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@maedoc
Last active September 11, 2023 15:08
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discretized linear delays
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{
"metadata": {
"language_info": {
"codemirror_mode": {
"name": "python",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8"
},
"kernelspec": {
"name": "python",
"display_name": "Python (Pyodide)",
"language": "python"
}
},
"nbformat_minor": 4,
"nbformat": 4,
"cells": [
{
"cell_type": "code",
"source": "try:\n import micropip\n await micropip.install(\"matplotlib\")\nexcept ImportError:\n pass\n%pylab inline\nimport tqdm, autograd",
"metadata": {
"trusted": true
},
"execution_count": 2,
"outputs": [
{
"name": "stdout",
"text": "%pylab is deprecated, use %matplotlib inline and import the required libraries.\nPopulating the interactive namespace from numpy and matplotlib\n",
"output_type": "stream"
}
]
},
{
"cell_type": "markdown",
"source": "# Stability of a discretized linear (stochatic) delay differential equation\n\nTo get started, let's use a linear stochastic delay differential equation (SDDE), parameterized by `D` the number of steps for the delay,\n\n\\begin{align}\n\\dot{x}(t) &= -l \\: x(t) - y(t) + k \\: y(t - D/dt) \\\\\n\\dot{y}(t) &= -l \\: y(t) + x(t)\n\\end{align}\n\n## Simulation w/ Euler-Maruyama scheme",
"metadata": {}
},
{
"cell_type": "code",
"source": "def run(D):\n T = 3000\n #D = 50\n dt = 0.05\n l = 0.05\n k = 0.2\n\n np.random.seed(42)\n z = np.random.randn(T-1,2)*np.sqrt(dt)*1e-1\n x = np.zeros((T,2))\n x[0,0] = 1.0\n for t in range(T-1):\n dx = np.r_[-l*x[t,0] - x[t,1], -l*x[t,1] + x[t,0]]\n if t > D:\n dx[0] += k*x[t-D,1]\n x[t+1] = x[t] + dt*dx + z[t]\n return x\nx = run(50)\nfigure(figsize=(8,1)); plot(x), grid(1)",
"metadata": {
"trusted": true
},
"execution_count": 3,
"outputs": [
{
"execution_count": 3,
"output_type": "execute_result",
"data": {
"text/plain": "([<matplotlib.lines.Line2D at 0x3889640>,\n <matplotlib.lines.Line2D at 0x3885e88>],\n None)"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 800x100 with 1 Axes>",
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rIxnx4SRSRnvUe6B8X5POhGMRn09hxe4SdhVW6Ss8AVQVwkt94Ntbjmzj/gBPfm94mNNiw+mRFsNExxJjh6oCWPkRzP07lDaeH3EkWas6payGpPguSkrv1mhSkxz7hmThNpy+ehS7E1tqX+IjQwAoqjQbktrSdsMXU06ZkUmVlWoknZxZ+hExtmqia/bDvqXwQg9Y86n14Fq/mMyjDEVRWKfGjVw6NAOHamwne4SRuMWdFHiQZkjWlkJB8BijGtXpGxvuMjZumwWAvcNwwEat2xeQVQdAfCfxf+nuwPdUCiqMmZvNLB2UIwTOV/u6UFbjhkFXwzlviPfWfgm+o295OBgfLg7+3ad8vwYKtwder83wFuwutoYSXP/hcq57f5nVmK/Ig/0rm9XGOo+X33cFCjun/KuT8cdvLzXrXMcqr87bTr8nZzF/y5+sbOe8v8O2n+DX52DrrCP60YWVwRMisnJNCXj9LkNJEqtMTU0QNe97epyxXBgR4uRe55fWHd9oeSKDx+tj8rQNfLAou8XHHlYUBXJWQ3Vxo7v9tCGP899YxGnPz2fIP+ZYYuUB8ds/11mEfq35FGqOTlFsf7Rs/BtHirGoTWQIN4b6TTim3Q4LnoeXeosxtQkq6zxc/NZibvt45WHJ9vd4fSxQtU0zVYcVACVqsmh8pyBHtT7HvCFpq1LjFBO6gjOEhChh5WveLMCabNPAw7jAVMGmo7o0Qm05MZ5mVEfYs7jF7T4o5kyGt08ThkAL0Nz/LoeNyWf10rfHVAtDZUlpXOBBYTHG699fC3hbURSqVbkrLZsa0I0fW+bJxIQJL+Lzs7b4Hw5RqvHaSJypNntOjAq1vqEup25V2hmeoF7ngd0pHjiNeFGPJjTb+NEzevLmFYP07V2WPQ7/GgRf+8WtupteqtbkT8zM3VzA92tzYPl78N/zRTnMd06D9V83eb6lu4oprXYTE+Zky1Pj6ZAQQSh+RsC+FcEPboQf1uYwedqGQyKt5fUpRiKQuwbqjlwRgS+W7eWF2SLW+G/frG9i76MMc8zgEV5Z2WOa8Fw1ogPPnN/HukPmyXDuG3jO/w8A9v3Lob5hsWlNqSMtNtyy/TLnPOuOzdCu9eeXrQd4f1E2j0/bwOq9LT/+sLHgn/D2KfBsR/j9zQZ3+261dSL/7Sq/if0nfkv+ZfvBc3RXdCsor9Vl/m45RZWq83po72vE4/zakCbPO2tDHkt2FTN9XS69Hv+JF2dvpaLWbS27/AcoMHmET++eLF546vQQMiWuQ7DDWp1j3pCkSngBlEhhmKTGCKPDknCjLW27qxqcbWllFQea4/0a0ye84msYckPT+x0qFEWUMsxZKQyBFnjd1uwrBaBnWgyhTiGnQ10lrhphxG2oDSLTA4YoeURiwFu1bh9eRVhCmsEIGEZuTBqPnymM1qJg3ocotVxiI4LneiyJvyGp3nQ5SgLF1eq5XWHGbG7jd0d9rE9ZjVtv4iVDMhjfO5XOSZG48HCxc37wg5rwyhRU1PLSHJH9d91JHU3vKDgXPAc/3A3b5xibf/5Hk+3UMmGHd0og1OngtKxkrnH8aN1pz6IWxUrmltVw+yereH9RNlmP/GgYk+W5B+VNPv+NRZzy3Hzen7cGXhkg/h2h5fYHvjKSj3LLavDVVTWr8IE/lXUe8sqOzMM7u7CKX9ftECssGnXlsPsITYiBPcWGQsaTZ/fmvIHtcOLBp44ptWeryg4JXal1qpPazT80eD5tadusZ2u+1kfVPWdsb8KDZ+aN+Tu47oPl+t8fLs5u9rGHmoLyWrIemUn/J2dxoKxaeJQ1fvxrg8e1a2M1rn/TqrdVHggeMvPzP3A+26FZSU6thbbC1jU5ijbqKqR5kvBO1r8DD1J8MP3+Rs9rjlGv9/h4ee42+kyeRceHZrA1v6KRI5vHyj3C/ogNd+nSdsL5ooArIuiz9mjgmDckdY+kakh2SRYxMhbPjMtY7mCvKYbCxDa1ok3XZJOWolot52PPKDrW/pfKia/BTQtE5Zcuo6Dz6WK/Td+Dr2WelZKqen5cnxs8fjAY/kkvb53cbGNpjTqL7tsuztQA4UovVqIoJ0o3Ni30vVj8H8T4Lq8Vs0GH3WaNX6xU45GiUhndI0Uc7vZS6/brn7S+4v9GMulzVePeEkviqdc/I09JsBqpWtzlrL8JoXJPA/FARwH71YlOfGQIkWr/fXjdMO7zX4oz886oRs95g+mBd0bfNG4c2Yn28RHc4vieSUXvBR7QjCWsXNW40aRU/jIuiwddnwXu+NPDTZ5LY84m6xJw1iM/wtaf4IXuwjPWgklAXlktq/eWEk85//frSKECUFUg4r38jFJFUah1e1meXYy3ufddI5h1ZwESlBIRN/rFlbDgBfjq+kaT1TQ8Xh+9H/+J4VPmcu3zH6P89/xAjdWaUiFv1YihXVpdH3if+eH2+hj3/CxGfjUw8M33xgvDYnKsMOobYNWeEk5+dh6/bm14NSEYXp/Cz1sK+PsPG7nnc/HADneJh6nLYWfLXZ2w2xTqFBfbKo0xuzBKXd5uYOwGyFGXttNMS9vmxLsdSlvKFdWgqm5eDe7qeg/P/GgN6/l65f5WEzh/4oeN1Hl8JNfsJOnFtGYfV1ojxmptPF61p5SdByo58N3frDt2OlX8v2UGNsXL8J0vHopmHxY0Q7JPW5MhrNoCpUokv1a3hwFXBh647J0GJxIVtY3HOX+98o+vdN2plicuqzF9Vmm2+D+uQ2D1t6OEY96Q1C4ezSOpBVvvakjd/seHgm7WDM+uKSYpGzUwe7+SiIKdR3f1NgwggC6jwRUpZkLZC1rU7Pu+XMPN/11Jp4dnBLjN3/plBx/5z3wXPG/9O389FFrLgTXEKt2QNN10a4QxUBEhsqf3+FegAYhUZ0fVgd4d7UaICXMa8YvVxUasR1QyMeFO/UER4G2JUb3EdeVCSikImnHbNdn0m1TmAQo+ewhFRLOrsMqQzBl+q/UEK94Pet7DwtafRFZoMwwHQJcqaW/S4ExVDnCz0+TdvvIbuPk3OEnNYq1p2JOiKApr1CDu9vER9M+I4+GJPZh33yn8NZjhB+KB2sQycJ72gI4VD+jIHdP1975JuBES1UStkMiAYxvCaoAo/Mf1LHxykfhzw9ew+F/NPtdv28W1+YDT7zu6qwMMjzs+XUX3R3/kgjcX0/nhGVappZoS2Dyj2R5Rj9fHxFeMez4pOpTLHPOw15bAlhkw9wlY9yX88myT5/rAFCs7ovQHbNvnwBdXWdsy9wkhbzXvyaDn2FtcTf8nZ9P90R9565dA7/DCbYVkPjidXo/9xHD7piBn8OPzyxt869zXF7G3uIar/rO0RUt+b/26g2veW8a7C43iAVoFGqqLcbx1EgDLfd0487VFbMmrQFEUiqK6i302zwh63pKqel3rV5vwUFMKG0SlrvczhOe9RFGdBFXNM4AfaSBUIUBe7jCyt7ia/PJaCivrmL5WGPe3OU2TDE39wuYIOgFTFEUvi3t2/3R9+10vvEfSts+NHVP7iHCC1mDDNyJ29flukNe88BAtxKC32ZA8IEKospUUlu4qxj3mKRhxO1z1Hdxvio9sIC5/5Z7SRj9z1Z4/HjsaHymcIj3TTKFjJWp72mT+4fMfLo55Q9KmLm0TKeINUtUHXoF/dloHNcjaHPtnQnNbdzEbLaq3LEdJAIRchQVnCHRRvZIbvm12m79Ytpd5mw2vzDXvL9MNrezCKqbM3Myj323QvQt5ZbW49wVJjnhtCOyYF7jdxO6iKlbsFjfA8E4JxhvqQ7YmWiyBrvGXNwKIUPevDEwiKK4SA7eW3ATAp5car6NSsNls+u+RV+5nSIbFisEPGvRKajGSXcxe4jIxK7TFpuNyOqms8+heMzJPsp6goBkPzD9K8U4Re/jJRSLR6LvbmnWY5s0yi9I6NhkPiF/GzxIe79TehiEJON8YhtMTOElav9/wjs26Z6Ru3Dtz/Zanrp8HD+2HsDjxd2GQ+FUT2pKh9jsy11hO+8xxBpymejVKgg/OZhRF4bvV+5ltyiQ/y76I0x2rrTuualzqxcx9X66hky2HS4KFA2wwYkAr6zz8sNbqZXvw63XGH59dAZ9dCk+2gUVNG7LbDxgG+LCO8aTHhpFuC+Lp2vN7o+dRFIUZ64x2dbKZ2rhvmciqnhwLy0WsIAtfDBor+M0qw1syZeZmJr2ygNJqw1t/xbvifq/3+njYaerfiz6EbhMCG7a/eXGvU2c2X+z72R8Dr7Wbtfi2l/vp2/7nHQnAuJd+5bJ3l1EToo5DFTlBwwYWqpOJrJRoYsLUeO39hnf+vEkTAditCI8chc2rv/21qU9vPbWz/vrlOVvFhHHd/8QKyWGitLqek5/9mROnzuN602pDX5tponDOG+AIBcUbNEzovd+yAREff2pWEt3VRNLzHb/q+9SlD4WbF+qrehpuu3VJ3J96j4/Pl+1hf2nNwccQlu6FL/9POEYq8+HNE5tMXt1fWqNPRod2jDfeKBAxvztsHajz+Nhd6YRx/xCe1qgkaKfGSDbwvNmsTu4n9Ukje+oktv1jAtlTJzHjTmFg784r/MMhM3FqPsHDE3sYG5eqYRxtjs74SDgODEnth1VU75kWbL27qIp6j2lGP0J9wNtd+OP2+nQPZldVzBZ3rT6Y3nTx2QDsOFDFO7/u9Dta9cateK9ZS3J7i6stcVUA87cc4MGvxbaX5hiD3D9nbeGkZ+Zxw9R3cOWtBuAK5z/hrFeNgz86t9HP+1XNEIsKdZKheb9KdusSOjm9bwRE6cSA5b4UNTEnd03Ad9PKUCWYDcm9podmqDDItc/c5h9f4nBCmvrwKAgUClYURTckLcaqOpu0xWbQTvU+aKK02GzweCmcfJ/4uynPQ00JbJvzx+IpXxkgYg81dswTD/7/nt/ogKi1uUOCSTpJNZLf9Uzg3Y2mJY6wWOg2HgBb8Q7aFy8MON/PasbwaVlJhKleYEAE5Ku81PMLaDdI/Daa0b1lZoNtVBSFbWqGZ+ekKNFPRcIL/oz7EvZXeCFR1Wor3NZkP74weyt3fbZa/95bn5rAmY4ghtaBTUYCT0m28HTXVwecX7s+LnLM17dNrHuaD1LVVYelb+tevTVBkiQ0Dw9562C3qU9n/S1gX3+emGZcs5/fNIK4iBD62oPEibobThABeO3n7fpE75nzetHDbjLI/zNWZFX7kxcoCu/xu3c35JTT/8nZ/L6ziFkbrLG1WXZTQkLPs+Hij4T3++71cIspTjJICVP/pfO3ft3ZrPCcb1cFXxYMczmEV7zOuFem+U7QXy/fXUpBjCkRJ8jEZ5u6mjTQNCkzK01EJYvJ8mZF9d7NfgzeHQcbpzXY3hK/MnsPjO/OpL5iOfnb1fuFesdX18H6w6cj/Oo84UXz+BRW7y0lmRL+6/oHHe35eBUbu2/YJO7j9sPFAXnrAs4xXzW4Ts1KJjrMxbTbxX3f1Wb8HhftOkNkvbcfYTnW5atpMMFvxe4Sznh1AX/9ah0nTp3HE5oUT9k+ISdV0UzZsZ1BhMPN42kQtuSV41PExMHikcwXcmrFkSLEKSDxUPPeBpn0KorCFHVS1ClJrK64HMJ8So4JBRTe8j4mstubuRIY7DO0pDBdXaCyQIx3AOHxDRzZ+hz7hqQW76J6z7omRxHmslNd77UKMoerg0yQ5cHdRVV4fAqRIQ7SNc/LvmXgqYGoVDp0NzJq/zHDz8s16GrjdTM0yhpacv9teyEP/G8N35oy7N5ZsIvckkq+D31E37awMhWl32VNfo7GDvVmMpd8ZN0X4v+Op9C97zB9s6VGORjJNp7agJlYUEPSqfbduKf1TVqizKPfBWom6qLnQbLQCyrqKKl247Db9BsbEJnrAFEptFWDyC1LTTYbpKvxX5VNDGbf3AIfnw+/v974fhq15fDfC8SDaOGLjWs7bp8jljYbYK+abJBhLi9ZLq6fPUpyYPzZpZ/pXvfo2sDrTCvvOTjTbzBSr/d1vkxWVpoetFnCS0N2oFGqUVhZT0m1G5tNNSRV75rPGc4H3rHkl9fijs0UO9eVNRl7pj0YAV67bCAhO2czxtGA5+uXqUL0/+V+Iiv16fSAB8yl74j2dFEfijts7dmoZPJqdntjpz2LAGs8o6ajWuP24v7hL/CmnycbmryXNXF/l0MY/NcPTSLLZjqmj5oJW7qn0Wz752cZE8fzM92k25qRCGJqm8frY/jTc3llrvFwm2T/neywy3ja+Q6XvL2YG00asu1sxnX1iPsaUZ/a4RLe77gMSOlpPNB+uNcS+712XyndH/VLtALu/3KN8Mw14J2rrvdwtypi3zYunNtP68LIbkmsf2Kc2GGxSRVi6I3cclqW5XjF5sCXoRpLQcqgaoZyRrzJg6YpaYx+Arsqd7ZDUceb2jIx6f35aRpip2mcfvzMngD8/Wyh8TfMZvLCBtNdPMiJaa3bqxvl5bVuflxvHRefd73JSQ4xjm5QMjnlVXW1IVU1tPOtY+zCbYX6OHLbacK4CnHamXPvKfRUJyz31N/CGqULpz0/H5K6wXWz4dpZKOqKhS3Iqk5uWQ3nv7GIrfmGofb+omzKatwUfXaLkJP6Z7eAMJEF2w6Q+eB07v1iNUt2FsGWH2HaHYEd0YDcnIYWhmV5LoBu4HkTRLjNjgP+hqTq8Qvikfx9p3HfWVbugDYuD1c45tDPrjqR/jU44Ddenl0sVlrqKmH3oqDXQFmNm+p6cT/pIRhmxZceZwQcc7RwzBuSNs0wVA1Ju92mlx6yiK9Gqcsa5bkBiTFaok2X5Cgj3u+AejG3G0xEqEtfEgC/2WqX0UJ2BppcJgTrEu9NIzux8tExALi9Cl8sD3x4Xe8w4oL+6xkF2Cir88FphnHJolcDjtPQbqasVNOSvaYh2H0S6XHhdFLljgKMXGeIMYvzWzbR5JUSolRD0lNvJLf0uUjfr0ea0W8BQerRauZ2EENyn+qxS4sNs3rYtJKKipd2qhB6QMxSlCqr0IghWVtbC1tVb1xzE0U2fgfbZ8NvLxsGbWPMfixows+eomo2q+XgdEOyrkLP/tdCKSzYbGKZBoiqDeyvr1aKayclJsz6hpow9prnHJbsLDI8SponsXhngw8+LdyjQ3yEyDBURaFt3SdhD43C7VXYVeaDeHXZrwHvuKIoRjUcoH9GnPAkfGJcJyvTLhbLdCfdKzZsmwUbvzWfRYgLq6zfX8b2gkoSKGO0QzxQky4VWqKFxFKersZ7vT8Jakr0++7GkZ24Z0w3/Zyu5aaqQcNuNpb38oNMfEzfJ1pNkPriJuHFOTk6F7tNIUeJp4/yhagnH95GtLuBsJeX5xjG392ju+LMFwkoe31BdF3NmAzJb1fnWMaUcb1SeC1ECPRf5vyZbibj1m6DN1xGAsUn3lHBtS/vWS/CTqoLhU6hyptBYi8B5q3aTNlTHeGppKCJDFqGNsBT5/bm/nFZfHjtUCNJz7zUPPYf3DCyE73SRQhSiNOOooCSoXrLiqzeoHqPT7+XUrSSc+5a2KUu3apetnG9Upjj9UswOrBJGMtB0FQ8BnVowzUnigl1fGQIF3UP5a2QF4IeA4h76Ysr4ZWBzdYX9vkUHvp6Ld0f/ZFOD88g88Hp9J08S2+DxkiH4XFc7BPG7fwtBcbKkZ82rBbOANaQrS6ebbSxiefCHJ9wktS61bE5Yyi0H4bSbigAtvWBk2HzpMVA4bWn7iAh11gy95eNu/JdoRLw88pNXPr2InyfXmK8ed1suEvNmC7YYLnu/NmtXk/m+HJ8XjGWARHpIqbW3xOvP8v8DEmfT9EnpSFOOyd0to6/jk8u4imXX7KiqbjJgYo6LnhzMdmf3A1T2sJ7E4xQFBPa75kYFWI80zQJrg4nGr/jUchBGZKvvfYamZmZhIWFMWzYMJYuXdr0Qa2FOnApJrewVpfZEifZJlMsa3tqAhIitKWRLkEytrUA2PevGaq/pS1F6WjZbtPvC9pEt9enzzS1Jd4TOidw/7gs67KtyuAObeiRHMbfnP/l1hDDkHzUI6o+5JXXGsu3ALMeCWoM1Ht8uop+J3M9bO1BpM7QeqiBv0E10tL6i/+Ld1k2a5WD9PaX7wMUcIYbSTqgD8IQZIaoSQAFkbXRYvPSzbpw5vioUx7UZS32N2RIVuQF9Eut20vmg9P54qkrLNv3TO7Ggk+foay4geXwugohbhuMic/Dw7mgeU006itF9q4fszYa31eX5thr3GPLfcLQ0YxpnSQxQMbUWvVQzROAxCjT9VRdrBveWyMHU+fxGUu8iV3Fb1WZD5uCL/H9rnrd9HAPVU7F1nUM3dSktM15FdBW9djnrQ0qdH7DhyssMXw3n9LZ4r3yKjbeCL+R2l4XQ7vBQdsCiDgwdw21bi9nvCo8qfc5v9DfjskcyLheYsK4w55pHLZjvp7gkRwdSqxSwT9dr3OW3U/uZtRjxr2c33DQf1FVvV66U7t3yBHG7DpfJxTAp2B46NUwEn9eNIWx3DWqKywTkiXzff14r99nomLTLYtEKEtce2ivLvmaDMldhcY95cDLSydaE9dmhf6VD11TeLvXejY/MZY+9mwAKkKS8WHnvd+yA0NaQiKhg/pZpspTM9YZ1+3dHbJZNGY3odQzxrGCWEQ7vJ9cij9aedmeaTGclpUc2BGaM+Ds18AZQmy4iy9vFgZgvcdHnQ+UBHWy4jd2m8eU0zRdvtLdYqk8JEq/nqLDXBQRi9vuJyW2/F0xfvoxd5OYhGaYpXOqi3k2+3zibNYJt9dtcizkrhYTwuIdYrLpblrSaeH2Qj5d2nCxjOcu6Ms/z7GW+/vOK2L+v1i+10iS2b9cXzmyhHWBYbQrCvxHhMkQFscXd43T99mcZxi+vu5nAuBY/o5lKdjrU4K29TLHPB52+RXqmPWI/ntpToQPXFNZFXYzO8OuoFwRhmBZXE9hwLbJhK5qe4KEVWgEXc0p2wc+NzhCSc0Q3tc1+8qM+u1gyMNtm2UZP7eaBNrPH9jWWvzit5etYS8qdfP/yQlT5tL/wc846R8zGGNfzg1OUzJYEOeE1m6L1qlm1LZWolMzabEh+fnnn3Pvvffy+OOPs3LlSvr168e4ceMoKDgKqza4a7C51ZvapL+UrGpJmkXGsTsgQjU2/Za3Nc9LN3PGtp8hmRobxsXq8vBUP0kI3cNZkh0gqVLr9tL1bzPp9PAMluws4p0Fu9TPitZjMM7ql2455vkL+zFzXAU3OGcQq4hBeGe7cxnUQcyU1uwtBbsdHCajYUagPtb6nDLKaoSYtCVjWxuMY0X1Gi22yDyQ6ESrMhMV1gFck93Rl7a1KixxGRYJA4fdxiD1/Gv3+iX0NOKR1AWGzXIemjfS7oLEbroRFmBwRaeLfbz18P1dlkFjWXYxWbY9XOW0LpG1J5+TtzxN7CtdgldAyl0TuA2E4THkegiJgGtmwqOFcMVXxvtBtO+05KCz+qUbup6qIaK0HUwJwjg56ZmfqawzGc+J3VBsDkK8VZbfw2xMJESay26pXrW49mSkCQNLW5IlvA0MVOUxVnwQ9Ktp8bWDO7QRsTxaH3Q+naxU0cYteeVw6oPGQV/fYDnHvpJq5mwyPMP9MuIY0ykUPjxL33ZR/WPM3phP90d/5O1NgTHMFop3WfTcLnOaYqxCIvRlqZ92GQbVmi2GwZYcEwZrP+d8x0JeCTEl1TxWLAyoZOHpaSxR6ys1C7Zdm3DDs6D+fhvoTGWdR3jJx09VOyHQkDTrtj53QV9sXre+zLVDSeeJJT4m7x/M71WpMPAquHsd9LlAHKAanIqi8NrPwkvYr10s60ZvJPzD8QGfNdKxjrE7nibkaWOMXD/yLf31gm0HKPcXXday8dWHqFmu5O9jUrk7/2HSFzzElrD/4zmX4dV17PtdTLpMbFDDCiyJEWbU2GBd7xdRlSbMJcbHKjfinoYAQ1ILX+qVHmNMajVDO6atGPcxvFevtn0OBv2fNUN20asB4QdaMqTFWHm2I8F48F8fGn+YRf6XvyuWeZtgwbaGY7lfvLgfFw5qx/lRpvjHCz9g0lhhcB2oqFNDEnoLncTdIpSjQU3Sr643xMbHT6V7arQur/b5MmPcU7TQF7CI1W/IMcbwSX3T+P2hUXx03VDucprGPDMv9ICaEjbnVmDHxykOI75XM8i/zDQpEbRXQ60WvtBgFvqmXHF9WZa2NYMsth0js1L0zcuyTc/6dkPUZ6YiEqVUVpuytXumm56TiiJWlVQ2driCTzwiuTZ09fucUjmdJaG3803I47zj76XWpOhMrFaff73bxhjnX/OJ3u6jmRYbki+88AI33HAD11xzDT179uTNN98kIiKC//wn0FXb6qjJFF6bE0INb6IWlxeQua1lIfstvwSV/tE8cG2MwWN0zxR9f4sO1Pgpxmu/mDPzjOjit43EAvOg/UjmZu5NXU331Gi+ve1EMhMjAwKnO3XsrC9P/PUr9b07Vxs7LPt3wPfSjLHuqSYhcnetIeejlkHUBlmtAo6FGNWQ9NOVC4iR1AZvrYqQCc2IXbDdL+OtgXNDoH4hYMg2xLYFu103JDUpHR1niGHMrvwAXh+hV9DZXVDKT6EP0igv9Yb/TLDE+Py8wvBQnVT3EjfX381w11coV3xjfJbdLuLNOp5qTGxKsgMGRG2Q769JnwCsFVIctv5Wj07vx38ykhlcYZAk4sdsJjHp7ELDkNYHKTAMyZTeFFWJe+El03Iq/VWJlz2Lg0ow7VGrxZySlWTE8qT0gahkPdTjnQW7IKEzhKj3n18y20nPGIbe17eewLe3noBj5l8ssUErFKPW+9NL3NBDeEMYeiPcOB9CTYP7/uUcqKjDjo+JEaYkrcvEEtyJXUS/f+s1SuGtXGV4Scd0i4cfg/z+qsGhx+0GSdRSFLjzszV6UP7JXU1L0KohWRonDNF/zt5iZInmb4B6qxfrxo+MLNwLB2dYwmKmeYU38P1F2Vzy9u/GUqLWNhTYOM2STPDo6LZELDSNQ00w7ITT9NcfLd7NgCdnc9snKw3vpOaZ3TwdfD79s2LCnFy5q4n7RzVmNDRPjGV81fD5jGVCv7EjPkKMLZUeULSxomy/ZR9t5UKTpwLgv+eJ/7XfFMNz/HN1ZzjzZbjJtAQLsMuQcqqodVNRKyZwV6vxtP64nYYR81zZfUJiZ+tPsOgV644Lnm80ZvLnzQW6c+HeMd0s782482TOHdBOxBH+71qxccgN0OscTlKvcz1sQPO2qZNtswE1516RBc/qT6zJQW0HYrPZeHiiWOlYZZa/CTPdc06jbx/4nzAEh2S24bXLBpJal83JH3chxSaOvaDuMc6o86vd/kwmnT49iXRb8Iznl38vNQzfGJNBVeyf2CqSCveX1hDuclh1kcsMR0aYy8FVI8RqmyVPIiTC8PxlG7+/OfTiwkHtxKTizZOFFrFGWCwHhj7IFsW4Rqe43iXU5tbjTS0U7wqIEdXaolfOMyWY+Sc6HW20yJCsr69nxYoVjB492jiB3c7o0aNZvDh41YO6ujrKy8st/wDcbvdh/+cpFrOQWlcb3B6Pvj0hUjzM8spqLPv71ABiT0WBvq2ovFpfHukYHy6219ejqB5Jd3Rbfd9Tuxoz6qenbzTO3aYLvp5qfNjnV+Au3oNn2fu462qo+PxGpjjfAayDyXUndhDHluWR/NPN3Fn6LN9fnk6v1EjcuRssupEKNtzD7yDZtGzpdrtxRyTjvtkwTj37V1u+b2G5uHDjIpzG9hLRZ4ozDLczCrfbTVKkM2h/ud1uPBFiuchXttd6btUjGRdmx+1241WNQV9kSsA5hnYQ/b7zQIX1vXBxbqUiJ+CYfWoJtZQol77NmysMI19CV9xuN+kxoj8qaj1szS21HO894W6jsw9swvfDvSzaVsD6GQ2XErOwZxGe3Yspq6oh88HprFwpvErfeU9gn5LMj76h5FXUcfHbv3PClLms2VNkfL5PwX2H6r2rr8Sz9F1L2/aWiO+WGKn+LvV1KOqg6e40mjP6pFqasrfI6DdvopCNsK38UN+2Q12auXlkRzym+8CnGjfexB6M72nM0n/bli/2SeyBEt4G3NV49q60tLG2rl4XMo4NteM9IIwZX1J33G43XZKEEV/v8ZFbUon7mll6X7sri3G73VRUW70ivVIi8dRUWJKQaq/6EV35QGXxoBdw/60Q95incSf1xn3/DnzdVA/JtDtYt6+Uyxxzed1nPLDc7U/C7XaT2UZMIvNIYEEP4U241vkjg22bmWBfgmtn8JrS9fX14noPUR+gO+fjLsvT+6O+vp5PdtiZucHwrp4/IE28X12Golb2caYLndnvVudQZGuDEpkMihdPzjr9XHkllXqiwqD2ceJz84UHtD5tMMVYJcpemL2V9xfuwB0SZ2z84koWbhNes+Ed2zBgi9Uj4h3bsFHpS+uP1+th8hnCgJi7uQCvT2HGujyenr5BtDPzVLFzdRHu/M2s3SsMk/EpZdaKOCa+Uw1gPrnIci1lqxOS9JjQwPFl5Ud6Zrs7qq3lPU0qpcptwx2mLlvXV+CuKAy49pOjQ/RtGkrhNn1b21gxVmwrqKCypg63IwL3PYan2vf76/q+U00JlbGhYnxz1xkGifuWJRTfupkqxfD+f/3Vx5aYXwtPxMHkWDzZSwK+/zXvG97qMd0T2frkGObcOZylN3Uga/u/ceduhFVGbLAnaxJut5vUaNE3+eV1VFTX4lUT8bxlYix9Vl01O6dfGh3ahIl+MSUGeU97FHdcJ9xuN33UOPYNOWWib9S2rWwvVhd8HnFvVNXU6fGo7dqIZyWvG8maFdGduf6yS3ju9iu4332TpQsiq/awMPTuoN1TQQTDp8wVn5tlSjh5dSDuulq9PaWVNVz7vpiAXTKkHaF2xRgXC8X954tph9vtJiVa/N5bcsut11uv88V+xbv0ba/PF8feeXpnHPjwLn4jQBnBfeUPDOyYxNfehpegS5QoTgn7EsXuBHcV7uLdls/WHDtJkeozrULVwMaGO7aD5fptyvY5lP+ag7PpXQwKCwvxer2kpKRYtqekpLB5c/BMqilTpvDEE08EbJ81axYRERFBjjh0JJWvZ6AzjpqQBH6bbSxV5hbYAAebdu1jxgwjsHZs7ibCAc8PD/DTbjHLyq4At9dJXIjC2sU/sxYIcZczwV2Fgo0fF2/AZzcGnEGJdlYU2vl8+T4Sq3fTLVYYiCm1mWgRcq5X1Cy66XdxEoATXvBcyAHiAJgyxMOq3+ZRcmAO/fYZyyL7Pv8Lm9IuZOI644Zf2+4qdiWNhjm/kO5RTwZ8NW0G4eqvOzy6DykV6yie9iiLO/9F95At2Sv6obIwjxkzRPxGQsVmTgKqHLHMnSmSTSrc4ryFlXVM+2EGTtP0I74yh5OBmtwtzJlhxIAUlDkAG5tWL6NoC/Tat5QuwI68Mjaa9gPIqxbn35FfzvTpM3QHntNTxSTAVlPCrO+/wuMwvI+b94rz79+2gRlFwhs4ZOfnpAM7ykP0z4gLcVBab+PTmb/SP8Ew1u2+LM40tcG+eRqXrb6EKU4jYeDXbo/RPfdrkivWUxSawTOV43nW9Y7+vvODiVQ4O5AdZsw4f/NZA6KXZotQhrNf/52XR1g17s5W/89ePosNecJ7VeWGdfvEdyvcupIZeyCiroAxPg8KNmYuWMFJYU6iOtn4bKfwqHzz0890VB1+nUtD6A1U5mczX+2D2WvF+cr3b2fGDGHwhbjLmbBeiHQvybORHLkJ7dp54NNlPNBPhGMMc7UntaaETbM/YGeyEWKwrwoUxYnTprD4l7kM2vMLHYCthR62zJiBV0E/33vfzaNXG0X/vrs+upNN6Reyv8rY56XhHn6cOZ0RO55Hi5LbkTSW9esK8B+mLv33MqYM8RBh2typKg5NBGblymU85jBkcSpC05j3k3H/j25rZ85+O5/vS0Ab9v8Xqi6fBUmkf9J9JVnfzyTMCXFVOzlFO+9bE1mQ9TgA64ptLD3gsBy3f+1v7F8LbYsXMxgFn81BhqNC/z5PfjyHx5Vo4ilg5S8/kBsnjNC9lUa/9AotYsaMGWTlTqc7kFsfyfVZXv69xfpZk3/YzK9pXszrQtN/WwuEkOAppGDnerRaJ6syrmVffjK+AR+SUrYKu+Jh6C4jIe+3qDMonjGDsgqjHRrv/rabvj5xj4wOSSayvoDiT27iZ8cDgJ3HCu6x7L8r8XQ6Fs5jT0gXKquN+3f1x5PJaTMUnwK7C8X1uXPtEsr9JBzPXnWn/nrGj1apI1+1HbBTWg+zf/mNMa4EItxFLP3uHQqjhef36xXi3HUFu5kxIxu7z63f94s63Ueheo8oCkS5HFS6ffR+Yg6PDfCQEAbdUs+jR97X2Hf+zPfTp4PNxsdLRZ/0jffp42Z0zV5OBzy2EGYs3gS2Lexr/zy37RVZx5+EGBngy3zdWOzrxZ3Obyzfx/n+WPbEn8zW1LOoCkliWaGDE+0b+ThkCm96zmTbslqyPdV0y59G8gEx4XHMM56t++KGs2JDOWyYgaJAqN1Bnc/Gx9/9xMjyUnoCtsWv8k3lQPIrVOdA7n5mzBDeOu3+3JR2PltLu4KpbyKdDqo88J+vfqSDOta0CRNXVG3+dmbPmGG5bgc79jBjxh79nACLM26lbudytu6E5eEjWVf/kx6Ta6Y8rB02TzURnjLG1k3Vt/d+/CeeGeqln3pNASz58iWKosXk+aX14rcGyKzdwYwZxlg+ZOd80oENBxR2zphBSbF49s3ZfIBPvplBnGrzJ5ftYARQlbudeTNmsLVM7AdQsW8rM2Zs4cStn2EEgUC1K57Zy3aAbRfndQ2l77a3WRl6M06b1eM4ru5ZCurcFEUnk+jLYdnMj9kc0geHDeJCYVeuaP+ujauYsW8VsdW7OBWoc8byk98zc7bJnjmcVFc3Lk+m0SJD8mB46KGHuPdeI/OtvLycjIwMxo4dS0xMcPHvQ8dE3O57+G3WLMaMGYPLJWZpUdsK+XTHSrwhMUycaGiSOfc+BYUlhHlKmThReDh+3JAP69eQmRLHxIlidmXbuwTWAzHpjD/jbMsn9imp5vQXxPL1J9lhLHnwVDU4dyLK2zOxHQhucGfYCjigxHHJkHZccFZPUBScU6+17NMhtIL2idZl3h6XPUUPl2GQv7rtV/aX1pLUYygju4rL3fHpe1AByRXrOSNhF77hIilk+fTNsG8P/Xp0ZuJoEaxtW18F2yEitaveBz6fwhOr5uD2wsATT7PWZq0YANueIsJdwsRxY8DhoqrOQ91icaOfM+404qLCcXw3DQ5Apz5DyRxuiq8B6txepq6dS63XxqCTTyfVlFmsZD+JrSKXcf3bopiSVf6+bj5Qz6TTT9QzOJ2vi4d6x9OuJLOL8JrPr13PN6tyiM3IYuKpnSyf6+lQh3OaUe0mnnKG28Vy6NpBTzNi/I1QeQnedZ8T0/dSztjv5rVP87nNaSSftPNYly3m2E6gITr0P0lvK4A36Wkcsx6my4Gf6HD9h2B3MPalhShUkxQVwpXnjQXAvvgV2AhK+xFMmCRiB88Htr6zlJV7SunUayATegsvpSe/E/z7U2K8RUycMIEdhdUULP5N/Banj2CAWive+bYhaTPk3NsYEhrNorp1fLsml/3VNiZMmIDNZsP+8wpYtIY++z+m+3l/1ZdPp63JhbXrGNAhnjMnDcHx0RtQDF2GjaVzb/H7/lojzhee3o2Jp3UGVY2ka/lvdLz+PZ74YROwl97pMUyaOAzX09Zs5PY3fkJ7YNRYHx8s3s1zs4xl99Sew4gLd3Hum8LjvvHxF1Ge/Ryb4qWktASvy5jtRPQcq1/LAKzLY84Xa/nhQBL/8kti1/BMfIFvbKP561dr8WHng16DRLZm6W7YOhmA+Ood+nk3z9oCW4xr4d2rBur3n/OFuwGwhcVwxbkT2enaxEdL9uKIzyAueRCs28Hg8H14J4rrd+6mAli3mj5tY3j0KnHNO77+CvKgXf/T+OvwCdxS42bHgSouesfw/s3LdeD+y1pcrwqv5xBlNcsZyvmnDyF1vhvKwHP+B/TuPone+lGi/d4Z5ThWiVjY4RfeCTY75TVuXlwfqON32uhxhIc4cK26CoCUirVEdk6jY/5qohRjOd1963LatcnEnbeOfWWxvPHxr1zunAvAINbQf+JkFmwvxPO7CC249Ozxely4OEGNfs14Rz3BRL9x4+GVcwEvn+908PgVpxFWexJs+o4RvmV4J96P16dwz+/igXvNpJPISo0WS5xrQHGEMPSi+yzx2tPLVjNbLc9ZHt+dK0/thG1/Mrwv4ho7tU/izC9K9f2fufwkPZzIPkskT9jbD2HiJJPX7B+B8jWX1j+CBydfekeyINRqeLcvXkD74gW85jmLUl8HPg4RBv7Nzu9h9fcB59LwZU0i5YIPMPfQ6zsXsbWgkrLYrnTrNQG+/h82oNfAYbBUSD799bwTRLiLqa+7XPI0XbQwL5Vvilbyy7ZCojr0ZuLw9rjdbhbMEJPkCHcRE08ZwjMLS4BsTuqSwEVnDxJZ6eo53Xdv4jSToHn/E2oY/8/HiKeCdFsRX2oTOSCqy3C8Z76Gz+6gZOrPahAs1PlsRHYdQrtxp8MzYol7+KC+KF3GUFRZx67FvwDgtNu47FzrteL44F9QBj2Gj6Z794mMrPPw76fEM+rxlU62/V2MtbZ9ibDzn0TX5TJx1MnsWnwANoqEsoeuGI8NcG57AADF7sI35AZco5/U+30icFVxNbkf9iKjSoSYbfJlkDpwEp3yO1Kwq4Tlde0Yb8+hf/sYLpspTLANj4/mgWXzAB9njz2V9vER2LbNgi0QmpChjzNut5vZs2db7JnDibaC3BQtWtpOTEzE4XCQn2+VTcnPzyc1NTXoMaGhocTExFj+AbhcriP2D5vN8nfPtnGAqD7hxa5vt2nB7/Gd9W255SJ2rH18pL7NuV8M3ra0/gGf1Sk5lhcuEkLaJdVuSmp9+nuefg2XFfs6dDLZ5+xh6nl9xf75q7H5rB4s+/5lOH42BR53m4ArItby+Sd0Fg+vF+Zsx2Z34HK5sPc3dCUdcyfj8tXhdDpZp1Y7SY4JN77b6v+KzwqN1reFhoboUjo7Cmus3zmuHbgisSleXPuX4HK5hPwQEGJXiIsS57ariRiOmNSAPouKCNPjMJdkl1nes6UPAMC562d9m93h1LPC09uov4vTiU2V83GmZOn7apn2u4trAj7X2fdCEdOnsjLsZjraxTnadhsg9mvTFsfIe3HFpTGyV3t29buf332mqgMmvMl9WPnUecy77xS+ve1E3rzCMPAA/vLVesvnO7TsccC1ZRoOh5NdqgbahYMzjP3UKkP2Hmdajk9T40MLKt3Gd0rshIINm7saV10JC7YbsVADMhPEforbmNB0HoUrKh6Xy8U9Yw19vlL1unW0MzRSXf8+Rf+crQViOTIzQfS/XQ31cCYZfd8nQyRRbcqrFPfh3WJgtdUU46ovI0+9t1Jjw3Dt9otJwxgjosJDue30bmRPnaS/t3pfuW5EAqzNrcKmCtin2Ypoa4q3coyZbOm3QR2Nh+SJtS8H+ylxDrySC4d04LLhmQB8szpXHB9rrWHswkt5nY83FhhG5NK/jWJUzzSjr9XkPduox0W/tBP9UlTlxj7kegDsm77DhReXy8UB9cGZFmvcl3Y1qcXRbjAul4uEmAiGdk7iL+OsmopV4Ub7/lr7EnZ8tI8Lw6bGWDrb9gs6RjpGPSISicb8HVdIqP4ZwXh29jbxe6YY5ujYvLeYFmLNbnbFqn2QMZDUlBT2KclcWi/E3H17l+Ny2PnXz0acW0RYqNGm+nJcz6rxZlEpOE66K6DN5sQxl8uFXU3EsO+ci2v3r1TUK/gUYSt2T48Tx1WJ+9sWnYorJMRyvouGmPRF1WeGs4Mxef3vV4YHMdRpp0fbNkb/qTG99n6XWp89GcbSLsCL7vPxqP6bvYp1Zc/Mbc5p/CukYdk2f+znvR3QP/FqqFNprQdnH7Fka1O8lOSICVnbuHBjTNin3kthcbhiUgLO1VuNY5+3pVDfVuuMQ1Fjnl0v9eCjhcKdfMXwTFzuClwfqvdrfCfjWlD/dUiK4fPbR7GfJJYp3XnObSz720++F1doGC6XiyUPG2F0+ueHR0NHsS7g/PxSXA47X6w0HCwfXz8soP12Ne7fGZ2My+WiTZS1Kk+tV1xDzjgjBtO1a54+Rt09uishISG46suwVeYBNmwP7sExYUrAZ3VOiSVj1I36eXo8+CttznmGhycJL/lmn/iMX+YZxR56PTGHOjWTvm18lGhLjVjatsVY+w6OsP3UDFpkSIaEhDBo0CDmzp2rb/P5fMydO5cRI47uYFAzqTFhRIU68Sl+GoPxauJMeY4eAJ2tPtgzzRVGtCBfc11tE+cNbKd77faaAnW/LDGCpWsd0QHH8eODsOZTEYT77hhj+61BqntMfB4u+yxgs2bwbcgp594v1Di8buOsO2UvJK+8VpfzGd3DNKDtFt4rcyA6GBIy13+43LIdu92QZFktMsw0fc4Y7Rr0+Ywa22oCjz+DO4j4UnNgMwCd1KB/U43Voqo6fIrQvUtQE6eoKzeqhEQZxltmQmTw84JIurllIXWdxgS8ldAt+PX8zPl9uaT+Eaa6L7FsL88cj+NW8bDvlBRF/4w4xvdO4+VLBuj7bCuoZHeRKanCLDC7dykHKo3krztHqXIePp9REai98VAD6KwGZVtkkxwhVGsl44p3slQNqv/r+O6Gt0cLPA+NgSuNLNIOCZF6pqN2HD2M7GlqSvSKFG+pFZz6ZsSJRBEtY167h0D3vmpZucS1N7J9c1bpZRunON8Wwu9mRj1OMLQg+Zf9tOqmr83VvaWTHEuIsqnxl7ctM9QYVLR7BGA/SZxa909qL/4fnHi32Dj6CXFtAKerkjFbNHHlkEi43MhALdqzkUFPzdH//s9VA3WdWsDol5AokQ0MdE4Wfbxidwm1qYNEspDi05UgNN1HPUFky0xDzN1vzLlxZCdLEsZ3q3Og40j97/H2pbT17hUKBSHRhuiyP1HJcOtiOPFOy+YHxmfRLyOOFY+M1iVi/vv7HpEMeIVx7Zxb9QXRNtNYOvhavXoVGElxS9RJmNNbg7LyQ71+8SVD/JLwvjNWCkjKsngONf51mbi3HDZFtMdcAvX31ymoEP2YEBmKU7v2taSlBKtcDsCYnilcMEg85F+as42KWrf4XFVKbYDNuOYmn2UKYVEUI9HPz3Dkkk/wnHAPA2rfJLP2E1Z2uomR3QzP3GfJwiNZGd6WIhopYBCMlN6QmAUP7LL0tcb5A8V3+XTpXvE91IlWVZ5Y8tVWJwCjXzJPCtrXmiTNwu2F1HlUFRKbDZvPiKEbbBfnGNUjWeizahVZRtwe9Jx9TFVnNqWdI+6DtoMMZQRE9ZidT0/k9cuFxucvWw6I31pL9gLIW8cLs4UR2ykxkmF+guHUVxsqK/HGqtTSh0fpr3Xx9DYd9IQeJXcNn6mZ6npSZ22p+D8sRiTnNMSAK2HCs3DNj/r4oyX/aPdAbyVQbzM+0qQhqVX/iQ7upDuaaHHW9r333ss777zDBx98wKZNm7jllluoqqrimmuuORztOyzYbDZdtsFs6OkSEp4aXaZHe/B3SDBJCajF3xsrou4RQWI8+YOROfrwb15urL+HO+tvo3vVW/zFfSO/evtYD/z2FlHPV6PdEEjuIcSYNQZeDSYvo5noMCNaYdqaHKHPFRYLt6+AZHXwy1nFW78IQ6BzUqQhYbHNeCAy8i8NfrcAhqsxm+u+gNy1uvGtxZ1QUwKad9XPGNLQjI7lZjkGENUUwJKhZ5RGDMWhVqXQM7vDYi03uCZdsWJ3SYOl2l5yBLl2gwx8IOSKRvdI4U3vWTzuvlq0x55EzEVvBN0/xGnn178YGbCnPDffGIhd4UKYGiBvra7LmBITagwm+5aJShuuCKNChUqqOrgfqLBWDKl1iYGrumS/fs5hnUzGlKb7FsSo2HlAXO+3f7LK6IfHSows87WfWxQJQp12+NVI/DIbbT3V33R/aQ1Ld6m/q/od6n57g7zyWqJt1SRtM7QemfAs3LfFMOr8sJQ8M/HR77spDRfGyNkONSs4fYBx/fix8clxerLGwP6DCesxBsY8AQ/uhRPv0vfrlCge0DsKKqnSpJa6jtYNBveH5zHKvoJ+NrH81a+dX/vK1SzimHT9mhqQ0YbYcBeVdR7hgdYeFKpHXVMkSIkNg8LtYBZmDrOe3+Wwc+eornpN9lfnbYPz/o3HJgzh10NeIXyGahym9hYTvxZw66ld+O62E0mICuXVS41JUWm1G6JThLSVP/dvgzNetGwKczk4NSsJn+mRUz7LSPi5/XSTHIq7BraaKuSMnhy0bVmp0dhtQme0sLJe11EFYO8yCktF4oc2BgCGwLN5XxPjehkP7e+0KmKqEPRgNRZ+6d9GcelQk/eypsTIsI3zM4gjE3GOncyqqZeSPXUSH147lHevHsxDE8TnP7hnMKPqnqN3ybMMqn2DW+rvoln0vgBu+Q1uXxowUdIwC3L/tCFPn2B7c0WiSKb5maaNrw30y0iTAkFuqZEk5+thhHYNsW8hPjIEV8kOa1nbvsGTjGw2G5v/Pp7XLhvIM1ePhrvXwNU/BIy9druN07KScdht5JTVCrWVoYbHrz7fCBebcp7f8xSEKoLiE5W/og2PfbIphOr8Nxbpq1wMFdd0RaGhADBCM05rSsX/YU0Y/TYbDLsJOlgdEmf1S2e7T9gZ6bZCHFiLn2iTI8DQT446Bg3Jiy++mOeff57HHnuM/v37s3r1an788ceABJyjnQ7qTWbxELnCjAemKlejSadkJqo3ZXmOkZWYHHyJE+D0HsKTsXZfGfmqh8HlsDHLN4RpPiE98qX3VK5yP0TNw8VGZR1/rleNu/6XwU0L4ME9cNYrwjMShCiTIQkmyYbELroHzJezik+WiCSjv4xTBw5FEWXnQJRDS+9vOc8Pdxizff96uro4McBbJ+vev+Rw1XDTvDLh8UL+Jggj1GoBmjixjjaDLMnW5RI0SQ/LA0LzCMSZBnjQyySCISzvzxvrILP2k6DvBePhieJ3/8A7js61HxHz8JYGB3OA9gkRehk1gKxHfuS2j1dy7uu/URQt+l/JXctzP6wGoEO86bfVvJEdTgjouzaqITRnU75FLqrOJQa531ZvoqLWQ/v4CMvsv6G+8kc3vO12GKAKtJfsYqfJA3pWv3QhdAxGbXSVmDCjvav3qvqpqn5aaPZcsmx7ODnOb+LQ50JhWDVg8IzukYI2d7h3TDcWP3S6/t5Fv2dad25EViUixMnqx8aya8pEXri4v/FGWIzlQdYhIYK2ceHUe328s8CYzLg7islBqq2Ed0P+yXehj/GPnnnEhPtd35quoS7NIx6MTvVLTHh5AfVR6nu7f0NRFH7ZIpa00mLDYNd841x9rV5wM1cMF5OCwsp6lhe5+GudKb5azc73n4i0FF3QG6N2e8XpT+vL1QCcdI8h+O/Ho2f05C/jsvjQI1YAYuvz6WzbT2ZChMVLbMluvn25IWjvR6jTKFm7p7ganKHw12xwRUJdGXa17yzjhHattvWrYqNi1tN95Nv1lNe6eWmrGJu62HO4L3Km1eMMxmpLRIKYHDaCzWbD5bBzqi68bmOH0hYtSWSmbxh31d/a4PE6JkOqIYaYyqFuyavQn1cheSImdZC59rgmLG/y2Jlpb1qRM1c78o43dDDvdn7N/WO66YUJADj3bYv0nj9hLgeT+qaJ3yi8TYNevvAQB53V1ZL1+8uEB3aw0K+s3S1+0xCHPbgWaZ66MpfWt0EHAQipJUCfYMds/Yos2x5O6pIonC2/Pg/vqkvtJl3qlhAX4aJQ9Tw7bApvdF7CkEzjdxhh9qbqHsmj37Y6qMo2t99+O7t376auro4lS5YwbNiwpg86ytBujN3+S57ajbRnMXUeLzmqtpPukfyfIb5KavClbYAHJxgzu49Voy06LLgRFR7isGo+avgvv6T1bXImdHb/dIabvE9msWfNWK3OXk69WklAq/RBwSbh/XKGwdmvB5y3V3oMKTGGd89CWCx0m6D/Wa56rCI1m1aLx0sMXE7S0GbPFXUesaSkEZ0uyrH53LrHRpOu2G8WGtd1PTMt521r0pnUygSaKTItJ/9+wXI44Q64JbiUlUanpChWPDKaabefyLonJxoanI1gruADMH1dLqv2lPJ5djhEJGLz1BBXJQyViWZ5n41qYk+QSUuWqSznBlOt6Dqn2F5SIGbUd43qak1i0MR5gxiS02439BWLzKU+tX5d/h/OfV2EP2QmRAjPaXG2eG/CswHnu1BdKtTLkfYzjKG/u96zVnsYeHWjBjmIpZ/t/5jIjqcncueorqTFhnNqlvCWbFUyWOsz9bOm09gItkYeLNr7miD/S3O26aU/z18U6M29fOe9AeVVDY+kNaTjFNPy5vPb1N/7l2dYsytP7/eeabFWMf6BVzXYznMGGOd/9LsNrFICBY/Nff9H0cJmZm08wGJfL/rVvs3yIS80upLROSmK207rQlkv43t0seUQ6298a+ULodExAyBRNRKL1bhSs5B+n/ViYqzpBgPGykUDBlNKTBjnmvqy7+RZvLTUcDbc4f3IUsmF+mqYrYZhRAY3oIPRISG4wQSwOHIUS094W4RlXD8P/m9G4E6NrIZp2O02bjlVVPwpqa4XDgKgk030gV4z2uc1+jwpK+A8/kz+3uRtjIjn5y6GbuiogvesOqz9Lm7yfM2ltyoGft0HyymrduurAkqO8LCmx4UFv5+1Qgl+E12A/15n2C56ycnOxgrST6EPcmFmtaiaNu/vxoGNOJEa46LBGSgms2vs/n/x5c0nsP6Jcex8eqK1/ZoD5lj0SB4rtA+2tA2iFBPAnsXsLa4RshChTkNYe49JTLeRh1BMmEuPhVm6S9Qw1lznP95taE2NVj2XhETAjb8YJ0jpA1eYxGGbSajTwWc3juDRM1T5C7PxpAo5R7mLSKRM/Qrqd9DEqdMHGkLgJmw2Gyd1Ed9n+rpAgXAm/VP8b3dSUS0etuEO1SOkhQI0sGwCEBnq1Jfl880VhxwmD+vO+QC6EZxqFhlWE1KCVQzIUkv4vf3rTiZPs9ZIXqbK83RLiWJ4764w9ilI6RlwDn8SokLp2y6OiJDmCx+sfiwwFnPBtiJ2esTsNs0mvHNXjsg0dtCqLAWJLe2UFKXPwD9dashY1TnFgKsFa3dP8/MIaKLIQQzJvu3i9Gu90GRkm42yWx3CuB3bK1UMsJqxFGSpXBOZ1g1Jk4D/UPsWBlTMF390HCk87c3AbrcZIQ3AdScZ57ys/m94YztAbHsY82Sww1vMnaZl18FPzWHKzE2srYzlZc95AfvacldZNwTxSAI8NNF4EP3gNZa/9m1bDUB6bJiYKGiGZNdxkHkijXGXGle7KbecnUo6f3ebkvuumdmgZ++PsFydVJYRxaCJ1za4UmLm6nMn8FuoiOO83fkNT48zjTfZvxmvRz1GU8SoY0a5efKpjnNxNXvpbdupVzLDU6dPRs1LnP6YPXka5mQQS433d8dAtipW7mj+WBDmcvD5jcN14f5Prh/GX8d3580rBrL0b6MZOvZiEZbRbpD43W/+TfxzhIpSqw14ff3RYvsWbCvEHS0mdWm2Ysb2SBYOjA3fwpOm76vFMAfh8mHGeLHKVC73G6+xWpWy0hTScIjL+nUzTZz7PTkLX1wmAD41/lEX8jajKPpzI5gheVLXRP6m3oubtMIV4W1Q+hmhYyPdiyDHr7RrkMIazaF321j+fk5vdnS2TgqjQp3Y7X72RDOu1aOF49aQ1ALZA6rbaDF8pXtM8ZERwuBSFKNChxbb1gh3q5I6K3aX6BVsokKdZKVEs+KR0cy//1TeucpUOzi9v/AGDr9NVFZoxqyzITSvXmFlvZi9gRh8VGOuv307t5+mPiAVBb5WY538Y3xMnNFXXNBfLt8buLwdlQzYwOdhX44wLOI1R4DmAYu3euX80X6TXP/yXTb1MlUHhDDVA/jIJJPBt1OVKcmahD+DTEsH7y/KtryneWxH+AdoHwbiIkIMD7DK77uKyK4R3/udkBe4cViSYSR56owg8V7nBj3n1arR+fGSPZRWi4lKharv1t0rgrktsVDbTPpjqUbWrZkENdtTK3MJWK7FB1yfY8fH/WOzxKxZ8YrSYkHCM5L86tpvzK1gSG2gx9ucINJShmTG0z8jjtO7J7P26Qtw3LMW7lnXeDB8C+iaEs2Vww0jWYsvftFzASNqX2VjlBH36/jYz7hswJBMig5l899FucIcEqlLFxPYMxZfwoWO+aKaDcAeNbShu1XOJBjje1s9F64T74DTHoGLPrSGn/wBzDFcC7Yd0B++r1w6oEnvrkZMmIsTR4kkrj72bHotN2V7//SQ8VpNcmnqXIAujg9YJj2n2VeTqHkki7aLazUsrtEEBvOKjsZr3nP42KMmZ2iC+XUV1prrF7zfZHvNDOuUwI93jyR76iRO6JLILad2ZnzvBoyG1N7i3/1b4f+mN+rEMDNArY61vaCSJ38RRn+4rZ4BSeok37+KU1jDknxPmBKM3l9keGX3VNo5qS6I+sHF/21WG5uL2VMMsKZSTJjbuPNx4uGMvumBB1UXG88fc4KOCa2qkXlVZ1bnh/XXsbYqa/IrNGu1oyGuHN6BzudNRi+0EKzkbuE2Y4IeGzxB9WjiuDUkI9UMREutYjC8KiW79aQRfRmiMh/qK4Rh09OqHxmM/u3iaBsXjtur8MT3whPWNi4cm81GQlQomYmRgYPvgMth/NMtDor3x5yJ/ch3xmDnTe0PQHfbHq45MVNs3G5k4QcszZk4NSuJyBAHbq/Cuv1+sYwOF0QKz1ptkfCCto9SB6tGyiOa0ZJHAurAaolF9ZUoiqIvQeiZdO5ao4Z5YqBH8tFJPS110qvrjd9ci4sxB9kfTszxWiFOO4oCWxVDcuKBDtuNnYt3iiDxkOgGY2gHm4zks18T3pyKMNHPPe27SY+y69c62+fCxxcYB3cwZbma0B68mkcyt6yGFXn1POs2lqk+7jyXEKfdMHRj2wW9ZjsniX5fu6+M8lo3F7+9WBfet3DSvYHbmkmYy8G3t53If/5vSOCs/hBxydDg124uCWw49d/63zZ3tYgR0+IztbCOIN7fMJeDZPV6yI80PJTPud4Wy+mr/gtFamZnM7wSltrCqMkEp/ylWWNVczGPK3d9tlpXfuiRGt3AEQ1gTrrbMkP0V+E2YxnyrOZJ32grS5b4Z2coVScL43SIfYuhe1ulSkJFpzZqiHVKiuLfVw2mR1oM43ul8vezhQG1SCs2kLcOCjbDc6Zl94jEoGPPISc8rkWeT7OX7qPl+ZTY4gDoH6WOlxWm1aUm7kGnw65PJHaZyq4WlNeyT7FqwNImU7T1EJISE0b21El6uNJH6w2VgGscP1riOI3GqcvwMe0aDAvrmxGLy2FjT3E12/KFw+eh7zbziuccAOy/v2Y94Px3RcLdHyEywVgheKk3zHjAalCaSsQ2mD9xFHHcGpKalEVVgCGpDvjVhZSUimXF1Bh1ICpUyy7EdRCB3U1gt9v0pUdN5uKs/kFmTYcBc3br92tyGPzUbBZsO0B5lPAKdnPkEq8t15tF0k95oMFz2mw2Pa5m8Y6iwB1UQzFZKcDlsNFG66Jy1ZBsQPpHI1VdggowJLsJzw2bf2BffhGVdR5cDpvxgNBmbs4w4W3wIzzEwU93Gx6vK98VyVJzN+Xr8Wj9MgKPOxzcNFLELA3JbCMEroF3PYa3yVmsXmPuWnj7VPE6sUuDD76UmDBdFHm3OvHR5X+ARZ5LxLnAqDEMYvmvgcmKZtxoBvuIKfM4/43FvO49mwIlTmzb/x7UVRrJQEHkVAB6psUQ4rBTWeeh7+RZeo3iHaeZstyv/iFAbupoo1d6LF/dYs3A/OqWETx1Tm8uGNQO7ymGB4P/nq+XvaN4p5h4NuDB0Dy1V623xlsPiquG724zNjQRKwgirGVSX8Pg9PdQHgrCXA5m3SPupWJTDK02YWg2qX3gElOC25aZ8Ikpnq7/5YHHBKG3LjFVoW9bsbuEy+aIsa2rfb9RBEDVEiSi6dWH0T1TmHnXybx55SCuGN6BFy/ux1233G7s8Powoe4BIvHlgR3BT9TK6JNIlZUeMf5n1W8UKx5m+lzY5Pm01Y1NeRV4FZGQp13DuXfsEhJXHUcGj+s8RDx1jlhJWW1KzLzVOc0aC6uRLSTZ/LOnzcSEufTEo9V7SymqrKO0up553iAJWeOfgT4XBG4/GMyTqaVvCYNSi/XXlrW7jm2297k1OW4NSd0jWetnSIbH6TMXh/qjakt9lKkGS5sGtNiC4B+3ccPJwYO8DwdmfbnCynqufHcpeS5h7J1lX4itbC9s+h5mqVmXfS5qMthay65e7++RBH3mlGArJ6NNuMiuVXxGvzXhotc8kpp2l45p2VOZLpa7eqbHGhI52qyzAb05sCZVrNhdgten8Oo8w/vnP+AeLjLiI8ieOokvbz6BW08VHowDxPF2tGo0LHwR5kyGb28Gj2oAdml89vvJ9UbAeNdHZ5FbH4bHZvo+m74XRp+ZSVZ5FjNd1ZjS537aQuaD0y3vPeo2SSVtnwM5q8XrBuLvnA47MeGBfdvuxIthcpn41/HQxlIdLgZ1iOfUrCSSo0NZ/NDpDOoQzxXDO2Cz2fCdeE/DB6b1b9AbonlXspU0i8c36v3TrTs2kBziz4sX9Wfp30axa8pEw2N/iOmWYvU+LnjgtIPzBHefZExApt9nJFqFxjR7YtErXbRle0GlHm7z1PSNFCjCMEi0ldFO64dqNd64GYakGZvNxrkD2tEtowHPkEku6mjkPNOS8Eqf6O/4hZON2EEQWpTNiA3XJq0A/95s54sV+/Go6g5JcXFw5stw9feHdTlWa8POA1V8YD8HgDa2ShK157QZLYkoufHvpp1z9sZ8nv1xCz4FvEl+CTVDb4KhN/yhtlsYfG3gtt/VsJ/Vn4r/U3oF7nMUctwakppxWFXvDVzeVrOx48qEgaIn2mhipOGNZ5aaGWuKiZt33yliOfAIcePIThZdSYA5+aaHwJrP4PMrjL8bEFg3o3k6zfEkOuFi8I6j0ihzWHVAZFzb7E0uz2nZm3r2nIZJbNeuLvUNMHsQNW245MZvupcv6a+/7vzwDH1ZzpypfCQZ2jGeT64fxq2nduaq80yVvxe+CBuMKhqk9W/0PBZ5E+DznQ7uqDN5s7bOhO2m2MiOp0CU31KUiYD7wYSj15nU91WvmaXvwOYfxOtGsq3NAswgYoSak+l+NPL+NUNZ8vAoXaBZx2Zje9K44AdNfD74duDzmwyvxOvesylW1Gtd854BXPkNzSXEaSc5uoHs1UPIxWoM52XD2hs6tAeDlmBVkSNUIwAu/qjZh2tx1R6fwr1frAagpt5LIbHUKw5ceIXc1ezHYMb94qAWGpIWzF5UgOvmiLCOo5jnLuzHTSPFRERfngf4WpUQ6jiySbUEjTCXQx+nN5baeXSakcHtdByZZ5u5RO87NUaGdSR+z42KfCM5NrLh8Q4MT+usjfl8vlw4MiIio40J4DlvwsRnD+3KSUJnOMFaAIClb4v/i1UPdyMSZkcTx60hGRPmMgyXEr8LUM3uSqgWHit9CVgTI21B7Ef31Bh2TZnIrikT6dTS5Z8/SJjLwdrHx1rK9L2wxvSAyVtnPWDoTU2eU1vCyimrweO1FqXXDUlblS4VZF8p6vei+BrUkNQYY4q/cvuf+3KRwa7UiyUsiy6iVpWhCUmGs/sHzpIjQxx6xYHW4IQuiTwwvjthmcPF0nwwmkiUsNlsnNzV0DXbXm5jns8kbLv+K5ilZsBmTdL7siHG9mw4Jic9NpyQjuoykVq2D2hUK05bigIhi/Xk2X+OWXZDNGSkbWh3Oe6H8uD+7SJRJDELrp0lMm8boF2bCBb+1XgYRvs/DP+yU5dtOZp4aKLIMH7sjKa9WI0SbJLUgiRD828xY10ebq+PzXkVuHHiTVLbtnEa/GZKBmki6a9Ruow2ZH7+bwZkHHzSxZHCYbdxv1pKc5ViCpHQHCPRLQu3MkvmaGgSXEcCm82mV7japyRSp4jnilaKVGe9aZxrINFGY0KfQCfHDSd3ggey4Z4N0P/SP9Lkhhn7dyHgb8ZnevY1I9zgaOC4NSTBWFbaZ9YjBD1OMqZexCnoS9t6eaS4Fn2OzWY77B6Cxj77jSsG6UHpCnYuq1fjuTZNM3Z8rFgvC9cYbSJcaAnsxdXWiiqaIRlDJSmqR9K2Vw0a9l8mCIJ5pmkRigd9aSLDs4cHnZ9al+0qVSHZmKYHxOcvtEpALPzrUfKQttngym8Dlzv+mt0sb8FH1w1jwQOGQVJHCNfW32/sUKZmLvY8u8nfeUD7Nnx243D+74TMgPcGdmgTXMapEa9pRIiT7KmT2DVlIjeN7NRq98IRwe4U3t5Rj4mqI+2b1tg1i3EvU/zuk8jDryZwMMRFhDC+d5oRXnKwhERYtScHX9titYpuscaDt+vfjPrFzlS1L2c/aj3gjyQfOUPhtiViKbgJOaajCZfDzpx7T+GqER3Yd9bn1jdbuAzdNSXQIfKfq4+sQX2/XmPeNJbMfFAkrLw6GBa+ZGyPSGhUjQSELWCe4MZFuBjdM0XEkR9uj3NUshDe19ASR6FROaajiePakNQMF0utYtCTQhI8QocvPlJdOjwIj+TRwkWDjZth8JAg2brNdNk7HXbdAN+w3295W+2XFFup3rc2LRGmGZp+5jir53/aan3TZCTe7PyeNF+O8Z4e+9S0wXXBoHZ63dbRPVJoE9m08XzE6DDCWloutr1unDcH/yXGeb6B+EY9Yd2pGYYNCLHiyWf1InvqJLKnTuLJs3vx0ITuwrvtHw95/ruQ3LBGqEZrTqiOdt6+chBdkqNIuuZjY2OwGKpjkdMfgXs3i0nTGQ3H7jbE9Vm+oNtdsUFCaU575A/JqgFinGnmUvDRRJfkKJ48uzft+o8Vda01GhG6D0aYy8HXNw+jf7yPyBAHE3qnHja1hIaICXPxr8sGEBPmJNSmSj9tnSkSVoq2wZzHYeWHYnszv595Zeq+MUfYgDPrgj5nioduhnPnaODIZBgcpWiJMMuzS7jRLGOnztDSEIak7pHU4hZa6JE8Grj+5E6kx4UztleqyFhfY3pz0P+16FxDMuPZV7KfjbnllrJp3rhMHMAQ+2Z2p0ewswAj+yyhc4s+Y82+UusGPwMkfflz0FUdKApUkfFmxj5N7JPG0odHERdxlN6kl30Jc59otgSKmTE9kpm9SXho3716MPasCVC8XcSfnfHiQT9ErzKLpIMwcpb/RyRLHKosxuOYsb1ShcA7wOOlQkkhiLj+MUuQIgjNJTTIHHjn0xNho19W8oRnRf3j4x27HR7YKeKmU/seVGJMn7axXJPlY+LEUbhcjYcsHS7O6JvOpD5psOpVmHZH4A4HNotymYOvC3wvCFmmJLIj7mBoqnb3Uc5x7ZEc0D4OCJLckdgNBTuJtnJGptYL0dv6KiMYvAk3+dFImMvBeQPb6bJHFs4MIibbCFqGm6a5pfFDVRYlShQxthqyPNtweGux1atL1M2sxPDCRWLp2ekInOHmjXtLf+0KU5e2s01xei2of5ocE3ZEE59aRLexcMtvDdYDboxXLu5LRqRCl6RITu6aJB4aZ/9LLMcdIlFqQMhgXPoZ3DC36X0lLcNmE/G+TcQUSwxeudhIFLxvTDfhIet1riEdBtD7/FZo2VGKwwlZE/4UYteNYbPZGvc4thvU7Od1eIiDcb1SSI0JC0gQPCLcON/6d3zLnC+tyXHtkWwfLzySu4uqqff4DMMiJJKiyE4kVm3nlBjVo5ZrcuG1G3qEW3oY6H2BCEYecEXT+/qhyX9szbeGBMzaVEi8L5OTHetx7FlIqEdd/nFFQEjzEo36q9nYJVrtXBO/Ok9kvftqnnR9gE2TFJptKqMW2XxD8ljF6bBzbx8vkyaecHgNZWeIeBBJJEcBE3qnkj3Az2Cw2eCyz4MfIDm2iEi0Kh1oZLasYtabVwzC61OOWAa6hVRT/H73M+DC9498Gw6S49qQzEqNJirUSWWdhz3FVXRJNlzbxa50EtlOOyUXPrvckDkBixzNn5ZJz0PXMdArsF5wU/RuKwR+N+WVU1btJjZCeE625VewXxHGnH3T98RFnCIOiE5rtqiqliFfWeexGvfAoh2F7PGpGZclaokuzQvpimiWSPzxgN3WcGaxRCKRHHOMvB9+eQZO+Sv0vVhoZEanWUW/m4HNZgu6GnZEsNvhlsWi9GYzY9mPFo7Stb0jg8NuVEfZW2xd3t7nEvIC4/a+ZDUiO53GMUF4G+h3yUEF86bFhpMQGYKiwCXviMom+eW1bM2v5GdNdqaqgKQKNXaxWwP6ekHQaucCbM6zJvPsK6lhr1aKq3wfeN1QolYC+BPN3iQSiURyCBl+i0jWGn6LSITqfZ5IXvyzTahTev7pjEg4zg1JMDJd9/pJAH3vaKCayCUfB99+nKHJfmzKLWdLXgVvzBeJSPltRFyfraqAzKL5YufM5lcusdttuhfyyneX4vMZgqy5ZbUUogYlKz5Y86lattLWYAk6iUQikUgkhw9pSKoabnuLDUNSURTm5vlVrmg7GB4thBBrycPjlXf/b7D+esG2AyzdJSR4RvYLUmKxhXprmiB2WY1bl2aqrvewv7QGxXzJapl66f3/lHIcEolEIpH82ZGGZHzg0nZRVT3ltR5meE1JNf0ukVmUJrqnxtA5SRjVT03fxMZcsQx9yVCr9qH3xHtbLG3wr8sG0iNNxGHuU6sO7SgQ2d8JkSGiJriZzqMO6jtIJBKJRCL5Y0hDUvVI7jZ5JHcUCC/Ys+H3iHJYIdHQdWyrtO9o5sx+1koydhui4syYvwOwLXkSvlMfPqhza7Gr+0pryCur5ZK3RYWczslRQs7GTPeJB/UZEolEIpFI/hjHvSHZPU1kam/Lr6C63gPAQ9+IGtQJbeLgjhVw91po06G1mnjUcuVwa5/01upfD7wS998K2dj24oM+t2ZIPvrtes557Teq6r0AjOyaKLKzrzFKoTWn/KJEIpFIJJJDz3Et/wOixmZKTCj55XVszCmnb7s4dh4w1XkOi2m9xh3lJESFkpkQQXaR8Oa+eumAQ3bu9qZyf3nltfq2205Tq31kDIcT7oCoFFGvVyKRSCQSyRHnuDckbTYbHRMjyS+v44vle7ngzcX6ey9e1L/1GvYn4YubRrA+p4zTspIPqXbh+YPa8cT3Gy3bPrlhmPEZdjuMfeqQfZ5EIpFIJJKWc9wvbQOkxoQB8MXyffq2NhEu2idIT1dTJMeEcXr3lEMugB0T5uLhid31v/95YT/atZG/h0QikUgkRxPHvUcSoN7rC9h2waB2rdASiZkbTu5EZkIke0tqOG/gn7smrEQikUgkxyLSkATuGd2NGevy9L+n33kSvdJbJlkjOfTYbDbG9kpt7WZIJBKJRCJpALm0DXRNibZI2XRLiW5kb4lEIpFIJBIJSI+kztTz+mC3Qe/0WFwOaV9LJBKJRCKRNIU0JFUiQ528fMmhk6+RSCQSiUQiOdY54oakoigAlJeXH5HPc7vdVFdXU15ejsslSxweKWS/tw6y31sH2e+tg+z31kH2e+twpPtds9M0u60hjrghWVFRAUBGRsaR/miJRCKRSCQSSQuoqKggNrbhBGSb0pSpeYjx+Xzk5OQQHR19yLUHg1FeXk5GRgZ79+4lJkZWqTlSyH5vHWS/tw6y31sH2e+tg+z31uFI97uiKFRUVJCeno7d3nDuyBH3SNrtdtq1O/IajTExMfKCbwVkv7cOst9bB9nvrYPs99ZB9nvrcCT7vTFPpIZMT5ZIJBKJRCKRHBTSkJRIJBKJRCKRHBTHvCEZGhrK448/TmhoaGs35bhC9nvrIPu9dZD93jrIfm8dZL+3Dkdrvx/xZBuJRCKRSCQSybHBMe+RlEgkEolEIpEcHqQhKZFIJBKJRCI5KKQhKZFIJBKJRCI5KKQhKZFIJBKJRCI5KKQhKZFIJBKJRCI5KI5pQ/K1114jMzOTsLAwhg0bxtKlS1u7SX9aJk+ejM1ms/zr3r27/r6iKDz22GOkpaURHh7O6NGj2bZtm+UctbW13HbbbSQkJBAVFcX5559Pfn7+kf4qRz2//vorZ555Junp6dhsNr799lvL+4eqr4uLi7n88suJiYkhLi6O6667jsrKysP99Y5amur3//u//wu4B8aPH2/ZR/Z7y5gyZQpDhgwhOjqa5ORkzjnnHLZs2WLZR17vh57m9Lu83g89b7zxBn379tUr04wYMYKZM2fq7/9pr3XlGOWzzz5TQkJClP/85z/Khg0blBtuuEGJi4tT8vPzW7tpf0oef/xxpVevXkpubq7+78CBA/r7U6dOVWJjY5Vvv/1WWbNmjXLWWWcpHTt2VGpqavR9br75ZiUjI0OZO3eusnz5cmX48OHKCSec0Bpf56hmxowZyt/+9jfl66+/VgDlm2++sbx/qPp6/PjxSr9+/ZTff/9dWbBggdKlSxfl0ksvPRJf8aikqX6/+uqrlfHjx1vugeLiYss+st9bxrhx45T33ntPWb9+vbJ69Wpl4sSJSvv27ZXKykp9H3m9H3qa0+/yej/0TJs2TZk+fbqydetWZcuWLcrDDz+suFwuZf369Yqi/Hmv9WPWkBw6dKhy22236X97vV4lPT1dmTJlSiu26s/L448/rvTr1y/oez6fT0lNTVWee+45fVtpaakSGhqqfPrpp/rfLpdL+fLLL/V9Nm3apADK4sWLD2vb/8z4GzSHqq83btyoAMqyZcv0fWbOnKnYbDZl//79h/lbHf00ZEieffbZDR4j+/2PU1BQoADKL7/8oiiKvN6PFP79rijyej9StGnTRvn3v//9p77Wj8ml7fr6elasWMHo0aP1bXa7ndGjR7N48eJWbNmfm23btpGenk6nTp24/PLL2bNnDwC7du0iLy/P0t+xsbEMGzZM7+8VK1bgdrst+3Tv3p327dvL36QFHKq+Xrx4MXFxcQwePFjfZ/To0djtdpYsWXKEvs2fj/nz55OcnExWVha33HILRUVF+nuy3/84ZWVlAMTHxwPyej9S+Pe7hrzeDx9er5fPPvuMqqoqRowY8ae+1p2H5aytTGFhIV6vl5SUFMv2lJQUNm/e3Eqt+nMzbNgw3n//fbKyssjNzeWJJ57g5JNPZv369eTl5QEE7W/tvby8PEJCQoiLi2twH0nTHKq+zsvLIzk52fK+0+kkPj5e/h4NMH78eM477zw6duzIjh07ePjhh5kwYQKLFy/G4XDIfv+D+Hw+7r77bk488UR69+4NyOv9SBCs30Fe74eLdevWMWLECGpra4mKiuKbb76hZ8+eLFq0CPhzXuvHpCEpOfRMmDBBf923b1+GDRtGhw4d+OKLL+jRo0crtkwiOTJccskl+us+ffrQt29fOnfuzPz58xk1alQrtuzY4LbbbmP9+vUsXLiwtZtyXNFQv8vr/fCQlZXF6tWrKSsr43//+x9XX301v/zyS2s36w9xTC5tJyYm4nA4AjKZ8vPzSU1NbaVWHVvExcXRrVs3tm/frvdpY/2dmppKfX09paWlDe4jaZpD1depqakUFBRY3vd4PBQXF8vfo5l06tSJxMREtm/fDsh+/yPcfvvt/PDDD/z888+0a9dO3y6v98NLQ/0eDHm9HxpCQkLo0qULgwYNYsqUKfTr14+XX375T32tH5OGZEhICIMGDWLu3Ln6Np/Px9y5cxkxYkQrtuzYobKykh07dpCWlkbHjh1JTU219Hd5eTlLlizR+3vQoEG4XC7LPlu2bGHPnj3yN2kBh6qvR4wYQWlpKStWrND3mTdvHj6fj2HDhh2hb/PnZt++fRQVFZGWlgbIfj8YFEXh9ttv55tvvmHevHl07NjR8r683g8PTfV7MOT1fnjw+XzU1dX9ua/1w5LCcxTw2WefKaGhocr777+vbNy4UbnxxhuVuLg4JS8vr7Wb9qfkvvvuU+bPn6/s2rVL+e2335TRo0criYmJSkFBgaIoQrYgLi5O+e6775S1a9cqZ599dlDZgvbt2yvz5s1Tli9frowYMUIZMWJEa32lo5aKigpl1apVyqpVqxRAeeGFF5RVq1Ypu3fvVhTl0PX1+PHjlQEDBihLlixRFi5cqHTt2vW4leVQlMb7vaKiQrn//vuVxYsXK7t27VLmzJmjDBw4UOnatatSW1urn0P2e8u45ZZblNjYWGX+/PkWmZnq6mp9H3m9H3qa6nd5vR8eHnzwQeWXX35Rdu3apaxdu1Z58MEHFZvNpsyaNUtRlD/vtX7MGpKKoiivvvqq0r59eyUkJEQZOnSo8vvvv7d2k/60XHzxxUpaWpoSEhKitG3bVrn44ouV7du36+/7fD7l0UcfVVJSUpTQ0FBl1KhRypYtWyznqKmpUW699ValTZs2SkREhHLuuecqubm5R/qrHPX8/PPPChDw7+qrr1YU5dD1dVFRkXLppZcqUVFRSkxMjHLNNdcoFRUVR+prHnU01u/V1dXK2LFjlaSkJMXlcikdOnRQbrjhhoCJqez3lhGsvwHlvffe0/eR1/uhp6l+l9f74eHaa69VOnTooISEhChJSUnKqFGjdCNSUf6817pNURTl8Pg6JRKJRCKRSCTHMsdkjKREIpFIJBKJ5PAjDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUEhDUmJRCKRSCQSyUHx/wtDLadfnkWxAAAAAElFTkSuQmCC"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": "## Numerical stability",
"metadata": {}
},
{
"cell_type": "markdown",
"source": "We can check how stable it is for varying delays,",
"metadata": {}
},
{
"cell_type": "code",
"source": "vs = []\nds = np.r_[5:450:10]\nfor d in tqdm.tqdm(ds):\n x = run(d)\n v = np.diff( np.abs(x).reshape((30,-1)).mean(axis=1) ).mean()\n vs.append(v)\n",
"metadata": {
"trusted": true
},
"execution_count": 11,
"outputs": [
{
"name": "stderr",
"text": "100%|██████████| 45/45 [00:05<00:00, 7.80it/s]\n",
"output_type": "stream"
}
]
},
{
"cell_type": "code",
"source": "figure(figsize=(8,1)); semilogy(ds,vs); grid(1); xlabel('D');",
"metadata": {
"trusted": true
},
"execution_count": 15,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 800x100 with 1 Axes>",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": "## Analytic stability\n\nGiven the Euler discretization, we can make a discrete time linear system which shows the same thing",
"metadata": {}
},
{
"cell_type": "code",
"source": "# D = 15\ndef linstab(D):\n L = np.zeros((2+D,2+D))\n dt = 0.05\n l = 0.05\n k = 0.2\n\n L[0,0] = 1-dt*l # x <- x\n L[0,1] = -dt # x <- y\n L[1,1] = 1-dt*l # y <- y\n L[1,0] = dt # y <- x\n L[0,-1] = dt*k # x <- delayed y\n for i in range(D):\n L[2+i,1+i] = 1.0 # store y value\n\n return L # ",
"metadata": {
"trusted": true
},
"execution_count": 4,
"outputs": []
},
{
"cell_type": "code",
"source": "ls = []\nds = np.r_[5:450:10]\nfor d in tqdm.tqdm(ds):\n L = linstab(d)\n ls.append( eig(L)[0].real.max() )",
"metadata": {
"trusted": true
},
"execution_count": 5,
"outputs": [
{
"name": "stderr",
"text": "<ipython-input-5-70704bb10056>:3: TqdmMonitorWarning: tqdm:disabling monitor support (monitor_interval = 0) due to:\ncan't start new thread\n for d in tqdm.tqdm(ds):\n100%|██████████| 45/45 [00:16<00:00, 2.70it/s] \n",
"output_type": "stream"
}
]
},
{
"cell_type": "code",
"source": "figure(figsize=(8,2))\nsubplot(211); plot(ds, ls); xlim([5, 450]); grid(1);\nsubplot(212); plot(ds, np.log(vs)); xlim([5, 450]); grid(1); xlabel('D');",
"metadata": {
"trusted": true
},
"execution_count": 16,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 800x200 with 2 Axes>",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": "This shows we can predict stability of the delayed system by its discrete stability.\n\n## Simulation via matrix application\n\nWe can also check that the matrix constructed above results in the same simulation as the SDDE discretization,",
"metadata": {}
},
{
"cell_type": "code",
"source": "def run2(D):\n T = 3000\n #D = 50\n dt = 0.05\n l = 0.05\n k = 0.2\n \n # construct linear system\n L = linstab(D)\n\n # sample noise\n np.random.seed(42)\n z = np.random.randn(T-1,2)*np.sqrt(dt)*1e-1\n \n # simulate SDDE w/ EM scheme\n x = np.zeros((T,2))\n x[0,0] = 1.0\n for t in range(T-1):\n dx = np.r_[-l*x[t,0] - x[t,1], -l*x[t,1] + x[t,0]]\n if t > D:\n dx[0] += k*x[t-D,1]\n x[t+1] = x[t] + dt*dx + z[t]\n \n # simulate SDDE with discrete time L\n x2 = np.zeros((T,2))\n x[0,0] = 1.0\n for t in range(D,T-1):\n x2[t+1] = (L @ (np.r_[x[t], x[t-D:t,1]]))[:2] + z[t]\n return x, x2\n\nx, x2 = run2(50)\nfigure(figsize=(8,1)); plot(x, 'k', alpha=0.4), plot(x2+0.1, 'r', alpha=0.4), grid(1); xlabel('Time steps');",
"metadata": {
"trusted": true
},
"execution_count": 19,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 800x100 with 1 Axes>",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": "*a small vertical shift is applied in order to see both lines*",
"metadata": {}
}
]
}
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