{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## A simple `A <-> B` reaction whose rate constants are to be estimated \n", "## from a given time evolution of [A] and [B] \n", "### (values given on a *variable-time* grid.)\n", "\n", "Assume the reaction is known to be 1st order (won't verify that.) \n", "\n", "In PART 1, a time evolution of [A] and [B] is obtained by simulation \n", "In PART 2, the time functions generated in Part 1 are taken as a _starting point,_ to estimate the rate constants of `A <-> B` \n", "In PART 3, we'll repeat what we did in Part 2, but this time showing the full details of how the answer is arrived at\n", "\n", "LAST REVISED: June 23, 2024 (using v. 1.0 beta36)" ] }, { "cell_type": "code", "execution_count": 1, "id": "4d9b4808-b2ec-4b90-a604-f7fa69af39b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "3924c013", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from life123 import UniformCompartment\n", "from life123.visualization.plotly_helper import PlotlyHelper\n", "\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": null, "id": "75411c8b-f0c5-411d-9e12-1eaa423449f9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# PART 1 - We'll generate the time evolution of [A] and [B] by simulating a reaction of KNOWN rate constants...\n", "## but pretend you don't see this section! (because we later want to estimate those rate constants)" ] }, { "cell_type": "code", "execution_count": 3, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 12 / kR = 2 / delta_G = -4,441.7 / K = 6) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "# Instantiate the simulator and specify the chemicals\n", "dynamics = UniformCompartment(names=[\"A\", \"B\"], preset=\"mid\")\n", "\n", "# Reaction A <-> B\n", "dynamics.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=12., reverse_rate=2.) \n", " \n", "dynamics.describe_reactions()" ] }, { "cell_type": "markdown", "id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2", "metadata": {}, "source": [ "### Run the simulation" ] }, { "cell_type": "code", "execution_count": 4, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 40.0\n", " Species 1 (B). Conc: 10.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.set_conc([40., 10.], snapshot=True) # Set the initial concentrations of all the chemicals, in their index order\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 5, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "39 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 0\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 24, 'norm_B': 22, 'norm_C': 22, 'norm_D': 22}\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(initial_step=0.01, duration=0.5,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True)" ] }, { "cell_type": "markdown", "id": "199b6238-f6ed-44a8-8130-a003444d7658", "metadata": {}, "source": [ "### Plots of changes of concentration with time\n", "Notice the variable time steps (vertical dashed lines)" ] }, { "cell_type": "code", "execution_count": 6, "id": "a2c0e793-5457-46a5-9150-388c9f562cf0", "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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(title=\"Reaction A <-> B\",\n", " colors=['darkturquoise', 'green'], show_intervals=True)" ] }, { "cell_type": "code", "execution_count": null, "id": "f3007827-f052-4d96-8064-47b10a42ad91", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "042a23ff-84de-4273-ae7b-09b73b740b4c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "1f447754-5017-4b48-a4f5-fc9049b7de64", "metadata": {}, "source": [ "# PART 2 - This is the starting point of fitting the data from part 1. \n", "### We're given the data of the above curves - i.e. the system history, and we want to estimate the rate constants (forward and reverse) of the reaction `A <-> B`" ] }, { "cell_type": "markdown", "id": "b5f75cfb-45b4-4fd2-ad4c-c2a2084ca62d", "metadata": {}, "source": [ "Let's start by taking stock of the actual data (saved during the simulation of part 1):" ] }, { "cell_type": "code", "execution_count": 7, "id": "f26c98c3-802c-4c38-a726-06ac4a77211a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.00000040.00000010.000000Initialized state
10.00160039.26400010.7360001st reaction step
20.00352038.40058411.599416
30.00544037.56037612.439624
40.00774436.57922913.420771
50.01050935.43982914.560171
60.01327434.34453215.655468
70.01603833.29163216.708368
80.01880332.27948617.720514
90.02156831.30651718.693483
100.02488630.18414819.815852
110.02820429.11391220.886088
120.03152128.09338621.906614
130.03483927.12026222.879738
140.03882026.00675423.993246
150.04280224.95531225.044688
160.04678323.96247426.037526
170.05156122.83747727.162523
180.05633821.78772628.212274
190.06111620.80818929.191811
200.06684919.71136530.288635
210.07258218.70257531.297425
220.07831517.77475532.225245
230.08519516.75073433.249266
240.09207415.82534334.174657
250.10033014.82182935.178171
260.10858613.93430136.065699
270.11849212.99236237.007638
280.13038112.01880637.981194
290.14464611.04497938.955021
300.15891210.26564439.734356
310.1760319.51722240.482778
320.1965748.83436041.165640
330.2212258.25059341.749407
340.2508067.79183542.208165
350.2863047.46931342.530687
360.3289027.27462742.725373
370.3800187.18032842.819672
380.4413597.14814942.851851
390.5149677.14269642.857304last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 40.000000 10.000000 Initialized state\n", "1 0.001600 39.264000 10.736000 1st reaction step\n", "2 0.003520 38.400584 11.599416 \n", "3 0.005440 37.560376 12.439624 \n", "4 0.007744 36.579229 13.420771 \n", "5 0.010509 35.439829 14.560171 \n", "6 0.013274 34.344532 15.655468 \n", "7 0.016038 33.291632 16.708368 \n", "8 0.018803 32.279486 17.720514 \n", "9 0.021568 31.306517 18.693483 \n", "10 0.024886 30.184148 19.815852 \n", "11 0.028204 29.113912 20.886088 \n", "12 0.031521 28.093386 21.906614 \n", "13 0.034839 27.120262 22.879738 \n", "14 0.038820 26.006754 23.993246 \n", "15 0.042802 24.955312 25.044688 \n", "16 0.046783 23.962474 26.037526 \n", "17 0.051561 22.837477 27.162523 \n", "18 0.056338 21.787726 28.212274 \n", "19 0.061116 20.808189 29.191811 \n", "20 0.066849 19.711365 30.288635 \n", "21 0.072582 18.702575 31.297425 \n", "22 0.078315 17.774755 32.225245 \n", "23 0.085195 16.750734 33.249266 \n", "24 0.092074 15.825343 34.174657 \n", "25 0.100330 14.821829 35.178171 \n", "26 0.108586 13.934301 36.065699 \n", "27 0.118492 12.992362 37.007638 \n", "28 0.130381 12.018806 37.981194 \n", "29 0.144646 11.044979 38.955021 \n", "30 0.158912 10.265644 39.734356 \n", "31 0.176031 9.517222 40.482778 \n", "32 0.196574 8.834360 41.165640 \n", "33 0.221225 8.250593 41.749407 \n", "34 0.250806 7.791835 42.208165 \n", "35 0.286304 7.469313 42.530687 \n", "36 0.328902 7.274627 42.725373 \n", "37 0.380018 7.180328 42.819672 \n", "38 0.441359 7.148149 42.851851 \n", "39 0.514967 7.142696 42.857304 last reaction step" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = dynamics.get_history() \n", "df" ] }, { "cell_type": "markdown", "id": "543b6f5a-f54c-426e-8dc6-342b62d50078", "metadata": {}, "source": [ "#### Let's extract some columns, as Numpy arrays:" ] }, { "cell_type": "code", "execution_count": 8, "id": "9e3a5eda-d426-4aa3-b1fd-65730a4af8d2", "metadata": {}, "outputs": [], "source": [ "t_arr = df[\"SYSTEM TIME\"].to_numpy() # The independent variable : Time" ] }, { "cell_type": "code", "execution_count": 9, "id": "44a76d0e-5bf0-4d34-b37f-37c11eff9a8f", "metadata": {}, "outputs": [], "source": [ "A_conc = df[\"A\"].to_numpy()" ] }, { "cell_type": "code", "execution_count": 10, "id": "2955b13a-483d-4ad1-962e-f2d968a3d11b", "metadata": {}, "outputs": [], "source": [ "B_conc = df[\"B\"].to_numpy()" ] }, { "cell_type": "markdown", "id": "1d41750e-d6bf-4288-8555-51acfce9e82a", "metadata": {}, "source": [ "### Here, we take the easy way out, using a specialized Life123 function!\n", "(in Part 3, we'll do a step-by-step derivation, to see how it works)" ] }, { "cell_type": "code", "execution_count": 11, "id": "344c1ead-1de4-49f7-b3cf-7958513d10b4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total REACTANT + PRODUCT has a median of 50, \n", " with standard deviation 5.617e-15 (ideally should be zero)\n", "The sum of the time derivatives of reactant and product \n", " has a median of 0 (ideally should be zero)\n", "Least square fit: Y = -96.25 + 14.11 X\n", " where X is the array [A] and Y is the time gradient of B\n", "\n", "-> ESTIMATED RATE CONSTANTS: kF = 12.19 , kR = 1.925\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "B'(t) :
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least-square fit" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.14269565072923, 40 ], "title": { "text": "A(t)" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -26.191440680042838, 494.2046894671411 ], "title": { "text": "B'(t)" }, "type": "linear" } } }, "image/png": 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gOgKUVdeVhAmRAAmQAAmQAAmQAAmQAAmQAAlQVjkGSIAESIAESIAESIAESIAESIAEXEeAsuq6kjAhEiABEiABEiABEiABEiABEiAByirHAAmQAAmQAAmQAAmQAAmQAAmQgOsIUFZdVxImRAIkQAIkQAIkQAIkQAIkQAIkQFnlGCABEiABEiABEiABEiABEiABEnAdAcqq60rChEiABEiABEiABEiABEiABEiABCirHAMkQAIkQAIkQAIkQAIkQAIkQAKuI0BZdV1JmBAJkAAJkAAJkAAJkAAJkAAJkABllWOABEiABEiABEiABEiABEiABEjAdQQoq64rCRMiARIgARIgARIgARIgARIgARKgrHIMkAAJkAAJkAAJkAAJkAAJkAAJuI4AZdV1JWFCJEACJEACJEACJEACJEACJEAClFWOARIgARIgARIgARIgARIgARIgAdcRoKy6riRMiARIgARIgARIgARIgARIgARIgLIqOAbudg4L9qBn85m5mcjMSEPv4LieJ5CiWWekp2He7By0dY+kKAF9T7uoIAcDw+MYHZ/U9yRSMHPOlXoWnXOlnnUzs55v/IzrMdYm4x7OlbpVcXHRDN1SZr4KCFBWBSFTVimrgkNIaXMuwJTilhqMsioVp7LOKKvKUEsNxLlSKk6lnVFWleKWGoyyKhVn0nRGWRUsJWWVsio4hJQ25wJMKW6pwSirUnEq64yyqgy11ECcK6XiVNoZZVUpbqnBKKtScSZNZ5RVwVJSVimrgkNIaXMuwJTilhqMsioVp7LOKKvKUEsNxLlSKk6lnVFWleKWGoyyKhVn0nRGWRUsJWWVsio4hJQ25wJMKW6pwSirUnEq64yyqgy11ECcK6XiVNoZZVUpbqnBKKtScSZNZ5RVwVJSVimrgkNIaXMuwJTilhqMsioVp7LOKKvKUEsNxLlSKk6lnVFWleKWGoyyKhVn0nRGWRUsJWWVsio4hJQ25wJMKW6pwSirUnEq64yyqgy11ECcK6XiVNoZZVUpbqnBKKtScSZNZ5RVwVJSVimrgkNIaXMuwJTilhqMsioVp7LOKKvKUEsNxLlSKk6lnVFWleKWGoyyKhVn0nRGWRUsJWWVsio4hJQ25wJMKW6pwSirUnEq64yyqgy11ECcK6XiVNoZZVUpbqnBZMvq57/8XZw8c2lajoVz8lHz2otS83ZzZ6EYmPmaHL7yxc/i+e/8CC/89Rdw4Km9MI/t7OrD6y+/4KpToqwKloOySlkVHEJKm3MBphS31GCUVak4lXVGWVWGWmogzpVScSrtjLKqFLfUYDJlddP+Zy0hCxZTU8iK583FP/zNX0nN3a2dxSKgsRyr8nwpq4K0KauUVcEhpLQ5F2BKcUsNRlmVilNZZ5RVZailBuJcKRWn0s4oq0pxCwVL7+1FzqH3kH34fWRevYKcI4eE+vM2NqXr6vXbUXdQP/Xs89i4bsU0cQ0WNvOYosICq2vvLm11Ran1/xsPvjwt330HnsPeHWW+/oJ3NV/5wddRVro65Dl+7ds/xBtvH4vapynhgV8lK5dE3AmNJKDnL13HM1/6Fsy8/vWX71jxA7/M8/zJ979q/ZN5buZXInalKauCHwvKKmVVcAgpbc4FmFLcUoNRVqXiVNYZZVUZaqmBOFdKxam0M8qqUtwxBUvveIDs07XIOlOHbONP1ulTSO/r8/cxNRVTf+EONoXu6Sd3R909tSurzS138MXPPY3n/vKPfSHNGIH/9tqbR6xLar0CGyyJL/74Vbz0L298SEYDzyFan8Hf90pkJIG0K6umREc6lrIqZWgmphPKKmU1MSMvvqhcgMXHzQ2tKKtuqELsOVBWY2fmhhacK91QhfhyoKzGx82JVmljYx+IqV9QM262+kL1F+Ti9LIMvLdg0Prvb37qEU7Du1vovQ8zUod2ZdXcWfXuMHr7CxY78+/ml3lc4I5l4E6qKXyf+eRj06Q3ML94+owGLNw9q+Zuqvnl3VmNJqvR4jj5fe6sCtKlrFJWBYeQ0uZcgCnFLTUYZVUqTmWdUVaVoZYaiHOlVJxKO6OsKsX9oWCZly4au6a1vh3UrAsNvmMmMtJRvyIHh4uHcXIJcMr4c2MuUJAzG7uXPILffe4N4eRVyWrwTqq56+kVZO/3Qp1M8A5t4DGR+jSPM+Xa3OU1v+w+KErWzqpwYQQ6oKwKwDObUlYpq4JDSGlzLsCU4pYajLIqFaeyziirylBLDcS5UipOpZ1RVpXiRsbdOwGX9RqSalzemzY85Evi+uI8HFk4iuOLJyw5PbMIWFGwGuXFFdiyYBvKF1SgbP425GcXQNYDlmRfBhxqZ9U8Qe9O6bIlC/C9l37mu58zWDpjqUi4PgP78N7f6v234HtnA4+lrMZCP0mPpaxSVnUa2lyA6VSt6blSVvWsHWVVz7pxrtSzbmbWlFVna5c2NDj9vlNDTjPu3fUF7ZiTjWOGmHrl1BTUwnkrUfaBmG4xxLR8wXZrNzX4S5asRnvAkil75tOAvQ9PCrzEN9wDloIvAzZzN/u5eKXV9wAm7zGx7O4GMwjXZ7iqhrqPlbLq7GdAu94pq5RVnQYtF2A6VYuyqm+1/JlTVvWsIudKPetGWXWmblnnzwUIai0ym/zvLh3JTkftkjQcW/Jw59T8gyXLrV3TLcauqVdO5+Qa1/tG+ZIlq2aYUK+u8e54eh++ZIrhkVPnP7QjGviE3VBC6z0Nr5Safw++R9Z7r2jgrqcZr7pio/VO03Bf4fo0c/+nV3437cm/3vOJ9JThWHZWIz0Eig9YijZ6Xfx9yipl1cXD80OpcQGmU7Uoq/pWi7Kqe+04V+pbQe6sitcuo7Xl4dN6zXtPraf21iLN43/4UcOiDJz44LLek0uBrjVLP5BS85Leh5f3Fs2YF3MiMmXVDB7q4ULBUmlKWFdPv5WrKanmJb+dXX0+KYwkq2Yb8/tdPX0hX+kSKn6kS3a9wML1GfzaGvP4SKLqZRB4PoFFCfUgqMD7YvnqmpiHsDsbUFYpq+4cmaGz4gJMp2pRVvWtFmVV99pxrtS3gpTV2GuX3tMz7am9GXUnkdXV5evo5tx0Q04nfTunLRsWoXThB7umxdute07n5y2IPXBQC9myKpwQO3AFAT5gSbAMlFXKquAQUtqcCzCluKUG4z2rUnEq64yXAStDLTUQ50qpOJV2Rlm1hzvwfadpdceRe6PF17AvNw0nlkz55PT62vlYtLrSuqzXfCCSuXO6IG+hvUAxHEVZjQFWCh1KWRUsNmWVsio4hJQ25wJMKW6pwSirUnEq64yyqgy11ECcK6XiVNoZZTU07sxrV63Lec3LelF7DDPP+V8pY7ao/eB+U/OVMlfXFCJvU5X/nlPjyb0LZy52vI6UVccRaxmAsipYNsoqZVVwCCltzgWYUtxSg1FWpeJU1hllVRlqqYE4V0rFqbQzyupD3OkdDz6477QOU6dqkHv2LLL7B321uFr08GFI5p9Lq2fDU1GFMuOSXu/rZBbPMm5GVfxFWVUMXJNwlFXBQlFWKauCQ0hpcy7AlOKWGoyyKhWnss4oq8pQSw3EuVIqTqWdpaqspo2N+d53Oll7BJl1pzDrXruP/YOZfjltXDULI9u2Y/XKHb5XyizNX660TqGCUVYTXgJXJkBZFSwLZZWyKjiElDbnAkwpbqnBKKtScSrrjLKqDLXUQJwrpeJU2lkqyWrmpYvG7mktJmprkFZ7AoWXr/tYe9Ifyqn5tN7zK/IwWL4F8zbttu45Nd95uqJgldK62AlGWbVDKfWOoawK1pyySlkVHEJKm3MBphS31GCUVak4lXVGWVWGWmogzpVScSrtLJllNePeXWv3dOLkIUyeOoK5F5qQPeJfh12c/1BQ61fkom/LJuRU7vM9EGnl7DVK6xBPMMpqPNSSvw1lVbDGlFXKquAQUtqcCzCluKUGo6xKxamsM8qqMtRSA3GulIpTaWfJJKtpQ4PWface457T8ePvo6ChEQWdfT6ed/MfyunZZdno2rIeaTv2YsPyauudp6vnrFXKXUYwyqoMisnXB2VVsKaUVcqq4BBS2pwLMKW4pQajrErFqawzyqoy1FIDca6UilNpZ7rLatb5c5g4dRjDx99B3tlzKG7133c6nGVc1mvI6ZllmWjfZOyUVu7CktKHu6clc9cr5exEMMqqE1T175OyKlhDyiplVXAIKW3OBZhS3FKDUVal4lTWGWVVGWqpgThXSsWptDPdZDXjZqslpwNH30TO2TNYeukWMiYmfczOGa8zrV2agfsbV1hP7C2sfMJ6pcy6wlKlXFUES2VZPX/pOp750rfwyg++jrLS1Rbu1948gue/8yN88XNP47m//OMPleDFH7+Kl/7lDbzw11/Agaf2qihRQmJQVgWxU1Ypq4JDSGlzLsCU4pYajLIqFaeyziirylBLDcS5UipOpZ25XVbTe3uNy3oPo+/Ib5Bx+hQWXryB2X2jPkatc0w5Tcet9Usxum0bZu5+EpsW78CGeZuUckxEsGSWVa+MBnMNFM1N+5+dJqv7DjyHr3zxs5aIhpJZr9B+76Wfoea1FxNRMiUxKauCmCmrlFXBIaS0ORdgSnFLDUZZlYpTWWeUVWWopQbiXCkVp9LO3Cirk8Y9p501byDt1DHMu9iMxff6fUx6cw05XZKGlnULMbClDLm7P4KS9fuxcV6ZUm5uCJYKshq4c/q1b/8QR06d94mmKade6TR3Td+pOY3XX37BKk04WTW/96lnn8cT+7aH3H11Q11Fc6CsChKkrFJWBYeQ0uZcgCnFLTUYZVUqTmWdUVaVoZYaiHOlVJxKO3ODrGZeu4quml+h/+hbKDh3Huuv90xjUGvcd3pxVT4GjNfJ5O96Eut3fwbLClYo5eTGYKkmq97LfBsPvvyhcgQLqCmyXT3+X3KUrFziE9lgsXVjbUVyoqyK0DPaUlYpq4JDSGlzLsCU4pYajLIqFaeyziirylBLDcS5UipOpZ0lQlbTOzvQW/Mb9Bz5tfH03tNYdbUdc4b99502Fxo7Y6tmordsI2bsfBwrn/hzLJvjvvecKi1UiGAyZbWlpwXmH9VfK+eshPkn+CvUzujnv/xd67CffP+rHzo++JLgSDur3u+Fkl7V5+9EPMqqIFXKKmVVcAgpbc4FmFLcUoNRVqXiVNYZZVUZaqmBOFdKxam0MxWymjY+joHjb+PBwVeBuuNY1nQby7o8vvPsyDPedbo8B12b1yF752NY9vj/gUXLtyjloGMwmbL6zUPfxDcOfkM5hm/s/wb+7tG/Cyurwd8I9/AkU1YD5TOSrJp9Bh+v/MQdDEhZFYRLWaWsCg4hpc25AFOKW2owyqpUnMo6o6wqQy01EOdKqTiVduaUrN6vfRPdxs5pVt0pFBsPRVp/a9B3Xp50oGHFDNzdsBxjFdtRsOcTWLv9D5GVka303HUPJlNWX65/GT8991PlSP6i/C/w7NZnw8pqqKf9htoRpaz6EVJWBYcxZZWyKjiElDbnAkwpbqnBKKtScSrrjLKqDLXUQJwrpeJU2pksWW2/WosHh17DVN1RFF24ilLjvtO8sSnfuVwtzkLr+kUYKt+KvF1PYPljn8WsrHyl55pswWTKqtvYhNsZDb7c15s3LwNOUVk1n7r1xtvHpj0W2kRh3sTc3HLHohJ4w7IXU6TvU1Ypq26bECPlwwWYTtWanitlVc/aUVb1rBvnSj3rZmYdr6x2dLbg3ns/x/ipQ5jdcBFrmh9gca//vtO2gnRcK5mP3i2bkFW9H4v3/ynmzOdDkWSOlFSTVe97Uu08YMnkbApsqHeq8gFLMkdhAvsyn7j1T6/8zpLSwC148+bmzq4+3xO1TDEtKizw3ewc7fuUVcpqAod1zKG5AIsZmWsaUFZdU4qYEqGsxoTLNQdzrnRNKWJOxK6s9o72oPXwzzF8/B3MPNeA5ZfvYcN9/5pmJCsNl1fPQYdx32la1R7Mf/QAitZWxpwPG9gnkAqyGmyK464AACAASURBVEwj3EORQgmoV26DN9f46hr7Y8zVR3q305/50rfCvnDXPAFTagNfrhv4Qt5Q36esUlZdPfCDkuMCTKdqTc+Vsqpn7SiretaNc6WedTOzjiSrty+8j5vv/isma49g2aXb2H57AtkT/nO9vCQX7ZvWIHPHI1jy+DPI3FKlLwgNM09mWY2nHMEOEqqPYG+JJ47b26TEPavmbxz+wzMfx5oVixEoq6GuHw/8N7N4wXIb3IaySll1+4c8MD8uwHSqFmVV32r5M6es6llFzpV61i1YVjvvX8X13/8UIyfew9zzl7C1dRQL/M9Fwp3CLNxZvxQT26uxcP+nkbv7I5jKztH35DXPnLI6vYDe97CGe2Kwd6c11KXBmg+Faeknvaya96m2dXRbl/UGi6YMWR0aDfiVXDKNjCjnkpmRhvQ0YMzjf9hACp2+tqeaZtQsNysDw2OpOW61LZyReE5WOjwTkzD+xy+NCHCu1KhYAalyrtSzbrf7b+H2u6+g9/A7yDt7wXrf6boO/zplIDcdresWYqhiC/L3fBQrnvwspooX6nmySZh1Xk5GEp4VT0mUQFLLavDWuBOy2jMwJloDLdvnGMKTbtjq8Kj/vWJankiKJZ1urMBm5WWib5A74rqVftaMLIwYv2QwhZVf+hDgXKlPrQIz5VypR90GxvvRdOJ19NT8DjmnT2OJ8b7TbbfGkRbwe/Srq+agZ8t6ZFYbl/Y+8Wlkl27V4+RSMMs5s/iqnxQse9RTTnpZff47PwoJwbulHuqeVLON94bnaN/nZcCUnqifMhcdwEvbXFSMGFPhPasxAnPJ4bwM2CWFiDENzpUxAlN4+KWm99BV8wbS6o6juPE6NrcOYu6wP4E7C2bg3saV8FTswNxHPon83U/B+O26wgwZKl4CvAw4XnLJ3S6pZTW4dKEu+432tN9o36esUlZ1miK4ANOpWtNzpazqWTvKqp5141zpnrq1dl2xXinjOXkYcy5cwtrmTqzq9ufXMzPz4ftOt5Zj5u4nUfqHz6AntwDjHl6F4p4q2suEsmqPU6odlfKyahac71mNfdhzARY7Mze04ALMDVWILwfKanzcEt2Kc2WiKxBffM6V8XGT0apruBM3TvwSQ8feRl59PZZfuYfyO/7nLEwYm6TNa4rQvaUUWTsexSLjfadYs84X2u6ra2Tkyj7kEqCsyuWZLL2llKw6UTTurHJn1Ylx5VSfXIA5Rdb5fimrzjN2IgJl1QmqzvfJudJ5xt4InkkPms6/he6aXyHzzCksutSKLa3DmBXwSJDWxTPRvnE1Jit3Yd4jBzBjx/6wCVJW1dVOdiTKqmyiydEfZVWwjpRVyqrgEFLanAswpbilBqOsSsWprDPKqjLUUgNxrpSK80OdNd8+i7bD/xuTp46g6MJlbLjei6V9/sM6ZmfhtvFKmZFtFcZTe59C4SNPY2pWvq2kKKu2MLnyIMqqK8uS8KQoq4IloKxSVgWHkNLmXIApxS01GGVVKk5lnVFWlaGWGohzpVScuD9wFzeP/AIjx9/DrIbzWHWlDZva/PeUjmal4draBejbsgk5Ox/D4v2fwcTSZXElQVmNC5srGqWqrIZ6po4rChIiiUTkSlkVHA2UVcqq4BBS2pwLMKW4pQajrErFqawzyqoy1FIDca4Uwzk0Pogr536LvprfIvtMnfFKmVvYemsMOQFvu7uxrAAPNq9FWtVuzH/0j5BdvlMs6AetKatSMCakk2SW1URIXrxF9OYa3L5k5RK8/vILvn9WdU6U1Xgr+UE7yiplVXAIKW3OBZhS3FKDUVal4lTWGWVVGWqpgThXxo6z6cZRPDj0S6TVHsP8xmZsbBlA8YC/n7bCHNzdsBxjFZWYve8PMHvvJzCVkxt7oCgtKKvSkSrrkLKqDHXEQHYl1O5xomdFWRUkSFmlrAoOIaXNuQBTiltqMMqqVJzKOqOsKkMtNRDnyug4W/tu4O7Bf8fYifcxu+EiSpo7sK5jytdwIDcdLWsXYnDrFszY9QQW7P8TTC4ojt6x4BGUVUGACWyeqrIaKH0m/me+9C188XNP46V/ecNXjRf++gs48NRe39/NV2uePHPJ9/dXfvB1lJWutv7+tW//EG+8fWxaJb3f98YK7D+wrdkokoQGfu///tp/R1dPvy9O8M6rrKFEWRUkSVmlrAoOIaXNuQBTiltqMMqqVJzKOqOsKkMtNRDnyg/j7BnpRnPtGxg89hZy689i2eU72H7LgzS/n6J59Vx0bV6PjB37sHD/p5G2oUxqXex0Rlm1Q8mdx0iV1ZYWwPyj+mvlSsD8E/RlVwDNZqasBorfiz9+1RLXxoMvW72aMnrk1HnUvPai9ffX3jyC7730M9/fg2MHHu/NI5JYxpprsOzKRk5ZFSRKWaWsCg4hpc25AFOKW2owyqpUnMo6o6wqQy01EOdKYHJqEheb3kXX4TeQceYEFjTeQFnrEAqH/ajvLpiB+6Wr4KmsRuHeTyJv90eBjAyptYi1M8pqrMTcc7xUWf3mN4FvfEP9yZkx/+7vhGU1UACD5XHT/mcRvNP6qWefx3945uPTdl+9SXjbm7Jr59LdcPesmjl5ZTr4/3t3dZ0ATlkVpEpZpawKDiGlzbkAU4pbajDKqlScyjqjrCpDLTVQqs6V1zou4t77/w7PqcMoPN+Edde6sbrbj7Z3ZiZurl+Moa1bMXP3k9Y7TycLC6WyF+2MsipKMHHtpcrqyy8DP/2p+pP5i78Ann3WcVkNdWKBArvvwHPTLtE1j49VVkPtmIa6ZJk7q+qHWUwRKauU1ZgGTIIPTtUFWIKxSwlPWZWCUXknlFXlyKUETJW5sn3wPm6ceA3Dx99B3rlzWHX5PsrvTvgYTqQD19bMQ09ZKbLNV8o8/hl4Vj68L86tX5RVt1Ymel5SZTV6OKVHiFxaG2pnNZIgBu+8xruzSllVOkScC0ZZpaw6N7rk95wqCzD55BLfI2U18TWIJwPKajzUEt8mWefKEc8wLjW+hd6a3yDrTC0WXbqJra0jmDXmZ35r0Sy0b1qDqcpd1s5p9o5HEl+QGDKgrMYAy2WHUlanX2brvbQ2WFbNhyt1dvV96DUy3nKa97wG7rJ6H7gke2fVzC/UJcmyhxUvAxYkSlmlrAoOIaXNk3UBphRigoJRVhMEXjAsZVUQYIKaJ9Nc2XSnDu0HX8VU7REUXbiC0ht9WNbrB9tZkI07G5ZipGI7CvZ8/OErZfILEkRePCxlVZxhonpIBVkNZltdUYr/8n/9qfVQpXD3gYbalY30xF/vA5m8scwY5pODnZDVwFh8GnCiPjlR4lJWKasuHZoh00qmBZhO3GXkSlmVQVF9H5RV9cxlRNR5rrzdfxO3jrxqXNr7LgrOXcDq5nZsbvM/snc0Kw03Shagr3wzcnd9BMWP/gkmli6Tgc0VfVBWXVGGuJJIZlmNCwgbWQS4syo4ECirlFXBIaS0uc4LMKWgXBiMsurCothIibJqA5ILD9Fpruwb7cWV+t+g/+ibyD57BsuabmHbrXHkePxgW5YVoGPzOqTv2IsFj/4R0rdUuZC6nJQoq3I4JqIXymoiqLs/JmVVsEaUVcqq4BBS2lynBZhSMBoEo6xqUKQQKVJW9ayb2+fKC82H0FHzOtJqj2PBxWvY3DKA4gE/6/bCXNwtXQHP9irM2fsH1pN7p3Jn6FmMGLOmrMYIzEWHU1ZdVAwXpUJZFSwGZZWyKjiElDZ3+wJMKQzNglFWNSvYB+lSVvWsm9vmyus9V3Hn0C/gOXEQs89fRElzJzZ0+NkO5magde1CDG4rR97OJzDv0QOYKF6oJ3zBrCmrggAT2JyymkD4Lg5NWRUsDmWVsio4hJQ2d9sCTOnJax6MsqpnASmretYt0XNlx/ADXKv7NQaOvYW8s2ex/MpdbL81gXT/rae4tmouuss2INN4Wu+ixz6DifWlesKWnDVlVTJQhd1RVhXC1igUZVWwWJRVyqrgEFLaPNELMKUnm2TBKKt6FpSyqmfdVM+V4xNjuHD5HXTX/BoZp09i0cUWbGkdRuGwn9/dBXlo27gKk9t3omjf08je9TiQkaEnYAezpqw6CNfhrimrDgPWtHvKqmDhKKuUVcEhpLS56gWY0pNL8mCUVT0LTFnVs24q5srL7edx/+C/Y/JUDeZeuIwN13qwutvPq29mJm6uX4KRbdswa8/HMGfPH2KyqEhPoAqzpqwqhC05FGVVMtAk6Y6yKlhIyiplVXAIKW2uYgGm9IRSKBhlVc9iU1b1rJsTc+Xdgdu4cfJ1jBx7BzPrG7Dqahu23Z30AZpMA66VzEdv+SZkV+/Hwv1/As+qNXoCTGDWlNUEwhcMTVkVBJikzSmrgoWlrFJWBYeQ0uZOLMCUnkAKB6Os6ll8yqqedZMxVw6M96Op8W301PwGOafrsLjpJrbeGkP+qJ/JrUWz0LGpBKjajXn7/wgZ2/foCcxFWVNWXVSMGFOhrMYILEUOp6wKFpqySlkVHEJKm8tYgClNmMF8BCireg4GyqqedYt3rrxw8zgeHP4lpmqPYV7jVWy60Y9lvX4GnbOzcXf9Moxtr8TsPR/HzD1PYSq/QE9ILs2asurSwthIi7JqA1IKHkJZFSw6ZZWyKjiElDaPdwGmNEkGC0mAsqrnwKCs6lk3u3NlS+813Dr6S4yeeB8FDY1Yc/UBytr8j+wdy0zDjXXFGCgvQ675SplHPoWJZcv1hKJJ1pRVTQoVIk3Kqr61czJzyqogXcoqZVVwCCltbncBpjQpBrNFgLJqC5PrDqKsuq4kthIKN1d2DXfiasPv0H/kTeTWn8HSptuouOVBrsffbeuy2ejavA5pO/Zh4aN/gskt22zF5EFyCFBW5XBMRC+U1URQd39MyqpgjSirlFXBIaS0OWVVKW6pwSirUnEq64yyqgy11EDeufJO5wAuXDuMzsOvIe30CRQ3XkdZ6xAWDvjDtRfm4n7pSni2V2Gu8UqZXOOVMlO5M6Tmw87sE6Cs2mfltiMpq26riDvyoawK1oGySlkVHEJKm1NWleKWGoyyKhWnss4oq8pQSwt0ufMS2mr+N6ZO12Dm2Uasa+7Chg5/90O5GWhdtwhDW8sxc/eThqB+EhPFC6XFZ0diBCirYvwS2Zqymkj67o1NWRWsDWWVsio4hJQ2p6wqxS01GGVVKk5lnVFWlaGOO9D9gbu4duY3GDr2NvLqz2H5lXuoujWBdP+tp7ixqhDdW0qRuePRh6+UWV8adzw2dJYAZdVZvk72Tll1kq6+fVNWBWtHWaWsCg4hpc0pq0pxSw1GWZWKU1lnlFVlqG0HGvIM4uLl99B95NfIqjuFhZdaUH5zFEVD/i7uL8hDZ1kJxrZVo+iRpy1JRWam7Rg8MHEEKKuJYy8ambIqSjA521NWBetKWaWsCg4hpc0pq0pxSw1GWZWKU1lnlFVlqCMGamw7i7aDv8DEqSOYd+EyNtzow5ouf5O+mZm4vX4pRrZVIH/vxzHH+FO4ejHaukfccQLMwjYByqptVK47kLLqupK4IiHKqmAZKKuUVcEhpLQ5ZVUpbqnBKKtScSrrjLKqDPW0QK19N9B68g0MH38X+Q0XsPpKGyru+q/rnUoDrpXMR1/5ZuOVMo9br5TxrC7x9cG5MjF1kxGVsiqDYmL6oKwmhrvbo1JWBStEWaWsCg4hpc25AFOKW2owyqpUnMo6o6yqQd0z0o2mi79H35HfIvtMHZZcvoWKm+PIH/XHv7MoHw82r0Va1R4sePQAprbvCpsc50o1dXMiCmXVCapq+qSsquGsWxTKqmDFKKuUVcEhpLQ5F2BKcUsNRlmVilNZZ5RVZ1BPTk2i4eYxPDBfKVN7DPMbm7GpZQDLe/3xuguycbd0OcaMV8rM3vMJ5O36KCYLCmwlxLnSFiZXHkRZdWVZbCVFWbWFKeUOoqwKlpyySlkVHEJKm3MBphS31GCUVak4lXVGWZWHurn7Mm4d/SXGTh7E7IaLKGnuwJY2f/9jmWloWbcQA+Vllphar5RZtjyuBDhXxoXNFY0oq64oQ1xJUFbjwpb0jZJeVr/27R/ijbePTStk48GXp/39U88+j+aWO9a/laxcgtdffsH29ymrlFWdZgkuwHSq1vRcKat61o6yGn/d2gfv48q5NzF4/C3knj2LZZfvoNJ4pUyux9/nzWVz0FW23nha7z4U7/80xjdviT9gQEvOlVIwJqQTympCsEsJSlmVgjHpOkl6WTVF9O+/+pcoK11tFe/FH7+Kn//qfdS89qL1989/+bvo7OrzCap5fFFhAX7y/a/a+j5llbKq06zABZhO1aKs6lstf+aUVftVHPEM4/yNGnQffgPpp0+g+OINbGkdxqJ+fx8dhbm4t3EVJrZXo9DYOc2qfhRTM/LsB7F5JOdKm6BceBhl1YVFsZkSZdUmqBQ7LOllNbie5y9dxzNf+hZe+cHXLYHdd+A5fOWLn8WBp/Zah7725hF876Wf+WQ22vcpq5RVneYMLsB0qhZlVd9qUVbt1u5i53ncPfwqJk8ewpzzTVh/vQelD/yth3MycHP9Ygxv3Yq83R/DbOOVMhMLF9ntPu7jOFfGjS7hDSmrCS9B3AlQVuNGl9QNU05WzZ3Uq9dvWzIaLK5mpQP/zfx7oNgGf9+UXcoqZVWnGYILMJ2qRVnVt1qU1XC1u91/E9fP/AaDx36PmfUNWHnlPqruTCJj0t/ixqoi9G4pNXZN92P+o38Ez/pS5UOBc6Vy5NICUlaloVTeEWVVOXItAqaMrJo7pF09D68l8t6zKkNWewbGtCi07CRzsjKQnp6G4dGAm4dkB2F/0gmkp6VhVl4m+gb5SwbpcB3ucNaMLIyMTcAzEbCqdzgmuxcnkOpzZe9oj/FL4PfRdfhXSK+rxcJLLdh2cwxFQ3629xfMROfmEqTt2IWF+w8gvXofkJkpDl+gB86VAvAS3DQ/LwtDoxOY4FyZ4ErEHn7OrOzYG7FF0hNIGVn1VtK8Z/Wlf3nDElYZsmpOiKn4lZmRBsNVMebxv2Q9FTnods6GqyLX+EXDsCE9/NKLQE5WuiWqXH/pVbdUnCvrbp/EnXd/gfETNZh7/gpKr/ehpMtft/6ZmbhnvFLGU1mJwkc/gdn7PoapefNdVVjOla4qR0zJ5Bpz5ZhnEpNcnsTEzQ0H5xmX/fOLBIIJpJysmgA27X824j2rz3/nR77d11D3rAZ+n5cBc4dOp2mFl7bpVK3pufJpwHrWLhUesHS95ypaTv0Ko8ffQ37DBay+2o7Ku/56TRm/JLtessB4pcxmZO98HEWPPA3P6hJXF5RzpavLEzE5Xgasb+14GbC+tXMy86SXVVM2vU/+NUGar7I5cuo8nwYsOKpSYQEmiMiVzbkAc2VZbCVFWbWFyXUHJeNc2TH8AJcvvoPeo79FzpkzWNZ0CxW3PCgY9eO/syjfuLR3HdKr9mDB/j+Bp6LKdbWJlBDnSq3KNS1Zyqq+taOs6ls7JzNPelkNfIeqFyTfsyo+pJJxASZOxf09cAHm/hqFy5CyqmftkmGuHJsYRcPNY+ioeR1pdcexoPEaylqGsLzXX5OegmzcLV2B8YodmLv3D4wd1McwOXu2nkUzsuZcqW3pQFnVt3aUVX1r52TmSS+rTsIz++ZlwLwM2OkxJrN/LsBk0lTbF2VVLW9Z0XSV1fahNlx6/5/Rd+xN46m99Sgz3ndaft9PZdx4bkHLumKMbzfk1HjfaXrVXkwsXyELW8L74VyZ8BLEnQBlNW50CW9IWU14CVyZAGVVsCyUVcqq4BBS2pwLMKW4pQajrErFqawzXWS1b7QX5878Et1HfoXMupNYe60LO+4AMwKm+JtLZ6PfuO901p6njHeefhTjm7co46g6EOdK1cTlxaOsymOpuifKqmriesSjrArWibJKWRUcQkqbcwGmFLfUYJRVqTiVdeZWWR2dGEHDtUO49d6/AXXHsLzpjvG+0ykseviGN+vrwdxctG9cbV3SW/jIJzFWUYmpGXnK2CUyEOfKRNIXi01ZFeOXyNaU1UTSd29syqpgbSirlFXBIaS0ORdgSnFLDUZZlYpTWWdukdXekR7Ut9eh4+ivrftO5zc2Y4txaW/pAz+KEeO1Ebc2LMXItgrM2v0x5O16AhOLFitj5aZAnCvdVI3YcqGsxsbLTUdTVt1UDffkQlkVrAVllbIqOISUNucCTCluqcEoq1JxKussUbJqPhSpvu00bp77PTwnDmHOhUvYcL0X1calvRmT/tO/tXqBdWlvzq6PIH/3U/BsKFXGxs2BOFe6uTqRc6Os6ls7yqq+tXMyc8qqIF3KKmVVcAgpbc4FmFLcUoNRVqXiVNaZSlk9/6Ael5trMHz8HcyqP4dVxvtOzftO5w35T/fBgnx0l21A+o59mGM8tXfcvLQ3K0sZD10Cca7UpVIfzpOyqm/tKKv61s7JzCmrgnQpq5RVwSGktDkXYEpxSw1GWZWKU1lnTspqc/dlnLtfh76jv0P2mdNY2nQTVbenUNLlP73BmdnGfadrMFFZjULjqb1j26swWTRP2fnrGohzpa6VA19do2/pQFnVuHgOpk5ZFYRLWaWsCg4hpc25AFOKW2owyqpUnMo6kymrbYP3cLatDvdOvw3UHsP8i82ouDmOyrvTT+f2hmUYrdiOAuOpvVOVu+BZs1bZ+SZLIM6V+laSO6v61o6yqm/tnMycsipIl7JKWRUcQkqbcwGmFLfUYJRVqTiVdSYqq40dDTjb8Ab6jvwWs85dwPbbHuvS3tkj/lPoWFpkPBRpO2bufhITxntPzaf28kuMAOdKMX6JbE1ZTSR9sdiUVTF+ydpauqx+7ds/xBtvHwvJ6+knd+Mf/uavkoolZZWyqtOA5gJMp2pNz5WyqmftYpVVU04bbp/A4NG3MKP+DFZeabPkdEWP//z7Z+ehe/N6ZFQ/glzjwUjjFcalvbNn6wnIpVlzrnRpYWykRVm1Acmlh1BWXVqYBKclTVY//+Xv4uSZS9bpNB58OeRpbdr/rPXv1RWl+Mn3v5rgU5cTnrJKWZUzktT0wgWYGs5ORKGsOkHV+T6jyeqtvlbjqb11aD/1JjJOn8SCizeM+04nUH7fn5snMx1tpaus+07NJ/aa951OLF/hfPIpHIFzpb7Fp6zqWzvKqr61czJzKbJqSmjhnHzUvPairVz3HXgOXT39YaXWVicuOYiySll1yVC0lQYXYLYwufIgyqoryxI1qWBZ7RvtNe47rUXLhffgOXUYcy80YXPLkPVKmRkB02n7ymIMbdtqve/UvO90vKw8aiweII8A50p5LFX3RFlVTVxePMqqPJbJ1JMUWTV3VWPdKY2njRvBU1Ypq24cl+Fy4gJMp2pNz5WyqmftTFmtb6/DqUuHMGS8Umam8UqZkuYO69Lexf3+c+otykdvWSkydz2GnOr91n2nU3kz9TzpJMiac6W+RaSs6ls7yqq+tXMycymy6mSCbu+bskpZdfsYDcyPCzCdqkVZ1bVa13uuWk/t7T5uvFLmbB0WNrZYcrrxgf+MRnMy8WBTibVrOnPPx6z3nU4sWqzrKSdd3pwr9S0pZVXf2lFW9a2dk5lLl1XzkuAX/voLOPDU3ml5v/jjV/HzX71v+1JhJ09aZt+UVcqqzPHkdF9cgDlN2Ln+ubPqHFvRnjuGH1j3nd489w6mao+g6MIVbG0dtQQ1c9Lf+/2SJb5Xyoxvr4ZnQ6loaLZ3iADnSofAKuiWsqoAskMhKKsOgdW8W2Wy+tqbR/D8d36UFPepBtacskpZ1WkO4AJMp2pxZ9Wt1RqfGLN2Ti9fq8HI8XeR33AB66/3oPo2MG/In3V38RwMbitD/r4nMF6+x9o9ncrOdutpMa8AApwr9R0OlFV9a0dZ1bd2TmauTFbNV9ocOXWeO6tOVlNh39GecKkwFYaKgQAXYDHActmh3FlNbEGaOi+i/v4p9B19E7lnT2PZ5TvWzunaTn9eQzNz0Ll5LdJ37MOMXU9Y953OWLoImRlp6B3kL/YSW8HYonOujI2Xm46mrLqpGrHlQlmNjVeqHC1FVr27ptGghbo8OFobt3+fO6tcgLl9jAbmxwWYTtWanitlVW3t7g3csXZP7515G6g7jgUXmlFx24MqQ1ADv+6VrrDec5q/9+PWzqlnzdpp3+cv9tTWTVY0zpWySKrvh7KqnrmsiJRVWSSTqx8pshqIJNw9q8mFzX82lFXKqk5jmwswnapFWVVZrcHxAeu+06tNBzF+8iBmn7+ETTf6rd3T2SP+TDqWzsNQ+RZj5/SjSKvabb3zNNIXZVVlFeXF4lwpj6XqniirqonLi0dZlccymXqSLqvJBMfOuVBWKat2xolbjuECzC2ViD0P7qzGzixai/MP6nH+9kkMHHsLM+rPYtWVNut9pyt6/C0HZuehq2wDsqofQXb149bu6eScOdG69n2fsmoblasO5FzpqnLElAxlNSZcrjqYsuqqcrgmGcqqYCkoq5RVwSGktDkXYEpxSw1GWRXH2dp3w9o9ba99Cxl1J7Hw4g1U3p7E1vv+vicy0tG2cRUmjFfKzNr9pHXf6cSKlXEHp6zGjS6hDTlXJhS/UHDKqhC+hDamrCYUv2uDS5HVz3/5u/jJ978a00nG0yamAIoOpqxSVhUNNSlhuACTgjEhnVBWY8feM9Jt3Xd6o/FdeGprUNjQhC2tw9alvXkBU9eDlcUY3roNs4z3nU5U7sR4WXnswcK0oKxKQ6m0I86VSnFLDUZZlYpTaWeUVaW4tQkmRVbN+1QL5+TbftLvvgPPoaunPyleY0NZpaxq82k3EuUCTKdqTc+Vshq9dpNTk9bOaWPLUQwffwd55xqwrrnTktPF/f72vUX56N2yETnVjyHTuLzXvO90Km9m9ABxHEFZjQOaC5pwrnRBEeJMgbIaJzgXNKOsuqAILkxBiqya52XulJ48c8k6xcaDL4c8VVNqza/qbvPEsQAAIABJREFUitKYd2JdyM5KibJKWXXr2AyVFxdgOlWLsmqnWs3dly1B7Tr+JrLO1GJx001LTje1+1uP5WSifVOJ9UAk88FI5n2nE4uX2Ole+BjKqjDChHTAuTIh2KUEpaxKwZiQTiirCcHu+qDSZNV7pi/++FW89C9vhDzxL37uaTz3l3/seiixJEhZpazGMl4SfSwXYImuQPzxubP6kF37UJslpzcb3gVOHUHRhSvYemvMEtSsCT/ftpIlxv2m25G/5+PGf6vgKd0YP3yBlpRVAXgJbMq5MoHwBUNTVgUBJrA5ZTWB8F0cWrqsuvhcHUmNskpZdWRgOdQpF2AOgVXQbarK6ujEiHXf6eVrNRg58R4K6i9gw41eS07nD/rBdxfPwUB5GXJ3Po60Hfus3dOp7GwFlYkcgrKa8BLElQDnyriwuaIRZdUVZYgrCcpqXNiSvhFlVbDElFXKquAQUtqcCzCluKUGSyVZvdRxAWfv16L/6O+QXX8aKy7fs14ps7bTj3R4Zg46N69DetU+5O563LrvdHLefKnMZXRGWZVBUX0fnCvVM5cVkbIqi6T6fiir6pnrEJGyKlglyiplVXAIKW3OBZhS3FKDJbOs3um/ZV3ae/fM75FWdxzzG5ux/faEtXsa+HV/wwp4tldj5p4nrZ1TT8k6qYyd6Iyy6gRV5/vkXOk8Y6ciUFadIut8v5RV5xnrGEGKrHofnOQFEO4BSzoCipYzZZWyGm2MuOn7XIC5qRqx5ZJMsto/1mfJ6dXLh+A5eRCzGy5iU8ugJadzRvxcOpcUYWhruSGnH8Pk9p3WO0+RlhYbuAQfTVlNcAHiDM+5Mk5wLmhGWXVBEeJMgbIaJ7gkbyZFVpOcUcTTo6xSVnUa/1yA6VSt6bnqLqvn2s/g/J2TGDj6FmbU12PN1XZLTlf2+M9zYHYeeso2GK+TeRRZxmtlzN3TyTlz9C2akTllVc/yca7Us25m1pRVfWtHWdW3dk5mTlkVpEtZpawKDiGlzbkAU4pbajDdZLWl95r1YKQHtW8j/fQJLLzYgh23p7D1vh/LZEY62jauxmTlTuTt/qj11N6JFSulckt0Z5TVRFcgvvicK+Pj5oZWlFU3VCG+HCir8XFL9laOymrgu1eT6d2qgYOCskpZ1WmS4AJMp2rptbPaNdyJ+vY6XL/4PiZOHsLc85dRfnME1beBvIBpomNFMYYrKpC/+ymMGw9FGt+yVd+i2MicsmoDkgsP4VzpwqLYTImyahOUCw+jrLqwKC5ISZqsnr90Hc986VvWKT395G4sLp6Hd2pO4/WXX7D+bd+B5/CZTz7G96y6oOgyUuACTAZF9X1wAaaeuayIbtxZbe6+jCOXf4PumjeQd7be977TJX3+s+4ryrfuO83d9QQmtu+w7judmjlLFhbX98O50vUlCpkg50o962ZmTVnVt3aUVX1r52Tm0mT1U88+j43rVuAf/uav8LVv/xBvvH0ML/z1F3Dgqb1W/i/++FX8/Ffvo+a1F508H+V9c2eVO6vKB51AQC7ABOAluKkbZLV9qA0HW9/GvWNvYPJkDTbe6LPuO93U7oczlpOJrs3rkbPzMUxV7bHuO51YvCTB9BIXnrKaOPYikTlXitBLbFvKamL5i0SnrIrQS9620mTVfCKwV069u6yBsvram0fw/Hd+BNVPCg68FNlbxuAcTNFubnn4joSSlUt8u8He4yN9n7JKWdVpeuACTKdqTc81EbI6OD6A43dq0HT6dQwdfwfLL9+13ndqCmrWhD+/B2uXIc0Q08wdjxhyalzau3GTvqAlZ05ZlQxUUXecKxWBdiAMZdUBqIq6pKwqAq1ZGEdk1WQQKK/m3xMlq+blx4G7ueau75FT533/ZspsZ1efT1BNMS0qLMBPvv9Vq5TRvk9Zpazq9JnnAkynaqmX1c6RDuuVMk3Xjlj3nZqvlClrHbYEdf6gP5+e4jkYNC7tnWFc2ms+HMncPZ3KztEXroOZU1YdhOtg15wrHYTrcNeUVYcBO9g9ZdVBuBp3nfSyGlwb767vKz/4OspKV1v30n7li5/1Xa5sSvX3XvqZT2ajfZ+ySlnV6fPPBZhO1XJeVkc8w8ZDkU5bgjp0/PeYefYc1l7rsnZO13X644/MzEH35g3IMF4pk1n9iHXf6eT8BfrCVJg5ZVUhbImhOFdKhKm4K8qqYuASw1FWJcJMoq5STlYD750NFlezroH/Zv7dfGiUV2yDv2/Kblt3wBvsk2hgRDuVPOO+tIyMNPQPUVajsXLT980F2Nz8bHT0jropLeZig4BZt8ERD8bGJ20cHf6QW32tOHb7MJpr3zB2T2tQer3XklPzT+BX56YS412nj2Kqchc8lVXwlKwTipuqjTlX6ll5zpV61s3MuqggG31DHox7xOZKfQnom3nx3Fx9k2fmjhGQKqt2slR9z2pgTsH30sqQ1YnJKTunnXTHpKUBxv+QoqevdT3NRViqjludC5dufOimpqYQ64wzMDaAQ60Hcdy477Sn5i0svnTbep2MKadzAn7X1re8GJk79yB39yNA1Q5MVVcbH3LzU84vEQKcK0XoJbYt58rE8o83ujlXThpzJb/0I2B+5vhFAsEEpMmq29F6xfSLn3va9/ocGbLKy4C5s+r2sR+YHy9t06la03O1+4Alz6QHDe1nUHP9LXQf+ZV132nl7UlLUFf2+Pscmj0TI9sqrN3TMfOhSOalvXPn6gvIpZnzMmCXFiZKWpwr9aybmTUvA9a3drwMWN/aOZl5Ssiq9+FOgZfzeqGGuic18KnF0b5PWaWsOvkBld03F2CyiarrL5ysTk5N4uz9Wpxtr0Pn6XeRe+YMVje3Wzun2+7585vMSEfn5nVIr9qL9Op91n2nEytWqTuBFI1EWdWz8Jwr9awbZVXfupmZU1b1rp9T2Se9rAY/MCkYZLSn/Ub7PmWVsurUh9OJfrkAc4Kqmj4DZfVqV5PxYKQ6tFw6hLTa41hw8brvlTIzx/z5dK9aDE/FDmQb7zwd227snm7ZqiZZRvERoKzqORg4V+pZN8qqvnWjrOpdOyezT2pZ9V7mGwpg4Dtg+Z7V2IcYF2CxM3NDCy7A3FCF2HNoH7qP5v5zqLtcg+Fj72H2+UvYenPUEtQlff7+BooKjFfKbDVeKfMR67JeU1CnZs6KPSBbSCPAuVIaSqUdca5UiltqMF4GLBWn0s64s6oUtzbBklpWVVSBO6vcWVUxzmTF4AJMFkln+xmZGMZZ43Uy5uW9fafexYyz9Vh/vdu6tHdzuz/2eE4WeoxXymTuNJ/au9sS1IklS51Njr3HRICyGhMu1xzMudI1pYg5EcpqzMhc04Cy6ppSuCoRyqpgOSirlFXBIaS0ORdgSnHHFKyxo8ES1DsXDiKj7gSWNt32vVIme8LfVdfaFZis3Gm87/RRQ06NS3s3boopDg9WS4Cyqpa3rGicK2WRVN8PZVU9c1kRKauySCZXP5RVwXpSVimrgkNIaXMuwJTijhjMfN9pvSGnl68fxURtDeaeb0LlrQlLUBcM+pv2LSzEyNYKFO5/EkPl2zFYXoGp7Bz3nAgziUiAsqrnAOFcqWfdzKwpq/rWjrKqb+2czJyyKkiXskpZFRxCSptzAaYU97RgfaO9xs5prSWoQ8ffwaxzDdjYMmC9UmZdp//Q0bwc9JZvRk71Y5iorLae2ju5oNh40X0OBobHMTrOF90nroqxR6asxs7MDS04V7qhCvHlQFmNj5sbWlFW3VAF9+VAWRWsCWWVsio4hJQ25wJMKW5LTM8Ygtp27n1kn67Dyqv3rZ1TU1ADvzo3rgGq9iBjx8NXynjWrv9QopRVtbWTFY2yKouk2n44V6rlLTMaZVUmTbV9UVbV8tYlGmVVsFKUVcqq4BBS2pwLMGdxX+u+Yr3v9NrVGkzVHsP8C1d9953OHfbH7l26wJLS7J2PP3xqr/EH6ekRk6OsOls7p3qnrDpF1tl+OVc6y9fJ3imrTtJ1tm/KqrN8de2dsipYOcoqZVVwCCltzgWYXNwPhtut3dOGO6cweuI95DdcwNbWEUtQV3X7Yw3Nnmnca7oFuYacjpkPRTJeKTM5d25MyVBWY8LlmoMpq64pRUyJcK6MCZerDqasuqocMSVDWY0JV8ocTFkVLDVllbIqOISUNucCTAz32OSo9cReU1A76t5F7tmzWHut03rf6bZ7/r4n09PQVbbBuqwXVQ9fKeNZuVooOGVVCF/CGlNWE4ZeKDDnSiF8CW1MWU0ofqHglFUhfEnbmLIqWFrKKmVVcAgpbc4FWOy4L3VcsAS1tekQ0mtPYFFT68P7To0/M8f8/fWsXAyP8UCkrOr91mW94+XbYg8WoQVlVSpOZZ1RVpWhlhqIc6VUnEo7o6wqxS01GGVVKs6k6YyyKlhKyiplVXAIKW3OBVh03Hf6b1k7p403T8Bz8hDmnL+EilvjlqAu7fO3HyyajaGt5cgx7zs1Lus1BXVqVn70AHEeQVmNE1yCm1FWE1yAOMNzrowTnAuaUVZdUIQ4U6CsxgkuyZtRVgULTFmlrAoOIaXNuQD7MO7+sT5LTs3d0/669zDjbD02Xu+z5HRzu//48Zws9JSVImvHo5iq3IkxQ1AnlixVVj/KqjLUUgNRVqXiVNYZ50plqKUHoqxKR6qsQ8qqMtRaBaKsCpaLskpZFRxCSptzAfYQ97n2Mzh7vxa3Gw8h6/QpLL9y1/dKmewJf0m61q7AVNUuZFQ9Yt13Or5ps9J6BQajrCYMvVBgyqoQvoQ15lyZMPTCgSmrwggT1gFlNWHoXR2YsipYHsoqZVVwCCltnqoLsBs9zdYrZS7fOIbJkzUounAFVXemLEEtHvCXoL+4EKPbKpC9y3xqryGn5qW9OblKaxQuGGXVFWWIOQnKaszIXNEgVedKV8AXTIKyKggwgc0pqwmE7+LQlFXB4lBWKauCQ0hp81RZgHUOd6DekFPz0t7hE+8iv74BZa3Dlpyu7/AjH83LRX/5JuRUG/edVu6wBHVyQbHSmtgNRlm1S8pdx1FW3VUPu9mkylxpl4dOx1FWdarW9Fwpq/rWzsnMKauCdCmrlFXBIaS0ebIuwDyT475Xytw/9z6yz5zGmuYH1hN7TUFNm/Jj7txYgvSqPUgz/pj3nXrWrldag3iDUVbjJZfYdpTVxPKPN3qyzpXx8tCpHWVVp2pRVvWtlrrMKauCrCmrlFXBIaS0eTItwC53XTLuOz2F5qtHkFZ7DMWXbvheKTN32I+1b8kCS0rNV8qYl/Wa/x/p6Uq5ywhGWZVBUX0flFX1zGVETKa5UgYPnfqgrOpULcqqvtVSlzllVZA1ZZWyKjiElDbXeQF2b+COtXvacPcUxk4exJyGRmy9OWYJ6upuP8bhgpkY3LrFeqXMWEWVJaiThYVKOTsRjLLqBFXn+6SsOs/YiQg6z5VO8NCpT8qqTtWirOpbLXWZU1YFWVNWKauCQ0hpc50WYIPjA75XynSdfR85Z8+i9FqPJacV9/zYJo1d0u7N65FRvc94cu9uS049K1cr5aoiGGVVBWX5MSir8pmq6FGnuVIFD51iUFZ1qhZlVd9qqcucsirImrJKWRUcQkqbu30Bdv5BvSWoN5oOI6PuBJZevo3q2w/vO5015kfVs3IJJiqrkbnjEeuy3vHybUo5JiIYZTUR1MVjUlbFGSaiB7fPlYlgoktMyqoulfpwnnzAkr61czJzyqogXcoqZVVwCClt7rYFWGvvdeuVMo23TmDi5GHMPd+EytuTlqAu7fOjGSwswHCF8UoZ732n5itl8guUskt0MMpqoisQX3zKanzcEt3KbXNlonnoFJ+yqlO1uLOqb7XUZU5ZFWRNWaWsCg4hpc0TvQDrHu6y5LS+rRZ9de9jVv05bGoZtHZOy9r8KDzZmegt24isnY9hYvvDV8pMLF2mlJXbglFW3VYRe/lQVu1xcttRiZ4r3cZDp3woqzpVi7Kqb7XUZU5ZFWRNWaWsCg4hpc1VL8AmJid87zu9feEQss7UYvXVNktOzT85Hv/pd69dganK3Ujfsc+673R802albNwejLLq9gqFzo+yqmfdVM+VelJyZ9aUVXfWxU5WvAzYDqXUO4ayKlhzyiplVXAIKW2uYgF2tbvJeKVMLZpuHANqj2JeY7PvfafFA/7T7S8uwti2CmP3dL+1czpu3Hs6lZOrlIdOwSirOlXLnytlVc+6qZgr9STj/qwpq+6vUbgMKav61s7JzCmrgnQpq5RVwSGktLkTC7C2wXvWK2XMByONnHwP+cYrZcpbRyxBXd/hP72xvBz0l5d98EoZQ07NS3uLFyo9f52DUVb1rB5lVc+6OTFX6klCv6wpq/rVzJsxZVXf2jmZOWVVkC5llbIqOISUNpexABv2DPleKdN2/hByTtdh3bVu67JeU1DTpvyn1F1agrTqvYBxea+5e+pZt0Hp+SZTMMqqntWkrOpZNxlzpZ5nrn/WlFV9a0hZ1bd2TmZOWRWkS1mlrAoOIaXN412ANXY0WLunzc1HkFZ7DEsu3fTdd1o47D+FviXF8BiX82YYr5QxL+s1BRUZGUrPMVmDUVb1rCxlVc+6xTtX6nm2yZU1ZVXfelJW9a2dk5lTVgXpUlYpq4JDSGlzuwuwW32t1n2n5+6fgufkIcxuuIjKWxOWoK7u9qc8XDATQ1vLkW08tde8rHesogqThYVKzylVglFW9aw0ZVXPutmdK/U8u+TOmrKqb30pq/rWzsnMKauCdCmrlFXBIaS0ebgFWO9Ij++VMl1nD2LG2XpsbOm33ndacc+f4lRaGrrLNiCz+lFMVFZbgupZtUbpOaRqMMqqnpWnrOpZN8qqnnUzs6as6ls7yqq+tXMyc8qqIF3KKmVVcAgpbe5dgN3vGva9Uqb1cg0yak9ixdV7vkt780f9afWuXILJyp3WK2Wsp/ZurVCaM4M9JEBZ1XMkUFb1rBtlVc+6UVb1rZuZOWVV7/o5lT1lVZAsZZWyKjiElDW/1nPFejDStbZaDNS8j8ILV3yvlFnW609jqGg2hrduQ7axezr2wX2nU/kFyvJkoNAEKKt6jgzKqp51o6zqWTfKqr51o6zqXTsns6esCtKlrFJWBYeQY809kx7U3juGgzffQcfJN5F/7oLvib1lbf6wE1mZGNxWjvSqfQ/vOzUEdWLpMsfyYsfxEaCsxsct0a0oq4muQHzxKavxcXNDK14G7IYqxJcDd1bj45bsrSirghWmrFJWBYeQ1ObN3ZdRc+t9XDr7BtLqTljvO/W+UibH4w/Vv3a18UqZfcaTe3dYgjq+qUxqHuxMPgHKqnymKnqkrKqgLD8GZVU+U1U9UlZVkZYfh7Iqn2ky9EhZFawiZZWyKjiEhJr3jfYacvoe6q6+jf6jb2L1lTbffacLB/xdDxbPw5Rx3yl27Ebevl1oW7cFU7kzhGKzsVoClFW1vGVFo6zKIqm2H8qqWt4yo1FWZdJU2xdlVS1vXaKljKyev3Qdz3zpW3jlB19HWenqafX51LPPo7nFeCeH8VViPEzm9ZdfsP19yiplVeWHvWekG2eMV8qcba/F0Ml3MLO+AVtahi1B3dDhz2QsLwf9W8qQY7xSxrys19w9nSheCC7AVFZLbizKqlyeqnqjrKoiLTcO50q5PFX2RllVSVtuLMqqXJ7J0ltKyOq+A8+hq6ffqlmwrH7+y99FZ1efT1BNcS0qLMBPvv9V6/ho36esUladngzq209b7zy9d+49ZJ6pxaqrbdYrZUxBTZ/yR+8qLTHuO90LVO2yntrrWV/6odS4AHO6Ws71T1l1jq2TPVNWnaTrXN+cK51j63TPlFWnCTvXP2XVObY695wSsmoWKNzOqimyX/niZ3HgKWORb3y99uYRfO+ln6HmtRetv0f7PmWVsip7AhgcH8DxOzWoa/wVBo6+hRVXHr5SxhTUwmF/tP4lxYax7sHk9p0PH4xk/EFmZsR0uACTXS11/VFW1bGWGYmyKpOmur44V6pjLTsSZVU2UXX9UVbVsdYpUkrLaiiBDfw3s5DBlw4Ht6GsUlZFP/DmU3sb2s/gcMvb6DnyW+OpvQ2ovD1pCeqaLn/vIwV5GNm2HRnVjzyU022VmCwqiik8F2Ax4XLVwZRVV5XDdjKUVduoXHUg50pXlSOmZCirMeFy1cGUVVeVwzXJUFaD7mONVVYnJgOuw3RNWZ1PJC0NMP6HFD19YcBNHU1498Y7uHLkdXhOHPU9tXf7XX/XUwbkga0bkbfnMePJvdWY2lFt3FRdIhzbXISl6rgVhpfADtKN8TA1NYXUnHESCF4wNOdKQYAJbM65MoHwBUKbc+WkMVfySz8C5meOXyQQTICyKiirbd0jKTmq8nIykZGRhv4h7qzaGQBNnY0421aHG5cOA6ePo7jxBqqNnVNz9zR/1N9Dz4pF1utkcnbux7j5YCRjJ1Xml/mDYG5+Njp6A4LKDMC+HCNg1m1wxIOx8UnHYrBj+QQ4V8pnqqJHzpUqKDsTo6ggG31DHox7OFc6Q9i5Xovn5jrXOXvWlkBKy6pZtVD3pD7/nR+h8eDLVlGjfZ+XAVNWQ3367/TfQr0hp423T2L85CHMabiIbbfGLUFd1utvMTg3H4PbtmLGzsete07HK6owWVDg2ITCS9scQ+t4x7wM2HHEjgTgZcCOYHW8U86VjiN2LAAvA3YMreMd8zJgxxFrGSDlZTXa036jfZ+ySlk1P/nm+07r2+ssQe2pew8zz55D6Y0+a+d0S5t/bvBkZaKnbAMyjftOpyp3W4I6sWy5ssmDCzBlqKUHoqxKR6qkQ8qqEszSg3CulI5UWYeUVWWopQeirEpHmhQdpoSsBr66xqxa4Zx839N+zb/zPauxj+VUX4CZdw6aYmpe2nu78bDxSplTWHn54VN7zT+5Hj/T7pLlmKzchYwd+x5e2rupLHbgklpwASYJZAK6oawmALqEkKk+V0pAmJAuOFcmBLuUoJRVKRgT0gllNSHYXR80JWTVySpwZzV1dlavdjdZgtrUcgyTp45iXuNV3/tOFw74R9nAgkKMVFQgu9q479R8aq8hqFO5M5wchrb75gLMNirXHUhZdV1JbCVEWbWFyXUHca50XUlsJ0RZtY3KdQdSVl1XElckRFkVLANlNXll9f7AXWvn9Fz7aQyfet94pcwFlN8csXZOSx/4B87YjBz0b9mEnF0f+eC+U+PS3oWLBEeWM825AHOGq4peKasqKMuPQVmVz1RFj5wrVVB2JgZl1RmuKnqlrKqgrF8MyqpgzSirySOrA2P9lpiagtp2/hByz5zBuuvdvkt7MwIeLNhdugbpVXsxVfXwvlPP+lLBkaSmORdgajg7EYWy6gRV5/ukrDrP2IkInCudoKqmT8qqGs5ORKGsOkFV/z4pq4I1pKzqLavn2s9Yl/Y2Nx9FWt0JLL18y/dKmaIh/+DoX7LAeqVMRtU+67JeU1CRmSk4etQ35wJMPXNZESmrskiq7Yeyqpa3rGicK2WRVN8PZVU9c1kRKauySCZXP5RVwXpSVvWS1es9V62d04Z7tdYrZeZeaELV7SlLUNd0+QfDaH6e9UqZLO99p+YrZYqKBEdL4ptzAZb4GsSbAWU1XnKJbUdZTSz/eKNzroyXXOLbUVYTX4N4M6CsxksuudtRVgXrS1l1t6y2D7X5ntrbfe4wZtbXo6xl2Lq0t/JuQPHT0j54pYzxUCTzib3mpb2rSwRHh/uacwHmvprYzYiyapeUu46jrLqrHnaz4Vxpl5T7jqOsuq8mdjOirNollVrHUVYF601ZdZesDnuGLDmtN+49bblyBFmna1FytcN332nBqL/gfSuXGO863QVU7Xn4YKRt2wVHg/ubcwHm/hqFy5CyqmftKKt61o1zpZ51M7OmrOpbO8qqvrVzMnPKqiBdymriZfVCxzlLUC/cPompU0ew8FKL75Uyy3v9BR4unI1RQ0gzduy17jsdNy/tLSgQHAF6NecCTK96BWZLWdWzdpRVPevGuVLPulFW9a2bmTllVe/6OZU9ZVWQLGVVvay29l237js1BXXg9GHkN1xA5e1JS1C3tPkLOpGVif7yMmTueOTh+06NPxPLVwhWXO/mXIDpWz/Kqp61o6zqWTfOlXrWjbKqb90oq3rXzsnsKauCdCmrzstq53DHw/tO2+twt+mI9UqZTTcGrEt7TUHN9fiL2FeyCuk79sFTucMS1PHNWwQrnFzNuQDTt56UVT1rR1nVs26cK/WsG2VV37pRVvWunZPZU1YF6VJW5cvq2MSotXN6ru00mm6eQLrxSplVV+777jtd1O8v2tCCIuuVMtixx7d7OjUjT7CqyducCzB9a0tZ1bN2lFU968a5Us+6UVb1rRtlVe/aOZk9ZVWQLmVVjqze6mtF3f0TOH3/JIZOvofCC1d87zstfeAv0viMXAxvLbd2T62HIhn3nk4sXCRYxdRpzgWYvrWmrOpZO8qqnnXjXKln3Sir+taNsqp37ZzMnrIqSJeyGr+stvRew+9v/A5Ntb9E9pk6bLs17hPUjEl/YYY3b8Zk5c4Pdk6r4NlQKli11G3OBZi+taes6lk7yqqedeNcqWfdKKv61o2yqnftnMyesipIl7JqX1bbh+6j9u4JNDUfgufkIcw93/TwvlPjT9GQvxADS4oxtX0npqp2P9w9Nf5MZWUJVorNTQJcgOk7DiiretaOsqpn3ThX6lk3yqq+daOs6l07J7OnrArSpaxGltXzD+px+u5x9B39nfVgpHXXuixBLenygx/Jz8NQeTmydu63Lus1BXWyaJ5gZdg8FAEuwPQdF5RVPWtHWdWzbpwr9awbZVXfulFW9a6dk9lTVgXpUlany2rPSDdOt53ErdrfYPLUUcy7cNV4rcwEKu/6QU+lAZ2b1iKtaq9x7+leS1A9q0sEK8HmdghwAWaHkjuPoay6sy7RsqKsRiPkzu9zrnRnXexkNX/XbjhPAAAWzUlEQVR2DnoGxzHuCbifyE5DHpNwAnzPasJL4MoEKKuCZaGsjqN9qA21Z3+BB4dfs+493do6au2eFoz64XYtW2Ddd5pVbeyefvDOU0H0bB4HAS7A4oDmkiaUVZcUIsY0KKsxAnPJ4ZwrXVKIONKgrMYBzSVNKKsuKYTL0qCsChYkVWW18d4RXH/7nzF09H0svXzHktMVPX6YfbNnoH/LZuTt+SgmjftPxyuqMDl7tiBtNhclwAWYKMHEtaesJo69SGTKqgi9xLXlXJk49qKRKauiBBPXnrKaOPZujkxZFaxOqsjq5a5LaD36S4ydeA9zGi5i/Y0elN/3w/NkpuPuhuXWO0/n7vukdd/pxPIVgnTZXDYBLsBkE1XXH2VVHWuZkSirMmmq64tzpTrWsiNRVmUTVdcfZVUda50iUVYFq5Wssto/1odL9b81Hoz0G2SfrcPSS7ex3bj3dEbALar3VhShz9g9nbHrCczY/VGMb94iSJPNnSbABZjThJ3rn7LqHFsne6asOknXub45VzrH1umeKatOE3auf8qqc2x17pmyKli9ZJLV67dP4/77v8BEbQ2KjAcjbbrRj0X9fkCdc3PRvmmN9UqZ5U/8KdKqd6AX2YIE2VwlAS7AVNKWG4uyKpenqt4oq6pIy43DuVIuT5W9UVZV0pYbi7Iql2ey9EZZFaykzrI6OD6A6+//K4aOvY28+nqsuHIfG9r9T88bzklH67pFGN62DbN2fQwFez+OiUWLLWJcgAkOnAQ15wIsQeAlhKWsSoCYgC44VyYAuoSQnCslQExQF5TVBIGXEJayKgFiEnZBWRUsqm6yeuf8e+g49BrSao+j+OINlLUOITPg6e7XVsxGV9l6ZOx4BIsf+wwmSzeHJMQFmODASVBzLsASBF5CWMqqBIgJ6IJzZQKgSwjJuVICxAR1QVlNEHgJYSmrEiAmYReUVcGiul1WRzvu4Pa7r2DkxLsoONeIkmsdKBqc8p31naJs3NmwzHpa75x9f4hC4+FIU1lZUalwARYVkSsP4ALMlWWxlRRl1RYm1x3EudJ1JbGVEOdKW5hceRBl1ZVlsZUUZdUWppQ7iLIqWHLXyerUlLFz+kt01/waWcY7T5c23cTyB2O+s+ydkYbmknno3bIJuTsfx/LH/wzpxUtipsAFWMzIXNGACzBXlCGuJCircWFLeCPOlQkvQVwJcK6MC5srGlFWXVGGuJKgrMaFLekbUVYFS+wGWZ28fMF4MNLPMX7qMArPXzZeK9M77azOr8xD28bVmKzcifmPHkBx+eOCZ817VoUBJqgDLsASBF5CWMqqBIgJ6IKymgDoEkJyrpQAMUFdUFYTBF5CWMqqBIhJ2AVlVbCoiZDV9Aft6Dnya/QfefODByPdw6zhCd+ZXJuXgZZ1xRgsL8esvR/Dqif+HDkZuYJnOr05F2BScSrrjAswZailB6KsSkeqpEPOlUowSw/CuVI6UmUdUlaVoZYeiLIqHWlSdEhZFSyjCllNGxs1Hoh0Au2Hf4n02mNYcPEaFnQM+zJvnwlcXJWPzk1rjQcj7cPCx/4Uy5dXCJ5Z5OZcgDmK17HOuQBzDK3jHVNWHUfsSADOlY5gdbxTzpWOI3YsAGXVMbSOd0xZdRyxlgEoq4Jlc0pWsy42ov/Ymxg+bj4Y6TyWtXT6Mh3PAE4vy8Tt9UswWrEds/f8ATZsfxp5WYa1KvriAkwRaMlhuACTDFRhd5RVhbAlhuJcKRGmwq44VyqELTkUZVUyUIXdUVYVwtYoFGVVsFiyZDXj7h1k1J2wHoyUeeYUlly6iewx/6W9jQuAy6vnoKdsI3J2PYZl+z6NkrnrBbOPvzkXYPGzS2RLLsASSV8sNmVVjF+iWnOuTBR5sbicK8X4JbI1ZTWR9MViU1bF+CVra8qqYGXjldW0wQFkG0/rHT72DsZPHsLcC02Y0zXoy+ZOAXDG2D29X7oSE8aDkYr2PY3y1Y9iVla+YMZymnMBJoej6l64AFNNXF48yqo8lip74lypkra8WJwr5bFU3RNlVTVxefEoq/JYJlNPlFXBasYiq1kN9ZagjhqX9qbVHcf81nZf9MFs4JTxBpmGFTMwtm075hlP7a3a/lkUzigSzNCZ5lyAOcPV6V65AHOasHP9U1adY+tkz5wrnaTrXN+cK51j63TPlFWnCTvXP2XVObY690xZFaxeJFnNaL1hyan5vtOpkzWYea4B6ROTvoj1C4GTS4F7G1Zgxu4nsH7vn2HH4t2CGalpzgWYGs6yo3ABJpuouv4oq+pYy4zEuVImTXV9ca5Ux1p2JMqqbKLq+qOsqmOtUyTKqo1qferZ59Hccsc6smTlErz+8gu+VoGymt7Tg6zTtYag1lqCmnH6JLK6un3Htsx5uHt6ftVMTFXuQvEjf4R9JZ/AgrxiG1m46xAuwNxVD7vZcAFml5T7jqOsuq8mdjLiXGmHkvuO4VzpvprYzYiyapeU+46jrLqvJm7IiLIapQqf//J30dnV5xNUU1yLCgvwk+9/1WrZ8fbhDwT14Q5q5vVmX489xqtNTTk1/9zcsATZ1fuxaeOT2LXkES0FNRAVF2Bu+PjGngMXYLEzc0sLyqpbKhFbHpwrY+PllqM5V7qlErHnQVmNnZlbWlBW3VIJd+VBWY1Sj30HnsNXvvhZHHhqr3Xka28ewfde+hlqXnvxYcusLMDj8fVydlkWji4atwS1qWQO1u44gKdLPm0JamZ6pruqL5ANF2AC8BLYlAuwBMIXDE1ZFQSYoOacKxMEXjAs50pBgAlsTllNIHzB0JRVQYBJ2pyyGqGw5y9dxzNf+hZe+cHXUVa62joy+N/ay9bhxqwx/GJxJ15bOoBrhWn46KpP4MnVn7D+W5xn3JiahF95OZnIyEhD/9B4Ep5d8p6SuQCbm5+Njt7R5D3JJD0zs26DIx6Mjfvve0/SU02q0+JcqWc5OVfqWTcz66KCbPQNeTDu4VypWxWL5xqXJPKLBIIIUFYFZTXtm2lWD7mZufj0xk/jP1f/Z1QuruRAIwESIAESIAESIAESIAESIAESECBAWRWU1Wd+8WfYOH8j/nLbF7BwVnLuooZClGY4uqnpk1MCo49NE0LA3DGYYOESwl4kaLrxoZuamgI/ciIU1bflXKmeuayInCtlkVTbjzlXThpzJb/0I2B+5vhFAsEEKKtRxkSoe1af/86P0HjwZatlLO9ZTabhx/uw9Kwm78PSs25m1rxnVc/aca7Us26cK/Wsm5k171nVt3a8Z1Xf2jmZOWU1Ct1oTwOmrPKeVSc/oLL75gJMNlF1/VFW1bGWGen/b+9+XqU6zziAn3+goZhdLUSsLRhxk0IDRcFCKemiRrJo3Qg2hmIWbtKFSQUXoebHotm4UEJ+CNnYLIKaRUMoJKAEGmg3kgqNiIVYCCQ22H+gvAPnMs49c+eYeea57zn34857zzzvez7PvGfme8+ZM8JqpGZeLcfKPOvokYTVaNG8esJqnvWQRhJWe3Sr7/es9ig1mk28ARtmK70BG2bfnFkdbt8cK4fZO8fKYfbNmdXh9q3MXFgddv9WNXthdUlZZ1adWV3yKZT6cG/AUrlDB3NmNZQzrZiwmkYdOpBjZShnajFnVlO5QwcTVkM5R1NMWF2ylcKqsLrkUyj14d6ApXKHDiashnKmFRNW06hDB3KsDOVMLSaspnKHDiashnKOppiwumQrhVVhdcmnUOrDvQFL5Q4dTFgN5UwrJqymUYcO5FgZyplaTFhN5Q4dTFgN5RxNMWF1yVYKq8Lqkk+h1Id7A5bKHTqYsBrKmVZMWE2jDh3IsTKUM7WYsJrKHTqYsBrKOZpiwuqSrRRWhdUln0KpD/cGLJU7dDBhNZQzrZiwmkYdOpBjZShnajFhNZU7dDBhNZRzNMWE1SVbKawKq0s+hVIf7g1YKnfoYMJqKGdaMWE1jTp0IMfKUM7UYsJqKnfoYMJqKOdoigmrS7ZSWBVWl3wKpT7cG7BU7tDBhNVQzrRiwmoadehAjpWhnKnFhNVU7tDBhNVQztEUE1ZH00o7QoAAAQIECBAgQIAAgfEICKvj6aU9IUCAAAECBAgQIECAwGgEhNXRtNKOECBAgAABAgQIECBAYDwCwup4emlPCBAgQIAAAQIECBAgMBoBYXU0rVztjly/cas5/OyLzcVzp5u9u3feN9iTR081N2/fmfxs147tzeULZ1Y7GdV7C8zr26UPrjWnXnljXZ3PPr7Qu7YNVyPw9HOvNn/7x437is/2xZpbjf0yVRf1zZpbRnd1j33hpdebKx9+Yr2tjnhllRf1zppbGX1Y4baHs+8tvcaFEY+ikLA6ijaudif2HzrR3P3mf5NBZg8o5Q3a13fvrQXUcoB5eNtDzVuvnVztpFRfKLBR38qL+J/O/7m5eunswjo2yBUofZvuS3kxv/bp9bWfWXO5/eg72qK+WXN9JXO3K69Zfzx5bO2PsGfffK959/2PrLfcNnyr0Rb1zpr7VqxpDyr9efviXyYnO6bfW3qNS2vBYAYSVgfTqs2d6LwzdOUN2u+P/6Y59MS+yQS9OGxun2ZH3+jMqrBaV6/mzWa2h9bcMPvm2DjMvllvw+hbmeXssdKaq7t3ew4cnYTU2av2rLm6+7YZsxNWN0N9gGN2hZ6+Pxvg7o5myg9yGbBLgOts+/SZHmuuzh51zWr2DF3XJYnWXH39LGd1Pr/1xeTMqvVWX382mtF079o/ns9+3MWaq6On5az4bw//svnBI9+7L6xac3X0p7ZZCKu1daTS+fQ9gGz02dZKd23U0+rbj9nLbkaNMqCda/t35vlnJlcv9F2HA9rFUU51tm9dO2nN1dX66Y9NtIHGequrR/Nm09U7a67e3pWPtnz51X8nHxebXWPWXL1928yZCaubqT+gsfseQPqGowHt+qCn2rcf7Xb+6lxPu9ueHD9ysDlx7KnJxPquw3r2YuvNpKtvXQrWXJ3PjXJG/Pw7V5pyLLTe6uzRvFlN986aq7N3s5dmC6t19qm2WQmrtXWk0vk8yGdWy2U3Qk8djewbVttLFPWtjr61/ei6+3bX53msufr7NjtDa66OnnXNov0sXbnzvfVWb58W9c6aq6938+7QXGba/mHWmquvb5s9I2F1szswkPHnhR53bau7gRv9kWH6jrPu4lxPHxfdFMSaq6dX0zNZ1LfZuwVbc3X0cdFdnK23OvrUNYtFvbPm6u1dO7Ou9yjWXP19y56hsJotPsDxpj8PUqa/7bvfue+rNXwfVp1N3ahv0z0rs3/8sd2+bqiCNrYv3F1TaT+3Wn5nzVXQrKkp9OmbNVdXz9rZzPal/Nz3GtfZq9lZLeqdNVd/H+f9Qd1rXP29y5yhsJqpbSwCBAgQIECAAAECBAgQ6CUgrPZishEBAgQIECBAgAABAgQIZAoIq5naxiJAgAABAgQIECBAgACBXgLCai8mGxEgQIAAAQIECBAgQIBApoCwmqltLAIECBAgQIAAAQIECBDoJSCs9mKyEQECBAgQIECAAAECBAhkCgirmdrGIkCAAAECBAgQIECAAIFeAsJqLyYbESBAgAABAgQIECBAgECmgLCaqW0sAgQIECBAgAABAgQIEOglIKz2YrIRAQIECBAgQIAAAQIECGQKCKuZ2sYiQIAAAQIECBAgQIAAgV4CwmovJhsRIECAAAECBAgQIECAQKaAsJqpbSwCBAgQIECAAAECBAgQ6CUgrPZishEBAgQIECBAgAABAgQIZAoIq5naxiJAgAABAgQIECBAgACBXgLCai8mGxEgQIAAAQIECBAgQIBApoCwmqltLAIECBAgQIAAAQIECBDoJSCs9mKyEQECBAgQIECAAAECBAhkCgirmdrGIkCAAIF0gSePnmpu3r7TXDx3utm7e2fn+Ndv3GoOP/tis2vH9ubyhTPpczQgAQIECBAgsF5AWPWsIECAAIFBCrQBs0x+XhA9++Z7zfl3rjSffXxhbR+ffu7V5uu79zpD6Z4DR5vjRw42J449NUgTkyZAgAABAmMSEFbH1E37QoAAgS0k8MJLrzf//Ne/m7vf3Gv2/WRv8/Iffrdu7/cfOrHudxuF1RJu333/o+bqpbNbSNKuEiBAgACBOgWE1Tr7YlYECBAgsECgBNFf/+pnzX++/Kq59un1dQGz66xqCbhXPvzkvsqPP7a7eeu1k2s/c3bVU48AAQIECNQhIKzW0QezIECAAIEHEJgOou3lwGeef6Y59MS+tSrlDGr5Nx1Ey/83OrPa/r7rcQ8wPZsSIECAAAECAQLCagCiEgQIECCQK1BumvTwtofWgujs/8tsys8e/dEj6y4PXhRWSxD+69W/u9FSbkuNRoAAAQIE1gkIq54UBAgQIDAoga4zqV2X/LaXCc/eLKlPWPW51UE9JUyWAAECBEYqIKyOtLF2iwABAmMV6PrcabuvB3/x07UzqcLqWJ8B9osAAQIEtoqAsLpVOm0/CRAgMBKBrjv8ll0rZ0w/v/XF2o2WymXAP9//43VfQ9PnzKrLgEfyZLEbBAgQIDBoAWF10O0zeQIECGwtgUsfXGtOvfJG5/eqtr9rb7Q07wZLXZcMTyvOe9zWkra3BAgQIEBg8wWE1c3vgRkQIECAQE+Bcra0/Lt84UznI8pZ1x/u/P7kxksbhdJS5+btO5MavrqmJ77NCBAgQIBAsoCwmgxuOAIECBDIE5h3yfC8GZSA6+ZKef0xEgECBAgQ2EhAWPX8IECAAIHRCiy65Hd2x/ccONocP3Jw3edcRwtkxwgQIECAQMUCwmrFzTE1AgQIEFheoL3k9+K5083e3Ts7C7Zfh7Nrx3bfr7o8uQoECBAgQCBEQFgNYVSEAAECBAgQIECAAAECBCIFhNVITbUIECBAgAABAgQIECBAIERAWA1hVIQAAQIECBAgQIAAAQIEIgWE1UhNtQgQIECAAAECBAgQIEAgREBYDWFUhAABAgQIECBAgAABAgQiBYTVSE21CBAgQIAAAQIECBAgQCBEQFgNYVSEAAECBAgQIECAAAECBCIFhNVITbUIECBAgAABAgQIECBAIERAWA1hVIQAAQIECBAgQIAAAQIEIgWE1UhNtQgQIECAAAECBAgQIEAgREBYDWFUhAABAgQIECBAgAABAgQiBYTVSE21CBA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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.estimate_rate_constants(t=t_arr, reactant_conc=A_conc, product_conc=B_conc, reactant_name=\"A\", product_name=\"B\")" ] }, { "cell_type": "markdown", "id": "94af05ee-037a-4223-a1a7-fa681baf5ae1", "metadata": {}, "source": [ "### The least-square fit is good... and the values estimated from the data for kF and kR are in good agreement with the values we used in the simulation to get that data, respectively 12 and 2 (see PART 1, above) " ] }, { "cell_type": "markdown", "id": "4ac5c182-7d13-459e-b073-b946867a9e49", "metadata": {}, "source": [ "Note that our data set is quite skimpy in the number of points:" ] }, { "cell_type": "code", "execution_count": 12, "id": "0cb00de3-91bb-4b6d-8e66-788ea743100b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "40" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(B_conc)" ] }, { "cell_type": "markdown", "id": "703cab8c-1850-4799-809f-a8fd43d61c26", "metadata": {}, "source": [ "and that it uses a _variable_ grid, with more points where there's more change, such as in the early times:" ] }, { "cell_type": "code", "execution_count": 13, "id": "0d1d5afc-4e04-457a-9548-f608a71cce1a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.0016 , 0.00352 , 0.00544 , 0.007744 ,\n", " 0.0105088 , 0.0132736 , 0.0160384 , 0.0188032 , 0.021568 ,\n", " 0.02488576, 0.02820352, 0.03152128, 0.03483904, 0.03882035,\n", " 0.04280166, 0.04678298, 0.05156055, 0.05633812, 0.0611157 ,\n", " 0.06684879, 0.07258188, 0.07831497, 0.08519467, 0.09207438,\n", " 0.10033003, 0.10858568, 0.11849246, 0.13038059, 0.14464635,\n", " 0.15891211, 0.17603102, 0.19657372, 0.22122495, 0.25080644,\n", " 0.28630421, 0.32890155, 0.38001835, 0.44135851, 0.5149667 ])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_arr # Time points in our data set" ] }, { "cell_type": "code", "execution_count": 14, "id": "b8aa3145-e2e7-4ac2-a565-9a20a990bbb4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.0016 , 0.00176 , 0.00192 , 0.002112 , 0.0025344 ,\n", " 0.0027648 , 0.0027648 , 0.0027648 , 0.0027648 , 0.00304128,\n", " 0.00331776, 0.00331776, 0.00331776, 0.00364954, 0.00398131,\n", " 0.00398131, 0.00437944, 0.00477757, 0.00477757, 0.00525533,\n", " 0.00573309, 0.00573309, 0.0063064 , 0.00687971, 0.00756768,\n", " 0.00825565, 0.00908121, 0.01089746, 0.01307695, 0.01426576,\n", " 0.01569234, 0.0188308 , 0.02259696, 0.02711636, 0.03253963,\n", " 0.03904756, 0.04685707, 0.05622848, 0.06747418, 0.07360819])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.gradient(t_arr)" ] }, { "cell_type": "markdown", "id": "742366ab-5fb7-4244-9203-6c89689f743c", "metadata": {}, "source": [ "#### The variable time grid, and the skimpy number of data points, are best seen in the plot that was shown at the end of PART 1" ] }, { "cell_type": "code", "execution_count": null, "id": "a14bf79b-ebf8-4696-a92b-ec98e78ecd90", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "81203644-93d4-4e88-b6f0-219458d0fe8e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "fb02e6dc-feb7-4b5d-9c7c-ee18ca4727bd", "metadata": {}, "source": [ "# PART 3 - investigate how the `estimate_rate_constants()` function used in part 2 works \n", "#### Again, the starting point are the time evolutions of [A] and [B] , that is the system history that was given to us" ] }, { "cell_type": "markdown", "id": "36f3e683-5794-460f-98a6-c0f404a641d7", "metadata": {}, "source": [ "Let's revisit the Numpy arrays that we had set up at the beginning of Part 2" ] }, { "cell_type": "code", "execution_count": 15, "id": "3df1e539-4874-4953-acd7-089fc38518c6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.0016 , 0.00352 , 0.00544 , 0.007744 ,\n", " 0.0105088 , 0.0132736 , 0.0160384 , 0.0188032 , 0.021568 ,\n", " 0.02488576, 0.02820352, 0.03152128, 0.03483904, 0.03882035,\n", " 0.04280166, 0.04678298, 0.05156055, 0.05633812, 0.0611157 ,\n", " 0.06684879, 0.07258188, 0.07831497, 0.08519467, 0.09207438,\n", " 0.10033003, 0.10858568, 0.11849246, 0.13038059, 0.14464635,\n", " 0.15891211, 0.17603102, 0.19657372, 0.22122495, 0.25080644,\n", " 0.28630421, 0.32890155, 0.38001835, 0.44135851, 0.5149667 ])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_arr # The independent variable : Time" ] }, { "cell_type": "code", "execution_count": 16, "id": "d29137a5-5dba-4470-9d74-919f14cd939a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([40. , 39.264 , 38.40058368, 37.56037599, 36.5792285 ,\n", " 35.43982899, 34.34453244, 33.29163175, 32.27948591, 31.30651739,\n", " 30.18414823, 29.1139116 , 28.093386 , 27.12026243, 26.00675446,\n", " 24.95531161, 23.96247447, 22.83747684, 21.78772586, 20.80818856,\n", " 19.71136465, 18.70257539, 17.77475483, 16.75073404, 15.82534273,\n", " 14.82182904, 13.93430053, 12.992362 , 12.01880624, 11.04497851,\n", " 10.2656443 , 9.5172222 , 8.83436019, 8.25059325, 7.7918346 ,\n", " 7.46931299, 7.27462691, 7.18032783, 7.14814942, 7.14269565])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_conc" ] }, { "cell_type": "code", "execution_count": 17, "id": "ef430e60-6431-44c9-9b50-469e433270fe", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([10. , 10.736 , 11.59941632, 12.43962401, 13.4207715 ,\n", " 14.56017101, 15.65546756, 16.70836825, 17.72051409, 18.69348261,\n", " 19.81585177, 20.8860884 , 21.906614 , 22.87973757, 23.99324554,\n", " 25.04468839, 26.03752553, 27.16252316, 28.21227414, 29.19181144,\n", " 30.28863535, 31.29742461, 32.22524517, 33.24926596, 34.17465727,\n", " 35.17817096, 36.06569947, 37.007638 , 37.98119376, 38.95502149,\n", " 39.7343557 , 40.4827778 , 41.16563981, 41.74940675, 42.2081654 ,\n", " 42.53068701, 42.72537309, 42.81967217, 42.85185058, 42.85730435])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B_conc" ] }, { "cell_type": "markdown", "id": "56744c87-7555-4bfa-a285-a06da3c39ff3", "metadata": {}, "source": [ "#### Let's verify that the stoichiometry is satified. From the reaction `A <-> B` we can infer that any drop in [A] corresponds to an equal increase in [B]. Their sum will remain constants:" ] }, { "cell_type": "code", "execution_count": 18, "id": "5c2b104b-7f9b-4cd6-9315-68a110351717", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50.,\n", " 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50.,\n", " 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50.,\n", " 50.])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_conc + B_conc" ] }, { "cell_type": "markdown", "id": "b61a3b6c-235b-4452-a7fb-38cf174be0f7", "metadata": {}, "source": [ "### Just as expected! We'll call that constant value, \"TOT_conc\"" ] }, { "cell_type": "code", "execution_count": 19, "id": "61c7d30e-2234-4998-b604-6cc3c83d2ed8", "metadata": {}, "outputs": [], "source": [ "TOT_conc = 50." ] }, { "cell_type": "code", "execution_count": 20, "id": "db27029c-4c13-40aa-a855-79ec186259f7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Incidentally, there's a function to verify that the stoichiometry of a single reaction holds true across the entire simulation run \n", "# (overkill in this case!)\n", "dynamics.stoichiometry_checker_entire_run() " ] }, { "cell_type": "code", "execution_count": null, "id": "dbd5a0eb-5c1e-4249-b219-20010b648c41", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "a723c800-5c7c-4579-88fb-1fe968f0193e", "metadata": {}, "source": [ "### Now, let's investigate the rates of change of [A] and [B]" ] }, { "cell_type": "code", "execution_count": 21, "id": "83278f03-9f66-44ba-88eb-45a2bd9f742b", "metadata": {}, "outputs": [], "source": [ "# The rate of change of [A] with time\n", "Deriv_A = np.gradient(A_conc, t_arr, edge_order=2)\n", "\n", "# The rate of change of [B] with time\n", "Deriv_B = np.gradient(B_conc, t_arr, edge_order=2)" ] }, { "cell_type": "code", "execution_count": 22, "id": "a85508f3-9149-4906-9320-e74dd21a95cf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-6.82121026e-12, 1.36424205e-12, 1.36424205e-12, -4.54747351e-13,\n", " 6.82121026e-13, 4.54747351e-13, 0.00000000e+00, -4.54747351e-13,\n", " 4.54747351e-13, 0.00000000e+00, 4.54747351e-13, 4.54747351e-13,\n", " 4.54747351e-13, -4.54747351e-13, 4.54747351e-13, 0.00000000e+00,\n", " 4.54747351e-13, 4.54747351e-13, 0.00000000e+00, 6.82121026e-13,\n", " -2.27373675e-13, 0.00000000e+00, -4.54747351e-13, 0.00000000e+00,\n", " -3.41060513e-13, -1.13686838e-13, -2.27373675e-13, 0.00000000e+00,\n", " -5.68434189e-14, -1.70530257e-13, 3.97903932e-13, -1.13686838e-13,\n", " 2.27373675e-13, -4.26325641e-14, -4.26325641e-14, -9.94759830e-14,\n", " -5.68434189e-14, -8.52651283e-14, 2.84217094e-14, 1.42108547e-13])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# As expected from the stoichiometry, the two derivatives are opposites: when [A] increases by a certain amount, [B] decreases by that same amount\n", "Deriv_A + Deriv_B" ] }, { "cell_type": "code", "execution_count": 23, "id": "964ab34f-364c-4a46-945f-f39d4e7149d9", "metadata": { "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "A'(t) :
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_curves(x=t_arr, y=[Deriv_A , Deriv_B], title=\"d/dt A(t) and d/dt B(t) as a function of time\",\n", " xlabel=\"t\", ylabel=\"Time derivatives\", curve_labels=[\"A'(t)\", \"B'(t)\"], \n", " legend_title=\"Derivative\", colors=['aqua', 'greenyellow'])" ] }, { "cell_type": "markdown", "id": "5eb72a33-d5d9-4675-9602-c8b3fa49d286", "metadata": {}, "source": [ "### Now, let's determine what kF and kR rate constants for `A <-> B` will yield the above data" ] }, { "cell_type": "markdown", "id": "f38690a4-b17d-4ba3-9fa8-26b597002528", "metadata": {}, "source": [ "Assuming that A <-> B is an elementary chemical reaction (i.e. occuring in a single step) \n", "OR THAT IT CAN BE APPROXIMATED AS ONE, \n", "then the rate of change of the reaction product [B] is the difference of the forward rate (producing `B`) and the reverse rate (consuming it): \n", "\n", "`B'(t) = kF * A(t) - kR * B(t)`       **(Eqn. 1)** \n", " \n", "We also know that A(t) + B(t) = TOT_conc (a CONSTANT), i.e. \n", "`B(t) = TOT_conc - A(t)`       **(Eqn. 2)** \n", "\n", "Replacing B(t) from Eqn. 2 into Eqn. 1:\n", "\n", "`B'(t) = kF * A(t) - kR * [TOT_conc - A(t)]`\n", "\n", "Simplifying and rearranging: \n", "\n", "`B'(t) = kF * A(t) - kR * TOT_conc + kR * A(t)`\n", "\n", "`B'(t) = - kR * TOT_conc + kF * A(t) + kR * A(t)`\n", "\n", "`B'(t) = [- kR * TOT_conc] + [kF + kR] * A(t)`       **(Eqn. 3)** \n", "\n", "`TOT_conc` is a known constant; `kF` and `kR` are the rate constants that we are trying to estimate. \n", "\n", "**If we can do a satisfactory Least Square Fit to express `B'(t)` as a linear function of `A(t)`**, as:\n", "\n", "`B'(t) = a + b * A(t)` , for some constants a, b\n", "\n", "then, comparing with Eqn. 3, we get the following system of equations:\n", "\n", "* `- kR * TOT_conc = a` \n", "\n", "* `kF + kR = b`\n", "\n", "which can be immediately solved as:\n", "\n", "* `kR = - a / TOT_conc`       **(Eqn. 4)**\n", "\n", "* `kF = b - kR` " ] }, { "cell_type": "markdown", "id": "37d4919c-9218-48c8-953e-e065d9a3fca2", "metadata": {}, "source": [ "Let's carry it out! First, let's verify that `B'(t)` is indeed a linear function of `A(t)`. \n", "We already have, from our data, B'(t) as the Numpy array `Deriv_B` , and we also have A(t) as the Numpy array `A_conc` " ] }, { "cell_type": "code", "execution_count": 24, "id": "ed4bb090-6951-46c6-b66a-575ce29bd885", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "A(t)=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_curves(x=A_conc, y=Deriv_B, title=\"d/dt B(t) as a function of A(t)\",\n", " xlabel=\"A(t)\", ylabel=\"B'(t)\", colors=\"green\")" ] }, { "cell_type": "markdown", "id": "edb3e52a-4a04-48d5-b8c9-2be9df1462de", "metadata": {}, "source": [ "As expected, it appears to be a straight line, and the rate of change in the product B is higher when the concentration of the reactant A is larger. \n", "\n", "If we fit a linear model (least-square fit straight line), we can estimate B'(t) = a + b * A(t) , for some numbers a and b. \n", "I.e. **we want to fit: Y = a + b * X , for some numbers a and b** \n", "where Y is `Deriv_B` and X is `A_conc`, the Numpy arrays we computed earlier:" ] }, { "cell_type": "code", "execution_count": 25, "id": "f0a11a40-5ad2-4b99-bc7c-d2d9039b06df", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 4.64683636e+02, 4.55316364e+02, 4.43652086e+02, 4.32261395e+02,\n", " 4.19601598e+02, 4.04133402e+02, 3.88490530e+02, 3.73453149e+02,\n", " 3.58997824e+02, 3.45721185e+02, 3.30434659e+02, 3.15086419e+02,\n", " 3.00451083e+02, 2.87114799e+02, 2.71889118e+02, 2.56734462e+02,\n", " 2.43056308e+02, 2.27599659e+02, 2.12376419e+02, 1.98794743e+02,\n", " 1.83636872e+02, 1.68897580e+02, 1.55931743e+02, 1.41678422e+02,\n", " 1.28621423e+02, 1.14530202e+02, 1.01857698e+02, 8.90860531e+01,\n", " 7.56977131e+01, 6.14464933e+01, 4.96702996e+01, 3.89563341e+01,\n", " 2.88956253e+01, 1.99661621e+01, 1.25889323e+01, 7.03327418e+00,\n", " 3.33147049e+00, 1.24469169e+00, 3.19817889e-01, -1.71634173e-01])" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Y = Deriv_B # The dependent variable (the time-gradient of the PRODUCT concentrations)\n", "Y" ] }, { "cell_type": "code", "execution_count": 26, "id": "33eab35f-818e-49e3-95f4-a933e7cdd149", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([40. , 39.264 , 38.40058368, 37.56037599, 36.5792285 ,\n", " 35.43982899, 34.34453244, 33.29163175, 32.27948591, 31.30651739,\n", " 30.18414823, 29.1139116 , 28.093386 , 27.12026243, 26.00675446,\n", " 24.95531161, 23.96247447, 22.83747684, 21.78772586, 20.80818856,\n", " 19.71136465, 18.70257539, 17.77475483, 16.75073404, 15.82534273,\n", " 14.82182904, 13.93430053, 12.992362 , 12.01880624, 11.04497851,\n", " 10.2656443 , 9.5172222 , 8.83436019, 8.25059325, 7.7918346 ,\n", " 7.46931299, 7.27462691, 7.18032783, 7.14814942, 7.14269565])" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = A_conc # The independent variable (the REACTANT concentrations)\n", "X" ] }, { "cell_type": "markdown", "id": "dff549b8-b9d3-4080-8c99-32a4f56c1b3c", "metadata": {}, "source": [ "#### Let's do the least-square fit:" ] }, { "cell_type": "code", "execution_count": 27, "id": "736b2321-53b9-4681-b52a-29652be70dce", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , 40. ],\n", " [ 1. , 39.264 ],\n", " [ 1. , 38.40058368],\n", " [ 1. , 37.56037599],\n", " [ 1. , 36.5792285 ],\n", " [ 1. , 35.43982899],\n", " [ 1. , 34.34453244],\n", " [ 1. , 33.29163175],\n", " [ 1. , 32.27948591],\n", " [ 1. , 31.30651739]])" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = np.vstack([np.ones(len(Y)), X]).T\n", "# M is an nx2 matrix , where n is the number of data points. \n", "# The 2nd column contains the values of X\n", "\n", "M[:10, :] # Show the first 10 rows" ] }, { "cell_type": "code", "execution_count": 28, "id": "664d211f-43bc-4bfb-bf12-8f9513276ac4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-96.24760283632102, 14.110812144902573)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a, b = np.linalg.lstsq(M, Y, rcond=None)[0] # Carry out the least-square fit as: Y = a + b X\n", "a, b" ] }, { "cell_type": "markdown", "id": "b5630424-9ae2-4506-af8e-5683ee1ad5f1", "metadata": {}, "source": [ "#### Visually verify the least-square fit" ] }, { "cell_type": "code", "execution_count": 29, "id": "4f99fd67-b1d7-4421-8c6c-0e648818e9aa", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "B'(t) :
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least-square fit" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.14269565072923, 40 ], "title": { "text": "A(t)" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -26.191440680042838, 494.2046894671411 ], "title": { "text": "B'(t)" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot both Y and its least-square fit, as functions of X\n", "\n", "PlotlyHelper.plot_curves(x=A_conc, y=[Deriv_B , a + b*A_conc], \n", " title=\"d/dt B(t) as a function of A(t), alongside its least-square fit\",\n", " xlabel=\"A(t)\", ylabel=\"B'(t)\", \n", " curve_labels=[\"B'(t)\", \"Linear Fit\"], legend_title=\"Curve vs Fit:\", colors=['green', 'red'])" ] }, { "cell_type": "markdown", "id": "e39163f0-24fd-47bd-9365-3c734a8f83db", "metadata": {}, "source": [ "_Virtually indistinguishable lines! And the same plot we saw in Part 2!_" ] }, { "cell_type": "markdown", "id": "e9f6c842-bf5c-4253-bf5e-35c384664599", "metadata": {}, "source": [ "Finally, from equations 4, repeated here:\n", "\n", "* `kR = - a / TOT_conc`\n", "\n", "* `kF = b - kR` " ] }, { "cell_type": "code", "execution_count": 30, "id": "9f1e4ff7-3651-4389-ab19-19b536e39a70", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.9249520567264204" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kR = - a / TOT_conc\n", "kR" ] }, { "cell_type": "code", "execution_count": 31, "id": "ccae0cf8-916c-4b11-82cd-95fbdea18025", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12.185860088176153" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kF = b - kR\n", "kF" ] }, { "cell_type": "markdown", "id": "c9bb3d0f-f964-4111-ba27-7492b78fa22d", "metadata": {}, "source": [ "#### We just obtained the same values of the estimated kF and kR as were computed by a call to `estimate_rate_constants()` in Part 2" ] }, { "cell_type": "code", "execution_count": null, "id": "306660cc-049f-43e2-a4f3-ff5f19b01e00", "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 }