslEAho1apV5O7uLvZ/9IjEv+5rQpLH8uTJE9LT06PCwkJa\nvnw58fl8cnBwIC0tLYqJieE63lclJyeTnp5ejRoQR0dHOnz4sNjM5BQWFtK6devI1NS0RuNwcXGh\nN2/ecB3/q+bNm0eNGzcmNze3qrVct27dIl1dXY6TfT/WQFVDbm4uOTo6komJCRkaGtKFCxcoMTGR\nmjZtSjt37uQ6HtPA7d+/nywsLOjMmTPk5uZGhoaGZGtrSw4ODmJ/WrQ4131NSepYhEIhzZo1i+zt\n7atue/78OZmZmVFcXByHyb6usLCQ/Pz8anT4a9GiRZSfn8919K9KT0+nYcOGkYKCQrXHNnfuXLFp\nBj9n7ty5NHLkSCL6Zz+7WbNmkYKCAp07d47jZN+HNVDVMHr0aJowYQKJRCLavHkzGRoakqmpKW3c\nuJHraAxDRP+cOWVkZET+/v4kEAhIJBLRtGnTaMiQIVxH+ypxrvuaktSx/Pzzz+Ts7Ex8Pp/+/PNP\nev/+PW3YsIHMzc2ppKSE63iftW/fvmo3GBYWFnTixAmJO5OtrKyM1q9fT2pqatU+rHfnzh2uY3/W\n3bt3ic/n09GjR8nc3JxGjBhBS5YsISMjo4/OJJY0rIGqBm9v74865T179lDfvn05TMQwnxo6dCht\n27at6vtLly6Rq6srh4m+TZzrvqYkcSzZ2dmkoaFBhYWFdOfOHXJyciIFBQVq3rw5PXz4kOt4nygu\nLqaePXtWq6Gws7OTmovZRkVFkYaGRrXWdM2fP18sm8Vjx46RlpYW/fjjj1W3XblyhaytrTlM9X2q\nW/MN9mLC58+fR35+Pnbt2gWRSITKykrs27cPDg4OXEdjmI84ODhg//79KC8vx6NHjzBhwgSUlJTg\n7NmzXEdjxFRiYiIUFRWhqqqK5s2bIzk5GS4uLoiIiECzZs24jveRO3fuwMTE5JvXGNXR0UFcXBzu\n378PJyenekpXtwYOHIjc3Fxs2LABioqKX3ycSCTCnDlz4Obmhvz8/HpM+G0BAQGYOHEizMzMAAAF\nBQVITExETk4OUlNTOU5Xx763U0tPTydvb2+ys7Mje3v7qrPZatrJ1adjx46Rvr4+LVmyhKysrEhb\nW5v09fWpa9euUnldn/ogFAopPT2dbt68SWfOnKFDhw7R4cOH6cyZM3T9+nVKS0sT62P54qy8vJx6\n9+5N2trapKKiQrNnz6Z169aRoaEh7d+/n+t4nyWOdf9vSdpYNm7cSIaGhmRsbEyhoaH04MEDWrFi\nBZmZmVFhYSHX8T6yZcsWkpGR+ersi7y8PEVERIjl7EttKisro+HDh39zNkpVVZVu3LjBddyP/P33\n36Sjo0N//fUXWVpaUufOnWnYsGHE5/MlcoPN6tb8d78zvH79mv7++28iIvrw4QM1bdqUHjx4UOMg\n9aldu3Z0+PBhIvrnD/+ECRMoMDBQ6gu0NmRlZdHq1aupc+fOpK+v/6/2ZZGTkyM9PT3y8/OjlStX\nUkZGBtfDEnsikYiCg4Np5syZVbedPn1abA/liWPd/1uSNJaKigpSUVGhZ8+eUXZ2NvXu3Zs0NTXJ\n3d2dnj59ynW8KiKRiMaMGUM8Hu+r7xXt27ev920IuJaSkkKGhoZffV1kZWVpx44dXEf9yJkzZ8jE\nxIQCAwOrbouMjCRvb28OU/071a357z6Ep6+vj5YtWwIAVFVVYWtri6ysrO/9sXWqvLwc6urqAAAZ\nGRk0adIEysrKUrGDam3Lz8/HkiVLYGNjAxkZGRgaGmLSpEk4ffo0srOzUVlZWeOfKRAI8ObNG5w5\ncwZTpkyBiYkJZGRkYGVlhQULFiA3N7cORiLZeDwelJSUqn5vAUBdXR0VFRUcpmLETXFxMXg8Hiwt\nLaGnp4fo6Gj4+voiNDQUVlZWXMcDAAiFQrRv3x4bN2784m7PcnJyOHjwIGJjY6GtrV3PCbnVokUL\npKenY/bs2V98jFAoRFBQEObNm1ePyb6uU6dOCAgI+Ojwqo2NDXJycjhMVcdqs2v73NXMa/kpvlt0\ndDS1atWKrKysKC4ujqKjo0lPT4/Onz/PdTSxUVhYSOHh4dVa3FhXX2pqahQWFib2pybXp6tXr5Ku\nri7t37+fdu7cSQYGBtSqVSvau3cv19E+IW51/z0kZSwZGRnUqlUrUlVVpTlz5lBJSQmdO3eO+Hw+\nvXjxgut4RERUVFRE1tbWX619BwcHVvf/ce/ePWrcuPFXX68RI0aIzdGTQ4cOkbW1NT18+JCCg4NJ\nTk6O5OXlaciQIRKxf91/Vbfma+2d4cOHD+Ts7Fx1aOx/g8ydO7fqi8tGZfv27WRubk7btm2jnj17\nkpaWFnl4eIj9hnL1QSQSUWxsLNna2nLWNH3py9ramk6ePCk2bxJcOnPmDHl4eJCqqir99ttvtHPn\nTrKysuJ8643z589/VOeS0nRUh6SMpW3btjR37lxKS0sjV1dXkpWVJRMTE7HZk+fNmzekr6//1Vqf\nPXs21zHFTmlpKXl5eX31devYsaPYXJJn1apVpKqqSi1btqT3799TcXExde3alX755Reuo1VbvTZQ\nX7uauTi9+bRs2ZISEhKqvg8LC6MZM2ZwmIh7QqGQ/vzzz2rvScLlV6NGjWjDhg0NfjH6vHnzKDQ0\ntOr7pKQksrGx4TDRp8Sp7r+XJIxFJBKRnJzcR5/yg4ODad26dRym+v/evn1LOjo6X6xtGRkZdhTg\nG+bPn//V90dPT0+qqKjgOiYREfXv3/+jS6HFxsZSu3btuAtUQ9WteTl8JyLCiBEjYGdnh9DQ0O/9\ncXVKKBR+dKqooqIiioqKOEzEHSLCnj17MHr0aBQXF//rn6OsrAxDQ0NYW1vD0tISJiYm0NHRgYqK\nCgCgpKQEubm5ePXqFVJTU/H06VO8evUKJSUlNX6u4uJijB07FlOmTMGGDRswbNiwBrlu7f/+Hisp\nKUEoFHKYiOFadnY2tLS0kJSUBC8vL1RWVuLWrVvo1KkT19GQn58PBwcHvH379rP3q6qq4vbt27C0\ntKznZJIlPDwcrq6u6NKly2fXjl2+fBmdO3dGbGws5++LhoaGuHbtGgYNGoTCwkJs374dRITi4mI0\natSI02y16ns7tW9dzbwWnqJW5OXl0c8//0y2trZ04sQJ2rp1K/H5/KozCBuSmzdv1vgaUwBIQUGB\nPDw86Pfff6esrKzvzpGdnU2bN2+mNm3a1OjyBv/94vP5dOXKlVp4RSTL/fv3ic/n0+bNm+nkyZNk\nbW1NQUFBYnW2krjUfW0Q97EkJSWRrq4uubm5kaqqKvXs2ZNatGhBvXr14ny2tqio6KsX1TU2Nqb3\n799zmlHSpKSkfPX9ctCgQZwvd8jJyaGmTZtS27Ztq84C9fT0JDs7O7F6n/qS6tZ8g9iJ/M6dO2Ro\naEjt2rUjfX19MjMzo4CAALp06RLX0epVUVFRja4xBYAaN25MEydOrLqKe116/fo1TZs2jdTV1WuU\n0dvbmwoKCuo8nzhJSkqi7t27k6mpKZmZmZGvry/p6+uLzQ7N4lD3tUXcx+Ls7Fx1IsGjR4/Izs6O\nJk6cSEKhkNNcpaWl1Lx58y/WbbNmzdi+e//S48ePSUVF5Yuv7dixY7mOSIWFheTr6/vR2qdx48Z9\ntPxAXLEG6n+0adOGtmzZQkT/rNdq164d/fnnnxynql8xMTHVnuXh8XjUvXt3Ts/cSUtLo379+n1z\nk73/fsnJyYntppJ1Zffu3eTu7l617uWvv/4iJycnjlP9QxzqvraI+1h0dXU/+oAze/Zsmjt3LneB\n/qNLly5f3OepefPmYrNeR1KlpqZ+8Qw9GRkZWr58OdcRycfHh86cOVP1/d69e6lPnz4cJqqe6tZ8\ng7iUy/Pnz+Hn5wcAkJeXh6+vL54/f85xqvohEokwcOBABAQEfHPPIAUFBfz6668oKSnB0aNHYW5u\nXj8hP8PU1BT79+9HaWkpFi9e/NXLHAD/7C3Vv39/9OrVCwKBoJ5Scuv58+fw9vauem06derUYH6v\nmX+UlpbC1tYWq1atgkgkQlZWFvbt2wc3NzdOc82ePRunT5/+7FodW1tb3LhxA/Ly8hwkkx6Wlpa4\nf/9+1XrT/yUSiRAWFoYzZ85wkOz/c3Nzw4YNG1BWVobc3FysWLECpqamEIlEnOaqNXXbx4nHp7eu\nXbvS7NmzSSQSUW5uLjVv3pwOHjzIdaw6l5mZSbq6utWavVm8eLHYnAb7OQKBgFavXl2tnc+1tbXF\nZt+bunTixAlq2rQp5eTkkEgkogULFpCvry/XsYhIPOq+tojrWNLT08nGxobs7OxIU1OTlJWVSVlZ\nmRYvXsxprrNnz36xNi0sLBrc4fa69vjxY1JUVPzs662kpEQvX77kLFtpaSn169ePlJSUqFGjRmRj\nY0Pm5ubUrVs3Ki8v5yzXt1S35qW+gXr58iX9/vvv1LRpUzIwMCBVVVWaPn0654vs6lpcXBzJycl9\ns9kICgqSqHUI5eXlFBwc/M1xycrK0smTJ7mOW+fmzJlDqqqqZGBgQObm5hQREUGpqalcx+K87muT\nuI6lV69e9OuvvxLRP9dR8/HxoZUrV3KaKTU19Yt/zLW1tSkvL4/TfNLq+vXrX3y/NzIy4vxkgp49\ne1J4eDgR/bOMpnPnzrRq1SpOM31NdWteqg/hJSQkwMXFBefPn4eysjKaNWuG58+fY+nSpZyf5lmX\n/vjjD7Rv3/6rh7JMTU2RlpaG7du3Q0lJqR7TfR8FBQVs2rQJWVlZaNKkyRcfJxQK4e/vj3Xr1tVj\nuvo3b948vHz5Ei1btoSamhouXboENzc3nD17lutoTB17/PgxevXqBeCfLVl69uyJ1NRUzvKUlJSg\nY8eOKC8v/+Q+JSUlJCUlQUtLi4Nk0q9Vq1bYtWsX5OQ+3Zno1atX+OmnnzhI9f+lpqZW/a7Ky8uj\nW7duePToEaeZaoNUN1BjxozBjh07cODAAdy8eRNCoZDzY8J1bd68eQgODv7mY16+fAlTU9N6SlX7\nDAwM8OzZMyxbtuyrzXBISAhmzpxZj8nq3/nz55GXl4ebN29i//792Ldv3zd/BxjJZ29vj6ioKBAR\nSktLcfjwYdjb23OWJzQ0FC9fvvzsfRcuXPjqBx7m+w0cOBDh4eGffT/cu3cvDh48yEGqf9jb22PP\nnj0gIpSVleHQoUNwcHDgLE+tqdN5MOJ2+rtx48b07t27qu+nTJlCS5Ys4SxPXZsyZco3tyR49OgR\n1zFrXWpq6jev2ycOp/XWlTVr1tC4ceOqvi8tLSV5eXlOD1NzWfe1TRzHcuXKFQoKCiJDQ0OytLQk\nPT09GjRoEGeHak6cOPHZM2Z5PN5nr1DB1A2RSEQBAQGffQ9UUVHhbG1odnY2OTo6UpMmTUhDQ4Ns\nbW1p8uTJlJ6ezkmeb6luzUv1DFTr1q2xdOlSEBFevnyJAwcOwN3dnetYdWLGjBlYuXLlF+93cnLC\n27dvYWNjU4+p6oelpSXevHmD1q1bf/ExGzZsQEhISD2mqj/u7u44fPgwnj59CiLC0qVL4eHhIdWH\nqRuy8+fPo0ePHrC3t8fo0aPx7t07bN26FX/99RdkZWXrPQ8RYciQIZ+cWSUjI4OOHTuK/RUqpAmP\nx8ORI0fA5/M/ua+kpASjRo3iIBWgp6eH69evIygoCGpqahg3bhxkZGTg4eGB169fc5KpVtRlF0fE\n7ae3169fU+vWravOThGX60LVtuXLl3919mXUqFFcR6w3oaGhX30t5s2bx3XEOrFlyxZq1KgRKSsr\nk4uLC2VkZHCah8u6r23iNhZ/f3+KjIys+n758uU0YsQITrKIRCIaPHjwZ2tNX1+f7TLOkTt37nx2\nUbmMjAxt3bqVs1zW1tZ07dq1qu9Hjx4tlkeFqlvzUjkDRUTYuHEjQkJC4OjoiL///huFhYUYP348\n19Fq3eHDhzFt2rQv3r969Wr88ccf9ZiIW98a79y5c7F79+56TFQ/Ro4ciYKCAty9exceHh6YPHky\n1q5dKz37rTBVysvLoampWfW9pqYmysrKOMny4MEDHDhw4JPbFRQUcODAAWhoaHCQimnevDnCw8M/\nWVQuEokQEhLy2f256oM4/e7Wijpt44ibT29hYWHk4uJCUVFRNGPGDDIzM5PK02dv3Ljx1dmW7du3\ncx2RM/v27fvqa5OYmMh1xFqXn59PVlZWNHnyZIqKiiIPDw/OLpvARd3XFXEby7Zt26hp06YUFxdH\nJ7FV+z8AACAASURBVE6cICMjIzp+/Hi95ygpKSErK6sGNdMrSQQCAbVt21asjkqEhYVRmzZt6PLl\nyxQVFUV8Pp/u3LnDSZavqW7NS10DJRKJqFGjRvT69euq2/r06cPptGVdyMnJ+eqmkjt37uQ6IucO\nHjz4xddHTk6OMjMzuY5Yq/bs2UP+/v5V3+fl5ZGCggInG6SKW9PxPcRpLOXl5XThwgWaMmUKubm5\nUZs2bWjfvn2cZNm4ceNn93zS19enkpISTjIxH7t37x4pKyt/8m+kpKREDx48qPc8AoGA5s+fTy4u\nLuTp6UkrVqyg5ORksduXsbo1L5WH8EQiERQUFKq+V1RUhFAo5DBR7SIiuLi4oLKy8rP3b9y4EYGB\ngfWcSvz06dMHO3bs+Ox9AoEArVq1kqrLvgiFwo8uefPfGiCOpuslwU8//QQ9PT00b96c6yjfVFBQ\nAE9PT0ycOBEXL15EUVERDh06hP79+9d7lvz8fMyfP/+TPZ9kZGSQmJgIZWXles/EfMre3h5r1679\n5ISSsrIyTJkypd7fG2RlZREeHo5169bhyZMnOHHiBHr37o3Ro0dL5vtUHTZxRMTNp7exY8dWXcRw\n2bJlZGBg8NGMlKQbO3bsF2dW/rvbK/P/LVmy5Iuv1+DBg7mOV2vevn1LxsbGtHDhQjp79iz5+fnR\n8OHDOcnCRd3/GxcvXqRbt26Rg4PDFx8jLmOZOnUq/fTTTyQSiUgkEtHkyZNp5MiRnGQZNmzYJ4uU\nZWVlP5oBZcRDWVnZZy/ppaKiQrt37+Ykk42NDR06dIiIiIqLi+mHH36gY8eOcZLlc6pb81I5AxUR\nEQFfX18sXboUycnJSEhIgL6+PtexakVcXBw2bNjw2ft69uyJ+fPn13Mi8TdjxgwMGTLks/ft3r0b\nMTEx9ZyobvD5fFy4cAH379/H4sWL4ebmhk2bNnEdS6y1bdv2o0Wt4uy/F0Xn8Xjg8Xjw8/PjZOdx\ngeD/sXffYU1d/x/A3yFhhbADYYsTQRQVEXEw6sA96ioO/Fpr3Va/atUOqXVQrVpXbV1VESeOthZX\npYLWgbbuvQcoskT2SPL5/eHPfEsDyso9Sbiv58nzNBfqfV+Sk5x77rmfI8ehQ4fURm+tra318gYN\nXWdsbIzjx4/DwKD0131+fj527tzJJNODBw/QtWtXAIBYLEZgYCDTKvpVJfj/3pbmdiAQ6ObQnBbK\nz8+HnZ0d8vPz1X7m7u6Ou3fvllnKn/f6sq6npyfu3Lmj9jNjY2OkpqbCwsKCQTL9pEvt/tGjR+jV\nqxeuXr1a5s8FAgEiIiJUz4ODgxEcHMxRuv+ZP38+zp49i71790IoFCI8PBxOTk5YsmQJpzlGjBiB\nbdu2lZoWYWxsjGnTpmHBggWcZuFVnL+/P86dO1dqm5GREdavX8/5lA9/f38MGzYMkyZNwvPnz9Gu\nXTv89NNPTNoV8HrZt/j4eNXzuXPnVuzzS3ODYK9xsAuV3NxcmjBhArVo0YK6d+9O169f52zfXOjf\nv3+Zl6EMDQ0pOTmZdTytl56eXu5Cp6GhoVo3kbE6bt++Tb169aLmzZvTmDFjKDs7m9P9c9nuq+vh\nw4c6cQmvqKiI+vfvTzY2NmRnZ0ehoaGUm5vLaYbCwkISCoVq7ad+/fqUl5fHaRZe5dy+fZtMTEzU\nXjtPT0/Os9y5c4caNmxIrq6uJJFIKDIykvMMb1PRNq9Xl/DCw8ORnp6OtWvXonv37ujYsSNevHjB\nOlaNSExMxL59+9S2CwQC7N69G05OTgxS6RZbW9tyL9cdPXoUx48f5ziRZmRmZqJjx44ICQnB+vXr\nUVBQgMGDB7OOxaumN7WVrl27hgsXLuDQoUMwMzPjNMOff/6pdkOOqakp5s2bB7FYzGkWXuU0atQI\nYWFhatsfPnyIp0+fcpqlYcOGuHHjBhISEvD06VPdXa9Uwx05zs7eCgoKyNjYmAoLC1Xb3n//fdq+\nfTsn+9ekwsJCcnJy0vtJ0FwZM2ZMmX9LqVSqF2fR+/bto65du6qel5SUkEQioaysLM4ycNXua4Iu\njEDFxMSQr68vNWnShObNm0cKhYLzDElJSSSRSNTajb29PV9xXEf89ddfaqNQBgYG1LBhQyYj8K9e\nvaKRI0eSh4cHhYSE0KVLlzjPUJaKtnm9GYF6swZUdnY2gNe3bmdmZpa6rVtXbdu2Dc+ePVPbbm5u\njrVr1zJIpNtWrFhRZoXk9PR0bNy4kUGimmViYoKsrCzVNfycnBzI5XIYGhoyTqZ9wsLC0LZtW9y5\ncweurq7YtGkT60hq4uLiMHnyZERGRmLLli04cOAAFi1axHmOs2fPqk1ENjAwwO+//85XHNcRvr6+\niIiIKLVmolKpxJMnT5CWlsZ5njcjYnv37sXQoUMRGhqKlJQUznNUmUa7ccTt2dvs2bOpefPmtGbN\nGhoxYgT5+Pjo/IhCRkYGicVitbM+gUBAhw4dYh1PZ508ebLMUSgTExNKSUlhHa9aCgsLqXXr1jRk\nyBBas2YN+fn5cV6RnMt2r2msj2X8+PG0bNky1fPTp09Ty5YtOc8xa9YsEggEavMv/znqz9N+CQkJ\nZY4knjhxgtMceXl5ZGJiUqrQb79+/Wjnzp2c5ihLRdu83oxAAcCCBQswZcoUXLx4Ee7u7khISND5\n6/JRUVFl3nXXoUMHhIaGMkikH9q3b49u3bqpbS8sLMSGDRsYJKo5xsbGiIuLg4eHBy5evIgxY8Zg\n2bJlrGPxqkgsFpc6K3/x4gXnn2uHDh3CihUrSt2ZZGhoiIULF+rFKH9t0r59ewQGBqqNJnbv3h1J\nSUmc5TA0NAQRISMjA8Drq0Ys3tvVwZcx0GIvXrxAvXr11DpQQqEQT5484SeOV1NmZibs7e3VJsWa\nmJjg7t27cHFxYZRM9+lTu2d9LI8ePUJAQACGDBkCW1tbrFixAps3by7zBEBTwsPDsXXr1lLbXFxc\nOJ98zKsZ+fn5MDc3L7XYuEQiwQ8//FBuzTxNiIiIwN69ezFy5EicPXsWT58+RUJCAvNOeUXbvF6N\nQOmbQ4cOqS2VAAATJ07kO081wMbGpsy7P0pKSvDLL78wSMTjqXN3d8fZs2dhamqKzMxM/Pzzz5x2\nnoDXdwD+ezkQmUzGaQZezTE2Ni41Dwp4XSD1n0ugceGrr77CnDlz8OTJE/j5+SEuLo5556ky+BEo\nLZWVlYW6desiKyur1HaRSITU1FSdqZ6s7fLz82FpaalWVdnc3BwPHjyAVCpllEy36VO716djqYqL\nFy8iKCgIOTk5qm2mpqaIjY1FSEgIw2S86pg/fz4WLFiAwsJCAK9vCKhXrx7Onz9f628KqFUjUIWF\nhfj888/RpUsXfPTRR7o1i78cZ8+eRXFxsdr2zz77jO881SCxWIxvvvlGbbtCocCff/7JIFHNSktL\nw9ixY9GlSxfMnDmzzPl0PN7bhIeHl+o8iUQiTJ06le886bgvvvgCzZs3V40svrkbb+7cuYyT6Q69\n6EANHz4c165dw9SpU2Fra4ugoCDk5uayjlVlRITly5erfdmJRCJ88sknjFLpr3HjxqkNZ+fn52PZ\nsmU6PfJQUFCA9957D6amppg6dSoePnyIQYMG6fQx1TZyuRzHjh3Dvn37mJ0YJicnq2X697xBnm7K\ny8sr9XlQXFxc5nJXXLh16xZiYmLw999/M9l/Veh8ByorKwuHDx/G7t270a1bNyxatAiOjo44ceIE\n62hVlpiYiJMnT6ptDw8Ph42NDYNE+k0sFmP8+PFq2y9cuFBqfSRdc/bsWYjFYixbtgzdunXDtm3b\ncPbsWTx//px1NF4FFBcXo0ePHpgxYwY2bdoEHx8fJl8urVq1KrXGppmZGdq0acN5Dl7N69ChA0xM\nTFTPTU1NmaxHt3nzZgQFBWHHjh3o168f5syZw3mGqtD5DtSba5Vv7iYgIsjlcrUJj7rkyZMnpe6O\nAF7f8jl//nxGifTf119/XeakykePHrEJVAMEAkGpkQKlUgmlUql2+zJPO23atAlEhL/++gsHDhzA\n0qVLMWHCBE4z/P3337h8+bJqjqBQKMTkyZPRt29fTnPwNOPbb79F+/btVZ8JhYWFiImJ4bSoZm5u\nLj755BOcPHkS+/btw8WLF7FhwwZcv36dswxVpfOfpJaWlujbty/69euHPXv2YPLkycjKykJQUBDr\naFVSUlJSamLfG/b29vxdLxpkaWkJNze3UtuKioqwaNGiMu+E1AUBAQFQKpUYO3Ys9u7di4EDByIk\nJIR/H+mIJ0+eoF27dqqOfWBgIKdlAwoKCtC5c2ekpqaqtpmammL69OmcZeBpllgsxhdffKG6842I\ncOnSJQwaNIizDKmpqbCyskKjRo0AvF6z1MvLi9OaVFWl8x0o4PWZWmBgIKKjo2FgYKDTBTTj4uLw\n4MEDte0HDx7kRw40SCAQ4PDhw2rbk5OTcfDgQQaJqu9NQU0zMzNs3boVrVq1wvbt23V6dLY28ff3\nx44dO5CSkgKlUokVK1agdevWnO3/wYMHanenCoVCnRgZ4FXcqVOnSt2wVFJSgsTERM727+LiAoVC\ngb179wJ4PYXl8uXL8Pb25ixDVYne/Svaz9DQEJ999hnrGDUiNzdX7QvO0NAQderUYZSo9nBzc4NQ\nKCx12YuIdPqGBGtra74KuY7q3bs3Ll++jHr16sHQ0BBNmzbFvn37ONu/nZ2d2p3AxcXFcHBw4CwD\nT/McHR1hbGxc6qYlLsu3GBkZ4eeff8b777+P0aNHAwC2bNkCZ2dnzjJUFT+koWUePXpU6pZhQ0ND\nNG/eHJaWlgxT1Q4mJiZo165dqUV38/LyyhwR5PG48OWXXyIzMxMPHz7EyZMnYW9vz9m+7e3tERER\nAbFYDDMzM5iZmWHChAlo2LAhZxl4mjd06FA0a9YMEokEEokEYrEYmzdv5jRDq1at8OjRI9y6dQup\nqano1asXp/uvKr6Qpha5cuUKAgICSp0JmJiYICkpCba2tgyT1R5ZWVlwcXFBXl6eaptYLEZ8fDz8\n/PwYJtMt+tTu9elYKkOhUODYsWM4d+4cjI2N0bZtW7Rv3551LJ4GyOVyxMbG4tKlSzA3N0dgYCBa\ntWrFOhYzFW3zenEJT19cunRJbZ6TXC4vdZspT7MkEkmZxSYvXrzId6B4tYZCoUBoaCgSExNVd3Me\nOHCAdSyehohEIly/fh2LFy+GgYEBlEolPv30U0RERLCOptX4S3hapE6dOmq9XlNTU52dEK+LRCKR\nWqV3AwMDfg4ar1bZvXs3zp49i9zcXOTk5CA/Px/Dhw9nHYunIc+ePcO8efOQn5+P3Nxc5Ofn45tv\nvsGTJ09YR9NqfAdKi7Ro0QJeXl4QiUQQi8UQi8XYuXMnf9cUx3bt2gUzMzOIxWKIRCLUq1eP07uf\neDzWkpOTUVJSUmpbeno6ozQ8TXv+/LnaQsLGxsZ80d134DtQWqKgoAB+fn64cuUK5HI55HI5xo0b\nh+7du7OOVut06tQJ//3vf6FQKCCXy3Hr1i34+vrq9N14PF5ltGnTplT1caFQiBYtWjBMxNOkNzWY\n/kmpVMLDw4NBGt3Bd6C0xIEDB/Ds2TNV0cbi4mKsWrVKrSI5T/OICEuXLi31WqSmpqrqlPB4+q59\n+/ZYvHgxjIyMIBKJ4OnpyWkJBR63zM3NcejQIdjY2MDQ0BDW1taIjY2FlZUV62hajZ9EriXy8/PV\n5j8pFAooFAq+gCYD/65/o1Qqy5xczuPpqwkTJmDMmDEoKCiAubk56zg8DWvbti3S09ORnZ0NCwsL\nfupIBfDfzFqiY8eOpd6wxsbG6NSpU6maRDxuCAQC9OzZs9TdjwYGBujSpQvDVDwe90QiEd95qkUE\nAgEsLS35zlMF8R0oLeHq6or4+Hi0bNkSTk5OGDhwIPbs2cM6Vq21bds2hIWFwdnZGc2bN8exY8dQ\nv3591rF4PB6PpyX4Qpo8Hq/G6VO716dj4fF471bRNs+PQPF4PB6Px+NVEt+B4vF4PB6Px6skvgPF\n4/F4PB6PV0l8B4rH4/F4PB6vkqrdgTp8+DAaN26Mhg0bYtGiRTWRqVLWrVuHIUOGIDIyUqeLThYX\nF2PmzJkYOnQo9u/fzzoO7//99ttvGD58OGbMmKHzdaCWLl2KIUOGYPXq1ayjaBXWn2FlKSwsxIwZ\nMzB06FAmi/hev34dH330EUaPHo379+9zvn8eO7///juGDx+OqVOnIjs7m/P9L1++HEOGDMGKFSs4\n33elUTXI5XKqX78+PXz4kIqLi8nHx4du3LhR6nequYu36tOnD0mlUgoPDyc3Nzfy9fXV2L40qaCg\ngKysrAiA6jF9+nTWsWq9L7/8stRrIpFIKC8vj3WsKgkICCBnZ2cKDw8nmUxGXbp00ej+NNnuaxLr\nz7Cy5OXlkZOTE/n4+NCwYcNIIpHQ559/ztn+4+LiSCAQqN73AoGAzp8/z9n+eewsXry41GeeiYkJ\nvXz5krP9BwYGkqOjI4WHh5OjoyOFhIRwtu9/qmibr9Ynw+nTpyk0NFT1PDIykiIjI6sUpLIePHhA\nxsbGlJSURERE2dnZZGtrS3v37tXI/jRp+vTppd60bx48tv75JfLmMXbsWNaxKu3o0aNkYWFBmZmZ\nRESUkpJCpqamdPnyZY3tU1fevyw/w8ozceJEatWqFcnlciIi+vPPP0kikXC2f0dHR7X3fYMGDTjb\nP48dkUik9tqHhYVxsu837/P09HQiIkpLSyMzMzM6e/YsJ/v/p4q2+Wot5ZKcnAxXV1fVcxcXFyQm\nJqr93ldffaX67+DgYAQHB1dntwCABw8ewNLSEs7OzgBer+VTt25d3Lt3r9r/NteePn1a5na5XF5q\nQU8et6iMOiDJyckMklTPvXv34OrqCmtrawCATCaDnZ0d7t27h2bNmtXIPuLj4xEfH18j/xaXWH6G\nlScpKQktW7aEUCgEALRo0QIFBQUa29+/lXXZJjMzk7P989iRy+Vq2549e8bJvu/duwdHR0fY2toC\nAKRSKRwcHHD37l34+/trdN9V/vyqTi9tz5499NFHH6meb926lSZOnFilnlxl5eTkkEQioXXr1pFc\nLqfY2FgSi8Vqw++6YNeuXWq9fjMzM9axaj1LS0u11+Wnn35iHavSHj16RGKxmPbt20dyuZyioqLI\nzMyMMjIyNLZPTbX7msbyM6w8W7duJUtLS7p06RIVFxfTlClTyNnZmbP9BwUFqb3v+/bty9n+eezY\n2dmpvfbfffcdJ/tOTk4msVhMu3fvJrlcTjt37iQzMzN6/vw5J/v/p4q2+Wp9Mpw5c6bU8PfChQvp\nm2++qVKQqvj111/J2tqaBAIBSSQSWrVqlcb2pWmTJ09WvWHFYjFdvHiRdaRa78aNGySRSFSvy+jR\no1lHqrKNGzeSubk5CQQCsrS0pF27dml0f7rSgWL9GVae8ePHk4mJCRkYGJCTkxNdu3aNs30XFBRQ\ngwYNVO/7pk2bUklJCWf757Hz4MGDUvNxP/jgA073v2XLFrK0tFR9TkVHR3O6/zcq2uartZSLXC6H\nh4cH4uLi4OTkhNatW2PHjh3w9PRU/Q4XyyAUFxfDyMhIo/vgij4di74oLi6GSCSCgYHuV/3g6v2l\nK8ufaMtnWFmUSiXkcjmzz4M3l3P4aQS1D+vPPNbfgxVt89VqGSKRCKtXr0ZoaCgUCgVGjRpV6oOH\nK/rU4dCnY9EX+vSa6NOx1ARt+Qwri4GBAdPXi+841V6sPydY77+i+MWEeTxejdOndq9Px8Lj8d6N\nX0yYx+PxeDweT0P4DhSPx+PxeDxeJfEdKC1z+/ZtJCQkICMjg3WUWu/ly5dISEjAjRs3WEfh8Xg8\nnpbhO1BaZMqUKWjRogX69OmDunXr4s8//2QdqdY6d+4c3N3d0adPH7Rq1Qoff/wxPw+Gx+PxeCr8\nJHItkZCQgB49eiAvL0+1zc7ODqmpqQxT1V6urq5ISkpSPTczM0NMTAy6devGMJXu0Kd2r0/HwuPx\n3o2fRK5j7t69q/aCpaeno7i4mFGi2ouI1JYvkMvluHv3LqNEPB73CgsLsXnzZixduhQXLlxgHYen\nYUSE2NhYfPvttzhw4AB/0lABfKEPLeHt7a22zdnZWWfqYegTgUCAevXq4f79+6oPEZFIhKZNmzJO\nxuNxo7CwEP7+/rh//z6Ki4thaGiIzZs3Y+DAgayj8TRk0qRJ2Lx5M4qKimBsbIyhQ4di7dq1rGNp\nNX4ESku0adMGn3/+OYyMjCASiSASidCzZ88yF3fkaZZCoUCPHj1Ur4ORkRGmTp2KkJAQ1tF4PE7s\n3LkT9+/fR15eHkpKSpCfn4/x48ezjsXTkMePH2Pjxo3Iy8uDXC5HXl4etm7divv377OOptX4DpQW\nmTBhAqysrEBEkMvliIqKwsiRI1nHqnXGjRuH9evXo6SkBEqlEhKJBFOmTGEdi8fjTGZmJkpKSkpt\ny87OZpSGp2mZmZlqVzsMDQ35u8Hfge9AaZGjR4+ioKAACoUCAJCfn48dO3bw86A4pFQqsWnTJuTn\n56ueFxUVITY2lnEyHo87ISEhEAqFqudGRkYIDg5mF4inUR4eHjA2NoZAIFBtMzQ0hJeXF8NU2o/v\nQGmRsibt8RP5uMe/DrzarkWLFti6dSvs7OxgbGyMkJAQ7Nq1i3UsnoaIxWLEx8fDw8MDRkZGaNSo\nEY4fPw6JRMI6mlbjO1BapEuXLjAzMyt1FiAQCHDs2DGGqWqX48ePq/39TU1N0aNHD4apeDzu9e/f\nH7du3UL//v3x+PFjjBo1CikpKaxj8TTgr7/+wtixY2FgYIBPP/0U169f52+aqQC+DpSWiY2NRZ8+\nfVSX8YDXNYhevXpVakidV/OICDY2NsjKylJtEwqF2LFjB3/3USXpU7tneSzZ2dnYunUrsrOz0bVr\nV7Ro0YKzfSsUCrRs2RK3bt1CcXExRCIRXF1dcePGDZiYmHCWg6dZ9+7dQ/PmzVU1CMViMT788EOs\nWrWK0xyxsbG4ePEi6tWrhw8++AAGBuzGd2pdHSilUokXL17o/HyhnJwciMXiUtuKiopKfanzNKOg\noEBtoqyJiQlyc3MZJaoZJSUlePHiRalOOU/7vXr1Cm3atEF8fDwyMjIQGhrK6Vy8+/fvq8oYAK9r\noaWnp+PSpUucZeBp3v79+0t9b+bn52PLli2cZpgzZw6mTZuGvLw8rFq1CsOGDdOJEzC96EBdvnwZ\n9evXR5MmTWBvb4+YmBjWkaqsadOmane/yOVyzt/QtVFUVJRaoyUi+Pj4MEpUfb/++itkMhmaNGkC\nd3d3nD9/nnUkXgVt3LgRzZs3R0xMDJYsWYLo6GjMmjWLs/0bGhpCqVSW2kZEfG06PWNoaKg22iMS\ncVci8uXLl1i+fDlOnjyJyMhIxMfH49y5c/jrr784y1BVOt+BUiqV6Nu3L+bPn4/09HTEx8djwoQJ\nOlu/okmTJpg4caLa9lmzZqGgoIBBotpBLpfjk08+UetAjRgxAi1btmSUqnqePn2KUaNG4ciRI0hP\nT8fy5cvRr18/nR+lrS1evnyJBg0aqJ43bNiQ05Fod3d3BAUFwdTUFMDry9m2traoU6cOZxl4mufv\n7w+hUKia+ykWi/HZZ59xtv9Xr17BwsICUqkUAGBsbAw3NzeduOqi8x2o1NRU5ObmYujQoQCA5s2b\nIyAgAJcvX2acrOratWsHc3PzUtvkcjmuXr3KKJH+ezPP458kEgk6dOjAKFH1Xbt2DS1atICfnx+A\n15OCDQwMkJyczDgZryJCQ0OxYcMGnDlzBs+fP8f06dM5XYtRIBDgl19+wcCBAyEUClXTJFq0aKET\nX268d7tw4QI6d+6MoqIiAK9HoyIjIzF9+nTOMri6usLKygrffPMN0tLSEB0djZs3b+rEiavOd6Bs\nbGxQXFyMK1euAACysrJw6dIluLm5MU5WdX5+fmrzVYgIAwcO5OexaAARoV+/fmrbFQoF2rRpwyBR\nzXB1dcW1a9dUxfBu3bqFV69ewd7ennEyXkW0b98eS5cuxbBhw9CsWTNYWVlh+fLlnGYwMjLCiRMn\noFAoQEQoLCxEamoqNm7cyGkOnmbMmDEDeXl5qtdXoVBwPvggFAoRGxuLY8eOoVGjRli+fDliY2Nh\na2vLaY6q0Pm18IyMjLBu3Tp06tQJbdu2xaVLlzBo0CC0atWKdbQqc3Z2xpdffonPPvus1CWl5ORk\n3Lx5s8x183hV9+jRIzx48KDUNoFAgOnTp6Nu3bqMUlWft7c3PvroIzRv3hy+vr44ffo0Vq5cCTMz\nM9bReBUUFhaGsLAwphn+fWNFUVERMjMzGaXh1aR/v45KpRLp6emc56hTpw7i4uI432916fwIFAAM\nHjwYp0+fxrBhwxATE4Nvv/2WdaRqe++991RzD95QKBQYPny42sROXtUREYYNG6b2NxWLxejYsSOj\nVDXn66+/xi+//IJhw4bh5MmTGDFiBOtIPB3Tq1cvtbIF165dU7vZhadbUlNT1S7FisVivmRLJfB1\noLQUESEkJAQJCQmltguFQpw/f57TejD67M6dO/D09FTrQLVu3Rpnz54tVVSTV3H61O716ViqoqCg\nAF27dsWJEydU20xNTTFhwgS9OFmtrfz8/HDx4sVS00JmzZqFyMhIhqm0Q62rA6VvBAIBFixYAGNj\n41LbFQoFwsLC+LlQNUCpVGLgwIFqnScTExMsWLCA7zzxtMZ3330HOzs7mJubY/To0apJv1wwNTWF\ni4tLqW0FBQX4+eefOcvAq1kFBQVqnSeJRAJPT09OcyQnJ6Njx44wNTVF/fr1dW7VDb3sQOlL58Lf\n37/MW4bv3LnDL25bA44fP17mnY0ODg4IDAxkkKjm6UtbqM327t2LH374AadOncLDhw/x7NkzfPHF\nF5xmkMlkarWBMjIy+LlQOuru3btlTgWxtrbmNEf//v3Rtm1bpKWlYe3atQgLC8PDhw85zVAt5td/\nMgAAIABJREFUpGEc7ELl8ePHFBAQQEKhkBwcHOjXX3/lbN+a8ueff5JIJCIApR7m5uaUm5vLOp7O\nKiwsJCsrK7W/q0gkoiNHjrCOV22HDx8mZ2dnMjAwID8/P7p//z6n++ey3Wsa62MZO3YsrVy5UvX8\n/Pnz5OPjw2mGZ8+ekVQqVWsrfn5+pFQqOc3Cq560tDS1zz4DAwNq27YtlZSUcJYjJyeHTE1NS71/\nBg0aRNu2beMsQ3kq2ub1agRqwIAB6N69OwoLC7Fv3z58+OGHuHPnDutY1RIQEAAvLy+17Tk5OZg9\nezaDRPph7ty5ZdayqV+/Pt577z0GiWrOo0ePMGzYMGzbtg1FRUUYPHgwevfuXavn8egyW1tb3Lhx\nQ/X8xo0bnN/i7ejoiG+//bbUlAK5XI5Lly7h5cuXnGbhVc/p06fVRqYFAgH27NnDaQVyU1NTGBgY\nqIpey+Vy3L59WyfKF6hoth/H3dlbbm4uGRsbl+rNhoWF0ZYtWzjZvybduHGDhEKh2miJgYEB/f33\n36zj6ZwbN26QQCBQ+3sKhUK9+Hvu3r2b+vbtq3quVCrJ0tKS0tLSOMvAVbvnAutjSUtLowYNGlD/\n/v3p448/JqlUSomJiZznOHr0KEkkErV2s2LFCs6z8KpGoVBQp06dyhx5Z3FF48cffyRnZ2eaNGkS\nBQQEUO/evUmhUHCe498q2ub1ZgTK1NQUxsbGuHnzJgCguLgY169fh0wmY5ys+jw9PTFo0CC17Uql\nEqGhoSgsLGSQSjeVlJSgY8eOZY7GdO/eXSeq376LTCbDzZs3Ve+L+/fvQy6Xw8LCgnEy7RITE4Mm\nTZpAKBTiwoULrOOUSyqV4vz58wgNDYW3tzfOnj2L1q1bc54jODgYHh4eattnz56tKmTM025r167F\nqVOnSm0TCoWYOHEik/pwY8aMQUxMDNzd3fHJJ59g3759auvyaTO9KmOwdetWzJgxA7169cKFCxdQ\nr1497Nq1S6dekPJkZ2dDJpOV2VkaNmwYtm7dyiCV7hk3bhx+/PFHte1GRkZITk5Wrceky4gI4eHh\nuHr1Kvz8/BAbG4u5c+di9OjRnGXQhVv/b926BQMDA4wZMwZLly4tt/OsTcdy//59bN26VXU3blmX\n9zUpLS0NDg4OpSYgC4VCzJkzB3PmzOE0C6/yAgMDcfLkyVLb7Ozs8OLFC87vOj569Cji4uIglUox\nZswYrTrBq5VlDIYPH45Dhw7B19cXERERetN5AgALCwts3ry5zJ9FR0cjOjqa20A6aP/+/WV2ngBg\nzZo1etF5Al43/qioKMyfPx++vr749ddfOe086YrGjRujUaNGrGNU2M2bNxEQEIDc3FzI5XIEBQVx\nvmK9VCpVG6lQKBSIjIzU6lE8HvDDDz/gzJkzpbYZGBjAx8eH887T2rVrMXr0aFhYWODChQvo0KED\n8vLyOM1QE/RqBOqfiouL8fjxY9ja2sLGxobz/WsCESEoKEjtDAJ4fRZ48eJFNG3alEEy7Xf37l14\nenqWeVt/q1atkJiYqDed7ZcvXyI9PR116tSBkZERkwzaNGrzLiEhIe8cgYqIiFA9Dw4ORnBwMEfp\n/mfUqFFo1KgRZs6cCeD1l9DRo0exd+9eTnMcPnwYPXr0ULsNvnfv3vjll184zcKrOHt7e6SlpZXa\nZmZmhqtXr3K+ZJW9vT3i4+Ph5eUFIkLPnj0xcOBA/Oc//+E0xxvx8fGIj49XPZ87d26FPr90fi28\nsty8eRM9evQAESEjIwOff/656kNHlwkEAhw8eBBSqVStkJ5CoUBAQACePHmiNx3GmpKTk1PmAs3A\n69XHjxw5ojedp5UrV+KLL76AVCqFQqHAgQMH0KxZM9axmOncuTNSUlLUti9cuBC9evWq8L/z1Vdf\n1WCqqsnNzS1V0NLFxQU5OTmc5+jatSu8vLxw7dq1UttjY2Pxxx9/6PxdrPooMjJSrfMEAOPHj2ey\n3uc/38sCgQAuLi7Izc3lPMcb/z4pmjt3bsX+xxqevK6Gg12o8fHxobVr1xIRUXJyMtWpU4dOnDjB\neQ5NOX78uNpdFG8ezs7OVFRUxDqi1igpKaG6deuW+/f67bffWEesMefPnydnZ2d68uQJERFt2bKF\nPDw8mGRh0e6rKjg4+K13X2rLsWzfvp0aNmxIiYmJdOHCBWrWrBmtWbOGSZbNmzeTkZGRWntydHRk\nkodXvtTUVDI0NFR7rUxNTenatWtMMoWFhdHgwYPp7t27tH//fpJKpXTr1i0mWcpS0TavH6fd/6BU\nKnH16lWMHDkSAODk5ISuXbvi8uXLjJPVnODg4HInbCYnJ6Nly5b8gsN4/V7w9/cvt7Lt1KlT0aNH\nD45Tac6VK1fQsWNHuLq6Ang9J/D+/fv8XZoVQDpwuTEsLAxTp07FiBEjMGjQILz33nvo0KEDk7Y+\nYsSIMtvO8+fPsWLFCs7z8MqmVCoxZMgQtYWfhUIhli5diiZNmnCeqaCgABMmTADweoR4wYIF2LNn\nT5l3eGo9zfbj2Jy91a9fX1WFPCcnh7y8vOjQoUOc59C0gICAckdWmjdvrhX1NFhRKBTv/PvoWwXl\n+Ph4atCgAWVlZRER0e+//05OTk5MjpNFu6+sffv2kYuLC5mYmJBMJqOuXbuW+XvadiyZmZnk7+9P\nDRo0oDp16lCXLl0oPz+f8xzHjx8nU1NTtbZlaGhIjx8/5jwPT92WLVvKHCk0Nzen9PR0zvPcu3eP\n6tevT97e3iSTyWjUqFFa+T1V0Tavlx2oU6dOkb29PQUFBZGLiwuNHz9e774siYiKiopIJpOV20lo\n0qQJyeVy1jE5J5fLydfXt9y/i42NDRUUFLCOqRHTpk0jJycnCg4OJjs7Ozp+/DiTHNrW6agObTuW\nMWPG0NixY0mpVFJJSQn179+fIiIimGSZMWNGmW3M29ubn0rA2OPHj8ssfAqA2ZSW9957j5YsWUJE\nr4tf+/n5UXR0NJMsb1PRNq+3d+Glp6fj8uXLSE9Px9OnT2FjY4OwsDCYmppynkWT0tPT4ebmhoKC\ngjJ/7urqihs3bkAikXCcjI2CggJ4e3vjwYMHZf7c2NgYjx49goODA8fJNKuoqAg7d+5EWloaXFxc\nIJVK0axZM9jb2zPJo0t34b2Lth1LUFAQIiIiVJO1d+zYgf3792P37t2cZ3n58iVcXV3VbkEXiUSY\nNWsW5s2bx3km3mvt2rXD6dOn1bb7+Pjg0qVLDBK9nlKTmJiommbw9ddfo6ioCAsWLGCSpzy1sg7U\nP0mlUmRnZ2Py5Ml4+vQpYmJiEBwcXG5HQ1dJpVLcuHGj3DWMnj59CkdHx3I7FPrkXccqEolw9epV\nvew8de7cGdHR0UhKSsKUKVOQlpbGrPPE0yxPT0/s2bMHRAS5XI59+/ZxXlDzDWtra/z8889q2+Vy\nORYtWoSEhAQGqXjffPONWs0nADAxMcH+/fsZJHrtzXsXAPLy8hAbG8vsvVsjNDUE9gYHuyhX3bp1\n6eTJk0T0ej2wbt260YYNG5jl0aQ7d+6QSCQq97KVQCCgAwcOsI6pMUePHi1zvcA3DwMDA7p+/Trr\nmBoRHR1NISEhqsvUf/31Fzk4ODDNxLLd1zRtO5aMjAzy8/OjRo0akYODA9WtW5emTZtGDx8+ZJYp\nJCSkzPUlra2tKTMzk1mu2ujatWtlvhaGhoa0YMECZrlOnDhB4eHhZG9vT02aNCEHBwf68MMPdXoO\nlN6OQAFAZmYmPD09AbwekmvcuDEyMjIYp9KMhg0b4ubNm+UWTiQi9OrVC0OGDCmzHpKuUiqVGDVq\nFLp06VLucQmFQly/fl23z3TeIjMzE40bN1ZVE/b09ERmZqZWXXbi1RwbGxucPn0a48ePBxFh3Lhx\nMDAwQEBAAB49esQk065du2BlZaW2/eXLl3xdKA6lp6ejTZs2ZbZ9Pz8/ZvUQf/vtNwwcOBDe3t4Y\nNmwYnj9/jm3btmHDhg26XYNPg504ImJ79jZw4EAaOXIkZWZm0pkzZ0gmk9H58+eZ5eHC06dPyczM\nrNyRGABka2urVTU3qurBgwdkb2//1mM1NTVlembOhStXrpCdnR2dOHGCXr58SePGjaOePXsyzcSy\n3dc0bT0Wf39/io2NVT2fPn06zZo1i1meX3/9tcw7vgDQ5MmTmeWqLQoLC8nT07PMv79YLKZHjx4x\ny9a2bVvVnfFERLNmzaLp06czy/MuFW3zOtz1e7f169cjJycHbm5u6Nu3L9q1a4e4uDi9HYUCXlcn\nTk5OLlWx+N8yMjLQuHFjjBgxAsXFxRymqxklJSUYO3Ys6tWrh9TU1HJ/TyaTISkpCe7u7tyF41hW\nVhYOHz6MoKAghIWFwdXVFcnJydiyZQvraDwNKygoKLV+o52dHdM5nr169cL48ePL/NmqVavw3Xff\ncZyo9lAqlXj//fdx8+bNMn/+yy+/oE6dOhyn+p9/v1elUql+zEfWcEdOK87e9uzZQw4ODhQREUH/\n+c9/qH79+kxqYHCpuLiYOnfu/NbRGQBkZGREW7Zs0YkyD0qlknbu3EkmJibvPK4OHTro/W3UWVlZ\n1LhxYxo2bBjNnTuXnJyctOaWYG1o9zVFW49lwYIF5OfnR4mJibR8+XKSSCQ0depUys7OZpapqKiI\nvL29y2yTQqGQduzYwSybPhs9ejQZGBiUOfd14sSJTLM9ePCAevToQc2aNaOzZ89SbGwsOTg4MCux\nUhEVbfO1ogPl5eVV6sUKDw+nxYsXswvEoYULF76zs4H/n+y5f/9+rexIKZVKOnjwIEml0gody5w5\nc1hH5sSqVato4MCBqudnz54ld3d3hon+RxvafU3R1mNRKBS0cOFCcnd3JwsLC5o6dSr169ePvL29\nmXaicnNzy60/JBQKVTf28GrGkiVLypw0DoB8fX2Zfqa/mV4wduxY8vf3J2tra2rZsiXt37+fWaaK\n4DtQ/+Dq6kr37t1TPf/iiy9qzZcs0es10szNzSvU+ZBIJLRy5UqtGL0pLi6mH3/8kSwtLSuUXSwW\n0+nTp1nH5szChQvpv//9r+p5cnIySaVShon+RxvafU3R9mPx9PSkY8eOqZ4PGDCAVqxYwTAR0d9/\n/13uXbFCoZASExOZ5tMXq1evLvfz0M7OjtLS0pjm+/d7MSIigkaPHs0wUcVUtM3r9RyoN/r06YNJ\nkybh7t27OHz4MNasWYPWrVuzjsWZVq1aITMzEx988ME7fzc3NxeTJ0+GiYkJevbsievXr3OQsLTb\nt2+jb9++MDExwdixY/Hq1at3/j99+/bFy5cvERAQwEFC7dC6dWtERUXh0KFDuHfvHiZMmIA+ffqw\njsXj2MuXL9GoUSPV80aNGiErK4thIqBly5aIiYmBUChU+5lCoUDbtm1x6tQpBsn0x4IFCzBx4sQy\nf2ZiYoLExMRS845YePnyJRo2bKh6rg3vzRql4Y6cVpy9FRYW0qRJk8jV1ZVsbGzI0dGRrKys6OOP\nP9bKGhSa9Ndff5GdnV2FRnTePIyMjKhnz570+++/a2RpGLlcTsePH6e+ffuSsbFxpbLZ2NjQqVOn\najyTNlMqlTR58mSytLQkqVRKtra25OrqSmPHjmWyJlpZtKHd1xRtP5aRI0fSoEGD6MmTJ/Thhx+S\nra0thYSE0LVr11hHo0WLFpU5Nwf/PxKl7ZdytNW0adPKvWwnEonozJkzrCPSL7/8Qo0bNyYfHx+6\nf/8+3bx5k7y9vWnjxo2so71TRdt8tT4Zpk+fTo0bN6ZmzZpRv379VIuYViUIFwYOHEjTp08npVJJ\n2dnZ1KZNG514MWuaUqmk77///q2FN9/2sLS0pC5dutCqVavo+vXrleqEKhQKunXrFq1Zs4a6detG\nVlZWVcogEolo6dKlWjlnS9O2b99OLVu2pKysLFIqlfTll18yL1vwb9rU7qtL248lNzeXRowYQRYW\nFtS+fXs6fvw4rVixgmQyGSUlJbGOR5999lm57djAwIBWr17NOqLOUCqVNGTIkHI7TwKBgOLi4ljH\npCNHjpCjoyPt3r2bBg8eTGKxmKRSKUVGRurEZzYnHaijR4+qvjxnzpxJM2fOrHIQLjRq1KhUNeql\nS5fSpEmTGCZiq7CwkGbMmPHWCt6V7dSYmZmRjY0NyWQykslkZGNjQxKJhAwNDWtkHwYGBjRp0iSt\nGWlhYebMmTR//nzV8wcPHpCrqyvDROq0qd1Xly4ci1KpJFNTU8rIyFBtGz58OK1du5Zhqv+ZPXt2\nuW1aIBDQJ598ohNfrCzl5+dT27Zt3/p3/O2331jHJCKioUOH0rp161TPf/75Z+rcuTPDRJVT0TZf\nrTlQnTt3VlUR9ff3R1JSUnX+OY2rX78+Dh48COB1XYq9e/fCwsKi1lZsNjY2xuLFi5GXl4evv/4a\nJiYm1fr35HI58vLykJmZiRcvXuDFixfIzMxEbm4uSkpKqp31iy++QG5uLlauXKl3i0JXFBHB3Nwc\nR48eVdXwOnjwIBo0aMA4GY81kUiE/Px8AMDVq1dx/fp13L59Wys+3xYuXIgJEyaoquX/ExFhxYoV\neO+991T5eaXdv38f7u7uZS4ODLxebWHHjh3o0aMHx8nUFRQU4MWLF6UWmM7Pzy93vVadVlM9tp49\ne9K2bduq3JPjwr1796hu3brUqlUrsra2JhcXF3JycqK+fftqxV1nrL0pF+Dl5VUjo0U18fDw8KCf\nf/651s1VK0tJSQl98MEHJJPJSCqVkpOTE7Vt25ZcXV3p5s2brOOVok3tvrp05VgiIiLIx8eHPv74\nY7K2tqb333+fPD09aeTIkVozuvO2uTvA6zmNV65cYR1Tq2zbtu2t0y20aS7Zq1evqEWLFuTr60vm\n5ua0ZMkSWr16NclkMjp8+DDreBVW0Tb/zt/q1KkTeXt7qz3+WZZ9/vz59P7775cbJCIiQvVgXTwr\nOzubunbtqhoyLioqoq5du9KSJUuY5tI2hYWFtGrVKqpTpw7nnSZXV1datmxZrb5MV5bVq1dTSEgI\nFRQUkFwup//85z8UFBREr169Yh2Njh8/Xqqd60qnoyJ05ViUSiWtW7eOTExMVFMV8vPzycPDg+Lj\n4xmn+58lS5a88zL9N998ozWdPlYKCwtp8ODBb+1wGhoaasWE8TfmzZtHQ4cOJaVSSefPn6fg4GCq\nW7cu8+/9yqqxDtS7bNq0idq2bUsFBQXVCsIlX19fOnv2rOr5unXraOTIkQwTaTeFQkFxcXHUv3//\nChezrMzD2tqa+vbtS0eOHOFHmt5i/PjxpWqqXL58mby8vBgmKp82tvuq0qVjefnyJUkkEtXz5ORk\nCgwMZF4X6t8OHjxY7t15bx4tW7ak1NRU1lGZOHfuHNna2r7172NpaVmqviFrSqWSBg8eXOq9dunS\nJWrSpAnDVFXDSQfq0KFD5OXl9dZiXdr44TNkyBD69NNPSalUUmJiIjVs2JCCg4O17jKINktLS6Pt\n27fTuHHjqH379uTm5kYWFhZkbGxMQqGQDAwMyMDAgIRCIRkZGZGFhQW5urpSu3btaMyYMRQVFUUp\nKSmsD0Nn3L17lzp27EhBQUGqy80RERHljvyypo3tvqp06ViUSiU1adKEVqxYQbt37yZra2vy8fEh\nW1tbWrlyJet4pdy8ebPciuX/HI2qTXfpFRcX07Bhw9550unl5aUVI89vKBQKGjJkCEmlUmrQoAE9\nf/6cCgsLaciQITRmzBjW8SqNkw5UgwYNyM3NjZo3b07NmzencePGVTkIl54/f05NmzYld3d3MjMz\no7lz59Lnn39OUqmUv/7O0zq3bt0iOzs7mjFjBvn4+JBUKiUvLy/y9PSkp0+fso5XJm1s91Wla8dy\n584d8vb2JmNjY7p48SIRET1+/Jjs7Oy0asSCiCgnJ4d8fHze2WGQyWR04sQJ1nE1RqlU0saNG8nI\nyOidf4sxY8Zo3eXNqKgoCggIoPz8fIqIiCAjIyMSiUTUr18/ysnJYR2v0ji7hPfOHWjph09hYSGF\nhITQTz/9pNq2aNEi+vDDDxmm4vHUTZgwgb766isiev1Bu3jxYmrdunW5l821gba2+6rQxWO5ffs2\n1atXT/X8/Pnz5OXlRWvWrGGYqnxz5syp0OX+wMBArT1pqKpTp06Ri4vLO49dKBTSkSNHWMdVo1Ao\naNiwYaWWR3vy5AnZ2dkxTFU9FW3ztWIpl7IYGxtDKBTC3t4eAFBSUoK8vDwkJSVV+5Z7Hq+myOVy\nJCUlqd6nAoEAvr6+MDQ0rHbZCZ7+cnV1RXZ2NuLj47Fw4UL07dsX7u7umDdvHr777jvW8dTMnTsX\nFy9ehIWFxVt/78SJE3B1dUVISAju3r3LUTrNiIuLQ7169dCuXbt3lgDy8vJCSkoKunTpwlG6ilEq\nlRg8eDASEhKwc+dO1TIt0dHR8PHxYZyOAxruyGn12dvatWvJy8uLjhw5Qt7e3uTm5kYeHh7k5+dH\nmZmZrOPxarns7GxVmQJbW1s6evQonTlzhnx8fGj58uWs472VNrf7ytLVYzl27BhZW1uTRCJRzTd8\n+vQpWVlZ0fPnzxmnK1tRURENHjy4wjegtGzZkv7880+tu6RVnuLiYtq2bRs5OztX6PiEQiEtW7aM\ndexy7du3j1q1akWFhYU0depUsrS0JJlMRp6envTo0SPW8aqsom2+VneglEolrVy5kpycnFS3XiqV\nSvr4449rdYVynnb49NNPKTw8nBQKBW3fvp3c3NzI2dmZvv32W63/wtDmdl9ZunwscXFx5OvrS0Sv\na/TMnj2bHB0dadq0aVRSUsI4XfnOnDlDMpmswh0pGxsb+vrrr8tcTkwbPHr0iMLDwys0x+nNo3Xr\n1vTs2TPW0cuVkZFBHTt2pFGjRqm2PXz4kIRCoc7XVaxom6+1l/CA15dDJk2ahJYtW2LAgAGqKrlt\n27bF5cuXtaKCL692IiJcuXIFvXr1goGBAcLCwrBu3To0btwY06dPL7OiM4/3by1atMCTJ08QGxuL\njh07IikpCYsWLcLFixfx0UcfsY5XrjZt2iA5ORnz58+HUCh85+9nZmZizpw5sLKygoeHB3744Qdk\nZ2dzkLR8SUlJ+Pzzz2Fvbw93d3dERUWpVg94GwsLC+zduxeJiYlwdHTkIGnl5efnIygoCObm5jhw\n4ADu3bsHIkJ0dDQCAgJgZGTEOiI3NNmLI9KNs7fZs2fToEGDKD8/nwYOHEiWlpZka2tLwcHBWnWr\nKK92yM3NpS5dupClpSV1796diouLSS6XU3h4OE2ZMoV1vArRhXZfUbp+LPHx8WRtbU0eHh6qkcsX\nL16QWCzWiTpLubm5FB4e/taCkuU97OzsaMSIEXTixAmSy+UazZmTk0N79uyh3r17k5mZWaWzmpiY\n0PLlyzWesybExMRQYGCgqnirmZkZGRkZUcuWLenx48es41VbRds834Eiory8POrSpQtZW1tTYGCg\nqtLzyJEjafz48azj8WqZadOmUVhYGGVnZ1NoaCjZ2tqSTCaj4OBgys7OZh2vQnSh3U+fPp0aN25M\nzZo1o379+pV7+UcXjuVdDh48SB06dCAioh9//JEkEglZWlqSu7t7qQXWtVlqaioNGzasSh2pNw8L\nCwtq06YNTZs2jQ4ePEiPHz+udPHe4uJiun79uqoOXpMmTcjY2LjKmYyMjCgiIoKKi4s19JerWfv3\n7yexWKx6PxG97uQaGxtTbm4uw2Q1h+9AVZJSqaTevXtTVFQUERHJ5XL64YcfyNvbW2/eFDztl5+f\nT/7+/nTo0CEiev2+XL16NXXq1EmnqrTrQrs/evSo6m86c+ZMmjlzZpm/pwvH8i45OTnUoEEDGj16\nNMlkMlU9qDc30uiSnJwcmjhxYrU6Lf9+GBgYkLGxMZmbm6vWmXR2diYHBweysbEhiURChoaGNbY/\nAGRra0s//PCDVs9F+7ekpCSytbWlP/74g9zc3Gj+/PkUHx9P77//Pg0YMIB1vBpT0TZfq+dA/ZNA\nIECzZs1w+PBh5Ofno2vXrli8eDEEAgGaN2+OJ0+esI7I03PPnj1Dy5YtkZycjF9//VU1B+/ChQvw\n8fGBgQHfXGtS586dVX9Tf3//d95KrsskEgmOHz+OK1euIDAwEPXr18eNGzfwxx9/4NmzZ4iMjIRS\nqWQds0IkEglWrVqFV69eYfPmzXB3d6/2v6lUKlFUVIScnBykp6fj2bNnSE5ORkpKCjIzM5Gbm1sj\n5W0EAgH8/Pxw/PhxpKWlYezYsRCJRNX+d7mQnZ2NiRMnon79+ggJCUF8fDyuXLmCAQMGwNraGlFR\nUawjck+z/TjdOnvLycmhdu3akYODA4WGhqquRc+bN09rl8zg6Y8hQ4bQZ599RmlpadSsWTPy9PSk\nxo0bk5+fn9beXVQeXWr3REQ9e/akbdu2lfkzXTuWt4mLi6NGjRrRjRs3SCaT0ZIlSyg2NpYCAgLK\nHYHTBU+fPqWpU6e+c/04Vo/69evTypUrda4dvyGXy6l9+/b0/vvvk1QqVZXBuH79OllaWurM1IKK\nqmib142uL0ckEgni4+MxaNAgdOrUCUKhEM+ePcOTJ09w+vRpnDx5Eh06dGAdk6eHzpw5gzNnzmD8\n+PGQSqU4d+4cvvrqK1y4cAEHDhyoPXe11LDOnTsjJSVFbfvChQvRq1cvAMCCBQtgZGSEIUOGlPvv\nfPXVV6r/Dg4ORnBwcE1H5URISAg6d+6Mdu3aoVevXpg2bRpevnyJ0NBQLFq0CIMHD0aLFi1Yx6w0\nFxcXLFu2DMuWLUNqaio2btyIqKgo3Llzh8nImpGREfz9/fHhhx9i0KBBEIvFnGeoSevXr8fDhw+R\nkJCAxYsXo0WLFmjQoAFu3ryJVatWwdzcnHXEaomPj0d8fHzl/0cNd+R08uzt+++/p8DAQLp//z65\nuLjQ2LFjaeHCheTg4EB79+5lHY+nZ2JjY8ne3p4CAgJo5MiRpFAoqKCggDp37kxLliz30Nx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0nK5W1KSkrC/PnzYWBgAB0dHbi6uuLAgQNITEzE3LlzkZqaiu7du0NaWhpRUVFwcnKCtDR/hn9d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\nEOzfvx/e3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XHQ0NCAnZ1dl/mahI4kdG35q3oQHByM4OBghISEYPny5YiOju7Q8YG3V49e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\ngWKMMcYYa6f/A05wr0GMGwMfAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These are the type of circles we want to distinguish between. We can try classification with a constant separation between the circles first."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def train_mkl(circles, feats_tr):\n",
" kernel0=GaussianKernel(feats_tr, feats_tr, 1) # four kernels with different widths \n",
" kernel1=GaussianKernel(feats_tr, feats_tr, 5)\n",
" kernel2=GaussianKernel(feats_tr, feats_tr, 7)\n",
" kernel3=GaussianKernel(feats_tr, feats_tr, 10)\n",
" kernel = CombinedKernel()\n",
" kernel.append_kernel(kernel0)\n",
" kernel.append_kernel(kernel1)\n",
" kernel.append_kernel(kernel2)\n",
" kernel.append_kernel(kernel3)\n",
" \n",
" kernel.init(feats_tr, feats_tr)\n",
" mkl = MKLClassification()\n",
" mkl.set_mkl_norm(1)\n",
" mkl.set_C(1, 1)\n",
" mkl.set_kernel(kernel)\n",
" mkl.set_labels(lab)\n",
" \n",
" mkl.train()\n",
" \n",
" w=kernel.get_subkernel_weights()\n",
" return w, mkl\n",
"\n",
"def test_mkl(mkl, grid):\n",
" kernel0t=GaussianKernel(feats_tr, grid, 1)\n",
" kernel1t=GaussianKernel(feats_tr, grid, 5)\n",
" kernel2t=GaussianKernel(feats_tr, grid, 7)\n",
" kernel3t=GaussianKernel(feats_tr, grid, 10)\n",
" kernelt = CombinedKernel()\n",
" kernelt.append_kernel(kernel0t)\n",
" kernelt.append_kernel(kernel1t)\n",
" kernelt.append_kernel(kernel2t)\n",
" kernelt.append_kernel(kernel3t)\n",
" kernelt.init(feats_tr, grid)\n",
" mkl.set_kernel(kernelt)\n",
" out=mkl.apply()\n",
" return out\n",
"\n",
"size=50\n",
"x1=linspace(-10, 10, size)\n",
"x2=linspace(-10, 10, size)\n",
"x, y=meshgrid(x1, x2)\n",
"grid=RealFeatures(array((ravel(x), ravel(y))))\n",
"\n",
"\n",
"w, mkl=train_mkl(c, feats_tr)\n",
"print w\n",
"out=test_mkl(mkl,grid)\n",
"\n",
"z=out.get_values().reshape((size, size))\n",
"\n",
"figure(figsize=(5,5))\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 3.70179551e-05 6.14303709e-01 3.83958304e-01 1.70096833e-03]\n"
]
},
{
"output_type": "display_data",
"png": 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8GX5+fgqz50BpaSlWrFiBbdu2kRbX19fXY8WKFbCwsMC8efMID1V9fT0iIiJw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\ndoQQWfg/hd7ZQYGHl5AAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So MKL classifier classifies them as expected. Now lets vary the separation and see how it affects the weights.The choice of the kernel width of the Gaussian kernel used for classification is expected to depend on the separation distance of the learning problem: An increased distance between the circles will correspond to a larger optimal kernel width. This effect should be visible in the results of the MKL, where we used MKL-SVMs with four kernels with different widths (1,5,7,10). "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"range1=linspace(5.5,7.5,50)\n",
"x=linspace(1.5,3.5,50)\n",
"temp=[]\n",
"\n",
"for i in range1:\n",
" c, feats=get_data(4,i) #vary separation between circles\n",
" w, mkl=train_mkl(c, feats)\n",
" temp.append(w)\n",
"y=array([temp[i] for i in range(0,50)]).T\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figure(figsize=(20,5))\n",
"_=plot(x, y[0,:], color='k', linewidth=2)\n",
"_=plot(x, y[1,:], color='r', linewidth=2)\n",
"_=plot(x, y[2,:], color='g', linewidth=2)\n",
"_=plot(x, y[3,:], color='y', linewidth=2)\n",
"title(\"Comparison between kernel widths and weights\")\n",
"ylabel(\"Weight\")\n",
"xlabel(\"Distance between circles\")\n",
"_=legend([\"1\",\"5\",\"7\",\"10\"])\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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WNXRviB7BPdAzuCcaV3/8KAl7K3t0CuiETgGdAAC5mlycuH0CB2P15dLRm0dx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\nljl2xAAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the above plot we see the obtained kernel weightings for the four kernels. Every line shows one weighting. The courses of the kernel weightings reflect the development of the learning problem: as long as the problem is difficult the best separation can be obtained when using the kernel with smallest width. The low width kernel looses importance when the distance between the circle increases and larger kernel widths obtain a larger weight in MKL. Increasing the distance between the circles, kernels with greater widths are used. "
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Mathematical formulation:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In MKL $\\alpha_i$,$\\beta$ and bias are determined by solving the following optimization program\n",
"\n",
"$$\\mbox{min} \\hspace{4mm} \\gamma-\\sum_{i=1}^N\\alpha_i$$\n",
"$$ \\mbox{w.r.t.} \\hspace{4mm} \\gamma\\in R, \\alpha\\in R^N \\nonumber$$\n",
"$$\\mbox {s.t.} \\hspace{4mm} {\\bf 0}\\leq\\alpha\\leq{\\bf 1}C,\\;\\;\\sum_{i=1}^N \\alpha_i y_i=0 \\nonumber$$\n",
"$$ \\frac{1}{2}\\sum_{i,j=1}^N \\alpha_i \\alpha_j y_i y_j \\forall k=1,\\ldots,K\\nonumber\\\\\n",
"$$\n",
"\n",
"\n",
" here C is a pre-specified regularization parameter\n",
"Within shogun this optimization problem is solved using [semi-infinite programming](http://en.wikipedia.org/wiki/Semi-infinite_programming). For 1-norm MKL using one of the two approaches described in\n",
"[1].\n",
"The first approach (also called the wrapper algorithm) wraps around a single kernel SVMs, alternatingly solving for \u03b1 and \u03b2. It is using a traditional SVM to generate new violated constraints and thus requires a single kernel SVM and any of the SVMs contained in shogun can be used. In the MKL step either a linear program is solved via glpk or cplex or analytically or a newton (for norms>1) step is performed.\n",
"\n",
"The second much faster but also more memory demanding approach performing interleaved optimization, is integrated into the chunking-based SVMlight.\n",
"\n"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"References:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[1] Soeren Sonnenburg, Gunnar Raetsch, Christin Schaefer, and Bernhard Schoelkopf. Large Scale Multiple Kernel Learning. Journal of Machine Learning Research, 7:1531-1565, July 2006.\n",
"\n",
"[2] Kernel Methods for Object Recognition , Christoph H. Lampert"
]
}
],
"metadata": {}
}
]
}
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