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"## A complex (multistep) reaction `A <-> C` derived from 2 coupled elementary reactions: \n",
"## `A <-> B` (slow) and `B <-> C` (fast) \n",
"A repeat of experiment `cascade_2_a`, with more DISSIMILAR elementary reactions.\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_a` \n",
"\n",
"LAST REVISED: June 23, 2024 (using v. 1.0 beta36)"
]
},
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"cell_type": "code",
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"id": "4d9b4808-b2ec-4b90-a604-f7fa69af39b8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "3924c013",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"from experiments.get_notebook_info import get_notebook_basename\n",
"\n",
"from life123 import UniformCompartment\n",
"from life123.visualization.plotly_helper import PlotlyHelper"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "75411c8b-f0c5-411d-9e12-1eaa423449f9",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
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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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"id": "72b4245c-de4e-480d-a501-3495b7ed8bc4",
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"name": "stdout",
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"Number of reactions: 2 (at temp. 25 C)\n",
"0: A <-> B (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products\n",
"1: B <-> C (kF = 80 / kR = 0.1 / delta_G = -16,571 / K = 800) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'C', 'A', 'B'}\n"
]
}
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"# Instantiate the simulator and specify the chemicals\n",
"dynamics = UniformCompartment(names=[\"A\", \"B\", \"C\"], preset=\"mid\")\n",
"\n",
"# Reaction A <-> B (much slower, and with a much smaller K)\n",
"dynamics.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=8., reverse_rate=2.) \n",
"\n",
"# Reaction B <-> C (much faster, and with a much larger K)\n",
"dynamics.add_reaction(reactants=\"B\", products=\"C\",\n",
" forward_rate=80., reverse_rate=0.1) # <===== THIS IS THE KEY DIFFERENCE FROM THE EARLIER EXPERIMENT `cascade_2_a`\n",
" \n",
"dynamics.describe_reactions()"
]
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"cell_type": "markdown",
"id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2",
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"source": [
"### Run the simulation"
]
},
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"cell_type": "code",
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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: {'C', 'A', 'B'}\n"
]
}
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"dynamics.set_conc({\"A\": 50.}, snapshot=True) # Set the initial concentrations of all the chemicals, in their index order\n",
"dynamics.describe_state()"
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"cell_type": "code",
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"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"102 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 15, 'norm_B': 16, 'norm_C': 14, 'norm_D': 14}\n"
]
}
],
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"dynamics.single_compartment_react(initial_step=0.01, duration=0.8,\n",
" snapshots={\"initial_caption\": \"1st reaction step\",\n",
" \"final_caption\": \"last reaction step\"},\n",
" variable_steps=True)"
]
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkturquoise', '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] = 0.08481 ; [B] = 0.06976\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.822525\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 4\n",
"Discrepancy between the two values: 79.44 %\n",
"Reaction is NOT in equilibrium (not within 1% tolerance)\n",
"\n",
"1: B <-> C\n",
"Final concentrations: [B] = 0.06976 ; [C] = 49.85\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 714.525\n",
" Formula used: [C] / [B]\n",
"2. Ratio of forward/reverse reaction rates: 800\n",
"Discrepancy between the two values: 10.68 %\n",
"Reaction is NOT in equilibrium (not within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"{False: [0, 1]}"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "markdown",
"id": "b56568ac-1e46-4242-9141-ca197b654c55",
"metadata": {},
"source": [
"We didn't quite advance to equilibrium this time. A separate run (not shown) displayed far-better values if we had progressed the simulation just a little more in time. "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bd55b103-2467-4034-aa03-6664a14603b0",
"metadata": {},
"outputs": [],
"source": []
},
{
"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",
" Initialized state | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.004000 | \n",
" 48.400000 | \n",
" 0.000000 | \n",
" 1st reaction step | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.008000 | \n",
" 46.864000 | \n",
" 0.512000 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.010000 | \n",
" 46.124672 | \n",
" 0.931738 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.011000 | \n",
" 45.761562 | \n",
" 1.167132 | \n",
" | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 98 | \n",
" 0.758938 | \n",
" 0.121082 | \n",
" 49.805302 | \n",
" | \n",
"
\n",
" \n",
" | 99 | \n",
" 0.771777 | \n",
" 0.110536 | \n",
" 49.816969 | \n",
" | \n",
"
\n",
" \n",
" | 100 | \n",
" 0.784616 | \n",
" 0.101044 | \n",
" 49.827470 | \n",
" | \n",
"
\n",
" \n",
" | 101 | \n",
" 0.797455 | \n",
" 0.092501 | \n",
" 49.836921 | \n",
" | \n",
"
\n",
" \n",
" | 102 | \n",
" 0.810294 | \n",
" 0.084812 | \n",
" 49.845428 | \n",
" last reaction step | \n",
"
\n",
" \n",
"
\n",
"
103 rows × 4 columns
\n",
"
A(t)=%{x}
value=%{y}",
"legendgroup": "wide_variable_0",
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"type": "scatter",
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""
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"source": [
"dynamics.estimate_rate_constants(t=t_arr, reactant_conc=A_conc, product_conc=C_conc, reactant_name=\"A\", product_name=\"C\")"
]
},
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"### The least-square fit is awful : the complex reaction `A <-> C` doesn't seem to be amenable to being modeled as a simple reaction with some suitable rate constants"
]
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"### But it looks like we'll do much better if splitting into 2 portions, one where A(t) ranges from 0 to about 40, and one from about 40 to 50 \n",
"Indeed, revisiting the early portion of the time plot from Part 1, one can see an inflection in the [C] green curve roughly around time t=0.028, which is when [A] is around 40 (turquoise). That's around the peak of the mystery intermediate B (orange).\n",
"\n",
"We'll pick time **t=0.028** as the divider between the 2 domains of the `A <-> C` time evolution that we want to model. \n",
"\n",
"Note that this is a much smaller time than we saw in experiment `cascade_2_a`"
]
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkturquoise', 'orange', 'green'], xrange=[0, 0.4], \n",
" vertical_lines=[0.028])"
]
},
{
"cell_type": "markdown",
"id": "6d4a4dbd-de22-471c-a1a4-5507941d92e1",
"metadata": {},
"source": [
"#### Let's locate where the t = 0.028 point occurs in the data"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "3795ba32-68ec-4d20-9b6b-c2a117810741",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" search_value | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" C | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 19 | \n",
" 0.028 | \n",
" 0.02728 | \n",
" 40.260772 | \n",
" 3.8859 | \n",
" 5.853329 | \n",
" | \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": [
50,
48.4,
46.864,
46.124672,
45.761561804799996,
45.40161192343552,
45.0447703652651,
44.690987798242915,
44.340217342705294,
43.99241438203294,
43.64753638880049,
43.3055427651394,
42.96639469614495,
42.63005501525445,
42.29648808061195,
41.965659661515964,
41.57191226864183,
41.182015261391285,
40.71869588451881,
40.26077194067098
],
"xaxis": "x",
"y": [
-64.00000000000001,
64.00000000000001,
182.5792,
226.88563882666676,
240.49093401548794,
250.15001326342644,
258.78465478242174,
266.48096894205366,
273.31796423218736,
279.3681319455884,
284.69798273293895,
289.3685389917721,
293.43578672475246,
296.95109020349764,
299.9615724995174,
302.4046265418533,
304.82997472725606,
306.7945637024859,
308.5490323652907,
310.11565307554883
],
"yaxis": "y"
},
{
"hovertemplate": "Linear Fit :
A(t)=%{x}
value=%{y}",
"legendgroup": "wide_variable_1",
"line": {
"color": "red",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
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""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"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_a`, trying to fit an elementary reaction to that region leads to a **negative** reverse rate constant! \n",
"This time, we won't discuss this part any further."
]
},
{
"cell_type": "markdown",
"id": "652e8cc0-b053-40d1-9d1c-2f2a30f59469",
"metadata": {},
"source": [
"### II. And now let's consider the LATE region, when t > 0.028"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "2d61a783-e1e5-473a-9fd8-cba5cb842a85",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total REACTANT + PRODUCT has a median of 49.59, \n",
" with standard deviation 1.353 (ideally should be zero)\n",
"The sum of the time derivatives of reactant and product \n",
" has a median of 2.347 (ideally should be zero)\n",
"Least square fit: Y = 2.263 + 8.377 X\n",
" where X is the array [A] and Y is the time gradient of C\n",
"\n",
"-> ESTIMATED RATE CONSTANTS: kF = 8.422 , kR = -0.04564\n"
]
},
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ACIAACIAACIAACIAAxCqeARAAARAAARAAARAAARAAARAAgZIjALFaci5Bh0AABEAABEAABEAABEAABEAABCBW8QyAAAiAAAiAAAiAAAiAAAiAAAiUHAGI1ZJzCToEAiAAAiAAAiAAAiAAAiAAAiAAsYpnAARAAARAAARAAARAAARAAARAoOQIQKyWnEvQIRAAARAAARAAARAAARAAARAAAYhVPAMgAAIgAAIgAAIgAAIgAAIgAAIlRwBiteRcgg6BAAiAAAiAAAiAAAiAAAiAAAhArOIZAAEQAAEQAAEQAAEQAAEQAAEQKDkCEKsl5xJ0CARAAARAAARAAARAAARAAARAAGIVzwAIgAAIgAAIgAAIgAAIgAAIgEDJEYBYLTmXoEMgAAIgAAIgAAIgAAIgAAIgAAIQq3gGQAAEQAAEQAAEQAAEQAAEQAAESo4AxGrJuQQdAgEQAAEQAAEQAAEQAAEQAAEQgFiVfAZ6Bscla0DxQgSaG2ro/vgUTUzFCpnifUkCc+rCVg2j4xHJmlC8EIGaqiDV11XR4MhEIVO8r4DAkuY6QrxWAFKgCsRsAUiKTBCzFYEUqAYxWwCSpAmP07hAIJsAxKrkM4HkRxKgQHEkPgKQFJkg8VEEUqAaJD4CkBSaQKwqhFmgKsRsc6wRs82xRszWzxpiVT9jP7YAsSrpNYhVSYACxZH4CEBSZILERxFIgWqQ+AhAUmgCsaoQJsSqOZgFWkLMNucKxGz9rCFW9TP2YwsQq5Jeg1iVBChQHGJVAJIiEyQ+ikAKVIPERwCSQhOIVYUwIVbNwYRYLRnWiNn6XQGxqp+xH1uAWJX0GsSqJECB4hCrApAUmUCsKgIpUA0SHwFICk0gVhXChFg1BxNitWRYI2brdwXEqn7GfmwBYlXSaxCrkgAFikOsCkBSZAKxqgikQDVIfAQgKTSBWFUIE2LVHEyI1ZJhjZit3xUQq/oZ+7EFiFVJr0GsSgIUKA6xKgBJkQnEqiKQAtUg8RGApNAEYlUhTIhVczAhVkuGNWK2fldArOpn7McWIFYlvQaxKglQoDjEqgAkRSYQq4pAClSDxEcAkkITiFWFMCFWzcGEWC0Z1ojZ+l0BsaqfsR9bgFiV9BrEqiRAgeIQqwKQFJlArCoCKVANEh8BSApNIFYVwoRYNQcTYrVkWCNm63eFarH65a9+jw4f68roeNPcOfTuay/rv5kSacGNAe8a5/C15z9PL373x/TSn/8JPfvMfuK2g0Mj9MtXXyqR3ie6AbEq6Q6IVUmAAsUhVgUgKTKBWFUEUqAaJD4CkBSaQKwqhAmxag4mxGrJsEbM1u8KlWJ1y5PPWYIsW5hyQbZw/jz6m7/4U/03VAIteBGgXmxN3hrEqiRtiFVJgALFIVYFICkygVhVBFKgGiQ+ApAUmkCsKoQJsWoOJsRqybBGzFbviuC9e1Tzzm+p+ndvUfjSRao5+I6SRrjoutR9s+AI6meee5E2r1+ZIVyzBRu3aW5qsPplj9Lua9tkfX/27Vcz+nvg2Rdof/s2p77sUc2f/fCbtG3Tatd7/MZf/4hef+O9gnVyEZ5+rW1dmnckNJ8APd3VTV/4yneI9+v//n/ftNpPv/h9/vQHX7d+xO+NXzMxKg2xKvmxgFiVBChQHGJVAJIiE4hVRSAFqkHiIwBJoQnEqkKYBapCzDbHGjHbHGvEbHnWwcEBqj56hKqOdSZfjxAXrM4Vj8s3wmrggu7TH3us4OipqFi9fPUWPf/FT9MLf/xZp3+8jfSfvfarg9aUWlvAZovEl3/yC3rl71+fJkbTb7hQndnv2yIyn4AUFatcROezhVhV8mjOTCUQq/q5I/HRz9huAYmPOdZIfMyx5i1BrJrjjZhtjjVitjnWiNlFsI5ELFFazcRp1bHEa+jaVaeiWHMzTbbtpam2PTS5u52aP/epIhrJLGKPFtrrMPNVKCpW+ciqPcJo15ct7Pi/+cXt0kcs00dSueD7o089lSF60/tXTJ2FgOVas8pHU/llj6wWEquF2tH5PkZWJelCrEoCFCiOxEcAkiITJD6KQApUg8RHAJJCE4hVhTALVIWYbY41YrY51ojZYqzDF7oS4tQWqadOpAqGQkyU2uJ0LxOqeyi6cpXzvoo1q6bEavZIKh/1tAWy/Z4bsewR2nSbfHVyOy6u+Sgvv0Q3ilI1sirmfT1WEKuSXCFWJQEKFEfiIwBJkQkSH0UgBapB4iMASaEJxKpCmBCr5mAWaAkx25wrELPdWYfu9KZN62XTe5lQDdwfdYwj6zdaonSKiVTrdceunE5TIVZ55aqnAbuNrPJ27JHS5Utb6Puv/NxZz5ktOr08pbnqTK/DXt9q/yx77Wy6LcSqF/plaguxqt+xEKv6GdstIPExxxqJjznWvCWIVXO8EbPNsUbMNscaMTvBOjDxcJo4Dd284Tgi1rLQEqXOCCr7Pj4nsUFRoUuVWC20wRIXe3w3YHvzpPQpvrk2WMqeBszvhddz7uI1ZwMm28bL6G42k1x15mLnto4VYrXQk1Zh70Os6nc4Eh/9jCFWzTG2W0LiY5Y5xKo53ojZ5lhDrJpjXckxu+rc2eS03sTmSFVnTzvg49U1yTWnyem9fGrv8hVFOUaVWOWNux1dY4942psvcWF4sOP0tBHR9B123QStfXO2KOX/zl4ja68VTR/15O3ta9tsnWma68pVJ+/7//6zf87Y+de+n3y7DHsZWc23CRQ2WCrqkS6NQhCr+v2AxEc/Y4hVc4whVs2z5i1CrJrjjphtjjXEqjnWlSRWQz23UmtOkzv3Bh6OO7AjmzZbGyJZ03r519btShyhUqzyDrltLpQtKrkIGxpOTFvmIpVP+R0cGnFEYT6xysvw94eGR1yPdHFrP9+UXRtirjqzj63h9vmEqs0g/X7SHeW2EVT6ulgcXaPksZ75SiBW9fsAiY9+xhCr5hhDrJpnDbFqljlitjneEKvmWJezWA2MPUgdKZPcHCnUe9uBG128JLXmNDnFN143Szl81WJVeQdR4YwQwAZLktghViUBChRH4iMASZEJEh9FIAWqKefER+D2jZtgZNUccsRsc6wRs82xLreYXXXmVNqZpx0UPt/lwORCNGNTJLY5Ehesui+IVd2E/Vk/xKqk3yBWJQEKFEfiIwBJkQkSH0UgBaopt8RH4JZn1ARi1Rx+xGxzrBGzzbH2e8wOXb+WPO+U79ibWHsamJx0APKpvNZ5p8kzT/lUX9MXxKpp4v5oD2JV0k8Qq5IABYoj8RGApMgEiY8ikALV+D3xEbjFkjKBWDXnDsRsc6wRs82x9lvMDo6MMEF6JOPM02B/nwOMb4Jkrzm1d+7lmyXN5AWxOpP0S7dtiFVJ30CsSgIUKI7ERwCSIhMkPopAClTjt8RH4JZK2gRi1Zx7ELPNsUbMNsfaDzG76sSxDHEavnTBARSvn5M6TiZ55ik/ZqaULojVUvJG6fQFYlXSFxCrkgAFiiPxEYCkyASJjyKQAtX4IfERuA3fmECsmnMVYrY51ojZ5liXYswOX+2eduYpRaMOlKkduzLWnkbWbzQHrIiWIFaLgFYBRSBWJZ0MsSoJUKA4Eh8BSIpMkPgoAilQTSkmPgLd9q0JxKo51yFmm2ONmG2OdSnE7ODdu0lx2pF4Pd5JwcFBB0J05arkmtPUmacUDpuD5KGlvrE7NBF5mFFi36rSFtMebg+mCglArErChFiVBChQHImPACRFJkh8FIEUqKYUEh+BbpaNCcSqOVciZptjjZhtjvWMxOx4PGNaLxeo4e7Lzk3H5s5NbIrEzjy1N0eKNc/3BIWLxpGJYepnr+kC8t7EPRqdvJdRl/V+dCLjZzdGrmX8eyL60Kor/brH6h9h9RW64t+KFzLB+xVIAGJV0ukQq5IABYoj8RGApMgEiY8ikALVzEjiI9CvcjWBWDXnWcRsc6wRs82xNhWzw1cuUdXR5MZIfPSUfaVfGUfKMKEaWbNuGoRILEI3R6/RB8Pd1qstRLlg5IKT/5sLVP79TF0tsxZSTbg2o/nrf3Z1prqDdkuYQNmL1W/89Y/o9Tfey3DB2bdfzfj3Z557kS5fvWX9bG3rUvrlqy8Jvw+xqv/pRuKjn7HdAhIfc6xNJT7m7qi0W4JYNecfxGxzrBGzzbHWFbODgwOp8075kTJMqAbvpUYhI6vX0lRyQ6TEKOpe66a50LzJRjU/uHfFer15/7olTq+yf9++n8hpRa6GmkZqrJlLy+asZK+N1MC+55f1fXVjRhULuMAMZe4YvLxhZYZNTaiWuF36xevn7RS6Kn3N6umubvrCV75DP/vhN2nbptUWrtd+dZBe/O6P6fkvfppe+OPPTkP48k9+Qa/8/ev00p//CT37zP5CiH35ftmLVS5E/+rrf+w4nTv1H/7xLXr3tZcth335q9+jwaERR6By++amBvrpD74u9D7Eqv7nHomPfsZ2C0h8zLHWlfiYuwN/tQSxas5fiNnmWCNmm2OtLGZHIpY45SOm1rpTJlBD1646NxJrbmbrTvfSg53b6eaGZXRmVT1djg/QtZFu4lNu7RFTPt0237W4fim1Nq4hLiaXz1lBc5jw5AKU/5sLUi5Es4WmOZruLVWKWN3y5HPTANgDafy9dLF64NkX6GvPf94Som5i1ha033/l5462mWk/qm6/7MVqNrBsR6c/BG4OL/Q+xKrqR3J6fUh89DOGWDXH2G5JWeJjvuu+bBFi1ZzbELPNsYZYNcdaJmaHL3SlxCkTqlWnTjgdjweD1LN5JV1a00wnV9TQu4smqbNugG7dv0F8Oq/bFQ5W0dL6ZbSEf81JvC6dszzx/ezEz/hopt+ucheruUZJ+SxQfv3NX/wpcd1hD6jxAbY33z3qDKjlEqu8LB9s+8iB3a6jr357DrL7W3FilY+kXuq+aT0Ibk5P/xmHlT0cn10GYlX/RwCJj37GEKvmGEOsmmfNW4RYNccdMdsca4hVc6y9iNXQnd7kqGknxTsOUt2J4xR+MO50tntRLR1aEqPfL56kw0uJji6Zfh98ZNQRo0kBmi5O+ZrPcrvKXaxyIfpHn3pKWFBmC1Befmh41HF7+tLFbGFbTs9GxYjVdAfbQ+0qxOrw/clyeh5K8l7q66ro4WSUItFYSfavnDpVWx2ybofzxqWXQDgUJM77/viU3oZQu0Vgbn01IV6beRgQs81w5q0gZptjnS9mBx4+pIeH3qKRg28QdbxHzWeuUFN/SlT01rMfM1HKvw4vS7xOzK6lFWxK7orGlbR6Lpuuy9aM8u/5z1bPW+PLkVFZb/A4req6OnyV+Jfpq3VuK/Gv7CvfqGiuPmZPCc5Xh/1e9r48pu9fR3sVI1ZtePZCZO5MFWJ1bAJJvY4HM71O/tdMLlShVXWTJqoKBaxGpqLYPl43baZViSc/E1P4I4xu1rz+WTUhQrw2QZoIMdsMZ94KYrY51nbMHnowShcGz1Nfx79Q9NDvqeHkOVp5oZc23kod6TLBjja1xen5NY00uGUtzV63ldYwEbpm3jr2tdb6fk5Ng7kb8EFLPE6ruv7ynb+kb7/9bVXVCdfz7Se/Td964lvT7O0pwF7EJBer6faFBG+2vXCnS9yw4sQq90f6Xyrc1qTyXbfsh6PQ+5gGrP8Jx5Qy/YztFjClzBxrL1PKzPWqfFvCNGBzvkXMNscaMVsva75m9MLQOTp55xgNXTnC5useogWnr9Cu65PUzjbcnZU2MebswgBdXD2Pbm9eRdHd+2j2nido7bz17GuD3k6WUe0qpwG/euJV+ruTf2eczpd2fIme2/nctHYLCU23jkKsJqiUvVhNX6jMb5gvYj7YcRq7ARv/+BbfIBKf4tl5LYnExyux4u0hVotnV0xJiNViqBVXBjG7OG7FlELMLoaaexl+3Mulu+fp0tAF6/XW7XPUcPocbewetoQp/1o6kio7MK+Wbm1cRqM7tlPVvieo+fFP06zG8ltHqo5w4ZpUitXCrZm34Jpkf/s2a5EMhE8AACAASURBVCMlkQvTgCtErKafoWo/GDhnVeQjUjo2SHzM+QKJjznWEKvmWPOWIFbN8UbMNscaMbs41vws0kt3mSgdYuKUvV4c6qLLTKSuvTFK+24mhCn/2tqXqn+qpoqGtq2jh7v20OxHP0bRPfsouoQtPsWljEC5i9VcuwHzJYo9dwamiVi3HX65gHU7UxUbLCl7DMuvIkwD1u9TJD76GdstIPExxxpi1RxriFWzrBGzzfFGzM7Pmk/jveyI0oQwtUZP2WskOkUrh4n2JYXpoz0h2nszRlWR1J4NDzZtoMDeD7FzT/cw9dpOdXt20eBIam2qOU9XRkvlLla5F+3pwOkebZo7x/WMVDcBau+9w8un7waMo2sq4zNS1F1CrBaFzVMhJD6ecEkZI/GRwuepMMSqJ1zSxhhZlUYoXAFitjAqaUPE7EyEfWN36EjPe3TszhE6O3CKfZ2kofFBx6iB6Uw+cvpIT5Ce6quntutT1HgvdaRMdNlymty9l6aYOOUCdYp9H6+uscojZks/rgUrqASxWhBClkH23jlu5fmI7fdf+bmr4PXaXinal/2aVd3QIVZ1EyZC4qOfsd0CEh9zrJH4mGPNW4JYNccbMdsc60qO2RPRh9bGRyf7jtGR3vfpFHu9MXJtGvwDfbPoU8OLaH9vNW24PExN13sdm3j9nAxxyoVqrMV93Slitv7nGmJ1OuNcU4dtS3uk1W1qsH6PmWkBYlWSM8SqJECB4kh8BCApMqnkxEcRQuFqkPgIo1JiCLGqBKNQJYjZQpiUGFVSzD4/eI4J0qN0qv84dbDRU75LL5/mm3411DTSH9Bm+ujAXLbmNE4rLvRQw6mzRNHUMYNTO3YlRk356CkTp5H1G4V8gZgthEnKCGJVCl/ZFoZYlXQtxKokQIHiSHwEICkyqaTERxGyoqtB4lM0uqIKQqwWha2oQojZRWErqlC5xmy+rvT8wFnqGjpL5wfPUNfAGbo+cnWaMN3cvI321K6jx+/U0Y6r47Ts/A2qPXGcgoOpqb/RlasyxKm1/jTMDkL1eCFmewRWhDnEahHQKqAIxKqkkyFWJQEKFEfiIwBJkUm5Jj6K8CitBomPUpwFK4NYLYhImQFitjKUBSsqh5htn2X63s3f5Z3O2zJrIbUtaqe2lj30kYFG2np1jOpPnKKqY50U7r7ssIrNnZtcc8rWnrKRUy5OY83zC7IsZICYXYiQ/PsQq/IMy7EGiFVJr0KsSgIUKI7ERwCSIpNySHwUodBeDRIf7YgzGoBYNccbMdscaz/GbL7W9FhvhzWVl6817eh5nx5M3c+AVhOqpS0LttNuJk73LnqU2h800YqLPVR99IglTqvZV/qVPq2XT++NrFmn3AmI2cqRTqsQYlU/Yz+2ALEq6TWIVUmAAsWR+AhAUmTix8RH0a0brwaJj1nkEKvmeCNmm2Pth5g9MnGPOm4zYXr7fXrv1u/obP8p4oI1/bJHTR9ZcoDalzxGW6iF6k+eoSomTquPMYHKXoP37jlFIqvXOmtO7bWnuqkjZusmnNgIDxcIZBOAWJV8JiBWJQEKFEfiIwBJkYkfEh9Ftzrj1SDxMesCiFVzvBGzzbEuxZjN15eeGThBZ/pPJr7Y8TH3J0cdKOFgmLbO30FbF/CvnbRl/nbaNm8LzT55Om3k9AiFrl11ysSam2lyV+Iomcm2xPRePt3X5IWYrZ82xKp+xn5sAWJV0msQq5IABYoj8RGApMikFBMfRbdWctUg8THrEohVc7wRs82xnumYPRmdcATpmT4mUJkw5QI1Gk/tvjunpoGJ051MmG5PiFT2/cb5Wyh88XxKnPLpvadOpMCFQs45p3yKL9+1l2+UNJMXYrZ++hCr+hn7sQWIVUmvQaxKAhQojsRHAJIik5lOfBTdhi+qQeJj1k0Qq+Z4I2abY206ZvMpvdaoaV9ixJR/f2GwK+OGW2YtckZNE6OnO2hlwyoK9t2xxClfb5qY3ttJgfupEdfIug2pM0+ZOOVHzJTShZit3xuVKlZPd3XTF77yHfrZD79J2zat1g9aooWZ6CvEqoTDeFGIVUmAAsWR+AhAUmRiOvFR1G1fVoPEx6zbIFbN8UbMNsdad8y+8+B2QpTao6bs++v3rmbcYGvjmqQ4TYyabm3ZQQvqWigwOeGIUluchm7ecMrGFrRkiFM+ghqf02AOnseWELM9AivCvJzF6kyIvCJcYBWx+5pdfm3rUvrlqy85PzZ1TxCrxXoyWQ5iVRKgQHEkPgKQFJnoTnwUdbMsqkHiY9aNEKvmeCNmm2OtOmZfG+mm03eS03mTI6j9430ZN8TPNt3awkQpm9LLd+zlr/XVcyybqnNn2W69qdHTqrOnnbLx6mq2KVLiKBl7U6To8hXmYEm2hJgtCVCgOMSqACQDJqIiVNROtssQq5IEIVYlAQoUR+IjAEmRierER1G3yrIaJD5m3Qqxao43YrY51rIx+/zgWbbGNLXWlK83HZ0ccW6gNlznjJpuabY3RdpBwUDQsgn13HKOknGm9o6POeUjmzYnNkRKrjud2rrdHBzFLSFmKwbqUl2litV00cex8CnBz3/x0/TK37/uUHrpz/+Enn1mv/PvL3/1e3T4WGoKfvoU4m/89Y/o9TfeyyBsv2+3lV5/9vTjfCI0/b3//hv/noaGU1P5s0deVT0xEKuSJCFWJQEKFEfiIwBJkYls4qOoGxVRDRIfs26GWDXHGzHbHGsvMXsqOpnaDIkL1OROvZFYxOlwU10z252XT+dlX2w6L39dO2+D835g7EFizSk/6zR55mnodo/zfnTxkoQw5aOn1s69bGrvrNnmgGhsCTFbI9xk1UrF6tWrRPzL9NXaSsS/si5RAciLcbGaLvxe/skvLOF69u1XrVq5GD3YcZrefe1l69+v/eogff+Vnzv/zm473d7uRz5h6bWvutfaQqxKPsQQq5IABYoj8RGApMjES+KjqMmKrQaJj1nXQ6ya442YbY51vpjNR0itUVMmSk9br2wzpKHMzZCWzlmecYwM3wxpSf2yjBuoOnPKEaf8zNNw1znn/XjdrIxpvVyoRpcsNQfAYEuI2fphKxWrf/mXRN/+tv5OZ7fA2/zWt6TFaroAzBaPW558jrJHWj/z3Iv0337hExmjr3Yn7PJc7IpM3c21ZpX3yRbT2d/r3BgKYlXyMYZYlQQoUByJjwAkRSYQq4pAClSDxEcAkkITiFWFMAtUhZhtjnV6zO4b602ebZo64/TayAcZnVk3b2NqMyQmTPnU3nl1TRk2oRvXM3bs5WtQA5OTjs3Ulm2pab18iu/mLeZueAZbQszWD1+pWH31VaK/+zv9nc5u4UtfInruOe1i1e3G0gXsgWdfyJiiy+29ilW3EVO3KcsYWTX/mHlqEWLVE66ijJH4FIWtqEIQq0VhK6oQEp+isBVdCGK1aHSeCyJme0ZWVIFr97rp8r0zdIrt1Hvs9jFLqPaN3XHqCgVDzqhp+tTemlBtRnuB0RFLnNrTevlrsD+1qVJ02fKMab18em+8uqaoPvu5EGK2fu8pFav6u+upBZmptW4jq/kEYvbIa7EjqxCrnlxcusYQq/p9g8RHP2O7BYhVc6yR+JhjzVuCWDXHGzFbD+vzg+cSZ5zytabW14mMzZDmVDdYo6Zb5rMdevn5puwYmU3zt7p2purk8QxxGr50wbGL18/JEKeTTJzGWhbquSkf1YqYrd9ZEKuZ02ztqbXZYpVvrjQ4NDLtGBnbQ3zNa/ooq73hkuqRVd4/tynJqp8UTAOWJAqxKglQoDgSHwFIikwgVhWBFKgGiY8AJIUmEKsKYRaoCjFbDevb92/Ruzd+S+/3HKSOnvfo6r0rGRXzEdK2xbvp0aUforaWD9HuRe3UUNPo2njo2geWOLU2R0q+UjTq2E5t35lx5mlk/UY1N1FGtSBm63dmJYjVbIr72jbRn/13n7M2Vcq1DtRtVDbfjr/2hkx2W7wNvnOwDrGa3hZ2A9b/GSmqBYjVorB5KoTExxMuKWOIVSl8ngoj8fGES9oYYlUaoXAFiNnCqDIMRybu0VvX36D3b71rfV2+mxrt5IZciHJB+siSA9S++DHasbCN5tfXW3WMjqd29OX/Dg4PJ0XpkcTr8U4KDg467UVXtmYcKcN37aVwuLiOV0gpxGz9ji5nsaqfXvm2gJFVSd9CrEoCFCiOxEcAkiITiFVFIAWqQeIjAEmhCcSqQpgFqkLMFmP9YOo+GzF9n9658S/03s3f0dmBUxkFZ1fV04HlT1ni9LFlj1vTe7Ov9JidvuaUHy0T7r7smMcaG5NHybANkZJHysSa54t1FFYWAcRs/Q8CxKp+xn5sAWJV0msQq5IABYoj8RGApMgEYlURSIFqkPgIQFJoArGqECbEalEw7zy4TSfuHKWT/cfo5J1OOtl3jO4+HHLqWly/lHa0tLGv3dbrzoV7qLFmbs62wlcuUcOZ4xQ80kHU0WFN8U2/rLNO+ZmnTJzy18iadUX1G4USBBCz9T8JEKv6GfuxBYhVSa9BrEoCFCgOsSoASZEJxKoikALVIPERgKTQBGJVIUyIVSGYww/v0om+o2y33qOOSO293+OUbaprZoJ0N21fYIvT3dQya1HOuoODA4k1p9bOvR3WK5/ua1+R1WsT4pSL1OToKQUCQn2FUWECiNmFGclaQKzKEizP8hCrkn6FWJUEKFAcYlUAkiITiFVFIAWqQeIjAEmhCcSqQpgQq64ExqYeJEdN2egpGzU9yUZR08855dN6U6OmXKS20YrG1tw0I5E0cZrYHIlvlGRfseZmiu1pp+iePXR/e2IUNTZvnjlHV1hLiNn6HQ6xqp+xH1uAWJX0GsSqJECB4hCrApAUmUCsKgIpUA0SHwFICk0gVhXChFh1CNwYucY2Q/odvX39TXr35m9paDy1iRE3WjtvA9ut9wAdWPYUW3/6dM7deu0KwxfPp46U4aOo7IgZ5wqFMs87ZeK0btN66+3sDZbMebtyWkLM1u9riFX9jP3YAsSqpNcgViUBChSHWBWApMgEYlURSIFqkPgIQFJoArGqEGYFi1W+KdK7N96igzffsl6zd+xd3rCSidPH6dEl++nJlR9j03rzn08a7LtjjZimb44UuD/qEI6s25ApUHe2ZdBHzDb3XCNm62cNsaqfsR9bgFiV9BrEqiRAgeIQqwKQFJkg8VEEUqAaJD4CkBSaQKwqhFlBYpWPlJ7o66TjbEOkE3eO0HH2/d3x1KZIrY1raBfbCGlnyx5qW7TX2hQpGAjmJBSYnEiuOWVHyiRFaujmDcc+tqAlQ5zyzZHicxpy1oeYbe65RszWzxpiVT9jP7YAsSrpNYhVSYACxSFWBSApMkHiowikQDVIfAQgKTSBWFUIs4zFaiQWYaI0IU6PM3HKv09fd9pcN98SppZAXbjXep1bm3+daLjrnLUhkrU5EjvztOrsaYdgvLo6uSlSYsdeLk6jy1cIOwsxWxiVtCFitjTCghVArBZEVJEGEKuSbodYlQQoUBxiVQCSIhMkPopAClSDxEcAkkITiFWFMMtMrF4Y6kqMmlqjp510uv+Ec4fhYFVSmLKRUyZO+cjpiobWvARCt3ssUWqLU/4aGB9zykQ2bmKitD11rMzW6eeninoLMVuUlLwdYrY8w0I1QKwWIlSZ70OsSvodYlUSoEBxiFUBSIpMkPgoAilQDRIfAUgKTSBWFcL0uVjtfdBDx3oTo6a2QB2LPHDuamPzZmfUlI+ibl2wI+8dcyGavuaUT+/lgtW+oosWO0fJ2EfKxGfNVuIQxGwlGIUqQcwWwiRlBLEqha9sC0OsSroWYlUSoEBxiFUBSIpMkPgoAilQDRIfAUgKTSBWFcL0mVjlmyKlC1O+7jT9vNPF9UsT602d6b1sl93wrLx3WXXmlLPmtPrYEeJTfe0rXltnTee1p/Xy1+iSpVocgJitBatrpYjZ+llDrOpn7McWIFYlvQaxKglQoDjEqgAkRSZIfBSBFKgGiY8AJIUmEKsKYfpArJ7qO562MVInXWRTfe2rvnpOhjDl604Xzl6c965CN65nTOvlo6d8syT7mtqyLU2cMqG6eYsR4IjZRjBbjSBm62cNsaqfsR9bgFiV9BrEqiRAgeIQqwKQFJkg8VEEUqAaJD4CkBSaQKwqhFmCYvXaSLczpdfaHIlN843Go05Pd7S0WetNExsj7aF18zbmvYvA6EjmkTJMnPJjZuwrumz5tDNP4zW15iAnW0LMNoccMVs/a4hV/Yz92ALEqqTXIFYlAQoUh1gVgKTIBImPIpAC1SDxEYCk0ARiVSHMEhCr046UYQL17kOXI2W4QOXTe9k033xHyvBbqjp5PLX2lInT8MXzzp3G6+dME6fRhYvMQc3REmK2ORcgZutnDbGqn7EfW4BYlfQaxKokQIHiEKsCkBSZIPFRBFKgGiQ+ApAUmkCsKoQ5A2I1/UgZ69xTNnIqe6RM6NoHlji1du1NnnlK0dRo7NT2nam1p2zdaWTDJnMQBVtCzBYEpcAMMVsBxAJVQKzqZ+zHFiBWJb0GsSoJUKA4xKoAJEUmSHwUgRSoBomPACSFJhCrCmEaEqsXBtmRMn3qjpQJDg8nj5RhZ51ycco2RgoODjp3E13ZykZPkxsjJc88pXDYHLgiWkLMLgJakUUQs4sE56EYxKoHWBVkCrEq6WyIVUmAAsUhVgUgKTJB4qMIpEA1SHwEICk0gVhVCFOTWOVHytjrTQseKcOm926dn/9IGd7N9LNO+dmn4e7LTu9jjY1sU6S9GTv3xprnmwOloCXEbAUQBatAzBYEJWEGsSoBr4yLQqxKOhdiVRKgQHGIVQFIikyQ+CgCKVANEh8BSApNIFYVwlQkVkWOlOEbIu1auNfZGKnQkTJcjHJRmi5S07s7tWu3JU4n2cgpP/M0smadOTAaWkLM1gA1R5WI2fpZQ6zqZ+zHFiBWJb0GsSoJUKA4xKoAJEUmSHwUgRSoBomPACSFJhCrCmFKiNXT/Ses9ab8rFN+9qnskTJ8Gi+fzptYc9phvfLpvvYVWbXGEqW2OOWvFAiYg6G5JcRszYDTqkfM1s8aYlU/Yz+2ALEq6TWIVUmAAsUhVgUgKTJB4qMIpEA1SHwEICk0gVhVCNODWM0+UoYLVL5Zkn1tX7DL2qlX9EgZvgES3xTJ3hCJj6DyjZLsK9bUlFp3urvdOvs0Nm+euZs33BJitjngiNn6WUOs6mfsxxYgViW9BrEqCVCgOMSqACRFJkh8FIEUqAaJjwAkhSYQqwph5qmKHylzZfQkvXf9EHXe7rDWoOY7UoafeRoKhvJ2jh8hk7H2lB0x41zBYMaaUy5OI62rzdxsCbSCmG3OCYjZ+llDrOpn7McWIFYlvQaxKglQoDjEqgAkRSZIfBSBFKgGiY8AJIUmEKsKYaZVlXGkDBOmfHrvtXvdjkVz3XzigpSfdbozufZ0bm3+kc5g3x1LnDojqOz7wOiIU2dk3YbMM093tum5OR/UiphtzkmI2fpZQ6zqZ+zHFiBWJb0GsSoJUKA4xKoAJEUmSHwUgRSoBomPACSFJhCr6mAWOlJm75J22tmym7Yt2G0J1ZUNq/I2HpiccKb1Jo6UYVN7b1x3ysQWtGSKU7aDb6yhQd0N+bgmxGxzzkPM1s8aYlU/Yz+2ALEq6TWIVUmAAsUhVgUgKTJB4qMIpEA1SHwEICk0gVgtHqZ9pAxfb2ofLTMWeeBUuLF5szNqysXpE6vb6f74FE1MxXI2Gu46Z22IZE3v5V9nTjm28epqa61p+pmn0RUri7+BMi6JmG3OuYjZ+llDrOpn7McWIFYlvQaxKglQoDjEqgAkRSZIfBSBFKgGiY8AJIUmEKviMKcdKcNEKhes9rW4fqmzIVIbm9rLBWr6kTJuMTt0uyd1pExyim9gfMypM7JxE1t7mtgQydq5d1vhM1TF76h8LRGzzfkWMVs/a4hV/Yz92ALEqqTXIFYlAQoUh1gVgKTIBImPIpAC1SDxEYCk0ARiNT9MfqQMHzk9dueI9JEyPGY/GLpH8UOHE9N7+cgp28GXC1b7ii5anDpShgtUdrxMfNZshR6vjKoQs835GTFbP2uIVf2M/dgCxKqk1yBWJQEKFIdYFYCkyASJjyKQAtUg8RGApNAEYjUTJt8EyT7rlE/tdTtSho+YtrFjZfjrunkbC3qDT+Xl4nTO6WNEhw9T6NxZp0y8ti61ay8fOWXiNLpkacE6YZCfAGK2uScEMVs/a4hV/Yz92ALEqqTXIFYlAQoUh1gVgKTIBImPIpAC1SDxEYCk0KTSxSo/PsZab2qNnB7Jf6QME6c72e69hY6U4Zsg2WtO7Z17+WZJ9jW1ZVtq7SkTp1Obtyj0KKriBBCzzT0HiNn6WUOs6mfsxxYgViW9BrEqCVCgOMSqACRFJkh8FIEUqAaJjwAkhSaVJlYLHSnTVNfM1p3u9XSkDD8+Jl2c8u/5MTP2FV223FpvWvXoIzS2Yzc92NFG8ZpahV5EVdkEELPNPROI2fpZQ6zqZ+zHFsperH75q9+jw8e6Mnxz9u1XM/79medepMtXb1k/W9u6lH756kvC70Os6n/sIVb1M7ZbQOJjjjUSH3OseUuVIFatI2X4qCk765RP6+XrUO0rHKpKClN25ikfORU4UoaXrTp53FlzysVp+OJ5p854/ZzEZkjJNaf8NbpwESFmm3u2EbPNsUbM1s8aYlU/Yz+2UPZi9cCzL9C7r73s+OYbf/0jOthx2vkZF7ODQyOOQOXCtbmpgX76g69bZQq9D7Gq/7FH4qOfMcSqOcZ2S0h8zDIvR7GafaQMF6h8J1/7yj5SZuv8wjvshq59YIlTe1ov/54iEafOqe07M848jWzYNM2RiNnmnm2IVXOsEbP1s4ZY1c/Yjy2UvVjNdsrprm76wle+Qz/74Tdp26bVxMXs157/PD37zH7L9LVfHaTvv/JzR8wWeh9iVf9jj8RHP2OIVXOMIVbNs+YtlotYPTtwit669gYdvPk2dfS8RxPRhw7QmlAtPbbsAD2y5AA9tfJjtGX+9oKwg8PDiR172Zmn9s69wcEBp1x0ZWty9HSvM4oar6rKWy9idkHsygwgVpWhLFgRxGpBRNIGEKvSCMuygooTqy//5Bf0D//4liVGs4Ur93D6z/i/04Vt9vtc7EKs6v9cIPHRzxhi1RxjiFXzrP0sVvvG7tC7N35L71x/03rl/06/drS00YHlT9P+ZU9S+5LHiAvWQpd9lIy9/jR85ZJTJNbYyKb1MmHKN0RKnnkam7+gUJUZ7yNme8IlZQyxKoXPU2GIVU+4ijKGWC0KW9kXqiixagvRl/78T6yRVBVidXAktfNh2T8tM3SDDbOqaXwyQlOR2Az1oHKarasJWTc7PhGtnJueoTutCgeprjpMI2OTM9SDymqWCyg/xOuJyEM6xEZMf3f9LfrN1TfoTP/JDEctqV9KT6x8mp5e+VF6fMWHqZltlFToCl25TOHOIxRmZ51aX+z79CvCRGlkz16KMIEa2c3Wna5bX6jKvO8jZkvh81QYMdsTLiljxGwpfEKFeZzGBQLZBCpGrNrC9Pkvfppe+OPPWhxUiNWJKQgo3R+rqnCAotE4xeK6W0L94WDAghABbO0PA0cdCgXYH2HwYGuHzRrgoyKlGK8no5N0pOcwddzqcF5vjt5wkCxvWMFGTNtp79J9zmtVMP803MDAAAU6OijY2UGBI+yVfU937zp1xtespXh7O8X2tlN8716Kte8jCiQ++youxGwVFMXqQMwW46TCCjFbBcX8dfA4jQsEKlKs8nWoL373x8461XQIbmtSua29Y3Ch9zENWP+HClPK9DO2W8CUMnOsMaXMHGveUimtWb04xHft7aRj1nmnRzJGT2dVzbaOlGljX3zHXv7aMntRfljRaMaGSHxzJL5Rkn3FmprYelN7Wi97ZSOosXnztDkAMVsb2mkVI2abY42YrZ81pgHrZ+zHFsp+ZDV7w6RsJxXa7bfQ+xCr+h97JD76GUOsmmNst4TExyzzmRSrA+P9lig91psQp8fZ6/2pUQfApvlbqa2FnXm6iH0tbCe+i2+hix8hk37mKT9ixrmCwYw1p1ycRlpXF6pS2fuI2cpQFqwIYrUgImUGiNnKUOasCGJVP2M/tlDWYtWe5uvmGHvdKn8P56yW9qOLxMecf5D4mGONxMcca96SSbEajUUTopSNnlqvfUfo+r2rzg0vql9ijZjyEVR+5il/rQ3X5QUS7LuTIU65UA2MjjhlIus2ZJ55urPNLOC01hCzzaFHzDbHGjFbP2uIVf2M/diCcrHKzzF9/Y33XFl8+mOP0d/8xZ/6kVPOPmNkVb87kfjoZ2y3gMTHHGskPuZYmxCr3cOXEtN6k6OnJ/uOOTdYHayhNmvUNDF6yoXqYrZRUr4rMDnhHCVTxab1cnEaunHdKRJb0JIpTtk031hDg1moOVpDzDbnBsRsc6wRs/WzhljVz9iPLSgTq3y67OFjXRYDe71nNpAtTz5n/Whf2yb66Q++7kde0/oMsarfjUh89DOGWDXH2G4JiY9Z5jpGVo/1dtDb1/+F3mJfp5g4jcQizk01sV16Dyx7mp5c8RF6kp152jJrYcEbDnedY6KUCVMmTvmZp1VnTjll4tXVzlEy1tEybAff6IqVBeucCQPEbHPUIVbNsUbM1s8aYlU/Yz+2oESschHaNHeOdXapyMU3LRoaHs0pakXqKBUbiFX9nkDio58xxKo5xhCr5lnzFlWI1ZGJe0yYvsEE6pv05tV/oqHxQedm+PmmbYvaLXHKzz3l558WukK3exKjp0lxyl8D42NOscjGTYmNkdiaUy5Op7btKFRlSbyPmG3ODRCr5lhDrOpnDbGqn7EfW1AiVvmoqteR0mLKlCJgiFX9XkHio58xxKo5xhCr5lnLiNWzA6fozQ/+id6+8SbbIKkjY/SUT+V9ip13+uGV/3bxJwAAIABJREFUn2AC9SmaXVWf9+a4ELU2RUpO6+VCNdRzyykTXbQ4MXrKxKn1yr7is/PXOTM087eKmG3OKxCr5lhDrOpnDbGqn7EfW1AiVv1446r6DLGqimTuepD46GcMsWqOMcSqedZexOq1e93U2XuYjvKv24fpzMBJp8Pzaptoz+JHaPeifbSHffHX6lD+Q+yrzp5OE6dseu+5s0598do6R5xaI6d8au/SZTMDSGGriNkKYRaoCmLVHGuIVf2sIVb1M/ZjC8rFKp8SnL7Trg3l5Z/8gv7hH98SnirsF5gQq/o9hcRHP2OIVXOMIVbNs84nVvk606N3EsKUC9TO24eIHzVjX/xYmd0LmThdnBCnq+euy3sDoZs3Ms485aOofLMk+5raspWJUj6tNzF6yv9dbhditjmPQqyaYw2xqp81xKp+xn5swZhY5eedvvjdH5fFOtV0R0Os6n/skfjoZwyxao4xxKp51tli9dbojYQw7T1kidQTfUedTs2paUiMmjKBao2gLnmEZoVn5+x04P5ohjjl6075MTP2xUdK06f18vWn8ZramYFgqFXEbEOgWTMQq+ZYQ6zqZw2xqp+xH1swJlb5kTYHO05jZNWPT8kM9xmJjzkHIPExxxqJjznWvKVrYyfo1xd+R53JUdTeBz1OB9bN20i72cipPbV3fdOmvJ2rOnk848zT8MXzjj1fY5otTqMLF5m92RluDTHbnAMQs82xRszWzxpiVT9jP7agRKzao6aFALhNDy5UptTfx8iqfg8h8dHP2G4BiY851kh89LK+8+B2Yu0pn97LBSr7Ph6PW43WhWc5a0/t9acNNY05OxS69kGGOOWbJFEkdUzN1PadGWeeRjbkF7t673zma0fMNucDxGxzrBGz9bOGWNXP2I8tKBGr6Teea82qH+GI9BliVYSSnA0SHzl+Xkoj8fFCS84WiY8cP7fSJ9lZp/bGSHyK783R647ZuuZ1tGNBuzN6unn+tpwdCA4PJ46UYWee2jv3BgcHHPvoytaEON2V2rk3XlWl/oZ8WiNitjnHIWabY42YrZ81xKp+xn5sQblY9SMEmT5DrMrQEyuLxEeMkworJD4qKIrVgcRHjFM+q8GHA9bIKd8UKbEG9TA7WmbKKlIVqqY9fN1pcmOkP9z8JE2O5157ah0pk3bmafjKJafpWGNjclMkJlCTZ57G5i+Qv4EyrQEx25xjEbPNsUbM1s8aYlU/Yz+2ALEq6TWIVUmAAsWR+AhAUmSCxEcRSIFqkPgIQHIx4eeepkZPD9PVe1ccq+UNK5M797LjZZhI3b5gl/MeT4LS43W4+3KGOOUbI6VfU7t2W6On9vrTyNr1xXW4AkshZptzOmK2OdaI2fpZQ6zqZ+zHFpSI1S9/9Xv00x983dP9F1PGUwOGjCFW9YNG4qOfsd0CEh9zrJH4iLG+93DYWnPqrD9lo6fjkTGrcID9x3frdXbuZQK1ZZb7ZkZL4g9o6DcHk9N6E9N7+XRf+4qsWuOcecqPlOEilQIBsU7CKoMAYra5BwIx2xxrxGz9rCFW9TP2YwtKxCpfp9o0d47wTr8Hnn2BhoZHy+IYG4hV/Y89Eh/9jCFWzTG2W0Lik5v5haEuZ2MkPsX38t0LjvHi+qWJI2X48TLsq21Ru3tF0WhiUyQmSvlr3Qm2KVJ3t2Mba2pKiFP7zFMmTmPz5pl/EMqwRcRsc06FWDXHGjFbP2uIVf2M/diCErHKb5yPlB4+1mUxOPv2q64suKjl1762TZ5HYksVLsSqfs8g8dHPGGLVHGOI1emsH0zdT6w5Ta49PdrbQaOTI47hzoV7nLNP+Ujqkvplrg4LX7qQOvOUiVR+xIxzBYOJTZGSa075a6R1tXnHV0CLiNnmnAyxao41xKp+1hCr+hn7sQVlYtW++Zd/8gt65e9fd2Xx/Bc/TS/88Wf9yClnnyFW9bsTiY9+xhCr5hhDrCYIXLl7MbH2NLkx0vnBs44TFtS1JM49XZyc4su+DwVC05wU7O/LEKd8BDUwmhK5fJ2pvea08en91LNqi3lHV2CLiNnmnA6xao41xKp+1hCr+hn7sQXlYtWPEGT6DLEqQ0+sLBIfMU4qrJD4qKAoVkelJT4T0YfJ0dOEQOXrUO+ODzmwti3YaU3rtXfvXdmwahrIwOQk2xQpMa3Xnt4bupE6nobv0GuL08Qrm9rb0GDVk73BkpiXYFUMAcTsYqgVVwYxuzhuxZSqtJhdDCPZMhCrsgTLszzEqqRfIVYlAQoUR+IjAEmRCRIfRSAFqqmExOfayAepnXvZFN8zAycdMvPqmlIbIyVFak2odhq5cNe5xHmn9rEyZ045NvxsU2dab/LM0+iKla70IVYFHkpFJojZikAKVIOYLQBJkUklxGxFqIquBmK1aHRlXRBiVdK9EKuSAAWKI/ERgKTIBImPIpAC1ZRj4hONRxPnnvYmzj3l3/eP9zk0NjZvcTZG4lN8V89dN41U6HZPQpimjZ4Gxh44dpGNm6xNkewde6e27RCgjZFVIUiKjBCzFYEUqAYxWwCSIpNyjNmK0CirBmJVGcqyqkiJWLU3TrLJ5NpgqazIJW8GYlW/V5H46Gdst4DExxzrckl8bo3eyFh7euIO23U3ec2pbmBTe9uZQE2ce8qn+c6uqs+AHBgfSwhTe+SUvYZ6bjk20UWLk7v2pjZHis/OrEPEaxhZFaGkxgYxWw1HkVoQs0UoqbEpl5ithoaeWiBW9XD1e61KxKrfIcj0H2JVhp5YWSQ+YpxUWCHxUUFRrA4/Jz7H2G699sZI/PX2/ZS4XNe0MbH2dGFi/emGpk3TgFSdPZ0mTtkU33OpzZXitXWOOLXXn0aXuu/+K0Y6YQWx6oWWnC1ithw/L6URs73QkrP1c8yWu3NzpSFWzbH2U0sQq5LegliVBChQHImPACRFJkh8FIEUqMZPiU/fWC87VsbeuZdN8WXfx9l//KoLz3I2RrLOPmUitbF2bgaB0M0bGdN6+eZIgckJx2Zqy9akQG23Xvm/VV8Qq6qJ5q4PMdsca8Rsc6z9FLPNUVHbEsSqWp7lUpsysWofWeN2PE2+9/wOEmJVvweR+OhnbLeAxMcc61JPfE71H6fOnuTaU7Zz742Raw6c1sY1qbWn7NzTzc3bMsAF7o9miNNqJk6DfXccGz5Saq85tc8+jddM31xJpTcgVlXSzF8XYrY51ojZ5liXesw2R0JfSxCr+tj6uWZlYvUzz71IzU0N9NMffN2Vx5e/+j0aHBqhX776kp95Tes7xKp+dyLx0c8YYtUcY7ulUkt8BscHnLWn1iZJTKBORSet7oaDVZY4tc49Te7c21w7PwNa1akTGWeehi+ed97na0xtUWq/RhcuMgodYtUcbsRsc6whVs2xLrWYbe7OzbUEsWqOtZ9aUiZW+SZLL/35n9Czz+x3vf/XfnWQXvzuj6ncNl+CWNX/uCPx0c8YYtUc41ISq+cGTyd3701M8f1g+LIDYnnDSmfdKReoO1raMiCFrl3NOFKGb5JEkYhjw3fpTT/zNLJh+tpVk9QhVs3RRsw2xxpi1RxriFX9rCFW9TP2YwsQq5Jeg1iVBChQHImPACRFJkh8FIEUqGYmEp+RiXvsWJnk2lN27ikXqOORMau3gUAgY2MkPpK6cPZi506C9+4RX2tqnXlqvXZScHDAeZ+fb2qJ0+R5p3yaLz8HtVQuiFVznkDMNscaMdsc65mI2eburjRaglgtDT+UWi+UidUDz75AX3v+83lHVr//ys/p3ddeLjUGUv2BWJXCJ1QYiY8QJiVGSHyUYBSqxFTic3GoK7E5EpvWy6f3Xrqbmp67aPYSa8fePWxTJD7Ft40dM5N+ZR8pE75yyXk71tBAU7vbM6b3xuYvELr3mTCCWDVHHTHbHGvEbHOsTcVsc3dUei1BrJaeT0qhR8rE6jf++kd07uK1nGtSC61pLQUYxfQBYrUYat7KIPHxxkvGGomPDD1vZXUlPg+m7luilI+acoHKR1JHJ0aczu1s2Z1ae8pGT5fOWe68F+6+nHHeqTW1N57Y9ZdfU7t2W+LUnt4bWbve203PoDXEqjn4iNnmWCNmm2OtK2abu4PSbwlitfR9NBM9VCZWeef56Cq/skdP+c+HhkfLbr0qv1eIVf2PLRIf/YztFpD4mGOtMvHpHr6UOPc0OYLaNXDGuZEFs1oS03uTGyPxo2XCwbD1fnBwkKqPdyYFaof1Grx71ykbWbXGOfN0ik3x5UKVgkFzkBS2BLGqEGaBqhCzzbFGzDbHWmXMNtdrf7UEseovf5nqrVKxyjvNR1hff+O9jP7va9uUc5dgUzeqqx2IVV1kU/Ui8dHPGGLVHGO7JZnEZzI24WyM1Jlce3r34ZBzE1vn77Cm93KByteermxcnXgvGs0875SJ0/DVbqdcrKkpKU65MGXrT5k45T8rhwti1ZwXEbPNsYZYNcdaJmab66W/W4JY9bf/dPVeuVjV1dFSrRdiVb9nkPjoZwyxao5xsWL1+shVNqWXbYqUnOJ7uv+E0+m5tfOsnXv38PWnyeNlakKJc0vDly6kjpRh4rTqxLHUzbJR0owjZZg45aOp5XhBrJrzKmK2OdYQq+ZYQ6zqZw2xqp+xH1uAWJX0GsSqJECB4kh8BCApMkHiowikQDWFEp9oLOqsO7UFat/YHafmjc2b2ahp6tzTNXMT60eD/X0Zo6fVbOfewGhqzSpfZ8pHTPm6U0uosnWolXBBrJrzMmK2OdaI2eZYF4rZ5npSvi1BrJavb2XuDGJVhh4rC7EqCVCgOBIfAUiKTJD4KAIpUI1b4tNz/2Zi5DS5MdLx3iNOTXOqG9i03vbU+lM2vbe+eg4FJicTa075kTL8lYnT0I3rTjm+Q2/G6CnbwZfv5FtpF8SqOY8jZptjjZhtjjXEqn7WEKv6GfuxBYhVSa9BrEoCFCiOxEcAkiITJD6KQApUYyc+b146aG2MZE3xZZsk3b5/yym9dt6GjI2R+Ggqv8Lnu5goTWyIxMVp1ZlTThl+tqk9cmqfecrPQK30C2LV3BOAmG2ONWK2OdYQq/pZQ6zqZ+zHFiBWJb0GsSoJUKA4Eh8BSIpMkPgoApmnGj6Vl2+KdKK/g471dtDhW+9TLB6zStSG6pyNkfYm15421sylUO9tqmKi1Dr3NPkaGHvgtBLZsMk5TsY6VmbbDv034rMWIFbNOQwx2xxrxGxzrCFW9bOGWNXP2I8tQKxKeg1iVRKgQHEkPgKQFJkg8VEEMquaU/3HM84+vX7vqmOxsmE1WcI0uXvvlvnbKfBwPLUpEh85ZSI11JMacY0uXET2UTL2a3x2vZ7Ol0mtEKvmHImYbY41YrY51hCr+llDrOpn7McWIFYlvQaxKglQoDgSHwFIikyQ+KgBOTQ+aK075etPO/n5p2yK71R00qo8HKqiPWzn3vYlj9CBVR+i9Q1tNL9uAVWdPZ2a1svXn54763QmXlPriFNr5JRtjBRdukxNZyukFohVc45GzDbHGjHbHGuIVf2sIVb1M/ZjCxCrkl6DWJUEKFAciY8AJEUmSHyKB9k1cMYSqEf4uadMpH5w77JT2bI5K5yNkfjRMjta2qjuzi2qP32cJt59LzG9l30FJh46Zaa2bE2eedpuvfJ/4yqeAMRq8ey8lkTM9kqseHvE7OLZeS0JseqVmHd7iFXvzCqhBMSqpJchViUBChRH4iMASZEJEh9xkCMT96yNkawRVDZ6yr/GplLrSHez3Xr51F5+vMwe9v2ieH3mkTLHOynY2+s0yEdKM46UYQI1Xlsn3iFY5iUAsWruAUHMNscaMdsca4hV/awhVvUz9mMLEKuSXoNYlQQoUByJjwAkRSZIfPKDvDjUlRSmHdYr/7d9LapfYo2e8im+9vrTqlMnUmtP2chp+ELKnq8xjbfvpbEd7MxTPnLKp/YuWqzIk6gmmwDEqrlnAjHbHGvEbHOsIVb1s4ZY1c/Yjy1ArEp6DWJVEqBAcSQ+ApAUmSDxyQQ5FnmQsTHSkZ5DNDo54hjtbNntCNPdTKSuvBtLnXeaPFaGIhHHnu/Sa685pfZ2qmvbQYMjE4q8h2ryEYBYNfd8IGabY42YbY41xKp+1hCr+hn7sQWIVUmvQaxKAhQojsRHAJIiEyQ+ZK017WSilG+MxKf48rWo9sU3QrKn9/LX9rpNVHf8eEqgsp17g4MDjj0/39QSp7uSo6fse34OKr+Q+Ch6aAWrgVgVBKXADDFbAUTBKhCzBUEpMEPMVgCxQBUQq/oZ+7EFiFVJr0GsSgIUKI7ERwCSIpNKTHwmoxPWlF5LnCbXoPLdfO2LHyXDN0WypviyNahrr9y1pvbaZ56Gr1xybGMNDWw6796MM09j8xe4egeJj6KHVrAaiFVBUArMELMVQBSsohJjtiAa5WaI2cqRTqsQYlU/Yz+2ALEq6TWIVUmAAsWR+AhAUmRSKYkPP+c0fWOkU33HHYKNNXMtcco3ReIC9ZHxFqo/eSpjcySKxx37qZ1tGeI0sna9kDeQ+AhhUmYEsaoMZcGKELMLIlJmUCkxWxkwiYoQsyXgCRaFWBUEVWFmEKuSDodYlQQoUByJjwAkRSblmvjE4jFnx95OfrQMG0XtG7vjUNvYvJn4mlO+MdIjtRtpAxs95UfJVB/tsF6Dd+86tpHW1c6Zp1NsWi/fHImCQc8eQOLjGZlUAYhVKXyeCiNme8IlZVyuMVsKiqbCiNmawKZVC7Gqn7EfW4BYlfQaxKokQIHiSHwEICkyKafE5/b9W+xoGSZM2bpTfsTM8TtHHEr1VXOcjZH2trTTY7fD1HjqnLNzb/hqt2MbmzcvKU65MGXrT5k4jTU1SRNH4iON0FMFEKuecEkZI2ZL4fNUuJxitqcbnwFjxGz90CFW9TP2YwsQq5Jeg1iVBChQHImPACRFJn5PfI73HnE2RuLrT3vu33TIrJm7PnHuKZvie+DBQtrYzUZP7bWnJ46lCAYCGdN6uTiNrFqjiHCqGiQ+ypHmrRBi1RxvxGxzrP0es82Rkm8JMVueYaEaIFYLEarM9yFWJf0OsSoJUKA4Eh8BSIpM/Jb48Km8fEqvvTESH0nlU375VRuuS+zcy77212ygR24Gae7prsTa02Ns196R1BE0fJ0pF6V8517rzNNduxURzV0NEh/tiDMagFg1xxsx2xxrv8Vsc2TUt4SYrZ5pdo0Qq/oZ+7EFiFVJr0GsSgIUKI7ERwCSIhM/JD6n+08kdu9Nrj29PnLVufuVjautjZHa5++hJ+/MToye8rWn7Ct0/Zpjx3fotUSpLU7Z9N5YY6MiimLVIPER46TKCmJVFcnC9SBmF2akysIPMVvVvc50PYjZ+j0AsaqfsR9bgFiV9BrEqiRAgeJIfAQgKTIpxcTn7sMhR5hax8uwL37cDL/CwbCzMdJHxpfS3hsxmnf6fGL09PRJhwo/29QeObXPPI2ubFVErbhqkPgUx63YUhCrxZLzXg4x2zuzYkuUYswu9l5KvRxitn4PQazqZ+zHFipGrJ7u6qYvfOU79LMffpO2bVqd4avPPPciXb56y/rZ2tal9MtXXxJ+H2JV/2OPxEc/Y7uFUkl8ugbOOBsjcXHaPZw6y3TpnOVs9PQRerJqEz3eW0PrnZ17j1Bg7IEDK7JhU2rtKR9F3b7THEiBlpD4CEBSaAKxqhBmgaoQs82xLpWYbe6OZ64lxGz97CFW9TP2YwsVIVYPPPsCDQ2PWv7JFqtf/ur3aHBoxBGoXLg2NzXQT3/wdcu+0PsQq/ofeyQ++hnPtFgdnRhJbYzEp/j2HKKxSEp4WkfKNO2mZ/qbaNf1SWo+e9HaHCnUk/gjE7+iCxelTetNrD+Nz643B89jS0h8PAKTNIdYlQTooThitgdYkqYQq5IAPRRHzPYAq0hTiNUiwZV5sYoQq9yHuUZWuZD92vOfp2ef2W+5+rVfHaTvv/Jzeve1l61/F3ofYlX/JwSJj37GMyFWL909b22MZE/tvTjU5dzowtmLrbWnnxxbQY/1VNG67kFLnFadO+vYxGtqp4nT6NJl5mBJtoTERxKgx+IQqx6BSZgjZkvA81gUYtUjMAlzxGwJeIJFIVYFQVWYWUWLVTcBm/4z/ixkTx3OLgOxqv8Tg8RHP2MTYnU8MuasPbU2SGJfIxP3nJvb0dJGHw1voY/2N9K2a+PUfPqCtTlSYOKhYzO1ZWti7al13in7Yv/264XEx6znIFbN8UbMNscaYtUca8Rs/awhVvUz9mMLEKtZ61i9itXBkcRGL7j0EWiYVU3jkxGaiiSOJMGlj0BdTciqfHwiqqSR7ruX6QgbPT3Cdu7lr2f7Tzn1NtfNpyea99Kn7y6ifbeCtOpiLxOnRynY2+vYxNhIaYRN543sZmed7mm3XuN1dUr6NtOVVIWDVFcdppGxyZnuSkW0zwUU4rUZVyNmm+HMW1Eds8313H8tIWbr9xmP07hAIJsAxKqkWJ2YgoDS/bGqCgcoGo2z8zN1t4T6w8GABSFSJOzJ6CQdvvU+Hbp5yHp9n30Njg04YHcs3Emfe7iWnu6fTZu6R6nx5HkKdJ1Lga+vp9hettZ0bzvF2vexV/b94iVl6RiOOhQKsD/C4ME24WA+KoJ4bYI0EWK2Gc68FdmYba6n/m8JMVu/D3mcxgUCEKtZuwG7rUl98bs/prNvv2qxKvQ+pgHr/1BhSpl+xnYLxUwpuzFyLblz7yFrDeqp/uNOhxtr59Ing9vpk3cX0J4bUVpx8TbVstFTikQcm6ltO9LOPGWjqBs3mbvhGWwJU8rMwsc0YHO8EbPNsS4mZpvrXXm1hJit35+YBqyfsR9bqOiRVe6wQrv9FnofYlX/Y4/ERz9jL2I1TnFrt96jdxJnnnYygdo3lpq6u7duPX12tJUev11DG7vv0dzTXRQc6HduIrpiZUKcsjWniVc2tbe62txNlkhLSHzMOgJi1RxvxGxzrCFWzbFGzNbPGmJVP2M/tlARYjX96BrupKa5c5zdfvm/cc5qaT+6SHzM+SdX4nP7/q2EMGVf/PVYb4fTqdlV9fRfP9xMHx+YRzvZsTJLz1+n6itXnPdjDQ0JYcrWniY2R9pDsQUt5m6qRFtC4mPWMRCr5ngjZptjDbFqjjVitn7WEKv6GfuxhYoQqzodg5FVnXQTdSPx0c/YbiE98Tlxp9M5+5SPpPbcv+l05OnoKnp2eCk7ViZM6y4PUsOpM0Tx1NrLqZ1tGeI0sm6DuZvwSUtIfMw6CmLVHG/EbHOsIVbNsUbM1s8aYlU/Yz+2ALEq6TWIVUmAAsWR+AhAUmDSP95H5wY7nY2R+PrTaDyxK/DiiRr6Lx+sp48MNNC2q+O06Fw3hYaHnVYjraunnXlKQWyUkM8tSHwUPLQeqoBY9QBL0hQxWxKgh+IQqx5gSZoiZksCFCgOsSoAqQJNIFYlnQ6xKglQoDgSHwFIRZqc7j9hTevlwpS/Xhv5wKopyAZJP3N3Cf3hMD9WJkCrLvXSrOu3nFZi8+Ylxak9tXcvxZqaiuxFZRZD4mPW7xCr5ngjZptjDbFqjjVitn7WEKv6GfuxBYhVSa9BrEoCFCiOxEcAkqDJ3fGh1MZISZE6EX1old4yGKIvjK2hJ+/Mpo1X7tH8ru5UrYFAxrTeKX726ao1gq3CzI0AEh+zzwXEqjneiNnmWEOsmmONmK2fNcSqfsZ+bAFiVdJrEKuSAAWKI/ERgJTH5PzgWWdjpM7bh6h7+JJlvfA+0SeG5rMv+1iZWxQefeDUFFm73tkQydocadduuY6gdAYBJD5mHwiIVXO8EbPNsYZYNccaMVs/a4hV/Yz92ALEqqTXIFYlAQoUR+IjACnNZHRyhE3p7WACNXHuKZ/e+2DqPlWz5aftbCbvZ0dW0AF2rMyG7mGaczt1pExs/gKK7W2n6J49dH/7bmsH31hjo7fGYS1MAImPMColhhCrSjAKVYKYLYRJiRHEqhKMQpUgZgthkjKCWJXCV7aFIVYlXQuxKglQoDgSn8KQLg2dT6w95WefMoF6YajLKrSlj9imSI3OsTKLL/c4lcWrqpyRU/vM01kb11rvj45HCjcKCykCSHyk8HkuDLHqGVnRBRCzi0bnuSDEqmdkRRdAzC4anXBBiFVhVBVlCLEq6W6IVUmAAsWR+EyHNB4ZczZGss4+ZSL13sNhWjKaGD391N1F9GhPiNZeHqCq8QmngsiGTdY5p3zNqfW6fWdG5Uh8BB5IRSZIfBSBFKwGYlUQlAIzxGwFEAWrQMwWBKXADDFbAcQCVUCs6mfsxxYgViW9BrEqCVCgOBKfBKSr966k1p6yc0/PDZ6muqmEOH2qbzZ9uG8OO1ZmjBoHRhyq0YWLEqOnfM1p8jU+uz4ndSQ+Ag+kIhMkPopAClYDsSoISoEZYrYCiIJVIGYLglJghpitACLEqn6IZdgCxKqkUyFWJQEKFK/UxCcSm7LEKd8UyT5eZvDhAG2/Q7TvJtHHBpvYsTJEy68NORTjNbWZ4pQJ1Oiy5QKUEyZIfIRRSRsi8ZFG6KkCiFVPuKSMKzVmS0ErsjBidpHgiiiGmF0ENI9FMLLqEViFmEOsSjoaYlUSoEDxSkp8boxcc9adcoF6su8YLb/HxCkTpft7a9ixMrNoywejFJ5MrSmd2rwl48zTqS3bBKi6myDxKRqd54JIfDwjkyoAsSqFz1PhSorZnsBoMEbM1gA1R5WI2fpZQ6zqZ+zHFiBWJb0GsSoJUKB4OSc+8Xg8Y2MkPpL64O5ta+SUT+99un8O7bkRobl3xx1S0SVLU2tO7am9tXUCJAubIPEpzEiVBRIfVSTF6oFYFeOkwqqcY7YKPirrQMxWSTN/XYjZ+llDrOpn7McWIFYlvQaxKglQoHi5JT69D3qsHXs72aZIfIrvMXbMTNvthDh97HYVO1ammlp7UuedxmfNTq05TW6OFF20WICcdxMkPt6ZFVsCiU+x5IorB7HpayckAAAeHklEQVRaHLdiSpVbzC6GgakyiNmmSBMhZutnDbGqn7EfW4BYlfQaxKokQIHi5ZD4nOg7mlp7ykZPq6/fsMQp/3qit452Xp+gUDTm0JjatiOxW681ctpOkY2bBEjJmyDxkWcoWgMSH1FSauwgVtVwFKmlHGK2yH2Wgg1itjkvIGbrZw2xqp+xH1uAWJX0GsSqJECB4n5MfPrH+hLTe/kXG0W9cu0wtbHpvFycPnoraB0rM2+UbeWbvKIrVqbEaVti5954dbUAHbUmSHzU8sxXGxIfc6x5SxCr5nj7MWabo6O2JcRstTwRs83xdGsJYnVm+Zdq6xCrkp6BWJUEKFDcL4nPmYGTljDlApWvPW05122JU7450ofY9N7VfSlxGmtoYII0edZp8szT2IIWARp6TZD46OWbXjvEqjnWEKtmWfslZpuloqc1xGw9XN1qRczWzxpiVT9jP7YAsSrpNYhVSYACxUs18Rl+eNfaubeTrz9la0+Hzx2ypvPyzZH29QSo/WacAvHUDU7tbEuMnibFaWTdBoG7N2uCxMccbyQ+5lhDrJplXaox2ywFM60hZpvhzFtBzNbPGmJVP2M/tgCxKuk1iFVJgALFSynxOT94jo2aJs49vXL5PTZ6esUaObWn984dS607jbSuzjzzlIlUCgYF7njmTJD4mGOPxMcca4hVs6xLKWabvXPzrSFmm2OOmK2fNcSqfsZ+bAFiVdJrEKuSAAWKz2TiMzo5woRphyVOj7PRU+p8n7Z/MOZM710zlLqByNxGirLNkPiGSNbGSGyab6ypSeAOS8cEiY85XyDxMccaYtUs65mM2WbvdOZbQ8w25wPEbP2sIVb1M/ZjCxCrkl6DWJUEKFDcdOJz+e4FZ2OkodPv0oIzlxPilE3v3dOT1uFAIGNaL5/eG1m1RuCOStcEiY853yDxMccaYtUsa9Mx2+zdlVZriNnm/IGYrZ81xKp+xn5sAWJV0msQq5IABYrrTnweRsedjZEuXfgdVR3toK1XHzjTexsfpjr5cFUrxfc+ZonUSSZOp3btFrgD/5gg8THnKyQ+5lhDrJplrTtmm72b0m4NMducfxCz9bOGWNXP2I8tQKxKeg1iVRKgQHEdic+1kW46wqb1nrj5PkUOvU0L+NpTNnLKR1Bbh1OdmpjXSLE9j1KEb4rExSmf2tvYKNBrf5og8THnNyQ+5lhDrJplrSNmm70D/7SGmG3OV4jZ+llDrOpn7McWIFYlvQaxKglQoLiKxCcSnaJOtnMvX3s60Pkm1Rw/Rls+GLXE6a7bqU7EQkG6v3MHBdv3O0fLRFe2CvSyPEyQ+JjzIxIfc6whVs2yVhGzzfbYv60hZpvzHWK2ftYQq/oZ+7EFiFVJr0GsSgIUKF5s4nNz9Hpi195zv6Vox7vWuaf26Gn9ZKrhkdUriNjU3jgbQbVGT7fvFOhVeZog8THnVyQ+5lhDrJplXWzMNtvL8mgNMducHxGz9bOGWNXP2I8tQKxKeg1iVRKgQHEviQ8Xp6euHqTR939Ns06cYqOnI9bo6fJ7qYYeNDfS+K5dVL3vSefM03j9HIGelL8JEh9zPkbiY441xKpZ1l5ittmelV9riNnmfIqYrZ81xKp+xn5sAWJV0msQq5IABYrnS3x67/dYo6e9h/8/Chx5nxad+8ASp9vvpCqOVIdpaOsGCu97ggJ7P2RtjhRdtlyg5cozQeJjzudIfMyxhlg1yxpi1RxvxGxzrBGz9bOGWNXP2I8tQKxKeg1iVRKgQPHsxOdE31G6dOrX9PD931DjqbO0iY2e8um9tZFUZf2rl1hnnc760Met16kt2wRaggkSH3PPABIfc6whVs2yhlg1xxsx2xxrxGz9rCFW9TP2YwsQq5Jeg1iVBChQPBa6RwfPvkl9b7/OjpU5QkvOX6P2m3FaPJoqPDx/Dt3btplqH/0wG0F93Fp7Gq+tE6gdJukEkPiYex6Q+JhjDbFqljXEqjneiNnmWCNm62cNsaqfsR9bgFiV9BrEqiTAHMXPDpyiG7/7TxQ5/A41nTlPm7tHaXN/yvhhTZjubGql2N5HqXH/J621p9FFi/V0poJqReJjztlIfMyxhlg1yxpi1RxvxGxzrBGz9bOGWNXP2I8tQKxKeg1iVRJgsvi9iWE6f/R1uvf7f6La48dp5YVbtOdmjKqiqfpvrlpA93ftoFmPfpSNoH6EIhs3qWkctTgEkPiYexiQ+JhjDbFqljXEqjneiNnmWCNm62cNsaqfsR9bgFiV9BrEavEAL1/toDvv/CeKdxykBWcu05ar96nlQaq+vvmzqH/LOpq1/3FqOvCvaGx7G8Wrq4tvECULEkDiUxCRMgMkPspQClXEkyDEayFU0kYQq9IIhStAzBZGJW2ImC2NsGAFEKsFEVWkAcSqpNuR/IgDvD81Sh+8+X/S2Ptv0Gx2rMyqi3do3UDMqeBBbYiubVxCD3e2UcP+T1D9h56h2IIWQuIjzljWEomPLEHx8kh8xFmpsIRYVUFRrA7EbDFOKqwQs1VQFKsDMVuMk4wVxKoMvfItC7Eq6VuI1fwAe07+hgbeeS1xrEzXB7Tt2jgF46kyl1bNpbvb+LEyT9KSpz5PsfUbp1WIxEfyIfVQHImPB1iSpkh8JAF6LA6x6hGYhDlitgQ8j0URsz0CkzBHzJaAJ1gUYlUQVIWZQaxKOhxiNRPgVP8tuv6b/0ATh35DDafO0drLA9Q0llKnN+bXUM+m5WxDpHaat/8Pad6BTxGFQnm9gMRH8iH1UByJjwdYkqZIfCQBeiwOseoRmIQ5YrYEPI9FEbM9ApMwR8yWgCdYFGJVEFSFmUGsSjq84sVqLEZDv/slDb37n6n6GD9W5gat6J9wqN6dFaDLa+bTyI4tVPvIh2nFh/81hRYs8UQdiY8nXFLGSHyk8HkqjMTHEy5pY4hVaYTCFSBmC6OSNkTMlkYoXAFitjCqog0hVotGV9YFIVYl3VuJYjVwsYt63vq5dazMvNMXaP0Hww7FeIDo9Mo66t28muJ7HqEFT/wrWrTjaSnKSHyk8HkqjMTHEy4pYyQ+Uvg8F4ZY9Yys6AKI2UWj81wQMdszsqILIGYXjU64IMSqMKqKMoRYlXR3JYjV4EA/jR78Jxr5/T8nj5Xpofrx1Jkyl+cH6YP1C+nBju00+7GP06qPfpFmhWdLkk0VR+KjDGXBipD4FESkzACJjzKUQhVBrAphUmKEmK0Eo1AliNlCmJQYIWYrwZi3EohV/Yz92ALEqqTXylGsBqamqOpYJ915+/+h+BF2rMzZy7Swf8wh1c906NnWeurfuo6Cez9EC5/8L2h1a7skydzFkfhoQzutYiQ+5lgj8THHmrcEsWqON2K2OdaI2eZYI2brZw2xqp+xH1uAWJX0WrmI1fCFLnr43pv04P1/ofoTJ2l5d79DJhIk6lwWouv8WJld7FiZD/0Bbdz9aWqoaZSkJ1YciY8YJxVWSHxUUBSrA4mPGCdVVhCrqkgWrgcxuzAjVRaI2apIFq4HMbswI1kLiFVZguVZHmJV0q9+FauhO71UdfQI3T34nylkHStzlWofRhwaXQvY6OmqBnaszEaq2vcELX/8c7Rp/lZJWsUVR+JTHLdiSiHxKYZacWWQ+BTHrdhSEKvFkvNeDjHbO7NiSyBmF0vOeznEbO/MvJaAWPVKrDLsIVYl/ewXsRqYeGiJU74p0sP3f0ON7FiZeQOjzt331hMdWR6kng0rrGNlmp74FG1f9SQ11TVLEpIvjsRHnqFoDUh8REnJ2yHxkWfopQaIVS+05GwRs+X4eSmNmO2FlpwtYrYcP5HSEKsilCrPBmJV0uelLFarzp6x1p4+eO9X1mvLlR7nbifCRIeXEnWtbqCR7Vup9tEP07odz9D2BbskiagvjsRHPdNcNSLxMccaiY851rwliFVzvBGzzbFGzDbHGjFbP2uIVf2M/dgCxKqk10pJrIZu3bREabzjIEU63qEmdqxM1WRqau/phWz0dGmAHSuzih0r8ygtfPQPac+ifdQye5EkBb3Fkfjo5ZteOxIfc6yR+JhjDbFqljVitjneiNnmWCNm62cNsaqfsR9bgFiV9NpMitXAg/tUzcQpn947eegtqj1xnOoH7jl3dLOBqIONnp5b3UhjO7dTPTtWZkfrAdq1cK/kXZstjsTHHG8kPuZYI/Exxxpi1SxrxGxzvBGzzbFGzNbPGmJVP2M/tgCxKuk102K16vRJqmbiNND5PjtW5vfUeOW6cwcPqhPilE/v7d+yhkLtj9OazU/T7sX7aEn9Msk7nbniSHzMsUfiY441Eh9zrCFWzbJGzDbHGzHbHGvEbP2sIVb1M/ZjCxCrkl7TLVZD169Z4rTqeCfFOt5lx8qcomAk6vT6BJvBe5jp0K7WBprYvZvm7/kI7V64j3az6b2hYEjy7kqjOBIfc35A4mOONRIfc6whVs2yRsw2xxsx2xxrxGz9rCFW9TP2YwsQq5JeUy1WgyMjbFpvR2J6L/sKdR6iqsEhp5fX5iZGTvkI6pV1C6hh/ydo/6qP05MrP0qzq9iWvmV4IfEx51QkPuZYI/Exxxpi1SxrxGxzvBGzzbFGzNbPGmJVP2M/tgCxKuk1FWK16vhRR5xyoVp1+ZLTq5GaxMgpF6dHl4VovK2Ndm37FH2k9Q9oY/Nmyd77ozgSH3N+QuJjjjUSH3OsIVbNskbMNscbMdsca8Rs/awhVvUz9mMLEKuSXitGrIavdlubItmbI/FXisWcnhxdkho9Pbt6Dq3c+4f04dZn6KkVH6OGmkbJHvuvOBIfcz5D4mOONRIfc6whVs2yRsw2xxsx2xxrxGz9rCFW9TP2YwsQq5JeExGrwbt3k+KUC1S2/pSJ0+BQampv97zU6Cmf4ju0dQM9tfoT9OSKj9CjSx+ncJAdilrBFxIfc85H4mOONRIfc6whVs2yRsw2xxsx2xxrxGz9rCFW9TP2YwsQq5JecxWr8XhiUyQmSu3X8AdXnJZGZoXovSXRxM69bIrvtfWLadWaR9mZp4/QHrZzr9+OlpFEWLA4Ep+CiJQZIPFRhrJgRUh8CiJSasCTIJE/LipttEIrQ8w253jEbHOsEbP1s4ZY1c/Yjy1ArAp47TPPvUiXr96yLNe2LqVfvvqSU8pOfsKXLzri1Jrey9ahpl+dy0P0PhOo9uZIszftZsL0EWvXXv61dM5ygZ5UpgkSH3N+R+JjjjUSH3OseUsQq+Z4I2abY42YbY41YrZ+1hCr+hn7sQWI1QJe+/JXv0eDQyOOQOXCtbmpgX76g69bJUf/7Teo5p3fUnVnR0ZNo3Uh+vWqKP1mNdGv1jK7RfNpz5KUOOWjqJU+vVf0A4PER5SUvB0SH3mGojUg8RElpcYOYlUNR5FaELNFKKmxQcxWw1GkFsRsEUpyNhCrcvzKtTTEagHPHnj2Bfra85+nZ5/Zb1m+9quD9P1Xfk7vvvay9e9YbQ0FJyYpGgrQoZVV9C8rJunXTJx2sk2S1rVsTUztZSOnfBS1tXFNuT5HWu8LiY9WvBmVI/ExxxqJjznWvCWIVXO8EbPNsUbMNscaMVs/a4hV/Yz92ALEah6vne7qpi985Tv0sx9+k7ZtYkOk7Mr+2df+IEQX58Xo7VaiwJwGemTpo7SPjaA+suwxal/6CDv7dLYfn4uS6jP/BRGJxoj9D5dmAlXsjy78morGNbeE6kNBojD7v4kpPNgmnoZZNSEam4iaaKri20DMNvcIIGabY42YrZ81j9O4QCCbAMSqpFh99CePUuvcVvrkuk/SM2ufofmz5uMpAwEQAAEQAAEQAAEQAAEQAAEQkCQAsSopVofvT0q6AMULEaivq6KHk1FrdBWXXgK11Ym/anLeuPQS4KOqnPf98Sm9DaF2i8Dc+mpCvDbzMCBmm+HMW0HMNscaMVs/ax6ncYFANgGI1QLPhNua1Re/+2M6+/arVkkchaD/Q4X1T/oZ2y1g/ZM51lj/ZI41bwlrVs3xRsw2xxox2xxrxGz9rLFmVT9jP7YAsVrAa4V2A4ZY1f/YI/HRzxhi1RxjuyUkPmaZQ6ya442YbY41xKo51ojZ+llDrOpn7McWIFYFvCZyzqpANTApkgASnyLBFVEMiU8R0IosgsSnSHBFFoNYLRJcEcUQs4uAVmQRxOwiwRVRDDG7CGgei0CsegRWIeYQq5KOxsiqJECB4kh8BCApMkHiowikQDVIfAQgKTSBWFUIs0BViNnmWCNmm2ONmK2fNcSqfsZ+bAFiVdJrEKuSAAWKI/ERgKTIBImPIpAC1SDxEYCk0ARiVSFMiFVzMAu0hJhtzhWI2fpZQ6zqZ+zHFiBWJb0GsSoJUKA4xKoAJEUmSHz+//bu4EWOKo8D+PsHViQes2AIcWEMuSgoLAlkQcTLxpDD6iUwGJF4yEUPUQM5yI6rh/WSQ4JoGPASPUgSLyKCQoKwwu4luAENIYIRhDVI/AeWN1BNT011dzn9que915/cMjP96vc+vx89/Z2qrk4E2WMZL3x6ICX8EWE1IaawujhMYTUba8/Zw7dCWB3euMQjCKtzdk1YnROwx8OF1R5IiX5EWE0E2WMZL3x6ICX8EWE1IaawujhMYTUba8/Zw7dCWB3euMQjCKtzdk1YnROwx8OF1R5IiX5EWE0E2WMZL3x6ICX8EWE1IaawujhMYTUba8/Zw7dCWB3euMQjCKtzdk1YnROwx8OF1R5IiX5EWE0E2WMZL3x6ICX8EWE1IaawujhMYTUba8/Zw7dCWB3euMQjCKsldk3NBAgQIECAAAECBAgQqFxAWK28wbZHgAABAgQIECBAgACBEgWE1RK7pmYCBAgQIECAAAECBAhULiCsVt5g2yNAgAABAgQIECBAgECJAsJqiV1bkpovf3Y9nHn7/S27/far9SURGH6bN27eDs+//Ga4dP5sOLCyd9MBn109E27dubvxtX17docr62vDF1TxESZZm/N0TX/hlXfCv/5zc9OC7ecLc704b7Odzvr1t94LVz//2mynI5240ixrc72AJjgEgTEBYdU4ZCsQfyH888JH4drlc9nWWHJhh46eCvd+/W1jC+2wGl/0/3Lv/iigxhf4D+16IFx893TJW96x2qdZm/N0bYnO488X8UXn9W9ujL5mrtNZx5VmeZvtdN7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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 meaningful rate constants : kF of about 8 and kR of about 0. Do those numbers sound familiar? A definite resemblance to the kF=8, kR=2 of the SLOWER elementary reaction `A <-> B`! \n",
"\n",
"#### The slower `A <-> B` reaction dominates the kinetics from about t=0.028 on \n",
"\n",
"Let's see the graph again:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "0c1a9e04-5622-480c-beca-525857353618",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkturquoise', 'orange', 'green'], xrange=[0, 0.4], \n",
" vertical_lines=[0.028])"
]
},
{
"cell_type": "markdown",
"id": "57e7c2b9-c693-4e16-92f6-6e0a94b18a2b",
"metadata": {},
"source": [
"Just as we concluded in experiment `cascade_2_a`, the earlier part of the complex (compound) reaction `A <-> C` cannot be modeled by an elementary reaction, while the later part can indeed be modeled by a 1st order elementary reaction, with kinetics similar to the slower `A <-> B` reaction. This time, with a greater disparity between the two elementary reaction, the transition happens much sooner."
]
},
{
"cell_type": "markdown",
"id": "310322af-ca59-4d41-b533-ec3336d6f3a8",
"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, and in the previous one, that the complex reaction could be roughly modeled with the rate constants of the slower reaction only after some time - especially if the 2 elementary reactions are relatively similar (as in the previous experiment). "
]
},
{
"cell_type": "markdown",
"id": "2360a0ce-db41-4965-963c-a2356f01e32f",
"metadata": {},
"source": [
"If we were interested in early transients (for example, if diffusion quickly intervened), we couldn't use that model."
]
},
{
"cell_type": "markdown",
"id": "25991209-add1-4828-a07a-35c3cbd94211",
"metadata": {},
"source": [
"#### In the continuation experiment, `cascade_2_c`, we explore the scenario where the 2 elementary reactions are reversed in their relative speeds"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dab5c28c-042e-4b36-9574-3880f2b4a614",
"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"
}
},
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}