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"## A complex (multistep) reaction `A <-> C` derived from 2 coupled elementary reactions: \n",
"## `A <-> B` (fast) and `B <-> C` (slow) \n",
"A repeat of experiment `cascade_2_b`, but with the fast/slow elementary reactions in reverse order.\n",
"\n",
"In PART 1, a time evolution of [A], [B] and [C] is obtained by simulation \n",
"In PART 2, the time functions generated in Part 1 are taken as a _starting point,_ to explore how to model the composite reaction `A <-> C` \n",
"\n",
"**Background**: please see experiment `cascade_2_b` \n",
"\n",
"LAST REVISED: Dec. 6, 2023"
]
},
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"cell_type": "code",
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"id": "4d9b4808-b2ec-4b90-a604-f7fa69af39b8",
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"name": "stdout",
"output_type": "stream",
"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
]
},
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"cell_type": "code",
"execution_count": 2,
"id": "3924c013",
"metadata": {
"tags": []
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"source": [
"from experiments.get_notebook_info import get_notebook_basename\n",
"\n",
"from src.modules.reactions.reaction_dynamics import ReactionDynamics\n",
"from src.modules.visualization.plotly_helper import PlotlyHelper"
]
},
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"cell_type": "code",
"execution_count": null,
"id": "75411c8b-f0c5-411d-9e12-1eaa423449f9",
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"# PART 1 - We'll generate the time evolution of [A] and [C] by simulating coupled elementary reactions of KNOWN rate constants...\n",
"## but pretend you don't see this section! (because we later assume that those time evolutions are just GIVEN to us)"
]
},
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"cell_type": "code",
"execution_count": 3,
"id": "72b4245c-de4e-480d-a501-3495b7ed8bc4",
"metadata": {
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"name": "stdout",
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"text": [
"Number of reactions: 2 (at temp. 25 C)\n",
"0: A <-> B (kF = 80 / kR = 0.1 / delta_G = -16,571 / K = 800) | 1st order in all reactants & products\n",
"1: B <-> C (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'B', 'A', 'C'}\n"
]
}
],
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"# Instantiate the simulator and specify the chemicals\n",
"dynamics = ReactionDynamics(names=[\"A\", \"B\", \"C\"])\n",
"\n",
"# Reaction A <-> B (much faster, and with a much larger K)\n",
"dynamics.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=80., reverse_rate=0.1) # <===== SPEEDS of 2 reactions ARE REVERSED, relative to experiment `cascade_2_b`\n",
"\n",
"# Reaction B <-> C (much slower, and with a much smaller K)\n",
"dynamics.add_reaction(reactants=\"B\", products=\"C\", \n",
" forward_rate=8., reverse_rate=2.) # <===== SPEEDS of 2 reactions ARE REVERSED, relative to experiment `cascade_2_b`\n",
" \n",
"dynamics.describe_reactions()"
]
},
{
"cell_type": "markdown",
"id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2",
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"source": [
"### Run the simulation"
]
},
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"name": "stdout",
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"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (A). Conc: 50.0\n",
" Species 1 (B). Conc: 0.0\n",
" Species 2 (C). Conc: 0.0\n",
"Set of chemicals involved in reactions: {'B', 'A', 'C'}\n"
]
}
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"dynamics.set_conc([50., 0., 0.], snapshot=True) # Set the initial concentrations of all the chemicals, in their index order\n",
"dynamics.describe_state()"
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},
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"cell_type": "code",
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"* INFO: the tentative time step (0.01) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.004) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.004) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0016) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.0016) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.00064) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.00064) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.000256) [Step started at t=0, and will rewind there]\n",
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"152 total step(s) taken\n"
]
}
],
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"# These settings can be tweaked to make the time resolution finer or coarser. \n",
"# Here we use a \"mid\" heuristic: neither too fast nor too prudent\n",
"dynamics.use_adaptive_preset(preset=\"mid\")\n",
"\n",
"dynamics.single_compartment_react(initial_step=0.01, reaction_duration=0.8,\n",
" snapshots={\"initial_caption\": \"1st reaction step\",\n",
" \"final_caption\": \"last reaction step\"},\n",
" variable_steps=True, explain_variable_steps=False)"
]
},
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"plot_curves() WARNING: Excessive number of vertical lines (153) - only showing 1 every 2 lines\n"
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EAIVVnDiC1SABEiABEiABEjA+AQor4/uQLSABEiABEiABEogTAhRWceIIVoMESIAESIAESMD4BCisjO9DtoAESIAESIAESCBOCFBYxYkjWA0SIAESIAESIAHjE6CwMr4P2QISIAESIAESIIE4IUBhFSeOYDVIgARIgARIgASMT4DCyvg+ZAtIgARIgARIgATihACFVZw4gtUgARIgARIgARIwPgEKK+P7kC0gARIgARIgARKIEwIUVnHiCFaDBEiABEiABEjA+AQorIzvQ7aABEiABEiABEggTghQWMWJI1gNEiABEiABEiAB4xOgsDK+D9kCEiABEiABEiCBOCFAYRUnjmA1SIAESIAESIAEjE+Awsr4PmQLSIAESIAESIAE4oQAhVWcOILVIAESIAESIAESMD4BCivj+5AtIAESIAESIAESiBMCFFZx4ghWgwRIgARIgARIwPgEKKyM70O2gARIgARIgARIIE4IUFjFiSNYDRIgARIgARIgAeMToLAyvg/ZAhIgARIgARIggTghQGEVJ45gNUiABEiABEiABIxPgMLK+D5kC0iABEiABEiABOKEAIVVnDiC1SABEiABEiABEjA+AQor4/uQLSABEiABEiABEogTAhRWceIIVoMESIAESIAESMD4BCisjO9DtoAESIAESIAESCBOCFBYxYkjWA0SIAESIAESIAHjE6CwMr4P2QISIAESIAESIIE4IUBhFSeOYDVIgARIgARIgASMT4DCSgUfNrd3ornNrYIlmtCKgM1iwqAUO2oaO7QqgnZVIpDksMBus6ChxaWSRZrRikB6sg2dHi9anZ1aFUG7KhHITnegqdUN8cpDWwIUVirwFaJKiCse8UuAwip+fRNYMwor4/iKwso4vqKw0s9XFFYqsKawUgGixiYorDQGrKJ5CisVYWpsisJKY8AqmqewUhFmGFMUVgpZ33bbbb0smEwmeL1eiNek5BS0tbbC4XDAZrfD5XIhJTUNmVnZsFgsaG5qQmX5buTmFSIlLQ0wmdBYvxd1NVXILyxCcnIKPJ5O1NZUo729DQWFQ2GzO+B2u1BdWS7ZyM7Jg81mR3tbKyrKdmNIUTFy84fg200bkZObj6ycXGwuXYfxE6eitbUFzvY2FBYVo2zXDunV2dYmfT7z8NlYvuwJzD72JGRmDcZ7K1dg1JjxKC4ZJbVv7eefSm2YPHVmr/auWf0hklPSMGHytJAkn1x6P8676HIpv5xDjk05dt55YzkOHDcJRcNHQi1htWfXdmwqXYcTTj5TThWiTrP643eRmZ2DseMnR21D7Yxq+SVcvfQUVnr5M1ybjfS9/7WAwso4nhPCavEdt2PRokXGqbRBa0phpdBxFFYUVgq7UNDsFFb6xFhRWEXeeymsImcWDzkorPTzAoWVQtYUVhRWCrsQhVUAAY5YadGj1LNJYaUeSz0tUVjpR5vCSgXWjLFSAaLGJtR6FKhxNWkegJ7CisCVEeCjQGX89MzNGCv9aFNYqcCawkoFiBqboLDSGLCK5imsVISpsSkKK40Bq2heS2H18spPsWb9t7jt+ouRmCAvllbFpqlmqr6xGZfdeB+uW7gA0yePidouhVXU6H7OSGGlAkSNTVBYaQxYRfMUVirC1NgUhZXGgFU0r0RYbd1ZjoU33IOKqrqeGuXnZmHp3ddhxLACxFJYibJfeP1jPHzXNchIT1VEjMJKET71MjPGijFW6vWmny0xeJ3B61r0KzVsMsZKDYr624g2xkoIl1vufhxP3n9jr1GctaXf48XXP5ZGqd76cA1HrPxcyhErhf2bworCSmEXCpqdworCSot+pYZNCis1KOpvIxph5RupWnzTpf0+GvONWJ30i0OkR2ni8B/R8rU2cOTrknPm4tqFC6SvhVC7Z+kLuOis43HtrQ/1svHVNz9J4k4cEw4s6TU6FWy0zCcGfeX6ygk28nb7DRfjtLlHSEk5YqV/vwxaIoUVhZUWXZHCisJKi36lhk0KKzUo6m8jGmEl9zGbT8j4C6V7l76Ayuq9PXFXQtT8cfGjuOOmS6XHh+1OFxYteRx5OZmSuBLC6sLf34VAG48tW9nnM0HPJ8gChVVgnUU5y9/8BKefeCTKq2rxwar1+M0v50kOCBSOFFb698ugJZpMwLyTvXjkcWec1IjVCEaAMVbG6ReMsTKOrxhjZRxfRRNjFSiOQrU22KiRbwTKF/skbBUPzesZHfIfpRJpftpeJo1Y+cdKBdoIzCNiqvzLdnZ0RBx87l8vCqs46c9CWM0+2ov/vkBhFScuCVoNCqt49k7vulFYGcdXFFbG8VUshVWCwyGNTr35wZo+wHyP9tQQVmJEaslDz2HxzZeGDGT3jYz5V8Q3SkZhFSf9WQirqdO8eO1tCqs4cQmFVTw7QkbdKKxkQIqTJBRWceIIGdWIRlhF8igwcLkF/9Emn7CaOXVsrxEr/2rLGZ0KN2IVTliJ0amVH37RM5tR2BOfiUM8WqSwktGR9EjCGCvGWGnRzxhjxRgrLfqVGjYZY6UGRf1tRBNj1V/wun/sUrBZgcEeBfoETLDWqyGs+nsU6IvpOnPeUb0C8Sms9O+LYUuksKKwCttJokhAYUVhFUW30SULhZUumFUvJBphJSoRbLkF38hOUUFOyOUWAoWS7xFc4Cy8J557C5ddcAo2f79NcYyVWJxUCKUvS7/vidXyCcC5cw7BXQ/+tydY3jf65R8wzxEr1btddAYprCisous5/eeisKKw0qJfqWGTwkoNivrbiFZYiZoGW6bAf/aenOD1UHZ8QkuNESvfqu9CXInZhL4jMIZq03fbpK/E576DjwL175MhSxQxVuIoq22Po1qxKoEEGLxunD7BGCvj+IoxVsbxVTQxVsZpXXzVlAuEKvRHWhrQ3Az8sKMdKSkKjTG7ZgQorDRDq7phCivVkWpmkMJKM7SqG6awUh1p6AEXr9fr1a+4gVdSYSFQXg6s3+xEXh5RxquHKazi1TN960VhZRxfUVgZx1cUVvr5iiNWClkzxooxVgq7UNDsjLFijJUW/UoNm4yxUoOi/jaUxFjpX1tjl0hhpdB/FFYUVgq7EIVVAAE9R6z27NqOTaXrcMLJZ2rhxgFpk8LKmG6lsNLPbxRWCllTWFFYKexCFFYUVlp0Ic1sUlhphlZTwxRWmuLtZZzCSiHrU08FXnkFeOwpF46f61Fojdm1IsAYK63Iqm9XzxEr9Wu/f1lkjJVx/M0YK/18RWGlkPUFFwBPPQXc/08XzjyLwkohTs2yU1hphlZ1wxRWqiPVzCCFlWZoVTdMYaU60pAGKawUsr7ySuCf/wTu+KsbF17SqdAas2tFgMJKK7Lq26WwUp+pVhYprLQiq75dCiv1mYaySGGlkDVjrBhjpbALBc3OWYGcFahFv1LDJmOs1KCovw3GWOnHnMJKIWsKKworhV2IwiqAgJ4jVpwVGHnvpbCKnFk85BiIwirY/oPxwJrCSqEXKKworBR2IQorCistupBmNimsNEOrqeGBKKzEnoDiqKzeK20G7dsrUFOQMoxTWMmA1F8SEbguAtjPOMuDv//TpdAas2tFgDFWWpFV366eI1bq137/ssgYK+P4e6DFWNU3NmPxA8/gtxfMx93/XIbrLz8bI4YVxIVDKKwUukEstSCWXBBLLYglF3jEJwEKq/j0S7BaUVgZx1cUVsbxlRJhVVYGbNmif1vFlnGjRgUvVzwGXPXF17h24QKIkavioXk4be4R+lcySIkUVgrd8MEHwDHHAIcf0YXnX+5QaI3ZtSJAYaUVWfXtUlipz1QrixRWWpFV364SYfWPfwBXXaV+ncJZFLPuH3wweCohpmbNmIjpk8dAiKx7lr6Ah++6BhnpqeHMav49hZVCxIyxYoyVwi4UNDtnBXJWoBb9Sg2bjLFSg6L+NpTEWK1YATzwgP51PuUU4He/61vu1p3lWPLQc1h886WSkBKPBS+78T5ct3CBJLRifVBYKfQAhRWFlcIuRGEVQEDPESvOCoy891JYRc4sHnIoEVbxUH//Ory88lPccvfjfap1yTlzpUeDsT4orBR6gMKKwkphF6KworDSogtpZpPCSjO0mhoeKMKq3enCoiWPY+bUsb1iqgJHsTSFGcY4hZVC+s3NQFoakJwM/LizXaE1ZteKAGOstCKrvl09R6zUr/3+ZZExVsbxt5IYq3hqpRBQf1z8KO646dJeswB9guvMeUfF/HEghZVfj/E5RnzkvyaG/7DjiXNm9lkvw2TqNlJWS2EVTyegf10orOLVM33rRWFlHF9RWBnHVwNFWBmBOIXVPi/5RNWbH6yBv3gKnG3gW5DM/zmuGLESI1ffb29HauwnJBih3+leRwor3ZFHXSCFVdTodM9IYaU78qgLpLCKGl3EGSms9iHzrYMh3q5Z/23PqFTg+hiBQosxVoyxivisk5GBswI5K1BGN4lJEsZYxQS74kIHSoyVYhA6GKCwAqTFxcQhRqHEYz+fsBKfBQbJBT7fDSus2lrhcDhgs9nhdrmQkpqGzOzBMJstaGlqREX5buTmFyI1NR3ikWJD/V7U1lShYMgwJKekoLOzE7XVVXC2t6FgSBFsdgfcrg5UV5bDbLEgJzcfVpsN7W1tKN+zC0OHDZfsfbtpo/Rddk4eNm1ci/GTp6GtpRnt7W0YUjQcYjaUeBXvxeeHzDoaLzzzOI45fh4yswbjnTdXYPSYcRg+YrTE5ovPPoHd7sCUaTN7dcvPVn2IlJRUTJwyPWR3feyR+3D+xVfAZrfL6tJybMox9NbryzF2/CQMGz4SVosJ4td1XZOyRVx379yOrzeuxYmnaDvzZNVH70r9ZNyEKXKaqksatfwSrrKJdgtsNjOaWt3hkir+Xi9/ioq2uJvh9rjh6nLB7XHte3X7/e2Cx+uR/nu9Xni9XfDCiy7pb/G67z26AP/33q7u7/Z9BpEHP7/vtiHei2w+m/u+F+l6vg+Wp9uWZHNfGdZdJnjNXrgKuuCwmdHlBdydIg2PeCaQ6LDAusqMRYsWxXM1B0Td9nthJYTUjt2VPVM0gwkr/2C4SIRVamoqWlpaJGEl/nd0dCA9PR05ObkwW8xobGzErp07MWToUAxKF8LKhLq6OlRUVKC4eDhEfiGsKisr0NraimHFxZIdV4cLZWV7YLFYkF9QALvdLn2/c8cOlIwYgaFDhmL9+nUoKChEXn4evvziC0w/+GC0NLdI6UpGlGDb1m3Sq3gvPj/mF7/Av5Y+glNOPQ05OTl48cUXMHHCRBwwpntNkI8+/BB2hx2HHXZ4r47/3rvvIi09DTNm9BZc/onu/utd+P0110r1lHPIsSnHzvPPP4eDphyEUaNHQ4TBCb7iJqXk2LZ1K9Z8sQbnnnueEjNh8761ciVycnMwdeq0sGn1SqCWX8LVV/zAMCG8rzq7OuESAsXvvyRY9omWnz9390knvhNpW6pa0LqtFbbJNilNh6cjtM2AslxCJAWU11O+f526tBeI4Ziq+f0xOAZOOLEaq9U0S1s6ELgVt1JY6cB5vxdWYrTqsWUr+6AWcVY3XvVL3PXgf3tN6ww2I2H20V58/JEJzy3vwKwj+ctNh34bcRGMsYoYmaIMLe4WtLqaIV5bXM1oc7eiydWIVleLNHLT4ur+vsnV1JNOvHcKYdPlRKfXBadbiBw33F3dYkm8ihGfVneLorrFKnOSNRk2iw12sx02ix02sx12i016Fe/F5xazFWaTSfoRYDaZJYFphln8Kvj5vfh833shQXvS+dLv+z7QhnhvCkjTXxm+evTkQXe5FpOlB6HDbkFXl5cjVrHqVBGUm5RgxcF5R2De2DkR5GLSaAjEVFj5Vkvd9N22PnWfcGBJTJan9x+xEjtlh4uxEhU/eb4Xr79mwr//48IJJ3pk+8HathXJ2+6FxV0Dd8p4dKZNgnPwL+A1J8m2wYTyCFBYyePkn6rBWY+q1gpUt1Xte61EvbNOEkXd4qhZEjniVfq/7289hY/DktBbnOwTLP4Cxm76TFr9AAAgAElEQVR29BEwoQSO3erYJ3y6BY9d2AsQQeIzUa7FbAkqkqQ8kliyIdmWEjl4A+Vg8LpxnMXgdf18FVNhFWyGnX5ND15SoLCSMyvw3PO6sOxZM+7/hwtnni1PWCXUvoOM0vNh8jT3qojHkY/6ycvgGnRwrFEMqPIprH52Z52zFtWtlZJYqmqrlP6ubCnv+Vt8vqd5lyL/J1gSkWpPRbI9FSm2lJ7XVHsaku0pSLGlItWRhmRbMvw/E+9TEhKQ5EhAR4epR6D4Rnm6X20Q9nnEngCFVex9ILcGFFZySSlPFzNhJUarbrrzUVx/+dm9FvlS3iRlFgKFlbDW3zpWYYPXW/cFr9vtcO0LXs+1VyOheR0aOgdhp7ME+VkJSLc2wtpRgb1tFlR0FGBIbgoSMkfD4+lEbU21FGReUDi0O3jd7ZKC10WMlQhOF4Hx7W2tqCjbjSFFxcjNH9ITvJ6Vk4vNpeswfuJUtLa2SEHwhUXFKNu1Q3p1trVJn888fDaWL3sCs489SQpef2/lCowaMx7FJd1bi/vPBPInvGY1ZwUq63HBc0c7K7C2vQa7GrdjZ9MO7G7egfLmPZJwEqNOla3lqGgpk11dMdqSk5SHnOQ85CXnY1TDCDiSE5BYlIaUfYIpzTEIidZEpNjFZ92CKc2RLruMYAn1XG6BW9pE7irOCoycWTzk4KxA/bxAYaWQdaTCKi3RhALPZ7DAg1r7dJTVm5CbV4gUsRiWyYSW8lJUN3oxPGk7EgYVwZkyhcIqSh+988ZyHDhuEoqGj4RaI1Z63Yj7E1ZbG7ZgV9N27Gzcjt1NO7CjcZv0966mHbLij8RIkhBMucn5yJVEU4EknsT/3KR9n6UUQMQERSqio3RVr2wUVmpQ1M4GhZV2bLW0TGGlJd3etmMmrEQ1AuOX9Gu2eiVFKqwGmauRZ92KrkGTsddbjEqx3IKfsGqs34u66nIMT/gRqdYmdNiHodwzhiNWUbjMyMLqtbefRYutHbWD6rCjfit2Ne/EzsZtKG/Z0y8JIYaK0opRlF6M4ekjUZBauE9A5SMnKRd5KQVRP0aTMzoZhZv6ZKGwUoOidjYorLRjq6XlgSSsRIjOhb+/qxeueNmAWVQqpsJKzLB75uX3cf1lZ0MEihv1uOc+D/7vWgsuuLgTd94demq1pX0Hcj8dC68lBZVH74LXnBCyyfaGz5C54QyY3Q1oz1uA+klPGhVPXNRbrRErtRvj9LTjm5qv8XX1Rmyq3ohvar/G5tqv+i1GjDANSy/BsPTi7te04dL/oenFGJyYo3YVdbenp7DSvXEDrEDGWBnHoQMpxiow9tk3Ee66hQtivk9gTIVVfzMCRcViNSswmtPk0X978JtLLTj9TA8eeDj0ApSpWxcj9afb0Vb4SzSM/1fYohx7P0HmhjNh8rSg6cC/oaXo8rB5mCA4gXgQVmLW3OaajZKIEv+/rduEH+q+DVrhoWnDMCZzHIYPGimNQBUPKsHQ1GKMzOhesHUgHxRWxvEuhZVxfDWQhZVvS7qZU8fitLlHxNwpMR2xinnrVarAsuc7ce7ZVhx3ggePPx1aWOV+MhYW5w7UTXsdHVny1hJJqHkbmRtOA0wW1B78AWcLRumzWAir9ZVfYG3FGmysXItNNaXY2dR3WRHRHPHIbmLOFEzMOQjjB0/CpJyDpJly++tBYWUcz1NYGcdXioRVexnQtEX/xiYVAqndE6j8j2AjVvE0GY7CSmFXkRtjZbd0wd1ej3R7G1KHHQmL1YLmpqbgMVY1VcgvLEJycoo0K3Bv2Wa0tztRnFyOroK5cHnMnBUow296xlg1u5qxtuIzrKtYgzVlq1FavR4dHmefWo7OPBATBk/GpNyDMD57EsYPnhx0raNoZwXKwBJ1EsZYRY1uQGVkjJUx3akoxurHfwDrrtK/4aOvBKY9GFRYBcZY5edmYend18XFKgMxF1bBgtCevP/GuHhOKqcXyRVWDjTB5XIjNdmO9MJJ0lIJcoWV2Duwo6kCwxO2wJqQhuZBx6C6qoLLLYRxkJbC6qA5h+OzslVYX9ktpL6r29ynNvkphTg4/1BMK5iJSYO7R6PEwpJyDgorbsIsp5/EIg2FVSyoKy9TkbDavQL44QHllYjUwtBTgAN+F3bESiQIHMWKtCg108dUWAUDIQLaF95wDy6/YH5cPCsNB1uusErwVKLDY0PyoFxk5BRFKKyq0d7WguGOb5DobURb4ljsacuhsNJZWK3a/RE+2Pgmuso68JjnsaCjUYcUzsKMgsMwNW8GhqQWhes+Ib+nsKKwirrzaJyRwkpjwBqZVySsNKpTtGaDaYd4WhszZsLKF2zmv8GxD7KA9uLrH+O26y82xGzBH7e6ccBIG3JzvdjwTd/HPwlVryCz9Fx0Jg5H9RHfRNuXYGsqRfaaI2HyuqXV2dtz50dta3/LGG2M1f/2fILXtryE139ajsaOhl7YpucdgoMLD5WElBiZ2p/jotTsT4yxUpOmtrYYY6UtXzWtK4qxUrMiKtgKJqw4YgWgP3UpRq2WPPQcFt98KTLSU1Vwg7YmyqvcKMyzISkZ2LKzvU9hg76+CEkVz6N59G1oHn69osoklz2J9M2Xw2tORO0hq+BOGavI3v6SORJhtaZ8Fd786VVJTNW0VfUgEiuKzx91Jk4ccSpmDZ29v6DTvZ0UVrojj7pACquo0emecaAJq8AYq3haSYAjVip07+Y2N9KSbZKl3dXtMJt7G839qAQWVyWqD9+AzuQxikvM+OpCJFa+AE/CUNQcthZd1v13BplcmOGE1drKz/Haj8vx5tYV0h56viPdMQgnlJyMeaPPwKwhs2ExWeQWyXRREqCwihJcDLJRWMUAepRFDiRhFSUC3bLFTFiJFoo9+F54/WM8fNc1PSNTAy/GqgUJ5lY4zG60W/KQkpqGzKzsyGOsAvYKrNu5HhZvB/LSu9CVO4d7BQY5ZcIFr2+o/BKvbVmON7a+3GsPPbHly3El83DyqDNw5NBjYDVbe6zHw5Y2ul0dAgrirMBYkY+vchljFV/+kFubgRRjJbfNsUoXU2ElGj3wZwV2Cyu7xQSnOVM1YVVTsQs2VzkKHbuBQePRZB3FTZgDzqJgwur9LZ/ti5l6GWXNu3tyiA2Hjx0+F/NGnYGji46FzRJ8JwAKqzRMmDxN0+uVniNWevlTU2A6G6ew0hm4SsVRWKkEUoaZmAsrGXWM6yThZgW2tzbDYW6D3WaHE6mqCavqynJY0YGhWAe7yYW9qXNQVtOOIUXFyM0fgm83bURObj6ycnKxuXQdxk+citbWFjjb21BYVIyyXTukV2dbm/T5zMNnY/myJzD72JOQmTUY761cgVFjxqO4pHtxNv+Lqb9D5IxiPLn0fpx30eWw2eVtWyTHppxO4RNWjSkteOOnl/DGTyuwo3F7T9ZEaxKOKT4BJ486HccMPwF2syOsWb1uxJwVyFmBYTtjjBJQWMUIvMJiKawUAowgO4VVBLBCJRUxVkfOsmDjBjNef6cDB03t6kk6aNOvkVT+LBrHPoDWob9WobTeJlK234e0H/8IrzkZNYesQmeK8hgu1SsZA4Mi6PyJrx/B8h+WYU/zrl41OL7kZJw08lQcXzIPQlzxiC8Ceo5YxVfLjVcbxlgZx2eMsdLPVxRWKrAWwmruCRas/tSMZS914IijfhZWgz8/VFomofbg9+HKOFSF0vqayCg9H4lVL0nLOdQe+vl+Hcy+tWELHlp/D5777qleoMRjvgXjz8CRhfOQZE3WxA80qg4BCit1OOphhcJKD8rqlEFhpQ5HOVZ0F1a+zZcvOut4PPH829j0XfD90+Jp6mQ4kEJYnbXAjLfetODRJ12Ye5KnJ0v+e4Ng6nKh4pgaeC3a3NBN3g5kf34UbM1foSPzKNRNewMwBUxNDNcIg38vlkhYuvEBvLv9zZ6WlAwahaumXY8TSuYjMzENg1LsqGnsMHhLB371KayM42MKK+P4isJKP1/pLqx8TetvHSsjLRAaGGMFmAB4YTKZkJSUIM3Wc5g7YE3Og8vlUjXGSmyLk52TB5uI32qpQ8XurRiRtBW5hSXYUFUw4GOsvPBi5dZX8NCG+1Bata7nrJlRcDiunHod3JtacOC4SSgaPhLhlluQe8oxxorB63L7ykBNxxgrY3qWMVb6+S0uhZWRFgjtT1glJ1jR5uyAw+KBNSlbU2ElBFzFnu0YmbAJRY6d+KJjPrILRg3I4HVXVwee+/YpPLLh79jZ1D3iaTaZpSUSrpp6PSblHCR9Fm65hWhOMworCqto+s1AykNhZUxvUljp57e4FFZifas16781xJY2/QorhxdtHV1wWAFrYob2wqpsN4Zld2GE6zWsbToY2UMnIaNg9ICaFfjKlhdw++qbUdlaLp0lYibfGWPOxVXT/g9FacN7nTkUVupeSNSarRmuVno+CtRLKIdrs5G+p7Aykrd+riuFlX5+011Y+RYAraiqC9nK/NwsLL37OowYVqAfCQUliRirxXcBi2+34fKrOvHHRW7JWsZXFyGx8nk0jHsYbUMuUFBCZFkHbboUSeXPwJMwBDWHfoEuW0ZkBuIw9Te1X+NPn1yLLys+k2qXYkvB+RN+g99MuRqDE3PC1litR4FhC2ICxQT0FFaKK7ufG2CMlXE6wECMsbp36Qt4bNnKHiecOGdmXAzI6C6sfATiaSdqpaeGEFYP/gP44x9sOP+iTixe0i2sBn82E7bmr1Ez81O407VdVNG/DaYuN7K+nAN74zq4Bh2K2oPfAQy6FUuDsx53fn4Lln37JLq8XZKIuvmwv+DMMefBJMWzyTsorORxiodUFFbx4AV5daCwkscpHlINJGHV7nRh0ZLHJay3XX8xEhO610gUT7uGFuRg+uTYLjsUM2EVDx1NrToIYfXEf7z43eV2nHaGBw8+4gK8Xch/P1PzGYGh2mB21yJn1UEQr63DrkDjmCVqNVcXOx6vB//Z/C/8bc3taOxogNVsw8UTL8N1M/4kjVZFelBYRUosdukprGLHPtKSKawiJRa79ANJWIkJbvcsfaHXdnixI9u3ZAorhd4IjLHyek0wmbpnBaZaGtHiSYXdkSStOq7lrEApeL1sd6+V1/My7RjW/DS+qJ+OiWNHoMFcYoiV119++2m8XfYG3mx/XfLOzILDseToh1AyaGRE3mKMVUS4wiZmjFVYRPtFAsZYGdPNSmKsyprLsKVui+4NL0wrxKjM7t0//A/xCFAc1y5coHud5BQYU2HVX7yVUdaxCi2sgFRLU0yFldjSJt++B199txMHZ6xHTc4laO1MjtstbSpayvD/Vl2Prq1ONKAB5amVWDTrr9IK6dEcFFbRUAudh8JKXZ5GtUZhZUzPKRFW//jyH7jqrat0b/iVB1+JB094MKiwKh6ah9PmHqF7neQUGDNh5XtGOnPqWEwaNxLPvPw+rr/sbOlZqVCjs2ZMjPlzUjkAwwurNNgdiTEZsfLtFfjt2vcwM+UDNHlzUJd5BgqLD4irvQI7PE48uG6JtB6V+PtE80mYOPQg/ObEa2Tt3xfKTxRWcnqw/DQUVvJZDeSUFFbG9K4SYbXi+xV44IsHdG/4KWNOwe9m/I4jVnLJ+wevizxLHnoOi2++FBnpqTDSAqGi7iLGqnSTB0fMTMDwEV6s/sKJjK/OR2LlS6if+Dja88+Wi0WbdF4Psr88DvaGz+BKn4baGR/FTTD76z8tx+3/uxllzbultp804jTcOuuvyE8pVJUFY6xUxampMcZYaYpXVeOMsVIVp6bGGGOlKd5exmM2YuUvrDIHpWLxA8/gpqvPk4SVkRYI9QmrLds9mDo+ATm5wMZv2jH4fwfD1rIZNYd9CXfKeP08GqIks7sOg/83E5aOMrQOvRSNY/8e0zptqf8BN3x4Rc/yCaMzD8Tio+7HzIJZmtSLwkoTrJoYpbDSBKsmRimsNMGqidGBJKw4KzBEF/F/FCiek4rHf75npkZaINQnrCprOjG6OBGJScBPu9qR/24mTF4nKn5RB685UZMTJVKjtpZvkf3ZYRB7CzaMfxRthedFakKV9EtL/44/r75JspVqT5Vm+l06Sdvn9xRWqrhOFyMUVrpgVqUQCitVMOpiZCAJKx8wrmMVpuv4NmcWmzIbaYHQkDFW8CLV1oLmznQ4HI6YxlhtLl2H8ROnorW1Be7673Cg8ylsbR+FnAlnoQW50uczD5+N5cuewOxjT0Jm1mC8t3IFRo0Zj+KS7hkZ/nEV/q6UE3fz5NL7cd5Fl6Ohsx5XvXcxVu3+SDIxb+TpuPOo+5GZkNWrd8ixKedKxBgrOZTkp1HLL+FK1FNYceX1cN7o+z1jrCJnFg85lMRYxUP9jVSHmD0KNBKk/urav7ByorkzOa6ElbO9DSNtX6Js51YMT6tG9dA/oMVp1lxYZR81DNd/cjmaXI3ISsjGHUfdJwmrYIdaN3AKK3XPMrX8Eq5WFFbhCMX2ewqr2PKPtnQKq2jJRZ4vZsJqoKy83p+wSrG70OJOjDthVTh0GGpLn8Aoy//QZBuFmuwLMePwOZqMWLW6W/DfR/+Bu7ruggsuSUwJUSXEVahDrRs4hVXkF4T+cqjll3C1orAKRyi231NYxZZ/tKVTWEVLLvJ8FFaRM+uTQ8wKbG7vxPy5Dqz70ozSV/+FSS0L0VbwKzRMWKpCCeqbMLsbMfjzmbC070TLsKvQNOavqheys2kbLnzjDPy493vpcd9fZz+IuSNOUb0cOQYZYyWHUnyk0VNYxUeLjVsLxlgZx3cDMcYqXunHTFgJIEZar6o/B/qE1aUX2rHyDQvW/fd2TDX9PzSX/B+aR/05Xn0Pa8v3GPzZoVKQfdOBS9BSdIVqdf1w5zu4/J3z0exqxqScqXhq3svIThysmv1IDVFYRUosdukprGLHPtKSKawiJRa79BRW+rGPqbASyyr4LwyqX7PVLcknrG663oannrBi3b+uwNTkh9B04N/QUnS5uoWpbM1R9z6y1p0sWd077VU4s36huIT71i7GPV/8BV54ceros3DvnKWwW7o3yYzVQWEVK/KRl0thFTmzWOWgsIoV+cjLpbCKnFm0OWImrPxnAQarvOG3tIEXyYk2tDq74i/Gqqi418rrHTXrcbL3Wjy863L8YtYkJI35VVSzAptdTbji3YvwwY63YDaZ8cdD78Bvp/wOvlmBYr9EOYdasTyMsZJDW34atfwSrkQ9hRVnBYbzRt/vGWMVObN4yMEYK/28EDNhpV8TtS2pv+D15CQHWts7415YieUWZo+sxXOvf4HTc1+CfdqdeLU0MaLlFpKGpeFXr5+KnU3bkWJLxb/nLsOsoUdL8CmsIu+Dqz9+F5nZORg7fnLkmTXKQWGlEViDmaWwMpjD9lWXwko/v8VMWPU3K9BIW9r0J6ySkpPQ1tZhCGEl1rF6+en7sWDQA8ixV+G/LXeiZMpcWetYlbn24A8/Xov2zjYUp5fgv/NexfBBI3p6MYVV5Cc0hZUFDS2uyMFFmIMjVhECC1jTjo8CI+cXqxwUVvqRj0thZcQtbcSswPXrzDj5eAfcT9lhtbhRMacCXmu6ft5UoaTEqteQ8dV5gNeDxgPvRWvRb0NaFTFUf1tzO/6+7q9SPNXhQ2ZLI1Wp9jQVaqKuCcZYqctTS2t6PgrUsh37g20KK+N4mTFW+vkqLoWVEbe0EcJq104TfnFYJ5ofS4XXZEPFsY36eVLFkvzFVdMBi9FS3Hd3cRFPtfCtX+KT3e9LJV8y8Qpp82QRWxWPB4VVPHoleJ0orIzjKwor4/iKwko/X+kurMRo1MIb7kFFVV3IVhppSxvRCN+swE43cMyUPfjxntHwJA5D1RHf6edJlUvqFle/BLydaB55C5pHdO/tJ46t9T/2xFPZzDZp1t9pB5ytcg3UNUdhpS5PLa1RWGlJV13bFFbq8tTSGoWVlnR729ZdWPmK3x9WXk9KSUNba6thYqwC9wocm+/C9JpLJXH1VueN8OYdC2e+G+e/fjrEiuqDEjJw59AlKMkdjQmTp4XstYyxivyEZowVY6wi7zX65GDwuj6c1S6FMVZqEw1tL2bCSr8maltSYPA6vABM0j8kpaQaWliJTZjHpG5F5sYF+KDmKOxIHI4rq/4Lp6cd47Mn4cmTXsLO0h+QnJJGYaVyN6OworBSuUupZo7CSjWUuhqisNIPN4WVQtZ9hNU+ewNFWBWXjEJCzdt4deXD+E9zOz7Balw4YSHuOPI+qaVypuBzxCryTkZhRWEVea/RJweFlT6c1S6FwkptonE6YtXfIqFGWSBUoPXFWIm/V997OxaMW4z1nluQP/fnuCT9XKp+SZ+VfYozVxwvGf5rNnDluHPRMOHR7qE5gxyMsTKIo8RIr8MCu00fYWUcKvFZU8ZYxadfgtWKMVb6+SqmI1Zir0BxXLtwgX4t1qAkf2H10xNX4IiCJ7Cy/hFMPvt8DUrT1+QXFf/Dea/Ol9aoWnzQJbix+TGpAmIZBrEcg1EOCiujeIrCyjieAiisjOMtCiv9fBUzYTVQgtcDR6yaXjoNY1Lfxr+3voK5lx+rnyc1KGlD5Vqc+crxcHa24/oZt+D3029CQt17yNhwDkxdbejIOBz1U15Ely3+1+qisNKgg2hkkiNWGoHVwCyFlQZQNTJJYaUR2CBmKawUsg6MsTJJS2WKR2QmJKekGDZ4/cUVT+Dxyn/ha89XWDj5dzjBcgLEXn+Tp86ErfkrZK4/DZaOCrxVvwC2Eedg7PTjQpJkjFXknYwxVvo8CuTK65H3TcZYRc4sHnIwxko/L8RMWIkmikeBxUPzcNrcI/RrscolDURhVebZg6dfegjru9bjoLGHYMnR/4T/xVQgtHRUInPDGfhwaw5SE0044Kgr0JHVvTdg4EFhFXmno7CisIq81+iTg8JKH85ql0JhpTbR0PZiKqzEYqHPvPw+rr/sbCQm2PVrtYolhRJWXq8JKanGG7EaMm0kLvjoTJzomovEglTcfur9MJlMfYSVQGjqcmLDK4uQ5VqLmRlr0DxqEZpL/kBhpUL/orCisFKhG2ligsJKE6yaG6Ww0hxxTwExE1b9zQgUtTPirEBzRxXyPh6O+tYMTPhzHb4sdernSRVK+q5uM05dfgzEdjXzRp6Oh477j6wtalK234e0H28B0AXn4BNQP/FJeK2pKtRIPROMsVKPpdaWGGOlNWH17DPGSj2WWltijJXWhH+2HzNhpV8TtS/JNyvQ2vQ1cj6fie/KDsTEP36LnRXt2heuUglCVJ3x8nFo6KjH0cOOw5MnvgSL2SLbumPvJ8jcsAAmTzM6E0tQf9CLcKccKDu/1gkprLQmrJ59Civ1WGpticJKa8Lq2aewUo9lOEsUVuEIyfjeJ6wcte8ha/18fPrDbBz55w/x7dZ2pMf/hDn8VP8D5r90tCSqDh8yG0/PWwG7JfJHs9b2bchcdyqsbVvgNSeiYcJStOedIYOg9kkorLRnrFYJFFZqkdTeDoWV9ozVKoHCSi2S4e3EVFi1O11YtORxvPnBGvg2Xi7IzZY+mzl1rCGC2vuLsUpITIGrI773CtxTtxMvfPU0XvO8iuts/4dzT12IvJxCvLdyBcSWNmLldXEEBq/7ulbgyusmTysyN54DR937UpKWoivwwKeFOO+iy6VZhXIOOau5y7HzzhvLceC4SSgaPhJqCSu9ZpExxooxVnL6eCzSMMYqFtSVl8kYK+UM5VqIqbDyzQo84eiZWPLwczjvtGMwYlgB1pZ+jxdf/xi3XX9x3Ae19yes7PYUdHbGr7CyZyXhkS/vh6XThIrBNbjEczHmHHcyMrMGRy2sfB0vdcttSN32V+nt4m1/wrmX/B+FldyzUqzg//G7yMzOwdjxkyPIpW1StQRvuFrqOWKll1AO12YjfU9hZSRv/VxXCiv9/BYzYeW/QKgYpfIXVmK24JKHnsPimy9FRrq2QdD+o2Y+7E/efyOmTx7T44WXV36KW+5+XHp/4pyZvQRff8LKYk2Btys+hdX27T/gid2PorPDjWGJw7HoV/fg3eXLMfvYk1QRVoJVYtVrGPTVhbjrp2vx+9H/QdvkR9CRPSds71brBs4Rq7CoI0qgll/CFUphFY5QbL+nsIot/2hLp7CKllzk+eJSWOk5YiUE3hPPvYXLLjhFGh0TZd+0+FEsvfu6ntGze5a+gIfvukYSecG24fHFWGWUno/Eqpfw2PdP4Ne3X4g/3+nGJb/pjNwrOuQ477X5+HjXexgxaBRePeMjZCRkalKqreUbZJT+CtbW7yX7LcOuRtOYuzQpqz+jaj0K1L3i+2GBegqr/RCvqk1mjJWqODU1xhgrTfH2Mh4zYSVqIUaC1qz/FjddfR4efHyF9Cgwc1AqLrvxPiyYd1RMYqx8y0Bct3CBNGoVuIipEF7+Qku0wyesstceB/veVfj3jjdx6R/n4qrfd+LGP7n186bMku5fdxeWrPkzMhOy8OaCT1GUNlxmzuiSmbrcSNl6J1K33wN4O9GZfAD2TnlOetXroLDSi7TyciislDPUywKFlV6klZdDYaWcoVwLMRVWopJCqFz4+94jGIGP4uQ2Ro104jHkHxc/ijtuuhTBAun9vxfxYP7CKmf1ZFhbf8R/6tfjwisPwlnnenDvAy41qqWajVW7P8TZr54EE0xYNv91zBoafLV01Qr0M2Rr3oRBX/8atpZN0qcNEx5DW8E5WhTVxyaFlS6YVSmEwkoVjLoYobDSBbMqhVBYqYJRlpGYCytZtdQpkS/eyjcj0ff+zHlH9cRcBQqr/mKsXK5UJCS2IMHhgM3ugKujA6lpacjKzoHFYkFTUyPK9+xCfsEQ6XOxwnn93r2oqa7EkKHDkJySis5ON2qqq9De1obCoUWwOxxwu1yorCiHxWxGTl4+bDY72tpaUbZnF4qGDUdBwVBs+mo9cvMKMDg3D6Ub1mLSlGkor9uNN759Fd93fYdTB4Z99e4AACAASURBVJ+OY6edJNltbWnG4UfOwbNP/RvHzZ2PrOzBePO15RgzdgJGjBwt0f989cdSG6YdfEgvb6z6+H2kpqVj8kHTQ3pp6T/uwUW/uQr2fbMCE7csRuL3t0rpOzNmoG3C/ehMP6gnvxybcrrEG6+8iHETp2B4yUhYzSYkJ1rR2KpsBHHXjm3YuGEt5p92lpwqRJ3m4w/ekfwwYdLPXKI2plJGtfwSrjoOmxlWixmtTu0fo+vlz3BtNtL3/teC5AQrPF1eOF0eIzVhv6xrWrINd9z+ZyxatGi/bL+ejY6psBKP2Sqr9/YKBg8UN3rB8JWbl5OJaxcukIoNVpdIhJXTmYrk5BY4HA5JEAlhlZaWjsE5QliZ0djYiN27dqFwyBCkpw0CTCbs3VuHqsoKDBtWjJTUVHS6O1FVVSkJp6KiYZKtDpcL5eVl0gKe+fn50my7ttZW7Nq1E8OHl6Bw6FBsXL8e+QUFyMvLw9q1X2LilMl4dM0jcDvdSMpJwvycU6W0wm5zcwuOnnMMHv/3vzBv/ikYPDgHK5a/iHETJmL06O7HdZ98/BEcDjtmHnJYL5d8+P57SE1Pw/TpM0K66r577sYVV/2+R1iJhKam72DbcCXMtZ9I+TxFv0TnxMXwJuRDjk05/WL5i89j0pSDMHLkKIEWNosZrs4uOVlDptm+bRvWrl2DBWedq8hOuMzvvvOW5IcpB00Nl1S379XyS7gKW8wmmM0muBX6Klw54nu9/CmnLkZJ438tsFpM8HohiSse8U3AbjXjdgorXZwUM2EVbDTI12I9g9f9BZS/qPLVJVyMVX8jVq2tqUhN7RZWQvy4XC6kpKYhMytbGrFqbmpCZflu5OYVIiUtTRJWjfV7UVdThfzCIiQnp8Dj6URtTTXa29tQUDhUGjVyu12oriyXbGTn5EkjVu1trago240hRcXIzR+CbzdtRE5uPrJycrG5dB2+tX+LPXW7kGvLxS8P/w1qyytRWFQMpxixam3BzMNnY/myJ1SdFehj2N8mzIlVK5D2/Y2wOHfDa05Cy/Df472KGUhOzcCEydMUnQScFagIX5/MnBWoLk+jWuOsQGN6jrMC9fNbzISV/3ILvlglX7NjsdxCqAVJA4PVQ80KbK/7DjmrJqEzaRTKZ36FYfmJ0ijJ7up26TWWx6Ol/8Ctq29AgjUR75z1GUZm6Bc0LqfdYjPnlO33IvWnv0jJPY5CNB/wF7Tlq/e4jTFWcjwRH2kYYxUffpBTC8ZYyaEUH2kYY6WfH2ImrOJlxEqIuIU33IOKqrpe1C85Z27PI8H+1rESmcSsQGflFxi8ZhbcaVNQc8j/MG5kIhoagE0/tCMzSz+HBpa0vvJLnLL8aHR5u/DoCcswd8T82FUmTMkWZxnSvr8eiVWvSCld6dPROPZ+ianSg8JKKUH98lNY6cdaaUkUVkoJ6pefwko/1jETVqKJgWtGic98QufyC+bHZLmFaNALYeXa8x6y1p0IV8YRqD34bRx5SAJ+2mLCh6udOGBMbOIPKlsrcOxzM1HXXoPfTLkaiw7Tf/2oaHg66lch/ZurpBmWgAlt+QvQfMBieBx50ZiT8lBYRY1O94wUVrojj7pACquo0emekcJKP+QxFVb+Qsp/xCiWyy1Eir5PjJXJC69XBHSa0NycivT0WMVYbcDXzq/xnfMbHGE5EkfNOF6aAehsb5Niq8p27YiLGKtgvLtjeVIwM3M9Un+6HWZ3Q3f8Vcm1aBl+LbzmBFluYoyVLEyyEzHGSjaqAZ2QMVbGdC9jrPTzW8yFlX5N1aakUMJKjLQ0NaUiLa0FCQn6B69/8sXb+N71HZpszTjWcRwmTpouBakbR1ilScHrZnc9Un+8Bcl7ngTQFVH8FYWVun2ewkpdnka1RmFlTM9RWOnnNworhaz7CitI049jKayqrNXY+f0WVJgqcNKkM1C3tQLjJ041pLDyucfW/DXSv70W9obPpI+cg09AW9FCOLOPDelBCiuFnTsgO4WVujyNao3Cypieo7DSz28xFVa+7WM2fbetT4snHFjSsz+ffjiiK0nEWHm/uRNpW25Fy/D/Q9PoP+PB+6246y82XHZlJ/50q7JFKSOp1abqjTj5pdlwdbmw+Ki/4/zxl0aSPe7TJla8gLQfboalo1yqqztlAlpKrkN73umAyRKy/oyxinvX9lSQMVbG8RVjrIzjK8ZY6eermAqrYEsX6Nd09UoSwsr01c1I2f43NI26FS0lN+D5Zy249mo7zjjLg7//U59tbeqdezHn2WmoaqvEKaMW4J/HicdnA+8weTuQtOdpJG//O6ztW6UGehKHoaX4arQNuRBec2KfRlNYGacfUFgZx1cUVsbxFYWVfr6KmbDqbx0r/ZqvTklCWJnXX4nk3f9C44H3orXot/jgPTPOP8eBI2d34dkXO9QpKIyVs189Eat2f4Rx2RPx7tlrdCkztoV4kVj1KpK33wd741qpKl22TIl/67Ar0WUb1FM9CqvYeiqS0imsIqEV27QUVrHlH0npFFaR0FKWlsJKGT+EirES+/41NnavvJ6YqH3w+paq79Fa24hd5l04ZerZKNuyo9fK60aPsQrnJrFEQ/L2B5BQ86aU1GtKwDN7r8G40UOQN/EMWB1pGJRiR02jMpG7Z9d2bCpdhxNOPjNclRR9v/rjd5GZnYOx4ycrsqNmZsZYqUnTuLYYY2VM3zHGSj+/xUxYiSYGbhejX7PVKymcsEpJaUFSkrbCymsG3vvxDRR2FSI1NwPTRh/aZ0ubgS6sfB4Va1+lbLsXSeVPYVn5uZiavg6jk39ER85cWIvPQHXaPHgtyVF3AAqr7tmaWh56jljp5U8teeltm8JKb+LqlEdhpQ5HOVZiKqzEYqDPvPw+rr/sbCQm2OXUN+7S9BVWYg0rL3wjVkJYJSY5pA2ItdorcGPtOpTv3Y0RppE4YMS4oHsF7i/CytdBLK4qvLvicUxP/hBjbP/r1W/ac05GR96paM+dJ62PFcmh142YI1YWNLRoH5uolz8j6WPxnpbCKt49FLx+FFb6+S1mwqq/GYGi+UabFZjw4QzYmjaiZuYquNOnSh489igHKspNePWtDpSM0Gb19W9qv5ZWV7earfjkvFIUp5fo13sMUpKtqRTJlS9BbPhsatveU2shqsSyDc780+HMOQFek8MgLRrY1dRzxGpgk9S+dYyx0p6xWiUwxkotkuHtxExYha+acVKI4PXEd8fB2rYF1YeXojN5tFT5yy6147UVFjz4iAunneHRpEEnvjALpdXrcfW0G/CHmbdqUsZAMOoLXm/c9RkSKoTIehkW5+6fRZYlBc7Bc9GefwY6so+F12zMEdSB4CsKK+N4kcLKOL6isNLPVxRWKrAWwir5rSKYOypReeRWdCXkS1bvvduKe+624eprOvGHP6q/ltXyH5bh6vcuQU5SHj771WYk2iJ7rKVC0w1jItisQHvDl/tE1gpYOsr8RFaq9JjQmXcGnNnHACarYdo5ECpKYWUcL1JYGcdXFFb6+SrmwkpsxHzh73tvDmzsvQJ/jrEymVPQ6W6Fx+NAZpa6MVZVFWUoa92N3d7dOHjIYcix5aCibDeGFBUzxmrf+SN/5XUv7A1rkFj+EhKqVsDiquw5A8WSDc7BJ6O94Ax0ZM7Gnt27OCuQwev6XaHjsCTGWMWhU2RUiTFWMiCplCSmwkqIqnuWvtBrhXUR0L7whntw+QXzcdrcI1RqpnZm+gtet9tT0N7eCpfLgcE56gqrLTu/RaOrAe2JHZhTIjZYbqWwCnCzfGHVO6OjfjUSyp5FYvVrMLv3/iyyrOn43nY21tRNxPGnXqRdpwLA4HUGr2vawRQYp7BSAC+GWSms9IMfM2HV7nRh0ZLHcea8ozB98pheLRaC68XXP8Zt118c97MF+xNWSUkpaG5uhdPpQE6uHW63CympacjMyobFYkFzUxMqy3cjN68QKWlpgFj7qn4v6mqqkF9YhOTkFHg8naitqUZ7exsKCofCZnegoW0vftixGV3owoHFE5CRnE1hFeSciVZY+Zty7P0ECRUvSjFZZncDtraNxOf1M/HLwv/ClX4IOjIPhTvjMLgyDkWXNU21M5fCisJKtc6ksiEKK5WB6mSOwkon0GKnYK9YGyAGR38rr4tRqyUPPYfFN1+KjPTUGNQusiJb67Yj+Z0SeBKGourIH3plPnxGArZvNeHD1U4cMEYd1Ge9ciJW7/kIv550BW6btSSyyu6nqdVYed1R9xESy5+FEFsW554+JN3J4+DKOASurFlwpc+AJ7FoP6WtrNmMsVLGT8/cjLHSk7ayshhjpYxfJLljJqwGyoiVgN1a9RWSP5gMd8pY1By2rhf/i35px7tvW/DIYy7Mm698ZuDKra/i0rfOQWZCNj4//xuk2ONfeEbSIbVKq4aw8q+bpaMC9r2rpNgs+97VsLVs7lN1j6MQrozD0Fb4K3htaXCnjg+6j6FWbTaqXQor43iOwso4vqKw0s9XMRNWookvr/wUL7z+saFjrEQ72vasQtKnR8A1aAZqZ3zUy3uLb7fhH3+34rob3Lj2hk5Fnu3wdODwpyegvGUP7p3zCM468HxF9vanzGoLq0B2ps5mOBo+g23v53DU/w/2ht6LkvrSi1Etd9oEdKYfBHfaZLjSJsNrSdmfXBG2rRRWYRHFTQIKq7hxRdiKUFiFRaRagpgKK9GKgTwrMCk5Ba0trWhrc8BidSAtrUNRjFVzYgs27S1FjiMXY+wHSnFa2Tl5sNnsjLEKckqoEWMVaDaSlbrtjWtgr18DW8N6iEVKre1bg564nUkj4U6bArcQW6mTpNdPV6/hXoFceV21C72ahhhjpSZN/Wwxxko/1jEXVvo1VZuS+g1eT05BW2srWlsd6OpyICs7emHV2taMr5ylaEc7flF0IjrqWymswrg01sKqz6iWpwX2po3SCv3WxlLYmr+GreXboK14Y+/ZGJQzHJOGmdBlz4InaQQ6E4t7Fp/Vpjf3b5WbMMeCevyVSWEVfz6RUyMKKzmU1EkTU2ElNmGurN7ba/afL/Zq5tSxhl9uQYxY+YRVR4cDefnRC6vqxkr86PkBQzKGYUr2NFRXllNYGUxYBauuqasdtqavYWvaAJsQW02lsLVswpvVJyHXXolpg3rH7AkbHkcBOpNK4EkqlgSXRwgu8T9pOLrsOepcGYJYobDSDK2hDFNYGcpdPZWlsNLPbzETVgMpeL1j8/1wfH0NWoZdhaYxf+3jvemTElBeZsKqL5xR7Rm4aveHOPvVk5BsS8GXF/yAQQkZ+vWQAVKS1jFWamMSQsva+hOs7Ttgad0KS/tOWNu3BZ2N6F+215wsiSwhukSwvCvraOlrr9kqiS5PQkHcB9Azxkrt3qSdPcZYacdWbcuMsVKbaGh7MRNWA2m5BdfG22D/7lY0l9yE5lG39KF97pkOfPKRGY8/7cJxJ0Q2M9DtcePIZyZjZ9N2/OWIe3HRxN/q1zsGUElGE1b9obe2boHFuRNWSXDtgLVtGyxt2yURZvK0hPWa15IKjyNPElld9tzu14Q86bMuez480t8F8FqSw9rSIgGFlRZUtbFJYaUNVy2sUlhpQTW4zZgJq4E0YuX68lrYf7oPTQcsRkvx7/qQXvRHG/691IqbbnHjyt9FNjPwoQ334o7P/oSRGQfgw3PWwWK26Nc7BlBJA0lY9ecWs6sG1rbt3YKrfQfMzjKIpSHMHdWwdJSHHfHqNfplSekWYEJwOfKl146cE8Xydz3JxGbVYtsfrzUdXbY0eM3K96uksDLOiUdhZRxfUVjp56uYCSvRRDEj8KbFj2Lp3ddhxLACqdUDaUsbX4yVFw7U73UgNbUDufnyV143J1jw5o8rkOPNQYGjEEVDS6SV18UK7oyxCn+SxFvwevga/5xCy5XXze5aWDoqpU3DheiS/naW73u/77P2XX2q+07N8Ui3NmBmxpp+m9Jly5bEVpc1HV5bOrqs4u806W+vLWPf593fd4nPxKvvb0sK9BRWkczyjMR/AzktY6yM6V3GWOnnt5gKK38hVVFV19PqgbIJs09Ymc0O1NY6kJTUgYIh8oVVacMG7GncidH2A5BhyezZ0obCSt4JQmElj1OoVGZ3/b7RrirpddXGcqTZWjCtoAbmzkaYOxtgcovXRmm7HyHYlB7u1Mkw2VNhMpnQ6ZG5U4HJBJhs8JpsgHnfq8kKr+/vns9sUqwZzA5AvMKGHXVmrN/WhVMPTevOC5FG2LF22+uxa4dXjBYHliPSYV+5Ip/4XnymwsidUpZa5aew0oqstnYprLTl62895sJKv6ZqU5Kc5RbEKFNVpQMORweGDpMnrJKyU/FR5ftwmBw4JP0wuDvcFFYRupDCKkJgYZLLmRUoZjma3Y0w+cRWp+9vIb4aAU8LzK7an9P4CzSRz+tUt9JhrPnv/ahVwV5zIhBU6HWLv24xZpOEniT8hFAUj1tN5n2PXc3w+r/3fW7y+9zrl158HsSGsOn1y9tThkjr9eUx7yvf97ovz740om6rt9hht3pxcEkXHHYLurq8cHd2aYWPdlUikJRgxV9eMWPRokUqWaSZUAQorFToG553ZsFStxq109+DK/OwoBYnjklEXS3wxUYnhgzt/5e4p8uDo5dNw0/1P+DmQ2/HFQddp0It928T+0uM1UDwcpKtEw5LFxqb2wCvGyavu/u1yw10dfZ6L30nPoN43ZdGSitiGX15fDb25RV2PK59dn7+TLIv5en0K8+9z3Znd/m96hPsM7/6eCObqDIQfMc2xDeBtlG3IGn6n+O7kgOgdhRWKjjR8+YUWBpLUXPoF3CnTghq8fSTHVjzmRn/fb4Ds+f0/+vuia8fwZ8+vRbD0objk/NKYbOIX7M8lBCgsFJCT9+8esZY6dEyMVOzR6yFE4leLyAJMvHaBZi8MIlX33u/157P0dWdVvpOjG3tyytexXf73vf6XKQXZe373hRgQ+SR7Is0Jr+0PfXrJscRKz16kDpliBGrlrQjkD58jjoGaSUkAQorFTqH95USmNq2o2rWN/AkDQ9q8eYbbHj+WSvu+psbZ54demZgg7MeB//nALS6W/Dc/Dcwa2j3OkQ8lBGgsFLGT8/cA01Y6clO77I4K1Bv4tGXx1mB0bOLNCeFVaTEAtLLibFyOBzocDnQ2tIBrzcdk6dmSaumNzc1obJ8N3LzCpGSlibFNny1Yy1sbVaIfQEPGX4EPJ5O1NZUo729jTFWEfqKMVYRAguTXE6MlRol6imsOCswco8xeD1yZvGQg8Hr+nmBwkoha7nCCiY79ta50NqajkNnBRdWDR0NWLftMxSgAPlDipCVlk1hpcA/FFYK4AXJSmGlLk+jWqOwMqbnKKz08xuFlULWcoWVzW5HdVW3sJowKRvpg8x9Rqze274SJicw1FwkrVmVnJxCYaXAPxRWCuBRWKkLbwBZo7AypjMprPTzG4WVUtYdtcDyweiyD0bl7J39WrvmKjteWGbBn25147Ire8dZPf/dU7j2g9+iIGUIVv9qExwWh9KaMb8fAcZYGac76Pko0DhU4rOmjLGKT78EqxVjrPTzFYWVUtYt24DXRkhB6yJ4vb/j9Vct+O0ldhxyWBdeerWjJ2mLqxmHPDUOe521+NcJz+LEEacorRXzBxCgsDJOl6CwMo6vKKyM4ysKK/18RWGllHV9KfDWFLjTJqHmkM/7tdbcZMK4UQlSmm+2OJGa1r2e1aJV1+PfX/0T0/MPwSunf6C0RswfhACFlXG6BYWVcXxFYWUcX1FY6ecrCiuFrCOJsXK5XKipSce2rbk45FATMrMaUFG2C9u6tqEBDThhxMnoavOgrqYK+YVFjLGaPE2RdxhjpQhfn8wMXleXp1GtMcbKmJ5jjJV+fqOwUsg6UmHldKbhq9I8FA0zYcLEBuzavRW7sRs5mfmYnDcNjfV7KaxWf4jklDRMoLDC2PGTFfZQ9bJTWKnH0siWKKyM6T0KK/38RmGlkHWkwspqTcP/VufBajXjoCO+R9veZlSaqzBr5NGwWe0UVgDUuoFzxEph5w7IrpZfwtVKz0eBXMcqnDf6fk9hFTmzeMhBYaWfFyislLL+aSnw5W/RNuQSNIx7UJa1qRMSUFnbjoxbR6DeXYn7j3kUZ445T1ZeJoqOAGOsouMWi1x6CqtYtG8glckYK+N4kzFW+vmKwkop6+/+Bmy8Hi3F16DpgDtkWbvhWjueKbsFmLUYk3Om4s0Fq2TlY6LoCVBYRc9O75wUVnoTj748Cqvo2emdk8JKP+IUVkpZf/3/gM23o3nk/0PziBtlWXvq1R24acdEwNyJd89Zg3HZE2XlY6LoCVBYRc9O75wUVnoTj748Cqvo2emdk8JKP+IUVgpZRxpjlZKahk2tX6GirQwZzeMwclAy8vz2CmTwOmOsRJdc/fG7yMzOYfC6wvMzXHbGWIUj1Pd7xlhFziwecjDGSj8vUFgpZB2psPI6vPiycQ28XRak7ZyLkuHlKCz8eRNmCisKKworC+w2CxpaXArPzvDZKazCMwpMQWEVObN4yEFhpZ8XKKwUso5MWHWgzFWGPV27MSJxBqo3F6K4eCeGFlFY+btBrdlnnBWosHMHZFfLL+FqpeejQAqrcN7giFXkhOIzB4WVfn6hsFLK+sPjgMp3UTftdXRkzenX2t/X3oW7v/gzxmZNwLtnr8EJcxKw6Wsz/nKXGxf9uvfegUqrxfy9CTDGyjg9Qk9hZRwq8VlTxljFp1+C1YoxVvr5isJKKet3DwVqP0fNjI/hHnRwSGtVrRU49OnxcHa2440zP8WU3GlYt9aM+Sc4MCjDizUbOpCa2r3FDQ/1CVBYqc9UK4sUVlqRVd8uhZX6TLWySGGlFdm+dimslLJ+czzQ+A2qD1uPzpQDQ1pb+PZ5eOOnFTj9gHPwwC8e60n36wvseOtNC357RSduuc2ttDbMH4IAhZVxugaFlXF8RWFlHF9RWOnnKworhazlxFiZbWbUumrggAP5WUOQMzgfFosFzU1NqCjbjW3bhqKxcRBOnOeB280tbdSK5WGMlcLOHZBdLb+Eq5WewooxVuG80fd7Bq9HziwecjDGSj8vUFgpZB1eWLWgzdsGJ5wYZM1AdkYuMrOye4RVZflutLYNwfffZWBIETBuXA33CuRegVxugbMCFV6ZtMtOYaUdWy0tU1hpSbe3bQorhazDCavW1mZJWHlMHmQ7BiMlNb2PsMrKLsQH72eisxM4fFYtOpyVyC8sQnJyCjyeTtTWVKO9vQ0FhUNhszvgdrtQXVkuibPsnDzYbHa0t7VKo19DioqRmz8E327aiJzcfGTl5GJz6TqMnzgVra0tcLa3obCoGGW7dkivzrY26fOZh8/G8mVPYPaxJyEzazDeW7kCo8aMR3HJKImQ/8XUH5mcUYwnl96P8y66HDa7XRZtOTblGOKIlRxK8tOo5ZdwJXLEKhyh2H5PYRVb/tGWTmEVLbnI81FYRc6sd45nTYA1BeVzqvtYWlO2GqevOBYmmKSA9cm5U0OW9tADNtzxZysmH9SFJ552ISeXgexKXeOfnzFWatLU1paewkrblgx864yxMo6PGWOln68orJSyftYEb0IBKo78qZcll8eFWf+diD3Nu3D1tBvwh5m3hi3puNkObN5kxpChXjy3vAPDSyiuwkKTmYDCSiaoOEhGYRUHTpBZBQormaDiIBmFlX5OoLBSyvpZE7pSx6Dy0A29LN352S3454Z7MDLjAHxwzlpYzdawJdXVmXDO6XZ8s9mM7Gwvnl/hwpgDu8LmY4LwBCiswjOKlxQUVvHiifD1oLAKzyheUlBY6ecJCiuFrEPFWHnhRTOakW5Kh8ORIMUXuVwuiL0CA4PXc/32Cqyv3Yuqyips/f/t3X9sF/Udx/H3F5EWaClUAy21trSMFRwTZWplSNhE53C4BEOncUsU03W6f0QCoRqDxLgSCOpfso6M6UImlkyzEFlchjaokcwZ2dj4oRRa6FokFtC2tGDXLp/r7su3x/f7vfve93PXu+/3+U2MtL37/Hi87/v9vnr3+V5bZkhfX74sWHhRrh77OWusXNSJNVYu0JLswhorvZ5hbY01VuGsHGus/KsbwcqB9Rt79skzm7YbW957Z7VsWLNSxucOL8ROFqxkXETGfD1GcnJyHAcr828Fnj1XLp99OknGjh2QG27okPHjL0hpGYvXHZQrugnBKhUt+20JVvZG2bAFwSqcVSZY+Vc3gpWN9UcHjsiWxibZunGVTCnIlxcam4w9nqyriRus1JkqtVhd/T8vb5Jc6O11FazUpwJbjk2Sw4cGpbi4U/LyeuXcuXK5vnycXHddv3R9wacC7Z4mBCs7odR+TrBKzStTtyZYhbOyBCv/6kawsrFWQaq8tEiWL11kbGkNWvKHiHxd+jNpqdwky9+4Sw53/UuKJ06XN+/fK6WTytKuZGdHRJp2jpWdO66SkycjRnsTJojcfc9/paJyUHJzI1JaNihl5UNSOVOFORa8x0NnjVXah6JvDbDGyjfqtDtijVXahL41wBor36iFYJXEuq//kqzfvF2q58+JBquWtg55umGbPF9fK5Vl0+XU7yOyK/cO+c2ZLjnadUiK80rkzfv/KqX56Ycq69A+eO8qeW3HGHnzj4kXwk8pHJKbbh6U5SsGpahIf8iKRC63GRnOeSLm/9U/nfw7ZmKOto9pM15fTtpQwSp/wtVyrudS4jEmGJfd/Eb2H8fHoUvCfmy8nMw/0TZ2czPKG1vTOGNx0n/ifq70MoPVl72Xhg+vBMdUTo5/L5T0FF+AYBWeI4Ng5V+tCFYOgtWKZYvllnlVxpbWYFWzJSK7eoYbKckvkX2P7JOKKRWeVrCnR+S990Q++0zkxAmRTz8VaWkROXrU025pHAEEEEAgxALr14s8a3/nnxDPMBhDJ1g5CFbJzlglu/N6fn6+9PT0GGus1H8XUSmHYQAADYpJREFUL16UgoICmTZtmnHX9PPnz0tbW5uUlpbK5MmTjZF0dXVJZ2enzJgxQ9T+AwMDxte9vb3G98x22tvbjTZKSkpk3LhxRj+tra1SXFwpItdLa+tHMjhYIgMDxTJ27H7p779NRLolEumV3t5Kyc1tkZ6eSuPrMWO6pb39bqmq2ipHj94v3d1TZfbs16Wz80b54osqGRoSqajYKwMDOdLWttD42nzMmvW29PUVyMmT1SO+b26j/r9kSYO8++5qGRi4fOf12Das/54zZ7jN48ero/0k297cyLrN7be/JsePz5fTp2cZm7hpw9p2cXGLzJr1oTQ3/9RRm277XLDgLenqmiZHjnzHUT+J5ue2/3jtLVr0tnz1VYF88onzuqTTf3+/9y+SM2e2SHX1h7Jjx3A9edgLLFmyV/r7c+T99xfab8wWgRJ49tkNsl6lKx6eChCsbHjt1ljZ/UmbdBav8ydthkOF2weL193Kxd+Pxet6PcPaGovXw1k5Fq/7VzeClY11qp8KjEQiMjQ0JOr/EybmpfWpQIIVwWrOt+b592pg0xPBKjClGNWBEKxGld915wQr13Qp70iwckCW7D5WavfuC19Ld9+Ag5bYZLQE+FTgaMmn3i+fCkzdbLT2YPH6aMmn3i+L11M3c7sHwcqtXMx+BCsNiB43QbDyGFhj8wQrjZgeN0Ww8hhYY/MEK42YNk0RrDRYE6w0IHrcBMHKY2CNzROsNGJ63BTBymNgjc0TrDRiEqy8xWTx+jsyMW+SzJ2XeD3UK40vyUOPPG78WR8nD11reVi87kTb+Ta66mLXo5/Bqv3kCTl44O/yw/tW2A2Ln/9fgDVW4TwUWGPlX904Y5WmNcGKYJXmIRR39/eb/yKF104VFq97oXu5TYJV6r4Eq9TNgrAHwcq/KhCs0rQmWBGs0jyECFYWAc5YeXFE6WuTYKXP0s+WCFb+aROs/LOmJwQQQAABBBDIcAGCVYYXmOkhgAACCCCAgH8CBCv/rOkJAQQQQAABBDJcgGCV4QVmeggggAACCCDgnwDByqX1uS+75bF1L8rBw8eNFl55aZ3cMq/KZWvspkNA/fmhh5/YaDQ1d3aFbN24SqYU5MdtuqWtQ+rWbpHOz7scba9jfLRxWcDurxkksjJrzPPNn6Opr/+SrN+8Xd7au9/o8Lm1K2X50kVJO499bhVPu0YaN62WyrLp/gw4i3tJtVbW97BHH1wqT9bVZLGgvqkTrFxYmgdw9fw5xouMeiF5umGbPF9fywuIC08du1hroN649398SDasWSnjc6+8f5Z6gz7VcSb6JqH+2PbpM2cTbq9jjLQxLGD39zftQhW/yPh3JKnnhXqoN1zzjXh1XU3CXyJ5LfSvNtaeUqmV9T3M+vXozSIzeiZYuaijevHY/PJOaXiq1jgjwkHpAlHzLipItZ46Hf2NK9UXeOubvebh0VyMgHoDKC8tioZaJ/bmc27tLx+Upxq2SbI3d7D1CKggVf+rbbLm8QeivzDGvnlbezFfB1csW8zZez0lcNxKqrWKF5KT1dbxQNjQECBYuTgQ4r0RcFC6gNS4i9XfyW/Xsd3bneHSONSsbireLyF2ITj254WT841L8AQr7w+jeHVJ9jyxXlpSI7z3zmrOAntfqrhXTexe08zL8eqy+swZJVeEaB+GnbFdEKxclFYFq127m0e8YBCsXEBq3MV6FiSVYGX3xq5xmFnfVLyzGsn8rb+Jp1LXrMdOE8B6Zl41l+zNOtGZ/KKphazdSbMWdrunWivVnvm8U/8+eOSEsMbKTtn5zwlWzq2iW3LGygWax7u4PWNlLrRtqK/l8oXHNVLNp3rGyvohg9ghsoDd24KlesYq3pu7k8u83s4iO1pPtVbWX1jM5yUhWM/xQrBy4cgaKxdoHu/iZo0VocrjoiRo3s0aK7Mpzlj5VzM363asa7Lind33bwbZ01OqtXJzhit7NNOfKcHKhSGfCnSB5vEudp8KtIYoLv95XJAkzdt9KlCF5KbdzXFvl0Gw8rdudp80s36aNvZrNVJ1qwbz09P+jjz7ektWK/N5U7NssfGhEevXnLHSe7wQrFx6ch8rl3Ae7pbsPlbWYBV7HyUuL3lYlARNJ7uPFcHK/3ok6tHu3kjWYGXdnnU7/tUyWa2sQUqNynqZnVrpqxXBSp8lLSGAAAIIIIBAlgsQrLL8AGD6CCCAAAIIIKBPgGClz5KWEEAAAQQQQCDLBQhWWX4AMH0EEEAAAQQQ0CdAsNJnSUsIIIAAAgggkOUCBKssPwCYPgIIIIAAAgjoEyBY6bOkJQQQQAABBBDIcgGCVZYfAEwfAQQQQAABBPQJEKz0WdISAggggAACCGS5AMEqyw8Apo8AAggggAAC+gQIVvosaQkBBBBAAAEEslyAYJXlBwDTRwABBBBAAAF9AgQrfZa0hAACCCCAAAJZLkCwyvIDgOkjgAACCCCAgD4BgpU+S1pCAAEEEEAAgSwXIFhl+QHA9BFAAAEEEEBAnwDBSp8lLSGAAAIIIIBAlgsQrLL8AGD6CCCAAAIIIKBPgGClz5KWEAicwBt79skzm7aPGNfc2RWydeMqOXbiP/LwExvllZfWyS3zqkZs80Jjk/ztwBFjuykF+ZKsnbPnu6Vu7Rbp/Lwr4fyfW7tSSqdPNfqL9zDH8NGBI8Y2995ZLRvWrJTxueOimyf7mdro3Jfd8ti6F+Xg4eMJx/Hog0ulvLRohIka2/Kli6SlrcOYx7WFBdF5mw3F+5k5nmTzCdwBwYAQQMBzAYKV58R0gMDoCFjDkTkK9f07bvu2EaZUYGra3TwiSKgQ8XTDNnm+vlYqy6aLk3ZiZ6ja3P/xobjBqL5hmzRuWm20G+9hhpXiadeM2K6v/5Ks37xd3tq7P27oStTWlsamK0KS2lb1Yx2LGZ5UQLSGTWXw29f2iBlKVdiM18boVJpeEUAgSAIEqyBVg7EgoEnAPHtTs2yxcTYm0cMMLEVTC+XJuhoxv66eP8fYz2k7OoOVCkPf/+5N0tPbZ4zJDEK7djdLXt4E6em5cEVo0xWsVKD80V0L5J+HWqJ9qMC1+eWdcvPcb8g7H3wSDWoEK00HK80gkGECBKsMKyjTQUAJWANTMhXzTE1Dfa2c6jgz4gxWKu2YfaR7xkoFq9V1NbLl16+POGumLuG1njotp8+c9TRYrf7FT8Qcg3lWT/Wr+o89u0ew4rmGAALxBAhWHBcIZKiAdQ1Q7GUs65TNS13q+9bLYKm0o/ZPFqycrLEyL9/9buefjWH++J6FxhmjhqdqRX3P62ClLoH+49/HjMuZq36+Qja88KqsefwB43vWYGU3nww9tJgWAggkESBYcXggkOECseuT1FSt65fU98xLfrfOq4pefrOyOGnHLlg5WWNlBiu1KF5dmlOPmvu+Z1yaVAHQj2BVODnfWAhfkD9RvllZaphY16NxxirDnzhMDwGXAgQrl3DshkAYBRJd2rOurbKbW7JLhDouBZqfRrQunPcrWKnF9WoeL7/6p+gieoKV3VHBzxFAQAkQrDgOEMhAAXUGSt12YFH1jVfMToUT9TAXhqt/JwpWqbaj84yV+uSdWv917ES7/GDxrcaY/QxWau579u6Xh5bfZfRNsMrAJwpTQsADAYKVB6g0icBoC5iX9q6fPnXEQm9zvZR1HVWyYKUuiTltR3ewsjr6GaysfROsRvuopn8EwiFAsApHnRglAikLxLthZrz1VcnOWKmfpdKOXbCyW+ytgl+ie0/pOmNlvdlp7A1CY+/f5SRY2c0n5aKxAwIIhF6AYBX6EjIBBBBAAAEEEAiKAMEqKJVgHAgggAACCCAQegGCVehLyAQQQAABBBBAICgCBKugVIJxIIAAAggggEDoBQhWoS8hE0AAAQQQQACBoAgQrIJSCcaBAAIIIIAAAqEXIFiFvoRMAAEEEEAAAQSCIkCwCkolGAcCCCCAAAIIhF6AYBX6EjIBBBBAAAEEEAiKAMEqKJVgHAgggAACCCAQegGCVehLyAQQQAABBBBAICgCBKugVIJxIIAAAggggEDoBQhWoS8hE0AAAQQQQACBoAgQrIJSCcaBAAIIIIAAAqEXIFiFvoRMAAEEEEAAAQSCIkCwCkolGAcCCCCAAAIIhF6AYBX6EjIBBBBAAAEEEAiKAMEqKJVgHAgggAACCCAQegGCVehLyAQQQAABBBBAICgCBKugVIJxIIAAAggggEDoBQhWoS8hE0AAAQQQQACBoAgQrIJSCcaBAAIIIIAAAqEXIFiFvoRMAAEEEEAAAQSCIkCwCkolGAcCCCCAAAIIhF6AYBX6EjIBBBBAAAEEEAiKAMEqKJVgHAgggAACCCAQegGCVehLyAQQQAABBBBAICgCBKugVIJxIIAAAggggEDoBQhWoS8hE0AAAQQQQACBoAgQrIJSCcaBAAIIIIAAAqEXIFiFvoRMAAEEEEAAAQSCIkCwCkolGAcCCCCAAAIIhF6AYBX6EjIBBBBAAAEEEAiKAMEqKJVgHAgggAACCCAQegGCVehLyAQQQAABBBBAICgCBKugVIJxIIAAAggggEDoBQhWoS8hE0AAAQQQQACBoAgQrIJSCcaBAAIIIIAAAqEXIFiFvoRMAAEEEEAAAQSCIvA/y5mmmBPfFNUAAAAASUVORK5CYII=",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['blue', 'orange', 'green'], show_intervals=True)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "042a23ff-84de-4273-ae7b-09b73b740b4c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 0.01218 ; [B] = 9.998\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 821.034\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 800.0\n",
"Discrepancy between the two values: 2.629 %\n",
"Reaction IS in equilibrium (within 3% tolerance)\n",
"\n",
"1: B <-> C\n",
"Final concentrations: [B] = 9.998 ; [C] = 39.99\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99992\n",
" Formula used: [C] / [B]\n",
"2. Ratio of forward/reverse reaction rates: 4.0\n",
"Discrepancy between the two values: 0.001889 %\n",
"Reaction IS in equilibrium (within 3% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.is_in_equilibrium(tolerance=3)"
]
},
{
"cell_type": "markdown",
"id": "b56568ac-1e46-4242-9141-ca197b654c55",
"metadata": {},
"source": [
"#### A profoundly different plot than we got in experiment `cascade_2_b`"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bed9100c-f575-4591-bf8e-a32de741fa7a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "1f447754-5017-4b48-a4f5-fc9049b7de64",
"metadata": {},
"source": [
"# PART 2 - This is the starting point of fitting the data from part 1. \n",
"### We're given the data of the time evolution of `A` and `C`, and we want to try to model the complex reaction `A <-> C`"
]
},
{
"cell_type": "markdown",
"id": "b5f75cfb-45b4-4fd2-ad4c-c2a2084ca62d",
"metadata": {},
"source": [
"Let's start by taking stock of the actual data (saved during the simulation of part 1):"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "f26c98c3-802c-4c38-a726-06ac4a77211a",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" C | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 50.000000 | \n",
" 0.000000 | \n",
" Initial state | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000256 | \n",
" 48.976000 | \n",
" 0.000000 | \n",
" 1st reaction step | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000563 | \n",
" 47.772397 | \n",
" 0.002517 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000717 | \n",
" 47.185404 | \n",
" 0.005250 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000794 | \n",
" 46.895519 | \n",
" 0.006975 | \n",
" | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 148 | \n",
" 0.450771 | \n",
" 0.012844 | \n",
" 39.746776 | \n",
" | \n",
"
\n",
" \n",
" | 149 | \n",
" 0.516094 | \n",
" 0.012619 | \n",
" 39.905478 | \n",
" | \n",
"
\n",
" \n",
" | 150 | \n",
" 0.594482 | \n",
" 0.012517 | \n",
" 39.971659 | \n",
" | \n",
"
\n",
" \n",
" | 151 | \n",
" 0.688547 | \n",
" 0.012538 | \n",
" 39.988899 | \n",
" | \n",
"
\n",
" \n",
" | 152 | \n",
" 0.801426 | \n",
" 0.012177 | \n",
" 39.990107 | \n",
" last reaction step | \n",
"
\n",
" \n",
"
\n",
"
153 rows × 4 columns
\n",
"
A(t)=%{x}
value=%{y}",
"legendgroup": "wide_variable_0",
"line": {
"color": "green",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "C'(t)",
"orientation": "v",
"showlegend": true,
"type": "scatter",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.estimate_rate_constants(t=t_arr, reactant_conc=A_conc, product_conc=C_conc, reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "8951650d-cb8c-4def-99c3-4e465a12b9d4",
"metadata": {},
"source": [
"### A terrible fit! But it looks like we'll do much better if split it into 3 portions, one where A(t) ranges from 0 to about 0.04, one from about 0.04 to 5, and one from about 5 to 50 \n",
"\n",
"This is a larger numer of splits than we did in experiments `cascade_2_a` and `cascade_2_b`\n",
"\n",
"Let's visually locate at what times those [A] values occur:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "6ef1f912-d7c9-401c-b037-2e4d2b6cf8fa",
"metadata": {},
"outputs": [
{
"data": {
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"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
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"hovertemplate": "SYSTEM TIME=%{x}
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"type": "scatter",
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"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(chemicals='A', colors='blue', xrange=[0, 0.15], \n",
" vertical_lines=[0.028, 0.1], title=\"[A] as a function of time\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "781a0677-4d2a-4222-b5f8-4ce031157faf",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
"
\n",
" \n",
" \n",
" \n",
" | 72 | \n",
" 0.020462 | \n",
" 9.428805 | \n",
"
\n",
" \n",
" | 73 | \n",
" 0.021645 | \n",
" 8.540614 | \n",
"
\n",
" \n",
" | 74 | \n",
" 0.022828 | \n",
" 7.736565 | \n",
"
\n",
" \n",
" | 75 | \n",
" 0.024012 | \n",
" 7.008682 | \n",
"
\n",
" \n",
" | 76 | \n",
" 0.025195 | \n",
" 6.349747 | \n",
"
\n",
" \n",
" | 77 | \n",
" 0.026378 | \n",
" 5.753223 | \n",
"
\n",
" \n",
" | 78 | \n",
" 0.027561 | \n",
" 5.213195 | \n",
"
\n",
" \n",
" | 79 | \n",
" 0.028745 | \n",
" 4.724310 | \n",
"
\n",
" \n",
" | 80 | \n",
" 0.029928 | \n",
" 4.281718 | \n",
"
\n",
" \n",
"
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
"
\n",
" \n",
" \n",
" \n",
" | 126 | \n",
" 0.090918 | \n",
" 0.062461 | \n",
"
\n",
" \n",
" | 127 | \n",
" 0.093371 | \n",
" 0.057137 | \n",
"
\n",
" \n",
" | 128 | \n",
" 0.095825 | \n",
" 0.052750 | \n",
"
\n",
" \n",
" | 129 | \n",
" 0.098769 | \n",
" 0.048391 | \n",
"
\n",
" \n",
" | 130 | \n",
" 0.101714 | \n",
" 0.044909 | \n",
"
\n",
" \n",
" | 131 | \n",
" 0.105247 | \n",
" 0.041540 | \n",
"
\n",
" \n",
" | 132 | \n",
" 0.109487 | \n",
" 0.038396 | \n",
"
\n",
" \n",
"
\n",
"
A(t)=%{x}
value=%{y}",
"legendgroup": "wide_variable_0",
"line": {
"color": "green",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "C'(t)",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
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47.18540424081068,
46.89551869293061,
46.607416414927755,
46.321086435338806,
46.03651785020284,
45.753699822646006,
45.472621582468776,
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"xaxis": "x",
"y": [
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""
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],
"source": [
"dynamics.estimate_rate_constants(t=t_arr_early, reactant_conc=A_conc_early, product_conc=C_conc_early, \n",
" reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "49e2b683-f622-4d9a-a6e8-e687a7b44f34",
"metadata": {},
"source": [
"Just as we saw in experiment `cascade_2_b`, trying to fit an elementary reaction to that region leads to a **negative** reverse rate constant! \n",
"We won't discuss this part any further."
]
},
{
"cell_type": "markdown",
"id": "a9250abb-943b-40b0-a546-a556e58b6a8e",
"metadata": {},
"source": [
"### II. Let's now consider the MID region (not seen in earlier experiments in this series), when 0.028 < t < 0.1"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "4f3723d4-6c1d-44de-9f74-a1d791e1b0a3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total REACTANT + PRODUCT has a median of 14.9, \n",
" with standard deviation 3.612 (ideally should be zero)\n",
"The sum of the time derivatives of reactant and product \n",
" has a median of 199 (ideally should be zero)\n",
"Least square fit: Y = 224.4 + 24.68 X\n",
" where X is the array [A] and Y is the time gradient of C\n",
"\n",
"-> ESTIMATED RATE CONSTANTS: kF = 39.74 , kR = -15.06\n"
]
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"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.estimate_rate_constants(t=t_arr_mid, reactant_conc=A_conc_mid, product_conc=C_conc_mid, \n",
" reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "87f852fc-8df8-4aef-ab74-fcea926b354f",
"metadata": {},
"source": [
"For this region, too, trying to fit an elementary reaction to that region leads to a **negative** reverse rate! \n",
"We won't discuss this part any further."
]
},
{
"cell_type": "markdown",
"id": "652e8cc0-b053-40d1-9d1c-2f2a30f59469",
"metadata": {},
"source": [
"### III. And now let's consider the LATE region, when t > 0.1"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "2d61a783-e1e5-473a-9fd8-cba5cb842a85",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total REACTANT + PRODUCT has a median of 34.37, \n",
" with standard deviation 6.092 (ideally should be zero)\n",
"The sum of the time derivatives of reactant and product \n",
" has a median of 62.73 (ideally should be zero)\n",
"Least square fit: Y = -55.81 + 5,404 X\n",
" where X is the array [A] and Y is the time gradient of C\n",
"\n",
"-> ESTIMATED RATE CONSTANTS: kF = 5,402 , kR = 1.624\n"
]
},
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"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.estimate_rate_constants(t=t_arr_late, reactant_conc=A_conc_late, product_conc=C_conc_late, \n",
" reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "5e2ab9aa-c84d-41d1-948f-16d1e437b2a6",
"metadata": {},
"source": [
"This time we have an adequate linear fit AND positive rate constants, but a **huge value of kF** relative to that of any of the elementary reactions! \n",
"\n",
"Let's see the time evolution again, but just for `A` and `C`:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "ffa91f21-a726-46df-88dc-5fdc38fa4673",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(chemicals=['A', 'C'], colors=['blue', 'green'], xrange=[0, 0.25], \n",
" vertical_lines=[0.028, 0.1], title='A <-> C compound reaction')"
]
},
{
"cell_type": "markdown",
"id": "1ddc931c-2bf1-4e8e-9156-fdb7268648a1",
"metadata": {},
"source": [
"For t > 0.1, the product [C] appears to have a lot of response to nearly non-existing changes in [A] ! \n",
"\n",
"That doesn't seem like a good fit to an elementary reaction..."
]
},
{
"cell_type": "markdown",
"id": "be6a8d74-8ad7-4930-9c24-681ced6e1bb0",
"metadata": {},
"source": [
"#### This time, modeling the compound reaction `A <-> C` as an elementary reaction is not a good fit at any time"
]
},
{
"cell_type": "markdown",
"id": "310322af-ca59-4d41-b533-ec3336d6f3a8",
"metadata": {},
"source": [
"### EXPANDED conclusion : "
]
},
{
"cell_type": "markdown",
"id": "d94c2e0d-4b50-4616-b248-74c07809aa21",
"metadata": {},
"source": [
"### While it's a well-known Chemistry notion that the slower reaction is the rate-determining step in a chain, we saw in this experiment that the complex reaction CANNOT always be modeled, not even roughly, with the rate constants of the slower reaction. "
]
},
{
"cell_type": "markdown",
"id": "7e352310-17ae-48bb-854b-d98b8c3ca89e",
"metadata": {},
"source": [
"We saw this in a scenario where the slower reaction is the later one."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "58f279e3-c420-4a57-a753-fab458bec80c",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}