{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "To be as self contained as possible, we are only using numpy and matplotlib." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from matplotlib.patches import Arc\n", "%matplotlib inline\n", "\n", "\n", "def exponential(t, tau=1, N=1):\n", " 'Exponential of lifetime tau, normalized to N photons.'\n", " y = np.exp(-t/tau) / tau\n", " return N * y / y.sum()\n", "\n", "def gaussian(t, t0=0, sigma=1):\n", " 'Gaussian of center t0 and width sigma, normalized to 1.'\n", " y = np.exp(-((t-t0)/sigma)**2)\n", " return y / y.sum()\n", "\n", "def phasor(x, n=1):\n", " 'Calculates the phasor corresponding to the n-th harmonic.'\n", " return np.sum(x * np.exp(1j * n * np.linspace(0, 2*np.pi, x.size, endpoint=False))) / np.sum(x)\n", "\n", "def single_lifetime_circle():\n", " 'Draws the single lifetime circle.'\n", " ax = plt.gca()\n", " ax.add_patch(Arc([0.5, 0], 1, 1, theta2=180.0))\n", " return ax" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we will show a theoretical (that is, not corrupted by noise) decay, a gaussian IRF and its numerical convolution." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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fHx996NChnDKllA4ICNCHDx/OKUtISNBKKf3ee+8VuFduJfndy64DtNal/Dz2\n2h4JMOZJnD0Le/eaHYlnWLBtAQ2rNOS22rfZdF3zas25o+4d/POXfzopMiHKgD17IDrauT979jgk\n1IsXLwJQsWLFYuuuXLkSpRRjxozJUz527Fi01qxYsSJPedOmTenYsWPO49DQUBo1asShQ4dyyvr3\n78+1a9f4/PPPc8pWr15NSkoK/fv3ByAzM5O1a9fSu3dv6tSpk1MvPDycgQMH8uOPP3L58mUbXnXp\nrVq1Cl9f35whn2xjx44lMzOTVatW5Sm/6667iIiIyHncokULKlWqlOe9cAdeu2oDjKENi8WYJ9Gk\nidnRuLcLVy+wfNdyJt4+0a5lUM/e+iy9l/XGetJKdI1oJ0QohJdr3BisVuffwwEqVaoEwKVLl4qt\ne/ToUSwWCw0aNMhTHhYWRnBwMEePHs1TXrt27QJthISE5OnOj4yMpHHjxixbtowhQ4YAxrBGaGgo\nXbt2BeDMmTOkpqZyyy23FGivSZMmZGZmcvz4cZq48MPh6NGj1KhRgwoV8q6Gy44h/3tRq1atAm3k\nfy/cgVcnEhUrQsuWRiLxxBNmR+PePt75MekZ6QxqOciu6++75T7qVK7DP3/5JwsfXOjY4IQoCwID\nofWNV0q5i4oVK1KjRg1+++23El9T0i8oPj6Fn+Gj862O6N+/P2+++Sbnzp0jKCiIr776ikceecRh\n+zYUFW9GRga+vq756Czpe2E2rx7aANmYqqTmx8/n3lvuJTwo3K7rfSw+PNXmKT757ROuXLvi4OiE\nEO7m3nvv5eDBg8WugKhTpw6ZmZns378/T/np06e5cOFCnmEHW/Tv35/09HT+85//sGrVKi5dusSA\nAQNynq9atSqBgYHsLWRse/fu3VgslkK/8WcLCQnhwoULBcrz9xrY0oNbp04dTp48yZUref9GZk8k\ntfe9MJvXJxK33QaHDsEff5gdifuKT4xn26ltDGs9rFTt9GnSh7SMNNYdXuegyIQQ7mrcuHEEBgYy\nbNgwTp8+XeD5gwcPMmvWLHr27InWmnfeybtL7vTp01FK0atXL7vu37hxY1q0aMEnn3zCsmXLqF69\nOrfd9r/5XRaLhe7du/Pll19y7NixnPKkpCTi4uK47bbbCAoKKrL9+vXrs2XLFq5fv55T9vXXX3P8\n+PE89bKHKQpLOvLr2bMn169f51//+lee8pkzZ2KxWLjnnnuKbcMdefXQBhiJBMDGjZBvpZHIsnjH\nYqoHVee8k6EFAAAgAElEQVTuBqU74azhTQ1pWKUhK/at4P5G9zsoOiGEO6pXrx4ff/wxAwYMoEmT\nJnl2tty0aRPLly9n6NChjBo1ikGDBjFv3jzOnz/P7bffzs8//8zixYvp06cPt99+u90x9O/fn9de\ne42AgACGDSv4Rejvf/873377LZ06deLpp5/Gx8eHefPmce3aNd566608dfMPFwwbNozly5fTo0cP\nHn74YQ4ePMjSpUsLzPWoX78+wcHBzJkzh6CgICpUqED79u0L7V2477776Nq1K6+88gqHDx8mKiqK\n1atX89VXXzFmzBiPPZfD63skwsKMiZbr15sdiftauX8l9ze6H19L6fPKXg17sfLASrcbwxNCON59\n991HQkIC/fr147///S/PPPMM48eP5/Dhw7z99ts5vRALFixg0qRJbN26lTFjxrBhwwZeeeUV4uLi\n8rRX2L4LuZ/Lr3///mituXr1as5qjdyaNm3KDz/8QIsWLZg6dSqvv/46devWZcOGDbRp0+aG7Wfv\nY7F//37GjBnDzz//zIoVK6hZs2aeur6+vixevBgfHx+eeuopBg4cyPfff19ou0opvvrqK0aPHs2K\nFSsYM2YMe/bs4e233+btt98u0Xtxo/fILMpT/+ArpVoDVqvVSutiJiiNHAlr18K+fa6JzZMcPn+Y\nerPq8fnDn9O7Se9St7f24Fq6L+3Ojid3EBkWWfwFQnip+Ph4oqOjKcnfKCEcqSS/e9l1gGitdakO\nk7CrR0IpNVIpdVgp9adSaotSqm0x9WOUUlal1FWl1D6l1KB8zw9SSmUqpTKy/s1USqXaE1thYmJg\n/36ZJ1GYNQfX4KN8uKPuHQ5pr0udLlTwq8CKfSuKryyEEMLj2ZxIKKX6A9OBCUArYAewWikVWkT9\nCOBrYB0QBbwLzFdK3ZWvagoQnuvHYdNXs4fgcvU2iSyrD66m/c3tqRxQ2SHt+fv6c1f9u1ixXxIJ\nIYQoC+zpkRgDzNVaL9Za7wGeBFKBgqebGJ4CDmmtx2mt92qt3wOWZ7WTm9Zan9Fan876OWNHbIWq\nVg2aNoUNGxzVondIz0hn3eF19Kjfw6Ht9mrYi80nNnPuz3MObVcIIYT7sSmRUEr5AdEYvQuA8ekP\nfAt0KOKy9lnP57a6kPpBSqkjSqljSqkvlFJNbYmtOF27yoTL/H7+42cupl2kRwPHJhL3NLiHTJ3J\n6gPud0qdEEIIx7K1RyIU8AGS8pUnYQxHFCa8iPqVlFL+WY/3YvRo3A88khXXT0qpGjbGV6SYGDhw\nAE6ccFSLnm/NwTVUKV+F6OqO3dK6ZqWatAxvKcMbQghRBrjFPhJa6y3AluzHSqnNwG5gBMZcjCKN\nGTOGypXzju/HxsYWOJ429zyJRx5xRNSeb/XB1dxV7y58LIVvw1oavRr2Ys7WOWRkZjilfSGEECUT\nFxdXYKltSkqKw9q3NZFIBjKAsHzlYcCpIq45VUT9i1rrtMIu0FpfV0ptAxoU9nxuM2fOLNHSqqpV\noXlzY56EJBJwNvUsv/7xKyOiRzil/V4Ne/HGD2/w8x8/07FWx+IvEEII4RSFfbnOtfyz1Gwa2tBa\npwNWoFt2mTJ2xugG/FTEZZtz18/SPau8UEopC9ACSLQlvuLExMg8iWzfHvoWjaZ7/e5Oaf/Wmrdy\nU/mbWLl/pVPaF0II4R7sGdqYASxUSlmBXzBWXwQCCwGUUlOAGlrr7L0i5gAjlVLTgA8wkoq+QM/s\nBpVSf8MY2jgABAPjgNrAfDviK1JMDPzrX3D8ONzgrJYyYc3BNTSr2oybK93slPZ9LD50rduV74/K\nmltRtmUfyCSEq7j6d87mREJr/WnWnhGTMYYotgM9ci3XDAdq5ap/RCnVC5gJjAJOAI9rrXOv5AgB\n5mVdex6j16ND1vJSh8k9T+LRRx3ZsmfRWrP64Gr6Nyu4pawjda7VmRe/fZG062n4+/oXf4EQXiQ0\nNJTAwEAeLct/bIRpAgMDCQ0tdHsnh7NrsqXWejYwu4jnhhRSthFj2WhR7T0PPG9PLLYIDYUWLYx5\nEmX5/9u7k3fzx6U/nDaska1T7U6kZaRhTbTKPAlR5tSuXZvdu3eTnJxsdiiiDAoNDaV27douuZdb\nrNpwpa5d4b//Ba3Bzc49cZkfj/2Ij/KhU+1OTr1PVFgUgX6BbDq2SRIJUSbVrl3bZX/MhTCL15/+\nmd+dd8KRI3DokNmRmGfzic1EhkUSVC7Iqffx8/Gj/c3t2XR8k1PvI4QQwjxlLpG4/Xbw8TFOAy2r\nNh/fTIebi9qI1LE61erEpuOb5FhxIYTwUmUukahUCdq3h2/zb9pdRpxNPcves3tdNtTQqVYnklOT\n2XdWznAXQghvVOYSCTCGN777DjIyzI7E9bacMDYQ7VDLNT0SHWp1wKIs/HjsR5fcTwghhGuVyUTi\nrrvg/HmwWs2OxPV+Ov4TYRXCqBtc1yX3q+RfiRbVWsg8CSGE8FJlMpG49VaoWLFsDm9sPrGZDrU6\noFy4ZCV7noQQQgjvUyYTCT8/Y5fLsjbh8nrmdX754xeXTbTM1rl2Z/ad3cfpK6ddel8hhBDOVyYT\nCTCGNzZtgitXzI7EdXYm7eRK+hWX7+mQvV/FT8eLOo5FCCGEpyqzicSdd0J6Ovzwg9mRuM7mE5vx\ntfgSXd0xJ76VVO3KtalVqRabjsnwhhBCeJsym0g0bgw1a5at4Y3NJzbTKrwV5f3Ku/zenWp34sfj\nsnJDCCG8TZlNJJQyeiXK0oTLn47/ZNpW1Z1qdcJ60sqf6X+acn8hhBDOUWYTCTDmSSQkQFKS2ZE4\n3+krpzl0/pDLJ1pm61SrE+mZ6Ww9udWU+wshhHCOMp1I3Hmn8W9Z6JXYfHwz4LqNqPJrXq05Ab4B\nWBPL4OYdQgjhxcp0IhEWBlFR8M03ZkfifD8d/4maFWtSq1ItU+7v5+NHVFiU9EgIIYSXKdOJBEDP\nnkYikZlpdiTOZcZGVPlFV4+WHgkhhPAyZT6RuOceSE6GrV78RTkjMwNropV2NduZGkebGm3Ym7yX\nS2mXTI1DCCGE45T5RKJDB6hcGVatMjsS59l3dh+p6aku3z8iv+ga0Wg0205tMzUOIYQQjlPmEwlf\nX2P1hjcnEvGJ8QC0qt7K1DiaVm1qTLg8KcMbQgjhLcp8IgHG8MYvvxhDHN7ImmilXkg9ggOCTY3D\n1+JLy/CWbE304nEkIYQoYySRAO6+G7SGNWvMjsQ54hPjaV29tdlhAFkTLqVHQgghvIYkEkCNGtCy\npXcOb2TqTLad2mb6/IhsbWq0Yd/ZfVxMu2h2KEIIIRxAEoks99zjnctAD50/xMW0i27VI6HRbEuU\nCZdCCOENJJHI4q3LQLOHEdwlkWhStQnlfcvLfhJCCOElJJHI4q3LQOMT46lduTahgaFmhwL8b8Kl\nJBJCCOEdJJHI4q3LQONPuc9Ey2zR1aNlq2whhPASkkjk0rOnsQz0zBmzI3EMrTXWk1Zah7tXIiET\nLoUQwntIIpFLz57GvytWmBuHoxxNOcr5q+fdr0eihrGCJHujLCGEEJ5LEolcwsKgfXv473/NjsQx\nsj+osz+43UXj0MYE+gXKfhJCCOEFJJHI5/77YfVquHrV7EhKLz4xnupB1QkPCjc7lDxkwqUQQngP\nSSTyuf9+SE2F774zO5LSsyZa3W5YI5tMuBRCCO8giUQ+TZpA/fqeP7yRPdHSXXa0zK9VeCsOnDvA\nlWtXzA5FCCFEKUgikY9SRq/EV1959i6XJy+d5EzqGbftkYgKj0Kj2Xl6p9mhCCGEKAW7Egml1Eil\n1GGl1J9KqS1KqbbF1I9RSlmVUleVUvuUUoNuUHeAUipTKfW5PbE5wgMPwMmTEO/BiwqyJ1q6ayLR\ntGpTfJQP209tNzsUIYQQpWBzIqGU6g9MByYArYAdwGqlVKFbJyqlIoCvgXVAFPAuMF8pdVcRdf8B\nbLQ1Lkfq1AlCQjx7eCM+MZ7QwFBurnSz2aEUKsA3gCZVm7Dj1A6zQxFCCFEK9vRIjAHmaq0Xa633\nAE8CqcDQIuo/BRzSWo/TWu/VWr8HLM9qJ4dSygIsBV4DDtsRl8P4+kKvXvDll2ZGUToJpxOICotC\nKWV2KEWKCotiR5IkEkII4clsSiSUUn5ANEbvAgBaaw18C3Qo4rL2Wc/ntrqQ+hOAJK31h7bE5Cz3\n3w8JCXDkiNmR2CchKYHIsEizw7ihqLAoEpISyNQePBlFCCHKOFt7JEIBHyApX3kSUNRmBeFF1K+k\nlPIHUEp1BoYAw2yMx2l69AA/P2PSpae5fO0yB88dJCosyuxQbigqPIor6Vc4eO6g2aEIIYSwk6/Z\nASilgoDFwBNa6/O2Xj9mzBgqV66cpyw2NpbY2NhSxVWpEnTtCl98Ac8+W6qmXO6307+h0R7RIwGw\nI2kHDW9qaHI0QgjhneLi4oiLi8tTlpKS4rD2bU0kkoEMICxfeRhwqohrThVR/6LWOk0p1RioA3yl\n/jegbwFQSl0DGmmti5wzMXPmTFq3ds7KhD59YORISE6GUPc4hbtEEpIS8FE+NKnaxOxQbigsKIzw\noHB2nNpB36Z9zQ5HCCG8UmFfruPj44mOdsw+QzYNbWit0wEr0C27LOvDvxvwUxGXbc5dP0v3rHKA\nPUALoCXGqo4o4L/Ad1n/fdyWGB3pwQdBa8+bdJmQlECj0EYE+AaYHUqxosKi2J4kS0CFEMJT2bNq\nYwbwhFLqsazehDlAILAQQCk1RSm1KFf9OUA9pdQ0pVQjpdTTQN+sdtBap2mtd+X+AS4Al7TWu7XW\n1+1/eaUTFga33QbLl5sVgX08YaJltqiwKFkCKoQQHszmREJr/SnwV2AysA2IBHporc9kVQkHauWq\nfwToBdwJbMdY9vm41jr/Sg631LcvrFsHFy6YHUnJaK2NRKKaZyQSLcNbcvzicc79ec7sUIQQQtjB\nrp0ttdaztdYRWuvyWusOWuutuZ4borW+I1/9jVrr6Kz6DbXWS4ppf4jWuo89sTla796Qnu45qzeO\npRwjJS2FqHD3XrGRLTvOhKQEkyMRQghhDzlroxg1a0KHDp4zvJH9gewpQxu33HQL/j7+slW2EEJ4\nKEkkSqBvX1i9Gi5dMjuS4iUkJRASEELNijXNDqVEfC2+NK/WXHa4FEIIDyWJRAn06QNpabBypdmR\nFC/htDHR0p23xs6vZXhLmXAphBAeShKJEoiIgOhozxje2HFqh8cMa2SLCovi9zO/k56RbnYoQggh\nbCSJRAn17Wv0SKSmmh1J0VLTU9l/br/bb42dX1R4FNcyrrEneY/ZoQghhLCRJBIl9NBDRhKxapXZ\nkRRt15ldZOpMj+uRyI5X5kkIIYTnkUSihBo2hFat4JNPzI6kaAlJCSgUzao1MzsUmwQHBBMRHCHz\nJIQQwgNJImGD2Fj4+mu4eNHsSAqXkJRAw5saEugXaHYoNosMi2Tn6Z1mhyGEEMJGkkjYoH9/uHrV\nfc/e2JHkeRMts7Wo1kI2pRJCCA8kiYQNateGzp0h32msbsHTtsbOLzIsksTLiZy5cqb4ykIIIdyG\nJBI2io2FtWuNo8XdyclLJzn35zmP2Ro7v+yeFBneEEIIzyKJhI369TOOFne3PSU8bWvs/BpUaUCA\nb4AMbwghhIeRRMJGVavCnXe63/BGQlICFctVpE7lOmaHYhdfiy/NqjZjZ5L0SAghhCeRRMIOsbHw\nww9w4oTZkfxP9kRLT9oaO78WYS1IOC09EkII4UkkkbBD795QrhwsW2Z2JP+TkJTgscMa2SKrRfLb\n6d/IyMwwOxQhhBAlJImEHSpVgl693Gd4I+16GnuS93jc1tj5RYZFcvX6VQ6cO2B2KEIIIUpIEgk7\nDRwIVivs3m12JLA7eTcZOsPzeySy4pcJl0II4TkkkbDTvfdCSAgsWmR2JP/74G1erbnJkZRO1QpV\nCQ8KlyWgQgjhQSSRsJO/vzHpcskSyDB5SH/HqR3UC6lHRf+K5gbiALLDpRBCeBZJJEph0CA4eRLW\nrTM3joTTnj/RMltkWKQkEkII4UEkkSiFtm2hUSPzhzc8eWvs/CLDIjl84TAX09z0ZDQhhBB5SCJR\nCkoZvRL/93/mnQiadDmJ01dOe+zW2Pll96z8dvo3kyMRQghREpJIlNJf/mKcCGrWltmevjV2fk1C\nm+CjfGSHSyGE8BCSSJTSzTdDt27mDW/sSNpBoF8g9ULqmROAg/n7+tMotJHMkxBCCA8hiYQDDBoE\nGzfC4cOuv3dCUgItqrXAorznf8rIsEjZKlsIITyE93z6mKh3bwgKMqdXwhu2xs4vspqxckNrbXYo\nQgghiiGJhANUqAADBsAHH7h2T4n0jHR2ndnl8Vtj5xcZFsnFtIscSzlmdihCCCGKIYmEgzzxBBw/\nDmvWuO6ee8/uJT0z3ft6JLJej+xwKYQQ7k8SCQdp2xaiomDePNfdM3tCYouwFq67qQvcXOlmKvtX\nlgmXQgjhAXzNDsBbKGX0Sjz3HCQmQvXqzr/njlM7qF25NsEBwc6/mbMlJsKhQ3D+POr8eV7aW43E\nCpvgNrMDE0IIcSPSI+FAjzwC5crBwoWuuZ9XbI3988/w8MPGOtrOneG+++Cxx3hx4X7eGbUSGjSA\nUaNgyxazIxVCCFEISSQcKDjY+Ex8/33IzHT+/Tx6a+wtW4zEoX172LYN/vlP+P134/CSP//kgx9m\n8eBAC9fv7AZffgkdOhjrbE+fNjtyIYQQuUgi4WBPPGHsJ/Hdd869T3JqMicvnfTMrbGXLoXbbze2\nBP3iC9izB55+Gpo2NcaEAgJoGtGWL2/JZOeEJ403dN48+Ppr43CT2bPNP3JVCCEEYGcioZQaqZQ6\nrJT6Uym1RSnVtpj6MUopq1LqqlJqn1JqUL7neyulflVKnVdKXVZKbVNKPWpPbGbr2NH4PHT2pMvs\nLaQ9amgjMxP+9jdjX/FHHoGffoIHHgAfnwJVm1VtBmRNKLVYjAxt71546CEYOdL4NzXV1a9ACCFE\nPjYnEkqp/sB0YALQCtgBrFZKhRZRPwL4GlgHRAHvAvOVUnflqnYW+DvQHmgBfAh8mK+OR8iedPnF\nF87thd+RtIMA3wAaVGngvJs40rVrEBsLb7wB06bBggXGhJIiVPSvSL2QenlXboSGwvz5Rs/E2rXG\n3uTJyS4IXgghRFHs6ZEYA8zVWi/WWu8BngRSgaFF1H8KOKS1Hqe13qu1fg9YntUOAFrrjVrrL7Oe\nP6y1ngUkAJ3tiM90jz1mfMlesMB590hISqBZ1Wb4Wjxk4c1zzxnHpP7nPzBunJFxFaPIrbJ79YLv\nvzdWeXTsCAcPOiFgIYQQJWFTIqGU8gOiMXoXANDGPsbfAh2KuKx91vO5rb5BfZRS3YBbgO9tic9d\nVKkCAwfCv/8N16875x4etTX23LkwZ47xhvTuXeLLIqtFFn0KaJs2sHmz8d8dO8L+/Q4IVAghhK1s\n7ZEIBXyApHzlSUB4EdeEF1G/klLKP7tAKVVJKXVJKXUN+Ap4Vmvt5CmLzjNypLHT5VdfOb7t65nX\n+f3M756xNfYPP8AzzxhvyOOP23RpZFgkSVeSSLqc/9cnS716xjyLKlWgRw84dcoBAQshhLCFO63a\nuIQxh6IN8AowUynVxdyQ7Ne6tfFF+V//cnzbB84d4Or1q+7fI3H8OPTtC506wcyZNl+evWPnDbfK\nDg2Fb76BtDS45x64eNHeaIUQQtjB1gH2ZCADCMtXHgYU9XXwVBH1L2qt07ILsoZIDmU9TFBKNQVe\nAjbeKKAxY8ZQuXLlPGWxsbHExsbe6DKXeOYZY4jj99+hWTPHtbvj1A7AzbfGzsgwNtUoXx4++wz8\n/Gxuon5Ifcr7lichKYE7691ZdMU6dYxk4rbbjKGTlSvB37/o+kIIUYbExcURFxeXpywlJcVh7duU\nSGit05VSVqAb8F8ApZTKejyriMs2A/fkK+ueVX4jFqDYT4OZM2fSunXr4qqZ4qGHIDwc3nvP2PrA\nURKSEqhRsQahgYUulHEPc+cam079+CNUrWpXEz4WH5pXa16yMzdatDA2rurRA4YNg8WLSzShUwgh\nvF1hX67j4+OJjo52SPv2DG3MAJ5QSj2mlGoMzAECgYUASqkpSqlFuerPAeoppaYppRoppZ4G+ma1\nQ9Y145VSdyql6iqlGiulxgKPAkvse1nuoVw5GDHC+ExzYPLn/ltjnzwJL71krIPt1KlUTUWGRZb8\nFNDbbzfOcl+61JjYKYQQwulsTiS01p8CfwUmA9uASKCH1vpMVpVwoFau+keAXsCdwHaMZZ+Pa61z\nr+SoALwH/Ab8CPQGHtFaf2hrfO5m+HBj+H7RouLrlpTbb409ZowxtDB1aqmbigyL5PfTv3M9s4TL\nXwYONMaURo82zvEQQgjhVHZtQqC1ng0U2lmvtR5SSNlGjGWjRbX3N+Bv9sTi7mrUMIY4/vUv4/PN\nUsrprReuXuBYyjH33Rr7m2/g009hyRJjNUUptajWgrSMNPaf3U+Tqk1KdtH06bB1qzHRMz7e7qEV\nIYQQxXOnVRtea/RoY5sDRywFzZ4v4JZDG6mpxpkZ3boZW2A7QPaE0hLNk8hWrpwxwTMtzeihkHM5\nhBDCaSSRcIH27Y2pAtOnl76thKQE/Cx+NLqpUekbc7Tp0+GPP4yZpQ6a6BgaGEqNijVsSyTAOJb8\nk0+M09OmTHFILEIIIQqSRMJFxo419mb65ZfStZOQlEDTqk3x87F9OaVTnTsHb78NTz0Ft9zi0KaL\n3Cq7OHfcYUz6nDQJfv3VoTEJIYQwSCLhIvffD/Xrl75Xwm23xp4+3dgPfPx4hzcdFRaVs3eGzSZM\ngJYt4dFH4coVxwYmhBBCEglX8fGB55+H5cvhyBH72sjUmew8vdP9tsY+cwbefdeYTRpe1E7p9osK\ni+L4xeOc+/Oc7Rf7+RnLQY8fh7/+1eGxCSFEWSeJhAsNHgzBwfDOO/Zdf/DcQVLTU92vR+Ktt4zl\nKOPGOaX5luEtAezvlWjUCGbMMA4OW7HCgZEJIYSQRMKFAgONRQ3z58P587Zf75YrNhITjbWto0fD\nTTc55Ra33HQL5X3Ls/3UdvsbGTHCOH586FA4e9ZxwQkhRBkniYSLPfMMpKcbX45ttf3UdqpVqEZY\nUP6jS0w0ZQoEBBjjNk7iY/GhRVgLtieVIpFQysjgrl0zNswSQgjhEJJIuFhYGAwZYhyGmZpq27Xb\nk7bTKryVcwKzR2KicabG2LHGmI0TtQxrWboeCTDmb8ycaWyWtXKlYwITQogyThIJE7z4orFacv58\n267bfsrNEol//cvY/OmZZ5x+q5bhLdl1Zhdp19OKr3wjgwYZB3uNGCFHjgshhANIImGCunWNDRf/\n8Q+jp70kklOTOXHxRM7EQ9NduWKMzwwb5vTeCDASieuZ19l1ZlfpGlLK6EW5cMHI6IQQQpSKJBIm\neeklYxPIxYtLVj+7W79VdTfpkVi0yPgwHjXKJbdrEdYChSr98AZAnTrGgWJz5sCGDaVvTwghyjBJ\nJEzSpIlxmNeUKcY+TsXZlriNCn4VqB9S3/nBFScz05hr8NBDRveKCwSVC6JBlQbsSLJzCWh+Tz0F\nnTsbPSq2TlYRQgiRQxIJE738Mhw6BMuWFV93e9J2IsMi8bH4OD+w4nz1FRw44NSVGoVpGe6ACZfZ\nLBZjksqJE8bul0IIIewiiYSJWrWCnj3hzTeNL/k34lYTLWfMgI4djdPIXCg7kdBaO6bBRo2Mczhm\nzJCzOIQQwk6SSJjs1Vdh1y5j6+yipKansid5j3tMtNy6FTZuNJZ8uljL8JakpKVwNOWo4xodO9bI\n6IYOLfnMVyGEEDkkkTBZhw5wzz1G73pGRuF1fjv9G5k60z0mWs6cCfXqwQMPuPzW2YmUw4Y3AHx9\nYcEC2LPH6BoSQghhE0kk3MDkycbn2McfF/78tsRt+CgfmlVt5trA8jtzBj77zNjn28f1czWqB1Wn\namBVxyYSAFFRxqmlb7wBO3c6tm0hhPBykki4gTZtjC/4kyYZ22fnt/3UdhqHNqa8X3nXB5fbwoXG\nJMXBg025vVLKsRMuc3v1VWjYEJ54ouiuISGEEAVIIuEmJk+GgweN7Rny25603fxhjcxMYyOnfv2c\ndjhXSTgtkfD3N1Zx/PILvPee49sXQggvJYmEm4iMhIcfhtdfh7Rcu0BnZGaQkJRAyzCTJ1quW2dk\nOk8+aWoYUWFRHE05yoWrFxzfeMeOxrDNyy/DUQdO6BRCCC8miYQbmTjR2NYg9xkc+8/tJzU91fwe\niTlzoHlz48PWRNkTLnecctDGVPm9+SaEhBgbVjlqmakQQngxSSTcSJMm8OijRq/E5ctGWXY3flRY\nlHmBnTwJX35p9EYoZV4cQKPQRgT4BhCfGO+cG1SqBP/+N6xaBXFxzrmHEEJ4EUkk3MzkycYRFtOn\nG4+3JW6jVqVa3BRo3rwEFiww5hA8+qh5MWTxtfgSFRaFNdHqvJvcey/07w/PPQfJyc67jxBCeAFJ\nJNxMnTrGOVj/+AecOuUGEy2vX4d584zjSitXNi+OXNrUaOPcRALg3XeN1Rsu3gZcCCE8jSQSbujl\nl40OgAkTNdsSt5k70fKbb4yJGyNGmBdDPtHVo9mbvJdLaZecd5OwMGPr7CVLYPVq591HCCE8nCQS\nbig42NjWYP6yPziTesbcHokPP4SWLY3NLtxEmxpt0Gi2ndrm3BsNGgTduhlJVPakFSGEEHlIIuGm\nnn4aQqOMg6Ta1mhrThDJycZJnyZtQFWUJlWbUN63PNaTTh7eUMrYO+P0aXjtNefeSwghPJQkEm7K\n3x86PrQVLoWzP76GOUHExRlLIAcONOf+RfC1+BIVHsXWxK3Ov1n9+sYM2HffNTarEkIIkYckEm7s\nSvBWglPbMnq0MmfX5oULjRUMVauacPMba1O9jfN7JLKNHm0M7wwbVvge5kIIUYZJIuGmtNZYE7fS\nr2V72GQAACAASURBVFMbduyA9993cQAJCRAf73bDGtmia0Sz9+xeLqZddP7NfH2NXcJ27TKW0wgh\nhMghiYSbOnzhMOf+PEfvW9syZAi88gqcO+fCABYtMnoievZ04U1Lrk0NY/LntkQnT7jM1qoV/PWv\nxjDH3r2uuacQQngASSTc1K9/GBMto2tE8+abRo/6hAkuunl6OixdamxA5efnopvapnFoY2PCpbP3\nk8htwgS4+WYYPtw4xEwIIYR9iYRSaqRS6rBS6k+l1Bal1A2XFSilYpRSVqXUVaXUPqXUoHzPD1NK\nbVRKncv6WVtcm95u68mt1K5cm2oVqhEebnyGzZ4NO3e64OarVhkrFdx0WAOMCZetqrdi60kXTLjM\nVr68Mca0caMJY01CCOGebE4klFL9genABKAVsANYrZQKLaJ+BPA1sA6IAt4F5iul7spV7XbgYyAG\naA8cB9YoparbGp+32Jq4Nc+yz2efhYYNjV0vnX6W1MKFRld+ZKSTb1Q60dWjXdsjAdC1qzHpctw4\nY6MuIYQo4+zpkRgDzNVaL9Za7wGeBFKBoUXUfwo4pLUep7Xeq7V+D1ie1Q4AWuu/aK3naK0TtNb7\ngGFZsXWzIz6Pl6kzsZ605swDAChXDmbNgg0b4KOPnHjzM2fccu+IwkRXj2bf2X2kXE1x7Y3/8Q8I\nCoInnpATQoUQZZ5NiYRSyg+IxuhdAEBrrYFvgQ5FXNY+6/ncVt+gPkAFwA9w5fRCt7Hv7D4uXbtU\nYCOq7t1hwAAYMwbOnnXSzePijI2Y3GzviMLkTLh09g6X+QUHG0Mb33wDH3zg2nsLIYSbsbVHIhTw\nAZLylScB4UVcE15E/UpKKf8irpkG/EHBBKRMyJ5o2bp66wLPzZxpzIV88UUn3fzDD+G++yC00JEq\nt9I4tDGBfoGu208it549YcgQI6s7dsz19xdCCDfhdqs2lFLjgYeBB7XW18yOxwxbT26lQZUGhJQP\nKfBceDhMnWqc7L1xo4NvvH278eMBwxoAPhYfWoW3cs0Ol4WZMcM4EXXYMBniEEKUWb421k8GMoCw\nfOVhwKkirjlVRP2LWuu03IVKqb8C44BuWuvfSxLQmDFjqJzveOvY2FhiY2NLcrlb+vXkrzc8X2P4\ncGObhxEjjM99/6L6dWy1aBFUqwZ33+2gBp0vuno0qw6sMufmwcHGRlV3320cte5GJ6QKIUS2uLg4\n4uLi8pSlpDhwbpnW2qYfYAvwbq7HCmOVxQtF1J8K7MhX9jGwMl/ZOOA80LaEcbQGtNVq1d4kPSNd\nB/w9QE//afoN6yUkaO3rq/XkyQ66cVqa1qGhWj//vIMadI3F2xdrJqLPpZ4zL4hhw7SuUEHr/fvN\ni0EIIWxgtVo1oIHW2sY8IP+PPUMbM4AnlFKPKaUaA3OAQGAhgFJqilJqUa76c4B6/9/eeYdHUa0N\n/Hd200hoAWLQUILSO0gLigIWUBT1KiriBbEj91Pw44qKXpF77VfsCFc+KRZUuCpduqIGEIIgVZEQ\nelV6Sdvz/fFuZIkJIcluZjd5f89zntmdOXPmzcxk5533vMUY85IxpoEx5iHgFu84ePcZCoxAIj+2\nGWPivS2mCPKFNOv3r+dU1qkCK342awZ//zv8859+yi0xe7ZU++zXr+C+QUSHGh0AWLZzmXNCjBwJ\n8fHQty9kZTknh6IoigMUWpGw1n4GDEEe/D8CzYFu1tr93i7VgZo+/dOAHsCVwCok7PMea62vI+WD\nSJTGFGCXT/vfwsoX6izfuRyDodX5rQrs+8wzklvirrv8UEtq3Dho3Troc0fkpm6VulSLrsaS7Uuc\nE6JCBfjgA1i2TBxYFEVRyhBFcra01o6y1iZaa8tZa5OstSt8tvW31nbN1X+xtfZib/961toPcm2v\nY61159FGFO3PCl2W71pOo7hGlI8oX2DfyEjJHbVqFbz8cjEOum8fzJwpUQghhjGGDjU6sGSHg4oE\nQMeO8MQT8OyzsMIh509FURQHCLqojbLO0h1LaZ/Q/pz7t20rSRaffRbWri3iQT/+WHJHhKiDaoeE\nDizbuQyPdbj+xTPPQIsWUqPkxAlnZVEURSkhVJEIIo6kH2HNvjVcUvOSQu03fHgxpzjGj5fcEVWr\nFmFn50mqmcSR9COs37/eWUHCw6XY2bZt8OijzsqiKIpSQqgiEUQs2yFv1R1rdizUfr5THM89V8iD\nrloFq1eHTO6IvGiX0A6XcTnrJ5FDw4bw+uswZgz8979OS6MoihJwVJEIIpK3J1OlXBUaVGtQ6H3b\ntoWnn5YojuTkQuwYgrkjclM+ojzNzmvmvJ9EDvfdB716SaKqrVudlkZRFCWgqCIRRCTvSCapRhIu\nU7TLMmwYdOggU/RHjpzDDpmZUgGsTx8xy4cwSTWSWLpjqdNiCMZIgqpKlaRmiYaEKopSilFFIkjI\n9mSzZPuSQk9r+BIWJlP0Bw5I2fECmT1bqn2G8LRGDkk1k9hwYAMHTx50WhShcmUpgLZsmTixKIqi\nlFJUkQgS1u1fx9GMo8VSJADq1IFRo2DiRPjkkwI6T5gALVuGXO6IvEiqIcVkHU1MlZukJBgxAp5/\nHubMcVoaRVGUgKCKRJCQvD0Zt3HTLqFdscfq00ciOR94ADZvzqfTb7/B9OmlwhoBQZKYKi8efxy6\ndZOLolVCFUUphagiESR8v/17Wp3fiujw6GKPZQy8+674UN56K5w6lUenSZOkYuUddxT7eMFA0CSm\nyo3LJfNNMTFyMTLKZEFbRVFKMapIBAnJ25PpWKN40xq+VKoEkyfDunUweHAeHcaPhx49IC7Ob8d0\nmqQaScGRmCo3VavKxVi5EoYMcVoaRVEUv6KKRBCw59geUg+mckmtwiWiKoiWLeGtt2D0aEle+Qdr\n10JKSsgV6CqIpBpBkpgqL9q1k/wSb711Ds4riqIooYMqEkFA8nZJ/FBcR8u8uPdeCQe9/37YsMG7\ncsIEeUvu0cPvx3OStgltgycxVV4MGCC+EvfcI4nAFEVRSgGqSAQByduTqVmxJjUq1vD72Dn+ErVr\nw003weHfsmTO/o47ICLC78dzkvIR5Wke35zkHYXJyFWC5OSXaNgQbrxRQm8VRVFCHFUkgoDk7cl+\nn9bwpXx5+PJL2LsXXrtmLuzZU2qiNXLTqVYnvkn7xmkx8ic6Gr74Ak6elOyXxa7/riiK4iyqSDjM\nqaxTpOxO8aujZV7UqyeBGk2Wj2dPXFNo1Sqgx3OKLold2HJoC1sPBXFq6lq1YMoU+P57Le6lKErI\no4qEw6zYtYKM7IyA+Efkpnv7g9zknsor++/i089MwI/nBJcnXo7BsChtkdOinJ1OneDtt6WNHu20\nNIqiKEVGFQmHWbRlERUjK9KieovAH+yTT3CTzYkb+9C/vwRulDaqlKtCi+ot+Drta6dFKZgHHoCH\nH4a//Q2++sppaRRFUYqEKhIOszBtIZ0TOxPmCgv8wSZMwHTvzqsfVadZM7juutKZbLFLYhcWpS3C\nWuu0KAUzciRcc40kq/rpJ6elURRFKTSqSDjIicwTJG9Ppmti18AfbONGKSDVrx/R0TBtGkRFwbXX\nwuHDgT98SdIlsQvbDm9jy6EtTotSMG63OK/UrSvhuLt2OS2RoihKoVBFwkG+3/Y9GdkZXHHhFYE/\n2IQJEBsL118PQHw8zJoFO3fCLbeUruCBTrU74TIuFm0Jcj+JHMqXl7on1oqZ6JxqwCuKogQHqkg4\nyMItC4mPiadJXJPAHigrS8qB3n67mCG8NGokkYjffCPT9aEwE3AuVI6qTKvqrYLf4dKXhATR7DZv\nloQf6elOS6QoinJOqCLhIAu2LKBrna4YE+AIitmzxWR+771/2tS5M7z/PowbB088EVgxSpKQ8pPI\noXlzsUx8/72kI83OdloiRVGUAlFFwiEOnTpEyu4UutYpAf+I//wHWreWlgd33illIF56CV55JfDi\nlARd6nRh19FdbPp9k9OiFI7LLoNPP4XPP4eBA0uPmUhRlFJLCYQKKHnxddrXeKyHK+oE2D9ixw4x\nmb/zzlm7PfIIHDgAjz0mZTjuvjuwYgWaTrU64TZuvk77mvpV6zstTuG44QZ47z2pyVG1Kjz3nNMS\nKYqi5IsqEg6xcMtC6lSuQ53YOoE90Lhx4hdxxx0Fdh0xQpSJ++6TMuQ33xxY0QJJhcgKtLmgDYvS\nFnH/xfc7LU7huftuOHhQyo5HRcHTTzstkaIoSp6oIuEQC7YsCLw1wuOB//s/cbKsWLHA7sZIosXD\nh2WXyZOltlSo0iWxC+NWjcNaG3g/lEDwv/8Lp07BU09BZKSYixRFUYIM9ZFwgN1Hd7N+//rA+0fM\nmwdbt4qJ4RxxuyXA46abJEfS9OkBlC/AdE7szN7je9l4YKPTohSdYcPEGjF0KLzxhtPSKIqi/AlV\nJBwgJywx4IrEe+9B06bQvn2hdgsLg48+kpQTt9wiLhahyKW1LiXSHcmczXOcFqV4PPusWCMGDRKv\nWEVRlCBCFQkHWJC6gKbnNSW+fHzgDrJ3L0ydKtaIIpj1w8Ml4eI114h1IhQtEzERMXRO7MzMTTOd\nFqV4GAMvvihWicGD5bOiKEqQoIpECWOtZf6W+YFPiz1unMxT3HlnkYeIiIDPPhPLxF/+IlGJocZ1\n9a/jm7RvOJIe4tkijYEXXoDhwyXhx/DhGhqqKEpQoIpECbN231q2Hd7GtfWuDdxBsrLg3Xehd2+o\nUqVYQ0VEwCefyFC9e0vyqlCiR70eZHoymbd5ntOiFB9j4JlnxCLx7LNioVBlQlEUh9GojRJm2s/T\nqBBRgc6JnQN3kOnTpazn//yPX4YLC4Px4yEmRlIbHDki0/WhQJ3YOjSOa8zMTTO5uXEIx7P6MnQo\nlCsnyT/27xdfmDD9V1YUxRn016eEmfrzVLrX7U5kWGTgDvL225CUlG8my6LgcsGoURJFOngw7N4t\nlnZXCNi0rqt3HeNXj8djPbhMCAh8Ljz8sCSruusuSf7x6acQHe20VIqilEFKya9qaLDr6C6W71pO\nzwY9A3eQdetg4UK/WSN8MUbSaL/2mqTS7tsXMjL8fhi/c13969h3fB8rdq1wWhT/0qcPzJgBixbB\nlVfC7787LZGiKGWQIikSxpiBxpgtxpiTxpilxpi2BfTvbIxJMcacMsb8Yozpl2t7Y2PMFO+YHmPM\nw0WRK9iZ8csM3MYdWP+Id96B6tUDmpZy0CDxm5g8GXr0CP6q10k1k4iNimXmLyEevZEX3bqJ4rhp\nE3ToIEtFUZQSpNCKhDHmNuBV4BmgFbAamGOMqZZP/0RgBrAAaAG8AYw1xlzl0y0a2AwMBXYXVqZQ\nYerPU+lUuxNVyhXPATJfDh+WbFIPPCBekgHk1lth7lxYvlxmUVJTA3q4YhHmCqN73e7M2DTDaVEC\nQ7t2sHSpzDN16ACLFzstkaIoZYiiWCQGA2OstROttRuBB4ETQH5lngYAqdbax6y1P1tr3wGmeMcB\nwFq7wlo71Fr7GRACxvLCcyzjGAtSF9CzfgCnNcaNg/R0USRKgMsvl+dXerrkvPr22xI5bJG4rv51\nrNy9kl1HdzktSmC46CJYsgRatJBpjokTnZZIUZQyQqEUCWNMOHAxYl0AwFprgflAUj67dfBu92XO\nWfqXSuZtnkd6dnrg/CM8HpnW6NULzj8/MMfIg4YNYdkySaB5xRXBGx7avW53XMbFrE0hmqbzXIiN\nha++EueVfv2kVkdWltNSKYpSyimsRaIa4Ab25lq/F6iezz7V8+lf0RgTwNCF4GLaL9NoEteEi6pc\nFJgDTJ8Ov/4aECfLgqhaFebMgf79JTz0oYfEShFMVClXhY41OzLjl1I6vZFDRISEg77xhrRu3SRE\nVFEUJUCEfPjn4MGDqVSp0hnrevfuTe/evR2S6M9ke7KZ8csM7mt97sWzCoW1Ek5x6aXisOAAEREw\nejRcfLHoMitXwpQpUKOGI+LkyfX1r2f418M5lnGM8hHlnRYncBgj4aEtWoiFqk0b+PxzuTiKopQ5\nJk2axKRJk85Yd/jwYf8dwFp7zg0IBzKBnrnWjwe+yGefb4CRudbdBRzMp/8W4OFzkKU1YFNSUmyw\n8+3Wby3DsUu2LwnMARYvthasnT49MOMXkmXLrK1Z09q4OGsXLHBamtNsObjFMhz74eoPnRal5Ni2\nzdo2bayNiLD2nXes9XiclkhRlCAgJSXFAhZobQuhB+TVCjW1Ya3NBFKAK3LWGWOM93tyPrst8e3v\n5Wrv+jLBFxu+ID4mnnYJ7QJzgBdfFCeFawMYVloI2rWDlJTTfn9PPx0cU/WJlRO5pOYlfLTmI6dF\nKTlq1oTvvhMH3IEDJdzGn28iiqKUeYoStTESuM8Y09cY0xAYjYRvjgcwxrxgjJng0380cKEx5iVj\nTANjzEPALd5x8O4TboxpYYxpCUQACd7vAXIoKDmyPFl8vPZjbmtyW2CyKq5ZI3W+H3ssqNJMxsWJ\n39+//iUZMDt3lqzdTtOnWR/mbp7L/uNlyG8gMhLefFPmmubOlYynP/zgtFSKopQSCv3ksRKiOQQY\nAfwINAe6WWtzfpmrAzV9+qcBPYArgVVI2Oc91lrfSI4LvGOlePcfAqwE3iusfMHG/NT57Dm2h34t\n+xXcuSi8/DLUqgW33x6Y8YuB2w1PPgnffAPbt4uFwukKor2a9MIYw2frPnNWECe4+Wb48UeoVg06\ndoQRI4LDVKQoSkhTpFdYa+0oa22itbactTbJWrvCZ1t/a23XXP0XW2sv9vavZ639INf2rdZal7XW\nnasFuNZ24JmwegJN4prQqnor/w+elgaTJsGjj0J4uP/H9xOXXAKrVsHVV4u+07u3c9mcq0VXo9tF\n3crW9IYvF14oUx3DhkkF0U6dJNpHURSliASPLbwUcvjUYb7c+CV9W/RFXEn8zMiRUKkS3Huv/8f2\nM7Gxklb7449lyqNpU5g92xlZ+jTrw5IdS0g9GMTpOANJeLgoEd99J6GhLVrAW29JLhJFUZRCoopE\nAJmyfgoZ2Rn0adbH/4Nv3w7/+Y8UvoiJ8f/4AcAYsUasXQvNm4tvaN++8NtvJStHzwY9iQmPYdKa\nSQV3Ls0kJYmpqH9/CRe97DL45RenpVIUJcRQRSKATFg9gSsvvJKEign+H/yf/4QKFUSRCDESEsQa\n8f77kkerUSOxVkhUb+CJiYjhxoY38tGaj3JCicsu5ctL2fmvv4Y9e0TDe+GF0CjrqihKUKCKRIBI\nPZjKt9u+pW/zvv4ffNMmeQo/8YQoEyGIMfIivGGD1Ozo3Vs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 25, 128, endpoint=False) # time vector\n", "\n", "yexp = exponential(t, tau=3, N=1) # Exponential\n", "ygau = gaussian(t, t0=5, sigma=2) # Gaussian\n", "yconv = np.convolve(yexp, ygau, 'full')[:t.size] # Convolution\n", "\n", "# Plotting\n", "plt.plot(t, yexp, label='Exponential')\n", "plt.plot(t, ygau, label='Gaussian')\n", "plt.plot(t, yconv, label='Convolution')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we will add Poisson noise.\n", "\n", "The blue curve below corresponds to adding Poisson noise to the blue curve shown above.\n", "\n", "There are two ways of adding noise to the convolved decay (one of which is wrong):\n", "\n", "- Convolving the theoretical curves and then adding noise (red curve below, corresponding to adding poisson noise to the red curve above).\n", "- Adding noise to the exponential decay (blue curve) and then convolving with the theoretical IRF (green curve above). This, which by the way is wrong, gives a smoothed out decay shown in the black curve below." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ppUeNGqXfffdd/e677+r9+/drrbVOTk7WUVFRDq/v1auX9vPz0yNHjtSvv/66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C9sgL37nZ2X9K45eK75P1N+KOMAXAPwG4BC9u53dl2MXOtkAD319pP3uY2uuTXvczkhkkQikUgk\nEgAOUOZYIpFIJBKJYyBFgUQikUgkEgBSFEgkEolEIklBigKJRCKRSCQApCiQSCQSiUSSghQFEolE\nIpFIAEhRIJFIJBKJJAUpCiQSiUQikQCQokAikUgkEkkKUhRIJBKJRCIBIEWBRCKRSCSSFP4PQzXw\nYgJYHJAAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 1000 # A thousand photons (on average, since adding poisson noise changes the total number of photons)\n", "\n", "t = np.linspace(0, 25, 128, endpoint=False) # time vector\n", "\n", "yexp = exponential(t, tau=3, N=N)\n", "ygau = gaussian(t, t0=5, sigma=2)\n", "yconv = np.convolve(yexp, ygau, 'full')[:t.size]\n", "\n", "yexp = np.random.poisson(yexp) # Adding poisson noise\n", "yconv = np.random.poisson(yconv) # Adding poisson noise\n", "yconvwrong = np.convolve(yexp, ygau, 'full')[:t.size] # yexp has noise, ygau hasn't\n", "\n", "plt.plot(t, yexp, label='Exponential')\n", "plt.plot(t, yconv, label='Convolution', color='r')\n", "plt.plot(t, yconvwrong, label='Convolution done wrong', color='k')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As shown in the following, first adding noise and then convolving is equivalent to replacing each detected photon with a gaussian signal. This is wrong, as each photon is detected in a single channel, not smeared out over several channels." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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QoYLu2LHDZXsl0efdunXTwMBAPXz4sLNs9+7dWrFixTIXEsrYuEbxycoCbDZz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\nL473epkKCbluHvUSgJsBbIF586ggnza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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 1\n", "\n", "t = np.linspace(0, 25, 128, endpoint=False)\n", "yexp = exponential(t, 3, N)\n", "ygau = gaussian(t, 5, 2)\n", "yconv = np.convolve(yexp, ygau, 'full')[:t.size]\n", "\n", "yexp = np.random.poisson(yexp)\n", "yconv = np.random.poisson(yconv)\n", "yconvwrong = np.convolve(yexp, ygau, 'full')[:t.size]\n", "\n", "plt.plot(t, yexp, label='Exponential')\n", "plt.plot(t, yconv, label='Convolution')\n", "plt.plot(t, yconvwrong, label='Convolution done wrong')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we will perform a MonteCarlo simulation to obtain the phasor distribution for the \"unconvolved\", deconvolved and \"wrongly convolved\" cases." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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1DHpFu7raa7XL999DdDQMHqzfv+7sduY+96f7eiGEEKIr8cx6AII88lIF6PNg\nu7cce1Z07xgKUUda9+QBHoOltZR7t3LPSr6PSn9trVvrvQ/ff69fdJgyxTvXJe9FW5Iu5UIIA8/5\nKisD9Qqt+zIercLF5mPcOhu2/AWGlMKew3u87sM+E85Ydj+n5/njT+mV/AHHjFcInN3eW/V8Sg9p\nux3y8hq7naWn6/ezg97dXrqjCSGE6Io8sx5Ac4ShAtxqqLVh3jt5VmxD3fav106vIt0aMfl6y7pn\nJd9Ht/fmBlNVyjift3uuS96LtiQt3EIIA8+RTqdG/JOyYKg1QVmwvuzFbiH7OYiu1f+otGVlm4bz\nNXfOBLsDa5Hd1d3cAdgDNCaWlFMZoLE1Norzwj5pdjR1X3bu1K9y79xpXO/rC4sQQgjR2XlmPUDY\nSzn6QGWOQP3nczneOzV5P/dZmGo4Kl9vWQ+qbnzKqggIqjR2cz9N27bpLdqe3c0l78WZkBZuIXq4\nwkL9Sq7Npgfwww/DrFngvP16f+kP6eUM0Rq8WrcB2JBJeG2/s1VknzzvCQ8AohyN4T+lpJytgRcR\n1fBaksllU+AMLqj7stlzV1cb5zd18vWFRQghhOiM3PM+OhrCwxuzHqAybySsbKZL2L/+BLeP9n0V\nvL2b8erRu6O704DQChjwmb7cJxeunQG98vQu8rVh+oWD4pGeZ/Oprk5v2Q7w+FIheS/OhFS4hejh\nPLtNzZljDOAWqTCjtXWzdjuIrDNefR+j9njtEx6uj9qanw8OP7egh4TAxIkyj6cQQoiuwz3vT9vs\nW8+8G5vnKOgt1dIKfb89jecPsMPiqV4XEkwmSEiAkhJ8zu3tcOhTpsXF6ZVtyXtxJqRLuRA9nGc3\nqVPeY4x5MVPo1TX7aET7lO9sczjg0CFITPS/z8CB+r1cZrP/fYQQQojOpE26RTc3J3dLnO0L9J6D\nwaFPGXboEPRronNeXBwcPCh5L86cVLiF6AGaGm3Ts5uUr6kzQJ/ferM5mgPRQXwTNBAr2SSTi5Vs\nMknDFhbefi+gjXhm/Bdx3n8Cq6v1UUubmi7kyBF9VNPJk2UEUyGEEJ1DcyNrt6hbtK9pv9xVxvo+\n7mxq7lZxr+3eBziz/kgTA6xL1ou2IhVu0eUMHjyYRYsWnfXn/eSTTzCZTPzvf/876899ppzdyHJz\n9Z9pbtNV/nn1HrZYojkQE8QWSzQjEvb6PIf7/NYxtca+1hPYSWhdfXu+hDangIkF9ezsG+6aw9tp\nxw7/o5v/xuvzAAAgAElEQVSaw/fw35hoXv4qiFV50dgL9nq9p0IIIc6MZH3rNZX1heWF1F5rJeQX\nyYTcZiWol5+ao+e0X3f3h3tDYfFkvfLt76r82eSvhVwB9Sa8qjcmByyPgjjvrPc7RWhEIdXXWNl+\nQTI7RlnJLSySrBenTSrcndCKFSswmUwcP37c5/ZRo0Zx8cUXn+VSdR5aB94s3JHPfSY8u5G5L9de\nk8JUm53ksjqm2uw8W63PZ+3eor3ZHE38Kf83dodRzZjSqvYoervR0AdWm3DslGsO75Zwv/BgLbK7\njm2qRVwIITxJ1jdNsr71msr69A3pbC/Ipjo8l+p+2YRe31Bz9GzRjvEIM5PSRwRP2AFLE2Cgx3Qd\nnYkGmOr1h+f6kHJYPKXl5/K88NAw/7dkvTgdUuHuhDRNa/KPfVcNAtFxPLuRuS/3KjXe2zSg5hRD\nYvfwTd1oQ8Wyd7WfEcQadOVPpfvFBHP4HrbGRlAZoOnTicVFGlrALVXG98u57Os7c3Pd+4QQPZdk\nvWhrTWW9rdxYG++TaGPSRYVwxzBjxTLU9wUgAIJq2n+e7fYU7DY6WkSh3mp/b6j+uHGKsfu8573q\nDct+ro9J3osmSYVbiO7I4y//G+uKSE2FpCRITW0cbbOwEI4EhxkOLesdxj8CU4jx6FJdFmSiLFif\nlaMlulIku19MeD0yhSkllYQ5IMwBU4orDC3gtlDj++Vc7tPH+7xNde8TQggh2lJmJn6zvjjXWBuP\nj7EQvCAdQu3Gk1TH6HNwd6UQbyn3a1jz0vVW+6Bq/RG/3dWKDXjPN96w7CvrQfJeNE0q3F2c816j\njRs38vDDD5OQkEBYWBiXXHIJBw8e9Np/27ZtzJo1iz59+hAZGcnYsWNZs2aNYZ8PP/yQadOmERkZ\nSe/evZk7dy5fffWVYR9nV7iDBw9yww030Lt3b3r16sWiRYuoqmrsWjx69GhmzJjhVQ6lFAMHDmTe\nvHmudZWVldx9990MGjSI0NBQhg8fzuOPP97k69+1axcmk4l//OMfXtvee+89TCYT//73v13rjh49\nyqJFi+jfvz+hoaGMGjWKv/71r17HHjlyhLlz5xIZGUm/fv34+c9/TnV1Naoz3LvUEh5/+eNuSSMr\ny3u0zfR0+GFZDlnmKA5GB5JjicLyfg4WH0OVD6isJ6am5X80ulLbTFmQydWFfkqx3Wu7e6t2Wnnj\n+5VljiKtPAfQ31PPq9tNde8TQoiWkqyXrG8Jsxm/WW//SybkpcLxJKJKU8nMyPRq9QYg0qZXwrtS\niLeUI6ixC338Nu/t7t3pNzS+X+Sl6stAfLzv1mzJe9GU05qHW9O0nwLLgP7AbuAOpdQOP/v+APjI\nY7UCLEop6XDRRlauXElAQAD33HMPZWVl/P73v2fBggXk5OS49vnPf/7DnDlzGDBgAEuXLqV///7s\n37+ft99+myVLlgDw3//+l1mzZpGcnMyDDz7IqVOnWLNmDVarlU8//ZRBgwYBjV3d5s2bR1JSEitX\nruTTTz/lL3/5C/369eORRx4BICMjgwcffJCioiLMbnMqbN68GZvNxvz5813r5syZwyeffMKNN97I\n2LFjee+997jnnns4evSo3zCeMGECSUlJbNiwgWuvvdawbf369fTp04fLL78cgKKiIqZMmUJAQABL\nliwhNjaWd955h8WLF2O3213vQVVVFRdffDH5+fnceeedWCwW/vGPf/Dhhx92nS5+LfzLb7NBceVI\nplXq81MmxcLBIZDfNwzKjBXPwK75/aNFEirqOcJoAv3cph53qo6tcRH0O1VF75p6Sk8FkB8WTlp5\nDsWVI5k0CTTNOJ95WprenS83t/E8LRohVohOQrK+85Gsl6w/HTYbUGGGv2YBEJcE5ifAEmkhtzTX\nuHNA07ePdWkBtfogcP5aDqLyIW4PXLkI+n+hryscq1e2K8xERuq9BtLSJO9F67S6wq1pWgbwOHAz\nsB24C3hP07RzlFIlfg5TwDmA6xv82QrgwvJC0jekYyu3YYm0kJmRiTmibSbTa89zt1Z1dTW7d+8m\nICAAgF69erF06VL27dvHeeedR319PbfccgsDBw7k888/Jyoqyud57rnnHvr27cvWrVuJiYkB4Ic/\n/CHnn38+DzzwgNcV4gkTJvDss8+6lktKSnjuuecMIXz//ffz2muvcfvtt7v2W79+PVFRUcyaNQuA\nN998k48++ojf/e53/OpXvwLgtttuY968eTz55JP87Gc/Y8iQIT7LnJGRweOPP05ZWZmrzLW1tfzz\nn//kRz/6kes9+b//+z+UUnz++ef06tULgJtvvplrrrmGFStWcMsttxASEsK6des4cOAAGzduJK2h\nT9BNN93EmDFjWvrf0fFa+Jffc7fiYv1K7a/653Bf+VRSiuw9ohuMRtN/DKNrYUpxY208psbBYLud\nTPNUplWeJDjY9zWOnBw9iG02/b12du8TorOTrD87524tyXrJ+tPhmfVHjugts+tezGTsw2k4LNsg\noK7jCni2aDTdch/ggFvHQoDbzXPOruZ/zWLoUL3XgOS9aK3T+S59F7BOKfV3pdRXwK1AJdDc3A3F\nSqki5+M0nve0pG9IJ/twNrmluWQfziZtfdvdVNGe526tRYsWucIGYNq0aSilyG34C/vZZ59x6NAh\nli5d6jeACwoK2L17NwsXLnSFGehdxS699FJDdy3Qr3zfcssthnXTpk3j2LFjlJeXAzBs2DDGjRvH\n+vXrXfvU19fz+uuvc+WVVxISEgLAO++8Q2BgIHfccYfhfHfffTf19fW88847fl97RkYGNTU1ZLr9\ndXvvvfcoKysjIyPDtS4zM5M5c+bgcDg4duyY63HZZZdx4sQJPv30U1dZLBaLK4ABQkNDufnmm/2W\nodPxdyOXj93cPw52O8yZA5/sGsm0opNUBxj3P52Jv7pxwzhTSuxsNkdzqnivz8Fq/HXvE6ILkKw/\nC+duLcl6yfrT4fxK0PDfQHW13kK7KMNM4D+yIL8Vo3d3dwE+vunEb4OFVvbl6X/SJO9Fa7Wqwq1p\nWhAwAfjAuU7pN7r8F2hqXh0N+FzTtKOapr2vaVrK6RT2dHjen+LzfpVOeO7meHZ3SkhIMCz37t0b\ngNLSUgAOHjyIpmmMHDnS7znz8vIAOOecc7y2jRgxgpKSEk553Nvr7Hbm73lBD8ns7GxsDZcEP/ro\nI4qKigwBmZeXx4ABA4iIiPB6Xvey+TJmzBiGDx9uCPr169cTGxvLRRddBEBxcTEnTpzg2WefJS4u\nzvBYtGgRmqZR1DCkZF5eHkOHDvV6nnPPPddvGTods5nCd1/Heq+F5Hk2rP9Ko6jC+7uv2QxxcQ3/\nDt/D1thIPt6lUVqnsTUugn29jAOEfdY3jLpW9rTrXh3zjILqwVpkZ619akuvcQjR6UnWn71zN0ey\nvpFkvX+F5YVYn7eSvCYZ6/NWr7x3VgYHDkS/h/nGKXBvKNsvDaV6wWT41zp9oDR3p3OFvbsKqIPE\nbGobLs5I3ovWam2X8lj0qWsLPdYXAv7+QtmAW4CdQAhwE/CxpmmTlVKft/L5W83z/hRLZNvdVNFe\n5w4NDQXwCjynyspK1z5O7le83bX3wB8ted6MjAyWL1/Oxo0bWbJkCRs2bKBXr16u+63aQkZGBr/7\n3e84fvw4kZGRbNq0iZ/85CeYTPo1pfp6PTkWLFjA9ddf7/Mcnb0bWVVVFSdOnKCsrMzvz+rqaurr\n66mvr2d9xHpsQfoXn9zSXMY9Mo75p+ZjMpkIDg4mJiaGmJgYgoLSgDh9dO6ixikzphRXsi0unKx+\nUcRXVtK7Cvoe64uJnjUJpaL5iwYDak65vtAI0Q1I1p+Fc0vWt15PyPq6ujpXrvvL+srKSurr63E4\nHNTX17MhcgMFwQWAnvfnrzyfa6quISAggKioKHr16kWvXr0ICZmpj84dv73xCRN2wOxb4KkDetfp\nKJs+Inf8VqCJ+7lbEo5diQKU1uS0Z8F99O9UkveitU5r0LTWUEp9A3zjtmqrpmnJ6N3VfP81bHDX\nXXcZujsBzJ8/v1VXHzMzMklbn2a496qttNe5ExMTAfj6668ZOHCgYdupU6c4fPhwqwMsOTkZpRR7\n9uzh4osvbvZ5PX311VfExsYSFhbmta05gwcPZvLkyaxfv56f/vSnvPHGG1x11VUEBQUZnvuDDz6g\noqLCcOV7//79hrL54xyw5fXXX8dsNmO32/nxj3/s2h4XF0dUVBQOh8Pv63cvy969e73We47e2laU\nUhw/fpy8vDyfj/z8fE6cOEFNTY3P4zVNIzo6mpiYGEJCQggICMBkMlEyqwQa32JKqkv497//jcPh\noKamhrKyMsrKylDqPsz8hQnHvEfnjq2uYUzddt6r/CmDySGmh1W2Qf8+UUfTfyz7nKyj+Lu9xA0Z\nSWEhXHkl7N6tbxszBv71L1BKHynW/f4u6XLWOb3yyiu88sorhnVlZWUdVJquQbK+9STre1bWg34R\nxZnthw4dMmT94cOHOX78OBUVFX6Pj4iIICYmhvDwcAICAlx5f3zmcQhu3K+4qpi33nqL2tpa7HY7\nZWVl1NbWAnFwaZD3iaNsDYOq/Q9X59dfRUOA9/cCl+5U2Qb99TRz3ao6NJ8p66xsWqCP4+Ar759/\nHm69VbK+qzhbed/aCncJ+uWufh7r+wEFrTjPdiC1uZ1Wr17N+PHjvdY7779pCXOEmaxF7XMZqr3O\nPWPGDIKCgnjmmWe46KKLDF3K1q1bh8PhcA1A0lLjx49nyJAhPPHEE1x//fVeX24A+vfvz7hx4/jb\n3/7G8uXLiY6OBmDPnj28//77XHfddaf9mjIyMli2bBnPP/88JSUlhi5mALNmzeLZZ59l7dq1/PKX\nv3StX716NSaTiSuuuKLJ8w8fPpzRo0fz6quv0q9fPywWC9OmTXNtN5lMpKen88orr7B8+XKv7nYl\nJSXExsa6yvKf//yH119/nfT0dEAPyT//+c+n/fpBb6Heu3cvX3zxBbt37+bbb791Ba3zPjiAsLAw\nEhMTSUxMZOLEicydO9c1FYuzVdr57169ehEVFeW6uu/O+ryV7MPZruXJIybz+rIsV6Vv5Eh47bV6\nwsPLMV10IWE+fq0KwkO5+vJXGPj3/O59M3YzNKDKBMFuXezc3/GoWggcNoovhkRxjzmH7dsbP187\ndsDQoTBiBGxvaFRwjmoqV8g7p/nz5xtGVQY9dyZMmNBBJTrrJOvPwrkl67tn1jscDg4ePMju3bv5\n4osv2L9/v6tyXVLSON5gQEAA8fHxJCYmkpyczEUXXURsbKxXxjt/RkdHGy5euGsu7889V/Hii6c4\n6ThAyqspVHiMjxZYFYd5QC4VFYqysmR95XM5cNuonjWBsKagNlgfzdwRqA+iZnIL/oAathdkM3TN\nUA4sOUB6utmV66Dn/bhx4GjoGCBZ3/mdrbxvVYVbKVWradouYAbwFoCmJ8QMYE1Tx3oYh979TPgQ\nFxfH/fffz3333ceFF17IlVdeSXh4ONnZ2bz66qvMnDmT2bNnt+qcmqbxzDPPcOWVVzJu3DgWLlyI\nxWLhq6++Yt++fa6BSh599FFmzZrFBRdcwOLFi6msrGTt2rX07t2bBx544LRf07x581i2bBnLli2j\nb9++XvN1zpkzh4suuoh7772X7777zjVVyKZNm7jrrrv8jlrqzjlKamhoKDfeeKPX9pUrV/Lxxx8z\nZcoUbrrpJs477zyOHz/Orl27+PDDD11BeNNNN7F27VquvfZadu7c6ZoqxPOes+ZkZ2fz/vvvuyrY\nX3/9NQ6HA03TGDZsGMOHD+fiiy92Va6dj7i4uDaZksRXq0za5capLH70IxNZWdEc+f4rIt2OrQf2\nJYbT57WtHFg6kuLQTxhy6vAZl6mrCsD3OCruwhww5oCd++xTeZ+Thm12e+MVcCeZo1N0VpL1Z4dk\nfffI+s8++4ycnBxXBfvLL7+kslKf1cJisTBy5EjGjx/PVVddZcj6AQMGEBjYNh1Nm897jQULwmHR\n7VTUNbaga2hMHDCR569/i1v3mskrKaT8aiuO8IZu5SqAJruVdzcaEOTsTehR2XZjr7Ez9N40+uR7\n16QdHm+XZL2A0+tSvgp4oSGMnVOFhAMvAGia9ggwQCl1fcPyncB3wF4gFP2+rouAS8+08N3Z//3f\n/zFkyBDWrl3LQw89RF1dHUOGDOGhhx7iF7/4hWFff5Uzz/WXXXYZH330EQ8++CCrVq2ivr6e5ORk\nw4icM2bM4N133+WBBx7ggQceICgoiOnTp7Ny5cpmu3o1ZeDAgaSkpLBlyxZuuukmr/vBNE1j06ZN\n3H///axfv54XXniBwYMH89hjj3HXXXd57evrNWdkZHDfffdRVVXldVUdwGw2s337dn7zm9/wxhtv\n8Mwzz9C3b19GjhzJH/7wB9d+YWFhfPjhh9xxxx2sXbuW8PBwFixYwMyZM5k5c2aLX/OSJUuIjo5m\nzJgxTJ8+nTvvvJOxY8cyatSoVgf66fDVKuNvem5bFAx0m+jn0yEhTMytwGrVA3vh3Bq2/BvCayFA\n9awL3q1l8XM/ptd+Mken6Nwk688Cyfqun/U33ngjQUFBnHfeeYwdO5arr76asWPHMnbsWOKco5K2\nsxbnvceAf0N6D2H7TdtdWc/CdIhvqKX3ye3RPdv8Vbad7MoGx5s/jWS9ANBOZ6ANTdNuB36B3r3s\nc+AOpdTOhm1/BRKVUhc3LN+DPo/nAPQpRb4AHlRK/a+J848Hdu3atctvN7MJEybgb7sQHcn5+Xzr\nrbeYPXt2m7RWt4nCQr4Ylk6E3YYNC2lkUhVl5sABWPTyZH61ageWcrBFwsqfT+JfS7cz4dw9PHki\nhQnH7IT5uMhdj1S+PWWZo7i49CR1dfp9206TJuGar1vu6+p63LqYTVBKtbyvcxcmWS+Ef87P56uv\nvspVV11FcHBw8wedRVOmYOjuPHkyBN1i7HqempBK1qIskpMht7AQliZCULX3yeppfg7r7s7zC09e\nKsEvZTFyJHz+uTHvo6L0GWAk67um9sj70+rLopT6I/BHP9sWeiw/Cjx6Os8jRFc2cODAzlPZBkhP\nZ4xdD9pkcskkjWn2LNLSIPO9f5EW7T0o0Fp7ClOL/A+aUhMAoT2ot5k/DvT34os+4aSV5+BwQEGB\nfu+WVLBFVyVZL0Tzhg0b1ukq22CsADqX/Q0AaLFA7g/SfVe2AU4kQXgxhDYxiFp35jBBfSBQC45g\nKBgDGzKpqYHwcMl70bx2H6VcCNE51B3JN/zCWzR9IDSbzbs7WnHuHr64fCgTC5sOV9WSYT27KQVU\nAWHo93iHOSCwXlFcqQ/S086z9AghhBBeCssLSd+QzmcX2mCUBTZkQoWZY8e8s945f3d+ug1Km5iF\nxG4Bk8O7wt3dpgbzJ6AeAhru7TZVg6lWH9Ud/TuU5L1ojlS4hegh9gUex332UVvccSjyfX+R7fIU\nxhzwXdlWQHUA7O0VyrCyalo/eUz3oKHfqOpu/LFTnAjWKA0JIPf8cL4py6G4ciS5ufpI5QcOyFVv\nIYQQ7Sd9Q7rebTwKiMrV59b+a5bPrHftC/qVY08KKBwFphqI8DFBQU+obPsy4HO4V/8GUFg+lpnp\nm/g8Ww/33FyYPdvYnV8Iuf1SiB7ixhv6kJUAB3tDVgLMS+9Daqre9clTr1L/A39p6N3Ih9mriK5r\nvKzbEy/wen7X0ICYGhhsdzDVZievajSbsRJHEXY7DBoEVisUFXVEaYUQQnR3No+B0QL72Pxmvee+\nXjQgbh8k7Gjsbt4Tw96Thv5+BFVT0Xs7n5+TZti8cyckJ0vei0ZS4Raihwi2xDNtMQy9E6YthqSJ\n8WRl+W5xtUd7tt16i6wxLvfUC91NCatXWMkm0zQHgOpqfSTYNLdsLizUQ1nCWQghxJmyRBqbsqec\nZ/Gb9Z77+tTMaN0CGJQNiydDhB7gSukt3e55L1nfs0mFW4geIjMjk9SEVJJ6J5GakEpmRqbfABjW\nZ1jHFraLae6CvyXcOAm3+3Qt6el6KHuGsxBCCNFarcl6931brKdfXfcV+Bp6L4B53gHuzHvJ+p5N\n7uEWoofwNU+n9fKGuTfRQyAtDbKyILi0zOc56tFH495tNjG2oJ5Q6VoGNP/9I7ammgPRQdhCw0gr\nz8FiGena5m9udCGEEKK1WpP1zn0Lywvp/+hAfWA0JwXUREJAFQTWnb0X0JUN2AlLkvVB5hoGq3Pe\nOy9Z37NJC7cQPZjfAPA1ugqww2IiLLSQC2wOan0NsCIMFPqUYTE1kHyyDmuRnTeiprJuXeM+nm+1\nn7deCCGEOC3NVfbSN6QbK9uOAPjjHnjErk+DJRo1dYU9qBr65EJiNmSkMWlS473zkvU9m7RwC9GD\nWSz61W73ZUBPiLQ0ardkE+TWit3PrrmmwgiS1u1maXgP/JpQUcE1t+itC+B6qw3zdwohGu3fv7+j\niyCEl670ufSb9Q3ySg8bV5yMh+KGnljuFXHhn+cUaTF5BAc33jsvWd+zSYVbiB7MGQCHD0NpKeTn\n6/d3ZWaaMWdlURmiEeM2OFrvGgneMzWgot41gqnFAn/6U0eXSIjOKTY2lvDwcBYsWNDRRRHCp/Dw\ncGJjYzu6GM3yn/V6hdBWWgpBbgeEHe+wsnZZni3fkTbJeuEiFW4hejCzWW9ptVqhqmQPL55KwfLl\nKQ6OC0PLzqEiNIAYt0p2SB3EUUQxZmo0E6HI6KWtpdBHK8/N1R8pKWBvmPLc/d46IXq6QYMGsX//\nfkpKSjq6KKKD1NXV8cEHH/Dyyy+zZ88e4uPjueaaa5g9ezYREREdXTxiY2MZNGhQRxejWe5Z//2x\nQuwXp5MXZWPo7ywceDgTrboPBNkbD6jq0/jvwrEQL5NKnw7JeuEkFW4hBDYbvB6ZgrVIT4Pkk3aq\nzxlNsMnYbzy0HjJJYxpZHHf0IxoZ9aO1TgUCtW7LHlOeO1se3Lud+ZrORYieYNCgQV2iQiPaVmlp\nKevWrWPt2rUcOXKEiy++mE2bNjFr1ixMJhl+6HTZbMC8dP0eY8BOLmnr0wh19KOcvMYdy/s1/vvN\n5+C2MWCS+8i8eHYj9xRR5LoNzzPrbTZ9qrD0dMn7nkAq3EIILBawfGlMg5A6RQj6oF/u9yEPIpey\nwACi6qR1+3Ro9XBe2Mesi7oSS9UpCsLCuMqeQ3Glfr/c8eOQ1/C9R66CCyF6krKyMp544glWr15N\nVVUVP/nJT7jzzjsZM2ZMRxetW7BYIDfKeKHcVm5j8OC+7Cl1W6kaKtcRhbA4RSrb/nhWtt0r4AEO\n+PFsqA+GKBuq0gKvZLoq4BZL41RhIHnf3cllwk5m48aNmEwm3nzzTa9tY8eOxWQy8cknn3htGzRo\nEFar9WwUUXRDmZlQFBHmc1uNx6hf8diIrqvv8VNxtpTn15QoB+TUXoy1yE7yyTpSC+28GTOVkBAI\nCdG7oLmTqUOEEN3dyZMn+e1vf8vgwYNZuXIlCxcu5NChQzz33HNS2W5DmZkQpRlHTLNEWvj2yDHj\njv2/0Ke3uiMZQu2IFvIM/IE79N4EfXJxxGcTuTjNlfU1NXqPNneS992XVLg7GWelOcvjEpfdbmfv\n3r0EBQWR7bwc1iA/P5/8/HymTZt21sopuhezGYZm5/DF0CiqPSrY+2KhzG1WEPmj0Tq+LkxE1hlT\nuV/lKaqr9cp2TY1xX5k6RAjRXdntdh555BGGDBnCb3/7W6677jpyc3NZvXo1/fv37+jidTtmMxx4\nOJPUhFSSeieRmpBKZkYm6qRH0Dintwqt6JiCdlWeX5A8lmtDba6s37FD79HmTvK++5Iu5Z2MxWJh\nyJAhXhXunJwclFJcffXVXtuysrLQNI3U1FSf51RKUVNTQ0hISLuVW3R9cUNGEvftSZgyBbY3DpBS\nRzAl4TWG0crFmfG8CG4LC4OyxuWQEBg4UKYOEUJ0TxUVFTz99NM8+uijnDx5kptuuonly5czcODA\nji5at2eOMJO1yPg9Migzk5r/lwYx+RD9vXQhby92Y426Tx8YM0amCusJpLGqE7JarXz22WdUu/Ut\nzc7OZtSoUVxxxRVs3brVsL+zwu1sHTeZTCxZsoSXX36ZUaNGERoaynvvvQdAZWUld999N4MGDSI0\nNJThw4fz+OOPe5XBeY4333yT0aNHExoayqhRo1zncffxxx8zceJEwsLCGDZsGM8++ywrVqyQgU26\nKo8RgWOra7FFNX+YxHPLVQbBqQD9saNfBPcPyjFsnzgRtmzR/z11qj6IWlFRBxRUCCHaUHV1NatX\nryYpKYlf//rXpKen8+2337J27VqpbHeAwvJCrM9bqV4wVV9R3k8q222tXoPaECJPTOa8L4016vh4\neP11vbJts+n3cEvWd0/dv4W7PYcAbKdzW61WXnzxRbZt28aFF14I6BXulJQUpk6dyokTJ9izZw+j\nRo0CYMuWLQwfPpxevXq5zvHBBx+wYcMGfvaznxEbG8vgwYMBmDNnDp988gk33ngjY8eO5b333uOe\ne+7h6NGjXhXvzZs3k5mZye23305UVBRr1qzhRz/6Ed9//z29e/cG4LPPPuOKK65gwIABPPTQQ9TV\n1fHQQw8RGxuLpsldvl2SxaKP3tHAFqVIy4DM9WAph7gKiPbR2t3cYJ1Cf48cGkS5jVJerUzY1UhS\nU41/StLSZDAVIUT3oJTiX//6Fz//+c/57rvvuOGGG/j1r3/t+m4iOkb6hnSyD2dDNBCdC7XSE7LN\nmRSYqikvCyKw2ixZ30N1/wp3ew4B2E7ntlqtKKXIysriwgsvxOFwsG3bNhYuXEhSUhL9+vUjKyuL\nUaNGUV5ezpdffsnixYsN5/jmm2/Ys2cP5557rmvdm2++yUcffcTvfvc7fvWrXwFw2223MW/ePJ58\n8kl+9rOfMWTIENf+X331Ffv373cF4vTp0xk7diyvvPIKt99+OwAPPPAAgYGBbNmyhX799Gkk5s2b\nx6xKVMAAACAASURBVPDhw8/4fRAdJDOTHRck0OdEDbZISMswVqSD6zV8tWf7qmxLJdxIAwI93jpL\n1SmOHgXP752eg6fIYCpCiK5o37593HXXXbz//vtceuml/POf/2TkyJEdXSwBHD552GONtG63mygb\nRUWwbVtjW11amgyc1lN0/z6/7fmttZ3OPWLECPr27eu6V/vzzz+nsrKSlJQUAFJSUlwDp23ZsgWH\nw+E1Qvn06dMNlW2Ad955h8DAQO644w7D+rvvvpv6+nreeecdw/pLL73UcPV59OjRREdHk9vQ+llf\nX88HH3zA3LlzXZVtgKSkJK644oozeAdEhzKbmXFTCEPvhGmLoTgSXl8P1sOQXAqhdb4D2VfFWirb\nzbOFhlFQoF+7y83Vf6aleQ+eIoOpCCG6kuPHj7NkyRLGjBlDbm4ub731Fu+9955UtjuR0lOlxhWO\nQKiK0n86AnwfJE6P3cKxY41tdc68l4HTeobuX+Fuz2+t7XjulJQU173a2dnZmM1mV+uze4U7Ozvb\ncP+2k69uWnl5eQwYMICIiAjD+hEjRri2u0tISPA6R+/evSkt1f9AFxUVcerUKYYOHeq1n691ouvo\nE9bHsGzxmBXEcRbL0l3VapBljiKtPAeHxxtqs+ldzVJTISlJ/ymDqQghuoK6ujr++Mc/MmzYMF54\n4QUeeeQR9uzZw5w5c+RWs07GM+sJcOjTgAXU6f/2pNDvSfZFGsd9cwRCXipsyKS8HDy+atOnj2R9\nT9D9K9zt+a21Hc9ttVopKyvjyy+/ZMuWLa7WbdAr3Hl5edhsNrKzsxkwYIBXBTsszPecyq0REOD7\n6qZS8le1u4uPjgfAXA6bn4MBHhXunQMgK0Ef9EucnqbGpenbVx8OIisLDh7Uf7bV0BNCCNFePvjg\nA84//3x+9rOfMXfuXL755hvuuecemSWlk3JmfYtp+A8vuZbim2a8cOHZhTw+XrK+J+j+Fe72/Nba\njud2tlhv3ryZ7Oxsw5RfEyZMICQkhI8++oht27b5nQ7MU2JiIkePHqWiwjiv4v79+13bW8NsNhMa\nGsqBAwe8tn377betOpc4+woL9dGvk5O9R8HOzNDn6Xz79RCshyGsIS9OBegV7bnzIrh+WRLnLAsm\nKwEO9jbO1S2aFwBYi+xsCp/MZnM0B6KD2GyOJi58L9IIJIToSkpKSvjJT37CJZdcQkxMDDt27OC5\n556TubQ7gZZkfVLvJM7vmwqFYw3HBtRGuebrToxp3XdE0cCkIDEbfjwbFlphSbL+M6KIqChp0e4p\nun+Fu4uaOHEiISEhvPTSSxw9etTQwh0cHMz555/P008/TWVlpVd3cn9mzZpFXV0da9euNaxfvXo1\nJpOp1fddm0wmLrnkEv75z39SUFDgWn/gwAHefffdVp1LnH2e9xGlpTVuc87TOU4ZvywdjQxkVloq\n/70zl4NLDpJ4ziSmLYahd8KwJVAnFcVWm1hSibXITvLJOqxFdjIjp3rOzCaEEJ2SUopXX32VESNG\n8O677/K3v/2NzZs3M2HChI4ummjQkqzfsmgL4eEQP7yQgNooAssTiSpNZfeNBzi45CBZi7Ja3xou\njPp/oVe8++TqP+elERcnLdo9hVS4O6mgoCAmTZpETk4OISEhXuGVkpJCTo4+d29LK9xz5szhoosu\n4t577+XWW2/lmWeeYe7cuWzcuJGlS5caRihvqRUrVlBbW0tKSgqPPvoojzzyCNOnT3dNWSY6r5aM\n+bcv0DiaxwC7g6znwdzQScL96nhFzWSUVLhbzbNXvqXqFBZL060SQgjR0Y4ePcrcuXOZP38+06dP\nZ9++fVx33XVyn3Yn05Ksd04Pll+ehyPITkBFPGN2ZhEX3lgbdOZ9cGWi3K99OgKrjctRNsn6HkQq\n3J2Y1WpF0zQmTpxIUFCQYVtqaiqaphEdHc3YscYuQJqm+Qw8TdPYtGkTS5cu5e233+auu+7iq6++\n4rHHHuOxxx5r8Tnc148fP553332XPn36cP/99/P888+zYsUKZsyYQWho6Jm8fNHOWjLm34039DHc\nqx1Wrxhjz+ZIyhyg8er4wSUHcazbRmUzEw06gEMxktVNGVBRx9qCaK5L22tolRg6VIJYCNHxlFI8\n99xznHfeeWzbto3XX3+djRs3GmYrEZ1HS7LeVm6shVfHbiP7HCuzMxpDx5n32pOHoE7uyW81j6/U\npqhi8tOTGfaIlezPiyTru7nuPw93F/bwww/z8MMP+9w2d+5cHJ5DGzfwtx4gPDzcZwW7pedwTgnm\nbvr06ezcudOw7qqrriI+XrofdWaZmXrXMptND2Bf9xEFW+KZtjiPA0/qU4I5RbMbq9X72KmzR/LF\nG3u95pp22jkQajWNwWVS5fbknLM8zAHjDtr556HR7CKFNDIpxozdrv9/NcwWKIQQZ913333HzTff\nzH//+1+uv/56Vq1aRZ8+fZo/UHSYlmS9JdJCbqnb97uAOkjMZndIGlZrlvexBWMgYcf/Z+/e43Ou\n/z+OPz6bnTfCNi7ksKlvKMkxNiIVHfhq00aOM9GXiCTnDiSHCskxmWPJ+hm+RBTla3OeIqXCKtFs\nQ7KDnT+/Pz677LquHez8ua7tdb/ddtN1fl5u3bz2+nzen9e78A/OsgO7bBmmlg8FhWyHRP64mQg1\nYyAoANZoxV1qfeUkZ7hFqaWmpprdPnfuHLt27aJbt246JRJFUZSZf8YlZLHu5vf/5W5+TVivXvDg\ng3B2z34ueeR9nww7OGqwg3RXOvwlzXZ+LH8ncclS8SeKCHIvuMtvKaAQQpS37OxsFi9ezAMPPMAv\nv/zC7t27Wbt2rTTbNqA4tZ5s8/NwGc6x+dZ6PtupbXWVkc+01GwFUt2195JmO195NvvxMC/uUusr\nH2m4Ran5+PgwdepUPv74Y6ZPn07Hjh1xdnZm4sSJekcTpeTt5s2WpyMZ1KPd7WnkkXdDYNeWZs87\ndQp27AC/Vt7UTM1bYY/WcYIMZzokpOCQXVHpbcOdDj8YlNw9RPJbCiiEEOXpr7/+4rHHHuPll19m\nyJAh/Pjjj/Ts2VPvWKIMGWu9+40O5g8kmhcd01rvcyASp4x8VjJmOYBzEjikl2NiG6dYVH7XBHDL\nXUcutb7ykSXlotSefPJJPvvsM65cuYKTkxOdOnXinXfewdfXV+9oogwEBsLv3++kc1AAeMTioRhI\nW593TZrxKPpftR2ocT230GYBIzrdQ/S2MxWY2nZYHp7IwnyQWqz3dXzcCl4KKIQQ5eWLL75g6NCh\nODg48PXXX9O9e3e9I4lyEhgISd9HaMubjbU+IgLLttlY6+OS4mj6YTxplk+wz6ioyLbD2F+bFvxs\nJXdPc+dE7PoH0Hh/pNT6SkoablFqq1ev1juCKEexsUCy9+3ri9KdyHNatqXJCe/4Wo7UM2m47YHD\n//0Jp4JHC4gcWcADIxz4aHcGhiSIdYeAnrWI/0jvZEKIqiQtLY0pU6awcOFCnnrqKdauXYuXl5fe\nsUQ5sqz1tRrB1XTMGm7TWh8YHkhSepL5m6S6g3062Jm8yjigpCrL7/tnOYJd7uTybLdYLlyouEii\nYsmSciFEoSyXNqWlQXpOLXVyAj8/2Lkz9/ERQ2vfnmpuVCMjO88/NgWtLFcLeawq2BGunR3oGAqd\nQyEhq4FMLBVCVJhz587RqVMnlixZwoIFC9i5c6c021WAZa2/fh2Sk3Nve3iY13rLyeYApHhDXCvz\n++Luh1SPvNdPqUBGtaq5bUl+3znRILW+EpOGWwhRqIgIran28dEabFPGXWA6dszdP9LR0IDoegW/\nX4YCkfXtySrgiLdC5f6HqbADCvaA7w3w/xMiPlO0oTSbIwgIKOAFQghRhjZu3Ejr1q25efMmhw8f\nZvz48bKvdhVhWuv9/MByHl7Nmtr0bON+0Z5O+Vxo7JoA28O02nXdR/sz2wGcE/Oe5VUAh8yqefZb\nARxyzm5nOEmtrwJkSbkQolDG67VAK7JRUbmP/f03XLyo/XdMjFaMI/ZEMPhGTzZP+Y4a+cxMOar6\n0TkwlhsrYvJ9vLJTKNrvF4ab9reX9snEUiFEeUpKSmL06NGsX7+eQYMGsXTpUjw88tlyQlRaprUe\ntHr/xx+5ty3rfTuHCNoP6MXxy8dRyb0WmWdG3q5dAExzLv/wtiyxvtT6KqAyn0gSQpSxOx0Bv3QJ\nAnp4c27pSa65WGwvYgeR3h4EuK6ERAMdQ+EfR+2Md6YCt6riUe5C1EvO5KB3dbxcfwT+Qs2zj4gQ\nQpTeDz/8QOvWrdmyZQvr1q1j/fr10myLO9b704e9uTrnKI4pTcwfaHAUQvzNpm6bUdGWmAuNx6Xb\nf19JSb9y69YtvROJcmDTZ7jPnj2rdwQh8qjM/1/e6Qj49eu5t//ydsGHxNuPHa0PnUMTUf4cCZ9F\ncHZMU+6amvu417mHOBd+ihoZVfkK7lwuWeAfn8jWOh3wj3FlxIh/s3TpUhwd89n3VAghSiAiIoLB\ngwfj6+vLyZMnuffee/WOJKzEnep9Wpp2ppsEAzSKyX3APhMaRaH0C0BdHQlxD0KDY7mPX24P21dD\naEdwSqqaS8pNOaRDoyich/TiZtgVunTxZuvWrTRokM+Wa8Jm2WTD7enpiaurKwMHDtQ7ihD5cnV1\nxdPTU+8Y5S4iQltGHhurDVy5dAkSc3rogKTDbK3bkbppidq07eCcF7nHapNQPzwPQQF42//Olt1X\nMCT+gGO2NNuW7s5MY82aJYwcOZKzZ8+yZcsW6hgvnhdCiBLIzs5m5syZvPXWWzz33HOsWbMGNzc3\nvWMJK2Za7y9f1hpuAMIjcBocQFbdo2Sqmbefr7rlrI/etOP2VmMk19Ya7BFtc69hFgDU+9dVPo/a\nSp8+fWjbti0RERF06tRJ71iijNhkw92wYUPOnj3L1atX9Y5Sqfz++++MHz+e69evM3fuXDp27Kh3\nJJvl6elJw4YN9Y5RJuLitP05jU31ihXw4ou5tyMitGFpnTrlNtsACSktmPTQTY408yerQRTeSXBw\nNTS4fomaDtX4W4FLX7jioGbTIUH2DCvIjZouDB06lPvuu49nn32Wtm3bsm3bNtq0aaN3NCGEDUpK\nSmLw4MFs3bqVt99+m6lTp8pgNAGY1/vatUFR4OrV3Fq/ZQv07g2//WbyomRv2p6O5LSjP4k1TYa8\npHhqS6U9YiHRAKsPa2e9G0Tl+dwCVaEtxQzuBlq3bs3x48fp27cv3bp1Y/ny5QwbNkzvaKIM2GTD\nDVrTXVkaGmuwa9cuQkJCqF+/Pl9//TX33HOP3pGElQgMzB2UFhNj3lgbB6WdPm3ebCsKuLtrZ7yz\nvo+AoAD+u+s4HeLSMe7qWSMDGicl5tlCLAttWndVYfl9s4DTXi7Uys7gn5ouGPYehrg4Hn71Vf50\ndOTM9ev09vNj3po19O/fX6fUQghbFBMTw7///W9+//13tm/fTu/evfWOJKyIZb03MtZ6gGPHzF/j\n7g4ZGZCyJgICA6DGJXC+DnW+15ZLA9SKgaAAHGvHUqzz2pW52c5WsMtyo17N2jSq2YCI4AgA6tSp\nw759+xgzZgyhoaGcOnWK999/n2rVbLZlE8jQtCpPVVXmz5/PM888wyOPPMKRI0ek2RZmLKdmWs7z\niI3Ne5+qag34H3+gLR9fE0nLhIwifd4Jgx3/VPLLlLOAW/bade0n6ps/dtjgRF+PFAbcl0HdqJt4\nNWlBep/eEBVFtYsXaZWUxJ4a7jz//PNMmTKFrCxZHSCEuLP9+/fTrl07bt26xZEjR6TZFnkUNiU7\nNjb/xzMytCY866ZW6/mngTat3MF8GxJHz1ge9LHYSixbqZr7cAPcaIL6TiKNtv5OxDOReLt5E5cU\nh3+YP81WNOPHDj8y98O5LFu2jB49enDt2jW9E4tSkIa7Crt16xYDBw5k0qRJTJkyhW3btlG9enW9\nYwkrY7Cojy4ueR+3vC/f1YlK/lX1QgNXTjf14EKNakR6ezDsxn5+ru5Gqn3R6nA2tlevT9QH1xnw\n8AvQK9iOo/W1BvyWPTioGSRe+ZGoqNwzCgnnT5m9vnp2Eu+99x7z58+nd+/e/PPPPzp8CyGELVBV\nlSVLlvDEE0/QunVrjh07RosWLfSOJayQZb23fKywx2/zyL9rb3efgR0DI/C7249qiTl7dL9/BTKd\nzJ9oawW9MIV9F9cEVNd4s1ofGB5I1J9RxPwdQ9SfUexw3cFXX33FqVOnaN++PWfOnKmQ2KLslajh\nVhRltKIovymKcktRlCOKorQr4uv8FEXJUBTlZEk+V5Sd2NhYOnfuzNatW/nss8+YPXs2dnZy/EXk\nZbk1yOHD5rcjIrT7PDygWjXtzwcfNH8PPz+Iaehudl+qPZxu6kGdb47R8txNhtyfQef4m6y8NY0O\nV5NxziraajI7bG/VWbvLkDILjqxQYHMEGdjjkqVNJu9wJZsId21+gvFsQqzFDiqxHjBhwgR27dpF\nVFQUHTp04MKFCxX8LURlJ7Xe9mVkZDBixAjGjBnDmDFj2L17N7Us93cSIodpvW/XDtq3N6/1ERHa\nfU5O2k+7dtCypfl7eCjmXbmTvRN+d/sRERyBt5s3kcMi6XDkgnY2PNkbrli8ga0V9DvJViDDES63\nglST34OcE7VhcpjU+iTzgxWxSbF07dqVEydO4O7uzsMPP8yOHTsqKrkoQ8W+IEBRlGDgfWAEcAwY\nD+xRFOVeVVULnGKmKEoNYB3wNSAjdnX066+/8sQTT5CZmUlUVBQPPfSQ3pGEFbPcGgTy3vb2hps3\nc2/Hx5tPL4+IACX5CKef6Mhdf9/iRs61yS2b5J5lMU5ArRdVyJq2SsIOY3OtEuE9CEOq+W8YhlRt\njb7xbMKbY1syecFxDEkQ6w5zx7ZkJ9CjRw+OHTtGr1696NSpE7t376Z169YV+2VEpSS13vYlJycT\nFBTE3r17CQsLIyQkRO9IwsrlV+8tHT1qftuy3q8cF8HI/QHEJsVicDfcbrRNRUTAM8/A8ePAZzth\nXMPKObVcQVvdZ5cOmW6Q4g3OSbmP56wGMNZ6g7uBmL9zL543uGsPNG7cmKioKAYPHkyfPn1YuXIl\nw4cPr6hvIcpASU5pjgdWqqq6XlXVn4EXgRTgTmP0VgCfAEdK8JmijBw/fhw/Pz9cXV05dOiQNNui\nzMXF5W22vb3Bq0kL6nx3jufnd6D3KC98PxhJ4xbx+PvDmTO5r7lKbbP3u+lAnsFqRWGNq9Ly2/Ss\nQ0IinrfM08a6uNw+owAQ9sJOJr/pxxNv+jD5TT/CXth5+7n33nsvkZGRNG7cmEceeYR9+/aV4zcQ\nVYjUeht27do1unfvzoEDB/jiiy+k2RZlLi5O25vbuKHN4cNas96isTdbgrZgcDcQmxRLr40BtO8W\nj68vZvX+2rWcy8+SveGvtrp+lzKX3y8gxmntphINeHjk1vqIYG3JvU9Nn9urAozc3d35/PPPGTly\nJC+88AJvv/02qmqNv+mI/BTrDLeiKA5AG+Ad432qqqqKonwNFLiHlKIoIUATYAAwo2RRRWnt2bOH\nwMBAHnjgAXbu3Ent2rXv/CIhislyymlAQO4Rc+P1SQDUjCGxQwB/rIk0m3yuVrsFuVt5craWA726\ntyBi33kaJN+iZnoWf7tAnJsC2WBIUrk7Ke8qNL1WpaXaQ7odVDeZEZcFJDuAYzY4W8w4c1ChRkYW\n/zjYc9VFIdbFhdcbHr59oAK4vQyvIF5eXuzbt4++ffvy5JNPsmHDBoKDgwt8vhCFkVpv2y5evEiP\nHj24evUq33zzDe3aFelKACGKpai1PoYYaBIA30aa73TiFgehvaFOzoySVDdIrQnO/0BqLUiuCZ7n\noVoqoIKSZV2Tp4y9rmJxX5ob2GfmPWOfaIDwiNw9yZMMuH0RweHDRa/19vb2LF26FIPBwIwZM7hy\n5QoffPAB9vZVaW8X21TcJeWeaDvYxFncHwf8K78XKIpyD1rR9ldVNVv2etTHJ598wtChQ+nRowfh\n4eG4urrqHUlUUpZTTE1vW16fZFxOlZKSe5en+49ww+R2WiYJn35HZ9PXpQPGOWFeP5Jy635crGRY\n96m64JkC1f/Ovc+evA24gvnvDtczG9H05gW4CcSZ//JSFO7u7uzYsYNhw4bRv39/4uPjGTNmTKm+\ni6iypNbbqDNnztCjRw8cHR2Jiori3nvv1TuSqKRKUuvBZFeToEBoYLLHmEMaxLWCRQUUPq8fIbQj\nOCUWfkS9ovbuznc4LOCcnHs7W0FRHVH/aqk12zm7thglAyNHFq/WK4rCjBkzqFOnDv/5z3+Ii4tj\n48aNODk53fnFQjfleqxIURQ7tKVlb6iqapzoI1W4gi1YsICBAwcycOBAtm7dKs22KFeWU0xNbxuv\nR7rNcnkVEOuhFnrbyNv1DAe9q3M+rRUZhfxLlt8y7nKlatdZF+b36tU4hJ/ZfX9h/ndR2PYsBXFw\ncGDdunVMmDCBsWPHMnXqVFlyJsqd1HrrcPDgQTp37oyXlxeHDh2SZluUq5LW+tu7muQ3zbyACee4\nxcEzIyHFC9IsfodVMS/05fkvjwpkFeNc5Y0mNFyfCquPac12PkpS6wFGjBjBli1b2LFjB08++aTs\nVmLlinuG+yrayRnLQSh1gCv5PN8DaAu0UhRlac59doCiKEo68ISqqt8W9GHjx4+nRo0aZvf179+f\n/v37FzN21ZSdnc3kyZN59913mTJlCrNnz0bOOojyZhx+ZnoN9+3HgiNoOi2ARDU2d3kV2vMaNdJe\n81xvNz7fknx7QFhAHzf4MO/nbHHvhH984u3bmQpUy6e3vFO7aXkwPL9VYsXheQs6hsK5xVAjPf/n\nxDq7EHAzgggCMBBLLAYC1Aiz5xRp+5V82NnZ8e6771K3bl1effVV4uLiWLlyJdWqFXtGZpW1adMm\nNm3aZHZfFftlRmq9jdm+fTv9+vXj4YcfZtu2bXn+PoUoayWp9U5O2rXeI0fCiQwDacSYv2k+B+EB\n7Wx4o6jc21n2YJ+zrE2hdE12cYp+mjvEPWiepTCJBv78s/CnlLTWA/Tp04evvvqK3r1707VrV3bv\n3k3dunVL/oZVUEXVe6W4Zz8URTkCHFVV9eWc2wpwEVisquq7Fs9VgGYWbzEa6AYEAr+rqnrL4nEU\nRWkNREdHR8vE3RLKyMggNDSUDRs2sGjRIl5++WW9IwkBaBNNmzbNvWYbtC1HjEuqfoz/kY6rO3Ir\n8xZqmgtZHx2GhLx7xp6v7oDvzdyLvX93t+eSRzXaxKeZLS9Ptc973fQ/jnDVTWvoO/6prZ01yqZ4\nS38sn3/LHqI93RjRuQEfHfkVQ5LKVQftiLxnWrrWbCcdJkHx1H6J8DD5hSTZGycnaNsWtq6Iw+vF\nwLzT54ph48aNhISE0LNnTzZv3iyrW0rh5MmTtGnTBqCNqqqVfrsrqfW2Y9WqVbz44osEBASwYcMG\nnJ2d9Y4kxB1rfXxyPL029eLUFe0a7mrXWpK8amf+Z4LH+kItk+Y8q5p2nXRR5bfMvChLz01bpAxX\n2LgLHp8IdU9r9yU0B1UF77O5t7Oqgds1s7qOW1y+9d7DA86fL3Zpz8N4KYmTkxN79uzhnnvuKd0b\nVnHlUe9LcspjAbBWUZRocrcKcQXWAiiKMgeop6rqEFXr5n8yfbGiKPFAqqqqZ0sTXBQsPT2d5557\njt27d7Np0yb69eundyQhbvP21gpMQUfGW3i34OYUbY+x+Hh4Zi+cvgnp6eDoCM2aQWYmxMa74Hsz\nt5JfcnWl81P34VXzOBGbuX2G3CELOvyV+/7/OMI9L9mR8H/fwPPPkDI/EZdSrDtPt4cTde1pcyXr\n9l7a/nHJHN5+jqsu9lx1dIar9+Cp/qOdyb4ZQQLeEOKfe5S8Vow2SGVNJPXr5/xC4l/IRJoiGjhw\nIJ6envTt25eePXuya9cu3N3vsN5dCI3UehuwYMECJkyYwKhRo1i8eLEMTxJW40613tvNm6PDc/cY\nO3MGOn4MSWjTyx98EBYtgq5d0ZpU04Y7wylvw53qBk7JeZesXWqnPbfed8X/EqbvZZ8Gg3qYD0Or\ndQ4SmkFiffMG25LpGXqTeu/lVfpmG+D+++/n0KFD9OjRA39/f7755huaN29e+jcWZabYDbeqquGK\nongCM9GWl30P9FBVNSHnKXWBu8suoigOY7P95Zdfsn37dp588km9IwmRR1H2+oyLg9694cQJ7QAy\nQFoaXLigHTEPcD1MhHdHDKm3bp81RhlGgjt0Ds15kzR3vC41JuLbMyZL1F1JWPmbVhQ/PM/punXM\nGvIkB/MBZ7fs4XTOwlrPpGo0vplpdkZcBTq/kMX5D8DXZFBajYxsamRk40sSoBV6X2KIIIDOROa9\nVs1iP85CJ9IUQ8+ePfnqq6/o0aMHTz/9NF988YU03eKOpNZbP2OzPWnSJObMmSOXjAmrU5xaf/x4\nbq1XVXBzg2nTcp5kOt070QAOKeYNdJo7XG1uPoQtyx5WnNJWyLnFwysGsDc5up5tZ3779v0K3GgC\nNWMsGu6s3GXsRs5JcPdx7b9NGuk87lTvy0CjRo2IjIyke/fudOvWTZpuK1OioWmqqi5TVbWxqqou\nqqp2VFX1hMljIaqqPlrIa99SVVXWjpUD02Z727Zt0mwLmxYYCMeO5RZgI+OE04SUFnSOv0nTmxl0\njr9JQkoLcL1q/uRkbxJqptA5FJq+rDXiCUrd3CPQyd70SjtAZH17LtwFkfXtebj2WiIbKFyoCZF3\nQ6Px8PAIePip9jS9mcEJg/k/m6dzLpe606A0IwM5hdfiWjWnDMPtvbfjkuI4bZdg8cKSV+aOHTvy\n5Zdf8t133/H000+TlJRU4vcSVYfUeuu1cOFCJkyYwOTJk6XZFjatoFofG2tynNk43XvxBe1PZ4tr\nbJO989b/fxrlXo6W7A0rTkOqh7bkO9UD1n2jnSm39Fc77XPSPIr/ZQoa+naHeu8f5o/vYl/898WD\nwwAAIABJREFUw/yJT44v/ufm8PT0ZN++fdSpU4du3brx008/3flFokJY0452ohSk2RaVTUEndG9P\nOM2P5cCVREP+95lIuNaFzpczaXpDpfPlTM5eGULnxzvlNujuaMV50w68Xc9ApjO37LUz30frQ6+c\nuU4Bz9kReTdcqKktWy/we+VMI3fcFkH7un741PTB724/Lr4bQWSkdkYgMDyQx/ok3n6/0009zNfi\nlUCnTp3Mmu7k5OQ7v0gIYXUWLlzIK6+8wuTJk3nnnXek2RY2raBabzAUcpy5BLWehBYw9ybMytD+\nvNgF/mpr/pycWg/Apzu0s+SWU9ALU8DQtzvV+6g/o4j5O4aoP6MI2BxQxA/Ln6enJ/v376dOnTo8\n+uij0nRbCRlbWwlIsy0qg7g47Ui38Vqv2rW1S5dNeXjkTjhN/zOOBRcDc6d8E0GC5bKznMmo+d5X\nmPzeJ9mbLd5N6RCfu2l4BvYkpDeCPwwk7FxJ52dGgkcsXtdqEPH1ORokp1ArLRvHbK1mn67lSkDy\nSkiBds29iRyZ/1q72KRYs6XxPjW9uFAGF3oZm+6ePXvy1FNPsWvXLtzc3Er9vkKIiiHNtqgMTOt9\nQkLexz1MjjEHBMDRo9rsltsKqPVKvwBUt9LXegC6TzOfhJ7qoW1Lllxbu8jc9SqkeGqn5t3jwPU6\n1DsO05zhSkv4LHcA3J3qfWG3S8J4prt79+48+uij7N+/X5aX60wabhuXnp5OUFCQNNvCKlk20YUN\n2g60mBHWvr32c0obYErLlrBzp/b6LV/GEffQPbREG5p2+9ro5Mg810+1awc752r3BQTA8QwoYLeu\nXMblaxYMqeaDljvEZnHwswQCkv6rLWnPeU0C0Bk46F2dxkm5g90ynFO42nsk7X+IJD0dfH3hHsMZ\n5l7pRK0bt7hR0wXD3sMY3A3E/J17tMF0T9Pi/J3mx9h09+jRQ5puIWyIsdmeNGmSNNvCqhS3LpnW\newB3d8jImZ1iWutBq/f3TA8032Isnxrt6Ah/vhOJt7c2cNX3c20AW6EKqPVA3uXhDrcKHowW4g81\nL+bevvs49v0DaPBVJNevw6VL0P7ROJTgQK6mxWJwNxARHIG3m3eB9b60td7Ly8us6f7mm29o1sxy\nMwlRUWRJuQ0zNtu7d+9m69at0mwLq2MsqjEx2p8BhayUslxWdvIknD0Ldetq22SZFuDA8EDcriWa\nPf/2tdEm/Pxyrg1zjSP0k/Ys+suZ8x7OHLTrgBfFv04q1tl8PbtDNvjHJ3Iu40HO48tB/M3e17JB\nNyRB64Z/suqsP5uO+7Iuxp+3fnmYVhcSaXgtk5bnE7n8eEfSN0TgFOeHU4oP7ev6ERGce6S+OH+n\nBenUqRN79uzh5MmTsrxcCBuwaNGi2822XLMtrE1x65JlvU9Ozr/Wg1bvE2tGaUPJGkVpZ6Tz0a6d\n9rq4pDgCdvpTe6YvSqi/NjCtJCyXh9tnFvz5+Vy73aB5LA0aaENe//gDjjcO5NiV3KXjvTYG4O8P\nl96PwONvPxpV15abG+t9WdR6Y9Pt7e1Nt27dOHtWNo3QizTcNsqy2X7qqaf0jiREHsUZtG15rVZm\nZm6hsiw2sUmxeYaUXVEshpI45S5JCwwPZNLC47T9LY27r6Xhn32MCIpfvQKTDhPp7UGGxb+cNTKy\n8CUGf6KIsOuVm9OiQY91h0UfXaZlYtTt57f827zZrX71Fse/9SZteSRp8y/gsCESb7fc3z7KaHj5\n7aY7Ojpamm4hrNiiRYsYP368NNvCahW3LlnWe1XNv9ZDPkusLZrbatW4PYAMcq+J/uNmDOrdBTfo\nhVEUtDPZf/hpQ9ZMNTiqndE2beTzuXb7j7O1ibrXX9tDPMQfql8ye/xUTCxRUfDHT94kfhBJgy0X\niByWW+/LqtYbm24vLy9punUkDbcNysrKYsCAAdJsC6tnWVQLG7QdEaEVzWoFXOhy9Cj4+2tLxQzu\nBgKCMRsqNqet+fVabdvmHO2OgxO/xGKwWFuW3xlxS3Z20KqV1rw7OYG3TwseuXqTo54FTy81uJ66\n/d8BSYeJrOOuTUBvoBDQxxVDisW2Iqr5L8+xFlPhLpnX6GL9nd6JadP973//m7S0tDu/SAhRYVas\nWCHNtrB6xa1LERFaTc3PiRPa5Vam9d6Uh8XB9Q4dtK3HVFV7zdGfCm/QC+LmllvrW7UCN3KWm1/q\nYP7E/M50h0fApfba1PMMJ/iznVbbG5mcmXe5bv4+Fk36iRPa9zUqy1rv5eXF/v378fLy4tFHHyXG\nckCOKHfScNsYVVUZO3YsERERhIeHS7MtrJqxifbxMT8CnR/jfp0dOuT/eGZm7tHviOAI7m3mx5BX\nfRjynh91vz/P3DBvPDy0ht3DA1au1F4XGAhpCYY8Z8SN08ILk52t7fudlqb9nDmj3ReQc6b7QvVq\neSaSx5r04gkpLegcl6hNQL+UTYJSN0+OM3at+M7Hg4u1q3G6qQcDMw+bPX7dokYX5++0KDp16sQX\nX3xBZGQkgwcPJju7qONYhRDlacuWLYwaNYoxY8ZIsy2sWnHrkre3dlA8P2lp5suoI4Ij8Ls7d8L3\njoERBdb6qCjIvH6HaeWFMNb6777TlrkDBZ/pNm3kk73h46MwO1X7WX0s7zZlqbVwv567dLzlWfO/\npLQ087P7ZV3rjWe63d3d6dGjB/HxJd9+TJSAqqpW9wO0BtTo6GhVmJs5c6YKqKtWrdI7ihDlIi5O\nVf38VLVRI1X18FBVe3tV1Y5daz9OTqrq46M9Jy4u93V+fubP8/PT7vfxUVXc4lSvfu3UgwYn9by7\nk3rQrr3qRZzZ80v649WvnXrwbtTzNVEP3o3q1a/d7ce8XX9QD3p7qOerV1MPenuoXgMeUr1eJff5\n3h6qF3G3s6qq9r1N379Ro4r5e9+6datqZ2enjhkzRs3Ozq6YD7Uh0dHRKtqw+daqFdTJyvAjtb5g\n3377rero6KgGBwerWVlZescRosxZ1vpGjbT6blr/qlUrZq1Hq/eE+KmM9dH+dCubWk+In8qb5P6E\n+OU+5nYl72cW8Hxj3ri4vN/Xx6f8/95jYmLUunXrqm3atFFv3rxZ/h9og8qj3suUchuyatUqXn/9\ndWbNmsXw4cP1jiNEuTCe6Tby9zefZmo8+h0Tox0NNj63oOudDAaIifEm4bNjdLb4LBcXSE3VSl1J\nJezYSeegAJQasaj/mG9FssW9E/7xOZPUbyYS8fU5Oj/lR+dnTbct8TY7UN6ggXYtm+ntitCnTx+W\nL1/OyJEjMRgMTJkypWI+WAhh5vTp0/Tu3ZvOnTuzbt067OxkMaKofCxrPeSt96Yr24pW68l38riL\ni/a7Q6kWcOVsIebkGYtjuoFE023HggK1ZeOgLSEPCsjdcqx6LNzM/d3AmNd4lt/0+5Zm2XhRNWnS\nhN27d9OlSxcCAwPZuXMnjo6Od36hKBX5V9xGbN++nRdffJHRo0czbdo0veMIUWFMl1VZXvNlWngL\nut7J+PpGjXIGoZi4dSv/Ztu4XM2Sk5M2CdXsfXKKe8OtF/D7NRLHjNwBZ3mmlN9KhTWReKy5oP1C\nkLO1iGn2sl5GVhwjRozgzTffZOrUqYSFhVXcBwshAPj999/p2bMnvr6+RERE4FTQha5CVEIFzXIp\nba1PTc2/2S5Jra+/5QLnp0biYWcySt3yOnGPWEj2xu/XSPxOWF+9b9WqFdu3b+fAgQOEhITIpWQV\nQM5w24DIyEj69etHQEAAH3zwgVzHJaoU06Pglke/LQtXQID5npWQ21BfuXLnM9nVqkHr1trzTp/W\njq6battWy9K4sflZaNDOREdGakNPjDnib7ngezN3+7JYZxc8VDh8GEaOzJvV8vvq4fXXX+fKlSuM\nGDECLy8vevXqdecXCSFKLSEhgR49euDq6sru3bupXr263pGEqFDG+lfWtT6/2u/nBytWQKdO2o4o\npgqr9QaDlvP8eZNaj4EkTAaRJRrw8MjNll9e0++rh27duvHJJ58QFBREnTp1eP/996W/KEfScFu5\nM2fO0KtXLx5++GE2bNiAvb293pGEqHBxcdpAlEuXtCPStWppDe6KFVphNi1kpvt3Qu4glaKwt9f2\n/jYtvooCjo7QsmVuobRc9m1aWE0LaMJvh/n+8Y5Uv3qLWBcXZvkc5vxW/ZvqwiiKwpIlS4iPjyco\nKIh9+/bRqVMnvWMJUaklJyfzzDPPcOPGDQ4dOkSdOnX0jiSELuLiID09d0Xbgw+WrtYrSv4Nd0YG\nhIbmrfdt2xa/1scnR9BrYwCnYrTLxVr+FsHO87kZrbXe9+3blyVLljB69GgMBgMTJ07UO1KlJQ23\nFbt48SI9e/akUaNGbNu2DWdnZ70jCaELy0LasmXeo+DGa7q3bNGebyzMlttqGTk5add0mTJOKDXV\npIk2qdxUfkfYLYs/gFeTFnidvwmAD7Cn6F9ZV/b29nzyySf06NGDZ555hsjISJo3b653LCEqpYyM\nDPr27ctPP/3EgQMH8PX11TuSELoJDITjx3NvOzjAiy/mrfWRkbkH42Nj4fLl/N/P0TFvXQc4dizv\nZWpNmmj3GxW11nu7eXN0pJV21XcwatQoYmNjee2116hTpw6DBw/WO1KlJA23lbp+/To9evTAwcGB\n3bt3U6NGDb0jCaGbgoak5He/aXMeE6MdkTbl5KQdwc7IMC+sBclviIk1n6EuK87Ozmzfvp0uXbrQ\no0cPDh06xN133613LCEqFVVVCQ0NZd++fezatYvWrVvrHUkIXRVU7/O7r7AVbMWt9ZC33leFWg8w\nc+ZMrly5wrBhw/Dy8uLJJ5/UO1KlI0PTrFB6ejqBgYEkJCSwZ88eDBUxtlAIK1bQkJT87rcszrVq\nmQ8luXhRK6A7duRtxo3s7fUZWmZt7rrrLr788kvs7Ozo3bs3ybc3JhVClIVZs2axYcMG1q9fz2OP\nPaZ3HCF0l19dL+h3AMt67+SUf63388t7Nhu0uS16DSm1JoqisHz5cp5++mmCgoL44Ycf9I5U6UjD\nbWVUVWXMmDFERUWxdetW7r33Xr0jCaG7giZ55ne/ZWE2DjO7cEH707gcTFWhWbP8i3CDBnmfn5+4\nOG1Zu6+v9md8fNl8X2tSr149duzYwblz5xg8eLBMMxWijPzf//0fb7zxBjNnzqRfv356xxHCKuRX\n1wv6HcCy3rdtm7d2e3trl5o9+GDez/L0zP/3A0tVodZXq1aNTz75BF9fX3r37k1CQoLekSqXstrQ\nuyx/gNaAGh0dXWabmNuKxYsXq4C6evVqvaMIYZPi4lTVz09VfXy0P+Pi8n+en5+qam133h8/v6J9\nluV7ODkV/plFdeVK0b5DRdq+fbuqKIo6ffp0vaPoIjo6WgVUoLVqBXWyMvxU5VofHR2turi4qP36\n9VOzs7P1jiOETSptvS9prffwKJv6bI21/o8//lC9vb1Vf39/NTU1Ve84uiiPei9nuK3I3r17GTdu\nHK+88grDhg3TO44QNsl4zdWdjlgXtBStXTvtmq+iHMm2fI+0NO16soCA0n0H43VpMTFl835loXfv\n3syZM4e3336bTZs26R1HCJsVGxtL7969uf/++wkLC5OteIQooZLW+2rVSlfrExPLpj5bY61v2LAh\n27Zt49ixY/znP/8xHhwVpSQNt5X49ddfCQoKomfPnsyfP1/vOEJUegUtRXN01AasFKUAFjReIb8h\nL8VRlKExenjttdcYPHgwISEhHDcdIyuEKJLU1FSeffZZALZt24aLi4vOiYSo/CxrdYcOZVProXT1\n2VprfceOHfn4449Zs2YNCxcu1DtOpSANtxW4efMmffr0wWAw8Omnn8pe20JUgIKuCStOATS+h+V1\n4KWdc1jQgBi9KYrCypUradWqFQEBAcTFxekdSQiboaoqo0eP5vvvv2fbtm3Uq1dP70hCVAn51fuS\n1Hofn7zDVktTn6211gMMGjSIiRMnMnHiRL7++mu949g82RZMZ9nZ2QwaNIjLly9z7Ngx2f5LiApS\n0HYfBoN2xNv09p3eIz4+716dpZHf3p/WwtnZmS1bttC2bVv69u3Lvn37cHR01DuWEFZv6dKlhIWF\nsW7dOtq2bat3HCGqjPzqfUlqPZRtvbfmWg8wZ84cTp06RXBwMCdOnKBJkyZ6R7JZ0nDrbObMmezY\nsYMdO3bwr3/9S+84QlR5JSmAZbFXZ1ycdj2X6ecWNiFdT/Xr12fLli107dqV8ePHs3TpUr0jCWHV\nvv32W8aNG8e4ceMYPHiw3nGEqPJK2uyWtt7bUq23t7dn06ZNtG/fnj59+nDo0CHc3Nz0jmWTZEm5\njrZt28Zbb73FrFmzePrpp/WOI4Sg6ENY8lOarUOscXhKYTp16sTSpUtZtmwZH3/8sd5xhLBaFy9e\n5LnnnuORRx7h3Xff1TuOEAKp9UVVq1Yttm3bxoULFxg2bJgMUSshabh1EhMTw5AhQwgICGDq1Kl6\nxxFClIHSFFJrHZ5SmBdeeIGRI0fevi5VCGEuIyODoKAg3Nzc2Lx5M9WqycJCIWxdVav1999/P+vX\nryc8PJwPP/xQ7zg2SRpuHaSnpxMcHIynp6dsCSJEJVKaQmrNw1MKs2jRIlq0aEFwcDCJiYl6xxHC\nqkybNo3o6Gg2b96Mp6en3nGEEGWgKtb6gIAAxo0bx8SJE4mOjtY7js2RhlsHkydP5tSpU2zevFmG\npAlRiZSmkBY0Nd3aOTs7s3nzZv766y/Zs1MIE7t37+bdd99l7ty5dOjQQe84QogyUhVrPcC8efNo\n2bIlwcHB3Lx5U+84NkXWNlWwHTt2sHDhQhYuXChTSoWoZEozcbQsBq/p5Z577mHlypUMGDCA7t27\nExISonckIXR1+fJlBg8ezFNPPcX48eP1jiOEKENVtdY7Ojry2Wef8dBDDzFy5Eg+/fRTWaVbRNJw\nV6A///yToUOH0rt3b15++WW94wghypgtF9LSev7559m/fz8vvfQSHTp0oHnz5npHEkIXWVlZDBgw\nAEdHR9atW4ednSwmFKIyqcq13tfXl48//pjg4GC6d+/O8OHD9Y5kE6QKVJDMzEyef/55XF1d5bpt\nIWxEaSaRVkWLFy+mcePGBAcHk5KSonccIXQxa9YsDh48yKZNm+S6bSFsgNT64gkKCmLEiBGMGTOG\nM2fO6B3HJkjDXUHefPNNDh8+zKZNm6hdu7becYQQRWBr23fozdXVlfDwcC5cuMC4ceP0jiNEhdu/\nfz8zZ87krbfeokuXLnrHEUIUgdT64lu0aBFNmzYlKCiI5ORkveNYPWm4K8DXX3/NO++8w8yZM/H3\n99c7jhCiiGxx+w69tWjRgsWLF7Nq1So+++wzveMIUWHi4+MZMGAA3bp1Y8qUKXrHEUIUkdT64nNx\ncSE8PJw//viDsWPH6h3H6knDXc6uXLnCwIEDeeyxx5g8ebLecYQQxWCr23foLTQ0lP79+zNixAjO\nnz+vdxwhyl12djaDBw8mOzubjRs3Ym9vr3ckIUQRSa0vmWbNmrF06VLCwsLYuHGj3nGsmjTc5UhV\nVYYMGQLAhg0bZHCKEDbGlrfv0JOiKKxYsYI6derQr18/MjIy9I4kRLlasGABe/fuZePGjRjkt3Uh\nbIrU+pIbMmQIgwYN4sUXX+TChQt6x7Fa0gGWo48++oi9e/eydu1a6tSpo3ccIUQxGSeRXrig/ent\nrXci21G9enU+/fRTvv/+e+bOnat3HCHKzU8//cT06dN55ZVXePzxx/WOI4QoJqn1JacoCsuWLcPb\n25uQkBCys7P1jmSVpOEuJ7///juvvvoqL7zwAj179tQ7jhBCVLh27doxefJkZs6cyalTp/SOI0SZ\ny8zMZOjQoTRp0oRZs2bpHUcIISqcu7s7YWFhHDx4kA8//FDvOFZJGu5ykJ2dTWhoKLVq1eK9997T\nO44QQuhmxowZNGvWjKFDh5Kenq53HCHK1HvvvUd0dDRr167FxcVF7zhCCKGLrl278tJLLzFlyhTO\nnTundxyrIw13OVixYgX79+9n9erVVK9eXe84QgihGycnJ9auXcsPP/zAO++8o3ccIcrMmTNneOON\nN5g4cSIdOnTQO44QQuhq7ty5GAwGQkJCyMrK0juOVZGGu4zFxMQwceJEXnzxRR577DG94wghhO5a\nt27NtGnTmD17Nt99953ecYQotYyMDIYOHUrTpk1588039Y4jhBC6c3NzY+3atRw6dIjFixfrHceq\nSMNdhrKzsxk2bBje3t7Mnz9f7zhCCGE1pk2bRosWLRgyZIgsLRc2b/78+Xz//fesXbsWZ2dnveMI\nIYRV6Ny5M2PHjmXq1Kn88ssvesexGtJwl6GlS5dy4MABwsLC8PDw0DuOEEJYDUdHR9auXcvZs2dl\nuJSwaadPn+att95i0qRJtGvXTu84QghhVd555x0aNGggS8tNSMNdRs6fP8+kSZMYPXo03bp10zuO\nEEJYnVatWjFjxgzmzJnDiRMn9I4jRLEZl5L/61//4vXXX9c7jhBCWB1XV1fWrl3LkSNHWLhwod5x\nrEKJGm5FUUYrivKboii3FEU5oihKgYd4FUXxUxQlUlGUq4qipCiKclZRlHElj2x9srOzCQkJwWAw\nyH6zQghRiClTptCyZUuGDh1KWlqa3nFEIaTW5zVnzhxOnz7N2rVrcXJy0juOEEJYJT8/P8aPH8/0\n6dP5+eef9Y6ju2I33IqiBAPvA28ADwGngD2KongW8JJk4EOgM3AfMAt4W1GU4SVKbIWWLVtGZGQk\nYWFhuLu76x1HCCGsloODA+vWrePXX39l9uzZescRBZBan9eZM2eYNWsWU6ZMoU2bNnrHEUIIq/b2\n22/TqFEjhg0bRnZ2tt5xdFWSM9zjgZWqqq5XVfVn4EUgBRiW35NVVf1eVdXNqqqeVVX1oqqqnwJ7\n0Iqyzbty5QrTpk1jxIgRPPLII3rHEUIIq/fAAw8wadIk5s2bJ/t1Wi+p9SZUVWX06NH4+Pgwffp0\nveMIIYTVc3FxYdWqVRw+fJg1a9boHUdXxWq4FUVxANoA+4z3qaqqAl8DHYv4Hg/lPPfb4ny2tZo4\ncSIODg6yv6wQQhTDlClTqFevHi+99BJaGRHWQmp9Xhs3buR///sfS5culaXkQghRRF26dGHgwIFM\nmjSJa9eu6R1HN8U9w+0J2ANxFvfHAXULe6GiKH8qipIKHAOWqqpq84c6Dhw4wMaNG5k3bx61a9fW\nO44QQtgMV1dXFi9ezN69e9myZYvecYQ5qfUmbty4wauvvkpQUBCPPfaY3nGEEMKmvPvuu2RkZDB1\n6lS9o+imWgV+lj/gDjwMzFMU5byqqpsLe8H48eOpUaOG2X39+/enf//+5ZeyiDIyMhg9ejQdO3Yk\nJCRE7zhCCGFzevXqRa9evRg3bhw9e/a0mhkYmzZtYtOmTWb3/fPPPzqlsTmVqtYDzJgxg5SUFBYs\nWKB3FCGEsDl169Zl9uzZjB07ltDQUNq3b693pNsqqt4rxVnKl7PMLAUIVFX1vyb3rwVqqKr6bBHf\nZxowUFXVZgU83hqIjo6OpnXr1kXOV5Hee+89Jk2aRHR0NK1atdI7jhBC2KTffvuN5s2bM3bsWObN\nm6d3nAKdPHnSOCirjaqqJ/XOU56k1uc6efIk7dq1Y/78+UyYMEHvOEIIYZOysrJo164diqJw7Ngx\n7O3t9Y5UoPKo98VaUq6qagYQDXQ33qcoipJz+1Ax3soesNmLoC5dusSbb77J6NGjpdkWQohSaNKk\nCdOmTWPBggX89NNPescRSK03ys7OZtSoUTRr1oyxY8fqHUcIIWyWvb09y5Yt4+TJk6xcuVLvOBWu\nJFPKFwAvKIoyWFGU+4AVgCuwFkBRlDmKoqwzPllRlFGKojyjKErTnJ9QYAKwofTx9fHKK6/g7u7O\nrFmz9I4ihBA2b+LEiTRp0oTRo0fLADXrUeVrfVhYGEePHmXZsmU4ODjoHUcIIWzaww8/zPDhw5k2\nbRrx8fF6x6lQxW64VVUNB14FZgLfAS2BHqqqJuQ8pS5wt8VnzMl57nHgP8BEVVXfKEVu3ezdu5fP\nP/+c9957L881Z0IIIYrPycmJJUuW8O233+a5lkroo6rX+mvXrjF58mQGDRpEly5d9I4jhBCVwpw5\nc7Czs+O1117TO0qFKtY13BXFWq/rSktL44EHHqBevXp88803aCvshBBClIXnnnuOyMhIfv75Z6s7\noFmVruGuKNZa6wFGjBhBeHg4v/zyC3Xq1NE7jhBCVBqrVq1ixIgRHDx4EH9/f73j5KH7NdxV3YIF\nC/jtt99YunSpNNtCCFHGFi5cSGJiIm+++abeUUQVdvz4cT7++GPefvttabaFEKKMhYaG0qFDB0aN\nGkVWVpbecSqENNxFFB8fz5w5cxg9ejQtWrTQO44QQlQ6DRo0YNq0aSxdupQLFy7oHUdUQaqq8uqr\nr9KiRQv+85//6B1HCCEqHTs7Oz788EN++OEH1q1bd+cXVALScBfRrFmzsLOzY8aMGXpHEUKISuvl\nl1/G29ubadOm6R1FVEE7d+7kf//7H/Pnz7fqbWuEEMKWtWvXjn79+jFjxgxSUlL0jlPupOEugvPn\nz7NixQomT55M7dq19Y4jhBCVlqurKzNnzmTz5s0cP35c7ziiCsnMzGTy5Mk8+uij9OzZU+84QghR\nqc2ePZuEhAQ++OADvaOUO2m4i2Dq1KnUrVuXl19+We8oQghR6Q0ZMoQWLVowceJE2SZMVJi1a9fy\n008/MX/+fJnTIoQQ5czHx4dRo0YxZ84cEhIS7vwCGyYN9x0cPXqUzz//nJkzZ+Li4qJ3HCGEqPTs\n7e2ZN28eBw4cYNeuXXrHEVVAcnIyb7zxBv379zdOpxVCCFHOpk+fjqIovP3223pHKVfScBdCVVVe\ne+017r//fgYPHqx3HCGEqDKeeuopunbtyqRJk6rMFFOhn0WLFpGQkMDs2bP1jiKEEFV92R+GAAAg\nAElEQVSGp6cnkydPZvny5ZV6WKo03IWQ4SlCCKEPRVGYP38+P/74Y5WZYir0kZCQwLx58xg9ejRN\nmjTRO44QQlQpVWFYqjTcBTAOT+nWrZsMTxFCCB20a9eO4ODgKjPFVOjDuAvJ9OnT9Y4ihBBVjumw\n1GPHjukdp1xIw10AGZ4ihBD6M04xXbRokd5RRCV0/vx5li9fzpQpU2QXEiGE0IlxWOprr71WKYel\nSsOdD9PhKW3bttU7jhBCVFm+vr6MGjWKuXPnVvoppqLiTZs2jbp16zJ27Fi9owghRJVlb2/P/Pnz\nK+2wVGm487Fs2TISEhIq/cQ8IYSwBcalvvPmzdM5iahMvv/+e8LDw2UXEiGEsAJPPvkkXbt2ZerU\nqWRnZ+sdp0xJw20hJSWF9957j6FDh+Lj46N3HCGEqPI8PT0ZO3Ysy5cvl7PcoszMmjULX19fBg0a\npHcUIYSo8hRF4a233uL06dPs2LFD7zhlShpuCx999BHXrl1j8uTJekcRQgiRY9y4cSiKwsKFC/WO\nIiqBM2fOEBERwdSpU6lWrZrecYQQQgBdunShS5cuzJo1q1Jdyy0Nt4nU1FTmz5/PwIED5ey2EEJY\nEU9PT0aNGsWSJUu4fv263nGEjZs9ezaNGjWSs9tCCGFlZsyYQXR0NF9++aXeUcqMNNwmwsLCiIuL\nY+rUqXpHEUIIYWHChAlkZmayePFivaMIG/bzzz+zefNmJk+ejIODg95xhBBCmOjevTsPP/wwM2fO\nrDRnuaXhzpGens7cuXPp168f9957r95xhBBCWKhTpw4jR45k0aJF/PPPP3rHETbqnXfeoV69eoSE\nhOgdRQghhAVFUXj99dc5cuQI+/bt0ztOmZCGO8e6deu4dOkS06ZN0zuKEEKIAkycOJHU1FSWLFmi\ndxRhgy5cuMCnn37KpEmTcHJy0juOEEKIfPTs2ZO2bdsya9YsvaOUCWm4gYyMDObMmUPfvn1p3ry5\n3nGEEEIUoF69eoSGhrJgwQISExP1jiNszJw5c/D09GT48OF6RxFCCFEARVGYPn06//vf/zhw4IDe\ncUpNGm7gk08+4bfffru916sQQgjrNWnSJBITE1m+fLneUYQN+f3331m3bh0TJ06UfbeFEMLK9e7d\nm5YtW1aKs9xVvuHOysrinXfeoU+fPrRs2VLvOEIIIe6gYcOGDB06lPfff5+UlBS94wgbMW/ePO66\n6y5efPFFvaMIIYS4A0VRmDFjBvv27ePw4cN6xymVKt9wb968mXPnzsnZbSGEsCGTJ0/m2rVrfPTR\nR3pHETbg8uXLhIWFMWHCBNzc3PSOI4QQoggCAgJo3ry5zZ/lrtINt6qqzJ8/n549e9KmTRu94wgh\nhCgiHx8fBgwYwPvvv09GRobecYSV++CDD3B1dWXUqFF6RxFCCFFEdnZ2TJ06ld27d/PDDz/oHafE\nqnTDfeDAAU6dOsWECRP0jiKEEKKYxo8fz6VLl9i6daveUYQVS0pKYtWqVbzwwgtUr15d7zhCCCGK\nISgoiHr16vHBBx/oHaXEqnTDvWjRIlq0aEH37t31jiKEEKKYWrVqRdeuXW26CIvyt379ehITE3np\npZf0jiKEEKKYHBwceOmll9i4cSMJCQl6xymRKttwx8TE8N///pdx48ahKIrecYQQQpTAuHHjOHTo\nEMeOHdM7irBC2dnZLF68mICAABo2bKh3HCGEECUwYsQIFEWx2bktVbbh/vDDD6lVqxYDBgzQO4oQ\nQogSeuaZZ2jSpImc5Rb52rNnD7/88gsvv/yy3lGEEEKUUO3atRk0aBBLly4lPT1d7zjFViUb7ps3\nb7J69WpGjhwpe3EKIYQNs7e3Z+zYsYSHh3P58mW94wgrs2jRItq2bUunTp30jiKEEKIUXn75ZWJj\nY/n888/1jlJsVbLhXrNmDbdu3ZJppUIIUQkMGzYMFxcXli9frncUYUV+/PFH9u7dK5eOCSFEJdCi\nRQsef/xxFi1ahKqqescplirXcGdlZbF48WKCgoKoX7++3nGEEEKUUvXq1Rk2bBgrVqzg1q1bescR\nVmLx4sUYDAaee+45vaMIIYQoA+PGjePEiRMcPnxY7yjFUuUa7i+++IKYmBi5nksIISqRMWPGcP36\ndT755BO9owgrcO3aNTZs2MCoUaNwdHTUO44QQogy0LNnT+69914WLVqkd5RiqXIN96JFi+jYsSPt\n27fXO4oQQogy4uvrS69evfjggw9sbqmZKHurVq0iOzubkSNH6h1FCCFEGbGzs2Ps2LFERERw8eJF\nveMUWZVquE+dOsU333zDuHHj9I4ihBCijI0bN44zZ86wf/9+vaMIHWVkZLBkyRIGDhyIl5eX3nGE\nEEKUoSFDhuDu7s7SpUv1jlJkVarhXrZsGfXr1+fZZ5/VO4oQQogy1rVrVx544AGWLFmidxSho//+\n979cvnyZsWPH6h1FCCFEGXN3d2f48OGsWrWK1NRUveMUSZVpuJOTk9m0aRPDhg3DwcFB7zhCCCHK\nmKIovPDCC+zcuZO4uDi94widrF69mg4dOtCyZUu9owghhCgHw4cP5++//2b79u16RymSKtNw/9//\n/R+JiYmEhIToHUUIIUQ5GTBgAPb29mzYsEHvKEIHly5dYs+ePYSGhuodRQghRDm577778PPzY/Xq\n1XpHKZIq03CvXr2a7t2706RJE72jCCGEKCe1atXi2WefZfXq1TI8rQpau3Ytzs7OBAcH6x1FCCFE\nOQoNDeXrr7/mjz/+0DvKHVWJhvvXX3/l4MGDcsRbCCGqgNDQUH7++Web26dTlE52djZhYWEEBQVR\nvXp1veMIIYQoR8899xxubm6sWbNG7yh3VCUa7rCwMGrWrCnD0oQQogp49NFHady4sc0sNRNl49tv\nv+W3336Tg+tCCFEFuLu7069fP9asWUNWVpbecQpV6RvuzMxM1q1bx4ABA3B2dtY7jhBCiHJmZ2dH\nSEgImzdvJjExUe84ooKsXr2af/3rX/j5+ekdRQghRAUIDQ3l4sWL7Nu3T+8ohar0DfeuXbu4cuWK\nHPEWQogqZOjQoaSkpBAeHq53FFEB/v77b7Zs2cKwYcNQFEXvOEIIISpAhw4daN68udWvaCtRw60o\nymhFUX5TFOWWoihHFEVpV8hzn1UUZa+iKPGKovyjKMohRVGeKHnk4lm9ejWtW7emVatWFfWRQggh\ndNawYUOeeOIJqy/C1syWav2nn35KZmYmgwcPrqiPFEIIoTNFUQgNDWXbtm1cu3ZN7zgFKnbDrShK\nMPA+8AbwEHAK2KMoimcBL+kC7AWeBFoD3wA7FEV5sESJiyE2NpYvvvhCzm4LIUQVNHz4cA4fPszZ\ns2f1jmJzbKnWg3Zw/ZlnnqFu3boV8XFCCCGsxKBBg1BVlY0bN+odpUAlOcM9Hlipqup6VVV/Bl4E\nUoBh+T1ZVdXxqqq+p6pqtKqqF1RVnQacA3qVOHURrV+/HgcHB55//vny/ighhBBWpnfv3nh6espZ\n7pKxmVr/3Xff8d1338nBdSGEqIK8vLz497//bdXbgRar4VYUxQFoA9y+Ml3VvtnXQMcivocCeADX\ni/PZxaWqKmFhYQQGBnLXXXeV50cJIYSwQo6OjgwaNIj169eTkZGhdxybYUu1HrSdSAwGA08++WR5\nf5QQQggrFBoayg8//EB0dLTeUfJV3DPcnoA9EGdxfxxQ1HVcEwE3oFwn2Xz//ff8+uuvDBo0qDw/\nRgghhBUbNGgQCQkJ7N+/X+8otsRman1WVhbh4eH079+fatWqledHCSGEsFKPP/44derUYdOmTXpH\nyVeFVidFUZ4HZgC9VVW9eqfnjx8/nho1apjd179/f/r373/Hz9q8eTO1a9fm0UcfLWlcIYQQNq5V\nq1bcc889hIeH06NHjyK9ZtOmTXmK9j///FMe8Sqliqz1Bw4cID4+nuDg4JLGFUIIYePs7e3p27cv\nn3/+Oe+++y52dkU7p1xR9V4pzlr3nGVmKUCgqqr/Nbl/LVBDVdVnC3ltP+BjoK+qql/e4XNaA9HR\n0dG0bt26yPmMVFXFx8eHxx9/nI8++qjYrxdCCFF5TJ8+naVLlxIXF4ejo2OJ3uPkyZO0adMGoI2q\nqifLNKCVsZVaDzBy5Ej27t1LTEyMbAcmhBBV2P/+9z8eeeQRoqKi6NSpU4nfpzzqfbGWlKuqmgFE\nA92N9+Vcp9UdOFTQ6xRF6Q+sBvrdqQCXhePHj/P777/LEW8hhBAEBwdz48YNvvrqK72j2ARbqfUZ\nGRls2bKFoKAgabaFEKKK8/f3p169emzevFnvKHmUZEr5AuAFRVEGK4pyH7ACcAXWAiiKMkdRlHXG\nJ+csLVsHTACOK4pSJ+eneqnTFyA8PBxvb28eeeSR8voIIYQQNuL++++nWbNmVlmErZjV1/pvvvmG\na9euycF1IYQQ2NnZ8dxzz/H555+TlZWldxwzxW64VVUNB14FZgLfAS2BHqqqJuQ8pS5wt8lLXkAb\nvrIU+MvkZ1HJYxcsOzub8PBw+vbtKwNUhBBCoCgKwcHBbNu2jdTUVL3j2ARrr/WgzWpp2rQpDz30\nUHl9hBBCCBsSHBxMbGwskZGRekcxU5Iz3KiqukxV1caqqrqoqtpRVdUTJo+FqKr6qMntbqqq2ufz\nk+9enqV15MgR/vzzT4KCgsrj7YUQQtigoKAgEhMT2bNnj95RbIY11/r09HQiIiJkObkQQojbOnTo\nwN133014eLlukFFsJWq4rVl4eDgGgwF/f3+9owghhLASzZo144EHHpBl5ZXE119/zY0bN2Q5uRBC\niNvs7Oz4//buPraq+77j+Ofra8CYB2Nj8xTADhUEmzlgsNukNOCKJSVcFW1SwU3atWunSV06bcum\nP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 25, 128, endpoint=False)\n", "yexp = exponential(t, tau=3, N=200)\n", "ygau = gaussian(t, t0=5, sigma=2)\n", "yconv = np.convolve(yexp, ygau, 'full')[:t.size]\n", "\n", "Rgau = phasor(ygau) # IRF phasor (to deconvolve)\n", "\n", "Rexp = []\n", "Rconv = []\n", "Rconvwrong = []\n", "\n", "for _ in range(10000):\n", " # Adding noise\n", " yexp_n = np.random.poisson(yexp)\n", " yconv_n = np.random.poisson(yconv)\n", " yconvwrong = np.convolve(yexp_n, ygau, 'full')[:t.size]\n", " # Calculating phasor\n", " Rexp.append(phasor(yexp_n))\n", " Rconv.append(phasor(yconv_n))\n", " Rconvwrong.append(phasor(yconvwrong))\n", "\n", "# Deconvolving (ie, dividing)\n", "Rexp = np.array(Rexp) # Unconvolved needs no deconvolution\n", "Rconv = np.array(Rconv) / Rgau\n", "Rconvwrong = np.array(Rconvwrong) / Rgau\n", "\n", "#Ploting\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "single_lifetime_circle()\n", "for R in [Rconv, Rexp, Rconvwrong]:\n", " plt.plot(R.real, R.imag, '.')\n", "plt.legend(['Deconvolved', 'Unconvolved', 'Wrong'], loc=0)\n", "\n", "plt.subplot(122)\n", "single_lifetime_circle()\n", "for R in [Rconv, Rexp]:\n", " plt.plot(R.real, R.imag, '.')\n", "plt.legend(['Deconvolved', 'Unconvolved'], loc=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the unconvolved and wrongly convolved distributions overlap (except for numerical errors in the convolution), on the left we only show the deconvolved and unconvolved.\n", "\n", "We can calculate the mean value and the covariance matrices of these distributions to make a comparison." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean values\n", "\n", "(0.648925966233+0.465070420347j) Unconvolved\n", "(0.648708309476+0.466396398608j) Deconvolved\n", "(0.648872556531+0.46644909795j) Wrong\n", "\n", "\n", "Ratio of covariances\n", "\n", "Deconvolved vs unconvolved\n", "[[ 1.18604524 1.32960313]\n", " [ 1.32960313 1.66457272]]\n", "Wrong vs unconvolved\n", "[[ 1.00209293 1.00457298]\n", " [ 1.00457298 0.98045896]]\n", "\n", "\n", "Ratio of deconvolved vs unconvolved eigenvalues\n", "[ 1.26909735 1.59785122]\n" ] } ], "source": [ "meanexp = np.mean(Rexp)\n", "meanconv = np.mean(Rconv)\n", "meanconvwrong = np.mean(Rconvwrong)\n", "\n", "print('Mean values\\n')\n", "print(meanexp, 'Unconvolved')\n", "print(meanconv, 'Deconvolved')\n", "print(meanconvwrong, 'Wrong')\n", "\n", "covexp = np.cov(Rexp.real, Rexp.imag)\n", "covconv = np.cov(Rconv.real, Rconv.imag)\n", "covconvwrong = np.cov(Rconvwrong.real, Rconvwrong.imag)\n", "\n", "print('\\n\\nRatio of covariances\\n')\n", "print('Deconvolved vs unconvolved')\n", "print(covconv/covexp)\n", "print('Wrong vs unconvolved')\n", "print(covconvwrong/covexp)\n", "\n", "print('\\n\\nRatio of deconvolved vs unconvolved eigenvalues')\n", "print(np.linalg.eigvals(covconv) / np.linalg.eigvals(covexp))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As can be seen, the mean values coincide, but the deconvolved distribution has a bigger covariance matrix in relation to the unconvolved one.\n", "\n", "The wrongly convolved vs unconvolved covariance matrices aren't exactly equal, which we associate to numerical convolution issues." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda root]", "language": "python", "name": "conda-root-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }