{ "metadata": { "language": "Julia", "name": "", "signature": "sha256:a3af3b9a695c6e7390c4dc2095a239cac53006e0ce011e95c2e9ccd2148aa180" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Time Series Analysis\n", "A time series is a sequence of data points, each associated with a time. In our example, we will work with a time series of daily temperatures in the city of Melbourne, Australia over a period of a few years. Let $x$ be the vector of the time series, and $x_i$ denote the temperature in Melbourne on day $i$. Here is a picture of the time series:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "using Gadfly, Convex, SCS\n", "temps = readdlm(\"melbourne_temps.txt\", ',')\n", "n = size(temps)[1]\n", "p = plot(\n", " x=1:1500, y=temps[1:1500], Geom.line,\n", " Theme(panel_fill=color(\"white\"))\n", ")" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n" ], "metadata": {}, "output_type": "pyout", "png": 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DR5+LIZRD7oraSj/RwCABZlfUCwuDcugcpnnWkIsUlEr1SOrmTnku/BQbv8FwkaZcdNoxtZ9oNBxUq40hfJPBfoXvC+O3cwFBDGjhs7paGcBd9TBmkRRMTo5EYoNNnou9gySfi4+tAp/fGN7eIsViDrmc6WoG24dtW5iZGdvpYhgMCYMyi8zODm8bAqNcpGB8vBhJXtMpz4Uxi+wuJEWLnGkC3ygPzyxSKOQwOpofwjftL5xqAJ/d2OlS7A7YtoWpqdGdLobBkDAocjFMgmrIRQrW1iqR+PJuo0U+ZaLGdhxJeS7cwBziDsksUqs1USrVh/BN+wufWQd+5+ROl2J3wPd9k0L+AkJShFuvWFgYHls35CIFjYYDzwunoG7yXKy5wLvPD75sBnpsuMAXN5PNIp4Id0tNU5k+twGUe8x/5TjeUJPX7Bc4HXa0vdDg+0C12tzpYhgMCYNy6KxUhteGDLlIwcGDEygU2JbrXfhcvPs8sGSCA3YMd1WAl9yfbBah3VA9pEuPP30v8HCPTvrj40VjL98GnA7K0tdKwF9dQAQ+k7Fx9OjMThfDYEgYlFnk2LHhpZA35CIFuVw22DJbIinPxZlGuEXu7ZtA1YSM7BhImUjaW4Q+78bnoh+mk0zGNptObQNuB+XiZ74NvH9huOXZSVgWkM8bp+ALBYMiF3yhPGgYcpGCxcVNNBoO1l3gjWeS81z8wLekFA/IQbFitpLYMbgi2jlVckCEwesweRE89C7Nl8t1rK0NLwRsvyBJuRAAFltA8wIi8J7nY25ueKmbDXYWgwpFPX16ZQB31cOQixR4ng8hBJZbwG+eABrBgBaT2gG0goOGXOwsuE8FvY98Dtlxu1Iu/N47ue+LiN+OQXdwfD2xc4JH2biAHqkQMJvfXUAYlKsRz9k0aBhykYKjR2cwMpJvkwka0NTK90S4kjLkYmdBe4YkKRdeYBLR+VxUPOC2Zfm/CK7tdQ6bmho1qZu3AVIuXCHrhPqeE1Tamgv82+qOFW+oyGZtXHHFwZ0uhsGQMCiHzquvPtz/mybAkIsUuK5ULmgF1VYuNOGNTRH+b8jFzoHMIkQKdKGopFyo9bjYAl58nzzH7RAZtBUY5WJ7oGiRmifrZMMNjwPAuSZw43d2rnzDhFEuLixwn7F+wigXuwhLS9Lngqqkk3LBzSItPxwE768Cj5o0B0ND26EzIbKnk0MnUQBHdI4M2gqMz8X2QL4xakixwyrkQqFsxufiwoPxudjnyOUysG2rPbDVOykXjFwAIdn4/88C77mAwuZ2GjQpJSXRaoeiasiFYHXXL+Uik7EjKeQNuoPDSCAQRmo5jFGUXOB/PSTVjf0MEy1yYWFw0SLDa0OGXKTg4MFJFAq59gDX0eeCmUX4K9n3DYYDT0S9rWOhqMExnc/FIJSL8fEipqdNnoutwvFDEgjolYu6D7xrfv87d5o8FxcWBuVzcezYbP9vmgBDLlJQr7fgeX7MoVMX3qgqFy5bcbmDoKEGWrTldGXFq36u87mgtw73ueixPCZD5/ZAykXbLMKOq9jn3AJCCJOh8wLCoDLTVirD25153+hsr375qw/7rvN837LWnZzz7+9617scAHjtDTdMVL2R51uW1cpVcx9/821v3pL3w1+ddnDKyuAlF8v3beVCI7W3ksiFiEvzBoODmkRLV1eJygUzi2QC6n1fFfi9U8Dnnrq98tRqTbRaLg4eHF4Cm/0AR0SVC4/VjYr9nibc8wSWl0sYGzMRIxcCBmUWWVjYxNVXFwdw5zj2Bbm46WU3zXqu+zUAXwUwl2/l3vraG2544kY226i1cl8E8DCAJWe0eROA523l3tVsHo/U7IhD51gmulKiyATVLMLlXEMuhgciDYK9j3zeyecieHUEkAvebLrAt3rwxywUciZD5zZAGTpVs4hOBdzvyoXZFfXCwqDIxczM8NrQvjCL2BnxHAF8+vitb3/JLX99y68BuKPuFV+Yd/I/Cwunb3nfLdcdv/X4TbCsi25+6c1XbuXe4yM5CMuKhKJ+32S04lUHTk8lGTDkYphQHTpVezxNWtx0QuDkwmP/97IyLhZzGBsrbP8GFyjaykXwnqrx9afi5+535cK2rYHvT/OyB4BvluX/P3kvcHJ4CrqBgkGRi9nZiQHcVY99QS4c1/9CNpv9LQB41ateVRDAE10h7oLAEyCsu9snCusBK+t/z1bu7TYdOL6ISLI5OzqY0WeJPhfGoXOoUDN01j3N50gIRSWnQRYt0mkDrW7QaDjGXr4NuEo90usdZcBSzt3vyoXvC6yvVwf6HV/clHleAODT62FeEYPhQ4jBOHSurpb7f9ME7Aty8c4PvHPpLe9+y+Krrn/FM0XF+4oF6x/f8f533AMhDlsQp+g8yxLnARxRr69WGxPlcgN+MHpVKo2244vTcNBwfNSbrKd5Pryg5hsNBxtlea5qFnF8gXK5gZbrwxMyIVe53ECjIZ37Wi0X5XKjndikXm8hqRx+cK96XfZ+x/HkvVtuuxzlcgOuK4fZWq2JcrnRbqTlcqM9wXne4MrRbCaVQ95re+XwqZ4Sy+G6shzNphsm0Qq+s+5Hy+EBcD0B1xcQIloO6s8b1RaaVI6WJwmiR+VotsshhCxHraaWw2k/j42NGiqVevA8Wlt+Hmod83KUy92XQ9aLFykHr+N4OaiOt1OOZkI53Eg5dG2tWpX3cn0BTwhU68G11H98IK+MXL4IyyHbvFqO4fW9aDmidbzdcvi+wMZGbZtjgOhqDPB8gWZwrSeAUrXV7nvdPI9mUx0DvFg5gG7HADfyPMK2Fi9H921+6+UIn61ajt77XqdykM9Yf/ueg5WVSscxoNFo5NEn7AtyAQA3X//KVwrYfwHLvvH4rcdfBwDCwj0C4hI6xwcOWB7uU69tNJzRer3Vrux6vdVuZBOjOTi+aE80AGD5HoI+h1bLRaUWVJ6iXHjBvRxPyFWY78v3QcdxHC+IRpH3bjZd1OutdmXX6612B/Z9gXq91e7AnucF9/KCe9G1Pv2m4FopsMlrneBaWQ5qsFQOanRhOdR7yQasuxf9plZLfy0NtPzZquVw3Wg5wnvR84iXg+7lumE5YsqFHy2HKwBPCLhCSNNI8GxbLbd9TSUglQDQcGWGVl4vNJCE9aI+D6oXD0IIjI4WgmdL5ehUx9HfRJMFXUvlaDRaXdRLWA7dvagctVpyWwvLodaLHylH5zqOttOkcsjnIa/1BeD5QIN+Q9A+6h5QUMkFom1eLUdy39M/W9214fPo3PfoXrq+t90xIJOxMDs7nlLHyf2WypHU9xzHi5ALXwCVusPa2tbHAM+LXhttH9TWksYAP3KvsH047b6nliMcA6idqnXstssR1nG3fS95bO6273Vqa2rfExABuUjqe7oxAMocofY9D2NjhY59r9Wy+uZ1rqqLexI3XX/T8wC8fqm69EO33XZbmwXc/As3fz8s8YfHb73lOa/4+VfM2Hn7Tvi49pb33xLZkUAI8WkAz9Xd+/0LwF+dB153BfCjgYHlxYeA79SAu66V79ccYPZLwGVFufU64Z6nA08aA37sHuBQDvjANX392QYJeNMZ4DdOANNZKe3+3weBDz0h/Pwl9wNf2pRD/7km4D877AjfLAPXfhP4/FOB2RzwxDuAmy8B3jEPuM/agR9zAeNnvg18rQR8+imyHu68FnjaOJD7PDCTBZZZdO+jzwCuGtm5su4HHPsK8KePkeOb/TnZB35oeqdLdWFi6nbgDVfKsWfIuMSyrPl+3GhfRIvAwo9ZAtccHjt08ubrb5KHLPGGhcriuw+PHVx81fU3fV0Al1kCf/Q2hVikoVFtoOUV4IuQh2Wgd+jkmQP5cROKOlyo0TpJPhekUgghMyACYb22BHPU7dGhs1ptwnU94+2/RZD6RPX42XXg90/JehnNAGDkYr/7XHiej5WVMg4fnhrYd9AmcbpkZVuBJ4DMvli27hy2u+X6T98L/O/LgWck7JM4P78+tGRs+4JcBBEiv5bw8UtuvuHmo6Oold/03vdu2ZtFuF6MHGQtxaEzeFVD5Hj6aOPQOTx4ymtdmXkog2c7xBGhfZAPrPS544fe2+qYudgCPrEOvLTDZoOu67VlX4Pu0Xa8Dd6vOFLJAIBnTgKnmUq436NFSPIe9Hfwdn/7JvDD25iH7qsCTx4P339kBXjyGPAYoyx1DR/bc+i8p9rZEZdMSsPAvvG56ITj7z0+vx1iAQAzU6PwLSuyMspaIat84beBu4McCCrTN6GoO4OYcqGQC9oMiyYtXjX0P98VtdMeIw/XgV97tHN5JiZGcODAeOeTDGKgNO2c8JWDSnueMuntd+Uik7Fx6aUHBvodbeUieP/J9e3d58ul6Ps/Og18fXhBCvsCtJjZKnwRX+RyXH75Rdst0pZxQZCLXlDIWhGpEIgqF/+2GoZvqZXKMwsacjE8qBkdVdKnyu18hUADKycXdL1uAtOlEFdh2xYyGdPVtgrKRcLrsRqQC3VFvd+VC8vCwBOxCZCzs3y/3S0LvqKQi276iEEU2zWL8P6iwzA3UDQjXgpK6xWZ54IdywTKRdWTHZCSNCUqFyls0qC/UMmF2tlIuaA6iSgXwZv3LYT12SYXmjok6b4TNjdrWF4upZxloIKnaQdkPQjIQeuIEjC335UL1/Vx6tTyQL/DF9GcLtv1ubirEt2llvqbQfcYlHLxyCOL2y3SlmHIRQqyFvTKBWRaaCCU3ZN8LoxyMVyopCFGLkQ4kALxVO6ANHXFyEXCd6WtyizLgm0bD7etwkPU8ZYcpvN2fOC6EFbGg25DacqFJ7rb2r7hR9Pl+130kQsZL7gX+Btlzt/u4+LmXo7n3wP8/RKQGaKnrSEXKTg0O44V18LDbLuzjCVXuJtBLZJyoU5iEZ+LgZfUgKDWQ5JyQZOVzizig5EL2glXp1wgfVU2OTky1LS7+wWq+YrqI2sB6jy731fG2ayNyy4brL3cF8E29wnk4oEaUPWBr5aA95xPvo8roj4WRrnojA03vkWBwPYcOpP2sdp0JTG88spD2yrjdmDIRRo8Dxsu8CgjF6RcVBRyoYIrFxvu9mVGg60htlGZ8l5ApnEX7H37M+aHQXvFOKweY9/VxarM8/x2EpwLCd/9DeCeHjZ8U6NFqD/lrAtPuRACA484aisXwXseWn+6AfzzinzOd5blKjgJrgBOsvHSKBedoRtDevG5SNrYzwPaib6GAUMuUlDerAGIEgOKFqHO19SQCwuy0Xw5yNf/9RJw3mwvMRRwEmBDbxbhdcarj/4X6M4s0o3PRaXSGPi+ELsRJxtArYclK5lE1LwLOfvCUy48z8f8/DbDN7qEmueCT1K/fxr4nZPhDtCdnrfjx/vUfq+fXqBTP3vxudAtguj42bNr27jr9mDIRQpGCzIViEouuOOMGuoISLuwI4BPrQMLQTRJy7D3oYAPiiMZYK4pM3YS1MGOy49czejaoTOlXnO5DAqFvmXV3TPQea7ftgzc9HB31/MN5gBGLgJiwQev/b4ytm0MfGddNc8FH/O4aTCtzbvKBGeUi87Q+W1tm1wggVwEx8fHh7c7syEXKTgwJTO/cIkwY8l4e7Ir6pSLoi1ldS6G684z6D945xqx5XN/RJFpOXREw+dmET9+Xvu7Eo5zjI4WMDl54WUQEiI+0M03gQdr3V0fixYJHnSbXDD1Yr93Ldu2cfBgQtrFPkHNc8FJOhGNbpQLfg+6r+EWEp9YA+5VREzd7szb3RU1KVqESOGRI8PL527IRQqcYGMbXmFZC1h1pA0S0PtcjNhSqeCDaxq5ONsEfu7+HgtsEHnmo5n4MbUadCaSfioXrZbb3jDqQoLOc93REA4Vn1wHfu9UOCmp+Ua05GKfz1604+VAvwNBKKrGLEKqK5mqOtWhqlyYPBchbpkHPqlYJnSm1e2S5aRoESKOpVJd8+lgYMhFCqxaHeOZuFkECFe2OnJByoWv6aBJWGhJRynTEXsD71yvu1y+8meqPl9u1upoFtF9V6rrtSsAACAASURBVBcDp9w2enidehhYdwHrc5JkJ0E3CXVDLh6uAR9bjYdEcp8LQDGLdFvwPQrPE1hdHWyaS6ovnleEwM0iPDwYAP77A8DvngrfqzK/8bkIITREQh1DhPK6FXTyufjdU8DS0vDy7RhykYInzhbwmKLQkotmcKyjcsGOpSkXlH2wuZ1WtU9xV0WuYrcCvuKaCJQLXS4LQK6CObmgTh4xi6QpFynlKRZzGBsrdlHyvQO+L0sSdPZfx08nFx6k2ZHv7QJEQ1GB6D4v+52Q27aFmZmxgX5H2+ShUS4iZhGlzatKhauMezqfi39Y6hxxsl+h86XwlGOCPeutomO0iABmZ4e3DYEhFykYHy8ia1t9Vy6afrzDUYIa45sR4mRDDkRbgbrJHKBXLrKWNJs00pSLFJ8L9f4qCoUcRkfzySfsIbzyIeCd84xcdPjd3KRB7//kTHrOF18AJS983mo96MwirgC+Wd6/4d62bfVtV91H6+GWBRy+iPrJRJQLVt+qcsFT5dP7NOXisxvAlzZ7+BF7FOqzA4anXLgCAyeoHIZcpGBtrQJLiIhDZzF4as00cqFUNCcNdV8mpeH4zEb8vAsdaelsdeDPnCR0st+3WJhczpIKE9+Svb0NO0Ly2GnjsvZnHcpTqzWHauscJM63gKVWcmp1Dt0Kt96NciGAstvBLKKJFil5wLXflGXbj/B9v28p5F/+HeD9mizQAsCXSsC7gwRZLqu8TsoFN3WRc2JatEjd79xn9it0ZhHVAVawc7cKrhaWPeA3T4RjnieAhYWNrd90mzDkIgWNhgMbUdUh341ZJBONFinY4WQFyM52h2JC/bwhFzFwG3An3PRwmEI3Sbn4+Bqw6oYDXc4OyIVGueDpwdN8Luj8JDiON9TkNYOEJ6Lmvk7jn7qKovafRi58hPv2APF60CkXqglrv8H3gWq1P4ly5lv69koJsqgfRcKA/eixJOWCZyVu3xfxvlP3tjd57nUIxH93v5ULqoOyC7zxjMw1Q4SwXBlesiVDLlIwOzuObMaKTECkXKSZRbjn9ZF81JfCh0ysxUF7lSRl/LwQodoQz7eAv9Wsuu6vyv1AgHhkD93n+LnoKiFnSRLYrUPnR1biYZTd+B6MjRX6JmnvNHwEpLkL5UJdwXbKdMpBfizUD1TioHPobCp1td+QyVg4cmSqL/c639S3V3p0fCFFOXrayoWIkwUduVDNkDrlYp9WVQx/tyhDsAE90VJDUbdLukTw1zbVBq98M7pDF8/ErhsUDLlIQaGQQwbRDXvyillEl0RLDUU9kld2CtQoFxsBuTAOnSFUs8gD1WhCLIIj5IoMiK6aaJX7aB34j9XoKoHMIpzMcbOIKsv/5gngC4qq2I1ykc1mkM9nk0/YQ2grFymkqj3QaZSLNDOXavOvKddlOykX+5SYW5aFYrE/fjtVL95eqb4AOa7ZkGor+UVw9U5VpHSbnamh3zHl4gIiF79xAngosIrq0nqruXK2q1z4yrPnqhN9VhgZnu+XIRcpWFzcBITQKxdBhenIRdEGlluy0Tx2FJjKSjLRlt0B3FONTmyb+8Ch859XZJhiv6BGHDiazknHiZzpzCKnGqEKQh/nLDmA8ufNzSKqQyH31yCoqwQdyuU61tZ62GRjF8ET8nmlkapOEQfaOHwhs3fWNI6cFEUVc+hk11Md7lflwvN8zM31nrqZ2rDaXvlquekDk1ngKeNx01TboZNd6/ga5YJ9nuhzsU/rSgVf0AgMzqGTnrlaB1y5OHl6dYt33T4MuUiB5/nIWFFykVeiReqa0bJoAx9akRPef7sIGLPl5j+UKZJCHe8K5pwTddnIRuy9TS6ufzC6yVuvUJWLpC3OHT+cfHTkgsBDRwu2/JxPSPQZHwT4ajhpx9VOA6XvC3jeHq5UBh9Rn4ukX0XHedcgMq4zi7gCePF9wKITt/NTsrqOPhf73CwiBPqy+V0zob2qDpqZYHM4cjpv7yCMOFngoac65UIXrl33LhzlgpzJgYRQVNUsQq+aB/S2czLSRvs9ScoFq6+mM7wNFA25SMHRozPI2naEQJByQXWv25xpxAZKLvCvq3IQHMtI7907Aj8LuuRsYIv7Rhl48hhwOL+3yYWfoCxs+36Ir36TlAuaWPj5OR25IInQlp/zCUmIcGM6VeoFOpCLDr9hamp04KmbhwVPRH0ufCFJswqhDHBAZ4dOnuJbVS6IgBOByGqUC7r3G053+UP2GLJZG1dccbDn+5BSGlMulPc25LhFptuIWUS53g1Uw89uhH5PEeUCF7bPBR8TiZhR6LQnNKG7TOVQ8bFV4N4EEVRVLqif/ejd4WeXmS3Xdw98XyBjRc0XReWp6RwwDwT7VNU8uQoYzcgt2qmzquy04kkpMmN1Fx2xW6GT/XqBTrnQ3d5l5KKTcsEdOvNWQC4Us4htRc0i/Pti27mzSfaflmVEigohBMQ+cY3X+Vx8tRQnDD47n9DJoZPvfKojdUBIIHQ+F7QiP9FFhuw3nonuNbNX4PehY9HChW4135SZG9Vbk3LxjXLUuVkIvXJxdwX4qXuBN5yRxx6sActO+F3qENnq8yJkN4OTK1IuNlwZOl3y4sqOUF4j9wrO/cBi3P+L9yH6XgBYcbgKO7yVqyEXKVhY2IDw/EhFq+RCN1geZptg2pBmEb7ZmcpOKx4wnpHn7mVbpM6e2+v9VOXCF8B//XYol9Px9sqYXR8zi6CzcuEDyCCZJMXspey6j63qJctSqY6VlcGmbh4W1GgRP1i13q9E0agSLQCsBZNN0t4HQFTCVaEqF7xqqe7nu4i0e9u5/pruhgHX9XHmzEr6iSlQlYvzLUm2YsqFJf9WHWmy5ROW6oDoCuln5YrQP+ZEXfqc0TVpfgb7DeeackwHosqFQNSPzBeaDJ0d7kvj1z8tA18pAdd8PdwIjepkXfE9azLycuKU8bnYNcjlMsja0RmKk4uZhCCAI8wpN0NmERf4Vjm6eqaGVPXlOba1txk9Zfnr5/1Uz3QBuY36eZYwicwiJVd+RlDNIlz5KNgyrFE1i2SscBBQ0cnnwhN6opnJ2MjlMp1/6B5B26EzeE/kTw2r1vlcfHApvMe91TCfAh0D4qmjOToqF8FnG104EzsirorsdlgWYhFHD9aAWxe6v8cbz4Shpe0094hnEgYCs0jw/zfKcZ8LVZHaDJKeVVnl8bBUtS8lKZD7BS/8tjSJA9EFl/r8iGj4yhhE56qgZ+kJqQw9WAujEOke6070fYs53GaGGLVmyEUKDh6cRDYjRzEayzi5uKQgXzNW9PjFhfB/MouUPWlrPNNgnTt4JeXCwt5m9EmT8nahRniQfdIXkqwRHF8OckuOfL4ErUNncLO2WURVLqz4ANq+XnnPPbM96K8ZHy9ienp4aXcHibZDJ2u/jpCK3P8+KSM+gLC++POgiccT0vfoT8+y+zJJN5JhVUnxzY9FfC4YOUlz6uSD7V5BJmPj6NFojoK7K8Bb5rq73hcylPpk0De42UogbtrNWCF5+04tPf03EWtOLtTwVY79Ti58yGdacqMLLlIx+PP32DNddzs7dBKxcEXor6f6fa2RcsGuo/o9bPJc7B7U6y3YQS0TeSjYIdE4GJg/rh4BLmKmkGOMXNjBtVTBXFak9tM2i1jAFzdDSW2voe8OncHNeASBANqbWxFIuVCdYdOiRcjngqRFAVlf3SoXfHWWlE10v2Xo5HkNfATkoiRXuG2HPqXeAKnO0TEPYdI4QHHoZNc8VbPPkk654JOjLnqLgzv/7hUIIWIZOtUNwzqBHg9lAVYXNyq54MoFJ2w0CapmEUKpS+XCE/1VOHcbfAF8eBn4obsQixbhCxdO2k40gAO3R1OtEz6/IYkhPUtXhAqFmriM1Dvej6hPlPuU5bUbGHKRgvX1KiCkU+dMQB6yVjjATQQq01XFcEVlAbg4L9k/IF/5JKfGPQOS8ZNy8SdnurMd70boVinbxetOhvut8Dh6+g6VXLR8OUiOZaRSBMj6+fVj4XncMzsfkIuH6sBHA3O2L5hZRKdcJJELJJtF9tPeItR2uXLhChmySLZ3IJxM/noB+FxQh1UPeNZ0qPBwchFRLtj3veCieBl00SI8t4ou7wzHXjSLeJ6I7S3SbWp8IHy+7wn2DaFHRK/qM7OZcuEKZhZJUC4IETVRsJW6pt/s4aC4VNB4QBtU8sWkQDzcmh8jMwd/ZK8/BXxqPex/rgidmNWwcF1UVtvHZml4vl+GXKRgdLSArG3haePA/7xYHstYYQpi2tKbH8tY8u9fnyTf24iSC7WxfbUkO33Rjq4W9iJ0q5Ru8dsngV95JHz/6Q3gocBRkCfzoQGOyMWyIzsxKRcTGRkKDACjNvADLGtyRLkISN9ty2GHFAjNIrrfoR7jK48kcpHPZzEyxMx4gwTZj/mARjlGHD902qRV6d0VGZnxqXXpHPj0iTBddInlOqDn+o1ydCIa17iq6JSLVSYMdSIXAqEJbS/Bti1MTBQjx7aiXKinqcrSgrLhG1cuWiJKRnjfOFGPhuKrigZ31P3UejRL6x6rgi2BiF8j8E9q+1GIaP/h4weNcbrUBm3fDITjjMOeJd2Dzl1qyeetYlRpQ4OEIRcpmJ4eRda2MGKHg1oGwA8GE9Z0oFzYVjy5Dzl7xpQLRG1wtIIbsaOrhb0Ige3LnRtu1Bzkc3bOlAtaCZEJ5OaHZSd2hHwtsLrK24htzR2JFrGjNniB0Cyi9bnopFwkXDMyksf4+PA69SBBA5uqXJB5ZFNRLgA52T/vbuBbFUn8+D24HwYA/NaJ6DMc04xQur1FVhyZIyZnxcnFFzaANwUhktR+9lr/sm0Ls7MTkWPbMYuo7+lV3f7ctkLllZtMBKLKxXsXQkKpgkf+lD3ZBkhhcsU+N4tAr1z4CMN5ASUKp4NyQYsXbhZRk9JxP44vlaQPlIqpGY2dcUAw5CIFpVIdlhAYyUTNHNcG/fyywLeCm0poscXJRiflggbkIvPl2IsuF77SyLeKph+91kdIILhyQatn6pifDRh6y5dkpGgHSpIlnydv5Dzsi8wiQHQFQfW8JXIhwtWKikbD6duOljsNvnoCovXQ9OOrKCAq005mo+SErn3bufB+9AxthOYtjiTl4nBenq/6XHxyXW46B8RXe3sFvi9w9Vf8SAhtEpnVXi/i7++qhGaMrylqOVcuiFxwR2c1I6cOXLlQEzsRybu/2l2Ez14DPaeGH/VDI3Kmtn+B8JmScsHJF1cuiNCre/Xw8XdZUaII316uD63tG3KRgkqlIckFVy6s8MFdNRIcQ1y5yDGy0cnngvYUKe5x5aLNzrdZdmL5BKHpQLTi4TJiU0iiUPeBf1uVzzEb7BsCRCchbhahaBFAmqYqXmgW4d/JoQ7m6lbUusG+2XTwrTUHH9Ds5rrXQIObGi0CBAMpO4/Ad9kcy+gnpxW2+qVnyhUoDl2eizVXHh+x48rF6UZY3naa8D1m8Pd9gVMtO+Kw3ClsV4XaLH0Az7ordGT+nJKfhUeL3BkQjzzzRfJZf0wCd85VEztRP3zRfcBnNPL9XgeNB9QnuFmEE4n2+MH6VKJygfC5cZ8LUp34s11OUJN+7tRI4mf9hiEXKZiZGUMuEzWLZFnHu6IoH+LVI/EQuRyb3PgCjFbegGxsJY1ysRfJhVBetwqe7AUIlAs2iK27obrhQ3ZCOjadla8fXAwnpbxGPn/dyZDV5xi5uH1TdshU5YL9X/XCVUYnn4vR0QIeskZw/NxWnsbg4ImtrRZ/+l5Jvuha1eeCkzzVURkICSIg/VwEku3F/NhIpjO5mM6G/9c9+X9RszcP9xnQpYjfC8hkrPYEQ0hqbzqohF8E1xLZUk0bNltAfSuIACrYoeqqKhKTmvQJv/Jo3CG76cvMlCIoAyek+wlUV2rSMpWccdKl+lxEyAWiqiFXLj65Hn4ngs87bR6p5v4ZFAy5SMHISB6ZwOeCCELGCknAeAb4L6PAL18adegEmHKREi1CDXCEOXR2O2jsJvRqFiEJkd+PJoqWAGZvlySAOuh/rsnQraYvHTcBqT6QoyZtMMeVi29Vwg6dt8M6AyRZEQjr2RXxbKy8fC99APiHpfA3J8nUuVwGIpPZNflL7qwAV341fvzBmlR+VNxTlQ5iQJxEceWCm7UiZhH2v7qjsG6zOSKUjx8N+xIH9aXbnwY8I9iyRQTH1bwl9FlbuQi+b685dApYsaiLXn0uPBEnYgTaW4QjbzOHToWkffgJ8Xs8Wg9X0FTPFU/uqQGEY99eHOvSQGRBXXARMdOFom7F54ITQ1UV4kRFB0MudglWV8uA57dXUTYCO35QQQUb+MFp4FC+e7MIZ/68oRmzSLLPBZks7q+FHtccFFXgCGl3z0CvXHBw5QIIN1PidTCiXKwL7wI6+1xUq01s1lq7xjs+KRfJ7ZvRxFYET4SmBko/zH0u+KpURzAjykXwPP8xIGVtWzw7n0wkP35Ar1zwOuP/k9+T2ne4j9NeVS6cYFdd/lw9TT8glFy5y2xFM1EBYR22ksiFFe83BUuGRN5ZiSsXT5+AFqpCpUaW1PezcsEeesQswsaJiM9F8L8ux9FWfC5I2UiCrk8NAoZcpKDZdHHNiMCTxmSl0EqKHlzeAn4oiBx5+oSMEElz6Py+O6MbAVFbijh07qHB7z/XZCruTmlru4Hqc8H9KsjxbKkVdjAOHrI4FcjlBY1ywcEdOgHgy5tRs8iSI6V5jqofbkMdKSuSZWrX9dBw/N1DLqAngOrKmJ/fJhds5YTgfJpAIj4XCcoFkYsHlBBj/twoLDKrmBMJ2Q7kQk3nTuVXV4p7TbnwmPmN0Em5KHkyxLqhuQ6I2+1VqMoFhdN/fkP6sNQ8wPoc8Jfz8nPu8M6hPm+ewZPMImlj3Wc3gIu/3Pmc3QZ1LIiYRcDMItysGpyzGox1EYdOESUYPFpk3QG+Vor2PR25oMWWUS52CQ4dmsKvXmHjl46G+SuAqHLxQ9Py/z++SkaRtJULZiZR2aKaq//7p4DHj+1N5eLVjwT5CYL3/VQuCGVlUEpSLgBgKpPsc8GhKhevPRE1i3ytFJpbCB9dYSYCXlaRTC4mJkaQGynsGrNIUg4PTnTV8+tsEOQDoQ/FLKIhmDrlgqAjF4vB89X1G0AhF3b0eKJyoQzmuv71xjOyzncjrIz8ofw5dfK5qCukgqrgcaPylST7bpWLnC33NwHi2TzJHEVj4xPGwu9RlaIaa2CkTKb1C1It9xI4oQWi5hGuUuh8LihnC//NbWIh4j4X51vAm+eA9wf7zHjQt+/JYGAzysUuQTZrwwp6FVcuqH7yVjTVN4VBAnJiuu6gdPpUK7TFBmFPANeMyqyee9Ghkxp7ks/FsgM83EWCSu4QCET/ryiDkjogjTFyMR1sXa/zueDIMwJCv8NXzlfNIqtOODCoK5MknwvbtuBa1q4ZIJOUi07HKbzTg8xo+ksPBZ+xVRKFCdNxgs7ngqDai4HQuZD3N8KtjwNedjh8T+HGdH5OQy5otUjlB/T96yMr0u9kGFhoyQRU3YKKy59TJ+WC1xcQ1sdTgjQHnBDqoCoXOUY21GdHdZq1pGr4vBng8mL0/m3lgn1fw49GTiSh6m1/wbJTUJ1v22OjQs51ZpEVHbkQyWYRQLbdPwlyuZTd6KaAhMlsNApo0DDkIgXz8+uo1+VSSmcWySlPcCQTfjaWAf7xCTLhlkouPsM8fD3E77uXzCJtchG8V4v+N4vAqx5Ov09LUS74fdTdH9XnM8qcYSfJLJKmXChmEV+Eu6ISVLMIEPWX4dcm+VxsbtawUW7uyAD53vNya2aOJJ8LPsCp53OziCfCCCeuXNC5dJygRotw6JQL+ldVLqaywDMno5EJOUv6OwGhchEzi4g4IdSZRdJs1f3EW+aA3zjR/fktN/C54MoFkifmBqsvIHymL7xIZqwlBaeV8HtjyoUVDf3loISCWQt47jTw5qvDelPz1PBJj1SMtLGu4u09v4w05SIWLcLaKEV6xJSL4LwvlaTZS+1jrpBzjoCeNE5kgOwQlziGXKTAsqy2HMgHO2J/KmngTpkc6nm3B7HJNKCr5hbdICcgVzu7TdWgFRTJcuokWu9C1jzViEbRANHOo0YxqM8gZ4dkYiITJReq2kTgeS7o+3xE7fx5TV1yf4P2MSTL1JZlwWPKxflWODkPGv+4HIaRErhDMUeiWQQdbPfKhNytzwVBRy6A0MbPid7lRRmZxfG6K4DXXCr/TzSLaMpF55xuRM8bVt9adrY2YepIm6pcrDrhqreukAu6/mcuAn70QFgn3SoXaqZbjucGG21mEO61RGoG+XTQJPrvrB+rppskVPaqcpFALvhnap4cgG1FoJB2WrzcWY76rnB810hymSYzeh+mQcGQixRcfPE0ikW5NOIOZhQ1oiMXOocZ9TwarKmxUUV0Mos0fOAxX9t9m5rRim9e44sASA/xtMHh7edCdk7odI3atziZKASmKTJp0KB4SNneQw1FBWRCGj6h6eyTarpdKmsSuZicHEG2mG8PMC+5Xy9bDgI8nJegkjgCX1Gp5/Nokcj9oVcuBGSbfuLY1n0uDuSAS4vRKKucpd9n5EljIeFoh6L6MhqFiANXZKj89J4cEqnswyIXS62tTZh2Vj64j66E26ar7e0PTsv9eQA2cSP6Spk3qc6SlAueKBCQJDtpsuD5f8iuT1sfUNt7VGMCail1wsHb7H5QLni/4OOcbm8RnarGfS464bGjyZ9NZoGCzut2QDDkIgWO48IPajTicxGsktSqKtrSf0JFJ3IRMYsErx7k6uZ5d4cDhaMMGLsF6qpd3TOglqJcnKgDH1vrrFyo4JOABTmpFBm5yFph6mhq5Nw5k65RlYl/WEqORlDLFYsWQfgM/vfJMOW05/louKJ9ft1L9tLvN3QSqZ8wSPFJWD1fp9bQe57tkk9mOVuukvkqS/W5cAXwwSXg6yz99Gw2VC7o+U9k9fuMAOE5XLn47ZPAFyhzIfu9PFwPAP5+KfTx2EpSql6x4W7NSTGwiuBPz4YZM1XlgtvhVeWCTqPdTqnOVAfW0YzMOqxTLqyEeYlnLj4Y7Bx9IHiltreqyQqZ1KaAMBcG/ZY9qVyw94Id5yRel/7bVeqMrktSHDkea5SLvYPl5TKaTdkzItEi0K9qi7Y+5juJXNDArUr3rpBe83wnQUfT6HYDSLngm3hxpCkX718MUgUr13ZULthnV40oykUwyYwqygV3+qQkWyp5ENBHI/DTOioXwfs7SqHDXqXSQKXhtOut5ifL0f0GeeSrx3SPNimKhNeLOvkmqU2kxmUQZhAE4sqFI4CHa9HJZzQTbpxFBPEJo8D/NQUtOLkgh04PYSZWXkbue7HsSBXgG+XwvGEpF0nOsyrmm8DH18I8F0BYd55moiI1QPW5oHMsRJULeu7UvvOWjLZSfS66VS6+Oxj7DijKhQ46x2gAeMVDMoyWn7fbFlRpUCM2BHuNmEVY/dAxTi4WWoFDK9KVi6eOd1YuJrKALYb3JA25SEGhkIUdzE4Rh04rLqkDklx872T8uKpGJZlF6PVtc8B/rMn/VbmsG+fIYYLIRdJKhJJTJWGpFTorbUe5mMnKSeXFB+X7vB3uMwEw5YKRizdfDTx9Ul+HnFzw3VXVcsWiRdgzaLGBPpvNwLft9nU1b3jkQoi4SkKrJ7VOOikXdI1OBUmK51fzuwB6h051QqdsuFkrVCuuPwL83hXxsgFhHXKHTl/IPCW8/AAjGQC+HeyrcV8NuP5B4GxziOSiywnzqyWZRltdxQLxBGSOH0+spBJhUi7Kii2CHJepzmxEx6y8nezQyckFbeg4ReSiiwWC+hw8AXynFn2/J5ULEX0PyHr84iZwS2CO0/lccHLR8IOkZSI6vuhwaSGuml89IqN3AEka80Oc8Q25SMHs7AQKBanxzWSBp4zJ40nKxUiCcjGRidqMqdP91gm5bbFqFrmjDPwzyeoKufjY6u5y6myTi+C9WrRawLznm1G5k+AwckIDzY3fAeYa8XP5dxIeNyrDfWllSz4XRCbGMnKwO5CVnc0G8L+OAlcW9Q6bOrNIwQZuvkSG8ulIlNr5W344cIyNFYBstm0u2g3KBRAfsAX0Ex4NfLp9INTVPlcudD5JOp8L1cZMTtG8DnVROwSdWcQT4f4p/HdxswglZmv6wD8tSyfb3aZcUHg25bmga4F4O+RJsaittcleUB+kXNxXjX7PgWxoDqG9kyJmEeU9B9XxFUXgSODXRPXcqZ0nOfN6kOMfHU5S2nYzEqNFhPQF+nJgstOFovIEi46QKmhbuVC+h88pRVumM+C4pCAVDUCOgYXs8KZ8Qy5SUK024QYGz2dOAv/yJHmcbPYqHj8KzObix68aAZ42Hr6nOPR6MNHoIhqoAao76AHDm5y6Afka6Mwibzojd14UAvj3NeBXH5VbPd9yDvjQsvQedxixoIFy3Q3vk5b05fVXAK++NKyPvBVVLq4eAZ49Levgbd8FzOSijoIqdOTi5w8BLzoo761bcZFJhA8Qbae5loumG2borPvxRET9RMsHfvOEXJ0mqQ1q+T+2Cvzrqn5l5AkZzvppze6VScqFD71ywfMlAB2Ui+BaMmWp+UbUewLRDJ0ewtwoulBUT4Q5F3gZ6PVNZ7rLzbJdJIUDq6DEch5jIvRfS/lNjgiVC66S/eYJSbSoKmwr3v7+yyjwx1eGz50cPwndKBfPZIotkfZO7ZwnYuPwhYx6+eVHwt+3i4a7rpCkXNDviO0LommDArI+7yiHPhwqIeUL2ayGAE5lw2PTWSCjOsQNEIZcpGBzswbHiccN2hp7PSBjyJPAB1pVLmybRTT31HkR7ypyIZLNIm+fBx6qhStcTwD3VID3nJcT2r9xciHinQ9Il/JyClEo2MDRPHCUJTcjm/H3TQKffSq71pYT1w0Xh8d0ZpEXzALPmpb1k+jQ+/7vbgAAIABJREFUydQbbhap11touV7ULDLAPt4UMtskhfDFokWCVz7OfHpd5l7xhRzU38Z2cPWFJIRfULblpnupg+jtmzLJFpfWbQSqkRWV2zkJI4xkgMsK0gGNktJ1Sy64ctEmF4gP7psucD6Iulp24pk7qd0OCtyP5WwzmrmSoxX4KznsIdNvoXBm7gjYUvrgsiPbwoYbji26R9lWKxBXLigCLk25iJCLLpSLJJ8Lev/WufguonsFqi+SUF5VPzofMncFECXbjgjIBaQPkfo41ZwvqsB3MBfW98V54AiGtN86AM1GuQYck5MjyOXimmySWeSARrUg8PPVtLtqEi0OXeKfYUUbdAOVXAjlMwFgrintqD7CidcDsOnJgd0T0hudBhH+fPIW0GmcJ5v7RFBNBVsqFOo5tiU745OUDpmzQy93IDr5qZvRZQLl4mQjDL0FwpVK27mOmUWKxRzsTAZChMluBkkOOckT0PtcAIpDKl0L4FwztJnzz6qaMvsCWGTjlQfgOXfJ33ggB/zkrHTYPd8EHn6GPCdjRdNCx8iFDXyI7bI5ancmFzSRcYdOX4RRKtxzn57NR1ZCn4u3zkXLT9fUB1hHfMJ87l2yvf74gfh5TQGsucCHVsNG2SZILAnViiP3a6EQUHqkawEBcQUjFwlqHZFBVbn4fy+V5NJOIEA5HbkIjjV9eR9fOZ9MofQsAEmwRjPRSZkI+54jF4py0SYXijrR3gZCyD2aIscgn9OJuiTcH1mJL7TGM7KfrTnhGMdxKBce++mLgOdkHQCK7WRAMMpFCsbHi8hmNeQiQbnohE4hxkmJnoAEcpEw8P34PaH3+7BAA4A6WADhoHK6Ic0jvghXq56QK0iHDSB0Pv99nZSLHz0gQxcB4GDQZ3R+FDpWD0gz1kefGPUF0EWLcPLnC2kHPdcMy6faRFts0iwUcrAy0qGTHOmGQS5o1adK0zrlRbBjuoEf0CfuWWgBZ5hvTNMPr7Ug7b2XFaJtnw+AXysBn1XMLSqR+NcnhWmrdZjKSkdC7tDpQfaDM41oRAUf8FWnRiBq2huk6YorF50cFpu+nDjes8DIRXAu+ZR4gbJ0X5UpF8G5FGbrCmYW0XwPVyvIcZ3qKW/Jv6Thi/rn4Xz8WFPE/WzIf0bNPfJ3S5K0f4a1B1XR3CtQnS91hB5gadhZG+BmESdwhidlS7covSR47nx/FwD47cuBG4+GxzIWMDMz1sOv2hoMuUjBxkYNrVbcLGJh6xvAdDq/K7NIB5+Lh2qS2X61JKXQYYGUiYhZhH3OB01K701e7UQuWiJMH04rRm4W6UTiLi2EA9mhQH1QBzO6h+7ZTmalPwYnJDqzCN0yY6Gdg4QwZsdtolzur9dbcFwPAsMlFz6rGw6tcsEm3wi5YOfotoL+spIngZ9Dg5qa3ZGTvLsr4Q6pBDUXxrOmo0qKimMFmb2TyMW3ytKnacOVz5s71/Hf05FcaEhZP+GLcBXrIdn/Qo3+ADt3k5ELCntu+sDXS3L3UkBRLoLrkpQLC6F6wUNR83bnDJ26/kn96VwzXp/0nrfTuysyimLdCXfFBZS62yPqhUA88koorwQaI9aDjK3XjIZ1/VAN+PBK5+/KWsDvXiH/V/2ZnjYunWxJhbIALC8Pb2c+Qy5SUKs14XnxUSYpFLUTOpGLXpWLj6wAv39Kri7rCfJlr/jCRpgBUC1bUrQI72AUItg2iwg5wJNZhFb+ZxvSDk0gsnD1SPwZ8olqMgv85WMl4VDxS0ejG16p+K8Xhf/TdxzIAd8fSL2c/XsiDHMEpNOhqry0/HBiaLVcOK4PX4QT2iAnLl4PuqgEn30O5X8ifzpPfp1fwFc2o+85uSBTk5ojga+uNjRp0LcTLnfTJXLfjKwl82rwDJW8XtJ+jxoGOChw5aLTyrydPpudQPVJz7olQhNJy5eRL38bZIDd1JlFNN9DykXELBK8vugg8OvHOigXCUohIBVLlVyQMsVNVe+cD4ktx3+sylw/wN5RL1QFAoibRQj0e9dceR3fG+eLm8Cfne38XZNsq3s1XT6PQKT/NzcH6KWswJCLFMzOjqNQiC+bbAzGLKJbHaipYoG4Hf1EQ05crhicrfhEIx4xQGV7pB4OZNS5/uRMdIVPu2aSV7sHOYBHHDqDVTOX2mlwumpE7o3AwZ+XBSkDTmtWud8zATy5g7T+OBYfTuRi1AYuC3Z35HlI7qvKvVAA4IOPl9+n+lxws8jYWAGZnNwyiJzwagNeFQPyWeu2p1ezVfL/OykXulTR51vR93zyviQgeeqql/uvcHJxVZBdUDdZpeE506FphKOd2VDze3QL4X6bRVadMOorVi72zJNW5W3lgl+rlHXTDU1WvN0BIYHqRrmgFS537rQtuZp+5mSycqEjg/xYzCxiR8vvQ4aoeyLexu6qhOnO05SLyS/qQ92HDR1553kuOIg0UnRczg6fi2oC0eFALpw7uHLx5HHgJ2bl/9yx+ujRmW5/Rs8w5CIFhUIOth1/TLowuzR0VC7ovprPdI1NVS5WndC+Oihy4WomKppM/m4xDN2jDqSuDEm5cPxQuWhycgFosyS203pbMuSUo1+p8nX7ifD9Fbhy8RdzMmsiEK4cyDuciu744SCfzWZgBRuXkXKRFB3QD3AZWadc6EwEXLmIZFtVlKdOj/sZzKGvGOQFASRZ4AoT/X8gGyUXlGCrl0Q/MXKBYEM2jRIDxPcr4b+7H/3o62XgZQ/Gj0eUC0QnnT86LU0bQHxXUbBz6bf8zsloSnBOLursekrfrXu8GUtOSH94paJcKORdh05mEaCDcsHqhMyqjvLM11n7SKuOVgcFaJjQkSDevzi+WpLPZ8WR4zvfeE+9zROYuwQ93pls2J+eNR2OUwUrrBeeWXp0dDjOnIAhF6lYXNxEoxF3YnjhRcCHn6C5oAM6+lxozCKfeIqU+rsxi5S9UDnYzorLFeHqodM5SRMV/146R40uaPtciNDngshFO4mWRhqlSadgR3OFAP3NlU+dgftZcFLBXxeDFTut8GglypULIoPlch2NlgtfhFK2LvKiXyDe8ry79YmxdA6d3GyQpFw4frIp8J2PBX7/ivD9aEaG7wKy3lTl4gWzMkMq3x2W7r1VRZBD7WOctArE2+/RQvx8BOe/+Sxw68L2ywKESpzuOCcJvFwfXAr9UEih1CUq45EvD9bCY0nkgvtQAHLTt4vZdvXHCsCLDynKBSsz2e0Jlxej9+Pgx1RyceNR4M8eE33WRIruV/xvOPlUH+P/eDDciVkgDNvtFQKhs/Z2oOvabTVDKd99VbmTad6S0Us5S99egKhT82hGmn8PZMMx6RmT8XEKiEY2nj6d4sTRRxhykQLP8yE0iUfGM/GBKQ1bNYt8z7icWLsiFyzp1HZWXKsOcO03w1hrHTopFwAjF8F7NbqAFAqaeD0hB0/yiKb7JyoXdrzBJkm12wG3XdK9VTt17PvBlAv2fLhy4fui7eRFzyRpy+R+gOrkZEP638R8LjQro3ZGR5VcKMpFksnimtGoOYpP8mq9ZSzpoDlmR9sT3Xs7ZhHd9wJRwrfhRsMcgbgJjf/udTdUA7cL7pCoHuckgZ/CM7iqKaHpWkD+FuobPEcCVzgj5CJ4NlMBI//ok8Lr+XMjxU5HCo8Vw/eU4CxNuRhVVgAHsjKyRFUuVpz41gacXKjteK4JrAaft/zkDLNbheMD75hPPy8JWuUiQY0gU8jRglwgcp8LFVxly1nSDDiTYBbJKvVG5zjOAAceBYZcpODIkXDL9V6RtaTj4NWaneuo3fB+mrdDB0IgOkipPhecFGzHoVPN9qeDzjbMv4rvlwJ0Nov4kL+h4YfXkTKikgu+lbq6M2M/dxDmvgD0SvWiWxHQe9tiDqlsNUa/a3JyBNlcFr6QE8d4ZjhmESCMluDoqFwg2aHTEckmCx66CEQnnBFNtAg5DnK0M6z22ywS/P8NjTKnhr2qik2v6cA9TXsGok6c3EQCRHfN1ZILdozy6pRc+dxWHZlpld+LzqVHQ5E3BStOqOl/25LkgT8eC1LdIPCMuCqKdthvR5VnnLHkvegnUZ9f1zj3bnQwi3DznZo8rBc4Avir891HdDX9qCOzbgwVyitHzgqJQyflgu8KnLNkdk6uXFC9WYgrFzSOXXXVwdTf0y8YcjFEZCClxMuL8c90CW5yVtQGFyEXGrMIYTvKhZqhUAd1i2e1TA2WtAiIS/9EKoiZN3w5yT6gbFLUyedCbbD9NIu0CQRCSVitF51y0jaLICq98zqhz6qejKIYqFlEJRcJyoXW50IkhxW3/GRVIavUDZ+sKJ03gUclEJ41HTrP9tMswifxO0rxZ6GSCzXs8TsJzvUfW42H0OqgJlNqH2ffoZL2mh9P453kc0GTUt0Hfu6Q7Ft8h1mdWYTIBW3wB2jIBeRkpioXR3kuC1oxa2aRy4oyQguIKxdZK7pIoBw5usghrvCpdcfJRVN5Xr2gJeRmiv++1t35fzEHvOT+8H0ns4iO/OQZuchayQs8rlzQJnEHcuEYyBP+qUpUPxdh3cKQixQsLGyg0Wiln9gFqNMe1GTx1GXopKQof3ga+MBidIBR/Sp4J9xOJEI3ykWaWcRXXtXVeSsYRNtpsTWrd04+CLQC+u+H405lfVUu6DUY/LicqCoY/BqbSZl8FUrkolSqo9l02+RiNtf/cOF7q8CL7wvLQKikKBf/zwPAtyrRia6TWSRp4k9VLpRzMwgnpRsuBm59XLijY7+VC/oN99fiZhGVXKht+POalOcA8Odz+nToKsjRN3ac9SXVLEL7DdFnQLLPhbpxlQqtWYSUiw7kgjaNU5WLi7lyEXyYRDjbToQa5YIf6qRctDTjC0FLLnpULn7podBZe71LkxhF6RG6NYvQuJazo8pFEiJmETsgF0y54An/dGQeAE6cYHvZDxiGXKQgl8u0t1zvFW9/LPDnVyeQi+DVYq/UKO4oy4QqfJC6V9nVkNtZOdG45uvS4SsNjmYQU5Hm0EmgjqQSoHYoanBcp7DUfeBzyqBNg+aTx+NmkUH4XJBsSwoG/54YuQgGSr4BET0jclbMZOQSkMwik9n+e7WvOWE+AF4naqZAKiMgB7rPb0hbd1u5QAeHzjSzCHsfUS4yygoYUnLne1JcUYzajrcLdZLkk3hD4/CnrqrVMN2T9WjOFX5eN3WoM/PR7rJ851Ju6mj5cZlfJfH0XrXDq9ApF1cWAfFsmS4/0SyCwCzCjv/zE4HXsGitto9MUpsIXosacsmLShl+daZCPq6pdcfbab+Ui8+sh86xurGw6QO3LYfRPIAkF/NNSdKTyqAzi0wyQkEmj05O/y88CDwUpND/wyulajGbC1VAuvQNV0bT53PHdF1ahUHBkIsUHDw42d5yvV8gOykP3YvJ76zT1/24SeKrJblXx2+ckO9pMPquEbmiolVVzY+Hd+mgywSoQqtcaM6jc9SYdScY3MmerItqWWoBbzgdPVZkjJwa7A0XB3J7cnG3DO60Sc6cKqnQOXR2Ui5WHeBX54tw7ExbuZjIdFaItgMf4USSRCYIfDdKnl+Eru2kXEwmPPAMtqZcHGQ701L9tqMZeiAX6r4wfBJv+nqfi8uKwA8H4f+qcuEjOpGAHe9mlaxu7AbIvBeqcvH5TeDNc+EE2/RlxMJXNd8toCcXukmeFDJHxIk5IOvgZw8B/01JImcHEx6/5XgmdOIE4hsGqnjWtHwtKGaxDKJl0TlxE7pVLrpRXrtBxZPkge6vYs2VCiHf2K/sysXee84H5dRcR2XnH1HdcbNIp8SMNrtG7U+8Dp41HW0X3Exy7Nhs8hf0GYZcpKDZdOD7/V1nTgZyI8Utj2VCNYPaCJfjmxpyUfWkt/RfBw2aCMRzZmS+iftqMva95CZ7H3M4XXTObpWLs8241zoQxqGXgxW9zmGKCAfvLAU2+dDhH52Rq84rNc6x24WqXHBHKFs5h2AHEj89fz5Rl13g0Trwrnmg6oq2kycN0P1MZ+wL+TwF4oQvZhZhxIHaFS8K3x9E9bmYzurzHXRULlSHTkvuA5NTyIUq724H6gr89afkb/iRmXCzPI7RDHAkDzw56Iu6BGO6vXp6US4+vRGSk5++V35+TwX40HLoGNj0JTHVbfvus98RIRddKhccWQt47jTwvWyh8wdXAn/+GFlHT1VCv6nOJrPSRLL2A8mp2Wl8I3LxgWtklAhfZQNRMkugNnGWJdPrxufihd+Wz+1t54CXPqAvVydUfeD+anh/Fe1+zo6pu5nqurXQtKsRRiheFPhZpqUroPrm49BERoZ1E9Q6yyAcx2q1/pj4u4EhFylYXa2g2dQYA3vAdDaQioP3rzwqd48E2Eo5+IwakUouqGM1RagoTGWB7w4ali+Ap39TOkl1Qy66US4ernf2uSC8dS7cM0Q9l1J+A3Ki5YMa/35uP44oF0zRuSgHvLiPzs9cnVA3b0rKoEordocNLHzV+0gwOdQcARHUFeXt6KfbBTmM6lbnSem/SbnwEK1XTi500SJEjngd8WdVtKMEoagoTC+/WJpCaCAlvwe+UdZ2oW46d6Iuf/+BnD4Pwogd3XdGt4/FHTpyge5Wyep5AuHW9j7CDKeOkET09wLVrlNCqCSziE65qLCJT2dC/IUjMnstx4gtSdfTxoFPPiX6GZELUp5mEsgmEPaZfNCXjhWA110uo+V4URt+fNyhbK38GSQpF3eUQyWh4sn2W/X0e8d0AimL/P4qdP2iqpCLTg6d/JY0DuSscOv0tP2nxux4NMjjRoHPPzV8rypJ3Odifl5JsTxAGHKRgtHRgrSZ9xFTWdmBqQ1EzCP0qthCOUvn7yl9NiAdfGjbcZpsgDi5ONOI+zu0ZcUO5b6jnK5c0G9abOlzOfgImX7Dl/ZfHUbYoEmdkO+/krOAX7w4KtP2Cq5O0IQTS6KlXmPFfS5edF/4+enAXu8GGTpdEU4C/VYuAL1fQZJyQWTHE9HkPp18LjJsIOT+Cjxa5JJCdJD8sQPA3z8+fP+aS2UCJ9Uskgnu2WmTsjREyIUlN8FyhfwOygrLcSgnd22ly1SzCBASRA6uUHWCGi3yaF2mjqf+SX2h5cuyvivIr9DU1KPunmnKBSmBH1/Tk4BXHI2Ti07g5CJtVKSikeNoxgJeeYk0Q3GzCCezPzAlv6OgKayabojGwG+VQ5MEELbfrfavuhdfwKng/Vw9zxXS92lJIw4I5RUI2z3fe4ee7xXFKGEAQjPtaGZr5mDuczE11UepNwXD8+4YAl5z3WtGnDHnp47fevw2OvbaG26YqHojz7csq5Wr5j7+5tvevKWdW6anR9NP2iKuGZUTI3lHcxYaM4sEr7SNNGHdlaFSLT8cQL53IpxsudSt+lw8407gvY8Dnn8gPJbm0LniyFWgGkar8oexjFw9/PoJOZCq8EXULKLbwRSIKxfcJGJBDla/eER/7XbB/V3ydhiOCiDZLIK4z8XXmJ2ckjA5sNq2ZfrN/TS2cafFmFmkk3KBaPIvQLYpagcfYzkTmr587kRgx2yAovX4c3nuNPBY1m2ms/r9XlSzyFPGgTddJXep3S5UcuEEBLxohxlibYS/92VHgF85Fvou6UhDkg29m/qjfuiJ0Dm77MkJhfcFdQHQEnp5HYjudJvm0AnI37vk9GclSYrUT8wmLwwIbSdCOx7BwIvKlYvLisCdFb0Kk6RcqO2dSORWubu6629H5UJTLlcAbzwrTVwq2tEi7J7U7nPMJ4XqcCSIBuGgRzKeiY9DncAXSQcPTnY+uY8YinLx4ue/+Hde/BMv+m1+7CU/9aJnv/gnXvQP1113XV+o1Cv/xyuPOWPNP4YlXkPHbrzxxlzNH/kigOsAPM8Zbf7LVu9bKtX7ntXs8WPAn1wVn7iAuFmEViOqWWSpBbw9kAJpgHrGZDjYqCoHR90PU4UTyCySJPWSNJymXNDg/rWEnX19hHKlD334HBANEXzMiEyFTqAdaQ/01882ok5QGHCaWaStXDCfCy7HUux+w5NmEYebRQakXKj3PdkAXvZA/Nwknws+ef01S3/tCflsfv2YfM8nNh5Z87OHgF87ll5mlVz88Izc3bQXqOQCkM+8aIcmo++fkmmu+TlUdh1p0Mrc3SoXwSs9zwdr0mmTIqeorcTIhd/BLMLGgllG2pKiNqZz8v79iKyyIE0lv3qpDA3vBG7m+vATgMczwhkjF8GPHQ1UDt2iI8nnQm3vRI63St7VUNg05eLvFoHfOxWWi8qiTZqmvAKKcqEo1bbyDJ5/QJqBAdnvtlKXPBng6urwdnYbCrmwbH8DsP6/F7zgBe3m5fu4EbAuuu222/qyB6ztW28H7GfwY3kn/7OwcPqW991y3fFbj98Ey7ro5pfefOVW7lupNOC6g0mnSO1DtzkQZ/2AvhMRaID6/qlwVanayjl05CJNuaCNkTzlmLoLIQ1wqwkx4r6IRonQRPsjgbf+uMaeP5kNvfmBULnoN04/E/ihaWYWgcahE9GBkSRHem4VJq2O2OGA1fRDr/iBmEWCVx25qHhy+2YCT5DV3ntDM3AD8fTXWSvMR0EqGZFayg743V3K7NS2kwjmdqD6XAAhuaAV7eE8cJWyLwb1wX4rF2ooadULbfueYLuZ6pyfk8wiCPvhQU1SK04ybMhcCI7fedO5reBHZuIhvDq0F0i2jGDg5i4+5p1rhs+SJH+diSdRudCoPrpswmlY2wK58ITMm/LlUpRAquZrgkDcubetXLDJX93XiOaBy4thf3nkGeG+Pd2AfMgAYH29i8xvfcJQyEXL8f4BQH7EG3k+AFz/7OuLsKwXWBB/06/vOP6+W14gfPErkYMCT4Cw7g7fWw9YWf97tnLfqalR5HKDsR7pdilUQ1HzjFwkTfxELg5kQ3s4P5eTi985KQeyJOUi6TvU7dQB4C/Py/A5jjRnvJIXlR95am8gHIC4cqESie3sSNstyEGTfC50KcG/i63A6Bx6xvxZT2ZDcuEg9LkYiFmkg3Khfhf9Tw62OgmZfoc64GbYioqI4KsvlSqSDakyzXTZXYpK3fcDnZSLlh8mAqN6pXO4z8UglQsKNRUI98OgMnLwz1QIhHXMc+bQWDGiEPOcJSfcfuaE6QZ8h04V/NCDbL4bCZSLn7ko7nuzVeViq9x9zZF7fFCK805mER9ykVZyu1MuhAAeqkcj5DqZRVTn5l76yA9OAX98lfz/0KF9Zhb5yCc+sgQLn4DAiwCgNlL7cQhks6LwoYF+sRCHLYhT9NayxHkAMUv9wsLGZXNzq22F4ty5tbZXbT6fxcLCOlZW5BK9Wm1gbm4VpZIUXNbWKpibW23vnLqwsIG5uVUIIeD7AnNzq1hclMvGRsPB3Nwq1tdlrJPTkiO305TXrqyUcXGrissKcpI7d24NIvis5QmsbehZZ8mVjXP+3CryrrznZjmM4WoF5VhY2GintJ1br2NtTRoHS6U6Flfl/56Q5Tg7t4r/XPZR96WH8WpwPx/A3NwqlpdLcAVwXtnkJKPZ5I2D2/MBoFmRz5E6z5iQdTCbAx6+poLZjA948tj8/DrOnVuTYaK+3y4HANRqTczNrWJzUz6jjY0q5uZWUa9L76qlpU3Mza0GG9HJ33D+vEwG0my6mJtbxdpaBbYFuE0HlucBvt/u9Avn19FqubAt4Kk5ec9vXQt8V95Hs97CBxfiU9BYBlgPRpOmLweYasNFo1RrP2tZDtnWWi1ZjtWgLspl2dbKwbNfXZVtrRW0m/PnZVsDADcY4ZbWKlqnXNeTbaBWa7UHw7mFzXY5qkqIWq3pYXGl3Da5EbIW0CrL8o9Y8kaldfmsLQDXjkfbfL3ewtzcKjY2ZJvf3KwF5Wi263x9cV3b9xxHPg/qe5UKPY9o32s2w77nr5dw7YR0UhRBX3AFkPU91F0f5VpLptRvOshYQLMmPW4bwavnC61ywctRrTbRdDzUg+9dD36/bgygevnwqRoEgApzgOL11FK+tKkpB6FcabYn1PzGBqYy8o0T/IYim7kzwm+T30nhYmGB2rzTbvOAHAPm5lZRrcq2trJSxtzcKhxHPkPqewDgul7HvkfPoxVkNm5U5L19P+x7G+tKFsAAI54Dy/dxmdWKZfb0g3LMzQXlEMBmpYnNSiNy3ltPufAALDZ8fOHEBq69Q+A/1qJjABAdA1otF48uVXBJxsPhQA1aK9VRqVDfk8+j1pS1Vm84WC41UWZKZa3hyjwxGna/UarjS6vRzlQI+k+z0sDqinyWtpBl8wI7UduPJqiHsM3HxwDPk2Pi0lK07002qvjhGdn3SqUaakE7WV4uQc578rvOnVvD6mq5b+xjeA6dwvob2OJd1z/7+mLdql4H4KN/+x9/m2CZ79dX4h5AtK24PnAg4+Hf1PNmZsYXLAtXU1QId3rZ3KxienoMxaJcIhSLeRw6lG1HkExOjmB8vIhsVi7jZmfHIQRgWRYsCzh0aApWIFHk81kcOjTVzvhZyMlrRoqyGqamRvHaSYHynLTnHTw4iYm1DFAF7qlZOJ+V7imXFmSOCwI5iB06NIVaILDlR8I8vR6soBxA7Yw8lh0pYHJSNu6xsQL+T3tvHiXJVd/5fm9sudVevbdarZYQkpEwEkKIbbDQPMywCDNjhDAegxC2sOiWjxkb/Dyex9MM9tgG27JxN3Me8wYk7Dc2yPazjceAj415gMdsBgGDddjU3Wqpu6uqq2vPPSLeHzd+GTduRmRkVWZFZlb9Puf0qc7MyIibcbdf/NbiOIB5OWELE0VYpQJe+SUDT7wAOLxnHNaq/L2eH/6mxiVgqRl9LMltMh/37HgOWAql+D15A9+ty0l11WwB7zkKXDcmP9yzR+rbxQ8AxxSReyv7ZbLVL2NjBRSLuVa/TE+Pwfd9GIbR6hfCccxWv5gCyDkWCnY0XHj/nnHYtgkTwEtnLXx8RWqKHMtAIW+jUm//3QUDKHvyDBRpISwTMxNGDTfiAAAgAElEQVR5YFEulmo7bNuMjI9i0UEuF461yckCxsfzsO1wrBF+8CxYGCtiNW5TMuT9siyztamNT48B5+Qm5+RsQFnvfdOAPVZse/ozBbBnQo6tiWDlm57MY99MDpd84NaJaL/kcnbwm6hf8igUHFiW2erzw3vHETf3LCt6PwoFB47Tee7dOQP8uCMFuVv+yQRq0iRQsg24QsBwbFgNIJ+zkDOAQkHO62JB7ii+ELGai2g7bBimgGHJdoyP51Eq5ZR2jMP3fQgh4AfD4q1PFfHGq4Gq8jwX1S4K7LGl47SsjNneDiJXcFob2kuuGMO/LAN/dgmYKMrfUDQBBOYs2zBgCinUv3av0Rozth1di0qlHPJ5u3Vvp6aK8LxC6zfR3ANkxtlOc298vIBSKYeGEcy9sRz27bUhRDj3Jpbi14mjJQu2KVDM2W1Oi54PfAYTmHGAK4L7Z+UcOPnoKG2aJpo+8FjZwJ80JnDJFSi70TUAaJ97zlgRYzXRSvLnFHIoBB6Bk5NFjI8X8J11+V3DtlC3gNVqaIo2bHldLyZbWbGUw2OVqLSUD37g1JiD2algHAaqNzv4mzeBF4z7eN3+6JiPWwMMw0ide6urlVYhzqmpEnzfhxm0Y+/eCbiuFS/1bYHMhIuKWfmLgpf/UKW0/jrfF3f6Aj+x3dcUvvgKBH4VwHvvf9P90wBudyF+UT8ul7Mij22OE96Wet1FqWS0JplpGpHQVHqf0E0o6rkMQ7S9BgAzGAw0YCgCwXEsBHIHvlMGvhNsIHvsqHCx4UrVmuNYsCFD/9QB3vDCdrTCQw0DVnBu0zRaRr+f/S7wketNXBeo/l1ffpdkCE/5TXGqx27Vd+SxXwwM46Q6nQo2LFvIe/tzV4bfoeteXQDGrPZ7qb62LDXWI7y3+rkAKQjS60euB4qGwB/OA2OWVPH/4DZgX96CEDLh0nXj8rymkKYtyxCxCcHyBjCnPKz4vhT0isFvpHsb1w4gfaw5joVzNWDWRWsT8w0DbkxaFs8H/vV3LPzcYUWNbJqtdug68yeqAs99rN2wbgmgFNzLVlZBy4TjAEZd5i3p1C/qb6KxMp6zWibCXu6HOveECOeVDyBnCOnHIARsQ/ZZ3kBr4bWMsE/iNBfR32TI+x005X1Pm5hvAL/7DGqHGfkuQaHj6mui4QM3FaVvzLTVOVpECAEXcvw5jgWLfFeCDWlcdfIMBOSaJwVhO5hvnfoFiB9r6vW7mnvBby3YBhzFEcRxLDiBOYfGAM2fIwWB//lcYK8j2oULAH9wycTzxoFXQd6/z68J/P1q9EAfojXGhWmg5sn7mbYGXPaETBlP5zEMmiKt+9EMv4BPLUvzTsvMCNEqwqYjDANf1R6lKSJt2jGQC7QlY2Z0T3AE8PJZgdtnRKQd8b8hfe7Vas3WvpNwP/rmYJiJWQQAPvGJT5Thiz/zffF+AJWFjYVPb/c158pzXwT8uQfuOf5l0zEeN3w8dOqjpxbTvxmyb99kS2vRb2hKJGV9BOLtlXpuh4oX2uYEpPChjhDVnkvVOPURRJPxiQrwjfVQCKH34woDxSXn6ja7Yj74DaT6pEXmmcGTQiefiv91a+hU2G8OONJOTcmiDCGFGdp7b1OSP6l+GHHCRcHQqjoimkSrHw6dL3sM+MyyZveNOc6DzHa4qhRZUutX6Nashg+cjWqbAcjfShoHGodqZNPNY+3fSWI7fC5U9HTk5FBHOTnUuUXCTZLPxcMXo74Bqs/F0/X4NN30XaLhR4sK6sIFzZ2khF/qOSm0FYg6TgJRPwxK5e1jc+GL/aBTUjR666YxWTqc2GPLcFQ9ZTwg78fTtehYX2y0Ox3TPAPkfap57Q6zcbz3rLxfZIro5NBZ88JEgWp7Ojl0/rNm1TYh+3xSKT5Gc0r1ueslqZzO0aN70g/qE5nmufDh/6EA3gzf/63Pfvaz/U17CeDUR0/9I4AX0etHH33UBfDGE/eeOFREee19H/7wpuNwLGv75C8aM/oVyFMYiA8vG9OEi4YfXTgMJDt0ll2Zc0A3C6qOSmUvdDyj4/QS0Pp5iW4nQt6Q1yCVYi5YTF4QaMW3y2GzW2zRXs0RkLHnVKBIzegZt6AUjPbY+bqvRIv00L5Xfwv4D0fDp2E6189+F/j3R9uPp4yQahhjy/N9E22xRJjgTE9FvNnQ4JyQc6CXKqidUE9rG/J3kkOnKiSpxyZFizz0FPDLVwJfWAmyfiIaoXO+Jje+w7nod9V5drkhBXdCHTOuH86dSSvapzp/fkmWV9eFXPq+Llzo2X6zQo94U1HzyKgOqKoTp95eH9JsRCG8SdFzPqKZVmvBHFlqJqevB6ICG9DZobMVTu9HnXaTHDrn62EhQ/X3OUL+ZroFFIVDrx3RWzp8HV1bsZ1kKlx4hnfG9AzfNf0PZXndkx8+eX6r371wYRnT08WWnaqftISLOM1Fh4mpay4afnvESVwoqhtMstfuSRYugCB9rqbh0Ks06t8hut0oaGEfC9S2jpDfpXTgugCVNbaIz/6pVvOkj69OyNSSN+KjAKhPe8lz8fU1WbGz6Ue1Jt+rxFeXVAWLlnCh5DbptimWCIUCquS41U0rb8h7sV17nl7EjBZ+eiqOCBcpmgt6Ij1dlRk7VSGEsuR+Y12aNNQwTXW+rDTl5jhlyfwn+vxRoz3UKARi0vAxZgtcqIc5R4BwPNL39ylLFWkugM1ldewHZDmKWxNeNiUFMco4SajJ1v636Wh2VA9BMkEfeNcPkq+rhnx6kPPj6+tS8F55SRhRp+P60ful9s8/b8jMqjSf1Vw93USLPKVV1s0bYb6eSSUpFs0pGrr91lycPj2PY8f29e+EHcjELHL77bdbd911V8FyjV+EwCf/9K/+9HtZXHfYaYWd6u8r78WZRfSNt+511lzQ/ynl97jZPgF04WKrmotuy2XTwv7MIvDxG8LcEsfy8slrX/9luU1hG8mpxfUnRjUHByEQn79BTaLVi+ai6QMLjXbNBQD81wvtx9MTlotQYKT+++Tl7k00tPg6RnwRpc2QM/qb40JHPbUVCBcNL9RcqIJ7muaiEUQ5VdxQAFE1Fw1fboQLMSp6Sq9N/hakWWhqA4A2kYIhN6PvaGr0Q5aL18yGbdGz+JLG85AydyhfC92DrKGn86TPDIQaQoFo1V0KnyRIaPD8zmYOMhsBYeI0KkZWSxjnfvA9tcKouiZ+Zhn4nafSNRdJZpFL2rg4HEQEfuQ6mReG+kg3i+TE9mn2tptMmr03v/casYGyL3CTgPFLWVyzXxw8OLUtWgsgxecieO+HSrIOg0qcWUTVfhgiXrigCVkwutBcKJOn4oWSd6rmYpPCxT4b+PG9waQO3juUi6p2B8HzxpP9OnThIm7RNhIWhbovf6eB9gRkKmUX+LsONYZU4eI/Pxntl8di0g/TE9a31kNfCtJGPb7RWXNxRKm9Qb/1FTNhRdqtPhHfNgGcfsEWv9wFus8FPVWSgKQKNnSoh/Z7oWouKl4ogOiai1jhwgeuDQp1kXBB16VNadYO2wiE5rQ57Vx5x4IB2W81PxSOVCHDEtFigJZoF0KyxOywOVI/FE35218zG+0zXWtL/UcajKTfo2ou6IGK1i/KH/J7Wn4eOl71uTgdzJMLdTlXFxrS/AWEJg7VAfira8CfLMSvi+q4+M7zpQBoCKlF3mPH+FwEx/7dTcDdfSzOmJXWAshIuLjhBTd8z7DMwx//60dv+9j/+Nj/yuKa/aLRaMLrZypFhUSzCMLB9tYDwK8cjX5e0nqt4UcXeANR4aGlfQj+5gP78x/NA388L99r+mF7an44KV0AF2rAtzai5wLaa5YA0YXEFDLjZRy0wKoVT0kwedtBqTYdJP/xKpnGOo6uhAvEm7TqXrio/vsn2j8/VwN+7nvAE1XgR7/R/jnhIkwK5ftI1YLQE9b7zwF/cUm+R/0XV+xMZZ8jK1kC4W/9ixtlDRFg65uWJeJrjvQL9fbnjKBqrK84dMaZRWLuJW1WVKeEtBY0F6g2xvcr7UWrKKrDMuScEmgfF88PNBuONifaNylf5qzw5OZG/ko/Oh3+3pwRdZCMmEUGJFzEaV+BUPApmXKD/ctnRz/XH1Q8yN/u+XItm7Xj556PUDtHGlgqEFfzgM8uA//hdDSRIPWlKYCf3C8Fna+vyz74wop06P3mOvD3Mi1GS1AkjYcq0DX99o1V1VzM2kGlYO2BEAgLWtLrcbO/mgvKCZMFmQgXDz74oPfHf/nHW/Z7GCQLC2vb1iGt8LsYzYXaMfrgatNceN1pLkgNTpqLTy7KifPlVeB3nwLumJYDvuqFk8f1ox7umzGLOAK4IeHpXxcuDOW7Jw7L+ivDiu5zQa8trQ/iFtWGHy6qcQLBXB34bxc7O/QB4RMc/U2Tf/2YY0hFXPM7ay5sAdw6Ef6fKJnAD4/1tzJtPzG0sQjIJ0tbyKigG5Ux1jKLIMYsgrDSZkRzEXxeceUcTNJc0NiuelG1O2Fp68DN48BBp114b9bdVgj3kiJcUISOKYAfLsn1QdU0DcqhE5CRXTcmzGUS8kpGvCBuCuAG5buq5qLuyXw/dA+o0jQQ1VzQ2kWahpoP/MOK1Ax9bT16bmrTa2blw03ZBb69EY1GUatJU781vGiRMTXFP6GGIJNJTj1E7aP3Hts+P6Rz5y6nH9QnRtSakx25nNWKC+43dPN1ByNVcwFEN6kXTgAvmoweX9dUhAIJmgsv9AVwfZna2fXlRFtqSn+H541L6V4VLipefD2MNIdOx0hOOZwTUZWpahYZwBq4KZI0F6pjmkD8E8eGK3+7gXiBoBFsXOr9j4Nsz00//mlbJ+4YcgRdd6UjKLVbxxbJIcLfeF579cZhIU5AJ83R3fuAk9cqx3ahuSDhgqJrVLNI05cOf3E+F5SuvhpcW/f+1x0yx814Z2DTEK0HksVGuG6oZg892ipiFmm7Q9vPVfnkJ2+a/0UzORz54evD/zf8UEhu+MA9B8KcHvceAP5FoElTtUp6Ybi6F4771TjNRfCa7t//eyla0KyiOEuTYNP0ow+ILqICpD6nSLhQ12zVb+bl08CbUorCbZViMTtnth1Vcn07mJ3dvpWTxta4NutVnwsgOvFeMQO8RBMu4qJFYn0uAonaFIFw0ZCORaq98ZpCu3BB4avzdTm5/aDtaaGojkh2IstrznydHL+GjSM54Ku3xAgXBkDpDoyE37Puyjh+yj2g0wg0FvSE5CF+U6CCY00vXiuhE/dETots3Qv9MGR2yOhxtiIkDjpEeDPEaS6A+NA++jguiZYPRXPhBlonRQihhFcNX2qenqjIQlN0HGkrutVcUMEqXXjPOWZrni82wnVDLXb1QkW4UMNu6bzDhCXkGlDqIFyob9eUOVH3gjBOxamYjvUR3rsfaGUxa4pwoVYvVtdA9e/7z4XXAKKai6IpBQ+1XhCdi/xfSIuhRnRZAnjf1WFIN6A49wtpYnn+NpUAOXQoxvt8m2DNRQobG7VW7vV+Q08hE7pwgWThggr7qDRSokXU0ENabFzIcDg1dMoSUsUaES4gVYuqAKSGXunVESNmEaN9IaUokJzR7q3fbaTJoMkZYQQAEG7+6r0wEL8R54zAUzzBLEJJeej+xwkNPqIqYjVyIYm4J/JqzJfi2jzoiIOtkmRaTHLABeSG/P/MtX9e82QV4Iric6HOA+IHFeCaL4UaDNcPx8JPf0f+1a/fKlpFWrzgPV3I81yv1c7LzXbhQtVcqIKvrmkbFlrChZHsl6Fm0iafMTfwubBFWBXWFFHtE615enXmuh+eRxUu6L+6cFF2pUMnoQoXJAzqmoumH2qr1OMIEzJ8/aATfQ/Y/g2ZamJlAQsXKayslFvFe/qNgNxsdLWh7nMRES6CPAvqeI3Nc6G8TtJckCNfQxEu8kaYdAYIokXcqB2X5lfDb3fIi5hFYhbS64vK79bUgv1MFpMlquaC0LVPRNEI4/9pc3rvWelcC7SbReKEBj36p5sKnU2/PRyuk3Bxx3T0vVHUXKj3P6K5iBMugr9LTeBXTrd/Xvekv8aGG97vLwXRPqpwQflhaE6RWcRW7p+uMqd2ks9AkubCc93WHNxww7nW0lwIGWkFhGvGoKNFOkHrzY/OAL9xdfwxSZqLRrCWUVSZqrn42jrwlYRIrIoXOnmuJTh0qn/jvq8Lg7qPBTnH073X1/e4c+vVsLeL+fltLecVYUSX8+yYmChsW1azG0vtJhGgXXOhmg9oAfqb54Tv6T4XbZqL4G9LTQoZMXC6ikgufEvIRelcNbQzkkNnUbERej5w+2PAd8tRlSGgmUViNBdFI3yaUj+LUxePCnE+F0maC1vZQGhvf2xdppa+7WvA75wLzCJKKLCOnr7bR7rmwkd7ivJOwsV1gY/FM4vAj0yNqOZCG4v098pc8rF6FkWCnGefroeai6+tAf+4GvWLoXuqCn4Gov2uO/7SvW05NwdzlASUA8ETrm2GZpGyF86XOJ+KCUWroTsgDwskXFyVjwqzKmofqiUIyCxCGkRTOfZyo11jQWy4YYbdNRf460UZOfLir4dtUv/qVNyooAjIvoiYRbxQE/u/Xwn8+Y3Rc8QJF6rPxXaiFjrbbli4SEGtuthv/s2eMMRPpc3nQvk/CRdqx7WZRUR0wVOfdB3t3KpnNWVf/NaGTGUMSOGj6oUaE0DGfNN3dM2Fqn2I01yUzHCBVSV6A6Pjc6FDv1ENEVb7UBWabGURIcGBnGq/uhr6PpCXe5xDZ1tis+BJ+jlj0VTKaXQSLqhvPngt8K4j7XkuRoGIWSRo914beNVs8rFxfkQqC0F2TKrF8mdaXgO6p38WhPt6iAoUulBtIFT9tzQXiGouyP5uW0ZrA92I2eTUeU1ptOlhQv98GNBTsMeR6HPhy7XmTfvCc3Uz9CtemAem6QNv+46sC0NavU7h5QCwomiMbKUv1LXLg+zTohlqMIikPqC2b7fmYno6uzA8Fi5SWF4uo17fHrOIYwA/f0X7+wY6mEWUpxuizSyCeJ8L1SyifqYKF5TQh+LCyXxiKwvkD6rhd6Zt4PYp4OvPC36Tcu73X9Nu6qD02ZbYeWaRd10ZvqdqLlShQ1Vh097u+jKVt4fwvlMSsx9UgZkvAB94CnjlN+V7bYXHgn9X5aNOYmlUvPb029Q+GnPPGQvbC4yWdukPfkhGQAHtOSR0uv1Z5DxLfUcZIAE5tkm4+HKgfSafi2P5UMiwNSGUXupmEQpFvS14OnebLq7IyePLbvtTtromTFkyVPPa4vD7XHRCKH/VEgQN7UFJ9bnQoTErIAVymj+//7R0wN1wQ41VnOZixg7nQ13RGKlzQXdIFZBF2VTfC/28KllpLhYW2CwyNJTLNbju9jh0AsDrY7KvvWgS+JmD4Wt14Kp5IYi2wmUi3aGTIPslIN9/9aw8Zl0RLh5bD1V89F5LuLBk+6aDJyVVGzFptU8mMq/omosXTwJvP4iRhH7jYcVBS9VcFA15sygTISA/o6df1w9rKNAiNxc4kS01pInqmxvSiQ9o97mgDc/A5lTfVU8KJPkY4SenLXajaBYZM8ONnATZpM1sM0+MqjMnmUsAmWNCDyEmn4tP/bDMRmtCM4so187rwkVwjlsngP2OdOg8cViGX2544W+LM3tMWsB9h4BfOzbcwkWapk2tDqprLtQHpU6aCyqod8CJrotlV84dtXJxnObi1TNRU1qccNGWqwgymVm3mgtTSL+T2W3OTLyywg6dQ8Ps7Bhyue2L2I0bbDePAW9QskMWDOldfG1BagqAGM2FtmDFmkVoQirXcv0wq6CqEldLrn92WU6kdxyWx6imlLcdlPkC4kwAB5z2J13SXNia5kL/zaOEE/TPuDJMVM1FIbg5U5ZmFgmOdQF8N5jzerriFTd83dA2LvVJjjaxzWwglHchFydcKBsdEKruR0m4AMKxTr8nrtItEL8QCgB/+5z291XNheeHPk0TVihc/M0S8JtPSgGSzt0SqrUHAXpJWidTyHY3femX9YIJYMYC8jl5wIQpfQrUp+yv3hKtyPrQM4CfPhieT70Xw8JhRwpNnaB754ioz8W6KzWCLZMPkgVE2rD3KcKFgTAUXK1cHKe5cIzoHGkJF8p7bZoLkSBcxDcRAsAvXRmtCrsdZBmKynkuUsjlBlzkAnLA/eC26HvqWK570UGbpLmI9bmAzIkPRCVyEi7OVOW/545J7cSPTEWdQA8HqaGXm/JJiZ5EBGSolSWkQPH8cZk691heJr9xNQ/rUWYq6B8KbSMVbWujDjpH9UGhHAiAvBe6s+XTgcC3HGgrqoo6ty1aBIrmYpPChR0jXAi0CxejqLkAokKvQFQAVInbmGwjzH6pomou1LkwoZhFNlwZjkr2d2pLnK+RbhYhbUbDlw7f44GfkmnIAyYtGR6pCu63aOl4yBwEyGvutWV+lWHiQ9elH6NqLkiYrnrS94VCuoEUzYUl72HRCPsqb4ZRIxvK3NOTaJFjpqrx0n0u1Pda7YbUOP3TenyyrEGRZRKtHbK8bx9zcyuoVrPLx94taZoL2qzI/6LqSaclPU+G64dhW3Gaiy8G3vCqt7tqFqFJNWUB/9czw0l43yG5QVlCLoav2yPfv7YA/NY17U9wOwGaTONm1ERhebIzHCO8jxHNRYwTIS18JFzUvFBN3hYt0oPmIk64UBOA6Y5moypckKkhLjoLiPe5cES80OHqmgsf+K/XyVTVagZHSsilai70ZHGGCIUP3SxS8cLPBIB6sA5NWtJc1q3/iymkZu36hFT8wwz9RFVz8XRNah0OOmH/5g2ZAPBYjAD1kkngvz8r+tClCgsbHTQXZMqM1Vwo91/P0yEgBbqr8+G5BAYvXJw9eymza7FwkYLrevD9mNV/wKT5XJDAkDfl09WvPwkc/55UvarHXmpIzQQQnTQUrfAlTathQGo6aNNrSxATvL5pLPyegfYnYf0JbidAG9GkpWkuFLt/6z5qmgsgan8mQWJV0Vw0tOOrmuaC1OndUg3s9urCaCX017UFuTGPmnAxoZoaOggXcUKEY0TnGdX0ifO5ePFk1CwCBFElUAoUIhz3qu9NrEMngM8tK4IJAFLkT1ryut32hSVGd6GP87lYaEgNlOpzUTSBXz0Wny/jilxQcRXhHFKFCxLkHSOsadQyaRrtZpH9juzrjpqL4LPbJqIPbYOeP42Gm35QnxjVMZcZBw5sX8n1XohoLrz2aBGiYIR1EYBovgogWsVRzShH0vyT1ehnpgD+24XQ4TApQYyqRlfLj6tRB6MUedANBqTpaK8dNVEUA3WFurhYQnn6Df5OKxY4MnnQZhWnuWilCCfNBfqoudD661/NAI/esH1pibcLSiqVKlygfTFUNReWkJsUEONz4YcbuBrKSjVI1KqkpLmge646dOqhqFC/awDFYB06RHkvNqG5GPQT81ahPrFFON7X3FDQa2XHJXNszO9UE1TFaS6oy8bNUMPaprlQznt9ETiaaw+7V6GX1xSiDxmD7oerr+5j/fYUWLgYUSI+FzGaC4IqoDaVp2N1ff2e4jxMk8U22nMg6Al7iDgvafW4luaCvh98vhM1FzkDuPwS4O2Hoo5ccZqLV8yEixppIt6yP0yPTiYP+lvzQ4fOlnARCIAULbJZtSs5dOrRIgaUOhfK8a+YiaYsHgXILi8gf5deJJC4ay/wmZui76lpz9WNIeJzEcwtE+2mFcqHQe+rPhdqwiwBKQTNKM7aLUda5bv0/5cFBbq6Dd1WM6yOGqrmQq1wWjKin8fl/2mdQ/kbJ1wQcSGjhUDL9MFnhtVdSVhTj9cdOg2l/1pOxZvULI46O2x57z8XLy6jWq2nH5gxaXkuiDbNRWAWmbGBf70nes6kXPhA1CyikqS5UM0fcU/CL58B3rxNlf8GTcGIbhBGU0oBOUUd/lP7280iE1a4aNITcEPRYLTMIsF11OJmlKypW+HihpL8fpzmwhRh/otR3ZSIKSs6JmcShAvHCDd39T36/apw0fRDwZCEv7gN/HPLwOdXFO0DQl+jiOYCwJ2zMiyYBERdA2j4QL0m1yFySt2MWWRUNzX6iY4IhemGr2guFA0DED9eVS0QrYOHYoRkde60cvEEZpGr8sB7rgqOQ2i6ov7R10G1GdRP+SHQXDzxxEJm12LhIgXTNCDidG0DRlUXxmXoJKi8umoWuX0K+NxNwCu1TIV6dsa4z9I0F6/bEySPofYZURs+vf/CCeDHNOFmp5A3oqGo+WDhKxjh0+aYGQ1Fpe/RIklmkZbmIs0sEjj1druJHM6lO3SOumABBGbA4P+mCDVDcaib9Usmgb+/KRoKSZ/T/f+Zg9EcMfq0ebws07rHaS5a80HI4luU4pv6sFXIStkYjWAdIhNA12YRDH5T2yoHHBmJVTJDzQUQChekkVKj1HTiNBfPiklUqc4dNVye7rOqLTFFVAjUHTrVsUDj5mXTwOduTvihGbFdpSzi4FDUFPbvn0w/aADQolMy46NFiIIpwxq/shq+nrTkvy8G7+2xpWNnnBc0oUaLEHFPa2OmXHSfPRY9Ri0nvdO5oSRNI2RiKAQTumhG4+x1zUXeCDeOlllE8bnQzSikeSDNxWZ8LnJCcehU/ARaZpEheMrqB5RuHpCbx94OkeWqoDxlAUdyYX/ljND0Qe/ZRtg/6lwwEK31opoKacOiJ2MDwP9xNHpsnObCMoCiY7d+E9C9cDHKZhFLyEgXS4SJ5oBQuADkvWppLmLOEedzEaf1Uc1MBx3gF48Af7sUPmxdV5TmK9JatLKCBtF0wX8BRH0/6FrjphxTg+To0eye6FhzkUKt1oDnbV+Gzq1CHVcyA58L9TNlYBcMWcjnHwNBYkKblICcvEC7WeTBq8IkN3FmkaRsh+84HOYHeOEE8JHrOqstdxrXF4FfOIJWSnMRLDlFxSwSFy2SN4APXCv/T+aQRgfNRd2T3yGnws2EouYMaSpiM0sAACAASURBVLsuGsDHbwj7izYi2kxHHdWB+U9ukFEdSVDfvHRKRh4AUZ8L0jqoG1Q9RnOh+3UIZe6Qmp3MT/p8UJ+K1e+aAPxgHSLholuzyGajiIYRUwDfWg9fl5Qf9KkfBp4ZrGFx60uc5iLufqjC5aEc8J+OyflL44JCXVuChXbuP3pW2Pfq0hiX9XNQlMvZmfhZuEhhcXEdtdr21BbphYjmwkvWXOgCwKFc+3H0NKcXQrplPAwpjTOLdJNNbo8t05lTevBRX+Q2A6lWvcDn4kWT0ikSQCRDoOtLNfy1BZnVD2h36Gz47Rk6AamJ8oPPLSGL4aUhIDe4qifHz5gJfP7msM3k0LkTBEFVc/HSqfZCeyr05HrYaa+pkhOhLwr1gy3CQnOWCAUB/Rppmgv9WH3TAqSASnkuSLulOxEmMcqaC0LXBqm//Y7pUNiINYsoaxeVQ48TwuPMwa/bI9O6EyQU0j9VK3L3PuCfbmlvR1zWz0Fx/vxSZtdi4SKFYjEH0xy+29TSXBjxeS4IPXe/Wv+CvkN582nwt6JGBPAvp8P/q98BNpeqlhzpRn2R2wwmgoJvwfj5sdmwZowQUijwIX0ufuWofKqm+0MbWF1ZUX1EnXOBsH+poBLVf2m1QbQvuOqTLG1UasglOeDuBLNI0exeoNWFa4I0DpaQQgZpkBwBfKcs/69qLnThgk7XEi42obkIN0YBJzCv0Ub6Q10mxRrlUFRCb/9masQYymdNn/xX2o+Lc2R/5xVSKCXahAvtGuMxGtqkcTUIJidjynBvE8O3aw4ZU1NFOM7wuabQ4B0zpcpc7UgSIBwDeKa2AO1RbM50DlIV65PAFmFsf5xZZHITaohWmF33Xxl5rMAsYgfChZ72GZBF4Vab0dBDgfApTS8B3vA1zYXio0GCgfpkFvfUaimbTUmzVR9wgB+ZlBqUlZds+icPHYcc6UjXDYnChQijRXJGqE1SbfTqfdZzaahPzrYAfiJ4wo3TXNwxJYX2uFDUXLAOFQPH3xu6rJ59TSE+jfkood+nROEi7j1l7WoGkXX6Pt9t3h3qM1XIUK9BZhH1VIaQ7R0G4WLv3uwS1eymtX5LrK9X0Wxml9WsW6jjxsz2PBcUBTJrAXdrOVOKqs9FcJ6f3B+NblA1GI723lY1F3kDeN81UbPMToc2E7KVq4sXLUYPXwQu1qNP1+o9rmvuPg0vjC4BwkVWLQVtiNDhTa+CS+cnQaekPWndOiF9MHYKzxkDPvas7o7tJFz8xL4wJ4hqFiHUsETd58JQjlEFzLgojr98tqzV0xaKCllyHZB9dvNY95vVXXul/9Qoo9+nJJNQN6GoarE4Yq/TXd6dltYCiCRAo69SeQW9HXrZhUGxtLSR2bVYuEhhdbWSacrUblE1F25CngsRs7GojlCGkF7oQOh8CESFDEd7j8596lrg4es31+Z3HYlqTnY6L5oE/ufNgO+GtUUI+i9tVElmrbqmuUgyi9S8aB+pTn+6gskUYehcyyyC6OvdiJpETsWA9Ilp+VyQ5kLpp06aC7VwWdt3EtryW9cEmV5b3/XRqDdb53nJcAaxbRv6Jp6kuYjbv3WHTlUoAGSfTlnd1TqKM4v87jOiyeXuP9TejuKQpM5fXFxPP6hP7OKlpDsmJ4uw7eEzi0xZskQvJdRRF0R1IrYJF+qTk4j6UuiaC0u0P83R+Q7n0ssl73YKhqxE6QSdE6e5oI0qySE3zSxyLDChklmEztVJc6Fm5dQ1F7qPzm6CKqfqm8AvHpHmIisQLpqacEHJtuhrbWYR+qsJF3E+F8ReO8yXIo8VyCvm2dun4r+3U2kJv8G93ZJZJEFzMWNJobobzUWcQ+d1xeh3Z+32dqiRYoNk3z42iwwNpVIOljV8t2nKkkV66AlUV9ECoXOYimoWMRBVpcf5XCSZRYZBCh8VLMNo27Tov60kTMrxEc2FZhb55SeAk0+Hr390OjxO9YvZY0vBwYoZAyZCtTIt0iL4V9yEH81OhKI4VN57TAoXJqKbGgn0OeW+AzGhqMFf3SwSJ/ip2EZU6+E4Yed0CqndidB9Kmj3XKebUFQD0Y1vxpYCYTeai/dfDbz1QDQUVR8vtmivcVIYEs3FxAQ7dA4Ni4trqNWGr+Q6oQoCRFxee0BOCHVxVAWKnz4YaiIimosEs8gwSOGjgtt026smBn/rcWYR5TjdLPLZ5TD8EQg1D7rm4t1HpNlKFy5uGQ+fwIGopsIQu9ssAsjxnrQJqOYkINyM1GybQLpDJxEnyETaIsL5K/wwFDXuGjudbjUXsWaROM2FcuCMFVZZTePqQiho6lk6iThzV3FIfC44FHWIqNWa8Dw//cABEZeyW5XU1YFf0hYkE6Hw8HvPCLPHxZlF9AydwzBRRgXh+7AQHUO6WSTJ56KhaS5OV6OmkpZw4UW1S7TA2UZUwPyxPaHvAKAJm5BPWLsZR0RNhyqqUAaEc6NVhCx4v83nIvirCxdqgqY4bBGaPU0ROnTuRmh+nDgMPLu0xVBUJGsuJrrUXKjtMYVMnHWTFoljieH1ucgyidbwORMMGXv3jsM0h3fFTdJcCLSbRX7vGdHv6jZgQjWPJPlcdFuRkQFyjglHW/VaDp0xwoU62nTNhfodIJou3FY2OVsATdGuuWgVJtM2RgB4/V5g/y5yuI3DFqEfi86LJoELNeBTl6OCu665SKqQqUbp0LXShAsK97YMAae0i0KtNGj9efGk9IFJQr31zy4B39pIjxaZtqQGL26uJUERI/8ixjwVFy3yd8/p/tzbyZEjM5ldi7eIFGzbgjHEmZ/0lN0ECRaWaD+WuLEk/TaSzmmLqBYDkAPmxlKYbpdJxxQiccPZrM+F/l6c5sII+u2mMZnGWhcu1CdwVbj478+SDqi7mfdcFb9hAMADh2XYNhB1xqR7SbdZ72t6X/VxAqLCexyWiKaTNod4Hdpu6J6mmWPVW/TgVcF7CP/q0SIvn5aJ7d58AHjLge7b87aDyYUXqc7IMJLLZff0wMJFChcuDGfJdULPqkkYkNK4vrGoXJED3rgv+ZxJmour8hwpshmajSbyiEoJ3fhcCLRHiwDxZpGvrUcdOm0DOJqXOQ5MES60pLnIxwgXjFS7X9VBwCLNg5qdseXQmaS5CP4+fL2sOUPYorMG0DbCXDLC91HeqCYfvMOhcZpmWlA/pr7qFC3ynDGpkXrBRLJQGcfLpqT/UhzDnG799On5zK7FZpERJ84sAsjFr6DZ28e6tO50cujUtSFMOgba7fjkUBaXM0FNxZ1mFqE+dRWHzvdcBVytbJAmZN2S37g6zBQYp7lg0lGr+7aZRYJj9EgG6mvd58lOmUvHD4VZOOMSP+0mutZcKP+nvuqkudgOISDO52I3wsJFCgcPDndAeSezSNGMPhHPdNnbnTQXcaFXTGfyOQuTmrlc97mI5CkJ/jpGullEFRipXx44HD3eFPIJ+E37gf/7ghQ2KJnZbnfg3CyqIGHo7wX3f8KSmr25enhsHGlmkTftD/9vGwL22O61WcWF3MehCgt6JeY4zcV2LGWv3wu8osuU81lz7FiMqnqb4OeWFJpND74//NEi3ZhFZro0t6nChe5zwZqLzSN8oGTER4vUY1JJq+r1aoxwoWo71KfkpIX3Zw/JlNJA6Ih4y7hcWFlzsTlUzQX106uDdPt0K59dAv7LM8PvJE2XtGgRFVMAGOJ1aLtpaS5Sxqt6O/Xss6rmQvWD6Tfj5vCWOcgy2zQvLSnMz6+gWh2tPBdAmLNAFS6mN6m5UL3Z6b03H5AVPJnuaTYacNxm5L02zUWMb0zeiKb6JihDZ8mMPqklCX2/cERmEQRCZ89pSxa0YuFic6g+FzS33hDU76Hbr+evSFK9d1ssCwCwy30uujWLPLMYRpPEaS4eLyNSFVVPdrXTOXv2UmbXYrNICrnccEeL0AKnm0VMRMtNP3J9906Yncwix3avZnbLPLsE7LU657mIEy5IK2EKKVAUTaCsPHgUzVBIubHUXQluNYTy1nEWLjZLRHMRvEdCO/WprlFKWj1Un6Y0LAHY1u61YXUrXIybci6ouVzUInCrTVnQcTs1F8NMsZidJz4LFynMzia4BA8JiWYRETWLJFUR7HTOOIdOZvO8+Ui7PYpuJyXJigsZpj7ba8vKqeOKcGEL6SRKT17PnwCe1UUJ7h+ZklFC9B0WLjaHY4SZb0kLNK6EiwLR2i1AfzQXpiFQynBjGDa69bkA5P3OGe1ZhVUNhhqRtZs4dCg7ZxAWLlLY2Kghl7OHsr4I0MEsgqhD52aEi2kr9KhOKkPNdE+9LrO85vOhkNEKRY1x6NSFiwOOFC4mTGAuOObOPcBHrotuaN1wNC//ATIhEXfr5nGMMInStPoUrMwVdb4lTb20aBGV/3zMx/p6DcDuVB3mDLme6XVb4jAghRG1xhK9T3+FiH62W1hdrWRWX2Q4d8whYmWljEajmX7ggFDt8ypm8GSbZDbpxDUFpfw0Cxc9U6nUsbZWibzXlVlE0VwAwP1KDoaCIRdaI0G47Iabx9KPYdpxApv99UVZ1IygKWgbUeGio1mky35zfB/lpbWtNHdHkDPkeO1mHSLNhakLFay5wPz8ambXYuEihbGxPKwhtnWSg5kuXBhCOvwJRO2P3fDiSeAfnyv/b4r4MtRM9+RyNorFdvdxAzJaRL+/us/FVFBU6Sf3yWQ/6jH0ta0IF9ynWyMX5I+5ugC8/VD4Pj0Nd20W2US0iGEITE524VSzQ8kZ0keoGwxowkWc5gLRz3YL09PZjSE2i6SQZYnarVBMEi4QJu3ZrHBRMKJPtb98lGtO9IJqDlEpmcCq2+4vo2ouBKRwUTCAaTsMKY1EI4AFhSxxjGgUFkHOsgLR+ZjUNa+e6d7nxTAEpqe7cKrZoeTEJoQLTXPRZh4RSrRIX1s5/GTpQ8iaixSWl8uo14fXLJJUgtgUoeBhYnNmEZ1fOwbs272+ZD1TqdSxvt4eRjhjR2uCEJThzzGkAOIYUriwRXxV2qQCdMz2kBMJwoVoN2nR+3H8m73Aq2a7u6bn+Vhc3N1mkVsnujxWSFNiR58LRN/bLSwssFlkaCiXa3DdmExGQ0KhC83FTx8EDg5pUpfdQL3eRKXSXp+GQhh1wYDqf1hCRohYApgNlB9xDpzDUs55t5DroLnQy7AD/Xk69jwfa2u7N8/FASfU2qXx2j3AF27u7HNBfbLb8lysrFTSD+oTbBZJYXZ2DLY9vD4XiWYREQoXH7g22zYxUUqlHAqFdtUPZUztKFxY8v+Hgq+rEQmt81jd50tgeidnAF5McjPVd0bNc9GPrjFNgQMHNlFZa4dxY2nzQpruczFOSbXQrs3YLXAo6hCRZYnarUBmkYI2S75/W/ZtYeJJcgimuiCdhIuSIaMS9nXQXMzYbBbJkpwRZklVmbaBO4K1u2gCn7kJuOOx/jwdCyGQz+9e22Scpqjb79CcIT8yVXOx2xw6s0yitdsEt02zsLCKWm14038naS6Y4WF9vYrl5Y2290kgOKEVGqP00baQm9TPHAR+6Ur5WZzmYtpis0iW5ER7hVNAZkj90xvC1/2067uuh/Pnl/pwpt2DpWkubg3q6aiai902bc6dW8zsWqy5SKHRcOHF6UCHhAlLFqEqDq/lZtfjul5swSBa/F67p/19M/irb2KtXArKqviHP9SuuWK2j1yXIaT9zKXg+xhqx/JhRAC4/BJgMphDM7bM4RPRXAyqcQOiVstuDLFwkcKBA1MQQ+z1s8cGvnrLoFvBdCIpnJmEC12A0M0iKnGaiwO7V1s+EHJGd5rCfmaBtCwDV165J/1AJoJerPGaAlDzFMFveJf2beHqq/dmdi0WLhhmQJCAUDTa328JFwmaCzaDDI6cEW8W0dmtWSCHGUsAjqkIfoNtzo6G720KFy8uo1ptDyNkmG5ZXa3g0qX2HAV2F5oL3dwVp7lgsiUXo1GKw+ij5qLZ9PDkk9mVy96pWCJImx+83m3T6IknFjK7FmsuUjBNY6jNIszwYxgCptm+G3XUXAB44HDbV1hzMQRQEa00+mnXFyI56ojpHsods1ujRbJMq8DCRQr79+/e2HKmP4yPx/tcUFVMfYEjzcV1MWUABGsuBs5Hru/uuH4+HZumgSuumOnDmXY3dqC5oHm026bR0aPZ+e2wWSSFWq0BzxveDJ3M8NNsurGe/nppbsJJSC8NhCmNWbgYfvrp0On7Pptn+8DPHATesLc9a+duoVzObgyxcJHC4uJ6puE7zM5jY6OGlZVy2/tJwsVeJ1m4YM3F6NBPzYXr+rh4caUPZ9rd3DEtQ/db6b8H2prsyTJXCptFUigWc7H2cobpFsexYseQbcQXlFOLLumwz8Xo0E+HTsMQGB/P934iBsDuTf89OZldlW8WLlKYmooxfDPMJoirKwJIASJOc3E0L//FQYsip/sefvr5dGwYItNy2Tsd6pPdJqTv3dtladk+sOOFi3ffe+/4hlt4pRCibm/Yn37o0Yc2VRZufb2KfN5mT21my9RqDbiu35bX3zbihYs7Z+W/OOhwZ7c9co0g1EVbqYuhI6uiVjA5yQ87/YCE9N2W2XhpaQPT06VMrrWjl6j77rvPLnuFzwO4C8DLG8XaX272HKurldjUzQzTLdVqAxsb7eWyLRFvFukELYpxQgkzXJB/zHgfNjDP87G01F6fhtkaVDSwm2RoO4nFxfXMrrWjlyin4dwNgbOnHjl118mHTx6HEHtO/NSJY5s5x+RkEba94xU8zDZSKDix4ahJDp2daGkudpk6dxShvprsw/JhmmwW6Sck8HWTDG0nsW9fdmaRnX1rfdwAX3wjfC0eF5a3qUocpVIOlrWzbxOzvTiOhXzebnt/S8JFIFSwWWT4ob6a7MPTsRDs0NlPJnap5iKpztF2sLOXKN/fL+CfoZdC+BcAHNjMKRYX14a65Doz/CSFotpbMYsEf3OsuRh6qIum+qC5cF0Pc3McitovJoI+2W0+F1mGou7oW3vrzc8/Bvh7vvzYVz4HALfe9PyfMDz87Ze+8ZUz6nFve9sD711cXJscGyvANA2cPj2PlZUypqZKWFxcx+XL66jXmxgby2N1tYKnn74MQKBQcDA/v4q5uWXk8w5s28S5c4tYXFzD5GQJvg+cPj2PjY0aJiaKKJfrOHfuEppND6VSDpcvr+PChSVYlolczsaFC0tYWFhFqZRva0e93sTZswuoVpsYH89jbS3ajoUF2Y5cLrkd6+s1TE4WUalE27G0tIELF5ZgmtSOZSwsrLTacebMQssRqNFwg3Y0MD5ewNpaFU8/vQjfl+r/S5fWcPHiMnI5G7Zt4amnLuPSpVVMTBQhRHw7Gg3ZjuXlDZw/H7bj4sVlzM+voFjMwbJMnDmzgMuXo+2oVGQ71tereOqp9nY4jg3HsfD002o7BE6fnsPaWhWTk0VUqw08+eQlNBouSqU8lpfLOH/+MgzDQD5vY25uJdKOs2cv4fLldUxPl9BsujhzZgHlch0TE2E7PM9HsZjD4uIa5uaWAcinBmrH+HgRE7bAzNoyZivrmJoK21Gvuxgby2Nlpb0dX16o4VPlPN5+CPDmLmFxcQ3T02NoNj2cOTPfasfGRg1PPbUYOJLmsLi4josXl2DbFhzHwvnzcqyNjxdgGAaeeGIeq6tyrNVqsh21WjPSDiFkO+bnVzA3t4JCQd6PJ5+U7ZiaGoPnyXZsbMS3g8a83o64uVerNfHkkwutdtDcE0Ign0+ee1NTJXieH7SD5l4N584tps69sbH0uaevATT39HZMT5YwYwNHl8Ixr68BNPfCdsTPvYmJIi5dWsPS0roy92Q7aMyHawDNvUVcurTWcgLtNPf0NYDmXqc1gOZe0hpAcy9uDQjnXl2be3INoDGvrwFnz4ZrAM09fQ3wPKBYTF4DxseLEIbAbzwJvMlcwpUzha7m3vx8OOblGkBzL7oGbGy0rwEXLy63xnzYDpp7c1hdrWJqqtiae3o7aO7p7Yibe53WgIWFVRSLudi598QT86jV/I/89m//el8KkOzo558TbznxYgj/V08+fOpl97/p/mnDMb4GD8879dFTi+pxvu//HYA74s7RaDRhmiaM3ZbKjekbruvB9/2+RBx9bB544z8D/3QL8Fw2we8afF+uRY7D/l/9wAdwugJcmd9d4ai1WgO5XLuJVuGwEOJ8P661o80ic+W5LwL+3AP3HP+y6RiPGz4e0gWLNGzbYsGC6QnTNPoWykxe7hwtsrsQAixY9BEB4OrC7hIsAKQJFn1lRy9Rjz76qHvy4Q++0TfE64pG5drff+TUBzZ7jgsXuOQ60xurqxUsLraXXN8KM8HawA6duwsuuc70g9On5zO71q4QhU9++OSW1Ty+78P3+9kaZrfh+z48rz+DaCaYsRyKuvvo1xhidi+um90Y2hXCRS8cOjQ96CYwI04/sypOk3DBmotdhWUZuOqqvYNuBjPiPOMZ+zO7Fi9RKTSb0hmPYbaK5/lwXa8v59rnAP7twMH4ciXMDsX3gWaTMwUzvZFltmkWLlKYn19Btcp5Lpits7ZWweXL2aXdZXYeruvhqacuD7oZzIhz9mx2fjtsFkkhl+NoEaY3uOgd0ytCJFfXZZhu0Ysnbie8a6JznguGYRiG2SVwnousqFTqfbOXM7uTRsPlFPJMT/i+j42N2qCbwYw46+vt1Zm3CxYuUlha2kC93hx0M5gRplyuYXW1MuhmMCOM6/pYWFgddDOYEefixezq07DPRQpjY3m2mTM9kcvZPIaYnjAM0deQZmZ3Mj2d3Rhi4SKFLEvUMjuTuHLrDLMZDENgero06GYwI87sbHYFidgsksLycpnNIkxPVCr1TG2dzM7D8/y+pZBndi9ZmtZYuEihXK6xQyfTE/V6E5UK16dhto7n+VhbYwGV6Y2Vlex8v9gsksL0dImrETI9USzm2DTC9IRpCuzdOzHoZjAjzoEDk5ldi3fNFDhxDdMrtm0CYIdOZusIIVAq5QbdDGbEGRvLZ3YtNouksLCwyjkKmJ5YX69ieXlj0M1gRhjX9XD+/NKgm8GMOOfOLWZ2LRYuUmg0XC51zPSE63qZFgxidh6+D3YsZ3qmVstuDHH6b3RO/+15PoQQEHynmC1CVXUFDyKmBzzP5zpHTE94ngfD6KhT6Fv6b/a5SIEnM9MrLFQw/YDXIqZXUgSL/l4rsyuNKOfPL3EYIdMTKytlTt3M9ESz6eHMmYVBN4MZcb7//bnMrsXCRQqmafCTJ9MThiFgmjzVmK0jBDiFPNMzMnItG3jXBJdcZxiGYRhwyfXsqNUa8DzO0MlsnWbTZU9/pid830e1yuZZpjfK5ezGEAsXKSwurmcavsPsPDY2alhZKQ+6GcwI47p+puWymZ1JlrlSOFokhXzeZns50xO2bbLfDtMThgHO0Mn0zNhYdmOIVzywzwXDMAzDgH0usmN9vYpmk7MrMlunVmtkautkdh6e57NpjemZpaXsyhCwcJHC6mqFUzczPVGtNrCxweWyma3jeX6mGwOzM1lcXM/sWuxzkcLkZBG2zbeJ2TqFgoNcjkuuM1vHNAVmZ8cH3QxmxNm3byKza/GumQI7UTG94jg8zZjeEEJgfDy7ctnMzmRiopDZtdgsksLly+uco4DpiXK5htXVyqCbwYwwnudxCnmmZy5eXM7sWixcpFCtNuC6nESL2TqNhotarTHoZjAjjOfJfCkM0wvr69mNIdbXprB37zhMk3P6M1tnbCzfKrvOMFvBNA0cOjQ96GYwI86RIzOZXYuFixTYmZPpFU7CxvSKEOy7w/ROlo7lvOqlcOHCMuf0Z3pidbWCxcW1QTeDGWGaTQ9PPnlp0M1gRpzTp+czuxYLFyn4vg/WaDO94Ps+PI8HEdMbPIaYXnHd7MYQp/8Gp/9mGIZhGHD67+xoNj12xmN6wvN8jjhiesL3wWUImJ7JMts0CxcpzM+voFrlMEJm66ytVXD5cnZpd5mdh+t6eOqpy4NuBjPinD2bnd8Oux+nkMtZMAy2HjFbx7I4lJnpDSFkGnmG6YViMbsxxLsm2OeCYRiGYcA+F9lRqdTZXs70BGfoZHrF933O0Mn0zPp6dtWZWbhIYWlpg2uLMD3BtUWYXnFdn2uLMD1z8eJKZtdin4sUxsbybDNneiKXs3kMMT1hGAKTk8VBN4MZcaansxtDLFykkGWJWmZnks9nl3KX2ZkYhsD0dGnQzWBGnNnZ8cyuxWaRFJaXy2wWYXqiUqlnautkdh6e53MKeaZnsjStsXCRQrlcY4dOpifq9SYqFa5Pw2wdz/OxtsYCKtMbKyvZ+X6xWSSF6ekSVyNkeqJYzLFphOkJ0xTYu3di0M1gRpwDByYzuxbvmilw4hqmV2zbBMAOnczWEUKgVMoNuhnMiDM2ls/sWmwWSWFhYZVzFDA9sb5exfLyxqCbwYwwruvh/PmlQTeDGXHOnVvM7FosXKTQaLhc6pjpCdf1Mi0YxOw8fB/sWM70TK2W3Rji9N/onP7b83wIISD4TjFbhKrqCh5ETA94ns91jpie8DwPhtFRp9C39N/sc5ECT2amV1ioYPoBr0VMr6QIFv29VmZXGlHOn1/iMEKmJ1ZWypy6memJZtPDmTMLg24GM+J8//tzmV2LhYsUTNPgJ0+mJwxDwDR5qjFbRwhwCnmmZ2TkWjbwrgkuuc4wDMMw4JLr2dFoNDlahOkJ1/XQbHK0CLN1OFqE6QdZplVg4SKFhYU1znPB9MT6ehVLS5zngtk6nOeC6Qfnzl3O7FocLZJCPm+zvZzpCds22W+H6QnDAGfoZHpmbCy7McQrHtjngmEYhmHAPhfZsb5eZXs50xO1WgPlMoczM1vH83ysrJQH3QxmxMnSPMvCRQqrqxVO3cz0RLXawMYGl8tmto7n+ey3w/TM4uJ6ZtfaUT4X77zrnYVGqfGakw+ffJTee/e9945vuIVXCiHqDWFNBQAAChhJREFU9ob96YcefWhTBe0nJgqZxgYzO4983oZt76ipxmSMYQhMT5cG3QxmxJmdHcvsWjtmxXvHW99xpOHXfgFCPB/AowBw33332eW6/XkA3wMw3yjWjgN4+WbOm2WJWmZnksvZg24CM+IYhsDkZHHQzWBGnCwF1B1jFjE88UHAuE19z2k4d0Pg7KlHTt118uGTxyHEnhM/deLYZs57+fI6x5czPVEu17C6uimFGcNE8DyPU8gzPXPx4nJm19oxwsXJR07d6Xv+v4u86eMG+OIb4WvxuLC8WzZz3mq1Adf1+tNIZlfSaLicK4XpCc8DNjZqg24GM+Ksr2c3hkbSLHLinhO3Q+B5ALBnfc8HHnz0wXhXfN/fLwS+QC+F8C8AOKAftrFRHfc8GUduGALr69L5bmwsj9nZMdRqTQB1FAoOGg0X1WoDuZwFx7FQrTbQaLgoFh2YpoGNjRo8zw/MKT7W12swTYFiMYdm00OlUodtm8jnbdTrTdRqzcAmb6JSqaPZ9GLb4Xk+NjZqsCyjYzsKBQeWZaBcrsF1/ZZZZ329CsMQKJVycF0P5fL2tKNWa6Bej2tHDkIIrK1tpR0ODMPAxkYVvh/fjmbTRaXSgONYyOXUdtiwLHOL7bBg2xaq1ToaDS/Sx74v763vUx8bKBbVdpjI5eyWUDE+LvuhXK7Ddb1NtSNtrI2Pd9eO6P2Q7VD7WAi9HQbyeQeNRhPV6mbbQWNeb0cT9Xqz1Y64sSYEUCrl4XkeNjbqqWN+2OZetB3RubfVdpRKeRw4MIW1teoW1oAcALHFNUDOvW7ux3bMPWpH2Mfta0D3Y37z7Qjvbfsa0Ovc69yO7Zh7DczMlNBsuolrgGXB2dqu3M5Iai48eHn4mICPicUDi4m5OnyBb/rwD4ffw4xw8W39uGq1UaxU6vB9mea7UqmjWpWbgmkaqFYbLdOI7LB6K4KkXm+iUqm3tBu1WiOootp+Ls/zgu/KczUabvBdN/iuPBelG69U6q2KrJ7no1KpB4IO4LrRdjQa9F2PfpPSDvpuI/iubAf9JmoHhdyG7dDPBfh+/LnoN9H90L/r+zKFsXo/9HbQvaV2hOei+9HeDjoXLdphO9xIv6jtCPslem/b20F92t4vFFoa9ot+P6hfXNRqzVYSLRof6lhr7+Pobwrb0Yi0o1qtd9EvYTvizkXtKJeTx1rYDr1fvEg7OvdxdJwmtUPej0akHd3OPXXM6+1Innvx9zbuu+H96Dz3omtAtF+2ugZQ4bLOfZw8b6kdSXNPXwP0ubeVNcB1o9+Njg8aa0lrgBc5Vzg+wrBuvR3hGkC/Qe/jZqsdYR93O/eS1+Zu516nsZY09xqNpLkXtwZA2yP0ueei2fQ6zr16XfTNQWxHJdE6/ubjLxQmfvvkR069CABOvOXEiyH8Xz358KmX3f+m+6cNx/gaPDzv1EdPLarf65REa25uBZOTReTz7JTHbI21NRnOPDOTnac2s7NwXQ8XLizjiitmBt0UZoQ5e/YSjh7d0+kQTqLVDXPluS8C/twD9xz/sukYjxs+HtIFizRc12tJdgyzFTzPZ78dpid8H5zMj+mZLHM27SjNRRIn7j1xqIjy2vs+/OG1uM85/TfDMAzD9E9zsSuEizQ6CRfNpgfTFFx4itkynufD930ugMdsGd+XflaWxQn9mK3TaLhpSSHZLJIV8/MrLScohtkKa2sVXL6cXdpdZufhuh6eeiq7ctnMzuTs2UuZXYuFixRs24RhsNaC2TqmaXAKeaYnhAAcZyQzBzBDRC6X3RjiXROA7/vvAXDjoNvBMAzDMAPk7UKIpUE3gmEYhmEYhmEYhmEYhmEYhmEYZoRgn4sOvPvee8c33MIrhRB1e8P+9EOPPsSlLZlY3nHPO/6VAWOcXted+p9/6EMfaiSNIR5bDPHOu95ZaJQarzn58MlH6b3NjhseT4w+jga9JrH7cQL33XefXa7bnwfwPQDzjWLtOICXD7hZzJAiIP4L4H+CXtfr9U/cd999iBtDPLYY4h1vfceRhl/7BQjxfACPAslrz2bfH8wvYgZB3Dga9JrEwkUCTsO5G8I/e+rhU3cBwIl7jn/9xE+dOHbyD06eHnTbmOHi+JuPz0Lg9MmPnPo59f0Tbz3xb+PGEBp4MY8tBgAMT3wQQuwBwhoDSWtP0rjh8cTo42gY1iTOc5GEjxvgi2+Er8XjwvJuGWCLmGHFxDOEj+kT9xz/m+P3HP/D4285/lIAyWOIxxYTcPKRU3f6nv/vIm9udtzweNr1tI2jIViTWLhIwvf3C/hn6KUQ/gUABwbXIGZYEZ6wBPAPMMQ98PERIfDofffdtydxDPHYYjqx2XHD44nRGIY1ic0iCfgC3wT8w/TaA2ZMF381yDYxw8nJR07+A4B/CF6ef+Ce45/O1e3XegljyDNg8dhikkhae5LGDY8nRmcY1iTWXCQgfPEVQNwBAPe/6f5pALe7EN8ccLOYIeTEW0687YF7jj8ESGc8H7gJvvH/JY0hHltMJzY7bng8MTrDsCaxcJHAXHnui4A/98A9x79sOsbjho+HTn301OKg28UMH3kv/8e+wG0n3vqOv3bqzllAfP73H/n9HySNIR5bTCc2O254PDE6vCaNACfuPXHo3ffeO55+JLPb+fl/e9/Bn7/n56f095PGEI8tphObHTc8nhgdXpMYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYZkcgBt0AhmF2J2949RveAt97lWnax//oE390CQDuftVdvw4f9Y998tH/c9DtYxhm63BVVIZhBkLDafwVIF7quc3fA4C7X/36N/rAuwDjk4NuG8MwvcGaC4ZhBsbdr3r9a3yIT8AXb4Pwf1P4+CBrLRhm9DEH3QCGYXYv3/7eP3/3xmtvOAKBBwF8e76y8JYzZ854g24XwzC9wWYRhmEGii/8OQCAwMJnP/vZ5oCbwzBMH2DNBcMwA+ONr/rx23wYH4bwfw2+eOsNz7jxwre//+2vDbpdDMP0BmsuGIYZCHfeeWfRg/FRAH/+8f/xJ+8BxPtg+L9z1513HRt02xiG6Q0WLhiGGQhFL/+bAPY1XfcBAFjz1/4jfJyDi0cefPBBXpsYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmF2PP8/Ghp0R7EZNBgAAAAASUVORK5CYII=", "prompt_number": 1, "svg": [ "\n", "\n" ], "text": [ "Plot(...)" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can quickly compute the mean of the time series to be $11.2$. If we were to always guess the mean as the temperature of Melbourne on a given day, the RMS error of our guesswork would be $4.1$. We'll try to lower this RMS error by coming up with better ways to model the temperature than guessing the mean.\n", "\n", "A simple way to model this time series would be to find a smooth curve that approximates the yearly ups and downs.\n", "We can represent this model as a vector $s$ where $s_i$ denotes the temperature on the $i$-th day.\n", "To force this trend to repeat yearly, we simply want\n", "\n", "$$s_i = s_{i + 365}$$\n", "\n", "for each applicable $i$.\n", "\n", "We also want our model to have two more properties:\n", "\n", "- The first is that the temperature on each day in our model should be relatively close to the actual temperature of that day.\n", "- The second is that our model needs to be smooth, so the change in temperature from day to day should be relatively small. The following objective would capture both properties:\n", "\n", "$$\\sum_{i = 1}^n (s_i - x_i)^2 + \\lambda \\sum_{i = 2}^n(s_i - s_{i - 1})^2$$\n", "\n", "where $\\lambda$ is the smoothing parameter. The larger $\\lambda$ is, the smoother our model will be.\n", "\n", "The following code uses Convex to find and plot the model:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "yearly = Variable(n)\n", "eq_constraints = []\n", "for i in 365 + 1 : n\n", " eq_constraints += yearly[i] == yearly[i - 365]\n", "end\n", "\n", "smoothing = 100\n", "smooth_objective = sum_squares(yearly[1 : n - 1] - yearly[2 : n])\n", "problem = minimize(sum_squares(temps - yearly) + smoothing * smooth_objective, eq_constraints)\n", "solve!(problem, SCSSolver(max_iters=5000, verbose=0))\n", "residuals = temps - evaluate(yearly)\n", "\n", "# Plot smooth fit\n", "p = plot(\n", " layer(x=1:1500, y=evaluate(yearly)[1:1500], Geom.line, Theme(default_color=color(\"red\"), line_width=2px)),\n", " layer(x=1:1500, y=temps[1:1500], Geom.line),\n", " Theme(panel_fill=color(\"white\"))\n", ")" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n" ], "metadata": {}, "output_type": "pyout", "png": 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", "prompt_number": 2, "svg": [ "\n", "\n" ], "text": [ "Plot(...)" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also plot the residual temperatures, $r$, defined as $r = x - s$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot residuals for a few days\n", "p = plot(\n", " x=1:100, y=residuals[1:100], Geom.line,\n", " Theme(default_color=color(\"green\"), panel_fill=color(\"white\"))\n", ")" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n" ], "metadata": {}, "output_type": "pyout", "png": 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", "prompt_number": 3, "svg": [ "\n", "\n" ], "text": [ "Plot(...)" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our smooth model has a RMS error of $2.7$, a significant improvement from just guessing the mean, but we can do better.\n", "\n", "We now make the hypothesis that the residual temperature on a given day is some linear combination of the previous $5$ days. Such a model is called autoregressive. We are essentially trying to fit the residuals as a function of other parts of the data itself. We want to find a vector of coefficients $a$ such that\n", "\n", "$$\\mbox{r}(i) \\approx \\sum_{j = 1}^5 a_j \\mbox{r}(i - j)$$\n", "\n", "This can be done by simply minimizing the following sum of squares objective\n", "\n", "$$\\sum_{i = 6}^n \\left(\\mbox{r}(i) - \\sum_{j = 1}^5 a_j \\mbox{r}(i - j)\\right)^2$$\n", "\n", "The following Convex code solves this problem and plots our autoregressive model against the actual residual temperatures:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Generate the residuals matrix\n", "ar_len = 5\n", "residuals_mat = residuals[ar_len : n - 1]\n", "for i = 1:ar_len - 1\n", " residuals_mat = [residuals_mat residuals[ar_len - i : n - i - 1]]\n", "end\n", "\n", "# Solve autoregressive problem\n", "ar_coef = Variable(ar_len)\n", "problem = minimize(sum_squares(residuals_mat * ar_coef - residuals[ar_len + 1 : end]))\n", "solve!(problem, SCSSolver(max_iters=5000, verbose=0))\n", "\n", "# plot autoregressive fit of daily fluctuations for a few days\n", "ar_range = 1:145\n", "day_range = ar_range + ar_len\n", "p = plot(\n", " layer(x=day_range, y=residuals[day_range], Geom.line, Theme(default_color=color(\"green\"))),\n", " layer(x=day_range, y=residuals_mat[ar_range, :] * evaluate(ar_coef), Geom.line, Theme(default_color=color(\"red\"))),\n", " Theme(panel_fill=color(\"white\"))\n", ")" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "