{ "cells": [ { "cell_type": "markdown", "id": "b1ba2dd7-6e80-4ed3-9610-9516692fc1c7", "metadata": {}, "source": [ "# Denpendency structures between uncertain numbers" ] }, { "cell_type": "code", "execution_count": 1, "id": "9a7e9324-eb49-457a-b2c2-8feada2a5f32", "metadata": {}, "outputs": [], "source": [ "from pyuncertainnumber import pba\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "81e0942b-855f-4406-aa53-d6e21f902f67", "metadata": {}, "source": [ "```{note}\n", "Dependencies between uncertain variables (e.g. probability distributions) are often ignored or assumed independence without justification. However, neglecting the incertitude about the dependency structure and assuming independence anyway constitutes a methodological bad practice. No only does the `pyuncertainnumber` ease the account for epistemic uncertainty in marginal distributions, but also provides user-fridendly syntax for various dependency structure.\n", "```" ] }, { "cell_type": "markdown", "id": "ea6919b6-2254-42cc-a915-ad0e0ecf8456", "metadata": {}, "source": [ "
\n", " \n", "
Dependency structures
\n", "
" ] }, { "cell_type": "markdown", "id": "a52ef325-3bcc-4d54-a5b6-28acd15d06e6", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "e2a1862f-0096-4977-996e-2c9754c26a55", "metadata": {}, "source": [ "## Binary dependency" ] }, { "cell_type": "markdown", "id": "ae19e117-6973-4dc2-aa77-9df7aae7910c", "metadata": {}, "source": [ "When the inter-variable dependency is unknown, the Frechet bound will be utilised to faithfully reflect the state of of knowledge that any dependency structure is possible and will be enclosed within the Frechet bound. In addition, when there is empirical knowledge about dependency, it can be specified with an addtional argument." ] }, { "cell_type": "code", "execution_count": null, "id": "9598ce56-8a7f-4fab-8009-22e76bd7e445", "metadata": {}, "outputs": [], "source": [ "# construction of p-boxes for illustrational purpose\n", "a = pba.uniform([1,2], 4)\n", "b = a" ] }, { "cell_type": "code", "execution_count": 3, "id": "4ba4aa02-c8d7-47d6-91c3-fdfaa733ec43", "metadata": {}, "outputs": [], "source": [ "c_f = a + b # frechet\n", "\n", "# for any other dependency {independence, perfect, oppposite}\n", "c_i = a.add(b, dependency=\"i\") # independence" ] }, { "cell_type": "code", "execution_count": 4, "id": "93d058e5-a93c-468b-b391-6d1def9a5f23", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "c_i.plot(ax=ax, label='independence', nuance='curve')\n", "c_f.plot(style='simple', ax=ax, label='Frechet', nuance='curve')\n", "ax.set_title(\"$C=A+B$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "451e8d9e-78d9-4490-963c-7757a3a8c555", "metadata": {}, "source": [ "More conveniently, users can utilise the `with` statement to specify an environment of a certain dependency, for example \"independence\" or \"perfect\"." ] }, { "cell_type": "code", "execution_count": 7, "id": "22b1c447-c386-49bb-bdd1-426562b239bc", "metadata": {}, "outputs": [], "source": [ "# define a dummy response function\n", "def foo(x):\n", " return x[0]**3 + x[1] + x[2]\n", "\n", "# define uncertain numbers\n", "a = pba.normal([2,3], [1])\n", "b = pba.normal([10,14], [1])\n", "c = pba.uniform([4,5], [10,11])\n", "x = [a,b,c]" ] }, { "cell_type": "code", "execution_count": 8, "id": "b6b79215-8d1d-4a2a-b49f-95f2f92d0d19", "metadata": {}, "outputs": [], "source": [ "with pba.dependency(\"p\"):\n", " y = foo(x)" ] }, { "cell_type": "code", "execution_count": 23, "id": "7ce84256-0179-4d13-a14a-0e9f23dd21d4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y.display(label=\"perfect\", nuance='curve', title=\"$y = x_0^3 + x_1 + x2$\")" ] }, { "cell_type": "markdown", "id": "1124d89d-06b6-46b3-9cb4-b5c8e1135934", "metadata": {}, "source": [ "```{tip}\n", "**smart dependency tracking**\n", "A smart dependency tracking mechanism is underway\n", "```" ] }, { "cell_type": "markdown", "id": "cfeb26ac-087e-43f6-b37e-caf1aff44d99", "metadata": {}, "source": [ "## Dependency object\n", "\n", "One can easily construct a multivariate copula to specify the dependency structure." ] }, { "cell_type": "code", "execution_count": 10, "id": "9944f2ef-e224-4613-8f05-a239c2c79d1f", "metadata": {}, "outputs": [], "source": [ "gaussian_copula = pba.Dependency(family='gaussian', \n", " corr=0.5)" ] }, { "cell_type": "code", "execution_count": 11, "id": "37ed0d85-7cb9-4ebd-ad49-c7cff140340e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g_s = gaussian_copula.u_sample(10_000)\n", "h = sns.jointplot(x=g_s[:, 0], y=g_s[:, 1], kind=\"hex\")" ] }, { "cell_type": "markdown", "id": "5ea6c432-3f73-4649-b3d6-45e085b6e798", "metadata": {}, "source": [ "## Dependency specification in non-intrusive propagation " ] }, { "cell_type": "markdown", "id": "22a7c4fe-7db0-4ed9-86d1-d03f3854d97b", "metadata": {}, "source": [ "```{note}\n", "**dependency when working with black box models**\n", "Various dependency structure (e.g. copula) can be specified when working with black box models, our non-intrusive propagation APIs provides an argument to take declared dependency structure.\n", "```" ] }, { "cell_type": "code", "execution_count": null, "id": "0c05602f-f2ed-4c3f-b44d-b445a7c3eed0", "metadata": {}, "outputs": [], "source": [ "import pyuncertainnumber.propagation.mixed_up as mix\n", "corre_matrix = np.array([[1, 0.5, 0.3], [0.5, 1, 0.4], [0.3, 0.4, 1]])\n", "de = pba.Dependency(family='gaussian', corr=corre_matrix)" ] }, { "cell_type": "code", "execution_count": 20, "id": "df4084c9-4d89-40f3-aeeb-b273a8527793", "metadata": {}, "outputs": [], "source": [ "p = mix.interval_monte_carlo(\n", " vars=[a,b,c], \n", " func=foo, \n", " dependency=de,\n", " interval_strategy='direct', \n", " n_sam=10_000\n", ") " ] }, { "cell_type": "code", "execution_count": 22, "id": "cfda08f9-6f2e-4e22-9508-c19468078dbe", "metadata": {}, "outputs": [ { "data": { "image/png": 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DSyh49V6mWhe+Uq8scgcAKD+CDHK6+8XdtNV7L/zzBaoxeTb2slIvAPiPIIO8nf+n86qqMn0dFLgbe+tS37NSLwDEPMgsLi6qyclJ1dbW5twfGBhQLS0tWbednp5Wra2tzv3e3l7n9+C/pEqm7ldXk3uzhZjr15X63e+qU5UYQgwABCO0M1NfX5+am5tz7ks46e/vVxMTExm3lcAzNDSU+n5wcFCNjo4Gtq+28jb5YrNEQqnnn09fsZfGXgCI+awlCS5uUl2Riks2Y2NjAewVcjb5PrpP1VU/HDrBRiXGG2Jo7AUAC4KMHiZyk+/n5+czbi8/O3ToUGqIqaenJ6A9tZd73Zj2lnZW8M0QYm7cqEiFmD17kurWLanG0NgLALEPMisrKxkfX15ezvi4HnJqb2937kuPTDb37t1Ta2traTeUtoqvhJjKCpYc8k6z3rOnMfXYlSsVqqGBEAMAQYtU92a2gCNVmBMnTjgVGemPEdl6ZI4fP65eeeUVX/fTpmoMF4XMXIlxT7NmOAkAwhPKP7NldpK3+iLfZ5q1JOFldnZWdXd3OzObFhYW1Pj4+KY+G21kZEStrq6mbktLS769jzhiFd/cjb2HD9enVWJkmjXDSQBgWZCRUJJJZ2fnpsekb6arqyutMVjCSrbqTW1trWpqakq7ofhVfKnG5GrsZZo1AFgZZLxrwEh1RUKMrshIeNEVl46ODqci4/bnP//ZeRzlxSq+uVft1SGmvT2h1tY2Vu3l8ACApT0y0rQ7PDzsVFskqLjXkJE+F3lc1o6R0COzlE6ePJkKOrpPBv45d+wcq/imrdr7sDI1N5dUjY00PwNAFFQkZTwhxmTWUnNzs9MvwzBTbrfv31aNxzf6Pz7614+4OORfydWsn3xy47Nz4EDSmaFEJQYAonH+jtSsJUSnyZchpY1KjAwpSW+MdukSIQYAooQgA1bxzbFWjPdq1vX1pBgAiBIG+rGpyZdVfDcqMd4QMzdHNQYAooaKDNKc/6fz1q/i623u/dOfvlC7dtUQYgAgguw+Y8GRVA/7vaurybbuqdb79ycIMQAQYQQZy3mvq2Q7bzWGVXsBINoIMpbzXlfJ9iZfdzVGplqzXgwARBv/l7aYtxpj+3WV5FpKTLUGALMQZCzmnq1k+3WV9LWUFhaqXFOtw94rAMBWCDIWczf5/tvRf7O6GuMeUvrKV5hqDQCmIMhYyjusVFlp70fB2+A7P1+hLD4cAGAU/ndtKZp8H4aYGzcqUtUYhpQAwCwEGQvR5Puwuffw4Xq1Z8/GhTLFzAxDSgBgEoKMhWjyfdjcqysx4rnnFNUYADAMy7haiCbf9ObePXsS6sqVSifEWHgoAMBoBBnL0OSbubm3oSHUXQIAFMm+s5jlvMNKNjb5uqsx0tzb0EAZBgBMRUXGMjYPK0klRkKMe/VemnsBwGwEGYvYPKwkIeYb36hT77zz8CN/8CDNvQBgOnvOZEhfO8ayYSWpxKSHGFm9l+ZeADAdFRlLqzE2DSt5m3s/+uiB2rmzmhADADFARcbSJt+GbQ1WNvceOJAgxABAjBBkLGzy/VXfr6ypxsjqvTT3AkB8EWQsHFaqqnq4mq0Nq/cuLDysxjDVGgDihSBjAVubfN1DSu3t62pujmoMAMQNQSbmbG3y9Tb4zs4mVFVV/N83ANiGIGNRk+/eHXutafJ1V2P2719XLS01Ye8SAMAHBBmLmnzPvnTWimoMDb4AYA+CjEXDStXV1VY2+DY28jEHgLji//AWDSvV19RbNaS0Z0+CBl8AiDmCjCVsGFbyNvhevpykwRcAYo4gY0l/jA3DSt4VfJua7FgvBwBsRpCxpD/GtmoMDb4AYAeCjCXXVor7Injp1ZgkK/gCgCUIMhYMK8V9ETzvdOtLl6jGAIAtCDIWDCtVVlZaM9364MGkqo//5CwAwF/F9wxnMZuGlZhuDQB2I8jE3Nne+E679jb4zs9XqBgXnwAAGfC//Zj3x1RVVVlRjZEhJRp8AcA+BJmYsWXaNddTAgAIgkzM2NAfQ4MvAEAjyMSMDdOuafAFAGgEmRixYdo1Db4AADdOATFiw7CS93pKNPgCgN0IMjEdVorjtGuupwQA8CLIxHRYKY7Tru/epRoDAEhHkInhsNLeHXtVfU38pvFIRUa7eFGmloe5NwCAKCDIxNCZF8/EflipqoqPLgCAIBNLcRxW8q7iWxe/PmYAQBEIMjFs9I3btGtW8QUAZBOvM56l4nxZAlbxBQDkQpCJYaNvnNaPYRVfAEAuBJmY+VXvr2JTkWEVXwDAVjgtxKw/Jk6Nvu5qzP79rBsDANiMIGO4uPbHbG7wZd0YAMBmBBnDxbE/xtvgK6v4NjbyUQUAbFatQrK4uKgmJydVW1ubc39gYEC1tLRk3X56etrZTrYX3d3dAe6tGc6+FI/rK7kvRdDevq4uX6bBFwAQsSDT19en5ubmnPsSUPr7+9XExETWECM/Gx0ddbbt6elRCwsLAe9x9MWpP0Z7550Hqrq6NuzdAABEVChBRsKIm1RZJKxkMzg4mAo9su3U1JTv+2iKOC6E576mUm3ttjB3BQAQcaGc+SS0tLa2pj0m38/Pz2cMPcvLy86wk/x8ZWUlNbxkO2+jbxybfOMwVAYAiFmQkTCSiQQWLwkvEnJ0P82pU6ec+9ncu3dPra2tpd1saPTdt2Of8Y2+mVbx5ZpKAIBI9sjkG3Ak3EhVRpp7pSojTcHbt293qhGZHD9+XL3yyivKtmGlX/WZvxBe+iq+SVbxBQBEsyIjgcRbfdHDR15ShZHH9c/010zDUGJkZEStrq6mbktLS8qGYSXTG303r+IrPT+h7hIAwAChnCqyTZ3u7Ozc9Fih/TC1tbWqqakp7RZHcVs/xl2NkXVjWMUXAODL0NKHH37oTIWWmUM3b95MPS59LDIture3Vz399NM5n8MbTmToSEKMu9oi92U7ucnPZNhJHtNryXR0dBS667Fl+vox3mrMzAxDSgAAH4LMD37wA+eEefToUfXyyy9v+vmVK1fU66+/7mwjvSq5SBgaHh5WXV1danZ2Nm0NGfldeXxoaCht20OHDjnTsJl+nc70YaXN1RjGlAAA+alIZuua9XjttdecRtvm5uYtt5XelFdffXXLMBMEmbUk+yz7FKdhptv3b6vG443O/Y/+9SPVsK1BmUg+fYcP16eCzNpaUjU2Uo4BANut5Xn+zjvImCqOQUb+ZB2nOlI9Mte+d03V1zwcmjGtGrNrV1OqGnPlSiXDSgAAle/5u7KUF5B+GQQvTuvHuGM0vTEAgEIVHWR+9KMfOc29QtLSG2+8UexToQRne81t9PU2+VZWmvk+AAAGBhlpxn3vvfec+1L6+c53vkOYCYHJjb7uJl9W8QUABBpkZPqzhJkf//jHqSGmmLfbRHJFX1OrMd5rKjGsBAAINMjINY9kZpKEF1k75pFHHlHt7e3FPh0sulBkpmsq1ZvZqwwAMDXIyKJ0R44ccdaTuXz5snNF62wXg0T5xKHR9+7dh0NK7e0JrqkEAAg+yMhlBqQnRl9denx8POPVq+GfOFwo8t13H3BNJQBA8Fe/fuaZZ5wGX01fTgDB9cdUGpoA3K1U27bVhLkrAABbg4xXf39/uZ4KefbHmFiN8Tb5mvgeAADRYeY/6S1len9MpiZfplwDAEpBkDGUiQvhuZt89+yhyRcAUDqCjKFM7Y/RLl9O0uQLACgZpxKDmN7o627yra42d0ViAEB0FHQ2PHfuXNafyeq+eip2ru1g50J43iZfAAACDzKyVkw2J06cSF1me2pqqvQ9Q2wafWnyBQBEIsgMDw8711byunr1atoaMlxzyV+mNfrS5AsAiMQ6MrII3vvvv7/p8dHRUfWTn/wk9b1JJ1kTmXzFa5p8AQDlVPApxVuVkd4YVvT1n8lXvKbJFwAQmZV9vVUZ6Y1xV2NQfiY3+tLkCwDwU1FF/sHBQacqQzUm+EbfvTv2GtPoS5MvACCSQebZZ591qjJSjXn55Zc3/ZxmX/+cfcmcRl+afAEAfiu67VKqMh0dHRl/1t7eXso+IYaNvrOzCZp8AQDRufq1VGXklglXwvaPKdUYQZMvAMBv/BvZACbOWPI2+Zqy3wAAsxBkIs7EGUs0+QIAgkKQiTgTL03gbvJtb6fJFwDgH4KMQc68dMa4IZrf/vY+Tb4AAN/kfYr55S9/6d9eILYzlmpqiu4nBwCgfEFmbGws303hE9OqMaaGLwBADIPM1NSUeuONN3Jus9XPYceMJfe0a1P2GQAQ8yDz1ltvqSNHjmQMK2tra+q1115zLigJu2cscW0lAEAkg4wsficXjOzr60td/frcuXPq2LFjavv27Wp0dFS1trb6ua/WMW3G0uZp14pp1wCAaASZq1evpoYK5DpL0vvQ09PjhJjLly87j42Pj/u5r1YzYcbS5msryecl7L0CAMRZ3lNK5LIDUnGZnp52rrH0+uuvq5WVFeeaS01NTc422S5ZAPuaZiXEMO0aABCZILOwsKAOHTrkVF/cgeX06dOqq6tLHZRxBPgm6tUYb5NvVRUpBgAQoSAzMjKiXn755YyVml/84hdqeXnZ+f7rX/96effQYibNWKLJFwAQhrz/2ZwpxGgvvfSSE2SkZwb2zVji2koAgLCUrf7f29vrBBqUf8bS3h17Iz1j6c4db5Mv11YCAASjrI0MMvyE8jv70tnIDi1JNeaFFx4OKc3PV9DkCwAITF6nnNXVVfXhhx9uuZ27CVgWyZMb4j1jyT3l+sCBhGpoiGbgAgBYHGSam5udSxTke+FIaf6VNWX0tGzEt9HXPVPp4kXWjQEARHgdmStXrqijR4+q9vZ2Z8p1W1ubamlpcdaTWVxcVO+++6764IMPnLVl6JcpX6OvKcNKTLkGAEQ2yOihI6m0yFCTfJXgIiFGwoyEGwkwchkD2NHo627yPXBAZipFM3ABAOKroCDjHmqSCg38d+bFaF6awFuNmZlhWAkAEDzGAiIuqo2+6dUYmnwBAIYFGemRybf5F8U3+lZGcC6ztxpDky8AICxFnyUHBgbUiy++mPbYuXPnyrFPVjOh0dc75bqxMXphCwBgh6J6ZPQJ9rvf/a7T5Cuzl+QSBRMTE1xryYJGX/eU6wsXklRjAADmBZlXX31VdXd3qxs3bjg3oS8cifJ481tvRq4i4x1Wqq6OZg8PAMAORQeZ0dFRdeTIkbTH3nrrrXLsEyLc6OsdVqqrY1gJAGBIkLl69aoaGxtTe/bsUd/+9rc3/dwbbFCaqDb6ajT5AgCMCTJSbenp6Un1w8glC37+85/7u3eWi/qwEiv5AgDClveZ6NSpU+rmzZvq/fffd4LM008/ndeFJBGfayx5146pi14fMgDAMnkHGbn0gKzoq42MjKj5+Xm/9stK3qnXUcLaMQAAo4OMTLN2k1AjJ15vDw3iOfXa3eS7f/86a8cAACIh77ORXN361q1bam1tLXWTK13rx2SYSWYyFfJ8J0+eVJOTk85XufhkPoaHh/Pe1mRRu8aSO7OeP5+gGgMAiISKpLeskmMGjffEKr+qH9P319fX83rhQ4cOqbm5uVSokYAiC+rlIkNZ8nvSqyNX3M6HhCypHskVu5uamlSU3bl/RzUcb3DuL313STV9KRr7K5+Qw4frUxWZW7eSXFsJAOCrfM/f1YVckuDEiRNZfy5BRhbJy4cEFzeZCTU9PZ3X78m2NojS1GvvsFJ9ffTWtwEA2Cnvs+Xg4KCTjLLdpEJy7NixvJ5LQktra2vaY/J9ruZhGYLq7e1VtojSsJLb22+vM6wEAIiMvCsyzz77bFm2Edl6XLJd4kC2z3co6d69e87NXZoycep1lLgHH7dtqwlzVwAASBOd8YscAWd8fNy5rlM+jh8/nlYp2r17tzJBVKdee6ddR7VSBACwUyhBRqor3uqLfJ+p6iLDUEePHs37uWV9G2kM0relpSVl2tTrfTv2RWbq9eZrK4W9RwAAlOGikaWQ6kqmqdqdnZ1ZKzLuhl+pukg/TkdHx6Zta2trnZvJzvaejUzlwz2sNDNTQX8MACBSQgky3plHEk4kxOiKjDT9yn3ZzjukJE3Hcovz7KWoXPXaO6xUWUmKAQBES2g9MrJmjKwdI7ORpDrjXkNGKi7yuLd/RhbOEzINPM6XR4hKNcZ9baWDB5MMKwEAzF0Qz1SmLIjnXgzv2veuqfqah5WQaCyCp1TDxu4BABCZ83ekZi3ZLGpTr71NvvXh5ioAADIiyERAFKde0+QLADABQSYCojb1miZfAIApCDIRE4Wp1+4m3wMHaPIFAEQXQSZiwp567a3GzMzILKpQdwkAgKwIMhETdjUm/UrXCdXQQIoBAEQXQSYCojRjyd3ke/48V7oGAEQbQSZkUZqx5B1WqqkJZeFnAADyRpAJmXvG0t4de0OdseQdVqqvpxwDAIg2gkyEnH0p/BlLGsNKAAATEGQipLKyMjL9MQwrAQBMQJCJkDCrMd7+mKhUhgAAyIUgEyFhhgfvtZVYBA8AYAKCTISmXoddkdEuXmQRPACAGQgyIYrK1GvvsFJVFR8LAIAZOGOFKCpTrxlWAgCYiiATEWFOvXYPK124kGRYCQBgDIKM5VOvvcNK1dXhXrQSAIBCEGQiIqxqDMNKAACTEWQiIgrrtjBbCQBgGoKM5VOv3f0xzFYCAJiGM5fFU6+9/TEAAJiGIGPx1Os7dx72xxw8mKQ/BgBgHIJMBJx58UzgQ0veaszMTAX9MQAA4xBkLJ167Z2tVM8IEwDAQASZCAij0ZdrKwEA4oAgY2FFhmsrAQDigjOYhdKHlWjyBQCYiyBj4Roy7mGlmRmGlQAA5iLIWLaGjHdYqbKSFAMAMBdBxrI1ZNxrxzCsBAAwHUHGojVkvNWYS5dYOwYAYDaCjEUzllg7BgAQNwSZkAXZ6Otu8j1/PkE1BgBgPIJMyMIaVqqu3qjMAABgMoKMJUHGPay0f78MK1GOAQCYjyBj4eUJzp9fZ1gJABALBJmQF8ML7DVdL1lTUx346wMA4AeCjAWL4Xn7Y8KoAgEA4AeCjAWL4XmnXbMIHgAgLggyFiyGx7RrAEBcEWRivhge064BAHFGkAlRENUYpl0DAOKMIGNBRUZj2jUAIG4IMjHGsBIAIO4IMiGuIeP30FL6sNK6amjgzw0AiBfObDFfQ0Y7d+4Bw0oAgNghyMR8DRmNYSUAQBwRZELy5rfe9H1oyd3oW1VFkAEAxA9BJiR+BwsuSwAAsAFBJqa4LAEAwAYEmZAEWSG5cCFJoy8AIJYIMiEJsj+GRl8AQFwRZGIYZLz9MQAAxBVBJoZBxt0fc/Bgkv4YAEBsEWRCWtXX19dxvczFixKaAnlZAAACV61Csri4qCYnJ1VbW5tzf2BgQLW0tGTcdn5+Xk1PTzv3Z2dn1enTp7Nua/uqvt5hpcpKUgwAIL5CCzJ9fX1qbm7OuS9Bpr+/X01MTGTcVkLM0NCQc//kyZPqyJEjqd81RVCr+m6edk3RDQAQX6Gc5SS4uElVRldcMlVjjh8/nvq+t7fXecz7HCY58+KZQKZfM+0aABB3oQQZCS2tra1pj8n3ElC8Ojo6nKEkbWVlJbW9qSor/TvsTLsGANgklKElHUa8lpeXMz4uVRhtbGxMdXd3Z+2RuXfvnnPT1tbWVNT4VY1h2jUAwDaRaqDIFnDcP5cG4Wy9NEKGoZqbm1O33bt3K1uCTHp/DNOuAQDxF0qQkWqKt/oi3281E2l4eFhNTU3l3G5kZEStrq6mbktLS8qmiow2M8O0awBA/IUSZGRoKJPOzs6svyOzlSTISGOwVGayVW9qa2tVU1NT2s2GIMO0awCAjUIJMhJG3GQGkoQYXWnxzkqS4SRp+tUhZnx83Lh1ZPx25w7DSgAA+4S2joz0uUiFpaury1nkzt33In0u8risHSOBRtaccZMQIwvomcTPVX291RiGlQAAtqhIypKzMSazlqTpV/plwhpmkkPccaojtSDete9dU/U19WWtxuzatfHe9u9PqKtXKwkyAAArzt+RmrUUV0Gt6ivOn18nxAAArEGQCdjZl876uqovi+ABAGxCkInBqr7uwUE/Vw0GACBqOOsFrNzVmERCqeefZzVfAICdCDIGBxmpxEiIWVjYGE46eJBp1wAAuxBkDA4y7ksStLcn1NxcBY2+AACrEGRi4re/va9ojwEA2IZTn8GL4bmbfLdtq/HlNQAAiDKCTACL4R3+2eEArq3EnxIAYB/OfgEuhrdvx76yLYbn7o85cCCh6utpjgEA2IcgE6AzL50pW7Ove1jpwoUkTb4AACsRZAJUVVXly7BSVRV/RgCAnTgDBqhc1Rj3sJJcJJJhJQCArQgyAc5Y8uMaS1wkEgBgM4KMgTOW3LhIJADAZgSZgGYs7d2xt2wzlrhIJAAAGzgLBuTNb71ZlqElb6MvAAA2I8gEpFyVkzt33OvHcJFIAIDdCDIB8aMaMzMjz1vy0wIAYCyCjEFBxjvtuqGBFAMAsBtBxrCKjHbhQoJqDADAegQZQ4KMd1iJadcAABBkjAkyrOYLAMBmBBkDvf32A4aVAAAgyAR3eYJyqqmp9uV5AQAwDUHGkMsTsJovAACbcUYM4PIE+3bsK+nyBKzmCwBAZgSZAJztPVtSsy+r+QIAkBlBJgBVVcVPlWY1XwAAsiPIBNDoW0o1htV8AQDIjiAT8UZfd5Pv+fPrVGMAAHAhyPjc6Lt3x96iG329w0pMuwYAIB1BxmdnXjxT9NBS+rDSOqv5AgDgQZCJcKOv29tvM6wEAIAXQcZnpTT6uvtjGFYCAGAzgkxEZyx5+2NYzRcAgM04O/o8Y6kc/TEHDiRYBA8AgAwIMhGesaTNzFTQHwMAQAYEGR+9+a03i6rIbB5WIsUAAJAJQSaCM5bc11Y6eJBrKwEAkA1BxkflqMYwrAQAQHYEmYgFGW+Tb/3DTAMAADwIMhGsyGhUYwAAyI0g46NCgwxNvgAAFIYg4+NieKU0+R44QJMvAABbIcj4uBheKdWYS5cYVgIAYCsEGZ8Ww9u3Y19Bi+HR5AsAQOG4EqFPzvaeLahHxt3ke/Gi9Nf4s18A7KgOP3jwQK2vr4e9K0DOtdaqq6tLuriyIMhEYDE877BSVRWFMgDFuX//vvr444/VXSnzAhFXV1endu7cqbZt21b0cxBkInDV680r+VKOAVC4RCKhPvjgA+cfUrt27XJODqX+axfwq2ooofv69evOZ/YrX/mKqqws7h/xBJmQG31ZyRdAuciJQcLM7t27nX/pAlH25S9/WdXU1Kg//vGPzmf3S1/6UlHPwxhGyI2+3inXNPkCKFWx/7IFTPysUpEJsdE3kVDq+eeZcg3Af1KpkcpxUOT/gaYFqvn5edXR0RH2bqBABJmQGn3l/ycSYhYWHvbG1NeTYgD4E2LW1tYCncUk/x9samoqOMycPHlSjY2NqcXFRdXa2qq6u7vV6OioCsKhQ4fU3Nyc72FGQl6QoTLq+1EqgkxIjb7udWP27EmoublKqjEAfCEnKwkxQVVJJDjJ6xV6kuzr63MCzMTEhGpra1MrKytqeHhYBSUOJ3UbEWRCXtFXzM4mjCvBAjCP/H8mqP/XFFr9mZycVNPT0+rmzZupx1paWgKrxsBcoZ09JXVLCVE+vPJVknc5tg3DnS/uFNzo6w7+NTXkSQB2O378uBoZGcm5jVRn2tvbnZu3UrN9+3bnXCHkHKEr43K/p6cn9Xv6HOJ9zPscuV5LHjt16pTzHPI7cm7KRQKa/I4MXXmfS15PHve+jjy37Jf8TF5D7+NWv9eeY9+K2Y9czye/ox+X7eRng4ODafsqx1p+7qtkSDo6OlL3FxYWkr29vWXZ1mt1dVUig/PVD4lEInnw9YNJ9X+Vc/vTZ39yXivbbWVlNfnRR6vJ9vYHyY04k0zevu3LrgGwzOeff578/e9/73x1e/DgQfLGjRvJmzdv5vz/U7lu8jryevK6+ZL/T09NTeXcZmJiInW/paUlbXv5Xs4PQl5fn95GR0eTQ0NDqe1km0yPeZ9jq9fS5yHZrq2tLes+633Rvy/bu0+98lxzc3POfXlOvZ08p95H+bn8jt4u1++1ZNm3Yvcj13uVn+njJM8vvy839zZyrAcGBgr+zBZy/g6lIqMTryZjoZIUS902CtOuG7Y1ZN1W/lP9xjfq1JNPNrmafGVlw8B2FwAiS5p7c+nt7U3dP3r0qDPLqJBhK30OyfZYIa917Ngx56s0I3vPU27j4+PONnLT27v3q7OzM9VcLBUp6Q/yvob8XPZHmqAL+b1u176VYz/czye/I38vfZxkGFB+Xz+HPl4yNChVGj+FMqYhHx7vB1a+zzT1rZBtg5JIJNWN1Y3lv2/fv63U/Y0k8ot//LW6e7ciY4D5/HNp8K1Q77zz8JDLTKW5OaZcA4CECTlJ6v+vy/CGnCzlsampKeckKsMUMsyxsLDgnBvk5LmVgYEBZyaSDIHI9nKCzvSY+8QutnqtTOEnE3mebNvKe9NDOpp3P7Suri5nX/L5vbYMr1fKfmT6Pdk+275KcJEAc+LECed1/T5XhxJksvW4LC8vl7StuHfvnnPTZMphuUmIebxVr/8iX+849776o/yf4+OPE+rxx5mpBAD65Cd9Mvpf+HISlJs+uep+DHlMgkghs5nkpCo3CSbyOhIIMj2m5fNa+YQovV22io38LN/p5bOzs06Yyef3WjLsWyn7ken5JNxIwMxEjpn83aQK5K5s+SVSU2UKaeLNtq38h9Dc3Jy6yVLdUfPcc0lCDAC4DA0NpaZgu///ru/LSVhOqHJilK+XL1/eVKnXJ2oJJ5pU7/XjuoKQ6TG3rV6rEDIsJRUdPdTi3jfvz+S9ulsn9H35uVSndCjY6vfKvR+ZyL7IcdHbye/oRmA9zBTEsFJoQUbepLeiIt9nS5H5bqvH9lZXV1O3paWlMu+9Ujua69Sny3fUJ3++ra5dX3NuKysP1Orqesbbysq6unZtXX3ySVLdusX1lACEQ9Z3CepWDBnukX/pHzlyJDUTRoKG9G/owCGPS9iR7R555JHU78oJU25SSXEPh0goke3l9+RncnLN9JjbVq9VCD10Je9JV5f0vumf9ff3O+9VtnGTKpH8jjyu19bJ5/fKvR+5/l5SrZLj5B6WEjrA5DsEV4oK6fhVAdMfIjkImhwIuQKmN6AUsm0mMrQklRkJNbLKJADE1V/+8hfn/43PPPNM2gX4TFrZFxskUEi4MPWSCZN/7W/SlbZCP7OFnL9D6ZHxJjR5s5K4dTCR8pbcl+222hYAkJuECTkRcK0lBEWqXO6ZT34KbSU2eYNSkpLmJWlicr9h6XORx3WSy7UtAGBrhAoEQXpvJMTIlO2gCg6hDC0FiaElALbIVaYHoqgcQ0tEdAAAYCyCDADETMwL7YiRZBk+qwQZAIiJmpoa5+vduxsrjwNRpz+r+rNbDC67DAAxIVOepcHys88+c76vq6tLXQUaiFolRkKMfFblMyuf3WIRZAAgRp544gnnqw4zQJRJiNGf2WIRZAAgRqQCs3PnTvXYY4+pL774IuzdAbKS4aRSKjEaQQYAYkhOEOU4SQBRR7MvAAAwFkEGAAAYiyADAACMVW3LYjuy1DEAADCDPm9vtWhe7IPMrVu3nK+7d+8Oe1cAAEAR53G55pK1F41MJBLq2rVrTqL7m7/5G7W0tMTFIwNM0xIgOebB4rgHj2MeDo578II85nLelhCza9eunFdvj31FRt78U089lSpRyYHnAx8sjnk4OO7B45iHg+Me32OeqxKj0ewLAACMRZABAADGsibI1NbWqh/+8IfOVwSDYx4OjnvwOObh4LgHL4rHPPbNvgAAIL6sqcgAAID4IcgAAABjEWQAAICxYr+OzOLiopqcnFRtbW3O/YGBAdXS0hL2bsXO/Py887Wjo8M5zisrK859wd+gvMe5v79fzc3NpT2e6xhz/P077nzu/SPHdnp62rk/OzurTp8+nddnmuPu33GP7Oc9GXMdHR2p+wsLC8ne3t5Q9yeuBgYGpGncuXV3dydv3ryZ+hl/g/KYmJhIzs3NOcfYK9cx5vj7d9z53PvnxIkTaffdx5PPezjHfSCin/dYBxk5mO6DK1paWkLbnzgbHR11PtTuD7bgb1B+3hNqrmPM8S+fTEGGz70/JDi6j5ccTzn+8pXPezjHPcqf91j3yEh5rLW1Ne0x+V6Xx1BeUkb0lhL5G/gv1zHm+PuPz335yXCFDGloMoShjyGf93COe5Q/77HukdF/BK/l5eXA9yXu5FjL+KgeVx0cHHTGSvkb+C/XMeb4+4vPvX96e3tT98fGxlR3d7dzAuXzHs5xj/LnPdZBJptsBx3Fczd2yQe7p6dHLSwsZN2ev4H/ch1jjn958Ln3nz55ehutM21XzM+Q/3GP6uc91kNLcsC9iVC+p4O9/KRLXdNd63Ljb+C/XMeY4+8vPvf+Gx4eVlNTU6ljx+c9nOMe5c97rIOMlMQy6ezsDHxf4kzGQY8cObLpcRkj5W/gv1zHmOPvHz73/jt58qRzQtXDF3Lj8x7OcZ+P8Oc91kFG/ghukhzlwJLOy3+cT5w4kdb4JeOscpz5G/jDXbLNdYw5/v4edz73/pFhDWk+1SfT8fHxLY8tx93f4x7Vz3vsLxopB3R0dFR1dXU5zUkjIyN8qH2gZwzIsZUxU/cHnr9BecjxlVKv/GtpaGjIOZ66MS/XMeb4+3fc+dz7Q45de3t72mNy7G7evJn6OZ/34I/7fEQ/77EPMgAAIL5iPbQEAADijSADAACMRZABAADGIsgAAABjEWQAAICxCDIAAMBYBBkAAGAsggwAADAWQQYAABiLIAMAAIxFkAEAAMaqDnsHAKBQcoE6uXidXLhucHDQuZgdFwgE7ERFBoBxJMQMDAyonp4e1dfX51yNenJyUi0vL4e9awACRkUGgHGOHj3qfJVKzLFjx5z7Up0BYB8qMgCMo4ePxsbGnGqMWFlZCXmvAISBIAPAKKdOnVLDw8NONUZ6Zdra2pzHx8fHw941ACGoSCaTyTBeGACK7Y+RANPa2upUZuS+kJ4ZAPYhyAAAAGMxtAQAAIxFkAEAAMYiyAAAAGMRZAAAgLEIMgAAwFgEGQAAYCyCDAAAMBZBBgAAGIsgAwAAjEWQAQAAxiLIAAAAZar/D6S6WN/hzxuJAAAAAElFTkSuQmCC", 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