{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## Exploration of variable time steps in the simulation of the coupled reactions `2 S <-> U` and `S <-> X` \n", "Both mostly forward. 1st-order kinetics throughout. \n", "\n", "Based on the reactions and initial conditions of the experiment `up_regulate_3`\n", "\n", "LAST REVISED: Mar. 2, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "d9efa3fd-e95d-4e1c-878a-81ae932b2709", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "# Extend the sys.path variable, to contain the project's root directory\n", "import set_path\n", "set_path.add_ancestor_dir_to_syspath(2) # The number of levels to go up \n", " # to reach the project's home, from the folder containing this notebook" ] }, { "cell_type": "code", "execution_count": 2, "id": "01bae555-3dcf-42c1-bddc-9477a37f49f8", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_data import ReactionData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import numpy as np\n", "import plotly.express as px\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'variable_steps_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "### Initialize the system" ] }, { "cell_type": "code", "execution_count": 4, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: 2 S <-> U (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products\n", "1: S <-> X (kF = 6 / kR = 3 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `variable_steps_1.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"U\", \"X\", \"S\"])\n", "\n", "# Reaction 2 S <-> U , with 1st-order kinetics for all species (mostly forward)\n", "chem_data.add_reaction(reactants=[(2, \"S\")], products=\"U\",\n", " forward_rate=8., reverse_rate=2.)\n", "\n", "# Reaction S <-> X , with 1st-order kinetics for all species (mostly forward)\n", "chem_data.add_reaction(reactants=\"S\", products=\"X\",\n", " forward_rate=6., reverse_rate=3.)\n", "\n", "chem_data.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 5, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (U). Conc: 50.0\n", " Species 1 (X). Conc: 100.0\n", " Species 2 (S). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)\n", "dynamics.set_conc(conc={\"U\": 50., \"X\": 100., \"S\": 0.})\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 6, "id": "bcf652b8-e0dc-438e-bdbe-02216c1d52a0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0 from the upcoming single step (for all rxns):\n", " Baseline: [ 50. 100. 0.]\n", " Deltas: [-1. -3. 5.]\n", " Adjusted L2 norm: 1.9720265943665387\n", "The current time step (0.01) leads to an 'L2 rate' (1.972) that is higher than the specified HIGH threshold (1.2):\n", "ACTION: IMMEDIATE ABORT. Will abort this step, and re-do it with a SMALLER time interval. [The current step started at System Time: 0, and will rewind there]\n", "reaction_step_orchestrator(): RE-DOING THE LAST REACTION STEP with the smaller time interval of 0.005\n", "\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0 with delta_time_full=0.005\n", "EXAMINING CONCENTRATION CHANGES at System Time 0 from the upcoming single step (for all rxns):\n", " Baseline: [ 50. 100. 0.]\n", " Deltas: [-0.5 -1.5 2.5]\n", " Adjusted L2 norm: 0.9860132971832694\n", "NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.986) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.0025) at the next round! [The current step started at System Time: 0, and will continue to 0.005]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.005 with delta_time_full=0.0025\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.005 from the upcoming single step (for all rxns):\n", " Baseline: [49.5 98.5 2.5]\n", " Deltas: [-0.1975 -0.70125 1.09625]\n", " Adjusted L2 norm: 0.43875098923598516\n", "NOTICE: The chosen time step (0.0025) results in an 'L2 rate' (0.4388) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.005) at the next round! [The current step started at System Time: 0.005, and will continue to 0.0075]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.0075 with delta_time_full=0.005\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.0075 from the upcoming single step (for all rxns):\n", " Baseline: [49.3025 97.79875 3.59625]\n", " Deltas: [-0.349175 -1.35909375 2.05744375]\n", " Adjusted L2 norm: 0.830136119114619\n", "NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.8301) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.0025) at the next round! [The current step started at System Time: 0.0075, and will continue to 0.0125]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.0125 with delta_time_full=0.0025\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.0125 from the upcoming single step (for all rxns):\n", " Baseline: [48.953325 96.43965625 5.65369375]\n", " Deltas: [-0.13169275 -0.63849202 0.90187752]\n", " Adjusted L2 norm: 0.37094445340529236\n", "NOTICE: The chosen time step (0.0025) results in an 'L2 rate' (0.3709) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.005) at the next round! [The current step started at System Time: 0.0125, and will continue to 0.015]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.015 with delta_time_full=0.005\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.015 from the upcoming single step (for all rxns):\n", " Baseline: [48.82163225 95.80116423 6.55557127]\n", " Deltas: [-0.22599347 -1.24035033 1.69233727]\n", " Adjusted L2 norm: 0.7034476536211219\n", "NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.7034) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.015, and will continue to 0.02]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.02 with delta_time_full=0.005\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.02 from the upcoming single step (for all rxns):\n", " Baseline: [48.59563878 94.56081391 8.24790853]\n", " Deltas: [-0.15604005 -1.17097495 1.48305505]\n", " Adjusted L2 norm: 0.6320146889296034\n", "NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.632) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.02, and will continue to 0.025]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.025 with delta_time_full=0.005\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.025 from the upcoming single step (for all rxns):\n", " Baseline: [48.43959873 93.38983896 9.73096358]\n", " Deltas: [-0.09515744 -1.10891868 1.29923357]\n", " Adjusted L2 norm: 0.5702595342894922\n", "NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.5703) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.025, and will continue to 0.03]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.03 with delta_time_full=0.005\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.03 from the upcoming single step (for all rxns):\n", " Baseline: [48.34444129 92.28092028 11.03019715]\n", " Deltas: [-0.04223653 -1.05330789 1.13778094]\n", " Adjusted L2 norm: 0.5170199771979221\n", "NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.517) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.03, and will continue to 0.035]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.035 with delta_time_full=0.005\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.035 from the upcoming single step (for all rxns):\n", " Baseline: [48.30220476 91.22761239 12.16797809]\n", " Deltas: [ 0.00369708 -1.00337484 0.99598069]\n", " Adjusted L2 norm: 0.47125745282035797\n", "NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.4713) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.01) at the next round! [The current step started at System Time: 0.035, and will continue to 0.04]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.04 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.04 from the upcoming single step (for all rxns):\n", " Baseline: [48.30590184 90.22423755 13.16395878]\n", " Deltas: [ 0.08699867 -1.9168896 1.74289227]\n", " Adjusted L2 norm: 0.8640799836300542\n", "NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.8641) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.005) at the next round! [The current step started at System Time: 0.04, and will continue to 0.05]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.05 with delta_time_full=0.005\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.05 from the upcoming single step (for all rxns):\n", " Baseline: [48.3929005 88.30734795 14.90685105]\n", " Deltas: [ 0.11234504 -0.87740469 0.65271461]\n", " Adjusted L2 norm: 0.3664388323328886\n", "NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.3664) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.01) at the next round! [The current step started at System Time: 0.05, and will continue to 0.055]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.055 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.055 from the upcoming single step (for all rxns):\n", " Baseline: [48.50524554 87.42994326 15.55956566]\n", " Deltas: [ 0.27466034 -1.68932436 1.14000367]\n", " Adjusted L2 norm: 0.685473353555872\n", "NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.6855) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.055, and will continue to 0.065]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.065 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.065 from the upcoming single step (for all rxns):\n", " Baseline: [48.77990588 85.7406189 16.69956934]\n", " Deltas: [ 0.36036743 -1.57024441 0.84950955]\n", " Adjusted L2 norm: 0.6071059448138537\n", "NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.6071) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.065, and will continue to 0.075]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.075 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.075 from the upcoming single step (for all rxns):\n", " Baseline: [49.14027331 84.17037449 17.54907888]\n", " Deltas: [ 0.42112084 -1.4721665 0.62992481]\n", " Adjusted L2 norm: 0.551908028188212\n", "NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.5519) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.075, and will continue to 0.085]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.085 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.085 from the upcoming single step (for all rxns):\n", " Baseline: [49.56139416 82.69820799 18.1790037 ]\n", " Deltas: [ 0.46309241 -1.39020602 0.46402119]\n", " Adjusted L2 norm: 0.512341359965445\n", "NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.5123) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.085, and will continue to 0.095]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.095 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.095 from the upcoming single step (for all rxns):\n", " Baseline: [50.02448657 81.30800197 18.64302489]\n", " Deltas: [ 0.49095226 -1.32065857 0.33875405]\n", " Adjusted L2 norm: 0.4830375500460132\n", "NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.483) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.02) at the next round! [The current step started at System Time: 0.095, and will continue to 0.105]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.105 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.105 from the upcoming single step (for all rxns):\n", " Baseline: [50.51543883 79.98734341 18.98177894]\n", " Deltas: [ 1.01646708 -2.52142713 0.48849298]\n", " Adjusted L2 norm: 0.920713822793345\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.9207) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.01) at the next round! [The current step started at System Time: 0.105, and will continue to 0.125]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.125 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.125 from the upcoming single step (for all rxns):\n", " Baseline: [51.5319059 77.46591628 19.47027191]\n", " Deltas: [ 0.52698364 -1.15576117 0.1017939 ]\n", " Adjusted L2 norm: 0.424768909765701\n", "NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.4248) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.02) at the next round! [The current step started at System Time: 0.125, and will continue to 0.135]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.135 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.135 from the upcoming single step (for all rxns):\n", " Baseline: [52.05888954 76.3101551 19.57206582]\n", " Deltas: [ 1.04917495 -2.22996141 0.13161151]\n", " Adjusted L2 norm: 0.8226527244153111\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.8227) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.01) at the next round! [The current step started at System Time: 0.135, and will continue to 0.155]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.155 with delta_time_full=0.01\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.155 from the upcoming single step (for all rxns):\n", " Baseline: [53.10806449 74.08019369 19.70367733]\n", " Deltas: [ 0.5141329 -1.04018517 0.01191938]\n", " Adjusted L2 norm: 0.386790195376169\n", "NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.3868) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.02) at the next round! [The current step started at System Time: 0.155, and will continue to 0.165]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.165 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.165 from the upcoming single step (for all rxns):\n", " Baseline: [53.62219739 73.04000852 19.71559671]\n", " Deltas: [ 1.00960758 -2.01652891 -0.00268625]\n", " Adjusted L2 norm: 0.751716813419431\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.7517) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.165, and will continue to 0.185]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.185 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.185 from the upcoming single step (for all rxns):\n", " Baseline: [54.63180496 71.02347962 19.71291046]\n", " Deltas: [ 0.96879347 -1.89585952 -0.04172743]\n", " Adjusted L2 norm: 0.7098188581459898\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.7098) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.185, and will continue to 0.205]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.205 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.205 from the upcoming single step (for all rxns):\n", " Baseline: [55.60059844 69.12762009 19.67118303]\n", " Deltas: [ 0.92336535 -1.78711524 -0.05961545]\n", " Adjusted L2 norm: 0.6708152962620689\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.6708) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.205, and will continue to 0.225]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.225 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.225 from the upcoming single step (for all rxns):\n", " Baseline: [56.52396378 67.34050485 19.61156758]\n", " Deltas: [ 0.87689226 -1.68704218 -0.06674234]\n", " Adjusted L2 norm: 0.6341666360749514\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.6342) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.225, and will continue to 0.245]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.245 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.245 from the upcoming single step (for all rxns):\n", " Baseline: [57.40085605 65.65346267 19.54482524]\n", " Deltas: [ 0.8311378 -1.59382873 -0.06844686]\n", " Adjusted L2 norm: 0.5996077454037625\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.5996) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.245, and will continue to 0.265]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.265 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.265 from the upcoming single step (for all rxns):\n", " Baseline: [58.23199384 64.05963394 19.47637838]\n", " Deltas: [ 0.78694079 -1.50641263 -0.06746894]\n", " Adjusted L2 norm: 0.5669711804381353\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.567) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.265, and will continue to 0.285]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.285 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.285 from the upcoming single step (for all rxns):\n", " Baseline: [59.01893463 62.55322131 19.40890943]\n", " Deltas: [ 0.74466812 -1.42412415 -0.0652121 ]\n", " Adjusted L2 norm: 0.5361294223890068\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.5361) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.285, and will continue to 0.305]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.305 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.305 from the upcoming single step (for all rxns):\n", " Baseline: [59.76360275 61.12909716 19.34369733]\n", " Deltas: [ 0.70444746 -1.34650215 -0.06239278]\n", " Adjusted L2 norm: 0.5069743721586161\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.507) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.305, and will continue to 0.325]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.325 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.325 from the upcoming single step (for all rxns):\n", " Baseline: [60.46805022 59.78259501 19.28130456]\n", " Deltas: [ 0.66628672 -1.27319915 -0.05937429]\n", " Adjusted L2 norm: 0.47940928759927104\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.4794) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.04) at the next round! [The current step started at System Time: 0.325, and will continue to 0.345]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.345 with delta_time_full=0.04\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.345 from the upcoming single step (for all rxns):\n", " Baseline: [61.13433694 58.50939586 19.22193027]\n", " Deltas: [ 1.26027073 -2.40786424 -0.11267722]\n", " Adjusted L2 norm: 0.9066904814971378\n", "NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.9067) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.02) at the next round! [The current step started at System Time: 0.345, and will continue to 0.385]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.385 with delta_time_full=0.02\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.385 from the upcoming single step (for all rxns):\n", " Baseline: [62.39460767 56.10153162 19.10925305]\n", " Deltas: [ 0.56169618 -1.07298153 -0.05041083]\n", " Adjusted L2 norm: 0.40405351934013756\n", "NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.4041) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.04) at the next round! [The current step started at System Time: 0.385, and will continue to 0.405]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.405 with delta_time_full=0.04\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.405 from the upcoming single step (for all rxns):\n", " Baseline: [62.95630385 55.02855009 19.05884222]\n", " Deltas: [ 1.0623252 -2.02930388 -0.09534652]\n", " Adjusted L2 norm: 0.764177119158623\n", "NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.7642) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.405, and will continue to 0.445]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.445 with delta_time_full=0.04\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.445 from the upcoming single step (for all rxns):\n", " Baseline: [64.01862905 52.99924621 18.96349569]\n", " Deltas: [ 0.9468283 -1.80867058 -0.08498602]\n", " Adjusted L2 norm: 0.6810935415626411\n", "NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.6811) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.445, and will continue to 0.485]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.485 with delta_time_full=0.04\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.485 from the upcoming single step (for all rxns):\n", " Baseline: [64.96545735 51.19057563 18.87850968]\n", " Deltas: [ 0.84388651 -1.61202675 -0.07574626]\n", " Adjusted L2 norm: 0.6070431239872686\n", "NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.607) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.485, and will continue to 0.525]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.525 with delta_time_full=0.04\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.525 from the upcoming single step (for all rxns):\n", " Baseline: [65.80934386 49.57854888 18.80276341]\n", " Deltas: [ 0.75213678 -1.43676265 -0.06751092]\n", " Adjusted L2 norm: 0.5410436794042834\n", "NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.541) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.525, and will continue to 0.565]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.565 with delta_time_full=0.04\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.565 from the upcoming single step (for all rxns):\n", " Baseline: [66.56148064 48.14178623 18.73525249]\n", " Deltas: [ 0.67036235 -1.28055375 -0.06017094]\n", " Adjusted L2 norm: 0.4822198810778668\n", "NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.4822) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.08) at the next round! [The current step started at System Time: 0.565, and will continue to 0.605]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.605 with delta_time_full=0.08\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.605 from the upcoming single step (for all rxns):\n", " Baseline: [67.23184299 46.86123248 18.67508155]\n", " Deltas: [ 1.19495731 -2.28265665 -0.10725798]\n", " Adjusted L2 norm: 0.8595831447977756\n", "NOTICE: The chosen time step (0.08) results in an 'L2 rate' (0.8596) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.04) at the next round! [The current step started at System Time: 0.605, and will continue to 0.685]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.685 with delta_time_full=0.04\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.685 from the upcoming single step (for all rxns):\n", " Baseline: [68.4268003 44.57857583 18.56782357]\n", " Deltas: [ 0.46755952 -0.89315144 -0.0419676 ]\n", " Adjusted L2 norm: 0.3363352629038791\n", "NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.3363) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.08) at the next round! [The current step started at System Time: 0.685, and will continue to 0.725]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.725 with delta_time_full=0.08\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.725 from the upcoming single step (for all rxns):\n", " Baseline: [68.89435982 43.68542439 18.52585598]\n", " Deltas: [ 0.83345025 -1.59209098 -0.07480952]\n", " Adjusted L2 norm: 0.5995358846406782\n", "NOTICE: The chosen time step (0.08) results in an 'L2 rate' (0.5995) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.725, and will continue to 0.805]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.805 with delta_time_full=0.08\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.805 from the upcoming single step (for all rxns):\n", " Baseline: [69.72781007 42.0933334 18.45104645]\n", " Deltas: [ 0.65222012 -1.24589772 -0.05854252]\n", " Adjusted L2 norm: 0.4691694121768126\n", "NOTICE: The chosen time step (0.08) results in an 'L2 rate' (0.4692) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.16) at the next round! [The current step started at System Time: 0.805, and will continue to 0.885]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=0.885 with delta_time_full=0.16\n", "EXAMINING CONCENTRATION CHANGES at System Time 0.885 from the upcoming single step (for all rxns):\n", " Baseline: [70.38003019 40.84743568 18.39250394]\n", " Deltas: [ 1.02079538 -1.94996535 -0.0916254 ]\n", " Adjusted L2 norm: 0.7343011251253482\n", "NOTICE: The chosen time step (0.16) results in an 'L2 rate' (0.7343) that leads to the following:\n", "ACTION: COMPLETE NORMALLY - we're inside the target range. No change to step size. [The current step started at System Time: 0.885, and will continue to 1.045]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=1.045 with delta_time_full=0.16\n", "EXAMINING CONCENTRATION CHANGES at System Time 1.045 from the upcoming single step (for all rxns):\n", " Baseline: [71.40082557 38.89747033 18.30087853]\n", " Deltas: [ 0.57686034 -1.10194237 -0.05177831]\n", " Adjusted L2 norm: 0.4149599485210064\n", "NOTICE: The chosen time step (0.16) results in an 'L2 rate' (0.415) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.32) at the next round! [The current step started at System Time: 1.045, and will continue to 1.205]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=1.205 with delta_time_full=0.32\n", "EXAMINING CONCENTRATION CHANGES at System Time 1.205 from the upcoming single step (for all rxns):\n", " Baseline: [71.97768591 37.79552796 18.24910022]\n", " Deltas: [ 0.65197758 -1.24543442 -0.05852075]\n", " Adjusted L2 norm: 0.46899494767126315\n", "NOTICE: The chosen time step (0.32) results in an 'L2 rate' (0.469) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.64) at the next round! [The current step started at System Time: 1.205, and will continue to 1.525]\n", "\n", "reaction_step_orchestrator(): entering WHILE loop at System Time=1.525 with delta_time_full=0.64\n", "EXAMINING CONCENTRATION CHANGES at System Time 1.525 from the upcoming single step (for all rxns):\n", " Baseline: [72.62966349 36.55009354 18.19057947]\n", " Deltas: [ 0.16979763 -0.32435443 -0.01524084]\n", " Adjusted L2 norm: 0.12214259081733582\n", "NOTICE: The chosen time step (0.64) results in an 'L2 rate' (0.1221) that leads to the following:\n", "ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 1.28) at the next round! [The current step started at System Time: 1.525, and will continue to 2.165]\n", "44 total step(s) taken\n" ] }, { "data": { "text/html": [ "
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SYSTEM TIMEUXScaption
00.000050.000000100.0000000.000000Initial state
10.005049.50000098.5000002.500000
20.007549.30250097.7987503.596250
30.012548.95332596.4396565.653694
40.015048.82163295.8011646.555571
50.020048.59563994.5608148.247909
60.025048.43959993.3898399.730964
70.030048.34444192.28092011.030197
80.035048.30220591.22761212.167978
90.040048.30590290.22423813.163959
100.050048.39290188.30734814.906851
110.055048.50524687.42994315.559566
120.065048.77990685.74061916.699569
130.075049.14027384.17037417.549079
140.085049.56139482.69820818.179004
150.095050.02448781.30800218.643025
160.105050.51543979.98734318.981779
170.125051.53190677.46591619.470272
180.135052.05889076.31015519.572066
190.155053.10806474.08019419.703677
200.165053.62219773.04000919.715597
210.185054.63180571.02348019.712910
220.205055.60059869.12762019.671183
230.225056.52396467.34050519.611568
240.245057.40085665.65346319.544825
250.265058.23199464.05963419.476378
260.285059.01893562.55322119.408909
270.305059.76360361.12909719.343697
280.325060.46805059.78259519.281305
290.345061.13433758.50939619.221930
300.385062.39460856.10153219.109253
310.405062.95630455.02855019.058842
320.445064.01862952.99924618.963496
330.485064.96545751.19057618.878510
340.525065.80934449.57854918.802763
350.565066.56148148.14178618.735252
360.605067.23184346.86123218.675082
370.685068.42680044.57857618.567824
380.725068.89436043.68542418.525856
390.805069.72781042.09333318.451046
400.885070.38003040.84743618.392504
411.045071.40082638.89747018.300879
421.205071.97768637.79552818.249100
431.525072.62966336.55009418.190579
442.165072.79946136.22573918.175339
\n", "
" ], "text/plain": [ " SYSTEM TIME U X S caption\n", "0 0.0000 50.000000 100.000000 0.000000 Initial state\n", "1 0.0050 49.500000 98.500000 2.500000 \n", "2 0.0075 49.302500 97.798750 3.596250 \n", "3 0.0125 48.953325 96.439656 5.653694 \n", "4 0.0150 48.821632 95.801164 6.555571 \n", "5 0.0200 48.595639 94.560814 8.247909 \n", "6 0.0250 48.439599 93.389839 9.730964 \n", "7 0.0300 48.344441 92.280920 11.030197 \n", "8 0.0350 48.302205 91.227612 12.167978 \n", "9 0.0400 48.305902 90.224238 13.163959 \n", "10 0.0500 48.392901 88.307348 14.906851 \n", "11 0.0550 48.505246 87.429943 15.559566 \n", "12 0.0650 48.779906 85.740619 16.699569 \n", "13 0.0750 49.140273 84.170374 17.549079 \n", "14 0.0850 49.561394 82.698208 18.179004 \n", "15 0.0950 50.024487 81.308002 18.643025 \n", "16 0.1050 50.515439 79.987343 18.981779 \n", "17 0.1250 51.531906 77.465916 19.470272 \n", "18 0.1350 52.058890 76.310155 19.572066 \n", "19 0.1550 53.108064 74.080194 19.703677 \n", "20 0.1650 53.622197 73.040009 19.715597 \n", "21 0.1850 54.631805 71.023480 19.712910 \n", "22 0.2050 55.600598 69.127620 19.671183 \n", "23 0.2250 56.523964 67.340505 19.611568 \n", "24 0.2450 57.400856 65.653463 19.544825 \n", "25 0.2650 58.231994 64.059634 19.476378 \n", "26 0.2850 59.018935 62.553221 19.408909 \n", "27 0.3050 59.763603 61.129097 19.343697 \n", "28 0.3250 60.468050 59.782595 19.281305 \n", "29 0.3450 61.134337 58.509396 19.221930 \n", "30 0.3850 62.394608 56.101532 19.109253 \n", "31 0.4050 62.956304 55.028550 19.058842 \n", "32 0.4450 64.018629 52.999246 18.963496 \n", "33 0.4850 64.965457 51.190576 18.878510 \n", "34 0.5250 65.809344 49.578549 18.802763 \n", "35 0.5650 66.561481 48.141786 18.735252 \n", "36 0.6050 67.231843 46.861232 18.675082 \n", "37 0.6850 68.426800 44.578576 18.567824 \n", "38 0.7250 68.894360 43.685424 18.525856 \n", "39 0.8050 69.727810 42.093333 18.451046 \n", "40 0.8850 70.380030 40.847436 18.392504 \n", "41 1.0450 71.400826 38.897470 18.300879 \n", "42 1.2050 71.977686 37.795528 18.249100 \n", "43 1.5250 72.629663 36.550094 18.190579 \n", "44 2.1650 72.799461 36.225739 18.175339 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "dynamics.verbose_list = [\"substeps\", \"variable_steps\"]\n", "\n", "dynamics.single_compartment_react(time_step=0.01, stop_time=2., \n", " variable_steps=True, thresholds={\"low\": 0.5, \"high\": 0.8})\n", "\n", "df = dynamics.get_history()\n", "df" ] }, { "cell_type": "code", "execution_count": 7, "id": "12da63da-9b3b-4c43-a68b-7dfb6585b9d0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.005, in 1 reduced step of 0.005 (1/2 of requested step)\n", "From time 0.005 to 0.0075, in 1 FULL step of 0.0025\n", "From time 0.0075 to 0.0125, in 1 FULL step of 0.005\n", "From time 0.0125 to 0.015, in 1 FULL step of 0.0025\n", "From time 0.015 to 0.04, in 5 FULL steps of 0.005\n", "From time 0.04 to 0.05, in 1 FULL step of 0.01\n", "From time 0.05 to 0.055, in 1 FULL step of 0.005\n", "From time 0.055 to 0.105, in 5 FULL steps of 0.01\n", "From time 0.105 to 0.125, in 1 FULL step of 0.02\n", "From time 0.125 to 0.135, in 1 FULL step of 0.01\n", "From time 0.135 to 0.155, in 1 FULL step of 0.02\n", "From time 0.155 to 0.165, in 1 FULL step of 0.01\n", "From time 0.165 to 0.345, in 9 FULL steps of 0.02\n", "From time 0.345 to 0.385, in 1 FULL step of 0.04\n", "From time 0.385 to 0.405, in 1 FULL step of 0.02\n", "From time 0.405 to 0.605, in 5 FULL steps of 0.04\n", "From time 0.605 to 0.685, in 1 FULL step of 0.08\n", "From time 0.685 to 0.725, in 1 FULL step of 0.04\n", "From time 0.725 to 0.885, in 2 FULL steps of 0.08\n", "From time 0.885 to 1.205, in 2 FULL steps of 0.16\n", "From time 1.205 to 1.525, in 1 FULL step of 0.32\n", "From time 1.525 to 2.165, in 1 FULL step of 0.64\n" ] } ], "source": [ "(transition_times, step_sizes) = dynamics.explain_time_advance(return_times=True)" ] }, { "cell_type": "code", "execution_count": 8, "id": "438e4ec0-44f7-4c0d-b6a6-4a435da6e683", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.005 , 0.0025, 0.005 , 0.0025, 0.005 , 0.01 , 0.005 , 0.01 ,\n", " 0.02 , 0.01 , 0.02 , 0.01 , 0.02 , 0.04 , 0.02 , 0.04 ,\n", " 0.08 , 0.04 , 0.08 , 0.16 , 0.32 , 0.64 ])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array(step_sizes)" ] }, { "cell_type": "code", "execution_count": 9, "id": "74d500e5-0b59-419c-90ae-4948eb7c8611", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.005 , 0.0075, 0.0125, 0.015 , 0.04 , 0.05 , 0.055 ,\n", " 0.105 , 0.125 , 0.135 , 0.155 , 0.165 , 0.345 , 0.385 , 0.405 ,\n", " 0.605 , 0.685 , 0.725 , 0.885 , 1.205 , 1.525 , 2.165 ])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array(transition_times) # Note: there will be one more transition time (the end time) than step sizes" ] }, { "cell_type": "markdown", "id": "cbf6c9c7-8cec-400f-9e70-49ff1a9f485c", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 10, "id": "c388dae7-c4a6-4644-a390-958e3862d102", "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=U
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"gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Changes in concentration for `2 S <-> U` and `S <-> X`" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 2.165 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { 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EStXdeiMIlYRKQqX0C0qoFGcnVIpzyt2qjR+0hUrxqyxUirdq416Pn72WTQkIlZqSdhwCaQJCpTQ3oVKam1CputuMEdRUygxqOAIZBdRUyohpKAI1CaipVBOsYQlkFCgTKl11zS7ha7csyHh0QxEgQKAegV87bmv43ZP3qGfwKRnV428ZFlqolAHREARqEhAq1QRrWAIZBYRKGTENRaAmAaFSTbCGJUBgrAJCper8QqXqhkGolAHREARqEhAq1QRrWAIZBYRKGTENRaAmgZRQ6aQTtoTnHL6tphkZlgCBfgGPv6XvB29/S7cregqVqvl5+9syNZUGt5C3v8VfVGoqxVmpqRTnlLtVG+vMqKkUv8pqKsVbtXGvx89ey6YEyoRKf3flw+FHd34sHPXClUKlphbIcaZeQKiUtgXUVEpz6+8lVKpoqFC3UEmolH4RCZXi7IRKcU65W7Xxg7ZQKX6VhUrxVm3c6/Gz17IpAaFSU9KOQyBNQKiU5iZUSnMTKlV3640gVBIqCZXSLyihUpydUCnOKXerNn7QFirFr7JQKd6qjXs9fvZaNiUgVGpK2nEIpAkIldLchEppbkKl6m4zRlBTKTOo4QhkFFBTKSOmoQjUJKCmUk2whiWQUaBMqNR9+5uaShkXwFAE5hAQKqVvETWV0u2Knh5/q+bX6S1UyoBoCAI1CQiVaoI1LIGMAkKljJiGIlCTgFCpJljDEsgkIFRKhxQqpdsJlarZ9XoLlTJBGoZADQJCpRpQDUkgs4BQKTOo4QjUICBUqgHVkAQyCgiV0jGFSul2UxsqnbjinHDbhrs6cocuOShcvXrVnIrPfNGKXpuVrz0hnHXGyZ1/V1NJTaXBzePtb3NeTr0GairFWampFOeUu1Ub68yoqRS/ymoqxVu1ca/Hz17LpgTKhEre/tbUqjgOgR0CQqW03aCmUppbf6+pe/zt9LddEO69b2MvSCoCpgMPWBQuu/DsoZrrb709LD/zvLDqHa8Ly44/Zqc2QiWhklAp/QeRUCnOTqgU55S7VRs/aAuV4ldZqBRv1ca9Hj97LZsSECo1Je04BNIEhEppbkKlNLepDpWOXXZWePvKU3oB0drr1oX3X/KJcMPai4ZqFqHTS489ondn0mAjoZJQSaiU/oNIqBRnJ1SKc8rdqo0ftIVK8assVIq3auNej5+9lk0JCJWaknYcAmkCQqU0N6FSmtvUhkrdu47WXHxuWHrYIR2HYX/WD1Q89nbA/vuF+x54qPfH/f2LP3z4p5vDjx/ZXH01jECAQHaB3XdbGPbZc9dw/0M/yz62AQkQyCOw7/ZrtPP71O/SPKBGIVCDwIGLdg8bf7I5PLp565yj/79XLwz//LUF4f86cWt47nO2zdleAwIEqgsUodLj9ts93PPgpuqDTdkIT3zcnlN2xnlPd6oefysbKg179O2d7/1guOazN4Zvfml1byW2btsWtv8/XwQItFBgwfY5LViwIBTXqS8CBNopsP0S7Xy5TNu5PmZFoBBYWOJ36Uc+vjXcePPWcNprFoajX7AQIAECDQkUwdKWrf7OW5a7cPOVLiBU+veaSYN3HxWko+5iKu5e6q+x5O1v6RtQTwJ1C3j7W93CxidQXcDb36obGoFA3QJlHn+76ppdwtduWRBOOmFLeM7hPuDWvTbGJ1AIePwtfR94+1u6XdFzqkKl4oSH1VQ65/xLZ9x51E86GCAV3+v/MzWV1FQavAS9/S3+h5KaSnFWairFOeVu1cY6M2oqxa+ymkrxVm3c6/Gz17IpgTKhkre/NbUqjkNgh4BQKW03qKmU5tbfa+pCpbne/lYU5i6+rl69qvO/Rfvv3H5nr5B38fjbupvX9/5dqCRUEiql/yASKsXZCZXinHK3auMHbaFS/CoLleKt2rjX42evZVMCQqWmpB2HQJqAUCnNTaiU5jbVoVJx8kVwdNuGuzoOhy45qBcgdb/XHyoNti+Kdve/KU6oJFQSKqX/IBIqxdkJleKccrdq4wdtoVL8KguV4q3auNfjZ69lUwJCpaakHYdAmoBQKc1NqJTmNvWhUnW2mSOoqZRb1HgE8gmoqZTP0kgE6hJQU6kuWeMSyCdQJlRSUymfu5EIxAoIlWKldm6nplK6XdFz6h5/q8Y1vLdQqQ5VYxLIIyBUyuNoFAJ1CgiV6tQ1NoE8AkKlPI5GIVCXgFApXVaolG4nVKpm1+stVMoEaRgCNQgIlWpANSSBzAJCpcyghiNQg4BQqQZUQxLIKCBUSscUKqXbCZWq2XV6q6mkptLgNvL2t/gLS02lOCs1leKccrdqY50ZNZXiV1lNpXirNu71+Nlr2ZRAmVDJ29+aWhXHIbBDQKiUthvUVEpz6+/l8beKhkIloZJQKf0iEirF2QmV4pxyt2rjB22hUvwqC5Xirdq41+Nnr2VTAkKlpqQdh0CagFApzU2olOYmVKru1htBqCRUEiqlX1BCpTg7oVKcU+5WbfygLVSKX2WhUrxVG/d6/Oy1bEpAqNSUtOMQSBMQKqW5CZXS3IRK1d1mjKCmUmZQwxHIKKCmUkZMQxGoSUBNpZpgDUsgo0CZUMnb3zLCG4pApIBQKRJqSDM1ldLtip4ef6vm1+ktVMqAaAgCNQkIlWqCNSyBjAJCpYyYhiJQk4BQqSZYwxLIJCBUSocUKqXbCZWq2fV6C5UyQRqGQA0CQqUaUA1JILOAUCkzqOEI1CAgVKoB1ZAEMgoIldIxhUrpdkKlanad3moqqak0uI28/S3+wlJTKc5KTaU4p9yt2lhnRk2l+FVWUyneqo17PX72WjYlUCZU8va3plbFcQjsEBAqpe0GNZXS3Pp7efytoqFQSagkVEq/iIRKcXZCpTin3K3a+EFbqBS/ykKleKs27vX42WvZlIBQqSlpxyGQJiBUSnMTKqW5CZWqu/VGECoJlYRK6ReUUCnOTqgU55S7VRs/aAuV4ldZqBRv1ca9Hj97LZsSECo1Je04BNIEhEppbkKlNDehUnW3GSOoqZQZ1HAEMgqoqZQR01AEahJQU6kmWMMSyChQJlTy9reM8IYiECkgVIqEGtJMTaV0u6Knx9+q+XV6C5UyIBqCQE0CQqWaYA1LIKOAUCkjpqEI1CQgVKoJ1rAEMgkIldIhhUrpdkKlana93kKlTJCGIVCDgFCpBlRDEsgsIFTKDGo4AjUICJVqQDUkgYwCQqV0TKFSup1QqZpdp7eaSmoqDW4jb3+Lv7DUVIqzUlMpzil3qzbWmVFTKX6V1VSKt2rjXo+fvZZNCZQJlbz9ralVcRwCOwSESmm7QU2lNLf+Xh5/q2goVBIqCZXSLyKhUpydUCnOKXerNn7QFirFr7JQKd6qjXs9fvZaNiUgVGpK2nEIpAkIldLchEppbkKl6m69EYRKQiWhUvoFJVSKsxMqxTnlbtXGD9pCpfhVFirFW7Vxr8fPXsumBIRKTUk7DoE0AaFSmptQKc1NqFTdbcYIaiplBjUcgYwCaiplxDQUgZoE1FSqCdawBDIKlAmVvP0tI7yhCEQKCJUioYY0U1Mp3a7o6fG3an6d3kKlDIiGIFCTgFCpJljDEsgoIFTKiGkoAjUJCJVqgjUsgUwCQqV0SKFSup1QqZpdr7dQKROkYQjUICBUqgHVkAQyCwiVMoMajkANAkKlGlANSSCjgFApHVOolG4nVKpm1+mtppKaSoPbyNvf4i8sNZXirNRUinPK3aqNdWbUVIpfZTWV4q3auNfjZ69lUwJlQiVvf2tqVRyHwA4BoVLablBTKc2tv5fH3yoaCpWESkKl9ItIqBRnJ1SKc8rdqo0ftIVK8assVIq3auNej5+9lk0JCJWaknYcAmkCQqU0N6FSmptQqbpbbwShklBJqJR+QQmV4uyESnFOuVu18YO2UCl+lYVK8VZt3Ovxs9eyKQGhUlPSjkMgTUColOYmVEpzEypVd5sxgppKmUENRyCjgJpKGTENRaAmATWVaoI1LIGMAmVCJW9/ywhvKAKRAkKlSKghzdRUSrcrenr8rZpfp7dQKQOiIQjUJCBUqgnWsAQyCgiVMmIaikBNAkKlmmANSyCTgFApHVKolG4nVKpm1+stVMoEaRgCNQgIlWpANSSBzAJCpcyghiNQg4BQqQZUQxLIKCBUSscUKqXbCZWq2XV6q6mkptLgNvL2t/gLS02lOCs1leKccrdqY50ZNZXiV1lNpXirNu71+Nlr2ZRAmVDJ29+aWhXHIbBDQKiUthvUVEpz6+/l8beKhkIloZJQKf0iEirF2QmV4pxyt2rjB22hUvwqC5Xirdq41+Nnr2VTAkKlpqQdh0CagFApzU2olOYmVKru1htBqCRUEiqlX1BCpTg7oVKcU+5WbfygLVSKX2WhUrxVG/d6/Oy1bEpAqNSUtOMQSBMQKqW5CZXS3IRK1d1mjKCmUmZQwxHIKKCmUkZMQxGoSUBNpZpgDUsgo0CZUMnb3zLCG4pApIBQKRJqSDM1ldLtip4ef6vm1+ktVMqAaAgCNQkIlWqCNSyBjAJCpYyYhiJQk4BQqSZYwxLIJCBUSocUKqXbCZWq2fV6C5UyQRqGQA0CQqUaUA1JILOAUCkzqOEI1CAgVKoB1ZAEMgoIldIxhUrpdkKlanad3moqqak0uI28/S3+wlJTKc5KTaU4p9yt2lhnRk2l+FVWUyneqo17PX72WjYlUCZU8va3plbFcQjsEBAqpe0GNZXS3Pp7efytoqFQSagkVEq/iIRKcXZCpTin3K3a+EFbqBS/ykKleKs27vX42WvZlIBQqSlpxyGQJiBUSnMTKqW5CZWqu/VGECoJlYRK6ReUUCnOTqgU55S7VRs/aAuV4ldZqBRv1ca9Hj97LZsSECo1Je04BNIEhEppbkKlNDehUnW3GSOoqZQZ1HAEMgqoqZQR01AEahJQU6kmWMMSyChQJlTy9reM8IYiECkgVIqEGtJMTaV0u6Knx9+q+XV6C5UyIBqCQE0CQqWaYA1LIKOAUCkjpqEI1CQgVKoJ1rAEMgkIldIhhUrpdkKlana93kKlTJCGIVCDgFCpBlRDEsgsIFTKDGo4AjUICJVqQDUkgYwCQqV0TKFSup1QqZpdp7eaSmoqDW4jb3+Lv7DUVIqzUlMpzil3qzbWmVFTKX6V1VSKt2rjXo+fvZZNCZQJlbz9ralVcRwCOwSESmm7QU2lNLf+Xh5/q2goVBIqCZXSLyKhUpydUCnOKXerNn7QFirFr7JQKd6qjXs9fvZaNiUgVGpK2nEIpAkIldLchEppbkKl6m69EYRKQiWhUvoFJVSKsxMqxTnlbtXGD9pCpfhVFirFW7Vxr8fPXsumBIRKTUk7DoE0AaFSmptQKc1NqFTdbcYIaiplBjUcgYwCaiplxDQUgZoE1FSqCdawBDIKlAmVvP0tI7yhCEQKCJUioYY0U1Mp3a7o6fG3an6d3kKlDIiGIFCTgFCpJljDEsgoIFTKiGkoAjUJCJVqgjUsgUwCQqV0SKFSup1QqZpdr7dQKROkYQjUICBUqgHVkAQyCwiVMoMajkANAkKlGlANSSCjgFApHVOolG4nVKpm1+mtppKaSoPbyNvf4i8sNZXirNRUinPK3aqNdWbUVIpfZTWV4q3auNfjZ69lUwJlQiVvf2tqVRyHwA4BoVLablBTKc2tv5fH3yoaCpWESkKl9ItIqBRnJ1SKc8rdqo0ftIVK8assVIq3auNej5+9lk0JCJWaknYcAmkCQqU0N6FSmptQqbpbbwShklBJqJR+QQmV4uyESnFOuVu18YO2UCl+lYVK8VZt3Ovxs9eyKQGhUlPSjkMgTUColOYmVEpzEypVd5sxgppKmUENRyCjgJpKGTENRaAmATWVaoI1LIGMAmVCJW9/ywhvKAKRAkKlSKghzdRUSrcrenr8rZpfp7dQKQOiIQjUJCBUqgnWsAQyCgiVMmIaikBNAkKlmmANSyCTgFApHVKolG4nVKpm1+stVMoEaRgCNQgIlWpANSSBzM08DucAACAASURBVAJCpcyghiNQg4BQqQZUQxLIKCBUSscUKqXbNRYqnbjinHDbhrs6M131jteFZccfE575ohXhyOceFi678OxqZzDm3moqqak0uAW9/S3+olRTKc5KTaU4p9yt2lhnRk2l+FVWUyneqo17PX72WjYlUCZU8va3plbFcQjsEBAqpe0GNZXS3Pp71f74WxEoHXjAok54dOyys8LbV57SCZUu+vCV4YpPfjHcsPai6mcxxhGESkIloVL6BShUirMTKsU55W7Vxg/aQqX4VRYqxVu1ca/Hz17LpgSESk1JOw6BNAGhUpqbUCnNrdFQqbgjac3F54alhx0yI1Rae926cM75l4Zvfml19bMoOUL/nVOHLjkoXL16VdQI73zvB8M1n72xdz5FJ6GSUEmoFHX5DG0kVIqzEyrFOeVu1cYP2kKl+FUWKsVbtXGvx89ey6YEhEpNSTsOgTQBoVKam1Apza3RUKm4O+mv3vfWnUKlcd2pdPrbLgj33rexFyT130k1G2cRgv31ms90HuPrhmTd9moqVd+IRiBQl4CaSnXJGpdAPgE1lfJZGolAXQJlQiVvf6trFYxLYLSAUCl9d6iplG5X9Kz98bfi7p51N6/vPObWffzt6Qc/JSw/87xwwsuODu971xuqnUHJ3v2P4BVdi7Do/Zd8Ys7H8Lp3XBXzFiqVRNecwBgFhEpjxHdoApECQqVIKM0IjFFAqDRGfIcmECEgVIpAGtFEqJRu10io1A1uikfd+r9WvvaEcNYZJ1ebfcne62+9vRNm9YdCw/5scNjibqb/tPzloRuGCZVKwmtOYIwCQqUx4js0gUgBoVIklGYExiggVBojvkMTiBAQKkUgCZXSkWbpWfudSrXMOnHQlFCpuNPqB/fc3yk0Pqx/UVPp3e9+d7j66qvD5s2bw7777huOPPLI8JGPfCQ88sgj4S1veUv4+7//+3DwwQeH/fffP1x//fXhtNNOCxdccMHI73VPrxhzsF/3e8WYixcvDkcddVRPozvmnnvu2fmzDRs29I43W78/+7M/68ypmN+or2HHi+lXnG/xddxxx/WG/sAHPhBOPPHE8KQnPWnk8Yb1G2z8wAMPdJwL49m+Yo530003hQcffDD8xm/8xsihYo9XzKk43yVLlowc65Zbbgnf/e53Ow6jvor9Uxifffbsb0j8xCc+EZ797GeHZzzjGYlXxo5u3f0820A5jze4Z1NPYNheTx1r2F5PHSvmGokZ+/vf/37nZ8wb3/jGmOaNtYnZ6zGTid3rMWPlbJNzr+ea17e+9a3w9a9/PZxyyim5hpy348T8Hpm3J1/yxNq410ueguYtE/jQR+4Nd9z+0XD8K94cfvXIhS2bnekQIECg3OcfXrMLCJWG3L3UJRt8NG5UqPS2339XuPbaT4Yt20OlvffZJzzzWUeET61dEzZteiS85tSV4cvrvhCe/JSnhv0WLQ5fvfnG8KqTlodugeJh3+se//rPf2anft3v3bR9zH32XRSWHv683goPFj2++647esebrd+ayz8QXrls9oLbw44X029YodQr16wOx730FeHAxz9h5O6MKbD60MYHO87LT539g3bM8dbf8k/hxw9vDEcd8+KRc4o93rVXrQlHvODo8OSDnjZyrG/fuj7c/b07w3EvefnINj/btCl8/PJLwmmvnz00y1lgtShU9/o3/cGsPzVyHk+h7rhfUQp1xznlbpVzr+eam0Ld8ZIxv0fiR5vfLdu41+e3+GSeXZk7lf7uyofDj+78WDjqhSvDcw7fNpknbNYEJkzAnUppC6ZQd5pbf6+pCpWKEx9WU2nUW+i6b6gbxtx9fM/b37z9bXB/CJXifzAJleKshEpxTrlbtfGDtlApfpWFSvFWbdzr8bPXsikBoVJT0o5DIE1AqJTmJlRKc2s0VCoKXB+65KDe29a6B+8GNt/80urqZ1FihLne/lbUTyq+rl69aqdRR9Vf8va3EgugKYGGBdRUahjc4QgkCKiplICmC4GGBcqESt7+1vDiOByB7QJCpfRtoFB3ul3Rs/Y7lbqh0m0b7gr9xbnHFSoVJ10ER8V8iq/BwEuoVG1D6U2gbQJCpbatiPkQ2FlAqGRXEGi/gFCp/WtkhtMtIFRKX3+hUrpdY6HSqne8Liw7/phQBEzFV3F30jhDpWpkO/d2p1JuUeMRyCcgVMpnaSQCdQkIleqSNS6BfAJCpXyWRiJQh4BQKV1VqJRu13ioVBzwog9fGS756DWdO4SKu4WafvytGtfOvdVUUlNpcFeoqRR/lampFGelplKcU+5Wbawzo6ZS/CqrqRRv1ca9Hj97LZsSKBMqKdTd1Ko4DoEdAkKltN2gplKaW3+vRh5/696p1H/gomD2fQ88JFQa8ma4rpO3v4Xw3Bf86shdHvs2Nm9/i/9B4e1vIQx702G84MyWMW9IjBlbqBSjlL9NGz9oC5Xi11moFG/Vxr0eP3stmxIQKjUl7TgE0gSESmluQqU0t0ZDpepTbPcI7lRyp9LgDnWnUvw1606lOCuhUpxT7lZt/KAtVIpfZaFSvFUb93r87LVsSkCo1JS04xBIExAqpbkJldLchErV3WaMoKZSZlDDEcgooKZSRkxDEahJQE2lmmANSyCjQJlQydvfMsIbikCkgFApEmpIMzWV0u2KnrU9/lYU5S7e9lbUT5rta9JrKhXnJlSqtgn1JlCngFCpTl1jE8gjIFTK42gUAnUKCJXq1DU2geoCQqV0Q6FSul2toVK1aU1Wb6HSZK2X2U6XgFBputbb2U6mgFBpMtfNrKdLQKg0XevtbCdPQKiUvmZCpXQ7oVI1u05vNZXUVBrcRmoqxV9YairFWampFOeUu1Ub68yoqRS/ymoqxVu1ca/Hz17LpgTKhEre/tbUqjgOgR0CQqW03aCmUppbf6/aHn+rPrXJGEGoJFQSKqVfq0KlODuhUpxT7lZt/KAtVIpfZaFSvFUb93r87LVsSkCo1JS04xBIExAqpbkJldLcGg2VTn/bBeE7t98Zblh7Uee4xy47K9z3wEOdf15z8blh6WGHVD+LMY4gVBIqCZXSL0ChUpydUCnOKXerNn7QFirFr7JQKd6qjXs9fvZaNiUgVGpK2nEIpAkIldLchEppbo2GSkWI9PaVp4Rlxx8TLvrwleGKT36xEzAV//y5G74arl69qvpZjHkENZXGvAAOT2AWATWVbA8C7RdQU6n9a2SGBMqESt7+Zr8QaF5AqJRurqZSul3Rs/bH34q3wK16x+s6oVJx11LxddmFZ4e1160L55x/afD2t2oLqDcBArMLCJXsEALtFxAqtX+NzJCAUMkeINBuAaFS+voIldLtGgmVTlxxTnjpsUeEs844ORQB08rXntD55/67lqqdwvh7u1Np/GtgBgRGCQiV7A0C7RcQKrV/jcyQgFDJHiDQbgGhUvr6CJXS7RoJldbfentYfuZ5nVkeuuSg3uNuRcB05HMP69y1NMlfaiqpqTS4f739Lf6KVlMpzkpNpTin3K3aWGdGTaX4VVZTKd6qjXs9fvZaNiVQJlTy9remVsVxCOwQECql7QY1ldLc+nvV/vhb9Sm2ewShklBJqJR+jQqV4uyESnFOuVu18YO2UCl+lYVK8VZt3Ovxs9eyKQGhUlPSjkMgTUColOYmVEpzEypVd+uNIFQSKgmV0i8ooVKcnVApzil3qzZ+0BYqxa+yUCneqo17PX72WjYlIFRqStpxCKQJCJXS3IRKaW5CpepuM0ZQUykzqOEIZBRQUykjpqEI1CSgplJNsIYlkFGgTKjk7W8Z4Q1FIFJAqBQJNaSZmkrpdkVPj79V8+v0FiplQDQEgZoEhEo1wRqWQEYBoVJGTEMRqElAqFQTrGEJZBIQKqVDCpXS7YRK1ex6vYVKmSANQ6AGAaFSDaiGJJBZQKiUGdRwBGoQECrVgGpIAhkFhErpmEKldDuhUjW7Tm81ldRUGtxG3v4Wf2GpqRRnpaZSnFPuVm2sM6OmUvwqq6kUZ/Wje0L49DVrw557Lw277/2LcZ20mkqBPXdbGH62eWvYum3u07/jjo1h963/Mxz1wpXhOYdHdJh7SC0IEJhDQKiUtkXUVEpz6+/l8beKhkIloZJQKf0iEirF2QmV4pxytxIq5RYdPV4ddyoJleLWb8OGEK65am348SPPCj99VKgUp6bVXAK7Lnww/NwiodJcTr5PIKeAUClNU6iU5tZ4qPTO934wXPPZG2fMds3F54alhx1S/QzGPIJQSagkVEq/CIVKcXZCpTin3K2ESrlFhUrNicYfqRsq7bL7s8LRv/r0+I5aTp3AfnvvFn6yaUvYsmXrnOe+6ZEHw7e/8fHwqpPfGA44YM7mGhAgkEFAqJSGKFRKc2s0VOoGSt/80urecddety6cc/6lYdU7XheWHX9M9bMY8whqKo15ARyewCwCairZHgTaL1DHnUrtP+t2zPD7P1gQ/uoDu4QnPXFb+L03bmnHpMyilQJlaiq18gRMisA8FxAqpS+wmkrpdkXP2h9/O3bZWeHtK0/ZKTy66MNXhs/d8NVw9epV1c6gBb2FSi1YBFMgMEJAqGRrEGi/gFBpfGskVBqf/aQdWag0aStmvtMmIFRKX3GhUrpdI6HSM1+0YugdSd27lfrvYKp2KuPrLVQan70jE5hLQKg0l5DvExi/gFBpfGsgVBqf/aQdWag0aStmvtMmIFRKX3GhUrpdI6HSiSvOCS899ohw1hknz5jpfAmV1FRSU2nwEvT2t/gfSmoqxVmpqRTnlLuVmkq5RUePV0eopFB33PoVodIVf3NV2G3PpeHMM9VUilObzlZlQqWHNj4YPrV2TVh+6hunE8tZExiDgFApDV1NpTS3/l61P/426jG3otbSD+65P1x24dnVz2KMIwiVhEpCpfQLUKgUZydUinPK3UqolFtUqNScaPyRhErxVtPeUqg07TvA+bddQKiUtkJCpTS3RkOl4vG32K9JfBROqCRUEirFXuE7txMqxdkJleKccrcSKuUWFSo1Jxp/JKFSvNW0txQqTfsOcP5tFxAqpa2QUCnNrdFQqfoU2z+CmkrtXyMznF4BNZWmd+2d+eQI1PH42+Sc/XhnqqbSeP0n6ehlQqVJOi9zJTBfBIRK6SupplK6XdGz9sffqk1vMnoLlSZjncxyOgWEStO57s56sgSESuNbL6HS+Own7chCpUlbMfOdNgGhUvqKC5XS7RoLlYpi3bdtuKsz01XveF1YdvwxoXgs7sjnHjbxNZWKcxIqVduEehOoU0CoVKeusQnkERAq5XFMGUWolKI2nX2EStO57s56cgSESulrJVRKt2skVCoCpQMPWNQJj45ddlZ4+8pTOqFSUcD7ik9+Mdyw9qJqZzDm3moqqak0uAW9/S3+olRTKc5KTaU4p9yt1FTKLTp6vDpCJW9/i1s/NZXinLQKoUyo5O1vdgyB5gWESmnmaiqlufX3qv3xt+KOpDUXnxuWHnbIjFBp7XXrwjnnXxomsTh3P6BQSagkVEr/QSRUirMTKsU55W4lVMotKlRqTjT+SEKleKtpbylUmvYd4PzbLiBUSlshoVKaW6OhUnF30l+97607hUruVPqz8JpTV4Yvr/tCePJTnhr2W7Q4fPXmG8OrTlreW5/rP/+Zkd+7aXu/ffZdFJYe/rxe+8EP6HffdcdOYw7rt+byD4RXLps9HErtN+y/FF+5ZnU47qWvCAc+/gkjd3DMf2GO/a9gMcdbf8s/hR8/vDEcdcyLR84p9njuVIr/wSRUirMSKsU55W4lVMotKlRqTjT+SEKleKtpbylUmvYd4PzbLiBUSlshoVKaW6Oh0jvf+8Gw7ub1ncfcuo+/Pf3gp4TlZ54XTnjZ0eF973pD9bMY8whqKo15ARyewCwCairZHgTaL1DH42/tP+t2zFBNpXaswyTMokyoNAnnY44E5puAUCl9RdVUSrcretb++FtxkO6jbv1TXfnaE8JZZ5xcbfYt6S1UaslCmAaBIQJCJduCQPsFhErjWyOh0vjsJ+3IQqVJWzHznTYBoVL6iguV0u0aC5WqTbH9vYVK7V8jM5xeAaHS9K69M58cAaHS+NZKqDQ++0k7slBp0lbMfKdNQKiUvuJCpXS7RkKlolD3qne8rvPGt/4vNZXUVFJT6c5w3EtePvIK/tmmTeHjl18STnv9W2a9ynPWfSmeKX79m/6gseOpqRT3A1xNpTin3K1yXlu55rbh9u+E73zrG+HXX3FSriFbMU4doVJMbb5WnPyYJ6Gm0pgXYIIOXyZUiq1DOUGnb6oEWi8gVEpbIjWV0tz6e9X++NuoUMnb34RKQiWhklAp7oe4UCnOKXcroVJu0dHjCZWasx48klBpfPaTdmSh0qStmPlOm4BQKW3FhUppbq0IlfoLeFc/jfGN8J73vCe87fffFa699pNhy+bNYe999gnPfNYR4VNr14RNmx4Z+Ya37odpb38bvnYx/4U59r+Ceftb/PXhTqUQhr3pMF5wZsuYNyvGjC1UilHK30aolN901IhCpeashUrjs570IwuVJn0FzX++CwiV0lZYqJTmVnuoNKww97CpDnssrvopNT+CmkrNmzsigVgBNZVipbQjMD6BOkKl8Z3NZB1ZTaXJWq9xzrZMqDTOeTo2gWkVECqlr7yaSul2Rc+xPf5Wbdrt6i1Uatd6mA2BfgGhkv1AoP0CQqXxrZFQaXz2k3ZkodKkrZj5TpuAUCl9xYVK6XaNhErVpjcZvYVKk7FOZjmdAkKl6Vx3Zz1ZAkKl8a2XUGl89pN2ZKHSpK2Y+U6bgFApfcWFSul2QqVqdp3eaiotD/stWjxSclhtpJgaR2oqheDtb/EX6N133RG+evON4VUnLd+pU9lQSU2lePdrr1oTjnjB0eHJBz0tvtOQlrF7vdJBEjqrqZSAltiljlAp5vdI4nTnVTeFuufVctZ6MmVCpdi6l7VO2OAEpkxAqJS24Goqpbn196rt8beiEPc1n70x9NdNuujDV4ZLPnpN5/gnvOzo8L53vaH6GYx5BKGSUGlwC8Z80P72revD3d/z9jdvf4v7AaZQd5xT7lZCpdyio8cTKjVnPXgkodL47CftyEKlSVsx8502AaFS2ooLldLcGgmVTlxxTjjwgEXhsgvP7hxv/a23h+VnntcLmYrvv/TYI8JZZ5xc/SzGOIJQSagkVEq/AIVKcXZCpTin3K2ESrlFhUrNicYfSagUbzXtLYVK074DnH/bBYRKaSskVEpzayRUOnbZWeHVv/lrvdCouEvpik9+Mdyw9qLO8Yt//9wNXw1Xr15V/SzGPIKaSmNeAIcnMItA2cffYBIg0LxAHXcqNX8Wk3lENZUmc93GMesyodI45ueYBKZdQKiUvgPUVEq3K3rW9vjbM1+0Ysajb6e/7YLOTLt3Lq29bl045/xLwze/tLraGbSgt1CpBYtgCgRGCAiVbA0C7RcQKo1vjYRK47OftCMLlSZtxcx32gSESukrLlRKt2s0VCoed/vlXzy4V0dJqFRt4fQmQCBOQKgU56QVgXEKCJXGpy9UGp/9pB1ZqDRpK2a+0yYgVEpfcaFSul2todJgzaS5Hoerdhrj662mkppKg7tPoe7461FNpTgrNZXinHK3UlMpt+jo8eoIlbz9LW791FSKc9IqhDKhkre/2TEEmhcQKqWZq6mU5tbfq7bH3/prJg27K6kInYqvSa+pJFQSKgmV0n8QCZXi7IRKcU65WwmVcosKlZoTjT+SUCneatpbCpWmfQc4/7YLCJXSVkiolObWSKhUHKSoo/SVf761c7xV73hdWHb8MZ1/LgKnSz56TVj52hO8/W3dF8KTn/LUsN+ixeGrN98YXnXS8t76XP/5z4z83k3b++2z76Kw9PDn9doPfkC/+647dhpzWL81l38gvHLZ7OFQar9h/6X4yjWrw3EvfUU48PFPGLmDY/4Lc+x/BYs53vpb/in8+OGN4ahjXjxyTrHHc6dS/A8moVKclVApzil3K6FSblGhUnOi8UcSKsVbTXtLodK07wDn33YBoVLaCgmV0twaC5WqT28yRlCoezLWySynU0BNpelcd2c9WQJ1PP42WQLjm62aSuOzn7QjlwmVJu3czJfAfBAQKqWvoppK6XZFz9oef6s2rXp7F4/e3bbhrs5BDl1y0KyP4PXfbdWd1eAb64RK9a6X0QlUERAqVdHTl0AzAkKlZpyHHUWoND77STuyUGnSVsx8p01AqJS+4kKldLupDJWKkOje+zb2gqQiYDrwgEXhsgvPHipZFBi/Ye1Fve+9870fDOtuXj/jz4RK1Tah3gTqFBAq1alrbAJ5BIRKeRxTRhEqpahNZx+h0nSuu7OeHAGhUvpaCZXS7aYyVCpCorevPKVX36koIv7+Sz4xIySajXT9rbeH5WeeF9ZcfG5YetghQaFuhboH94uaSvE/lNRUirNSUynOKXcrNZVyi44er45QKaY2X3Nn2N4jqanU3rVp28zKhEqxdSjbdo7mQ2CSBYRKaaunplKaW3+vqXr8bTAQKiCG/dlsrEWR8Ss++cVeCCVUEioJldJ/EAmV4uyESnFOuVsJlXKLCpWaE40/klAp3mraWwqVpn0HOP+2CwiV0lZIqJTmJlT697uMyoZK3QCq/012Raj0X889N1xz9TVh85bNYd999g3Pf8ELwv/86OXhkUceCW86683hHz772fC0g58W9t9///CP1/9jeO2pp4Y/+eP/MfJ73QX65DXX7NSv+71izEWLF4Ujjzyqt57dMffcc8/On333uxt6x5ut319c9Ofh/37tqZ35jfoadryYfv/4j9d3hnzhC4/rDf2hD30wnPCbJ4QnPulJI483rN9g4wceeKDjXBjP9hVzvK985aaw8cGN4ddf9rKRQ8Ue76OXXx5eeNwLw8EHLxk51te/fku447t3hN884YSRbYr9Uxj/l9//g1nP72+vuCI869nPCr/0S8+o/BPhj/77eeEP/+u5jR1vcM+mnsCwvd4da8H2f1iwYEHYum1b1PDD9npUxyGNYq6RmLF/8P3vh2s+eU14/evfENO8sTYxez1mMrF7PWasnG1yXlu55vWv//qt8C9f/5fw269+da4hWzHO9ku08xV5mUbNOeb3SNRA87zRnXdtCxd/4BNhz32eFf7r2b88z8/W6VURWFjid2ns35mqzEdfAgR2FiiCpS1b4/7Oy+8xgeLzz7vf/W4cFQTcqTTwONsoy26gtPK1J4Szzjh5RrOHf7o5/PiRzRWWQVcCBOoS2H23hWGfPXcN9z/0s7oOYVwCBCoK7Lv9Gi2+Hva7tKJk+e53f39B+ItLFoYnP2lbeNPKreUH0GNqBA5ctHvY+JPN4dHN9snULLoTnSiBIlB63H67h3se3DRR827DZJ/4uMduyvCVJjBVoVJBNKym0jnnXxoG3+jWz1nUXSradOsoDVIr1J22+fQi0ISAQt1NKDsGgWoCddRUqjaj6emtUPf0rHXVMy3z+FvVY+lPgEB5AY+/lTfr9lCoO92u6Dl1odJcb38r3gZXfF29elXnf2MKeQuVqm1CvQnUKSBUqlPX2ATyCAiV8jimjCJUSlGbzj5Cpelcd2c9OQJCpfS1Eiql201lqFScdBEc3bbhro7coUsO6gVI3e91Q6XuI2/DiLt1lRTqVqh7cH94+1v8DyWFuuOsFOqOc8rdSqHu3KKjx6sjVPL2t7j1U6g7zkmrEMqESt7+ZscQaF5AqJRmrlB3mlt/r6m7U6k62cwRhEpCJaFS+lUlVIqzEyrFOeVuJVTKLSpUak40/khCpXiraW8pVJr2HeD82y4gVEpbIaFSmptQqbpbbwShklBJqJR+QQmV4uyESnFOuVsJlXKLCpWaE40/klAp3mraWwqVpn0HOP+2CwiV0lZIqJTmJlSq7jZjBDWVMoMajkBGATWVMmIaikBNAnU8/lbTVOfdsGoqzbslre2EyoRKtU3CwAQIjBQQKqVvDjWV0u2Knh5/q+bX6S1UyoBoCAI1CQiVaoI1LIGMAkKljJglhxIqlQSb4uZCpSlefKc+EQJCpfRlEiql2wmVqtn1eguVMkEahkANAkKlGlANSSCzgFApM2iJ4YRKJbCmvKlQaco3gNNvvYBQKX2JhErpdkKlanad3moqqak0uI28/S3+wlJTKc5KTaU4p9yt1FTKLTp6vDpCJW9/i1s/NZXinLTy9jd7gEDbBYRKaSukplKaW38vj79VNBQqCZWESukXkVApzk6oFOeUu5VQKbeoUKk50fgjCZXiraa9ZZk7lR7a+GD41No1Yfmpb5x2NudPoDEBoVIatVApzU2oVN2tN4JQSagkVEq/oIRKcXZCpTin3K3aGCpdeum/hUcfWR8e2fpbuU93rOMtWPDY4bdtyzeN3Rfc0BnsZ9uOzTfoPBxp8+YQ9ljwd2GfRUvDGWc8fR6eoVPKJSBUyiVpHAL1CAiV0lyFSmluQqXqbjNGUFMpM6jhCGQUUFMpI6ahxi7wp3++a7j/gbFPwwTmocCSg7eF00/bMg/PzCnlEigTKuU6pnEIEIgXECrFWw22VFMp3a7o6fG3an6d3kKlDIiGIFCTgFCpJljDjkWgGyqdsWJLWLQo4209YzmbHQfdd89dO//y8CPbb5vxNRaBXbcvwX77juXQDjohAkKlCVko05xaAaFS+tILldLthErV7Hq9hUqZIA1DoAYBoVINqIYcm8BffWCXUNTA+b03bglPeuL8CZXqKNQ9tkVyYALzVECoNE8X1mnNGwGhUvpSCpXS7YRK1ew6vdVUUlNpcBt5+1v8haWmUpyVmkpxTrlbtbGm0sUXP1ZT6dW/c5JQaY4F9/a3+CuijXs9fvZaNiVQJlRSqLupVXEcAjsEhEppu0FNpTS3/l4ef6toKFQSKgmV0i8ioVKcnVApzil3qzZ+0BYqxa+yUCneqo17PX72WjYlIFRqStpxlWvI0QAAH3BJREFUCKQJCJXS3IRKaW5CpepuvRGESkIloVL6BSVUirMTKsU55W7Vxg/aQqX4VRYqxVu1ca/Hz17LpgSESk1JOw6BNAGhUpqbUCnNTahU3W3GCGoqZQY1HIGMAmoqZcQ01NgF1FQa+xKYAIGpFSgTKk0tkhMnMEYBoVI6vppK6XZFT4+/VfPr9BYqZUA0BIGaBIRKNcEadiwCQqWxsDsoAQLbBYRKtgGBdgsIldLXR6iUbidUqmbX6y1UygRpGAI1CAiVakA15NgEhEpjo3dgAlMvIFSa+i0AoOUCQqX0BRIqpdsJlarZdXqrqaSm0uA28va3+AtLTaU4KzWV4pxyt2pjnRk1leJXWU2leKs27vX42WvZlECZUMnb35paFcchsENAqJS2G9RUSnPr7+Xxt4qGQiWhklAp/SISKsXZCZXinHK3auMHbaFS/CoLleKt2rjX42evZVMCQqWmpB2HQJqAUCnNTaiU5iZUqu7WG0GoJFQSKqVfUEKlODuhUpxT7lZt/KAtVIpfZaFSvFUb93r87LVsSkCo1JS04xBIExAqpbkJldLchErV3WaMoKZSZlDDEcgooKZSRkxDjV1ATaWxL4EJEJhagTKh0tQiOXECYxQQKqXjq6mUblf09PhbNb9Ob6FSBkRDEKhJQKhUE6xhxyIgVBoLu4MSILBdQKhkGxBot4BQKX19hErpdkKlana93kKlTJCGIVCDgFCpBlRDjk1AqDQ2egcmMPUCQqWp3wIAWi4gVEpfIKFSup1QqZpdp7eaSmoqDW4jb3+Lv7DUVIqzUlMpzil3qzbWmVFTKX6V1VSKt2rjXo+fvZZNCZQJlbz9ralVcRwCOwSESmm7QU2lNLf+Xh5/q2goVBIqCZXSLyKhUpydUCnOKXerNn7QFirFr7JQKd6qjXs9fvZaNiUgVGpK2nEIpAkIldLchEppbkKl6m69EYRKQiWhUvoFJVSKsxMqxTnlbtXGD9pCpfhVFirFW7Vxr8fPXsumBIRKTUk7DoE0AaFSmptQKc1NqFTdbcYIaiplBjUcgYwCaiplxDTU2AXUVBr7EpgAgakVKBMqTS2SEycwRgGhUjq+mkrpdkVPj79V8+v0FiplQDQEgZoEhEo1wRp2LAJCpbGwOygBAtsFhEq2AYF2CwiV0tdHqJRuJ1SqZtfrLVTKBGkYAjUICJVqQDXk2ASESmOjd2ACUy8gVJr6LQCg5QJCpfQFEiql2wmVqtl1equppKbS4Dby9rf4C0tNpTgrNZXinHK3amOdGTWV4ldZTaV4qzbu9fjZa9mUQJlQydvfmloVxyGwQ0ColLYb1FRKc+vv5fG3ioZCJaGSUCn9IhIqxdkJleKccrdq4wdtoVL8KguV4q3auNfjZ69lUwJCpaakHYdAmoBQKc1NqJTmJlSq7tYbQagkVBIqpV9QQqU4uzvu+GH4yg2fDi995Yq4Dg21uv4f1oSlzzk6PP3Qp1U64gMPbAprr7gknPjqt1QaJ3fnL19/VXjaIb8SDvr5X8g9dPJ4l3/k9rBg67+E1/6nZeFx+ycP07qO++21a2dOD/10c7a5CZXiKYVK8VbT3FKoNM2r79wnQUColLZKQqU0N6FSdbcZI6iplBnUcAQyCsyHmkqXfWSXsOG7CzKq5BtqycHbwumnbak04FXX7BK+dks7z6/SidXY+a1v3ixUqtHX0AQI7CxQJlTiR4BA8wJCpXRzNZXS7YqeHn+r5tfpLVTKgGgIAjUJzKdQab99Q9j1sRs6xv61efsNJQ89HELOUGnvvbeFPXYXLsUs7hkrNodFi2JaTkabOu5UmowzN0sCkyMgVJqctTLT6RQQKqWvu1Ap3U6oVM2u11uolAnSMARqEJgPodLHr9gl3PqtBeE1r94SDnvGthqUyg+5YUMIl12+a5ZQ6brP7hJuvGlBOP5lW8LRR7Xj/MqL6FFFQKhURU9fAs0ICJWacXYUAqkCQqVUuRCESul2QqVqdp3eaiqpqTS4jbz9Lf7CUlMpzupjf3NPePBHnwq/9hsrWhUqXbv2E2GvRceEM04/KO5ERrT69HWPhv/znYvD0ue/pVWhUhvrzGy4/TvhO9/6Rvj1V5xUybxtnesIldRUil/lNu71+Nlr2ZRAmVDJ29+aWhXHIbBDQKiUthvUVEpz6+/l8beKhkIloZJQKf0iEirF2QmV4pxyt2rjB22hUvwqC5Xirdq41+Nnr2VTAkKlpqQdh0CagFApzU2olOYmVKru1htBqCRUEiqlX1BCpTg7oVKcU+5WbfygLVSKX2WhUrxVG/d6/Oy1bEpAqNSUtOMQSBMQKqW5CZXS3IRK1d1mjKCmUmZQwxHIKKCmUkbMvqHUVKrHdVpHrePxt2m1dN4E6hIoEyrVNQfjEiAwWkColL471FRKtyt6evytml+nt1ApA6IhCNQkIFSqB1aoVI/rtI4qVJrWlXfekyQgVJqk1TLXaRQQKqWvulAp3U6oVM2u11uolAnSMARqEBAq1YC6fUihUj2u0zqqUGlaV955T5KAUGmSVstcp1FAqJS+6kKldDuhUjW7Tm81ldRUGtxG3v4Wf2GpqRRnpaZSnFPuVm2sM6OmUvwqq6kUb9XGvR4/ey2bEigTKnn7W1Or4jgEdggIldJ2g5pKaW79vTz+VtFQqCRUEiqlX0RCpTg7oVKcU+5WbfygLVSKX2WhUrxVG/d6/Oy1bEpAqNSUtOMQSBMQKqW5CZXS3IRK1d16IwiVhEpCpfQLSqgUZydUinPK3aqNH7SFSvGrLFSKt2rjXo+fvZZNCQiVmpJ2HAJpAkKlNDehUpqbUKm624wR1FTKDGq4aIEf3RPCuht3iW4f0/AZv7g1HPaMbUOb1nG8mDlVabPLwhB23f7/bXp0a5Vhxtr3ttsWhIceDuH0UzeHJUvGOpXewbs1lfbbN4RDDx2+X2Jn+t07FoT77gvhpBO2hOccXm2s2GNq1y4BNZXatR5mQ2CYQJlQiSABAs0LCJXSzdVUSrcrenr8rZpfp7dQKQOiIZIEuh/skzqP6PRrx20Nxf8N+6rjeDnnPt/HamOolNNcqJRTc7LGEipN1nqZ7XQKCJWmc92d9eQICJXS10qolG4nVKpm1+stVMoEaZjSAt2Q5/GPD+HYo7eU7t/f4VvfXhhu/daCTqA0V6iU43iVJluic3GX0p677xIe/umjJXq1s2lxR1BxZ1Abvoo7p4o7qHJ+Hfy0beGAA3KOaKxJERAqTcpKmec0CwiVpnn1nfskCAiV0ldJqJRuJ1SqZtfpraaSmkqD26jJt799/wcLwhV/c1XYbc+l4cwzn15pR3/x+oXhtvXnh0OXvmNkqJTzeMVk1VSKW7J77/lhuP5znw4nL18R16GhVjF7PWYqP9u0KXz88kvCaa9/S0zzxtq0sc6Mmkrxy6+mUrxVG/d6/Oy1bEqgTKjk7W9NrYrjENghIFRK2w1qKqW59ffy+FtFQ6GSUEmolH4RCZXi7IRKcU65W7Xxg7ZQKX6VhUrxVm3c6/Gz17IpAaFSU9KOQyBNQKiU5iZUSnMTKlV3640gVBIqCZXSLyihUpydUCnOKXerNn7QFirFr7JQKd6qjXs9fvZaNiUgVGpK2nEIpAkIldLchEppbkKl6m4zRpjkmkrF40xFHZ2Yrz322BaOPuqxNzOV6Ve079boKdsvZl7T3OaBBxeEr92yICw5eFs4/bRqNZWKx9+K/yvG+g9Lhr+BK+fxmlq3PXZbGPbda7dw78ZNTR3ScQgQKCmgplJJMM0JjEGgTKg0huk5JIGpFxAqpW8BNZXS7YqeHn+r5tfpPcmhUhFIXHVN3CvpH7d/CG998+bOOZfpV7Q/79y0fhmWZyqGyBkqxYDlOF7McXK0ESrlUDQGgXoFhEr1+hqdQA4BoVIORWMQqE9AqJRuK1RKtxMqVbPr9Z4PodKTnrgtHPaM4XenbNq0INx404IwLFSarV8BVNz5MixUmqtfpqWZmmH2X7wtPOfw4esXi1C8Se5/f/ex9ZrrK8fx5jpGru8LlXJJGodAfQJCpfpsjUwgl4BQKZekcQjUIyBUSncVKqXbFT3dqRThd+KKc8JtG+7qtDx0yUHh6tWrer1y1VR68KH9w7/96/8Kv7T0Nb2xN3zn02H/A34+7Lvf4p2+93/+9+fD7rsvDk886Hm99l+76f8Jz3remWGXXffo/NlDD94RvnfHzDEH+91x54LwvdsvDj/31N8Nv3Xy8HeV3/9ACH996ZfCwl0WheN+7YjO2DH9inbv/+Mvd9q/+NeP7vW769/+OvzcQa8Mv/1bjx+pH1MLI/bNIleuWR2Oe+krwoGPf8LI462/5Z/Cjx/eGI465sUj28QeL+aNWN++dX24+3t3huNe8vKRx4t9I1bOWhjFM8Wvf9MfzHpV5DyemkoRP4C2N1FTKc4pd6ucez3X3NRUipeM+T0SP9r8btnGvT6/xSfz7MqESrF/Z5pMCbMm0E4BoVLauqiplObW30uoNIfh6W+7INx738ZekFQETAcesChcduHZnZ65QqUbvnxA+OnGdeGHG3+3N6MD9rk27LL708Le+yze6Xv77/25sGXrovDQIy/otT/ocReGux/4vbB1256dP9tj1++GxXvPHHNYvyfv/5dRodLg8ebqV8yhGyo9+NNje/N80uIPC5WESp39IFSK+yEuVIpzyt2qjR+0hUrxqyxUirdq416Pn72WTQkIlZqSdhwCaQJCpTQ3oVKam1CphNuxy84Kb195Slh2/DGdXmuvWxfef8knwg1rL+r8exEq7bH4XeFnP7k2hG2bw4KF+4QFuz0/bPnpx7b/+6awyz5nhq2bPh8W7PLzISzcf/sf3RAW7v27YcvDfzrje/c9sH/Ya9d1YfETfifsu/2GoU0/214M+7ufCo9ufdr2+8kWz/hecdwf3/+5sHDX7X++3/N7Z3PvnX8aDnjKmdvn8Fio9Ogjd4SfbLxh+5g7gqph/e7/3l+Fw579O+E//sf9hsr85CchXPm3X9zpeHP1Kwb72Ecfu1Np78WP+RVfD3z/snDoYa8Ixx77cyNXIubDQOx/BXOnUvyGd6dSCDet+0LYZ99FYenhO+4CjBec2XLN5R8Ir1w2+xsSY8YWKsUo5W/Txg/aQqX4dY75PRI/2vxu2ca9Pr/FJ/PshEqTuW5mPT0CQqW0tRYqpbn193Kn0iyG62+9PSw/87yw5uJzw9LDDum0HPyza67bGq75TLW3bvVP4Y2nbw2H/IcQ7tv+yNkF759Z36b7verLbgQC0yOw264Lw1677xo2/mR7UuuLAIFWCuy1x2MvjPjppny/T1t5oiZFYIIFFu+ze3j4kc1hy5atE3wWpk5g/gosXLAgLN53t3D/Q/7OW3aVD1z0WPkYX2kCQqVZ3GJCpXvu2xZu37AtfPAjO/4i/CuHLQzfuPWxX7i/euTCcPTzF0Svzs8/dWHYe6/tdxk9GraPO/OXdvd70YNpSIAAAQIECBAgQIAAAQIECBCoSUCoVDFUKrpv2bItbN5a7c1bNa2vYQlMvcDC7ZnuLrssCI9udo1O/WYA0FqBXYsLdfuX36WtXSITIxB233VB2Lz977z+ymszEGinwPYblcJuuywMP9vsbsKyK1S8LdpXuoBQaQ67YTWVzjn/0vDNL63u9MxVqHu/RYvDV2++MbzqpOW9GV3/+c+EJz/lqWHY94bVfRksenz3XXfsNOawfjF1X1L7DatpEVPjKKYWhppKj22VnLUw1FRSU6nMr5OYNx3GjBf7psOYsXK2yXlt5ZqXmkrxkjG/R+JHm98t27jX57f4ZJ6dmkqTuW5mPT0CaiqlrbWaSmlu/b2ESnMYNvX2N6HSzIWI+TAgVBIqdXfNsAC1+73ivzzsu9du4d6Nm6J+YirUHcXUaSRUirfK1VKoFC8Z83skfrT53VKoNL/XN9fZCZVySRqHQD0CQqU0V6FSmptQqaTbiSvOCbdtuKvT69AlB4WrV6/qjeBOpdnfbOVOpeGb7du3rg93f+/OcNxLXj5yN8bevZHzw4A7ldypVObHo1CpjFaetkKleEehUrxVzt8j8UfVctIEhEqTtmLmO20CQqW0FRcqpbkJlaq7zRjhoZ88Gh766ebMoxqOAIEcAmXvVMpxTGMQIFBOYL+9du108Lu0nJvWBJoUKBMqNTkvxyJA4DEBoVL6TnjKgdvflOUrWcDjb8l0OzoKlTIgGoJATQJCpZpgDUsgo4BQKSOmoQjUJCBUqgnWsAQyCQiV0iGFSul2RU+hUjW/Tm+hUgZEQxCoSUCoVBOsYQlkFBAqZcQ0FIGaBIRKNcEalkAmAaFSOqRQKd1OqFTNrtNbTSU1lQa3UUydGTWVHlMbfGNh6iWpUHeqXLV+MXs95gix9cNixsrZpo11ZtRUil9hNZXirdq41+Nnr2VTAmVCpdiXqTQ1d8chMA0CQqW0VVZTKc2tv5c7lSoaCpWESkKl9ItIqBRnd+89PwzXf+7T4eTlK+I6NNRKqNQQdN9hhErx5kKleCuhUrzVNLcUKk3z6jv3SRAQKqWtklApzU2oVN2tN4JQSagkVEq/oIRKcXZCpTin3K3a+EFbqBS/ykKleKs27vX42WvZlIBQqSlpxyGQJiBUSnMTKqW5CZWquxmBAAECBAgQIECAAAECBAgQIDDVAh5/m+rld/IECBAgQIAAAQIECBAgQIAAgTQBoVKam14ECBAgQIAAAQIECBAgQIAAgakWECpN9fI7eQIECBAgQIAAAQIECBAgQIBAmoBQKc2t0+vEFeeE2zbc1fnnQ5ccFK5evarCaLoSIJAqUOZaXHvdunDO+ZfudKhvfml16uH1I0CgosD6W28Py888L6y5+Nyw9LBDKo6mOwECVQRir0e/T6so60sgn8Dpb7sgfOWfb50xoL/X5vM10twCQqW5jYa2KC7ee+/b2AuSig+1Bx6wKFx24dmJI+pGgECKQNlrsfhL8Psv+US4Ye1FKYfThwCBzALHLjsr3PfAQ51RhUqZcQ1HoKRAmevR79OSuJoTqEmguG77/177zvd+MKy7eb2/69bkbdidBYRKibuiuHjfvvKUsOz4Yzoj+MWaCKkbgYoCZa9F12pFcN0J1CAQe2dEDYc2JAECAwKx16Pfp7YOgXYKxF7D7Zy9WU2igFApYdWGXagu3gRIXQhUFEi5Fofdru8W4YoLoTuBigJ+h1YE1J1ARoHY69Hv04zohiKQUeCiD18ZrvjkF92plNHUULMLCJUSdkjKB9mEw+hCgMAcAjmuxcHH56ATINC8QOyH2OZn5ogEpk8g9Xr0+3T69oozbp9A9/pd9Y7X9Z6oad8szWi+CQiVElY0xwfZhMPqQoDAgECOa7E7hruVbC8C4xNI/RA7vhk7MoH5K5B6Pfp9On/3hDObDIHuNbjytSeEs844eTImbZbzQkColLiMw+q4FG+U8sE0EVQ3AokCVa/F7u37rt3EBdCNQAaB1A+xGQ5tCAIEIv6DTQyS36cxStoQqEege/154UU9vkadXUColLhDyr5xKvEwuhEgMIfAXNdi8WbG4uvq1as6/zv4hgxvbrTFCIxfQKg0/jUwAwJdgVHXo9+n9giBdgoomt/OdZmmWQmVKqx28cv1tg13dUY4dMlBvQ+tFYbUlQCBBIHZrsXBvwT3ty0OdeRzDwuXXXh2wlF1IUAgh0D/K8yL8Q7Yfz/FRXPAGoNAgsBs16PfpwmguhCoWaAbAg87jLpKNeMbvicgVLIZCBAgQIAAAQIECBAgQIAAAQIESgsIlUqT6UCAAAECBAgQIECAAAECBAgQICBUsgcIECBAgAABAgQIECBAgAABAgRKCwiVSpPpQIAAAQIECBAgQIAAAQIECBAgIFSyBwgQIECAAAECBAgQIECAAAECBEoLCJVKk+lAgAABAgQIECBAgAABAgQIECAgVLIHCBAgQIAAAQIECBAgQIAAAQIESgsIlUqT6UCAAAECBAgQIECAAAECBAgQICBUsgcIECBAgAABAgQIECBAgAABAgRKCwiVSpPpQIAAAQIECBAgQIAAAQIECBAgIFSyBwgQIECAAAECBAgQIECAAAECBEo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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_step_sizes(show_intervals=True)" ] }, { "cell_type": "code", "execution_count": 14, "id": "3d012f8e-4066-40b6-9b9a-d1e9dd7532c7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2 S <-> U\n", "Final concentrations: [U] = 72.8 ; [S] = 18.18\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.0054\n", " Formula used: [U] / [S]\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.1349 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "S <-> X\n", "Final concentrations: [X] = 36.23 ; [S] = 18.18\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99313\n", " Formula used: [X] / [S]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 0.3437 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": 15, "id": "9dd856c0-58e6-4048-8b03-90f68e725232", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: 2 S <-> U\n" ] }, { "data": { "text/html": [ "
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TIMEDelta UDelta XDelta Sreactionsubsteptime_subdivisiondelta_timecaption
00.0000-1.0000000.02.0000000010.0100
10.0000-0.5000000.01.0000000010.0050
20.0050-0.1975000.00.3950000010.0025
30.0075-0.3491750.00.6983500010.0050
40.0125-0.1316930.00.2633850010.0025
50.0150-0.2259930.00.4519870010.0050
60.0200-0.1560400.00.3120800010.0050
70.0250-0.0951570.00.1903150010.0050
80.0300-0.0422370.00.0844730010.0050
90.03500.0036970.0-0.0073940010.0050
100.04000.0869990.0-0.1739970010.0100
110.05000.1123450.0-0.2246900010.0050
120.05500.2746600.0-0.5493210010.0100
130.06500.3603670.0-0.7207350010.0100
140.07500.4211210.0-0.8422420010.0100
150.08500.4630920.0-0.9261850010.0100
160.09500.4909520.0-0.9819050010.0100
170.10501.0164670.0-2.0329340010.0200
180.12500.5269840.0-1.0539670010.0100
190.13501.0491750.0-2.0983500010.0200
200.15500.5141330.0-1.0282660010.0100
210.16501.0096080.0-2.0192150010.0200
220.18500.9687930.0-1.9375870010.0200
230.20500.9233650.0-1.8467310010.0200
240.22500.8768920.0-1.7537850010.0200
250.24500.8311380.0-1.6622760010.0200
260.26500.7869410.0-1.5738820010.0200
270.28500.7446680.0-1.4893360010.0200
280.30500.7044470.0-1.4088950010.0200
290.32500.6662870.0-1.3325730010.0200
300.34501.2602710.0-2.5205410010.0400
310.38500.5616960.0-1.1233920010.0200
320.40501.0623250.0-2.1246500010.0400
330.44500.9468280.0-1.8936570010.0400
340.48500.8438870.0-1.6877730010.0400
350.52500.7521370.0-1.5042740010.0400
360.56500.6703620.0-1.3407250010.0400
370.60501.1949570.0-2.3899150010.0800
380.68500.4675600.0-0.9351190010.0400
390.72500.8334500.0-1.6669010010.0800
400.80500.6522200.0-1.3044400010.0800
410.88501.0207950.0-2.0415910010.1600
421.04500.5768600.0-1.1537210010.1600
431.20500.6519780.0-1.3039550010.3200
441.52500.1697980.0-0.3395950010.6400
\n", "
" ], "text/plain": [ " TIME Delta U Delta X Delta S reaction substep time_subdivision \\\n", "0 0.0000 -1.000000 0.0 2.000000 0 0 1 \n", "1 0.0000 -0.500000 0.0 1.000000 0 0 1 \n", "2 0.0050 -0.197500 0.0 0.395000 0 0 1 \n", "3 0.0075 -0.349175 0.0 0.698350 0 0 1 \n", "4 0.0125 -0.131693 0.0 0.263385 0 0 1 \n", "5 0.0150 -0.225993 0.0 0.451987 0 0 1 \n", "6 0.0200 -0.156040 0.0 0.312080 0 0 1 \n", "7 0.0250 -0.095157 0.0 0.190315 0 0 1 \n", "8 0.0300 -0.042237 0.0 0.084473 0 0 1 \n", "9 0.0350 0.003697 0.0 -0.007394 0 0 1 \n", "10 0.0400 0.086999 0.0 -0.173997 0 0 1 \n", "11 0.0500 0.112345 0.0 -0.224690 0 0 1 \n", "12 0.0550 0.274660 0.0 -0.549321 0 0 1 \n", "13 0.0650 0.360367 0.0 -0.720735 0 0 1 \n", "14 0.0750 0.421121 0.0 -0.842242 0 0 1 \n", "15 0.0850 0.463092 0.0 -0.926185 0 0 1 \n", "16 0.0950 0.490952 0.0 -0.981905 0 0 1 \n", "17 0.1050 1.016467 0.0 -2.032934 0 0 1 \n", "18 0.1250 0.526984 0.0 -1.053967 0 0 1 \n", "19 0.1350 1.049175 0.0 -2.098350 0 0 1 \n", "20 0.1550 0.514133 0.0 -1.028266 0 0 1 \n", "21 0.1650 1.009608 0.0 -2.019215 0 0 1 \n", "22 0.1850 0.968793 0.0 -1.937587 0 0 1 \n", "23 0.2050 0.923365 0.0 -1.846731 0 0 1 \n", "24 0.2250 0.876892 0.0 -1.753785 0 0 1 \n", "25 0.2450 0.831138 0.0 -1.662276 0 0 1 \n", "26 0.2650 0.786941 0.0 -1.573882 0 0 1 \n", "27 0.2850 0.744668 0.0 -1.489336 0 0 1 \n", "28 0.3050 0.704447 0.0 -1.408895 0 0 1 \n", "29 0.3250 0.666287 0.0 -1.332573 0 0 1 \n", "30 0.3450 1.260271 0.0 -2.520541 0 0 1 \n", "31 0.3850 0.561696 0.0 -1.123392 0 0 1 \n", "32 0.4050 1.062325 0.0 -2.124650 0 0 1 \n", "33 0.4450 0.946828 0.0 -1.893657 0 0 1 \n", "34 0.4850 0.843887 0.0 -1.687773 0 0 1 \n", "35 0.5250 0.752137 0.0 -1.504274 0 0 1 \n", "36 0.5650 0.670362 0.0 -1.340725 0 0 1 \n", "37 0.6050 1.194957 0.0 -2.389915 0 0 1 \n", "38 0.6850 0.467560 0.0 -0.935119 0 0 1 \n", "39 0.7250 0.833450 0.0 -1.666901 0 0 1 \n", "40 0.8050 0.652220 0.0 -1.304440 0 0 1 \n", "41 0.8850 1.020795 0.0 -2.041591 0 0 1 \n", "42 1.0450 0.576860 0.0 -1.153721 0 0 1 \n", "43 1.2050 0.651978 0.0 -1.303955 0 0 1 \n", "44 1.5250 0.169798 0.0 -0.339595 0 0 1 \n", "\n", " delta_time caption \n", "0 0.0100 \n", "1 0.0050 \n", "2 0.0025 \n", "3 0.0050 \n", "4 0.0025 \n", "5 0.0050 \n", "6 0.0050 \n", "7 0.0050 \n", "8 0.0050 \n", "9 0.0050 \n", "10 0.0100 \n", "11 0.0050 \n", "12 0.0100 \n", "13 0.0100 \n", "14 0.0100 \n", "15 0.0100 \n", "16 0.0100 \n", "17 0.0200 \n", "18 0.0100 \n", "19 0.0200 \n", "20 0.0100 \n", "21 0.0200 \n", "22 0.0200 \n", "23 0.0200 \n", "24 0.0200 \n", "25 0.0200 \n", "26 0.0200 \n", "27 0.0200 \n", "28 0.0200 \n", "29 0.0200 \n", "30 0.0400 \n", "31 0.0200 \n", "32 0.0400 \n", "33 0.0400 \n", "34 0.0400 \n", "35 0.0400 \n", "36 0.0400 \n", "37 0.0800 \n", "38 0.0400 \n", "39 0.0800 \n", "40 0.0800 \n", "41 0.1600 \n", "42 0.1600 \n", "43 0.3200 \n", "44 0.6400 " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_rxn_data(rxn_index=0)" ] }, { "cell_type": "code", "execution_count": 16, "id": "5ff51045-dfa3-4f04-94f4-5d66f1352d4a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: S <-> X\n" ] }, { "data": { "text/html": [ "
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TIMEDelta UDelta XDelta Sreactionsubsteptime_subdivisiondelta_timecaption
00.00000.0-3.0000003.0000001010.0100
10.00000.0-1.5000001.5000001010.0050
20.00500.0-0.7012500.7012501010.0025
30.00750.0-1.3590941.3590941010.0050
40.01250.0-0.6384920.6384921010.0025
50.01500.0-1.2403501.2403501010.0050
60.02000.0-1.1709751.1709751010.0050
70.02500.0-1.1089191.1089191010.0050
80.03000.0-1.0533081.0533081010.0050
90.03500.0-1.0033751.0033751010.0050
100.04000.0-1.9168901.9168901010.0100
110.05000.0-0.8774050.8774051010.0050
120.05500.0-1.6893241.6893241010.0100
130.06500.0-1.5702441.5702441010.0100
140.07500.0-1.4721671.4721671010.0100
150.08500.0-1.3902061.3902061010.0100
160.09500.0-1.3206591.3206591010.0100
170.10500.0-2.5214272.5214271010.0200
180.12500.0-1.1557611.1557611010.0100
190.13500.0-2.2299612.2299611010.0200
200.15500.0-1.0401851.0401851010.0100
210.16500.0-2.0165292.0165291010.0200
220.18500.0-1.8958601.8958601010.0200
230.20500.0-1.7871151.7871151010.0200
240.22500.0-1.6870421.6870421010.0200
250.24500.0-1.5938291.5938291010.0200
260.26500.0-1.5064131.5064131010.0200
270.28500.0-1.4241241.4241241010.0200
280.30500.0-1.3465021.3465021010.0200
290.32500.0-1.2731991.2731991010.0200
300.34500.0-2.4078642.4078641010.0400
310.38500.0-1.0729821.0729821010.0200
320.40500.0-2.0293042.0293041010.0400
330.44500.0-1.8086711.8086711010.0400
340.48500.0-1.6120271.6120271010.0400
350.52500.0-1.4367631.4367631010.0400
360.56500.0-1.2805541.2805541010.0400
370.60500.0-2.2826572.2826571010.0800
380.68500.0-0.8931510.8931511010.0400
390.72500.0-1.5920911.5920911010.0800
400.80500.0-1.2458981.2458981010.0800
410.88500.0-1.9499651.9499651010.1600
421.04500.0-1.1019421.1019421010.1600
431.20500.0-1.2454341.2454341010.3200
441.52500.0-0.3243540.3243541010.6400
\n", "
" ], "text/plain": [ " TIME Delta U Delta X Delta S reaction substep time_subdivision \\\n", "0 0.0000 0.0 -3.000000 3.000000 1 0 1 \n", "1 0.0000 0.0 -1.500000 1.500000 1 0 1 \n", "2 0.0050 0.0 -0.701250 0.701250 1 0 1 \n", "3 0.0075 0.0 -1.359094 1.359094 1 0 1 \n", "4 0.0125 0.0 -0.638492 0.638492 1 0 1 \n", "5 0.0150 0.0 -1.240350 1.240350 1 0 1 \n", "6 0.0200 0.0 -1.170975 1.170975 1 0 1 \n", "7 0.0250 0.0 -1.108919 1.108919 1 0 1 \n", "8 0.0300 0.0 -1.053308 1.053308 1 0 1 \n", "9 0.0350 0.0 -1.003375 1.003375 1 0 1 \n", "10 0.0400 0.0 -1.916890 1.916890 1 0 1 \n", "11 0.0500 0.0 -0.877405 0.877405 1 0 1 \n", "12 0.0550 0.0 -1.689324 1.689324 1 0 1 \n", "13 0.0650 0.0 -1.570244 1.570244 1 0 1 \n", "14 0.0750 0.0 -1.472167 1.472167 1 0 1 \n", "15 0.0850 0.0 -1.390206 1.390206 1 0 1 \n", "16 0.0950 0.0 -1.320659 1.320659 1 0 1 \n", "17 0.1050 0.0 -2.521427 2.521427 1 0 1 \n", "18 0.1250 0.0 -1.155761 1.155761 1 0 1 \n", "19 0.1350 0.0 -2.229961 2.229961 1 0 1 \n", "20 0.1550 0.0 -1.040185 1.040185 1 0 1 \n", "21 0.1650 0.0 -2.016529 2.016529 1 0 1 \n", "22 0.1850 0.0 -1.895860 1.895860 1 0 1 \n", "23 0.2050 0.0 -1.787115 1.787115 1 0 1 \n", "24 0.2250 0.0 -1.687042 1.687042 1 0 1 \n", "25 0.2450 0.0 -1.593829 1.593829 1 0 1 \n", "26 0.2650 0.0 -1.506413 1.506413 1 0 1 \n", "27 0.2850 0.0 -1.424124 1.424124 1 0 1 \n", "28 0.3050 0.0 -1.346502 1.346502 1 0 1 \n", "29 0.3250 0.0 -1.273199 1.273199 1 0 1 \n", "30 0.3450 0.0 -2.407864 2.407864 1 0 1 \n", "31 0.3850 0.0 -1.072982 1.072982 1 0 1 \n", "32 0.4050 0.0 -2.029304 2.029304 1 0 1 \n", "33 0.4450 0.0 -1.808671 1.808671 1 0 1 \n", "34 0.4850 0.0 -1.612027 1.612027 1 0 1 \n", "35 0.5250 0.0 -1.436763 1.436763 1 0 1 \n", "36 0.5650 0.0 -1.280554 1.280554 1 0 1 \n", "37 0.6050 0.0 -2.282657 2.282657 1 0 1 \n", "38 0.6850 0.0 -0.893151 0.893151 1 0 1 \n", "39 0.7250 0.0 -1.592091 1.592091 1 0 1 \n", "40 0.8050 0.0 -1.245898 1.245898 1 0 1 \n", "41 0.8850 0.0 -1.949965 1.949965 1 0 1 \n", "42 1.0450 0.0 -1.101942 1.101942 1 0 1 \n", "43 1.2050 0.0 -1.245434 1.245434 1 0 1 \n", "44 1.5250 0.0 -0.324354 0.324354 1 0 1 \n", "\n", " delta_time caption \n", "0 0.0100 \n", "1 0.0050 \n", "2 0.0025 \n", "3 0.0050 \n", "4 0.0025 \n", "5 0.0050 \n", "6 0.0050 \n", "7 0.0050 \n", "8 0.0050 \n", "9 0.0050 \n", "10 0.0100 \n", "11 0.0050 \n", "12 0.0100 \n", "13 0.0100 \n", "14 0.0100 \n", "15 0.0100 \n", "16 0.0100 \n", "17 0.0200 \n", "18 0.0100 \n", "19 0.0200 \n", "20 0.0100 \n", "21 0.0200 \n", "22 0.0200 \n", "23 0.0200 \n", "24 0.0200 \n", "25 0.0200 \n", "26 0.0200 \n", "27 0.0200 \n", "28 0.0200 \n", "29 0.0200 \n", "30 0.0400 \n", "31 0.0200 \n", "32 0.0400 \n", "33 0.0400 \n", "34 0.0400 \n", "35 0.0400 \n", "36 0.0400 \n", "37 0.0800 \n", "38 0.0400 \n", "39 0.0800 \n", "40 0.0800 \n", "41 0.1600 \n", "42 0.1600 \n", "43 0.3200 \n", "44 0.6400 " ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_rxn_data(rxn_index=1)" ] }, { "cell_type": "code", "execution_count": 17, "id": "03eec482-0b4a-4a15-ba33-1788f63fc60f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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TIMEUXSis_primaryprimary_timestepn_substepssubstep_numbercaption
00.000050.000000100.0000000.000000True0.010010
10.005049.50000098.5000002.500000True0.010010
20.007549.30250097.7987503.596250True0.002510
30.012548.95332596.4396565.653694True0.005010
40.015048.82163295.8011646.555571True0.002510
50.020048.59563994.5608148.247909True0.005010
60.025048.43959993.3898399.730964True0.005010
70.030048.34444192.28092011.030197True0.005010
80.035048.30220591.22761212.167978True0.005010
90.040048.30590290.22423813.163959True0.005010
100.050048.39290188.30734814.906851True0.010010
110.055048.50524687.42994315.559566True0.005010
120.065048.77990685.74061916.699569True0.010010
130.075049.14027384.17037417.549079True0.010010
140.085049.56139482.69820818.179004True0.010010
150.095050.02448781.30800218.643025True0.010010
160.105050.51543979.98734318.981779True0.010010
170.125051.53190677.46591619.470272True0.020010
180.135052.05889076.31015519.572066True0.010010
190.155053.10806474.08019419.703677True0.020010
200.165053.62219773.04000919.715597True0.010010
210.185054.63180571.02348019.712910True0.020010
220.205055.60059869.12762019.671183True0.020010
230.225056.52396467.34050519.611568True0.020010
240.245057.40085665.65346319.544825True0.020010
250.265058.23199464.05963419.476378True0.020010
260.285059.01893562.55322119.408909True0.020010
270.305059.76360361.12909719.343697True0.020010
280.325060.46805059.78259519.281305True0.020010
290.345061.13433758.50939619.221930True0.020010
300.385062.39460856.10153219.109253True0.040010
310.405062.95630455.02855019.058842True0.020010
320.445064.01862952.99924618.963496True0.040010
330.485064.96545751.19057618.878510True0.040010
340.525065.80934449.57854918.802763True0.040010
350.565066.56148148.14178618.735252True0.040010
360.605067.23184346.86123218.675082True0.040010
370.685068.42680044.57857618.567824True0.080010
380.725068.89436043.68542418.525856True0.040010
390.805069.72781042.09333318.451046True0.080010
400.885070.38003040.84743618.392504True0.080010
411.045071.40082638.89747018.300879True0.160010
421.205071.97768637.79552818.249100True0.160010
431.525072.62966336.55009418.190579True0.320010
442.165072.79946136.22573918.175339True0.640010
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" ], "text/plain": [ " TIME U X S is_primary primary_timestep \\\n", "0 0.0000 50.000000 100.000000 0.000000 True 0.0100 \n", "1 0.0050 49.500000 98.500000 2.500000 True 0.0100 \n", "2 0.0075 49.302500 97.798750 3.596250 True 0.0025 \n", "3 0.0125 48.953325 96.439656 5.653694 True 0.0050 \n", "4 0.0150 48.821632 95.801164 6.555571 True 0.0025 \n", "5 0.0200 48.595639 94.560814 8.247909 True 0.0050 \n", "6 0.0250 48.439599 93.389839 9.730964 True 0.0050 \n", "7 0.0300 48.344441 92.280920 11.030197 True 0.0050 \n", "8 0.0350 48.302205 91.227612 12.167978 True 0.0050 \n", "9 0.0400 48.305902 90.224238 13.163959 True 0.0050 \n", "10 0.0500 48.392901 88.307348 14.906851 True 0.0100 \n", "11 0.0550 48.505246 87.429943 15.559566 True 0.0050 \n", "12 0.0650 48.779906 85.740619 16.699569 True 0.0100 \n", "13 0.0750 49.140273 84.170374 17.549079 True 0.0100 \n", "14 0.0850 49.561394 82.698208 18.179004 True 0.0100 \n", "15 0.0950 50.024487 81.308002 18.643025 True 0.0100 \n", "16 0.1050 50.515439 79.987343 18.981779 True 0.0100 \n", "17 0.1250 51.531906 77.465916 19.470272 True 0.0200 \n", "18 0.1350 52.058890 76.310155 19.572066 True 0.0100 \n", "19 0.1550 53.108064 74.080194 19.703677 True 0.0200 \n", "20 0.1650 53.622197 73.040009 19.715597 True 0.0100 \n", "21 0.1850 54.631805 71.023480 19.712910 True 0.0200 \n", "22 0.2050 55.600598 69.127620 19.671183 True 0.0200 \n", "23 0.2250 56.523964 67.340505 19.611568 True 0.0200 \n", "24 0.2450 57.400856 65.653463 19.544825 True 0.0200 \n", "25 0.2650 58.231994 64.059634 19.476378 True 0.0200 \n", "26 0.2850 59.018935 62.553221 19.408909 True 0.0200 \n", "27 0.3050 59.763603 61.129097 19.343697 True 0.0200 \n", "28 0.3250 60.468050 59.782595 19.281305 True 0.0200 \n", "29 0.3450 61.134337 58.509396 19.221930 True 0.0200 \n", "30 0.3850 62.394608 56.101532 19.109253 True 0.0400 \n", "31 0.4050 62.956304 55.028550 19.058842 True 0.0200 \n", "32 0.4450 64.018629 52.999246 18.963496 True 0.0400 \n", "33 0.4850 64.965457 51.190576 18.878510 True 0.0400 \n", "34 0.5250 65.809344 49.578549 18.802763 True 0.0400 \n", "35 0.5650 66.561481 48.141786 18.735252 True 0.0400 \n", "36 0.6050 67.231843 46.861232 18.675082 True 0.0400 \n", "37 0.6850 68.426800 44.578576 18.567824 True 0.0800 \n", "38 0.7250 68.894360 43.685424 18.525856 True 0.0400 \n", "39 0.8050 69.727810 42.093333 18.451046 True 0.0800 \n", "40 0.8850 70.380030 40.847436 18.392504 True 0.0800 \n", "41 1.0450 71.400826 38.897470 18.300879 True 0.1600 \n", "42 1.2050 71.977686 37.795528 18.249100 True 0.1600 \n", "43 1.5250 72.629663 36.550094 18.190579 True 0.3200 \n", "44 2.1650 72.799461 36.225739 18.175339 True 0.6400 \n", "\n", " n_substeps substep_number caption \n", "0 1 0 \n", "1 1 0 \n", "2 1 0 \n", "3 1 0 \n", "4 1 0 \n", "5 1 0 \n", "6 1 0 \n", "7 1 0 \n", "8 1 0 \n", "9 1 0 \n", "10 1 0 \n", "11 1 0 \n", "12 1 0 \n", "13 1 0 \n", "14 1 0 \n", "15 1 0 \n", "16 1 0 \n", "17 1 0 \n", "18 1 0 \n", "19 1 0 \n", "20 1 0 \n", "21 1 0 \n", "22 1 0 \n", "23 1 0 \n", "24 1 0 \n", "25 1 0 \n", "26 1 0 \n", "27 1 0 \n", "28 1 0 \n", "29 1 0 \n", "30 1 0 \n", "31 1 0 \n", "32 1 0 \n", "33 1 0 \n", "34 1 0 \n", "35 1 0 \n", "36 1 0 \n", "37 1 0 \n", "38 1 0 \n", "39 1 0 \n", "40 1 0 \n", "41 1 0 \n", "42 1 0 \n", "43 1 0 \n", "44 1 0 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_conc_data()" ] }, { "cell_type": "code", "execution_count": 18, "id": "a479c269-4740-4866-9ec3-e736b8b09cb6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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TIMEDelta UDelta XDelta S
00.0000-1.000000-3.0000005.000000
10.0000-0.500000-1.5000002.500000
20.0050-0.197500-0.7012501.096250
30.0075-0.349175-1.3590942.057444
40.0125-0.131693-0.6384920.901878
50.0150-0.225993-1.2403501.692337
60.0200-0.156040-1.1709751.483055
70.0250-0.095157-1.1089191.299234
80.0300-0.042237-1.0533081.137781
90.03500.003697-1.0033750.995981
100.04000.086999-1.9168901.742892
110.05000.112345-0.8774050.652715
120.05500.274660-1.6893241.140004
130.06500.360367-1.5702440.849510
140.07500.421121-1.4721670.629925
150.08500.463092-1.3902060.464021
160.09500.490952-1.3206590.338754
170.10501.016467-2.5214270.488493
180.12500.526984-1.1557610.101794
190.13501.049175-2.2299610.131612
200.15500.514133-1.0401850.011919
210.16501.009608-2.016529-0.002686
220.18500.968793-1.895860-0.041727
230.20500.923365-1.787115-0.059615
240.22500.876892-1.687042-0.066742
250.24500.831138-1.593829-0.068447
260.26500.786941-1.506413-0.067469
270.28500.744668-1.424124-0.065212
280.30500.704447-1.346502-0.062393
290.32500.666287-1.273199-0.059374
300.34501.260271-2.407864-0.112677
310.38500.561696-1.072982-0.050411
320.40501.062325-2.029304-0.095347
330.44500.946828-1.808671-0.084986
340.48500.843887-1.612027-0.075746
350.52500.752137-1.436763-0.067511
360.56500.670362-1.280554-0.060171
370.60501.194957-2.282657-0.107258
380.68500.467560-0.893151-0.041968
390.72500.833450-1.592091-0.074810
400.80500.652220-1.245898-0.058543
410.88501.020795-1.949965-0.091625
421.04500.576860-1.101942-0.051778
431.20500.651978-1.245434-0.058521
441.52500.169798-0.324354-0.015241
\n", "
" ], "text/plain": [ " TIME Delta U Delta X Delta S\n", "0 0.0000 -1.000000 -3.000000 5.000000\n", "1 0.0000 -0.500000 -1.500000 2.500000\n", "2 0.0050 -0.197500 -0.701250 1.096250\n", "3 0.0075 -0.349175 -1.359094 2.057444\n", "4 0.0125 -0.131693 -0.638492 0.901878\n", "5 0.0150 -0.225993 -1.240350 1.692337\n", "6 0.0200 -0.156040 -1.170975 1.483055\n", "7 0.0250 -0.095157 -1.108919 1.299234\n", "8 0.0300 -0.042237 -1.053308 1.137781\n", "9 0.0350 0.003697 -1.003375 0.995981\n", "10 0.0400 0.086999 -1.916890 1.742892\n", "11 0.0500 0.112345 -0.877405 0.652715\n", "12 0.0550 0.274660 -1.689324 1.140004\n", "13 0.0650 0.360367 -1.570244 0.849510\n", "14 0.0750 0.421121 -1.472167 0.629925\n", "15 0.0850 0.463092 -1.390206 0.464021\n", "16 0.0950 0.490952 -1.320659 0.338754\n", "17 0.1050 1.016467 -2.521427 0.488493\n", "18 0.1250 0.526984 -1.155761 0.101794\n", "19 0.1350 1.049175 -2.229961 0.131612\n", "20 0.1550 0.514133 -1.040185 0.011919\n", "21 0.1650 1.009608 -2.016529 -0.002686\n", "22 0.1850 0.968793 -1.895860 -0.041727\n", "23 0.2050 0.923365 -1.787115 -0.059615\n", "24 0.2250 0.876892 -1.687042 -0.066742\n", "25 0.2450 0.831138 -1.593829 -0.068447\n", "26 0.2650 0.786941 -1.506413 -0.067469\n", "27 0.2850 0.744668 -1.424124 -0.065212\n", "28 0.3050 0.704447 -1.346502 -0.062393\n", "29 0.3250 0.666287 -1.273199 -0.059374\n", "30 0.3450 1.260271 -2.407864 -0.112677\n", "31 0.3850 0.561696 -1.072982 -0.050411\n", "32 0.4050 1.062325 -2.029304 -0.095347\n", "33 0.4450 0.946828 -1.808671 -0.084986\n", "34 0.4850 0.843887 -1.612027 -0.075746\n", "35 0.5250 0.752137 -1.436763 -0.067511\n", "36 0.5650 0.670362 -1.280554 -0.060171\n", "37 0.6050 1.194957 -2.282657 -0.107258\n", "38 0.6850 0.467560 -0.893151 -0.041968\n", "39 0.7250 0.833450 -1.592091 -0.074810\n", "40 0.8050 0.652220 -1.245898 -0.058543\n", "41 0.8850 1.020795 -1.949965 -0.091625\n", "42 1.0450 0.576860 -1.101942 -0.051778\n", "43 1.2050 0.651978 -1.245434 -0.058521\n", "44 1.5250 0.169798 -0.324354 -0.015241" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_delta_data()" ] }, { "cell_type": "code", "execution_count": 19, "id": "b4d5101f-f3c9-4e0c-a9ae-e2774136a88a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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TIMEDelta UDelta XDelta SL2actionsstep_factors
00.0000-1.000000-3.0000005.0000001.972027ABORT0.5
10.0000-0.500000-1.5000002.5000000.986013OK0.5
20.0050-0.197500-0.7012501.0962500.438751OK2.0
30.0075-0.349175-1.3590942.0574440.830136OK0.5
40.0125-0.131693-0.6384920.9018780.370944OK2.0
50.0150-0.225993-1.2403501.6923370.703448OK1.0
60.0200-0.156040-1.1709751.4830550.632015OK1.0
70.0250-0.095157-1.1089191.2992340.570260OK1.0
80.0300-0.042237-1.0533081.1377810.517020OK1.0
90.03500.003697-1.0033750.9959810.471257OK2.0
100.04000.086999-1.9168901.7428920.864080OK0.5
110.05000.112345-0.8774050.6527150.366439OK2.0
120.05500.274660-1.6893241.1400040.685473OK1.0
130.06500.360367-1.5702440.8495100.607106OK1.0
140.07500.421121-1.4721670.6299250.551908OK1.0
150.08500.463092-1.3902060.4640210.512341OK1.0
160.09500.490952-1.3206590.3387540.483038OK2.0
170.10501.016467-2.5214270.4884930.920714OK0.5
180.12500.526984-1.1557610.1017940.424769OK2.0
190.13501.049175-2.2299610.1316120.822653OK0.5
200.15500.514133-1.0401850.0119190.386790OK2.0
210.16501.009608-2.016529-0.0026860.751717OK1.0
220.18500.968793-1.895860-0.0417270.709819OK1.0
230.20500.923365-1.787115-0.0596150.670815OK1.0
240.22500.876892-1.687042-0.0667420.634167OK1.0
250.24500.831138-1.593829-0.0684470.599608OK1.0
260.26500.786941-1.506413-0.0674690.566971OK1.0
270.28500.744668-1.424124-0.0652120.536129OK1.0
280.30500.704447-1.346502-0.0623930.506974OK1.0
290.32500.666287-1.273199-0.0593740.479409OK2.0
300.34501.260271-2.407864-0.1126770.906690OK0.5
310.38500.561696-1.072982-0.0504110.404054OK2.0
320.40501.062325-2.029304-0.0953470.764177OK1.0
330.44500.946828-1.808671-0.0849860.681094OK1.0
340.48500.843887-1.612027-0.0757460.607043OK1.0
350.52500.752137-1.436763-0.0675110.541044OK1.0
360.56500.670362-1.280554-0.0601710.482220OK2.0
370.60501.194957-2.282657-0.1072580.859583OK0.5
380.68500.467560-0.893151-0.0419680.336335OK2.0
390.72500.833450-1.592091-0.0748100.599536OK1.0
400.80500.652220-1.245898-0.0585430.469169OK2.0
410.88501.020795-1.949965-0.0916250.734301OK1.0
421.04500.576860-1.101942-0.0517780.414960OK2.0
431.20500.651978-1.245434-0.0585210.468995OK2.0
441.52500.169798-0.324354-0.0152410.122143OK2.0
\n", "
" ], "text/plain": [ " TIME Delta U Delta X Delta S L2 actions step_factors\n", "0 0.0000 -1.000000 -3.000000 5.000000 1.972027 ABORT 0.5\n", "1 0.0000 -0.500000 -1.500000 2.500000 0.986013 OK 0.5\n", "2 0.0050 -0.197500 -0.701250 1.096250 0.438751 OK 2.0\n", "3 0.0075 -0.349175 -1.359094 2.057444 0.830136 OK 0.5\n", "4 0.0125 -0.131693 -0.638492 0.901878 0.370944 OK 2.0\n", "5 0.0150 -0.225993 -1.240350 1.692337 0.703448 OK 1.0\n", "6 0.0200 -0.156040 -1.170975 1.483055 0.632015 OK 1.0\n", "7 0.0250 -0.095157 -1.108919 1.299234 0.570260 OK 1.0\n", "8 0.0300 -0.042237 -1.053308 1.137781 0.517020 OK 1.0\n", "9 0.0350 0.003697 -1.003375 0.995981 0.471257 OK 2.0\n", "10 0.0400 0.086999 -1.916890 1.742892 0.864080 OK 0.5\n", "11 0.0500 0.112345 -0.877405 0.652715 0.366439 OK 2.0\n", "12 0.0550 0.274660 -1.689324 1.140004 0.685473 OK 1.0\n", "13 0.0650 0.360367 -1.570244 0.849510 0.607106 OK 1.0\n", "14 0.0750 0.421121 -1.472167 0.629925 0.551908 OK 1.0\n", "15 0.0850 0.463092 -1.390206 0.464021 0.512341 OK 1.0\n", "16 0.0950 0.490952 -1.320659 0.338754 0.483038 OK 2.0\n", "17 0.1050 1.016467 -2.521427 0.488493 0.920714 OK 0.5\n", "18 0.1250 0.526984 -1.155761 0.101794 0.424769 OK 2.0\n", "19 0.1350 1.049175 -2.229961 0.131612 0.822653 OK 0.5\n", "20 0.1550 0.514133 -1.040185 0.011919 0.386790 OK 2.0\n", "21 0.1650 1.009608 -2.016529 -0.002686 0.751717 OK 1.0\n", "22 0.1850 0.968793 -1.895860 -0.041727 0.709819 OK 1.0\n", "23 0.2050 0.923365 -1.787115 -0.059615 0.670815 OK 1.0\n", "24 0.2250 0.876892 -1.687042 -0.066742 0.634167 OK 1.0\n", "25 0.2450 0.831138 -1.593829 -0.068447 0.599608 OK 1.0\n", "26 0.2650 0.786941 -1.506413 -0.067469 0.566971 OK 1.0\n", "27 0.2850 0.744668 -1.424124 -0.065212 0.536129 OK 1.0\n", "28 0.3050 0.704447 -1.346502 -0.062393 0.506974 OK 1.0\n", "29 0.3250 0.666287 -1.273199 -0.059374 0.479409 OK 2.0\n", "30 0.3450 1.260271 -2.407864 -0.112677 0.906690 OK 0.5\n", "31 0.3850 0.561696 -1.072982 -0.050411 0.404054 OK 2.0\n", "32 0.4050 1.062325 -2.029304 -0.095347 0.764177 OK 1.0\n", "33 0.4450 0.946828 -1.808671 -0.084986 0.681094 OK 1.0\n", "34 0.4850 0.843887 -1.612027 -0.075746 0.607043 OK 1.0\n", "35 0.5250 0.752137 -1.436763 -0.067511 0.541044 OK 1.0\n", "36 0.5650 0.670362 -1.280554 -0.060171 0.482220 OK 2.0\n", "37 0.6050 1.194957 -2.282657 -0.107258 0.859583 OK 0.5\n", "38 0.6850 0.467560 -0.893151 -0.041968 0.336335 OK 2.0\n", "39 0.7250 0.833450 -1.592091 -0.074810 0.599536 OK 1.0\n", "40 0.8050 0.652220 -1.245898 -0.058543 0.469169 OK 2.0\n", "41 0.8850 1.020795 -1.949965 -0.091625 0.734301 OK 1.0\n", "42 1.0450 0.576860 -1.101942 -0.051778 0.414960 OK 2.0\n", "43 1.2050 0.651978 -1.245434 -0.058521 0.468995 OK 2.0\n", "44 1.5250 0.169798 -0.324354 -0.015241 0.122143 OK 2.0" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_L2_data()" ] }, { "cell_type": "markdown", "id": "ab5ebd8c-590d-4d35-8463-3f70e8859c99", "metadata": {}, "source": [ "#### Notice how the first step got aborted, and re-run, because of the large adjusted L2 value in the concentrations " ] }, { "cell_type": "code", "execution_count": null, "id": "c9469a67-c513-492a-8bff-a20d0958ba39", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "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 }