{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## An `A <-> B` reaction \n", "with 1st-order kinetics in both directions, taken to equilibrium,\n", "using a simple, **coarse fixed-timestep simulation.** \n", "\n", "Afterwards, perform some analysis of the results\n", "\n", "See also the experiment _\"1D/reactions/reaction_1\"_ for a multi-compartment version. \n", "\n", "#### This experiment gets repeated in _\"react_2_b\"_ , with a more sophisticated approach, \n", "#### involving adaptive variable time steps." ] }, { "cell_type": "code", "execution_count": 1, "id": "0fac88df-1c44-4419-8479-a20369b06499", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"July 24, 2024\"\n", "LIFE123_VERSION = \"1.0.0.beta.37\" # Version this experiment is based on" ] }, { "cell_type": "code", "execution_count": null, "id": "6b948942-a836-4881-a343-246c83cd5503", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 2, "id": "b0ce3cdd", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path\n", "\n", "import numpy as np\n", "import ipynbname\n", "\n", "from life123 import check_version, UniformCompartment, PlotlyHelper, GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "4f75ae66-3d5c-474c-8d88-bd8a7ca92aef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": 4, "id": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'react_2_a.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = ipynbname.name() + \".log.htm\" # Use the notebook base filename for the log file\n", " # IN CASE OF PROBLEMS, set manually to any desired name\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": null, "id": "46703103-a97d-426c-bf6e-ad6e397a7ddb", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ed390e55-5715-4736-aaf5-670981fab8e9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System" ] }, { "cell_type": "code", "execution_count": 5, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1\n" ] } ], "source": [ "# Instantiate the simulator and specify the chemicals\n", "dynamics = UniformCompartment()\n", "\n", "# Reaction A <-> B , with 1st-order kinetics in both directions\n", "dynamics.add_reaction(reactants=\"A\", products=\"B\", \n", " forward_rate=3., reverse_rate=2.)\n", "\n", "print(\"Number of reactions: \", dynamics.number_of_reactions())" ] }, { "cell_type": "code", "execution_count": 6, "id": "00ea560d-9a49-4041-b119-6de11bfcc7af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 7, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `react_2_a.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "dynamics.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [], "source": [ "# Initial concentrations of all the chemicals\n", "dynamics.set_conc({\"A\": 10., \"B\": 50.})" ] }, { "cell_type": "code", "execution_count": 9, "id": "a605dacf-2c67-403e-9aa9-5be25fc9f481", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 10, "id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABcaption
00.010.050.0Initialized state
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initialized state" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "ab7147fe-712c-4c92-b61f-20ff51675ab8", "metadata": {}, "source": [ "### Test your intuition: \n", "#### given that this reaction operates mostly in the forward direction (kF = 3 , kR = 2 , K = 1.5), \n", "#### do you think that A will be consumed and B will be produced??\n", "We can take a sneak preview at the final equilibrium concentrations without actually running the simulation:" ] }, { "cell_type": "code", "execution_count": 11, "id": "12cac04d-dd61-4646-9339-8b70e22139e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': 24.0, 'B': 36.0}" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.find_equilibrium_conc(rxn_index=0) # This is an EXACT solution" ] }, { "cell_type": "markdown", "id": "ee5b9d1c-3ebe-497a-a0e9-bfb02dcd0693", "metadata": {}, "source": [ "#### The reaction will actually proceed IN REVERSE, because of the large initial concentration of B (which we had set to 50), relative to the small initial concentration of A (10)\n", "Now, let's see the reaction in action!" ] }, { "cell_type": "code", "execution_count": null, "id": "d748df77-1b71-4d16-9e24-212d74a93ff4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 12, "id": "50c7e478-ad0e-4aeb-9cea-dfed47cded21", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 total step(s) taken\n" ] } ], "source": [ "# First step of reaction\n", "dynamics.single_compartment_react(initial_step=0.1, n_steps=1, variable_steps=False, \n", " snapshots={\"initial_caption\": \"first reaction step\"})" ] }, { "cell_type": "code", "execution_count": 13, "id": "c9115720-e66e-44f3-bb0a-fabec5b96673", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABcaption
00.010.050.0Initialized state
10.117.043.0first reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initialized state\n", "1 0.1 17.0 43.0 first reaction step" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "98ec8a03-7a9b-403a-8dcd-d9e19c49d656", "metadata": {}, "source": [ "We can already see the reaction proceeding in reverse..." ] }, { "cell_type": "code", "execution_count": 14, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 total step(s) taken\n" ] } ], "source": [ "# Numerous more fixed steps\n", "dynamics.single_compartment_react(initial_step=0.1, n_steps=10, variable_steps=False, \n", " snapshots={\"initial_caption\": \"2nd reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "code", "execution_count": 15, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.010.00000050.000000Initialized state
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
30.322.25000037.750000
40.423.12500036.875000
50.523.56250036.437500
60.623.78125036.218750
70.723.89062536.109375
80.823.94531236.054688
90.923.97265636.027344
101.023.98632836.013672
111.123.99316436.006836last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initialized state\n", "1 0.1 17.000000 43.000000 first reaction step\n", "2 0.2 20.500000 39.500000 2nd reaction step\n", "3 0.3 22.250000 37.750000 \n", "4 0.4 23.125000 36.875000 \n", "5 0.5 23.562500 36.437500 \n", "6 0.6 23.781250 36.218750 \n", "7 0.7 23.890625 36.109375 \n", "8 0.8 23.945312 36.054688 \n", "9 0.9 23.972656 36.027344 \n", "10 1.0 23.986328 36.013672 \n", "11 1.1 23.993164 36.006836 last reaction step" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "c7650ed4-365e-43c2-b001-280297c68ece", "metadata": {}, "source": [ "## NOTE: for demonstration purposes, we're using FIXED time steps... \n", "## Typically, one would use the option for adaptive variable time steps (see experiment `react_2_b`)" ] }, { "cell_type": "markdown", "id": "c034956a-683c-4c3d-8134-ecac9e19a45c", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 16, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([23.99316406, 36.00683594])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_system_conc() # The current concentrations, in the order the chemicals were added " ] }, { "cell_type": "markdown", "id": "d25eedf3-89f8-4f8c-a49a-d2689103528b", "metadata": {}, "source": [ "NOTE: Consistent with the 3/2 ratio of forward/reverse rates (and the 1st order of the reactions), the systems settles in the following equilibrium:\n", "\n", "[A] = 23.99316406\n", " \n", "[B] = 36.00683594\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "765f6f39-4b2e-4a86-b6a9-ace9d1941663", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 23.99 ; [B] = 36.01\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50071\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 0.04749 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "905adfdd-6d70-4dfc-bb34-c547c4d604b9", "metadata": {}, "source": [ "### As noted earlier, because of the high initial concentration of B relative to A, the overall reaction has proceeded IN REVERSE" ] }, { "cell_type": "markdown", "id": "6ac3dd4e-9dd0-4d3a-aa83-76102bd79524", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 18, "id": "86976e6f-f453-41c3-9553-b27b1328db6b", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 1.0999999999999999 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.000498640072529465, 1.1004986400725294 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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eZyb5lfW1VOKQdO8VOQ2Q9Ds3ulbCP6j0ey9c5vWpzA7C8L1+2v2YdNw+2rbfHyMRCH2882UMCEAAAhCIEkAg7NJIyl0S/tJP+sA5qGBBng/EWd7U5BEIq9j14uK26ffX+355WAaNXUbES7MdtZn1Q0zcVr98OGXmO4hH2efjeXMG2csqEGbd5SHjZbWZR+SIftgbNKf48+EHpkE7TqsQCLXvIBRWg8TkPK+Hg3YwJe16SnttKSsQ+notTfpdk7ZGo+tBhMBo4Ylnn3/RhIU+osJPG3YQhrt08t7b0n7QTsM8v3+z7hQM/Yy3H+RLmfkFc71zbWBi0JHTJAE9Pnba63SWtAh51nzS71Z5LPQx6++WPDsIQ0ayY1Le74kQGBVG5Zix5Om74xv3zsv1nNWXfnGsYgdhVoEwz2tpfA5h3+ju6Ky/y0Nug/5IrFEgjKd0yHOPpm1GCG0gEOahSVsIQAACEHBBAIGwSzFNzAn/Ohp9s5xF0HORG01cC3O5JB1fDhdA1nwoSR9cfO4gDN8IpX3w6CeoZVnsLoRCF8Jg9I1d2l+Gte4gFN/DtTboSJfsVJJ8fFk/AAz6QFrkiPGg3D/ROWTZiRd+KIwWFpLHsnzgjbIrMpe0NT7oQ63kpPKdgzB8XcoiXsq88giE/XZz5VlDaeMO+7VU5hBfX/34pH0Ij+cdjOZIkz5R0TZpffT7QJ4mJmT53RflnvSHtCp2EGa9t/v9Hun3QTzPmikrEIqPWTknzUfG/5d//e68Yj3hewmpHh4X1eKCTJ61mPbaH49xmTWf1De+nvOIcllzEEZfz+N5B8Px448ncQ5jNOwdhGmxivuV9XeJvN7IbmvZvRy94vdi1vcHWX/HDspVWEUV4zI5CONs4q/98nzamszKJMv7Y9pAAAIQgAAEshJAIOySShOnosciwzfS4S/tJAFF7ERz08QFolBwjPZNO9aZNYdX0huwcMdT9M1//Khhvw8iWY4XZl1kYbtBAuAgATHreFkEriRb/eKadexou7T5FvVvkA/hOiqa2yxqP/zAlSRwxkXzrB8AknZNRnPyFBXVktZ1Wt4q8T2Jj7SXo5pSICLp3sm6NqvYQShxCecTFdfjuxaquOeTbEbzQYWvIfJBMS40iH+Sr0s+QOYRCPt9YEoTgpJyZ0Zfu6PHw/v54uO1NCmWef9gkJb7Ky33XNK6zPNHrPC1IY9wlda2CoEwXDOD7u1+r6H9fuflWTMuBMKs7zGS5pP2fiL+OjnoDw8iJsYFXukTrWCetNs8tBu958qs+aTX7Pi4eQTCsG2WKuLR15CkirnCP84ojy9p67GKHYRJcYn+QTScX9bX0rQ1Gn/fk/X9gbAIX9/jrOX160cPPjavMIwcOY/+zgnXRJbcwUlrv8wR47Tf0fK4rAe55A95SfPrd5ok6x/gBr035HkIQAACEIBAHgIIhF1a/cSrpDdR4QeSOOy4aBjPzyJvaPrtzpAP2uEVtxUVU6JvTAe9AQvtJb1x8rWDMMuR2qQ3sHkWs7a2/fJiDTqiXmQuLgXCcPykOcTX5aD1l3TUMbrGw6TvRQVCsRXPtyW25EhYUt7A8INElHFcWEia96CjT2KvKoEw/KAhH9qjV5IoJ0dwXd7z8dxQSSJMWv6o0L+8AmH0NVfmEsax306x6Id56SN+/uWf/G6Qjy++Dob9WpqUHy7Lkc4wrmlpANKExrRdQfF8c9Eca2WqGIuf8XiE9qoSCGXMLPd22mvroB1eWdeMC4Ewz+tv0nzi94+0Sfr9nxZ/aZ9kQx6P/u4KX/uj71vibUL/iq75+DoK7+1oVfi8olzS3NLuv6Q/QIkPaX80yutLUvyqEAiTYiprIkxJEP39m/W1NH5PyBhl3h9I/ySb8nhcNIzf6/K8VM4exg7CMIbx+yl8PJ6TMZ5PMy11SZ4/yKS9rvE4BCAAAQhAIC8BBMK8xGgPAQioJ1BFHi/1k8ZBCECgFAE+kOfDV8VJg3we0BoCzSSQd1d5MykwKwhAAAIQGAYBBMJhUGdMCEDAGYHoUdbQKB9cneHFEARaQ6Bpu9irDhyvs1UTxn4bCSQd824jB+YMAQhAAALDIYBAOBzujAoBCDgikHS8NUseIkfDYwYCEGgQgfD1pGj1+gahGDgVBMKBiGgAgVwEwiPWLnJJ5xqYxhCAAAQgAIEuAQRClgIEIAABCEAAAhCAAAQgAAEIQAACEIAABFpMAIGwxcFn6hCAAAQgAAEIQAACEIAABCAAAQhAAAIQQCBkDUAAAhCAAAQgAAEIQAACEIAABCAAAQhAoMUEEAhbHHymDgEIQAACEIAABCAAAQhAAAIQgAAEIAABBELWAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEWkwAgbDFwWfqEIAABCAAAQhAAAIQgAAEIAABCEAAAhBAIGQNQAACEIAABCAAAQhAAAIQgAAEIAABCECgxQQQCFscfKYOAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEEQtYABCAAAQhAAAIQgAAEIAABCEAAAhCAAARaTACBsMXBZ+oQgAAEIAABCEAAAhCAAAQgAAEIQAACEEAgZA1AAAIQgAAEIAABCEAAAhCAAAQgAAEIQKDFBBAIWxx8pg4BCEAAAhCAAAQgAAEIQAACEIAABCAAAQRC1gAEIAABCEAAAhCAAAQgAAEIQAACEIAABFpMAIGwxcFn6hCAAAQgAAEIQAACEIAABCAAAQhAAAIQQCBkDUAAAhCAAAQgAAEIQAACEIAABCAAAQhAoMUEEAhbHHymDgEIQAACEIAABCAAAQhAAAIQgAAEIAABBELWAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEWkwAgbDFwWfqEIAABCAAAQhAAAIQgAAEIAABCEAAAhBAIGQNQAACEIAABCAAAQhAAAIQgAAEIAABCECgxQQQCFscfKYOAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEEQtYABCAAAQhAAAIQgAAEIAABCEAAAhCAAARaTACBsMXBZ+oQgAAEIAABCEAAAhCAAAQgAAEIQAACEEAgZA1AAAIQgAAEIAABCEAAAhCAAAQgAAEIQKDFBBAIWxx8pg4BCEAAAhCAAAQgAAEIQAACEIAABCAAAQRC1gAEIAABCEAAAhCAAAQgAAEIQAACEIAABFpMAIGwxcFn6hCAAAQgAAEIQAACEIAABCAAAQhAAAIQQCBkDUAAAhCAAAQgAAEIQAACEIAABCAAAQhAoMUEEAhbHHymDgEIQAACEIAABCAAAQhAAAIQgAAEIAABBELWAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEWkwAgbDFwWfqEIAABCAAAQhAAAIQgAAEIAABCEAAAhBAIGQNQAACEIAABCAAAQhAAAIQgAAEIAABCECgxQQQCFscfKYOAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEEQtYABCAAAQhAAAIQgAAEIAABCEAAAhCAAARaTACBsMXBZ+oQgAAEIAABCEAAAhCAAAQgAAEIQAACEEAgZA1AAAIQgAAEIAABCEAAAhCAAAQgAAEIQKDFBBAIWxx8pg4BCEAAAhCAAAQgAAEIQAACEIAABCAAAQRC1gAEIAABCEAAAhCAAAQgAAEIQAACEIAABFpMAIGwxcFn6hCAAAQgAAEIQAACEIAABCAAAQhAAAIQQCBkDUAAAhCAAAQgAAEIQAACEIAABCAAAQhAoMUEEAhbHHymDgEIQAACEIAABCAAAQhAAAIQgAAEIAABBELWAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEWkwAgbDFwWfqEIAABCAAAQhAAAIQgAAEIAABCEAAAhBAIGQNQAACEIAABCAAAQhAAAIQgAAEIAABCECgxQQQCFscfKYOAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEEQtYABCAAAQhAAAIQgAAEIAABCEAAAhCAAARaTACBsMXBZ+oQgAAEIAABCEAAAhCAAAQgAAEIQAACEEAgZA1AAAIQgAAEIAABCEAAAhCAAAQgAAEIQKDFBBAIHQR/26tTZtv2aQeWMAGBZhFYsnDcjI+NmC2vTDVrYswGAo4IvGbfhebnW3aamdk5RxYxA4HmEFg4OWYWLxgzm7btas6kmAkEHBI4YJ8FZrN9jzU1PevQKqYg0AwCCyZGzV6LJsyLW3c2Y0INmcXB+y1qyEyaOQ0EQgdxRSB0ABETjSSAQNjIsDIphwQQCB3CxFTjCCAQNi6kTMgxAQRCx0Ax1ygCCIQ6w4lAqDMuoVcIhA7ig0DoACImGkkAgbCRYWVSDgkgEDqEianGEUAgbFxImZBjAgiEjoFirlEEEAh1hhOBUGdcEAgdxeWP//iPzUV/8EmOGDviWdbM//qXfzRHHX28WXn4UWVN0d8BgZ8+cL95edtWc+JbT3VgDRNlCWzbusX887qbzdm//Z/LmqK/IwJf/Nvrza+tPtss3mupI4uYKUPgm//6FfPagw8xbzjmhDJm6OuIwDNPPmp++tCPzanvPtORRcyUIbBr507z939znfnwf/q9Mmbo65DA7V/8G/P2d73H7LPvAQ6tYqoogfvv/VbQ9cS3/EpRE/RzSODnzz1t7rMxOe29Zzm0iqkyBD7/V/+Pufzyy8uYoG/FBFq/g3DdHXebS6+6YQ/MD9y5tvfYmedcah7ZsDH4/5ErV5jb1q7pPYdAWPEKzWkegTAnsIqbIxBWDDineQTCnMA8NEcg9AA5xxAIhDlgeWiKQOgBco4hEAhzwPLUFIHQE+iMwyAQZgTlqRkCoSfQOYZBIMwBa0hNEQitQPiZ624xd627JjEEH7no0+bFTVt7oqCIhfstX2puvPrioD0C4ZBWbsqwCIS64oFAqCseCIS64iHeIBDqigkCoa54IBDqigcCoa54iDcIhLpigkCoKx4IhLriId4gEOqLSdwjBMIBAuGq1Reaj59/lll9+ikBO9lxGBcUyUGof6Hj4XAIkINwONwZtT4EyEFYn1jhqX8C5CD0z5wR60WAHIT1ihfe+iVADkK/vLOORg7CrKSG0w6BMOGIcXi8eP2Dj5mzL7jC3HztZeaEYw4PIpT0GALhcBYvo+ongECoP0Z4OFwCCITD5c/ougkgEOqOD94NnwAC4fBjgAd6CSAQ6oyNJoEwfjpUJ7Fkr5J0KRf+t14gjEOMHinOJBBu/Ccz++Cfman9/6OZPujXzOzS41zEBRsQaASBifFRMzo6YnbummnEfJgEBFwTWLJo3Ly6Y8bMzc25No09CNSewPjYqJkYHzHbd/I7pPbBZAKVEFi8cNzssO+xZmf5HVIJYIzWmsDY2IiZHB+zv0Omaz2Ppjm/9+IJb1MSbeee+x+cN97yZXv30ssNQyAMa2Cs+cR5vVOqRYAgEBahVqBPCFp2EWYRCCUH4eVH/VFvpNl93mxmlp9sv95qZvY92czudWQBL+hSlMDt6/7BHHvcG82RR72hqAn6OSTww+9/z2zdutWsevs7HVrFVFECW7dsMbfe8rfmvI9+rKgJ+jkmcOPnP2s+cNZvmb2XUsXYMdpC5r76lX8yhxz6OnPc8W8s1J9Obgk8/ujD5icP/Mj82hnvd2sYa4UI7Ny5w9zwuc+aj/3uRYX608k9gb+76UZz2nt+3ey//4HujWMxN4HvfPuuoM8vv21V7r50cE/gmY1Pmu98627z/g/+pnvjWCxE4Oo/vdJbFePjTj3HRMXA0GERDV+z/77mU5/8qBmGQFgIXEInBEJXJAfYCRXd8JhxUg5CqXocPi8C4cVnHWxmn/+Omdx8jxl/+Se9EWYnl5td+5xsppa9xX63X/b73NgSTzNp5zAUKdEVd4qU6IoHRUp0xUO8oUiJrphQpERXPChSoiseFCnRFQ/xhiIlumJCkRJd8aBIia54iDe+ipSICPjwY0+nFqINyYQCofw/3GmYJipGdyJGU9CJXnTKW04wd9+73mzavC0wff6HzjCHrnPSEusAACAASURBVDjQiG4UXmGfJGEvvtNR+l947vtM0g7IfunwXES89UeMJaDRCsZxFTlPFeORmZetSHhv8DWxxX63X6O7NvXiNLX0eDO1tCMUimA4vdfRLmKIjQgBBEJdywGBUFc8EAh1xQOBUF88EAh1xQSBUFc8EAh1xQOBUF88EAh1xQSBUFc8fAqEsnvwjHe/Ldgl2O8S7eeRDRsDQU8EOblEHzrq8EPMjVdfHPw/rgdd84Uvmetuur23YUzaizAYCoDh8/GjzGLrtrVr9jilGhczRUD8889/MRhfnvv9//SBXj0M8TfNjqtot14gDBdFCPTkE4/pLYbwsWibI1euCAIbvdKKlIy/8nAgEk6EouG2H/a6zU7s09lZGAiGJ3d2F45zxMzVwsaODgIUKdERB7zQS4AiJXpjg2fDJ0CRkuHHAA90E6BIie744N1wCVCkZLj800avukhJuEMvS46/pCPGl1x5vfnJT59IFPPCOYko+MH3viMQFcMdhKEYmbRDUGzKDkPZmBZ9XuxJUdwsvkpbER9v/fI39rATFtR1EfHWC4QuIGapYjwyt7MnFMpRZNllOLrr+d7w03sd09tZKILh9F7HunANGxAYKgEEwqHiZ/AaEEAgrEGQcHFoBBAIh4aegWtCAIGwJoHCzaEQQCAcCvaBg9ZJIAzTzyVNKtx1mCYQRkW/NGHv0SeeCY4hh8eGk8YJdyhGn0urlzEQfoYGCIQZIA1qkkUgjNsYe3WDmdzaPY4sOwy3/HuvydzYXh2x0H5Nye5Cexx5dmLfQW7wPATUEUAgVBcSHFJGAIFQWUBwRxUBBEJV4cAZhQQQCBUGBZfUEEAgVBOKeY5ULRDKYHmOGO+3fOm8E6TRHYTx+hRpAp7kIIzvIHQhEMo8oidco8ebKVKic30bKVJy0R980mzbXqJ8+txMJ3ehHEeW3IX257EdG3sznl58VEcstFWRRSyc2pvqimnLgRyEum4UchDqigc5CHXFQ7yhSImumJCDUFc8yEGoKx7kINQVD/GGIiW6YkIOQl3xIAehrniIN1qKlIgImFbFOOmIcb8jwGV2EAqTtCPGSeIkAqG+Nb2HR04EwphVEQflGHIoFopwaOZmg1Zzows7IqGIhd1iJ7OTB9SAlB8XEQj9cM46CgJhVlJ+2iEQ+uGcZxQEwjy0qm+LQFg94zwjIBDmoVV9WwTC6hnnHQGBMC+xatsjEFbLN691BMK8xKpv70sglJnI7rt4ReJQdAsLmAzKQSh2wkrC0WPAIiKefOKxZvXpp6TmIMyyg1ByB4oPmzZv7RXODYuUSHGSuHgoc5KLI8bVr9XCI1QhEMadkePHQaGTYHfhPWZs+xO9JjOLXt8rchLsMlx6YuG5NKEjAqGuKCIQ6ooHAqGueIg3CIS6YoJAqCseCIS64oFAqCse4g0Coa6YIBDqigcCoa54iDc+BcKouBclERXusgiEaXZCwbDMDsKwuEi8cG7oowiRt3/t2z33Je9hWEGZI8b61nfPoyI5CItOZ3Tnc12hsJu/0IqGI7M7O+ZGxjtiod1hGIiF9vvMwtcWHYp+EChNgByEpRFioOEEyEHY8AAzvVIEyEFYCh+dW0CAHIQtCDJTLEyAHISF0VXa0UcOwkon0HDjFClxEGCfAmHc3YmtP9idv9DuMhx/9ZFek5lFr+scQ14qxU46oiEXBHwSQCD0SZux6kgAgbCOUcNnXwQQCH2RZpy6EkAgrGvk8NsHAQRCH5Tzj4FAmJ+Zzx4IhA5oD1MgjLo/umtTUBk5OI780j3BTsORmVc6TUZGdu8stILhLpvDcGbhIQ5mjwkIpBNAIGR1QKA/AQRCVggE0gkgELI6INCfAAIhKwQC6QQQCHWuDgRCnXEJvUIgLBkfHzkIi7o4se2BTqGTbmXk8Zcf7JmaWXhwcAS5U+ikU/DEjIwVHUpNP3IQqglF4Ag5CHXFgxyEuuIh3pCDUFdMyEGoKx7kINQVD3IQ6oqHeEMOQl0xIQehrniQg1BXPMQb3zkI9RHQ7xECYckYaRYIo1MbndrarYrc2VkowuHo1JZek6l9TursMJTqyHaH4czilSXJDKc7AuFwuKeNikCoKx4IhLrigUCoLx4IhLpigkCoKx4IhLrigUCoLx4IhLpigkCoKx4IhPrikeQRAmHJONVFIIxPc/yV/907hixi4cS2H/eazE4e2NlZKAVPusVO5kYXlCTlpzsCoR/OWUdBIMxKyk87BEI/nPOMwg7CPLSqb4tAWD3jPCMgEOahVX1bBMLqGecdgR2EeYlV2x6BsFq+ea0jEOYlVn17dhBWz7jsCAiEZQna/lpyEBadysjMq51dhZK7UL623GNGd73YMze195s6OwvtDkMpdjK9+MiiQ9GvZQTIQdiygDPd3ATIQZgbGR1aRIAchC0KNlMtRIAchIWw0aklBMhBqDPQ5CDUGZfQKwRCB/Gpu0AYRzD+6qMdsbCbu3Bi6/d7TWYnlgc7C4OqyN0jyXOjix1QxEQTCSAQNjGqzMklAQRClzSx1TQCCIRNiyjzcU0AgdA1Uew1iQACoc5oIhDqjAsCocO4NE0gjKIZmZuyYqHNW9jdXSjHkcd2/qzXZGrv43cXO7HC4fSSX3BIFlN1J4BAWPcI4n/VBBAIqyaM/ToTQCCsc/Tw3QcBBEIflBmjrgQQCHVGDoFQZ1wQCB3Fpa45CItOf2z7k52dhXIk+SUpePK9nqnZiX06YmFY7MR+nxtfWnSoQv3IQVgIW2WdyEFYGdpChslBWAhbpZ3IQVgp3tzGyUGYG1mlHchBWCne3MbJQZgbWeUdyEFYOeJcA5CDMBeuyhuTg7ByxLkHIAdhbmTeO3DEuCTytgmE83HN7d5ZuLWTv3Bs+1O9JtN7HdMRC7vFTqb3OrYk7cHdEQgHM/LZAoHQJ+3BYyEQDmbkuwUCoW/i/cdDINQVDwRCXfFAINQVD/EGgVBXTBAIdcUDgVBXPMQbBMJOTI479Rxz5MoV5ra1a9QFCYGwZEjaLRDOhze24xkjR5A7hU46383cdNBobmyvXmXkMH/h7MS+Jenv2R2B0DnSUgYRCEvhc94ZgdA50tIGEQhLI3RqAIHQKc7SxhAISyN0agCB0ClOJ8YQCJ1gdGYEgdAZSieGEAidYHRqBIHQmGu+8CXz9bvuM5s2bzWf/dTvmxOOOdwp47LGEAjLErT9m5yDsAyeia33m8ngGHK4u/DxnrnpxUcFlZGDI8m24MnU3m8sMxR9lRIgB6HSwOCWGgLkIFQTChxRSIAchAqDgkuqCJCDUFU4cEYZAXIQKgtI15225yA885xLzbtWnWS+/8DD5jX772s+9cmPqgoUAqGDcCAQDoY4uuuF3VWRg4In95iR2R1Bx7nRhfMrI1vBcHbygMFGaaGeAAKh+hDh4JAJIBAOOQAMr5oAAqHq8OCcAgIIhAqCgAtqCSAQ6gyNT4Hwu6+8anbMznoH8dYli83C0dE9xl3/4GPm7AuuMDdfe5l59IlnzGeuu8Xcte4a7/71GxCB0EE4EAjzQ5zY9qPgCHJ4JHn8lZ/2jEwvPnx3ZWS7w3BqnxPzD0APFQQQCFWEAScUE0AgVBwcXBs6AQTCoYcAB5QTQCBUHiDcGyoBBMKh4k8d3KdA+PoHHjIbdu3yDuLx4442Kycn9xg3PF4c5h6UXIQiFmo6ZoxAWHK5kIOwJEDbfXRqs91deI+ZCHYWdvIXjkxvCwzPjU7srowsR5FtwZOZBQelDkoOwvLxcGmBHIQuaZa3RQ7C8gxdWyAHoWui5eyRg7AcP9e9yUHommg5e+QgLMevit7kIKyCanGb5CAszq6KnuQgrIJqOZu+cxD+xoYnzc+mOjURfF5/v/J15qCJ8T2GDI8XX3ju+4LnPnLRp9UdM0YgLLlSEAhLAkzoPv7yg8ER5E7uwnuM/D+8Zha9rlPsZKkVC20Ow137/NI8CwiE7uNRxiICYRl67vsiELpnWtYiAmFZgm77IxC65VnWGgJhWYJu+yMQuuXpwhoCoQuK7mwgELpj6cISAqELim5t+BYI3Xpfzlp4vDhuZfmyvVUdM0YgLBdng0BYEuCA7rKTMCxyEuww3HqvGd31UrfXSLcyshxDtmKhFQ7v+LfvmaOOPt6sPPyoah3DeiYCCISZMHlrhEDoDXXmgRAIM6Py0hCB0AvmzIMgEGZG5aUhAqEXzLkGQSDMhavyxgiElSPONQACYS5cXhq3WSCMHy8Ogcsx4zWfOM+sPv0ULzEYNAgC4SBCGZ4nB2EGSI6ajE5tMQte/JpZ8POv2+//ZsZ2bOxZDoqd7LfKTC05zszYPIaSy3B6yS+YmYUrHI2OmbwEyEGYlxjt20aAHIRtizjzzUOAHIR5aNG2jQTIQdjGqDPnrATIQZiVlN92PnMQ+p1Z/9FWrb7QfPC97zDh8eKwtRwzluvGqy9W4S4CoYMwIBA6gFjQxPi2n5iFL/yLFQutYPjSt23Swj1zDIhwOLPEioULD7PfjzDTi+zPi47oPLb4iIIj0y0LAQTCLJRo02YCCIRtjj5zH0QAgXAQIZ5vOwEEwravAObfjwACoc710VaBUGc09vQKgdBBpBAIHUB0YGJk5mUrFH7DTGx7wIy/+rAZe/VR+/1ReyT5xXTrI+OBSCi7DREPHQQhZgKB0D1TLDaLAAJhs+LJbNwSQCB0yxNrzSOAQNi8mDIjdwQQCN2xdGkJgdAlTfe2EAhLMiUHYUmAjrsnFSmRY8hj258IvsZ3PNn5ecdTVkDsPDYyN5XoxezEPvZ4st11aAujzCyy3xe+zu483P3/2Yl9HXvfPHPkINQVU3IQ6oqHeEMOQl0xIQehrniQg1BXPMhBqCse4g05CHXFhByEuuJBDkJd8RBv2pyDUF80kj1CICwZKQTCkgAdd89bxXhs57MdoXCnFQ7t9/FAPBQRsfP/kbmdiR7OjS+1YuGh8wTEQDy0IqKIibOT+zmeWT3NIRDqihsCoa54IBDqiwcCoa6YIBDqigcCoa54IBDqiwcCoa6YIBDqigcCob54JHmEQFgyTgiEJQE67p5XIOw3/Oiu5+wR5VAwtN9FQAyERPtlRcSRmVdTxMO9rFB4aGe3oQiGi+33BZ3v0/ZrduIAx7PWaw6BUFdsEAh1xQOBUF88EAh1xQSBUFc8EAh1xQOBUF88EAh1xQSBUFc8EAj1xUONQCgVXDZt3pZI6IE719aDXMRLchDWLmSlHR7d9UJnt6HsNNzR/S5HmIPHnrLi4cvJ4uHooo5gGAqI4ZHl8CjzgoNK+6bJADkINUUDXzQSIAehxqjgkxYC5CDUEgn80EqAHIRaI4NfGgiQg1BDFPb0gRyEOuMSeuV9B+GZ51xq9lu+VE0ZZxfhQSB0QbE5NqQoSifP4ZO7jywHOxFFQLTi4fTWZPFwZEFHPJSch0G+w27uw3An4sKDawcJgbB2IcNhzwQQCD0DZ7haEUAgrFW4cHYIBBAIhwCdIWtDAIFQZ6gQCHXGZWgC4XGnnmPWfOI8s/r0U3STyeEdAmEOWC1vOjr1UifH4bx8h53jy5IHcXRqS7J4ODrRO6Y8s9gKh/bIshxXDnMeziw8RCVZBEKVYcEpRQQQCBUFA1fUEUAgVBcSHFJGAIFQWUBwRxUBBEJV4eg5g0CoMy4IhAlxueTK683tX/u2ufnay8wJxxzeayG7Hh/ZsDH4/5ErV5jb1q7pPUcOQl0L3GUOQt8zE3EwLJbS24EYyYEo4mLiNTIWq7Dc3YEYCIidHYnDushBOCzyyeOSg1BXPMQbqhjrigk5CHXFgxyEuuJBDkJd8RBvqGKsKybkINQVD3IQ6oqHeEMVY30xiXs0lCPG71p1krnw3PeporPujrvN/7j5K4EQGBUIP3LRp82Lm7b2RMH4EWkEQlVhNHUWCPuRlGPJcjw5yHfYFQ13V1x+wsix5rRLqirPK5hi8x92HhMh8TBjRkYrCyICYWVoCxlGICyErdJOCISV4s1tHIEwN7JKOyAQVoo3t3EEwtzIKu+AQFg54lwDIBDmwlV5YwTCyhHnHgCBMDcy7x28C4QixH3mulvMXeuu8T7ZfgPK0WcRBs++4Ip5AqEUVPn4+Wf1jkTH/UcgVBXGxgqEfcVDWxBFCqP0BMNuvkMpoCKPSUGVdPHQioVhhWWpuCyiYffosoiKZmS8VIARCEvhc94ZgdA50tIGEQhLI3RqAIHQKc7SxhAISyN0agCB0ClOJ8YQCJ1gdGYEgdAZSieGEAidYHRqpM0C4foHHwu0pvilLf2ed4FQhLh+1zCqGMuuwN85+z3miMMOnicQhkGM7ihMeowchE5fNzDmkMDIzKvdnIdWLLQ5DoPdh2EBFfvz6K7n0sXDBQd3xcLOMeXOLkQrKHaPLs+NTg70lByEAxHRoOUEyEHY8gXA9PsSIAchCwQC/QmQg5AVAoF0AuQg1Lk62pqDMElHkhR3d9+7XtXmOe8CobZlKkF57ucvBVWV40HLKhBqmxP+QCATgdmdxry8wZhX5OuJ+d/l8e3PpJtZ9Fpjlqy0X3aXoXzfy35Z4TD4Lo+NLcrkAo0gAAEIQAACEIAABCAAAQhAAAJNJpCkLcnp1EuvusEMY5NcGutWC4Tx48JFBUJ2EDb5Vm7v3EZ3PmfGX33UjL/8UzO+47FO5WX7/7Htj6ZWWxZac6MLzcySw+2OwyPMyNKjrGh4hHl1ZqGZXbjCzI7tZWYn9zNz48vM7MQ+7YXLzCHQJcAOQpYCBNIJsIOQ1QGB/gTYQcgKgUA6AXYQ6lwdXncQ/vy7xszs8A9i/7faDTML542bJBBKvQu5ZLOalmsoAmGolEYhDOPsdZIfoU/nf+iMoJBKUg7CqMpLDkItS7njR1OLlOiibIKiKIFYKALiqw+b8Vfk+57i4Xc3v9VsmVpmTjvgjsQpzE6+xszZF88g3+HYAjMzeZCZs8Lh7Jj9EiFxbIk91ryiIzrK967AqI1HXfwhB6G+SJGDUFdMyEGoKx7kINQVD3IQ6oqHeEMOQl0xIQehrniQg1BXPMQb7zkIb3t955Sc7+vMxzun7CJXWg7CUHfy7WLaeN4Fwmu+8CVz3U23zysEEsIaNpw0VZcqxlqW62A/EAgHM6q6RVQ8fOChJ8y2l7eZUw97Osh3ODq12YxObwkExhFbXKXo1REP97IFVqzAKOKhFRjnRhdYUfE1ZnZ8n0BkFLExEB0jAmPR8ZrSD4FQXyQRCHXFBIFQVzwQCHXFA4FQVzwQCPXFA4FQV0wQCHXFYygC4bd+w5gdP/MP4m1/b8wi+1k0QSCM1rfgiLEFJDvyPvjedwS786KXCIe3fvkbQ03QmCQQio9SxOSRDRsDd49cucLctnZNz3V2EPq/3/qNiECoKx79qhiPzGyzQqEIhvZr6iUzIsKh/S4i4kjwWOdrRB4L/2+/j8hjkj8x72UrMs/K0ebJfe3x5mX2mLPdpTje/XnCfpf/y3d5zn4FP9udjHPBY804Do1AmHfRVN8egbB6xnlGQCDMQ6v6tgiE1TPOMwICYR5aftqyg9AP56yjIBBmJeWnHQKhH855RvG+gzCPcxW3TdOapIhvVDSs2I2B5r3vIBQASceJNaqnA+l1G5CDMCsp2rWNQBVVjKUyc0c47IqLocDYFRRFTAyeC4XF8P9WjByZfbVACEasqGhFwzERDbvCYSAw2p8DwVEERREY5f8dkTEQGAPx0QqLI2MFxqRLWwiQg7AtkWaeRQiQg7AINfq0iQA5CNsUbeaalwA5CPMS89Peaw5CP1PKNEqSQBierm11kRLNOwgzRTahEQJhUXL0azqBKgTCosxk12F0l2JHSJQdi52di7t3Lc7fzRiIkXa3Y5FrbnxpR1QMirJY4VAERNnBaP/fERG7oqMVE4P/W7ExeE6+RieLDEmfmhFAIKxZwHDXKwEEQq+4GayGBBAIaxg0XPZGAIHQG+pcA7VdIIzD0iQOim/edxBqzkGYa2VHGiMQFiVHv6YT0CQQFmY9N9PNndg9/hzuXAyPP3f/HxUYo8eki4wrxVnmHYMW4TAUGLtiY+co9O6j0Z1j0SIsLioyJH2GRACBcEjgGbYWBBAIaxEmnBwiAQTCIcJnaPUEEAh1hqitAqHOaOzplXeBUFzQUsXYRZDIQeiCojsb5CB0x9KFpX45CF3YV29jbtqM7dhodye+Ysamft4rzjK687kgj+LYjift7sQd8wu4BM/tKDw1OdYsOxCTCrhs3rXU/MN3d5nfOe3AoHiLsXkZ5ZqNVYeOPlfYETpmIkAOwkyYvDUiB6E31JkGIgdhJkzeGpGD0BvqzAORgzAzKi8NyUHoBXPmQchBmBmVt4ZtzkHoDXLJgYYiEJb0WVV3BEJV4TAIhLri0XqBsEQ4AmHRCoXB95lXrIhoBcYpW/1ZxMZdtmjS7IwZ2/5Ep42IikEuxi19R9w8tcz89cZzzO+t/H8zeyZVomdttejwCoXH4P9SJVqqRXcvaTc3siD4X1BVOtqvW1W685ytPB15LqxKndmpBjVEINQVTARCXfFAINQVDwRCXfEQbxAIdcUEgVBXPBAIdcVDvEEg1BeTuEcIhCVjhEBYEqDj7giEjoGWNIdAWBJgge6d3Yk7zLgVD024gzEQGF8027ZtNrfet6/56FufCIRHeV6u0emXA/ExvKLPFXChXBe7qzHYwdi9Zif2s3kZ9+r8L+E5OY7deW4s1q9TqTq8phcd1vs5KDCjpDI1AmG55eK6NwKha6Ll7CEQluPnujcCoWui5e0hEJZn6NICAqFLmuVtIRCWZ+jaAgKha6Lu7XkTCKV68fkfOsNcd9PtfWehLUljFuTkIMxCiTZtJNCIHIRtDFww5zm7c3F7cAR6ZM5+hT/Pbre7F+X/9sv+HDwu/w8e6/zfzNmCMN2fO49328rP07aN2BM7093H5f/dn33ill2O8mVs3sa5cfsl3+0OyN7Pdqfj3Jj9ksftz0bajMj/7Vf485h9rNvGBN+77YPnxX5o2z5u+5rRzrHu8CIHoc+IM1bdCJCDsG4Rw1/fBMhB6Js449WJADkIdUaLHIQ64xJ65U0g1I2hnHcIhOX40bu5BBAImxvbqmYmgqLsggyv4Ph0mJNxxuZt3PWz3nPhkevOA/bIteyK7F5yJFuOZss10t1Jufs5e1R75uWqpjDQbjTH4+iCvc3U2HIzN5fQLXaEO95iZuHrUseaWWB3YY6OJT4fHAu3tpOuTtXt3Tsvo23mYrkqB06UBhAoSQCBsCRAujeeAAJh40PMBEsQQCAsAa/CrgiEFcJ1YNq7QCg7Cdd84jyz+vRT5rkv1Y1v/fI3zF3rrnEwLb8mEAj98ma0+hBAIKxPrFrraYJ4OBoRDyXPY3iN2ByPo9O78zxKkZnw6lSu3v1ccMS7e2XJD1l3/vFclfH5RI94x5+btUfK57oFc/Z4LpLXco/nrJA5l3JUvJ+YGc+BOc9u7Bh73eNSd/8RCOseQfyvmgACYdWEsV9nAgiEOqOHQKgzLr3PLXP28ulimkAYVjau2xFjchD6XD2DxyIH4WBGPluQg9An7cFjbdu6xfzzupvN2b/9nwc3pkVlBKKi481f/LJZ/atHm70WT+45XmzHZLzB2PbdAuUez3UL2SRNItiFaW0nPmerbUshnKRLdl1KLssmX7c9t9octmiDefPSH+Se5uykLdJjj5nnvWTHpuzczH2VEDOjBYXyjCu+pomy/eyIACxCcN7ryWc2m4eefNn86jt+JW/XobfXlOvUFQxyELoi6c4OOQjdsXRhiRyELii6s0EOQncsXVkiB6ErktXZUbOD8JIrrzd337u+djsIEQirW5xFLCMQFqFWXR8EwurYFrGMQFiEWrV9mlKkJH40PEotfsQ7TnRUKnV3C+bs8VxwxDxZzAyOmHePke/RL7ajc54/3crfSZH98lO/YlZO/qSQQFjtSmmn9YdePtr8cNubzVmvvbmdAIYw6367gXfMTJq/eugD5r8d93dD8GzwkP12Kg/uPbwWRf+4IB7fdN+h5j1HP2f2X7LL+wSkSJgUEqvdFStq5tL/ex7qpC85+ehucTWXxrGVm8Czm6aMxGT12/bN3ZcO1RD4i3981lx++eXVGMeqEwJeBMJwd+Agj5OOHg/qM+znEQiHHYH54yMQ6ooHAqGueCAQ6oqHeNMUgVAf2WIelaliHFYQzzuyHFuXI+q5r9jx+Dz9O74mC6/97IzObDFy1D7vJQKwCMF5r0c2H2B+/Nwy83++7ut5uw69fRNTC+yYXWj+4vH/ai4+4qqh88WBDoHPPXm+OfM168xBC3bn54XN8Ah8c9OpweBvX37n8Jxg5B6BDdtXmm++eKr58CFroaKEwB8//EcIhEpikeaGF4EwOnjaEWPlnPq6Rw7COkcP36skQA7CKuliuwkEqGLchCgyh6oIkIOwKrLpdvvtBvbvTb4Ro7lf8/UcbuvRXVawn9lRyIm9F0+YV3fOmJmZ2UL9y3SSHdz1TDsxv6hZGQb01U1gbNSYcfvPzin/94duMsPzbseBv26WH/PB4TnAyAMJeBcIB3pUwwYIhDUMGi57IYBA6AUzg9SYAAJhjYOH65UTQCCsHDED1JwARUpqHkDcr5QARUoqxVvYOEVKCqPz0hGB0AFmBEIHEDHRSAIIhI0MK5NySACB0CFMTDWOAAJh40LKhBwTQCB0DBRzjSKAQKgznAiEOuMSeuVdIFz/4GPm7AuuSKVCFWPdC0a7d+Qg1BUhchDqigc5CHXFQ7whB6GumJTJQahrJs3w5pknHzU/fejH5tR3n9mMCdV8FlQx1hdAqhjriglVjHXFgyrGuuIh3lDFWF9M4h55FwhXrb7QnPKWE8zJJx5rPnPdLb2qxWeec6l516qTzIXnvk8/tYiHFCnRFS4EQl3xQCDUFQ8EQl3xQCDUFw8EQl0xQSDUFQ8EQl3xEG8QCHXFBIFQGRBK3wAAIABJREFUVzwQCHXFA4FQXzySPPIuEIZFSo447GDzXy75855AKJWOo4JhPfAZg0CoK1IIhLrigUCoKx4IhLrigUCoLx4IhLpigkCoKx4IhLrigUCoLx4IhLpigkCoKx4IhPrioUogXH36KUbEwvBIsQiEl151Q+//9cDX8ZIchHWKFr76JEAOQp+0GauOBMhBWMeo4bMvAuQg9EWacepKgByEdY0cfvsgQA5CH5Tzj0EOwvzMfPbwvoNQjhIf+4bDzKc++VET/fmSK683d9+7vrej0CeEsmMhEJYlSP+mEkAgbGpkmZcrAgiErkhip4kEEAibGFXm5JIAAqFLmthqGgEEQp0RRSDUGZfQK+8CYRyH7CIMr5uvvcyccMzhuokleIdAWLuQ4bAnAgiEnkAzTG0JIBDWNnQ47oEAAqEHyAxRawIIhLUOH85XTACBsGLABc0jEBYE56nb0AVCT/OsbBhyEFaGtpBhchAWwlZZJ3IQVoa2kGFyEBbCVmknqhhXije3cXIQ5kZWaQdyEFaKN7dxchDmRlZ5B4qUVI441wDkIMyFq/LG5CCsHHHuAahinBuZ9w7eBcKwSInkIGzChUCoK4oIhLrigUCoKx4IhLriId4gEOqKCQKhrnggEOqKBwKhrniINwiEumKCQKgrHgiEuuIh3iAQ6otJ3CMEwpIxQiAsCdBxdwRCx0BLmkMgLAnQcXcEQsdAHZhDIHQA0aEJBEKHMB2YQiB0ANGhCQRChzAdmUIgdATSkRkEQkcgHZlBIHQE0qEZBEKHMCsy5V0glMIk71p1krnw3PdVNCX/ZslB6J85I9aDADkI6xEnvBweAXIQDo89I+snQA5C/THCw+ESIAfhcPkzum4C5CDUGR9yEOqMS+iVd4Fw/YOPmf9yyZ/XslpxWigRCHUvcrwbHgEEwuGxZ+R6EEAgrEec8HI4BBAIh8OdUetDAIGwPrHCU/8EEAj9M88yIgJhFkrDa+NdIIxWLU6a9gN3rh0ejYIjIxAWBEe3xhNAIGx8iJlgSQIIhCUB0r3RBBAIGx1eJueAAAKhA4iYaCwBBEKdoUUg1BmX0CvvAqFuHPm9IwdhfmZV9iAHYZV089smB2F+ZlX2IAdhlXSL2SYHYTFuVfUiB2FVZIvZJQdhMW5V9SIHYVVki9slB2FxdlX0JAdhFVSL2yQHYXF2VfUkB2FVZN3Z9S4QplUxvuYLXzK3fvkbtTt6jEDobjG6sIRA6IKiOxsIhO5YurCEQOiColsbCIRueZa1hkBYlqDb/giEbnmWtYZAWJag+/4IhO6ZlrGIQFiGnvu+CITumZa1iEBYlmD1/dUIhOvuuNtcetUNpm5HjBEIq1+keUZAIMxDq/q2CITVM84zAgJhHlp+2iIQ+uGcdRQEwqyk/LRDIPTDOesoCIRZSflrh0Doj3WWkRAIs1Dy1waB0B/rrCMhEGYlNbx2agTCS6683tx97/ra7SCU0JGDcHgLmJF1EyAHoe744N3wCZCDcPgxwAO9BMhBqDc2eKaDADkIdcQBL3QSIAehzriQg1BnXEKvvAiE4e7AQSjWfOI8s/r0UwY1c/q8CJO3f+3b82zGdzGeec6l5pENG4M2R65cYW5bu2ZeewRCpyHBWIMIIBA2KJhMpRICCISVYMVoQwggEDYkkEyjMgIIhJWhxXADCCAQ6gwiAqHOuHgVCKMI0nIQDguTiH9/cvG55oRjDg9ciOdC/MhFnzYvbtraEwWl/X7Ll5obr7645zIC4bCix7jaCSAQao8Q/g2bAALhsCPA+JoJIBBqjg6+aSCAQKghCviglQACoc7IIBDqjMvQBELdOIxZ/+Bj5uwLrjA3X3tZIBquWn2h+fj5Z/V2NspuyM9cd0vvKDQ5CHVFlByEuuJBDkJd8SAHoa54iDfkINQVE3IQ6ooHOQh1xYMchLriId6Qg1BXTMhBqCse5CDUFQ/xhhyE+mIS98jLEWP9GHZ7KDsGH37s6UAAjIuF0ir+GAKhrugiEOqKBwKhrnggEOqKBwKhvnggEOqKCQKhrnggEOqKBwKhvnggEOqKCQKhrnggEOqLR5JHQxEIZVfeps3bEgkNq4px1KfQh6wC4Sc++Ydm19RsPSLecC9vX/cP5tjj3miOPOoNDZ9pPab3w+9/z2zdutWsevs76+Fww73cumWLufWWvzXnffRjDZ9pfaZ34+c/az5w1m+ZvZcurY/TDfb0q1/5J3PIoa8zxx3/xgbPsj5Te/zRh81PHviR+bUz3l8fpxvs6c6dO8wNn/us+djvXtTgWdZran93043mtPf8utl//wPr5XhDvf3Ot+8KZvbLb1vV0BnWa1rPbHzSfOdbd5v3f/A36+V4g729+k+vNJdffnmDZ1j/qXkXCJNy+GnCKDkIr7vpdiMiYRaBUHzfOTWDQKgpiPiihsDE+KgZHR0xO3fNqPEJRyCgicCSRePm1R0zZm5uTpNb+AIBFQTGx0bNxPiI2b6T3yEqAoIT6ggsXjhudtj3WLOz/A5RFxwcGjqBsbERMzk+Zn+HTA/dFxzYTWDvxRPgUEzAu0CorUhJUmzEx345CC+96oZAQAwvipQoXuG4NlQCFCkZKn4GrwEBipTUIEi4ODQCFCkZGnoGrgkBipTUJFC4ORQCFCkZCvaBg1KkZCCioTZovUAoR4sl32B4XXLl9ebue9f3HqOK8VDXJ4PXnAACYc0DiPuVE0AgrBwxA9SYAAJhjYOH614IIBB6wcwgNSWAQKgzcAiEOuMSeuVdIJQjxu9adZK58Nz3qSAj/jyyYeM8X+J5EKNtjly5wty2dk2vPUVKVISx5wRFSnTFgyIluuJBkRJd8RBvqGKsKyYUKdEVD4qU6IoHRUp0xUO8oYqxrphQpERXPChSoise4g1VjPXFJO6Rd4Fw3R13m89cd8u8XXv6MaV7iECoK3oIhLrigUCoKx4IhLrigUCoLx4IhLpigkCoKx4IhLrigUCoLx4IhLpigkCoKx4IhPrikeSRd4FQ8vv1u4ZVxbhouBAIi5Krph8CYTVci1pFICxKrpp+CITVcC1jlR2EZei574tA6J5pGYsIhGXoue+LQOieaVmL7CAsS9BtfwRCtzzLWkMgLEvQfX92ELpn6tqid4HQ9QQ02KNIiYYo4INGAuQg1BgVfNJEgByEmqKBL9oIkINQW0TwRxsBchBqiwj+aCJADkJN0djtCzkIdcYl9AqB0EF8EAgdQMREIwkgEDYyrEzKIQEEQocwMdU4AgiEjQspE3JMAIHQMVDMNYoAAqHOcCIQ6ozLUAXCaNGPNZ84z6w+/RQjR49PPvEYc+PVF+smluAdAmHtQobDngggEHoCzTC1JYBAWNvQ4bgHAgiEHiAzRK0JIBDWOnw4XzEBBMKKARc0j0BYEJynbt53EIo4uN/ypYEQuGr1hebj558VCITXfOFL5tYvf6N2xUvIQehppWYchhyEGUF5akYOQk+gMw5DDsKMoDw2IwehR9gZhiIHYQZIHpuQg9Aj7AxDkYMwAyTPTchB6Bn4gOHIQagrHuQg1BUP8YYchPpiEvfIu0AoOwVvvvYyc8Ixh88TCKW68aVX3WAoUqJ/0Wj2EIFQV3QQCHXFA4FQVzzEGwRCXTFBINQVDwRCXfFAINQVD/EGgVBXTBAIdcUDgVBXPBAI9cUjySPvAqHsGvzsp35/D4GQHYT1WDDavUQg1BUhBEJd8UAg1BUPBEJ98UAg1BUTBEJd8UAg1BUPBEJ98UAg1BUTBEJd8UAg1BcPFQLhJVdeb+6+d31wlDg8YnzEYQebsy+4wpzx7reZT33yo/UgF/GSHIS1CxkOeyJADkJPoBmmtgTIQVjb0OG4BwLkIPQAmSFqTYAchLUOH85XTIAchBUDLmieHIQFwXnq5n0HocwrPE4cneP5HzrDXHju+zxN2+0wCIRueWKtOQQQCJsTS2ZSDQEEwmq4YrUZBBAImxFHZlEdAQTC6thiuf4EEAh1xhCBUGdcQq+GIhDqRpLfOwTC/Mzo0Q4CCITtiDOzLE4AgbA4O3o2nwACYfNjzAzLEUAgLMeP3s0mgECoM74IhDrjMjSB8CMXfdrcc/+DexQjkeIlJ594TFDduE4XVYx1RYschLriQQ5CXfEgB6GueIg3FCnRFRNyEOqKBzkIdcWDHIS64iHeUKREV0zIQagrHuQg1BUP8YYqxvpiEvfI+w5CyTv4wfe+Y4/jxBQp0b9Y6uAhAqGuKCEQ6ooHAqGueCAQ6osHAqGumCAQ6ooHAqGueCAQ6osHAqGumCAQ6ooHAqG+eCR55F0glJ2Caz5xnll9+inz/AnzEj5w59p6kOt6yQ5CXeFCINQVDwRCXfFAINQVDwRCffFAINQVEwRCXfFAINQVDwRCffFAINQVEwRCXfFAINQXDxUCYdN2EApUchDWY7HjpX8C5CD0z5wR60WAHIT1ihfe+iVADkK/vBmtfgTIQVi/mOGxPwLkIPTHOs9I5CDMQ8t/W+87COUo8XU33W5uvvYyc8IxhwczXv/gY+bsC64wda1kjEDof+EyYj0IIBDWI054OTwCCITDY8/I+gkgEOqPER4OlwAC4XD5M7puAgiEOuODQKgzLqFX3gVCGTg8ThxFk3TsWDe63d4hENYlUvjpmwACoW/ijFc3AgiEdYsY/vokgEDokzZj1ZEAAmEdo4bPvgggEPoinW8cBMJ8vHy3HopA6HuSVY5HDsIq6ea3TQ7C/Myq7EEOwirp5rdNDsL8zKruQRXjqgnns08Owny8qm5NDsKqCeezTw7CfLx8tKaKsQ/K2ccgB2F2Vj5akoPQB+V8Y1DFOB+vYbRGICxJHYGwJEDH3REIHQMtaQ6BsCRAx90RCB0DdWAOgdABRIcmEAgdwnRgCoHQAUSHJhAIHcJ0ZAqB0BFIR2YQCB2BdGQGgdARSIdmEAgdwqzI1FAEQilUsmnztsQpUcW4oki3xCwCoa5AIxDqigcCoa54iDcIhLpigkCoKx4IhLriUVYgnJ6bM8/OTOuaVEZvnp2eNjNmLmNrf80ev+1Ws+Lt7zSTy/ZLHHTL7KzZOjvjzyFHI+20dl6o4VpZ8KPvG2H+wglvdkQCM2UI7P3Cz8z+639oHv/V08qYoa9DAsf+z7Xm8ssvd2gRU64JeBcIzzznUrPf8qXmxqsvdj2XodkjB+HQ0DOwcgLkIFQeINwbOgFyEA49BF4c2DQzY16Zm8091k4rqBT9kPzU9FTu8aTDJvvh9tVCvhrzfEEh4qmpZF9HR40ZGxkxUzPVCDMvzU2bV2arsV0IfsZOspZkTXFBAAIQgAAE6kTg4/ssN392+CF1crl1vnoXCI879RxT54IkSSsEgbB19w0TzkgAgTAjKJq1lkBTBcJ+gthWK25sTRE3XrGC2KaUXSODdpQ81UcwedaKZdMpOtALs9NGhLgsV1HRLYtt2kCg6QTGrdj72rHxWk7ztePjZmxuRJ3vk+MjZtoK6Gk69z5jo2bp6Jg6vwc5tMA2OHCsfn7LvA6p6RofFJM6Pj9u178Uu3p5e7E/mNVxztp9Pm7BQvMfD1qm3c1W+4dA6CD8CIQOIGKikQQQCBsZViblgMBOK5I9bwWt/fdZYF7atsvMdD/dvWAfk+eSLtnZ9UrKDi050rQtpV8gutnnk64Z+9wz9uhc2vX0TPqbajkqKEcGuQYTWG4/6C4Zsdvhcl4LrKBywGgxQeXQiYmco3WaL7fb9pbYcfNek7bPgQWFiEPHk32dHB8zCyZHjbzPquLa17JdMpp/rlX4ksemrCVZU1wQoIoxawAC6QSoYqxzdVDFWGdcQq+8C4RyxPhdq04yF577Pt1kMnpHkZKMoDw1IwehJ9AZhyEHYUZQnpqRgzAddPzIXjTf1A6rgb0QEcrkGOWurjC20z4XPVYp7XZ0tbidxuYhiuxqe94KavGdav/16181a9+2ymxevNjTKvAzTD9BbKkVN9J2tCy0GtoBY8li0fjInHltH7Gs364NsbkwRQeKikTrv/E1s/zgFWbFLxyXCCpNyPJDtX2jkINQV8zL5iDUNZtmeEOREl1xpEiJrnhQpERXPMQbipToi0ncI+8C4bo77jafue4Wc9e6a/TTyeAhAmEGSB6bIBB6hJ1hKATCDJA8NqmTQLjV7njbEtkt93Qkn1o86brsZAuzccV3y0WPlkpetU0Rm8PcARcetTvrq/9s/nnVqeblxUuClXCA3RW0wCTvNFtuj8osSdmhtY/d9bU0ZddXv51dkt/t4D7HoQ5J2dklvsrxrwUFdsV5XPK5h6JISW5klXZAIKwUb27jCIS5kVXeAYGwcsS5BkAgzIWr8sYIhJUjzj0AAmFuZN47eBcIJQdhv4sqxt7XQKMGRCDUFU4EQl3xKCIQivC2wwprO+yOuR1WtNtpqzjKjjr5ufN4+Lz92e6cC563O+c6z88F/99uj88G/W172UEX/rzDPi555QI7tv12ed6M2N15+Ys5lCG90IpcC+zuMvm+0Apmi+yRwwXWj+D/VnhbaH+OPh8+Jm0X2rZBf+tA8HhgQ+zNmUXysxX7pM1ue51xws1sVDEuEzn3fREI3TMtYxGBsAw9930RCN0zLWsRgbAsQbf9EQjd8ixrDYGwLEH3/REI3TN1bdG7QOh6AhrskYNQQxTwQSMBchAOJypyPFaOt8r38HhsmKNO8t6JKCdXPP9ctKKn5JaTHXbDuuI5tqIJ4iVn2PLIrjdJej9uhUi54rvlokdLZbeb7NALLw074JpapGRY64Zxm0VAkssvXjBmNtk8nVwQgMCeBMhByKqAQDoBchDqXB3kINQZl9ArBEIH8UEgdAARE40kgEBYLqxSMVV23L1ghbrwWG2Y/04qtoYCX3h0tl/l2HKeGJszbtTsEzneekgkT1y8SuKhERFubyvKyfHX8IrmcFtsH18esRkIfQWKI5Sd2zD7IxAOkz5jayeAQKg9Qvg3bAIIhMOOAONrJoBAqDM6CIQ64zJUgVDyEF561Q3zyKz5xHlm9emn6KaV4h0CYS3DhtMeCCAQ2iO33Wq1W+33rVbUE4Fvpz1OK7vz5DitfJfKtJtmZk24g69sbrywQITsupOjra+1eeSkKqlUJ93XCnJhhdJ4/rlosYbxoF+x6qkellZjhkAgbEwomUgFBBAIK4CKyUYRQCBsVDiZjGMCCISOgToyh0DoCGRFZrzvILzmC18y1910u7n52svMCcccHkxr/YOPmbMvuMKc/6EzalfdmCIlFa3MgmbJQVgQXEXdmpKDUI7bbrYC3xYr8MlOvi3ysxX1gp/tY5vtz1ttG3lssxX6tsxOm632yOtm+9w226bItZcV8oLCE/Y47bIR+7PdlSc7+KQQxbJgN9+4fcx+7+7Qk+ekjTw32ctwN3/kIjkIi/hOn+wEyEGYnZWPluQg9EE5+xjkIMzOykdLchD6oJxvDHIQ5uNVdWtyEFZNOJ99chDm4+WjNTkIfVAuN4Z3gXDV6gvNB9/7jj2EQBEOb/3yN2pX3RiBsNwCdN0bgdA10XL2tAmEUgxjqy2MIYJeKPAF4p59TEQ9Efw22y/Z7RcIf3O2XSD4zRo5xlvkkqO5y0Kxzwp9y0TU6x7XDUS94GcR+uS5jgAYiIFW+HN93BaBsEgEq+2DQFgt37zWEQjzEqu2PQJhtXzzWkcgzEus+vYIhNUzzjMCAmEeWtW3RSCsnnHeERAI8xLz3967QChVjJOOE4fHjqli7H8RNGlEBEJd0axKIHylK+DJrr2O2Bfu7rM/d3fydXbzWfHP7uQTkS9oFxTo6BSzyHPJUdxgN58V7YLdezZXXvB/u1NvWffnYPeefT7M1Se7+2Tnnwh+I0ry6iEQ5om6n7YIhH44Zx0FgTArKT/tEAj9cM46CgJhVlL+2iEQ+mOdZSQEwiyU/LVBIPTHOutICIRZSQ2vnXeBUNsOwo9c9Glzz/0PzotAXKQ885xLzSMbNgZtjly5wty2ds289uQgHN4CZmTdBAblIJTjt6HAJ7v2RNALdvYFAqAc5e3u4LPf5eju7p19s0aO/ea9JuR4rhzJDXbqWQEvOKIrR3O7R3btcd7Okd1wN1+422/U7B0pppF3XNpDII0AOQhZGxBIJ0AOQlYHBPoTIAchKwQC6QTIQahzdZCDUGdcQq+8C4TachCKYHnXumt6UbrkyuvN3feu7z0mAuKLm7b2REERC/dbvtTcePXFvT4IhLoXOd75JSDC3QZbfVe+njHT9pjunHl8x649CnE8L0U6Coh84WyyFOI4wFbaXThizCG2SMcCK/wdGKmu65cKo0EgmQACISsDAgiErAEIFCWAQFiUHP3aQACBUGeUEQh1xmVoAqEMrLmKcVgwJSyiIgLix88/q1dhWXz/zHW3zBMVEQh1L3K8c09AKvM+PjVtRcBdgRD4tBX75OfwsTwjvtYe0RXxTr4vsTv4lofHd+1uvwPkOWvs0K7Ad0BYqMMe7+WCQBMIIBA2IYrMoSoC7CCsiix2m0IAgbApkWQeVRBAIKyCanmbCITlGVZpwfsOwion48J2tFhKXCwU+/HHKFLigro7G+QgdMcyLgKGuwIfmdplnrWCYL9LxL4jJybNiY89YvbZ8arZ9xffZhZYUe9Ae0x3sf2+3H4PdwC68xhLgwiQg3AQIf/Pk4PQP/N+I5KDUFc8yEGoKx7kINQVD/GGHIS6YkIOQl3xIAehrniIN+Qg1BeTuEcIhBEiofgXFlHJKhBefvnl+iPdEg9vueUW86Y3vckcffTRLZlxuWk+K7sAd+00T+yyR4J32d2AO3eZJ6Y6P8tj222OwKRriRX5Vk5OmsMmJ4LvKxfYnyfsz93vr7E/y/Xd737XbNmyxZx22mnlHKW3EwKbN282f/3Xf21+7/d+z4k9jJQn8Bd/8Rfmwx/+sFm2bFl5Y1goTeC2224zhx12mHnzm99c2hYGyhN46KGHzA9/+ENz1llnlTeGhdIEduzYYeQ16+KLd6fZKW0UA6UIfO5znzNnnnmmOeigg0rZobMbAt/85jcDQ29/+9vdGMRKKQIbNmwwEhN5n8Wlg4BsrkI70RGLNC+8CYRh7sHzP3SGufDc983zp99zvvCFYmDUv6wC4UV/8EmzbXv/HVW+5tH2cdhBuOcK+Jnd7fdU9xhw8N0KgE/bQiBPyXf73C57XDjpkqIcK8bHzKE2j98h4+PBMd9DRsfNIXZnoDy23Bb2GHRVVcV40Lg8n0yAHYT6VgY7CHXFhB2EuuLBDkJd8WAHoa54iDfsINQVE3YQ6ooHOwh1xUO8YQehvpjEPfImECYV94g6Ey8G4hNdmBMxzDsYHTspB+GlV91gopWOyUHoM1qMlUTgma4IKALgxmkrCNr/Py3fbV7Ap+1jafL1UrsT8BB7HFjEv0Ptrr9DRu2XfO8+tqxkrr9BVYyJJgTaToAchG1fAcy/HwFyELI+INCfADkIWSEQSCdADkKdq4MchDrjEnrlTSA87tRzTHh0NwlJKNJFhTcf6JKKjvQTLqli7CMqjJFEIBD8Zro7AO33p+z/ZQegCIAiDCbvAzRGRL5g95/sBAxEQCsI2u+dx8aNiIRVXQiEVZHFblMIIBA2JZLMowoCCIRVUMVmkwggEDYpmszFNQEEQtdE3dhDIHTDsSorrRYIwyPESXCjYqaIgo9s2Bg0O3LlCnPb2jXzurCDsKrl2S67s3NzHcFPxL/YMeBQBEwjIsd9Dx2bDI4CixAY7Abs7gJcYSv/ynHhYVwIhMOgzph1IoBAWKdo4atvAgiEvokzXt0IIBDWLWL465MAAqFP2tnHQiDMzmoYLb0JhPGjuvHJDtrJNww4WcakinEWSv7aaM9BOB2IgHYXYHD8V3IAznR2AAaC4LQ9HjyVCmt/K/Id0jsK3NkFKCJg8JgVBhePVLcTsGgEyUFYlFw1/chBWA3XMlbJQViGnvu+5CB0z7SMRXIQlqHnvi85CN0zLWuRHIRlCbrtTw5CtzzLWiMHYVmC7vuTg9A9U9cWvQmEl1x5vfnJT5/YY/ddOKFBOQpdT9yVPQRCVyTd2NEgEE5ZEXB3UZDwGPCu3mPPWnEw7TowEPys+BctDBL8bIuFjE+ahSMjbkB5soJA6Al0xmEQCDOC8tgMgdAj7AxDIRBmgOSxCQKhR9gZhkIgzADJcxMEQs/ABwyHQKgrHgiEuuIh3iAQ6otJ3CNvAqEMLLsI5bpr3TXz/JDHN23eNq/wh350HQ8RCHVFypdAuNNYEbBbBTg8/tvLEWgFwOfsUeG066CICCi7AFcER4F3Hw2eNPUSAfutAARCXfcHAqGueIg3CIS6YoJAqCseCIS64oFAqCse4g0Coa6YIBDqigcCoa54IBDqi0eSR14FQnFAdhLe/rVvz/Pl5BOPMTdefXE9iCV4SQ7C2oaur+Pb52Y7u/6m7THgXl5AezTYCoMbrQD4fB8R8OBu/r/gCLAUBJm3I3DcjNdsJ2DRCJODsCg5+rWFADkI2xJp5lmEADkIi1CjT5sIkIOwTdFmrnkJkIMwLzE/7clB6Idz0VG8C4RFHdXcD4FQc3T6+/aKiIBTncIgUiAkzAX49FTnSPCLs2m1gc3uo8BBLsBOHsCoIKgvI6D/OCEQ+mfOiPUigEBYr3jhrV8CCIR+eTNa/QggENYvZnjsjwACoT/WeUZCIMxDy39bBEIHzBEIHUCs0MQ2KwI+bUXAp4LiILYgiP2+sVskRETAl1JEQBH4DrUFQFaEVYFtkZCgMIh9LKwQXKHbjTCNQNiIMDKJCgkgEFYIF9O1J4BAWPsQMoGKCSAQVgwY87UmgECoM3wIhDrjEnqFQFgyPuQgLAnQYXepEPwP//z/mVdff6R5csUh5nG7C3CDFQDlS55Luw4c61QHfr0tAnKE3QW4cmLSrOz+f+ko+wDLhIgchGXoue9LDkL3TMtaJAdhWYJu+5OD0C3PstbIQViWoNs1H1u4AAAd9UlEQVT+5CB0y9OFNXIQuqDozgY5CN2xdGGJHIQuKLq1QZEStzyrsIZAWJIqAmFJgCW7yw7AO3e8au6yX3duf9W8997vmB8ccqh56LUHz7MsIqAIf0faHYCH2R2BIgautD+LELhkBBGwZBhSuyMQVkW2mF0EwmLcquyFQFgl3fy2EQjzM6uyBwJhlXTz20YgzM+s6h4IhFUTzmcfgTAfr6pbIxBWTTi/fQTC/Mx890AgLEkcgbAkwJzdd9rjwvfu3G5Fwe3m69tfMY/YXYLR6/z7vmdmjzjK7LfyCETAnGyraI5AWAXV4jYRCIuzq6onAmFVZIvZRSAsxq2qXgiEVZEtZheBsBi3KnshEFZJN79tBML8zKrsgUBYJd1ithEIi3Hz2QuB0AFtchA6gNjHxP27dpj7rCB4n/0uP0v+wPA6enLSnDSx0Jy4oPP1hokF1TqD9VwEyEGYCxeNW0iAHIQtDDpTzkyAHISZUdGwpQTIQdjSwDPtTATIQZgJk/dG5CD0jjzXgAiEuXAlN0YgdAAxYkIKidy/04qBU1YYlO/2K7yW2ZyAJy1YZE6a7IqCkwvMEls8hEsnAQRCnXHBKz0EEAj1xAJP9BFAINQXEzzSRQCBUFc88EYXAQRCXfEIvUEg1BmX0CsEQgfxQSAsB1EKiIS7A0UM/Hd7hPj5mZme0eNs7sBAFOzuEjzc5g/kqgcBBMJ6xAkvh0cAgXB47BlZPwEEQv0xwsPhEkAgHC5/RtdNAIFQZ3wQCHXGBYHQUVzIQVgM5BMzU8HuQDk6LMeGf7RrZ8/Q/nZHoBwX7omCdpfggoyFRP7Xv/yjOero483Kw48q5hi9nBIgB6FTnKWNkYOwNELnBshB6BxpKYPkICyFz3lnchA6R1rKIDkIS+GrpDM5CCvBWtgoOQgLo6ukIzkIK8Fayig5CEvh89KZHYQlMSMQZgO43RYXkd2BwZFhySVov784u3uX4JusCHiiPTZ80sJFgTgolYaLXAiERahV1weBsDq2RSwjEBahVm0fBMJq+ea1jkCYl1i17REIq+Wb1zoCYV5i1bdHIKyecZ4REAjz0Kq+LQJh9YzzjoBAmJeY//YIhCWZIxCmA5QKw0GBkW4ewZ9M7d4l+Jqx8c6RYREFu9/HR0ZKRsMYBMLSCJ0aQCB0irO0MQTC0gidG0AgdI60lEEEwlL4nHdGIHSOtJRBBMJS+CrpjEBYCdbCRhEIC6OrpCMCYSVYSxlFICyFz0tnBEIHmMlB2IG4bdbuEuzuDrxvl606bIXBrfax8AqODUtxke5OwRVWJORqNgFyEDY7vsyuPAFyEJZniIXmEiAHYXNjy8zcECAHoRuOWGkmAXIQ6owrOQh1xiX0CoHQQXzaLBA+ZHcJ3meLitxvcwjKseGfRnYJrhif6OQSnJCKwwuCnIJc7SKAQNiueDPb/AQQCPMzo0d7CCAQtifWzLQYAQTCYtzo1Q4CCIQ644xAqDMuCIQO49ImgfAlW104ODbc3SkoP7/S3SU4ZpkGOQQDQbBzdPggdgk6XGn1M4VAWL+Y4bFfAgiEfnkzWr0IIBDWK154658AAqF/5oxYHwIIhDpjhUCoMy4IhI7i0oYchD+2uwLDAiOyW/Dx6akevdfZXYKyM/BEKTJiBcE32+PDw7zIQThM+nuOTQ5CXfEgB6GueIg35CDUFRNyEOqKBzkIdcWDHIS64iHekINQV0zIQagrHuQg1BUP8YYchPpiEveII8YlY9REgfAFW124Iwjao8PdysO7zFxAatKMBDsDA1FQiovYrwNGZe+gjguBUEccQi8QCHXFA4FQVzwQCPXFA4FQV0wQCHXFA4FQVzwQCPXFA4FQV0wQCHXFA4FQXzySPEIgLBmnpgiEPxAhMHJs+MnILsHXj09aQbCTQ1AEweMnFpSkVl13BMLq2BaxjEBYhFp1fRAIq2Nb1DI7CIuSq6YfAmE1XItaRSAsSq6afgiE1XAtY5UdhGXoue+LQOieaRmLCIRl6FXTlx2E1XB1aRWB0AHNOuYgfHZ6upNL0AqD90/Z7zu2m7De8OKR0c7uQHtc+Bclp6D9vu/oqANSmGgbAXIQti3izDcvAXIQ5iVG+zYRIAdhm6LNXIsQIAdhEWr0aQsBchD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SYSTEM TIMEABcaption
00.010.00000050.000000Initialized state
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
30.322.25000037.750000
40.423.12500036.875000
50.523.56250036.437500
60.623.78125036.218750
70.723.89062536.109375
80.823.94531236.054688
90.923.97265636.027344
101.023.98632836.013672
111.123.99316436.006836last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initialized state\n", "1 0.1 17.000000 43.000000 first reaction step\n", "2 0.2 20.500000 39.500000 2nd reaction step\n", "3 0.3 22.250000 37.750000 \n", "4 0.4 23.125000 36.875000 \n", "5 0.5 23.562500 36.437500 \n", "6 0.6 23.781250 36.218750 \n", "7 0.7 23.890625 36.109375 \n", "8 0.8 23.945312 36.054688 \n", "9 0.9 23.972656 36.027344 \n", "10 1.0 23.986328 36.013672 \n", "11 1.1 23.993164 36.006836 last reaction step" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = dynamics.get_history() # Revisited from earlier\n", "df" ] }, { "cell_type": "code", "execution_count": null, "id": "3f3556f4-2474-4233-b6f9-d05ec856dd13", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f72f4988-4e4b-4268-9f4a-e36300c9dcf1", "metadata": {}, "source": [ "## PART 2 - Now investigate A_dot, i.e. d[A]/dt" ] }, { "cell_type": "markdown", "id": "0ddc7f18-dcc7-4563-b6f7-75049d944669", "metadata": {}, "source": [ "NOTE: there's actually no need to compute this; it can be automatically saved during the reaction, as demonstrated in experiment `react_2_b`" ] }, { "cell_type": "code", "execution_count": 21, "id": "5ee8ec14-442f-4e76-bc86-26b8791f7e70", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10.0,\n", " 17.0,\n", " 20.5,\n", " 22.25,\n", " 23.125,\n", " 23.5625,\n", " 23.78125,\n", " 23.890625,\n", " 23.9453125,\n", " 23.97265625,\n", " 23.986328125,\n", " 23.9931640625]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = list(df.A)\n", "A" ] }, { "cell_type": "code", "execution_count": 22, "id": "a390ed46-f014-414f-9b14-69f6da95dc41", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(A)" ] }, { "cell_type": "code", "execution_count": 23, "id": "b3b1b169-bae2-493b-b652-ce9e82b2ddab", "metadata": {}, "outputs": [], "source": [ "A_dot = np.gradient(A, 0.1) # 0.1 is the constant step size" ] }, { "cell_type": "code", "execution_count": 24, "id": "35c7be1f-95ce-4bac-9fb3-02745a505f92", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([7.00000000e+01, 5.25000000e+01, 2.62500000e+01, 1.31250000e+01,\n", " 6.56250000e+00, 3.28125000e+00, 1.64062500e+00, 8.20312500e-01,\n", " 4.10156250e-01, 2.05078125e-01, 1.02539062e-01, 6.83593750e-02])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_dot" ] }, { "cell_type": "code", "execution_count": 25, "id": "f5fa1f8e-517f-4fd1-b3bf-51c12ab883f0", "metadata": {}, "outputs": [], "source": [ "df['A_dot'] = A_dot # Add a column to the Pandas dataframe" ] }, { "cell_type": "code", "execution_count": 26, "id": "e3773cfc-88ed-4565-a760-e90fa050d5b9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaptionA_dot
00.010.00000050.000000Initialized state70.000000
10.117.00000043.000000first reaction step52.500000
20.220.50000039.5000002nd reaction step26.250000
30.322.25000037.75000013.125000
40.423.12500036.8750006.562500
50.523.56250036.4375003.281250
60.623.78125036.2187501.640625
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80.823.94531236.0546880.410156
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concentration change per unit time (brown)" }, "type": "linear" } } }, "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(chemicals=[\"A\", \"A_dot\"], colors=['darkturquoise', 'brown'], \n", " ylabel=\"concentration (darkturquoise) /
concentration change per unit time (brown)\",\n", " title=\"Concentration of A with time (darkturquoise), and its rate of change (brown)\")" ] }, { "cell_type": "markdown", "id": "85d87078-8fc1-4166-95e1-343b546f9971", "metadata": {}, "source": [ "### At t=0 : \n", "[A]=10 and [A] has a high rate of change (70)\n", "### As the system approaches equilibrium : \n", "[A] approaches a value of 24, and its rate of change decays to zero." ] }, { "cell_type": "markdown", "id": "99cd0942-555b-444e-9c6f-ee1481a2a980", "metadata": {}, "source": [ "#### **NOTE:** The curves are jagged because of limitations of numerically estimating derivatives, as well as _the large time steps taken_ (especially in the early times, when there's a lot of change.) \n", "## In experiment \"react_2_b\", we revisit the same reaction using a better approach that employs **_adaptive variable time steps_** , and also automatically saves the reaction rates." ] }, { "cell_type": "code", "execution_count": null, "id": "531ce53b-7336-440e-bce4-716aafa6c692", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }