{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Transition path theory" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "import pyemma.plots as mplt\n", "import pyemma.msm as msm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Five-state toy model\n", "---------\n", "The only thing we need to start with is a transition matrix. Usually, such a transition matrix has been estimated as a Markov model from simulation data (see Emma's msm.estimation package). Here we will just define a little five-state toy model in order to illustrate how transition path theory works:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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roqPS17qxv9fiZzvQ3FSDehdTgEKYSiH8ANgFmICKUj0xEy3rtS2FcASFsNB5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\nI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Start with toy system\n", "P = np.array([[0.8, 0.15, 0.05, 0.0, 0.0],\n", " [0.1, 0.75, 0.05, 0.05, 0.05],\n", " [0.05, 0.1, 0.8, 0.0, 0.05],\n", " [0.0, 0.2, 0.0, 0.8, 0.0],\n", " [0.0, 0.02, 0.02, 0.0, 0.96]])\n", "M = msm.markov_model(P)\n", "pos = np.array([[2.0,-1.5],[1,0],[2.0,1.5],[0.0,-1.5],[0.0,1.5]])\n", "mplt.plot_markov_model(M, pos=pos);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The disks represent the five discrete states, with areas proportional to the stationary probability of each state. The labels 0-4 plotted within disks are just indexes that will be used to refer to states. The arrows represent transitions between states, with their thickness proportional to the transition probability" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transition path theory\n", "---------------\n", "For doing tpt with the function msm.analysis.tpt(), we only need to pass the transition matrix and the source or reactant state A, and the product or target state B. Here we choose A=0 and B=4:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "A = [0]\n", "B = [4]\n", "tpt = msm.tpt(M, A, B)\n", "#tpt = msmflux.tpt(P, A, B)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The object we get back is a TPT flux. It contains a number of quantities of interest. A quantity that we are normally not so much interested in is the **gross flux** of the A->B reaction. The Gross A->B flux is the probability flux of trajectory that start in A and end up in B. Compared to the equilibrium flux $\\pi_i p_{ij}$, this flux is smaller because a large part (generally the vase majority) of the equilibrium flux is just spend on nonreactive trajectories that never reach B." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "**Flux matrix**:\n", "[[ 0. 0.00771792 0.00308717 0. 0. ]\n", " [ 0. 0. 0.00308717 0.00257264 0.00720339]\n", " [ 0. 0.00257264 0. 0. 0.00360169]\n", " [ 0. 0.00257264 0. 0. 0. ]\n", " [ 0. 0. 0. 0. 0. ]]\n", "**forward committor**:\n", "[ 0. 0.35714286 0.42857143 0.35714286 1. ]\n", "**backward committor**:\n", "[ 1. 0.65384615 0.53125 0.65384615 0. ]\n", "\n", "**Gross flux illustration**: \n" ] }, { "data": { "text/plain": [ "(,\n", " array([[ 0. , 0. ],\n", " [ 0.35714286, 0. ],\n", " [ 0.42857143, 0.5 ],\n", " [ 0.35714286, -0.5 ],\n", " [ 1. , 0. ]]))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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LEJHqc/dPAZcRO7vNBp4CtskQficABxHzWRMxpeHDg3iInxI/58WD+JqVYWbPmNl+xILB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# get tpt gross flux\n", "F = tpt.gross_flux\n", "print('**Flux matrix**:')\n", "print(F)\n", "print('**forward committor**:')\n", "print(tpt.committor)\n", "print('**backward committor**:')\n", "print(tpt.backward_committor)\n", "# we position states along the y-axis according to the commitor\n", "tptpos = np.array([tpt.committor, [0,0,0.5,-0.5,0]]).transpose()\n", "print('\\n**Gross flux illustration**: ')\n", "mplt.plot_flux(tpt, pos=tptpos, arrow_label_format=\"%10.4f\", attribute_to_plot='gross_flux')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we have repositioned states such that their y-position equals the committor probability (or probability of folding, splitting probability, etc). The x-position is arbitrary and was chosen such that we will get a nice picture. Clearly, the source state has commitor 0 (it is a reactant, so it has no chance of hitting the product before hitting the reactant), while the target state has committor 1. States 1,2,3 are intermediates with a committor around 0.5 in this case. The forward committor is just one minus the backward commitor, i.e. these two probabilities are complementary. This is true for any transition matrix that fulfills detailed balance - if the transition matrix does not fulfill detailed balance, the committors are not redundant. \n", "As you can see, Flux is leaving the source state 0 and entering the target state 4. Except for this flux source and flux sink we have flux conservation: The flux leaving state A is identical to the total flux entering state B. In every intermediate state, the flux that enters the state is equal to the flux leaving the state (check for yourself)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The net flux\n", "------------\n", "Now we look at the quantity that is actually interesting: the net flux. Note that in the gross flux above we had fluxes between states 1 and 3. These fluxes just represent that some reactive trajectories leave 1, go to 3, go then back to 1 and then go on to the target state 4 directly or via state 2. This detour via state 3 is usually of no interest, and their contribution is already contained in the main paths 0->1 and 1->{2,4}. Therefore we remove all nonproductive recrossings by taking the difference flux between pairs of states that have fluxes in both directions. This gives us the **net flux**. The net flux is already computed by the TPT object, so normally you will just construct the TPT object and directly get the net flux from it:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "**Net-Flux matrix**:\n", "[[ 0.00000000e+00 7.71791768e-03 3.08716707e-03 0.00000000e+00\n", " 0.00000000e+00]\n", " [ 0.00000000e+00 0.00000000e+00 5.14527845e-04 8.67361738e-19\n", " 7.20338983e-03]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 3.60169492e-03]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n", " 0.00000000e+00]]\n" ] }, { "data": { "text/plain": [ "(,\n", " array([[ 0. , 0. ],\n", " [ 0.35714286, 0. ],\n", " [ 0.42857143, 0.5 ],\n", " [ 0.35714286, -0.5 ],\n", " [ 1. , 0. ]]))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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M7FUz2424YHA8cW50B7A2cJe7X5rv5ywi0tQ0AiwiC+XufYFLgIOoHG5xH7CvmU1JlOlV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\n0rLqy8uB53S4xn42lWMf4B/Ib86Xd7K4Akxl//8p8B8ppcUAKaVHOlx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# get tpt net flux\n", "Fp = tpt.net_flux\n", "# or: tpt.flux (it's the same!)\n", "print('**Net-Flux matrix**:')\n", "print(Fp)\n", "# visualize\n", "mplt.plot_flux(tpt, pos=tptpos, arrow_label_format=\"%10.4f\", attribute_to_plot='net_flux')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the Fluxes out of 0 and into 4 have not changed by this operation, because there was no unproductive backflux along these connections. State 3 became completely isolated - it is a dead end. Although reactive trajectories can pass through 3, they will have to return to other states they already have visited (here state 1), and therefore state 3 itself is not a productive state. In fact state 3 will trap trajectories for a while, so the flux would actually increase by removing state 3. \n", "It is also apparent that the flux 1->2 was reduced by removing the nonproductive backflux. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quantitatively, the flux can be interpreted as the number of transition events along a certain pathway per time unit (where time unit means the lag time used to construct the transition matrix). In our toy model, we don't have a physical lag time, so let's call the time unit just '1 step'. The total flux from A->B is given by the total flux that leaves A, or identically the total flux that enters B. It is identical between the gross flux and the net flux. \n", "The total flux can also be shown to be identical to the inverse round-trip time between A and B (that is the sum of the mean first passage times from A to B and from B to A). Often we are interested in the A->B time or the corresponding rate. This is already computed in the TPT object as well:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total TPT flux = 0.0108050847458\n", "Rate from TPT flux = 0.0272727272727\n", "A->B transition time = 36.6666666667\n" ] } ], "source": [ "print('Total TPT flux = ', tpt.total_flux)\n", "print('Rate from TPT flux = ', tpt.rate)\n", "print('A->B transition time = ', 1.0/tpt.rate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So when starting in state A=0, it takes on average 36.7 time steps to reach state B=4. \n", "Let us check that by computing the mean first passage times to state 4 using our original transition matrix using a different algorithm:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mfpt(0,4) = 36.6666666667\n" ] } ], "source": [ "print('mfpt(0,4) = ', M.mfpt(0, 4))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Et voilà, this confirms that we have computed the right quantity. \n", "Note that while this mean first passage time is fine, we should be careful with the interpretation of the A->B tpt transition rate, which is the inverse of mfpt(A,B). Whether or not this is a proper rate constant that corresponds to a transition rate in the sense of reactive flux theory very much depends on the metastability structure of your system and the choice of A and B. In general it makes no sense to just compute inverse mfpt's between all pairs of states (either using tpt or mfpt), and interpret them as rates for a rate matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our opinion the most useful information conveyed by a TPT flux analysis are not the absolute numbers, but the mechanism, i.e. which pathways is the system going to take from A to B, and what is their relative contribution to the overall reactive flux. Therefore we may want to get rid of the absolute flux numbers and just normalize them to the total flux, so that we can talk about percentages of taking this or that pathway. Let's do that:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0,0.5,'committor')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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1b5OmEOkjZnY7sCXwDPF+oRXYG3iwOGlSRGqUirDIUnL3YcS9glcG5hEf9A7Q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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mplt.plot_flux(tpt, pos=tptpos, flux_scale=100.0/tpt.total_flux, arrow_label_format=\"%3.1f\")\n", "ylabel(\"committor\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can nicely see that the 100% flux leaving A and entering B is split into several paths. The main path obviously is 0->1->4, and this path can support up to 67% of the probability. Pathway 0->2->4 seems to be the second-most important path that can support up to 29% of the probability. We will see below how the network is systematically decomposed into pathways. \n", "Of course any real trajectory might do much more complicated things, such as 0->0->0->0->1->1->3->1->1->4. But the point of TPT is exactly to remove all these detours, recrossings and waiting times, and just look at \"clean\" A->B pathways. This concrete trajectory would contribute to the flux 0->1->4." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pathway decomposition and sub flux\n", "--------------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let us have a look how the pathway decomposition works. It's really simple in this example. Here we just call the pathways function, and then list the pathways we have found:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "([array([0, 1, 4], dtype=int32),\n", " array([0, 2, 4], dtype=int32),\n", " array([0, 1, 2, 4], dtype=int32)],\n", " [0.0072033898305084278, 0.0030871670702178988, 0.00051452784503631509])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tpt.pathways()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Path flux\t\t%path\t%of total\tpath\n", "0.00720338983051 \t 66.7 %\t 66.7 %\t\t [0 1 4]\n", "0.00308716707022 \t 28.6 %\t 95.2 %\t\t [0 2 4]\n", "0.000514527845036 \t 4.8 %\t 100.0 %\t\t [0 1 2 4]\n" ] } ], "source": [ "(paths,pathfluxes) = tpt.pathways()\n", "cumflux = 0\n", "print(\"Path flux\\t\\t%path\\t%of total\\tpath\")\n", "for i in range(len(paths)):\n", " cumflux += pathfluxes[i]\n", " print(pathfluxes[i],'\\t','%3.1f'%(100.0*pathfluxes[i]/tpt.total_flux),'%\\t','%3.1f'%(100.0*cumflux/tpt.total_flux),'%\\t\\t',paths[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, we have the main pathway 0->1->4 contributing 66.7% of the flux, and the second pathway 0->2->4 contributing 28.5% of the flux while the remaining 4.8% flow along 0->1->2->4. \n", "Large Flux networks often contain a few major and many minor pathways. Therefore it is often computationally expensive to compute all pathways. Computing all pathways may not always be needed - in many publications only the most dominant pathways are shown for clarity, see e.g. [3]. If only the most dominant pathways are needed, call the pathways function with a suitable fraction argument. For example, let's compute the top 95% pathways:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Path flux\t\t%path\t%of total\tpath\n", "0.00720338983051 \t 66.7 %\t 66.7 %\t\t [0 1 4]\n", "0.00308716707022 \t 28.6 %\t 95.2 %\t\t [0 2 4]\n" ] } ], "source": [ "(bestpaths,bestpathfluxes) = tpt.pathways(fraction=0.95)\n", "cumflux = 0\n", "print(\"Path flux\\t\\t%path\\t%of total\\tpath\")\n", "for i in range(len(bestpaths)):\n", " cumflux += bestpathfluxes[i]\n", " print(bestpathfluxes[i],'\\t','%3.1f'%(100.0*bestpathfluxes[i]/tpt.total_flux),'%\\t','%3.1f'%(100.0*cumflux/tpt.total_flux),'%\\t\\t',bestpaths[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case we get only two paths with 95.2% out, because adding the next path would give us 100%. In more realistic (larger) flux networks you will typically get close to the flux fraction asked for. \n", "In order to plot the netflux containing all the main pathways corresponding to a requested fraction of the total flux, we have to sum up the subset of pathways to obtain a flux again. This is done automatically by the following method:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 0.00720339 0.00308717 0. 0. ]\n", " [ 0. 0. 0. 0. 0.00720339]\n", " [ 0. 0. 0. 0. 0.00308717]\n", " [ 0. 0. 0. 0. 0. ]\n", " [ 0. 0. 0. 0. 0. ]]\n" ] }, { "data": { "text/plain": [ "(,\n", " array([[ 0. , 0. ],\n", " [ 0.35714286, 0. ],\n", " [ 0.42857143, 0.5 ],\n", " [ 0.35714286, -0.5 ],\n", " [ 1. , 0. ]]))" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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RWlCYFWlT7j4FuIaYWzqSCLIXAB/VJenmV2wQ+yDwP8T/73Cid7iH+D9OdhCEiEgtKcyK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\nm+uqbx/501gxe0fNK2QPrl7YuKtkR6sfbN5a4OS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Fsub = tpt.major_flux(fraction=0.95)\n", "print(Fsub)\n", "Fsubpercent = 100.0 * Fsub / tpt.total_flux\n", "mplt.plot_network(Fsubpercent, pos=tptpos, state_sizes=tpt.stationary_distribution, arrow_label_format=\"%3.1f\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case the sub flux only consists of two pathways." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Coarse-graining of fluxes\n", "-----------------\n", "\n", "Finally, we will look into coarse-graining of fluxes. You will need this when you have large flux networks that arise from using TPT on Markov state models with many (100s, 1000s) of microstates. In is usually not illustrative to visualize path networks with so many states. Here we will learn how to coarse-grain path networks to coarse sets of states, such as metastable sets of just user-defined sets.\n", "\n", "We start with a somewhat larger toy model containing 16 states:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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wFJm+fddaK+EFKfN9pAPNWd3ZiKn51fgv3fpRxYgraW5zE3AYMMdaqx1UgeCc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\nkdCroYiRew7wfeA24H0K6j0K6k8U1FEN7a1zKJ0T+JrWOsm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fhQ/8A/ApJItAedW81chW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P2_nonrev = np.array([\n", "[0.5, 0.2, 0.0, 0.0, 0.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", "[0.2, 0.5, 0.1, 0.0, 0.0, 0.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", "[0.0, 0.1, 0.5, 0.2, 0.0, 0.0, 0.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", "[0.0, 0.0, 0.1, 0.5, 0.0, 0.0, 0.0, 0.4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", "[0.3, 0.0, 0.0, 0.0, 0.5, 0.1, 0.0, 0.0, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", "[0.0, 0.1, 0.0, 0.0, 0.2, 0.5, 0.1, 0.0, 0.0, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", "[0.0, 0.0, 0.1, 0.0, 0.0, 0.1, 0.5, 0.2, 0.0, 0.0, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0],\n", "[0.0, 0.0, 0.0, 0.1, 0.0, 0.0, 0.3, 0.5, 0.0, 0.0, 0.0, 0.1, 0.0, 0.0, 0.0, 0.0],\n", "[0.0, 0.0, 0.0, 0.0, 0.1, 0.0, 0.0, 0.0, 0.5, 0.1, 0.0, 0.0, 0.3, 0.0, 0.0, 0.0],\n", "[0.0, 0.0, 0.0, 0.0, 0.0, 0.1, 0.0, 0.0, 0.2, 0.5, 0.1, 0.0, 0.0, 0.1, 0.0, 0.0],\n", "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.1, 0.0, 0.0, 0.1, 0.5, 0.1, 0.0, 0.0, 0.2, 0.0],\n", "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.1, 0.0, 0.0, 0.2, 0.5, 0.0, 0.0, 0.0, 0.2],\n", "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.3, 0.0, 0.0, 0.0, 0.5, 0.2, 0.0, 0.0],\n", "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.1, 0.0, 0.0, 0.3, 0.5, 0.1, 0.0],\n", "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2, 0.0, 0.0, 0.1, 0.5, 0.2],\n", "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.3, 0.0, 0.0, 0.2, 0.5],\n", "])\n", "M2_nonrev = msm.markov_model(P2_nonrev)\n", "w_nonrev = M2_nonrev.stationary_distribution\n", "# make reversible\n", "C = np.dot(np.diag(w_nonrev), P2_nonrev)\n", "Csym = C + C.T\n", "P2 = Csym / np.sum(Csym,axis=1)[:,np.newaxis]\n", "M2 = msm.markov_model(P2)\n", "w = M2.stationary_distribution\n", "# plot\n", "P2pos = np.array([[1,4],[2,4],[3,4],[4,4],\n", " [1,3],[2,3],[3,3],[4,3],\n", " [1,2],[2,2],[3,2],[4,2],\n", " [1,1],[2,1],[3,1],[4,1]], dtype=float)\n", "mplt.plot_markov_model(P2, pos=P2pos, state_sizes=w, arrow_label_format=\"%1.2f\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us first decide what a natural coarse-graining of this system would look like. Looking at the timescales, we can see that there is clear gap after three timescales (corresponding to four states). So we use PCCA to find the four most metastable sets and assign each microstate to the nearest metastable set:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def assign_by_membership(M):\n", " return np.argmax(M, axis=1)\n", "\n", "def clusters_by_membership(M):\n", " a = np.argmax(M, axis=1)\n", " m = np.shape(M)[1]\n", " res = []\n", " for i in range(m):\n", " res.append(np.where(a == i)[0])\n", " return res" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "timescales: [ 13.72527308 10.71049274 5.3830411 2.24980237 1.9671322 ]\n", "PCCA clusters [array([2, 3, 6, 7]), array([10, 11, 14, 15]), array([0, 1, 4, 5]), array([ 8, 9, 12, 13])]\n" ] } ], "source": [ "print(\"timescales: \",M2.timescales()[0:5])\n", "# PCCA memberships\n", "M2.pcca(4)\n", "M = M2.metastable_memberships\n", "pcca_clusters = clusters_by_membership(M)\n", "print(\"PCCA clusters\",pcca_clusters)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PCCA clusters are the four sets of four states in the lop left, top right, lower left and lower right corner in our illustration. So for the sake of a TPT analysis we want to lump the microstates within these PCCA clusters and only resolve the pathways connecting them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we first to TPT for the full microstate transition matrix, and obtain the reactive flux in the set of 16 microstates:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# do TPT\n", "A2 = [0,4]\n", "B2 = [11,15]\n", "tpt2 = msm.tpt(M2, A2, B2)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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soS1VDW0bsAjYm3x4oUTPIR9DyWz3VWofxdVRBVyRdhDSRVYTcDTlXzvbil0M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\nSzAeDYKgcZ3nGg2s6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mplt.plot_flux(tpt2, attribute_to_plot='net_flux', pos=P2pos, state_sizes=w, \n", " arrow_label_format=\"%1.4f\", show_committor=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have chosen to do TPT starting from states (0,2) and ending in states (11,15). Note that this definition is not exactly compatible with PCCA states. We have defined A and B such that PCCA states are cut. This is fine, because we usually conduct TPT in such a way as to resolve a specific process that is of our interest. Whether the sets that we want to define as TPT endstates are metastable or not is a different question. So we have to deal with this. \n", "\n", "Now we call the coarse-grain method with the PCCA clusters we want to distinguish" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "(tpt_sets, tpt2_coarse) = tpt2.coarse_grain(pcca_clusters)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function redefines the sets on which the TPT flux will be coarse-grained in order to meet two objectives:\n", "\n", " * the states we want to distinguish will be distinguished\n", " * the boundaries between A, B and the intermediates will be respected. \n", " \n", "Because of this redefinition, you will get two objects as an output. First the actual set definition that was used, secondly the new coarse-grained flux. Let's look at the sets:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[OrderedSet([0, 4]), OrderedSet([2, 3, 6, 7]), OrderedSet([10, 14]), OrderedSet([1, 5]), OrderedSet([8, 9, 12, 13]), OrderedSet([11, 15])]\n" ] } ], "source": [ "print(tpt_sets)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that the PCCA sets are still distinguished. In Addition the PCCA set (0,1,4,5) was split into (0,4), which is the new A set, and (1,5), which is an intermediate set. Likewise (10,11,14,15) was split into the intermediate set (10,14) and the B set (11,15).\n", "\n", "Now we print the full information of the coarse-grained flux:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[OrderedSet([0, 4]), OrderedSet([2, 3, 6, 7]), OrderedSet([10, 14]), OrderedSet([1, 5]), OrderedSet([8, 9, 12, 13]), OrderedSet([11, 15])]\n", "[0]\n", "[5]\n", "pi coarse: \n", "[ 0.15995388 0.18360442 0.12990937 0.11002342 0.31928127 0.09722765]\n", "sum = 1.0\n", "committors : \n", "[ 0. 0.56060272 0.73052426 0.19770537 0.36514272 1. ]\n", "[ 1. 0.43939728 0.26947574 0.80229463 0.63485728 0. ]\n", "F coarse : \n", "[[ 0. 0. 0. 0.00427986 0.00282259 0. ]\n", " [ 0. 0. 0.00234578 0.00104307 0. 0.00201899]\n", " [ 0. 0.00113892 0. 0. 0.00142583 0.00508346]\n", " [ 0. 0.00426892 0. 0. 0.00190226 0. ]\n", " [ 0. 0. 0.00530243 0.00084825 0. 0. ]\n", " [ 0. 0. 0. 0. 0. 0. ]]\n", "F net coarse : \n", "[[ 0. 0. 0. 0.00427986 0.00282259 0. ]\n", " [ 0. 0. 0.00120686 0. 0. 0.00201899]\n", " [ 0. 0. 0. 0. 0. 0.00508346]\n", " [ 0. 0.00322585 0. 0. 0.00105401 0. ]\n", " [ 0. 0. 0.0038766 0. 0. 0. ]\n", " [ 0. 0. 0. 0. 0. 0. ]]\n" ] } ], "source": [ "print(tpt_sets)\n", "print(tpt2_coarse.A)\n", "print(tpt2_coarse.B)\n", "print(\"pi coarse: \")\n", "print(tpt2_coarse.stationary_distribution)\n", "print(\"sum = \",np.sum(tpt2_coarse.stationary_distribution))\n", "print(\"committors : \")\n", "print(tpt2_coarse.committor)\n", "print(tpt2_coarse.backward_committor)\n", "print(\"F coarse : \")\n", "print(tpt2_coarse.gross_flux)\n", "print(\"F net coarse : \")\n", "print(tpt2_coarse.net_flux)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed we have a normal ReactiveFlux object, just with less (6) states. In order to visualize what the coarse-graining has done to our flux, we will compute the positions of the coarse states as the mean of the fine states that were lumped:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "set\t\tposition\n", "[0, 4] \t\t [ 1. 3.5]\n", "[2, 3, 6, 7] \t\t [ 3.5 3.5]\n", "[10, 14] \t\t [ 3. 1.5]\n", "[1, 5] \t\t [ 2. 3.5]\n", "[8, 9, 12, 13] \t\t [ 1.5 1.5]\n", "[11, 15] \t\t [ 4. 1.5]\n" ] } ], "source": [ "# mean positions of new states\n", "cgpos = []\n", "print(\"set\\t\\tposition\")\n", "for s in tpt_sets:\n", " p = np.mean(P2pos[list(s)], axis=0)\n", " cgpos.append(p)\n", " print(list(s),\"\\t\\t\",p)\n", "cgpos = np.array(cgpos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the coarse-grained flux network:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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MzsClwO5UdpS2E7gIP+N0TQWfV7LKJ7fTgJkUamvX419LbwLz9FoSKZOcmQbk\ngb2ojjt64O/q3Qx8kXyyMnYwIgMpma2knGkAvgL8BD/C1V6mZ+rDn3zeBD5HPnmgTM8jIiKl5i8o\nvwT8B37ORXOkSDoprNynOnipWkpmY8iZscDHgW/h62mbKc0tpQ58GcON+NVY7lNtrIyEc64d/9qc\nZ63VREGRGHJmCvAH/OInlR6l7QAuB/42LPIgUrXUZzaGfLKOfHIx+WQ/4EDg98C7+JqklQx/0YV1\n/Y5/EV+XO5V88jHyyb1KZGUUvoZvL5eLHYhI3conrwMn4idqLsAnmOVcaasHPxr7MHAS+eRLSmQl\nC6qtwLz++GVwzwHOIWe2AfYDDgCOolAzlU4c68FPynkHf7K5D3gceHJgDaNzblvgI8BF1lotMyjF\n2i1s34oahUi984MSfwL+FFp4/Q1wJr6crFSjtavD9kLgv8gnC0v0uCIVoWS2mvgZojeFrxFzzv0J\nvxIZ+LpZ1TpJsXYK21ejRiEiBfnkMeBz5MzXgc/g62r3xM/BWI+fsDnUHdf1+J7QLRRW8foNcBX5\nJMaS1yKjpmS2Nh1AYaGGb6FkVoo3LWxfiRqFiLyfv/X/a+DXYbLY9sD+wEH4NnvpYj0t+ES3K3y9\nCNwDPIq/q7d0YDmac24mvk3fT6y1Sm4lE5TM1qafAj/EN8E/1Dk33Vr7UuSYJFu2B7DWrh7iOBGJ\nySejS8LXn0bzUM6504Ar8CUMLwCXjTo+kQrQBLDa9EcK/7cNwFcjxiIZ45wbh18oQaOyIvXlUfxI\n7lj8XT2RTFAyW4OstSuBq/BX12OArzrnYvUplOz5QNiqXlYkQ5xzY5xztzrn/mMkP2+tfR2/AhnA\nHs653QY7XqRaKJmtXT/Ht1gB3wnhtIixSLak9bJLokYhIsXaHjgO3+1gpH6G727QBHy9BDGJlJ2S\n2RplrX0UeC3stgPfjhiOZEuazD4fNQoRKdZ2YTuaEqFb8QMhzcAXnHNjRx2VSJkpma1tPwbS/rP7\nOOd2iRmMZEaazL4cNQoRKdb0sF000gew1vYB/4lflAdGN8orUhFKZmvbZfgSA8JWt4xkONKLHtXM\nimTL9mG7YJSP8/uwbUMTwSQDlMzWMGvtGuAS/PKHzcCXdMtIhiFdMEHdDESyZUbYvjiaB7HWvgnc\nge9ssItzbs9RxiVSVkpma99/4JfATemWkQxlathqZFYkW9IL0VKUCP0Uv1LYGOD/lODxRMpGyWyN\ns9bOpzCRpw1NBJOhTYf3RvZFJDvStnqlWCTnTgpdDT4b+k+LVCUls/Xhx/iTEvhbRnvFDEaql3Nu\nfPhWk79EMsQ51wBMCruvj/Yam3vFAAAgAElEQVTxrLUJ/s5eJ75neW60jylSLkpm68Of8Cs6gb9l\n9DcRY5HqphIDkWzaBn+ef8da21Oix7wQnydoIphUNSWzdcBauw5/UurBdzX4tG4ZySZsH7YLYwYh\nIkVL23K9NuhRRbDWvg3Mxk8E28E5t0+pHluklJTM1o9fAuvD973AGRFjkeq1c9jOjxqFiBQrTWZL\nvXLfz/ATwVrQXT2pUkpm64S1diEbTgTT7FTZmLS1z4ibrotIFOnqX8+V+HHvBVbg7+p90jnXVuLH\nFxk1JbP15T8prAi2t3Nu+mAHS11KJwe+EDUKESnWbmFb0pHZMBHs50AH/q6eJoJJ1VEyW1+uwLdZ\nAT9R4IsRY5HqlJYZLI4ahYgUK125rxRtuQb6I35ktg34RhkeX2RUlMzWEWvtauB6fDF/C/DV0M5F\nJG3t8wFgnbV2bex4RKQoaZlBydvqWWuX4/vOAsxwzu1Q6ucQGQ0lMvXnv/DF/ADjgSMixiLVZUrY\nqpOBSPZMDttyjMwC/Arfr7wB+FKZnkNkRJTM1p978E2wwSezX4sYi1SXdCnMUk8gEZEycs5tCYwF\n1pZx5b7ZYTsGOFt39aSa6MVYZ6y1fcD5QBe+bvajmp0qQZrMPhU1ChEp1q5hW65RWcJCDH/Et3hs\nRXf1pIooma1PF+DrZsGfmM6MGItUj3Q2tNpyiWRLOvnrmTI/z++AbvxEsHPK/Fwiw6Zktg5Za1+k\n0BRfPWcllbblUjIrki1pf+h55XwSa+084A0Kd/XGl/P5RIZLyWz96t9zdnfn3I4xg5GqkI7uqMes\nSLbsG7YLKvBcv6TQc1YrSUpVUDJbv67C9w0E/zr4csRYJDLnnCH0mLXWvhM5HBEpTloiVIlOJBej\nnrNSZZTM1qnQR/RqoA/NThXYImzVlkskQ8KF6NSwW/YSIWvtMuD+sLu3c267wY4XqQQlL/Xt1/jb\nReAXUTg6XigSWbryl5JZkWzZBj8g8W4Z23IN9F/4nrMG+EKFnlNkk5TM1rf78Sck8LeM/jpiLBJX\n2pbryahRiEix0rZcSyr4nDfgE9l0JUlTwecWeR8ls3XMWpvgR2fX4U9MJznnJsaNSiJJR2afjxqF\niBQrnbj5dKWe0FrbBVyKnwTWDhxaqecW2Rgls/KHft/3Ap+IFIfEtXfYqi2XSLbsEbZlbcu1Eb/F\nD4SMA75a4ecW2YCS2TpnrX0FmBt2x6Oes/UqnQ2ttlwi2bJP2Fa63v0x4G18HnGmc661ws8v8h4l\nswLwCwq1szs753Yd7GCpSemtyqVRoxCRYqXv3YqWCPUrU+vE39X7aCWfX6Q/JbMCcA2FnrNNwFci\nxiIV5pxrw0/keCV8QIlIBjjnGoEPhN3FEUL4Iz6PaAe+HuH5RQAlswJYazuBPL7nbDPw5XCSlPqQ\nrv6melmRbJmG/xx/K0zKqihr7VLgkbB7gHNuSqVjEAEls1LwG/ztIvCjs8dFjEUqK23LNT9qFCJS\nrLTEIMaobOqXFMrUPhcxDqljSmYl9TCQLmPajnrO1pO0LdezUaMQkWKl8xti9of+M75MbSxwjnrO\nSgxKZgV4r5j/V/hWKwAnOOc2jxiSVM7MsFUnA5Fs2TNso91VsdauA67Al6ltCRwQKxapX0pmpb+L\n8IsnAKwHPhUxFqmctE+lamZFsiXtDx17sZPz8Uujj0U9ZyUCJbPynlDMPyfsjkezU+tFWjP7ctQo\nRKRYaYlQpXvMDvQQsApfbnCWc64lcjxSZ5TMykD9e85Od87tMdjBkm3OuTHA5sBya+362PGIyPA4\n55qByUACvBQzllCm9ht8mVoCnBIzHqk/SmZloOsolBo0o56ztW77sI09siMixdkhbJdWyYXoH8JW\nE4il4pTMygZCr8JL8Su6NANfVM/ZmpaWGDwTNQoRKVbalqsqLkTD0ujzwu4HnXOTY8Yj9UXJrGzM\n+RS6GjQAH4oYi5SXesyKZFM1tOUaKO052wt8JnIsUkeUzMrGPI4v5gdoQ42wa1na2kdtuUSyZa+w\nfTpqFBu6Gr/ozjhUaiAVpGRW3icU8/8R6MHXz37cOdcUNyopk4PCtpo+EEVkaGkyWxVlBgDW2rXA\nNfies5Odc/tGDknqhJJZ2ZSL8cks+NmpH44Yi5TPPmG7JGoUIlKsdAJY7B6zA/0G33O2BTg7cixS\nJ5TMyqbMB5aH79uAL8QLRcrBObc1/pbgQmttX+x4RGR4nHOt+NW21gOvRw5noPuAtfhzy2c0gVgq\nQcmsbFQoNbgI6MaXGnw09CSV2pEuY/t41ChEpFjpxM1Xq+1CNMRzEYUytSPiRiT1QMmsDOYS/JU/\n+Nmpx0WMRUovrbmbM+hRIlJt0k4GVVMvO8Cl+IGQ8cBnI8cidUDJrGyStfZZYFnYbQe+GDEcKb10\n8pfacolkS9pj9omoUWzaPHyLrgbgEyo1kHJTMitD+W+gK3x/knNubMxgpKQOCFslsyLZknYJeDZq\nFJsQytT+B19q0AAcHjciqXVKZmUol+LbrIAvNTgxYixSIs65BmAGvlPFG5HDEZHi7B22C6JGMTiV\nGkjFKJmVQVlrFwKvhV2VGtSO6WE7L4yiiEgGhAvRtMzgqZixDOEJNiw1UL4hZaMXlwzHhRSWtz0x\ntIWRbEs7GTwSNQoRKdYOQDOwzFq7OnYwmxIuki/GTyJuRKUGUkZKZmU4Luv3fQ9wUqxApGTSTgaP\nRY1CRIqVLnSShVr3S/BzLsahUgMpIyWzMiRr7RLgxbDbDnw5XjRSIoeGbTXfphSR99svbO+PGsXw\nzAXW4Edmcyo1kHLRC0uG6wIKpQYfds61xQxGRi0d3Xk6ahQiUqz0dv3cqFEMw0ZKDT4YNyKpVUpm\nZbgu7/d9N3ByrEBkdJxzzcB2wGpr7crY8YhIUdJ693lRoxi+S/ADIeOAz0SORWqUklkZFmvtK8Ci\nsKtSg2xLVw/KyoehiADOuYnAJPyAwotxoxm2x4EO/MjsJ1VqIOWgF5UU4wL8SQngKOfchJjByIil\nk78ejhqFiBQr7S/7vLW2b9Ajq8RGSg0OixuR1CIls1KMPP5kBL6rwWkRY5GRS+tlq77mTkQ2kCaz\nWWup17/UQF0NpOSUzMqwWWtfp7B8YhvwlxHDkZFLOxlkobWPiBSk7905UaMo3mNAJ34w5CyVGkip\n6QUlxfo9hVKDQ51zm8UMRkYkHd15LmoUIlKsg8I2U/XuA0oNmigk5SIloWRWinUlG5YanB4xFimS\nc248sAXwhrV23VDHi0h1cM41AjuF3Sz2h1ZXAykbJbNSFGvtm8CTYVelBtmzZ9hmamRHRNgZP6r5\nhrV2bexgRuBRCqUG6mogJaUXk4zE74H0ZHqgc27LmMFIUdIelQ9FjUJEipVO3MzkhWgoNbgE6AXG\nAIfEjUhqiZJZGYmr8CME4GugzogYixTngLB9ctCjRKTapMvYPhA1itG5BD8624pKDaSElMxK0ay1\nb+MbYQOMB74SMRwpTjqBJIs1dyL1LF0K9omoUYzOI/i6WZUaSEnphSQj9XtgTfh+H+fc1jGDkWFL\nb1UujhqFiBQra8vYvs+AUoMW4OC4EUmtUDIrI3U10By+7wU+HjEWGQbn3CR8rdoL1tre2PGIyPA4\n57bAdyFZB7wcOZzR6l9qoAUUpCSUzMqIWGtXUGjcPQ6VGmRBOrKjlb9EsiXtDb0gjG5m2cNAFyo1\nkBLSi0hGo3+pwZ7Oua1iBiNDSpPZrK0eJFLv0vKgzL93QzJ+KSo1kBJSMiujcT3+tjVAN3BSxFhk\naJr8JZJNh4Xtw1GjKJ2LUVcDKSElszJiodRgfthtAz4VMRwZWtqWa/6gR4lItUnfu5md/DXAHDYs\nNTCR45GMUzIro5UuUQhwtHOuJWYwsnGhLm2PsPt6zFhEZPicc03AjmH36ZixlEooNbgMX2owFpUa\nyCgpmZXRuhZIJyR0Ax+KGIts2q5h+2gNTCARqSe74j+rX7PWdsYOpoQuBjrwpQafjhyLZJySWRkV\na+1C4J2w2wacGTEc2bR05OPOqFGISLEyvYztIOYAPfhSg0+r1EBGQ8mslMIV+NtFDcAZOilVpSPC\n9sGoUYhIsdJ62fujRlFi1to+Niw1OGDwnxDZNCWzUgpX4W8Xgb9lNHOQYyWOo8K2VmZDi9SLtJNB\nlpex3ZTLgbX4Fl2nRY5FMkzJrJTCgxReS83ARyPGIgM458YAuwGd1trXYscjIkXZM2xrrcwA4AGg\nCf+5kYsci2SYklkZNWvteuDmsDsGteiqNunqQQ9FjUJEihKWoJ6IH72suS4k4bMjrePf3jk3OWY8\nkl1KZqVULgdWh+93cs5tHTMY2UA6+ev2qFGISLFqaRnbTbkcv5JkDzArciySUUpmpVRuxtc9AawH\nTo4Yi2zo6LDN/FKYInUm7WRQy3dVZuPLDNqAsyLHIhmlZFZKwlq7ksIEhfGob2A1OTxsH40ahYgU\nK+3bXbMTN621bwEvhN2jnXPNMeORbFIyK6V0CX69bYAjnHNjYwYj4JxrB6YAy6y178aOR0SKcmjY\n1vLILPj2jt34u3qHD3GsyPsomZVSuhZIe8x2A8dEjEW8muxRKVLrwryDrfEDBM9HDqfcrsV/ZoxD\n3XBkBJTMSslYa5cAy8JuO1oNrBocErZ3xQxCRIqWjsrOreHJX6m5+FHZRuDjkWORDFIyK6WWx5+U\nDPBRrQYW3YfDtmZr7kRqVLpq361Ro6iAkKzfGHYnOee2jxeNZJGSWSm1qynUzY6lMBtX4qjl1YNE\natmxYVsvJUJXAquAPtQNR4qkZFZKrX/7p2bg9FiB1Dvn3Db4co8XrLXrYscjIsPjnGui0GO2Xu6q\n3IYfABkHfDJyLJIxSmalpKy1vcBNYXcMOinFdFDY3hs1ChEp1kz8Mq+vhLaHNc9au5rCkr0HO+fG\nxYxHskXJrJRD/9XAtnfOTYkZTB1LJ5DcEzUKESlW+t69L2oUlXcZsC58qRuODJuSWSmHW/CjsqDV\nwGJKPwweiRqFiBQrnbh5R9QoKu96fM1sO/CxyLFIhiiZlZKz1q4BHg+7Wg0sgtBFIp389WzMWESk\naOnCAbW+WMJAC/F39dQNR4qiZFbK5WKgI3x/mHOuNWYwdWjHsH0i1DGLSAY457bEr9rXBTwTOZyK\nCi26rsaPzo4F9owbkWSFklkpl+spvL66KLSZkco4OGzvihmEiBQtfe8+aa3tixpJHFcDa/AT4FSi\nJsOiZFbKwlr7ErA07LYDn4gYTj1KG64/EDUKESlW3SyWsAl34+dctKBuODJMSmalnC6nsBrYac45\nvd4q56iwrZcelSK14riwrZfFEjZgre2icBG+h3Nu85jxSDYouZByuhrfYgX8LaP9I8ZSN5xzzfg+\nlT3Ay5HDEZFhChf86aqJcwY7tsZdDqzFl6idEDkWyQAls1JOjwLp5KMWtBpYpaSTJh4KEypEJBt2\nx58rl1prl8cOJqIb8QMg7cCZkWORDFAyK2UTJi/cEHabUf1TpaQrf9Vbj0qRrEsXS6jrWndr7avA\na2H3RJWoyVD0ApFyuwJYFb6f5pybFDOYOvGhsK23HpUiWZcudHJ71Ciqw5X4ORdQuEAX2SglszIi\nxphZxpgFxphFxph/2sjftxhjLnfO/ey3v/1t+4oVK8DXPx1jjPlO+LkFxpgTw/HTjDF3GmOeNcY8\nbYz5m36Pta8x5iFjzBPGmEeNMQcPfD7ZQDob+tGoUYhIsY4M2wejRlEmw/3cMMYs+sEPfnDKihUr\n1uH7zZ42gs+NLYwxtxpjFoatJpLVMCWzUjRjTCPwX8BHgD2ATxlj9hhw2JeBFX19fTseeOCBr912\n220A7S+99NJn8eUGewKzgF+Fx1sPfDNJkt3xt9r+ut9j/ghwSZLsC/xb2JeNcM6NB6YD71hr344d\nj4gMj3NuIrAd/lw4P3I4JVfM50aSJDv39PR899Zbbx0LNL/xxhsj+dz4J+D2JEl2wY90vy95ltqh\nZFZG4mBgUZIki5Mk6QYuAz464JiPAhcB7L333v+7ePFikiRhyZIlxwCXJUnSlSTJEmARcHCSJEuT\nJHkcIEmS1fglWD8QHisBJoTvJwKvl/OXy7j9wraua+5EMii94zTfWrt+0COzqajPjb6+viteeOGF\nviRJeP7556e0tbXdUOTnxnuPFbaagFzDlMzKSHwAeKXf/qsUTiDvO6apqWl2S0tLX0dHB2vWrBm7\nzTbbrBvsZ40x2+OTsrQ1zd8CPzbGvAL8BPhOiX6PWnRY2N4ZNQoRKdYHw/a2qFGUT1GfG0mSrE+S\n5N2Ojo41q1atSnbbbbetBvvZjXxuTE6SZGl4rKXA1iX6PaQKKZmVkTAb+bOBLaD6H/OQ8QCSqVOn\nDlxv+72fNca0AX8C/jZJknTi2DnA3yVJMg34O+CC0QRf49LlH++NGoWIFCtdLOG+qFGUT7GfG/T0\n9HQYY8YYY5onTZp06IBjh/rckDqiZFZG4lVgWr/9qbz/1v97x5x77rm9HR0dva2trUycOLG5qanp\niI39rDGmGX9CujhJkqv6HfN5IN2/gsLtOOnHOddIoZPB3JixiMjwOecMhUVlarULSVGfG8aYpiRJ\n2ltbWxdMmDCB7u7u3Z1zYwb+7CCfG28aY7YNx2wLLCv5byRVQ8msjMQjwC7GmB2MMWPwhfnXDjjm\nWnwSCnDm5ptv/owxpmu33XZj8eLFu0ydOnWsMWYHYBfg4TBsewHwbJIkPxvwWK9TSNI+DCwsxy9V\nA/YK2wdqtOZOpFbtAowD3rLWvhk7mDIp+nMDuMMYk99111175s+f37B69eoPF/G50f+xPg/8uQy/\nk1QJJbNStCRJ1gNfB27GF9znkyR52hjz78aY08JhFwBbGmMWAX+/zz77/AvQvfXWW7PHHnusf+ON\nNxYCs4G/TpKkFzgc+Avgw6EF1xPGmJPCY30F+KkxZh7wfeDsiv2yERTTvsYYMyfUigF86N577+W8\n886b0b99TfiZC40xy4wx8wc81idCS5s+Y8yBZf3FROrACN+/hwLcdNNNbw9sPxV+ZlPv3x8bY54z\nxjxpjLnaGLNZmX+9ERvJ5wa+A8F1kydP7po5c6b59a9/fRnD/9z4IXC8MWYhcHzYlxplkkSrXUr5\nhRVcVgHj8f1m/9Va++O4UVWf0G7mefzJ91X8aMankiR5pt8xXwP2TpLkq8aYTwJnJEly1tlnn/3g\ntddee+inP/3pD/385z9/BT+RZNckSXqNMUcBa4A/Jkkys99j7Q70AecD30qSRL1pRUZopO/fc889\nt2PZsmVfuOiii15fu3btjsAUhvf+PQG4I0mS9caY8wCSJPnHCv26FRE+O1YCbcCz1tqB7bxENDIr\nlRGWtr0n7LagNimbUlT7GvwqOcfmcrmGxYsXHzJz5kwmTpz4YP/2NQBJktwDvDPwyZIkeTZJkgXl\n+mVE6syI3r9Jkhy1YMEC2tvbrx7YfgoGff/eEkY8wdfaTi39rxRX+OxIWw3u7JxrjxmPVCcls1JJ\n1wBrw/cHOOdaYgZTpYpuXwOsNMYcvmrVKtPS0vKCtbZnkJ8VkfIZyft3VUdHx46rVq1Kli9f/sgQ\nPzuYLwE3FR9yJlwLdIavI4c4VuqQklmppNsovOa6CHVisoGi29cATJo06TCAlStXPjHEz4pI+RT9\n/m1qamoxxtDd3b2ip6end4if3fiTGvMv+NWwLh52pNlyJ74cqg04IXIsUoWUzErFWGsX4+u+wM/c\n1Unp/YpuXwNM3GqrrY6ZMGECS5YsWT7Ez4pI+Yzk/btZa2srDQ0Nzw3jZ9/HGPN54BTgM0ntToJ5\nFp/MNgAnDXGs1CEls1Jpt4RtE++vJZORt685drfdduP1118/LMyWfq99TcUiF5Gi37/Tp0/vNMYw\nbdq0y4FPFvP+NcbMAv4ROC1Jko6S/iZVxFqbUFgIZrpzrmq7NkgcSmal0q4DVofvd3HOTYgZTLUZ\nSfuaY4455ndA89Zbb/04cDnwDBu2r8EYcynwILCbMeZVY8yXw5+fYYx5Fb8M7g3GmJsr99uK1JYR\nvH+/efLJJ08E2H///f8HyFPE+xf4JdAO3BraUv2mMr9pFNcBHcA6VDcrAzTFDkDqzh34bgbgT0of\nwp+kJEiS5EbgxgF/9m/9vl8HfCLdd859NXx7Y5Ik3wO+t5HH/NQmnutq4OoShC0iFPf+dc4dgR9x\nXGitXWGtLfb9u3MJQ692d4ZtG3Ai+tyQfjQyKxVlrX0LeC3stqP6p1I4OWzviBqFiBQrnTdwQ9Qo\nsuF5oBuft3wkcixSZZTMSgzX4Yv5DYVETEYgrOl+bNit1TXdRWpVWnqg8p4hhLrZu8PuVOfcFjHj\nkeqiZFZimE2hq8Ek59y2MYPJuJ2BVuApa21n7GBEZHicc+OAvcPufTFjyZDr8b3K0xI1EUDJrMRx\nLz4BA98b8dhBjpXBpSd03aYUyZbD8Xen5ltr1wx1sABwF/7frB21dpR+lMxKxYUTd7pWeRuFW21S\nvLTmWPWyItmSJmMDW3fJpr2AH5U1qG5W+lEyK7H8GUiXXT021H5KEcK/2XFh94HBjhWRqnNK2N4y\n6FHynlA3e1fY3dY5NyliOFJFlMxKLDfj19kGGAvsGjGWrNoef7vtGWvt2sixiMgwOecmAjOAXjRx\ns1jX4+dcqG5W3qNkVmJ5BBgTvu8/wijDl57Ib4oahYgU66iwfcxa2xU1kuy5E2gEJgCzIsciVULJ\nrERhre0B5oTdVuD0iOFkVVozdnvUKESkWGkSpnrZIllrX6TQDefEiKFIFVEyKzFdQ6HU4HDnXGPM\nYDLo+LC9P2oUIlKsdOLmbVGjyK50NbBJzrnJUSORqqBkVmK6Fb94AvgWXQdEjCVTnHPTgM3xy2Cu\nih2PiAyPc25rfL17N/BY3Ggy6wb86Gw3cHTcUKQaKJmVmJ7BJ7EALRRGGmVoqpcVyaajw/Yha+36\nwQ6UTboTaMJPgFWLLlEyK/GENivp7aIxqG62GGnNnW5TimRLWmLw56hRZJi19hVgZdjVIIgomZXo\nrsMvTwiwl3OuKWYwGZI2XL83ahQiUqz0vauJm6OTXshv6ZybEjUSiU7JrMTWf/JSN7BPrECywjm3\nLTAJWGytfTd2PCIyPKHWfVv8BfxTkcPJuhuB1ahuVlAyK/E93+/7ZuCDsQLJkLRednbUKESkWMeE\n7b3W2r5Bj5Sh3IUvT2unULohdUrJrEQV6mYfDbtjUd/A4Uj/jW6NGoWIFCtdwlb9ZUfJWvs6sDzs\natGdOqdkVqrBzfhbRQCHxQwkI9JkVvWyIhnhnDPAsWH3jpix1JD0gn5iKOGQOqVkVqrB/fh1tgHG\n6aS0ac65qfiau5estcuHOl5EqsZOwBbACjYsr5KRuwlfN7ueQgmH1CEls1INHsEvaQvQg+pmB5OO\nyl4VNQoRKdaHw/bOUF4lo3cXvm62DdXN1jUlsxKdtbYTeCHstqOZqYP5RNiq5k4kW04L2+uiRlFD\nrLVvAsvC7ocHO1Zqm5JZqRa3A+lohU5KG+Gca6YwMvtAzFhEZPiccw0UupDcOdixUrRb8J8dbc65\n7eOGIrEomZVqcRe+9glgB+fc+IixVKtDw/Y2a233oEeKSDXZE38r/E1r7Uuxg6kxs/GfHX2obrZu\nKZmVavEA0BK+7wQOihhLtTo1bK+IGoWIFCvtYqB2eqV3N76t43gK/85SZ5TMSlUIPQNXhd1W4MiI\n4VSrM8NWiyWIZEtaL3tD1ChqkLX2LSBdCfGImLFIPEpmpZqkdaDNFNYvF8A5tw2wA/C6tfbl2PGI\nyPA455oodGhRvWx5zAnbKc65tqiRSBRKZqWa3IIvMQDYP0yaEG9W2F4ZNQoRKdZ++BKql8Pseym9\n2/G9yjuBAyPHIhEoWZBq8gC++TX4Yv4ZEWOpNmmJgVpyiWRLutTqTVGjqG1z8KtItlKYKCt1RMms\nVJP5+AbYAAYtngC8d5vy5LB7X8xYRKRoHw9bJbPl8wQ+kW2mcPEgdUTJrFQNa+164MmwOx6dlFIH\nh+1d1tquqJGIyLA55zYDDsD3Qb09cjg1y1q7DlgSdg+IGYvEoWRWqs0tQG/4/qiYgVSRdFQ2HzUK\nESlWOpH1IWvtmqiR1L67w3asc25q1Eik4pTMSrW5F0hP+ls657aKGUyVSJewVUsukWzJhe0lUaOo\nD/fgPzt6gEMixyIVpmRWqs1D+Non8LNT67pu1jm3NbALfuWgJUMdLyLVwTnXSKELifrLlt8c/FyL\nNtRvtu4omZWqYq1dCSwNu20U1jOvV+ltyqujRiEixToEX/v/si5EK2IRPpk1aFnbuqNkVqpR2li8\nAU0CS1tyXRM1ChEp1ulhq97QFWCtTYB5YXdG6AIjdULJrFSjOyjUzc5wzo0Z7OBaFW5Tnhp27x7s\nWBGpOmmtu+6qVM7t+AnEPcCekWORClIyK9XoAQqvzXX4FXTq0QH4f4f7Q+sZEckA59x0YHv8ilQP\nxY2mrjwArMWfNzUJrI4omZVqtJjCSmAt1G8xf9qS6/KoUYhIsdL37s2hf7ZUxsPAWGAcqputK0pm\npeqE2qeHw24LhUlQ9Sa9TamVg0Sy5VNhq97QFWStXQ68E3YPjxmLVJaSWalWNwPpaleHOOdMzGAq\nzTm3JbA7sNxauyh2PCIyPM658RRaCt4cM5Y6NSdst3HOTYgaiVSMklmpVvdTSGbH4OvP6snxYXtV\n1ChEpFjH4j9bn7DWvjPUwVJyt+PnWnQCB0aORSpEyaxUq8fxtU/g62frbfGEj4etWnKJZEtaHnRp\n1Cjq1xx8N4NW4NDIsUiFKJmVqmSt7QKeD7vt+NGOuuCcawA+GnbvihiKiBQhlEOdEnavixlLHZuH\nHwhpRn3K64aSWalmtwNJ+L6eivn3xZ+IH7LWdsQORkSGbV9gM+BN4LnIsdSlMBDyQtjdv97mW9Qr\nJbNSzeZQWDxhhzpa0W9UgAYAACAASURBVCVt63NF1ChEpFjpHZWrQ1cWieOusG0BpkWMQypEyaxU\ns8fx62yDL+ifETGWSkpr7m6MGoWIFOussNXEzbjuxQ+E9KDFE+qCklmpZgvxt9vBJ7X7R4ylIpxz\nmwF7ASuBBZHDEZFhcs5Nxl9w9wD3RA6n3s3B5zdt1O+iO3VFyaxULWttH5D2WG2jPq6w05Zcuk0p\nki0nhe2doW5T4lkM9OEHQbQSWB1QMivV7sF+39dDe660xODqqFGISLE+GbaXRY1C0lUknwi7uznn\nmgc7XrJPyaxUu4eAteH73ULbqpoUTrhpMntbzFhEZPiccy0URgBV614dbsf3KO8CZkaORcqsZhMD\nqRmP428XgW/TtUPEWMrtQ2F7s1pyiWTKUfj6/uestW/GDkYAf1evA2iiPkrU6pqSWal2T7PhSmD7\nRYyl3D4TthdFjUJEipWu2Hd51Cikv4fxq4C1orrZmqdkVqqatbYbeCXstlOja2075xqBT4fdG2LG\nIiLDF5rynxF2/xwzFimw1q4A3g679TDfoq4pmZUseCRsDXBkzEDK6DBgDHCvtXZV7GBEZNhmAFsD\n71KYdCTVIZ1APNk5NzFqJFJWSmYlC+7HL5oAsGfMQMoonQn9h5hBiEjRTgvba9VOr+rcAXSGr4Mi\nxyJlpGRWsuBxoDt8P9Y5t23MYEot3Kb8i7B7bcxYRKRo6YXolVGjkI15GL+IRSt1sOhOPVMyK1kw\nD38yAt9mpdYmge0PTAAes9a+PdTBIlIdnHNbAPviO67cHjkceb+ngXH4ThOHRo5FykjJrFQ9a+0a\nCoX846i9K+xc2P4hZhAiUrQTw/Z+tdOrPuH/5K2wu2/MWKS8lMxKVjwetk3U3iSwz4etVv0SyZaz\nwvbSqFHIYOaH7TStBFa7lMxKVtxHoW62ZsoMnHN7AJOBZ621r8WOR0SGxzk3BpgVdtVOr3o9CPTi\nJ4HtGjkWKRMls5IVj+FPRgCbOec2ixlMCaXL1/4hZhAiUrTjgRb8ql8vxw5GNukJCkui7xUzECkf\nJbOSFXMpTALrpHbqn9ISgz9FjUJEivWFsL0wZhAypKeARqCNGrqrJxtSMiuZEGb5rwm7LdTASck5\ntyOwA/CStfaF2PGIyPA451qAU8NuPmYsMqTF+G4GBr84jdQgJbOSJU+FbQtwRMxASuRjYfuHmEGI\nSNFOwJ+HnrHWvhQ7GNk0a20fsCTs7h4zFikfJbOSJffiC/kBDowZSIl8IWyviBmEiBTti2F7QdQo\nZLjSbjgTtaxtbVIyK1nyKIVC/inOudbBDq5mzrkp+KV5lwHPRA5HRIbJOTcWODns6kI0G+bgF9zp\nAGZGjkXKQMmsZMlcfO0T+JNSlmemnhG2f9R67iKZMgsYA8y31r4SOxgZlieBdfj/t70jxyJloGRW\nsuQV/LKR4BdPyPIksC+E7eUxgxCRoqUlBr+PGoUU4yl8N5xW4KDIsUgZKJmVzAgjmM+G3XHAByOG\nM2LOuS3xNb+r8P1zRSQDQmnTR8LulTFjkeEL3XDSPuW1MN9CBlAyK1lzP5Delj80ZiCjcFrYXqwS\nA5FM+Qi+1GmeVuzLnOfCdmfnnIkaiZScklnJmjkU+s3u4JxrihnMCKULJWg9d5FsUReD7JoTtgkw\nLWYgUnpKZiVr5uKbX4Mv6J8RMZaiOecmAB8CuoEHIocjIsPknBuHn/wFKjHIosfwAyHr0SSwmqNk\nVrJmIX5GKvikNmuTwE4K20uttb2DHiki1eQk/MTTudbapbGDkaI9hZ9APA4lszVHyaxkSkgAF4Xd\nNrI3M/VzYXtJ1ChEpFhfCluVGGTTs/hEtgkta1tzlMxKFj3e7/v9o0VRpAEzoe+KGIqIFME5Nx6/\nhC3An2LGIiNjrV0HvBF294kZi5SeklnJosfxq7kA7BIzkCKlH4ZXWmu7o0YiIsU4GWgEHrPWvjHU\nwVK1ngrbbZ1zYwY9UjJFyaxk0XP4yV8AW2RoWdvPhu3/Ro1CRIqVlhhooYRsexA/AayTjE0elsEp\nmZUseo4Nl7Wt+tHZMApwZti9JWYsIjJ8zrk24Liwe1XMWGTU5gFr8ZOHNQmshiiZlSx6mUIya8jG\nFfaxYTvbWts56JEiUk1OwZcYPGKtXRY7GBmVp/CfHePJ0HwLGZqSWcmc0NHg1bA7HtgjYjjD9Vdh\n+9uoUYhIsVRiUDtewl+YGLK7gqRshJJZyapnw7YBOCBmIENxzrUDHw27N8aMRUSGL7x307sqV8eM\nRUbPWtsHvBB2s3BHT4ZJyaxk1WP4BthQ/SOzp4ftH621XYMeKSLV5FT85+RD1tq3YgcjJfFo2I53\nzm0RNRIpGSWzklXP4JcmBJjmnKvm1/LXwla3KUWy5cthq/du7XgY382gE9grcixSItWcAIgM5tl+\n3/cA02IFMhjn3Lb42qyVwP2RwxGRYXLOTQSOCbvXxIxFSuopoBtoQclszVAyK1m1EL80IfhkdveI\nsQzmM2H7m1CvJSLZcBp+otD91trlsYORknkKaAXGAodEjkVKRMmsZJK1tgNYEXbHUr3F/OeE7UVR\noxCRYqVdDC6IGoWUlLV2BYUStaqePCzDp2RWsmxh2LYA+8YMZGOcc/9/e/ceZ1dZ3X/888x9JjcC\nCYFcICGQEC4hAQIGIiD8oIi1RZEjKMYCAvVlKVqLyo+f3Xn8tSpCFQoKFGmhaFuOBilFgoCIIihC\nk0BISMIECBCSQAI4SeaWmdn9Y+3DTEImmcveZ5995vt+vc5rz5mc7L1m5lzWfvZ61nM4cBDQGATB\nC3t6vIiUBu/9XsAp0V2VGJSfwvvxQSU+30L6SH9EybLFPb4+KrUoendhtP1+qlGISH8VWuk9Ho3k\nSXl5CgiBTuCAlGORGCiZlSxbhi1nCzA1zUB2Fp3tFxZK+I80YxGRfit0MVCJQXlajn12bAcOTjkW\niYGSWcmyldibEUBtifUM/CAwHJs8sjHtYESkb7z3o7HXL8B/pRmLJKYR6ABqUDJbFpTMSpatxCZ/\ngfUMnJ5iLDu7NNrenGoUItJf50Xbx4IgeDfVSCQpjVgiW0/pdsKRflAyK1n2FnZ2DVBFiXQ08N7X\nAZ+K7mryiEi2/FW0vSnVKCRJ64HK6Gv1mi0DSmYls4IgCIFXorvDKJ03pT+NtguDINiWaiQi0mfe\n+xnY8tjNwP0phyMJiT471kd3VWZQBpTMStYt6/H10alFsaO/jLb/nGoUItJfl0TbHwVB0JZqJJK0\nxmi7n9pzZZ/+gJJ1i7GlCaEEama99/sApwFtwKMphyMifeS9r6J7oYRb04xFiuK5aNsBjE8zEBk8\nJbOSdS9gk78Axnrva9MMBvhktL0tCIKO3T5SRErJ6cAorHRpSbqhSBGsxMpJ2lGpQeYpmZWsW0l3\nIX8z6b8pFZav/ZdUoxCR/vpCtL0pqqmU8taItXasJv3PDRkkJbOSda/Q3Z4rJMWOBt77qcARwBvA\n0rTiEJH+iXpUnxXdvSvNWKRoGrFEtoES6YQjA6dkVjItupRfmJXaQLo9Az8bbX+gkR2RTDkfcMCj\nQRC8mXYwUhSvY71mAWamGYgMnpJZKQcrom0VKXU08N47ursYaGRHJFsKvWVvTDUKKZogCLqADdFd\nlRlknJJZKQf/g5UYQHq9ZucAY4ElQRC8mlIMItJP3vvDscvM24AHUg5HimtNtJ0QDUhIRimZlXKw\nAtgafT0ppTelz0XbH6RwbBEZuMLS03cFQdC+20dKuXk+2nYB49IMRAZHyayUg5V0j8x2AROKeXDv\nfTVwcXT3p8U8togMXNRb9i+iu+otO/SswFo7tqFSg0xTMivlYBU2+QusZ2CxZ6aegb2WFgVB8G6R\njy0iA3cmMBJYEwSBOpAMPY3YZ0YlMDXlWGQQlMxK5gVBsBVoiu7WUPyVwC6LthrZEcmW93rLphqF\npKURmzg8DJiWciwyCEpmpVwUJl3VA4cU66De+5HAR7Eyh0XFOq6IDE609PSZ0d0fpxmLpOZVoBZr\ny3ZUyrHIICiZlXKxusfXhxfxuB+Ptndo8ohIpnw62j4cBMFbqUYiqYj6lG+K7mpkNsOUzEq5WI5N\n/gI4qIjHLSxf+8MiHlNEBq/QW1YlBkPby9F2otpzZZeSWSkXa7A+kQDji/Gm5L0/EDgOeBv4XdLH\nE5F4eO9nYuVIW1F50FBXaM9VAeydZiAycEpmpVy8TPfIbAUwugjHvCTa3qDla0UypdBb9o4gCLan\nGomkbTnQGt3UniujlMxKuXiJ7nW2W0m41MB7XwlcEd29PcljiUh8or7Qn43u3pZmLFISGrE+sxUo\nmc0sJbNSLjZiLVYKpiR8vNOB4cCvgyBYl/CxRCQ+H8Zeuy8GQfBc2sFI6hqxPrNqz5VhSmalLESX\n+TdGdxtIfhLYX0fb6xM+jojEqzDx68ZUo5BS8QrW0rECmJluKDJQSmalnBRmpVaRYHsu7/2+2OhO\nO/DzpI4jIvHy3o/FrqoA/HuasUhpCIKgDXgnulvsBXckJkpmpZys6PF1km9KhXq7mzR5RCRTCr1l\nfxEEweZUI5FSUhgImZRqFDJgSmalnKzECvkBDkziAFHLr7+J7t6SxDFEJDHqLSu7UhgIqfXe75Vq\nJDIgSmalnLxEdzI7Juo4ELcTgP2AJUEQvJjA/kUkAd77WcBUoAl4MOVwpLQsw8rGWrDniGSMklkp\nJy9ja2yDJbUTEzhGYWTnewnsW0SSc1m0vSNaxlSkoBFLZEHtuTJJyayUk5exWakA24GD4lwJzHs/\nEjgvurswrv2KSLK89zXAZ6K7/5xmLFKSGrF8aBi2MpxkjJJZKQve+zrgQrpHZmuBh4C7YzzM+dH2\n9iAImmPcr4gk6yNYorIyCILlaQcjJeclbCCkEjgy5VhkAJTMSrmoA76NvRkV7ncAj8d4jMLErx/E\nuE8RSV6hL7Qmfsn7BEHQAmyJ7qo9VwZV7fkhIqUvCIJ3vfd/hTVCHxZ92zHIkVnv/YFACOyFrQ7z\nUhAEiwezTxEpHu/9AcApQCfqLSu92wCMBvZPOxDpP43MSjm5A3gGG5EFeDoIgjcHuc9vYCvEPBzd\n18QvkWz5y2j7kyAI3tntI2UoWxtt9/beKzfKGP3BpGxES9pegHUyaAVujmG3b2IjvPtG+/yG9/7r\nMexXRBLmva8GvhDd1Ymo7E6h1WIHMDbNQKT/VGYgZSVYvmDdnQd+9u8d4YKPr7unldyCc7D6WYcl\no61YC5bXgEbyYdcedrke6z9Y02M/JyT2A4hInP4MGInNVn865ViktBX6lLdhK4FtTDcc6Q8ls5Jd\nOVeBNbg+GjgO+CBw2Py1d7oQ2irgX7Dks9DhIIxuYM/9KnJuFfAE8HtgMbCSfNizB+VbdCezzcBP\ngYsT/blEJC5XRtvrois3Ir15DUtkHZbMPpNuONIfSmYlW3KuFvgYcAUwG7sk1IVN+qqAHbPXPpiJ\ntWL5DJbo1kUJ7k3Av3P4gk1Yh4Rm4DpggT4URUqf9/4Q4HjsZFQTv2RPXsM+A2qxZFYyRMmsZEPO\nTcVq3z4XfWdEtK2NYe8OGN7j/hFY4vq9L636x0f+44BP1Wyo3/9zQRDcEcOxRKQ4Cqv1/TgIgi27\nfaQIvE53OdmUlGORflIyK6Ur56qBPwe+DByFjZDWFOnowwFGdGz58KUv3dru4CvkFlQAd5MPtxUp\nBhEZgGgRlcKJ7/VpxiKZsZHuz5dpaQYi/aduBlKacu4s4A2s7vUD2OosxUpk3+OgytmxZwA3ABvI\nuYvJudiWyRWR2H0CaACWBUHwXNrBSOkLgqATKLRuOzDNWKT/lMxKacm5MeTcQuAnwBi6ywlKwfDo\ndgPwBDmnS1Eipakw8evaVKOQrFkfbbVwQsYomZXSkHOOnDsPWIOto96QckS7MwyYAzxPzn2RnKvc\n038QkeLw3h+JTexswbqPiPRVYeGEUd57va9niJJZSV/OTQAeAn6I9YSMY1JX0qqwhPvvgcXk3IyU\n4xERc0W0vT0IgpZUI5GsWR1t29HobKYomZV0WW3sKuBkbMQza4Zh3Q/+h5z7yz09WESS470fjrXZ\nA2uvJ9IfL2ML67Sj9lyZom4Gkp6cmw/cgk2wyrIK7Gf4R3Juf2AB+VC9aEWKxHtfWOlvL2yi6NNB\nEKxKNyrJoNewRLYCS2Z/l2440lcamZV05NyVwM1kP5HtqQFrI/bP0epkIlIcFwL/Svdo7O0pxiLZ\n9Vq01cIJGaMPXCm+nPs7YAGlPclroIYB5wP/poRWpGg2AtXR123A9d77u1KMRzLGe38acDmWyNYA\n/+C9b/beT083MukLfdhKceXcl4CvUp6JbMEw4Gxs5HlIcs6d6Zxb5ZxrdM59bRf/Xuucuzv696ec\nc5N7/NtV0fdXOef+JPpenXPuD865Z51zy51zvsfjT3XOLXbOPe+cu9M5p/KpoWdjj69rsWVJf59S\nLP0S92sl+v4rzrllzrmlzrlnenz/3Oj10+WcOzbpny1jTsLqrQsTkGuxkoM1qUUkfaY3fSmenPsI\n8A+UV2lBb4YBF5Bzz5MPb0w7mGJyzlUC3wdOx5aIfNo5d18Yhit6POxi4J0wDA92zp0HXAN80jl3\nGHAecDgwHnjEOTcNG207NQzDrc65auC3zrlFwB+AO4HTwjBc7Zz7BvBZdJk5m3JuHDAbmAXsi/V1\nrgK2AU3ASmAxsIp82NHjf24GtmOjs83AJ4MguL+IkQ9IEq+VMAw7o//3oTAMN+10yOeBjwO3JvdT\nZda3gIuAidH97cC/BkHQ0ft/kVLhQs1TkWLIuSOxYvosdiwYjBbgbPLhQ2kHUizOubnAgjAMC6Oq\nVwGEYfitHo/5RfSY30UjqRuAscDXqqurq6+++upbgOHf/va375o1a9adZ5555lossalvamqqvPnm\nm4MTTzzxlgMOOGDdXXfdde3VV1/9WaBj0aJFhy1btuzTX/nKV67APow6+nDbHgRBWzF+N7KTnNsb\nmI9dyZiJXbFpjbbVOz06xJLaEJvstQb4DfDDbxz2d0eGruJWLOE9PQiCxcX5AQanr6+VffbZ5zuX\nX375a62trROuvfba/7r66qu/ft99951TU1Mz+qyzznoHqLj99tsPP+WUU16fOnVq83XXXTfrsssu\ne2HEiBGd2DLgYFdiHVBx2223TT799NNfmjx58hqsTvQN4E3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mplt.plot_flux(tpt2_coarse, cgpos, arrow_label_format=\"%1.4f\", show_committor=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the same as percentages:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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ls1K5bcO4JGoUIvJ+dun/V8CvwmKx7YF9gQOwNnvZZj3tWKLbHb4WA/cAD2FX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\nZiVdgXsvVlQ/HOpk+1KHHbQ+A9ySbShbixPVcbw9UX0nsD8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Fpercent = 100.0 * tpt2_coarse.net_flux / tpt2_coarse.total_flux\n", "mplt.plot_flux(tpt2_coarse, pos=cgpos, flux_scale=100.0/tpt2_coarse.total_flux, arrow_label_format=\"%3.1f\", show_committor=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can treat this ReactiveFlux like the microstate reactive flux. For example, we can decompose it into pathways:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Path flux\t\t%path\t%of total\tpath\n", "0.00282258751971 \t 39.7 %\t 39.7 %\t\t [0 4 2 5]\n", "0.00201898833783 \t 28.4 %\t 68.2 %\t\t [0 3 1 5]\n", "0.00120685936301 \t 17.0 %\t 85.2 %\t\t [0 3 1 2 5]\n", "0.00105400896725 \t 14.8 %\t 100.0 %\t\t [0 3 4 2 5]\n" ] } ], "source": [ "(paths,pathfluxes) = tpt2_coarse.pathways()\n", "cumflux = 0\n", "print(\"Path flux\\t\\t%path\\t%of total\\tpath\")\n", "for i in range(len(paths)):\n", " cumflux += pathfluxes[i]\n", " print(pathfluxes[i],'\\t','%3.1f'%(100.0*pathfluxes[i]/tpt2_coarse.total_flux),'%\\t','%3.1f'%(100.0*cumflux/tpt2_coarse.total_flux),'%\\t\\t',paths[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Literature\n", "----------\n", "\n", " [1] W. E and E. Vanden-Eijnden.\n", " Towards a theory of transition paths. \n", " J. Stat. Phys. 123: 503-523 (2006)\n", " \n", " [2] P. Metzner, C. Schuette and E. Vanden-Eijnden.\n", " Transition Path Theory for Markov Jump Processes. \n", " Multiscale Model Simul 7: 1192-1219 (2009)\n", " \n", " [3] F. Noe, Ch. Schuette, E. Vanden-Eijnden, L. Reich and T. Weikl: \n", " Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations. \n", " Proc. Natl. Acad. Sci. USA, 106, 19011-19016 (2009)\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }