{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Utils: Compute and plot free energy surface and free energy differences\n", "\n", "Authors: Ioannis Galdadas & Luigi Bonati & Enrico Trizio" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/luigibonati/mlcolvar/blob/main/docs/notebooks/tutorials/utils_fes.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the following example we show how to use the function `compute_fes` from `mlcolvar.utils.fes` to calculate and visualize the free energy surface." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Colab setup\n", "import os\n", "\n", "if os.getenv(\"COLAB_RELEASE_TAG\"):\n", " import subprocess\n", " subprocess.run('wget https://raw.githubusercontent.com/luigibonati/mlcolvar/main/colab_setup.sh', shell=True)\n", " cmd = subprocess.run('bash colab_setup.sh TUTORIAL', shell=True, stdout=subprocess.PIPE)\n", " print(cmd.stdout.decode('utf-8'))\n", "\n", "\n", "from mlcolvar.utils.plot import paletteFessa\n", "from mlcolvar.io import load_dataframe\n", "from mlcolvar.utils.fes import compute_fes, compute_deltaG\n", "import matplotlib.pyplot as plt\n", "from matplotlib import patches\n", "import numpy as np\n", "\n", "# Load COLVAR file containing collective variables (and bias information)\n", "colvar = load_dataframe('https://raw.githubusercontent.com/EnricoTrizio/TargetedDiscriminantAnalysisCVs/refs/heads/main/alanine/deepTDA_enhanced_sampling/colvar')\n", "\n", "\n", "# In general, you should use the simulations parameters, for example:\n", "temperature = 300 \n", "kb = 0.0083144621 # Boltzmann constant in kJ/(mol·K)\n", "kbt = kb * temperature " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate statistical weights in case of a biased simulation (uncomment one of the options)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# (1) unbiased simulation\n", "#bias = None\n", "\n", "# (2) reweight for a single bias\n", "bias = colvar['opes.bias'].values\n", "\n", "# (3) reweight multiple bias potentials (e.g. OPES and harmonic walls)\n", "#bias = colvar[['opes.bias','lwall.bias','uwall.bias']].sum(axis=1).values\n", "\n", "# (4) reweight all field *.bias in the COLVAR\n", "#bias = colvar.filter(regex='.bias').sum(axis=1).values\n", "\n", "# calculate the weights\n", "weights = np.exp( bias / kbt )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate and plot 1d free energy surface. For the full list of options see the documentation. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cv_name = 'phi'\n", "cv1d = colvar[cv_name].values\n", "\n", "fes_params = {\n", " 'blocks': 3, # Number of blocks for error analysis\n", " 'bandwidth': 0.01, # Kernel bandwidth (sigma) for density estimation. if 'range', the bandwidth is expressed as ratio of the range of values (e.g. here it is 1% of it)\n", " 'scale_by': 'range', # Method to scale the bandwidth\n", " 'temp' : temperature, # temperature for proper energy scaling (alternative to kbt)\n", " 'units': 'kJ/mol', # units of the free energy\n", " 'weights': weights, # Statistical weights from the bias \n", "}\n", "\n", "fig, ax = plt.subplots(figsize=(6,3))\n", "fes1D, grid1D, bounds1D, error1D = compute_fes(\n", " cv1d,\n", " plot=True,\n", " ax = ax,\n", " **fes_params\n", ")\n", "\n", "# make a nice plot\n", "ax.set_xlabel(f'CV: {cv_name}')\n", "ax.set_xlim(-np.pi, 1.9)\n", "ax.set_ylim(0, 50)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2D free energy surface" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/etrizio@iit.local/Bin/dev/mlcolvar/mlcolvar/utils/fes.py:235: RuntimeWarning: invalid value encountered in log\n", " * np.log(kde.evaluate(cartesian(pos)) + e)\n", "/home/etrizio@iit.local/Bin/dev/mlcolvar/mlcolvar/utils/fes.py:235: RuntimeWarning: invalid value encountered in log\n", " * np.log(kde.evaluate(cartesian(pos)) + e)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Adjusting regularization (eps) to 1.0e-14 to avoid NaNs.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cv2d = colvar[['phi', 'psi']].values\n", "\n", "# or equivalently\n", "# cv1 = colvar['phi'].values.squeeze() \n", "# cv2 = colvar['psi'].values.squeeze()\n", "# cv2d = np.stack((cv1, cv2)).transpose()\n", "\n", "fes_params = {\n", " 'blocks': 1, # Number of blocks for error analysis\n", " 'bandwidth': 0.015, # Kernel bandwidth (sigma) for density estimation\n", " 'scale_by': 'range', # Method to scale the bandwidth. \n", " 'temp': temperature, # temperature for proper energy scaling (alternative to kbt)\n", " 'units': 'kJ/mol', # units of the free energy\n", " 'weights': weights, # Statistical weights from the bias\n", "}\n", "\n", "fig, ax = plt.subplots(figsize=(6,5))\n", "fes2, grid2, bounds2, error2 = compute_fes(\n", " cv2d,\n", " plot=True,\n", " plot_max_fes=55,\n", " ax=ax,\n", " **fes_params\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Free energy difference: deltaG" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# set bounds to identify states\n", "stateA_bounds = [-3.0, -0.4]\n", "stateB_bounds = [0.3, 1.8]\n", "\n", "fig, axs = plt.subplots(2, 1, figsize=(6, 4))\n", "\n", "# plot fes for reference and check states bounds\n", "ax = axs[0]\n", "ax.plot(grid1D, fes1D, color='fessa6')\n", "\n", "# highlight states over FES\n", "for b, (xmin, xmax) in enumerate([stateA_bounds, stateB_bounds]):\n", " rect = patches.Rectangle((xmin, 0), xmax - xmin, 50 - 0, fill=True, color=f'fessa{b*6}', alpha=0.3)\n", " ax.add_patch(rect)\n", "\n", "# add labels\n", "ax.set_xlabel(f'CV: {cv_name}')\n", "ax.set_ylabel(f'FES [{fes_params[\"units\"]}]')\n", "ax.set_xlim(-np.pi, 1.9)\n", "ax.set_ylim(0, 50)\n", "\n", "\n", "# plot and compute deltaG\n", "ax = axs[1]\n", "intervals_1D, deltaG_1D = compute_deltaG(X=cv1d,\n", " stateA_bounds=stateA_bounds,\n", " stateB_bounds=stateB_bounds,\n", " temp=temperature,\n", " units='kJ/mol',\n", " intervals=100,\n", " weights=weights,\n", " time=colvar['time'].values,\n", " plot=True,\n", " ax=ax,\n", " )\n", "ax.set_ylim(5, 18)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Adjusting regularization (eps) to 1.0e-14 to avoid NaNs.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/etrizio@iit.local/Bin/dev/mlcolvar/mlcolvar/utils/fes.py:235: RuntimeWarning: invalid value encountered in log\n", " * np.log(kde.evaluate(cartesian(pos)) + e)\n", "/home/etrizio@iit.local/Bin/dev/mlcolvar/mlcolvar/utils/fes.py:235: RuntimeWarning: invalid value encountered in log\n", " * np.log(kde.evaluate(cartesian(pos)) + e)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# set 2D bounds to identify states\n", "stateA_bounds = [[-3.0, -0.4], [0, 3.1]]\n", "stateB_bounds = [[0.3, 1.8], [-2, 0.5]]\n", "\n", "\n", "fig, axs = plt.subplots(2, 1, figsize=(6,7), gridspec_kw={'height_ratios': [3,1]})\n", "ax = axs[0]\n", "# plot 2D FES\n", "fes2, grid2, bounds2, error2 = compute_fes(\n", " cv2d,\n", " plot=True,\n", " plot_max_fes=55,\n", " ax=ax,\n", " **fes_params\n", ")\n", "\n", "# highlight states on FES\n", "for b, ((xmin, xmax), (ymin, ymax)) in enumerate([stateA_bounds, stateB_bounds]):\n", " rect = patches.Rectangle((xmin, ymin), xmax - xmin, ymax - ymin, fill=True, color=f'fessa{b*6}', alpha=0.4)\n", " ax.add_patch(rect)\n", "\n", "# compute deltaG on 2D data\n", "ax = axs[1]\n", "intervals_2D, deltaG_2D = compute_deltaG(X=cv2d,\n", " stateA_bounds=stateA_bounds,\n", " stateB_bounds=stateB_bounds,\n", " temp=temperature,\n", " units='kJ/mol',\n", " intervals=100,\n", " weights=weights,\n", " time=colvar['time'].values,\n", " plot=True,\n", " ax=ax\n", " )\n", "ax.set_ylim(5, 18)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare 1D vs 2D" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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f4eHhQWJiIomJiY5XI3h5eTFx4kRmzpzJpk2b2LNnD/fddx+RkZFOk8AjIiJYu3YtUJI5zpgxgxdffJGvvvqKgwcPMm7cOEJCQhg5cmRNXOYlaf9ImrDbajYQIYQQQpRSq27PLVq0CKDUe6KWLl3KhAkTAHjzzTfRarWMGjWKoqIihgwZwjvvvONUPjo62vHkHcCsWbPIy8tj8uTJZGZm0rt3b9avX4/ZbK7S6ykvu6sHsRYXcrQuNR2KEEIIIf6mVq/TVFtkZ2fj5eVFVlZWlc41+nTdTv71+moG92nD+/MmVFk7Qgghrn12u53i4uKaDqPGGQwGdDrdJY+X5zu+Vo00Xe8MhpIfqsUqc5qEEEJUXHFxMbGxsdjt9poOpVbw9vYmKCjoqtdalKSpFjHoS5Imq1X+kgshhKgYpRQJCQnodDpCQ0OvuGDjtUwpRX5+PsnJyQBOT9FXhCRNtYhnQjTvBUaRmZ4ATK7pcIQQQtRBVquV/Px8QkJCcHV1relwapyLS8k84eTkZAICAi57q+5KJGmqRfTKRoihELs178qFhRBCiIuw2UqewDYajTUcSe1xIXm0WCxXlTRdv2N2tZDeWLLkgE7JkgNCCCGujrwr9U+V1ReSNNUiuj/+VaBVMqdJCCGEqG0kaapFdH8sbqmVkSYhhBCi1pGkqRbR//G+O52MNAkhhLgObd26lREjRhASEoJGo2HdunVOx/v3749Go0Gj0WAymahfvz4jRoxgzZo11RKfJE21iN5UcntOhyRNQgghrj95eXm0b9+et99++5JlJk2aREJCAjExMaxevZpWrVpx1113MXly1T91Lk/P1SI6syuJVhPZmtr1ehchhBCiOgwbNoxhw4ZdtoyrqytBQUEANGjQgB49ehAREcH999/PnXfeyaBBg6osPkmaahFj/Ybcl9gRb09Xbq3pYIQQQlwTlFIUFNbM61RczMZqeYpv/PjxPP7446xZs0aSpuuF3rEiuEwEF0IIUTkKCotpdeO/aqTtIxtewtXFVOXtaLVamjdvzunTp6u2nSqtXZTLhdeoFEvSJIQQQpSLUqrKR7VkpKkW0RXlsSDgIDpUTYcihBDiGuFiNnJkw0s11nZ1sNlsnDhxgq5du1ZpO5I01SIGvZbmxpJXqFgtFvQGQw1HJIQQoq7TaDTVcousJn300UdkZGQwatSoKm1HkqZaxGD+8y91cWGxJE1CCCGuK7m5uZw8edLxOTY2lqioKHx8fAgLCwMgPz+fxMRErFYr8fHxrF27ljfffJMpU6YwYMCAKo1PkqZaxGD6c6kBS1EheLjVYDRCCCFE9dq9e7dT4jNz5kyg5Om4ZcuWAbB48WIWL16M0WjE19eXzp07s3LlSm677bYqj0+SplrE+Jd7v5YaejxUCCGEqCn9+/dHqUvP6928eXP1BXMRterpuSstn35h6fS/b6+99tol63zuuedKlY+IiKjiK6kYnd6A7Y+/K5aiwpoNRgghhBBOalXSdKXl0xMSEpy2Dz/8EI1Gc8WJX61bt3Y6b9u2bVURfqWwUfK4pKWoqIYjEUIIIcRf1arbc1daPv3CsukXfPnllwwYMIDGjRtftl69Xl/q3Noqw25Cp+wYLbJWkxBCCFGb1KqRpvJISkri22+/ZeLEiVcse+LECUJCQmjcuDH33HMPcXFx1RBhxcws6MW9iZ2we/rWdChCCCGE+ItaNdJUHh999BEeHh7cfvvtly3XvXt3li1bRosWLUhISGDu3Ln06dOHQ4cO4eHhcdFzioqKKPrL7bHs7OxKjf1y9DpZFVwIIYSojeps0vThhx9yzz33YDabL1vur7f72rVrR/fu3WnYsCGff/75JUep5s2bx9y5cys13rIyGEqSJovcnhNCCCFqlTp5e+6XX34hOjqaBx54oNznent707x5c6fFs/5u9uzZZGVlObazZ89eTbjlMll/gP/4H8J+7lS1tSmEEEKIK6uTSdOSJUvo3Lkz7du3L/e5ubm5xMTEEBwcfMkyJpMJT09Pp626hJFFK1Mu1rycamtTCCGEEFdWq5Km3NxcoqKiiIqKAv5cPv2vE7ezs7NZtWrVJUeZBg4cyMKFCx2fn3jiCbZs2cLp06fZsWMHt912GzqdjrFjx1bptVSUTVNye85WLItbCiGEELVJrZrTVJbl01esWIFS6pJJT0xMDKmpqY7P8fHxjB07lrS0NPz9/enduze//vor/v7+VXchV8Gu0YICW7GlpkMRQgghxF/UqqTpSsunA0yePJnJkydf8vjp06edPq9YsaIyQqs29gsjTRZJmoQQQlw/5s2bx5o1azh27BguLi707NmTV155hRYtWjjKNGrUiDNnzgBgNpsJDAykW7duPPTQQ9xwww1VHmOtuj0nQGlLkia7RW7PCSGEuH5s2bKFqVOn8uuvv7JhwwYsFguDBw8mLy/Pqdzzzz9PQkIC0dHR/O9//8Pb25tBgwbx0ksvVXmMtWqkSYBdW5LHykiTEEKI68n69eudPi9btoyAgAD27NlD3759Hfs9PDwcb/kICwujb9++BAcHM2fOHO644w6nkanKJiNNtYxVayTXrsNuv/xtSiGEEKI87IUFl96Kiyq97NXKysoCwMfH54plp0+fjlKKL7/88qrbvRwZaaplvg8ZzPotB3kxtPzLKQghhBCXEj3hxksec+sYSdhTrzk+H39wBKqo8KJlXVt2oOGzfz6lfvKR0dhyMkuVa7liW4VjtdvtzJgxg169etGmTZsrlvfx8SEgIKDUvObKJklTLaPXy4rgQgghrm9Tp07l0KFDbNtW9sRLKYVGo6nCqCRpqnWMfyRNVnn3nBBCiErUYtmGSx/UOs/Waf7e12Uu2/StVVcTVinTpk3jm2++YevWrTRo0KBM56SlpZGSkkJ4eHilxvJ3kjTVMu0yDtDZ7yimM/WB/jUdjhBCiGuE1uxS42UvRynFI488wtq1a9m8eXO5EqAFCxag1WoZOXJkpcRyKZI01TL1LJk0N2dxMif1yoWFEEKIa8TUqVP57LPP+PLLL/Hw8CAxMREALy8vXFz+TMxycnJITEzEYrEQGxvLJ598wgcffMC8efNo2rRplcYoT8/VNrqSPFbZrDUciBBCCFF9Fi1aRFZWFv379yc4ONixrVy50qncnDlzCA4OpmnTptx7771kZWWxceNGnnrqqSqPUUaaahmN9o+kySpJkxBCiOvHld4IAqXf+lHdZKSpttH/kcfKSJMQQghRq0jSVMtodJI0CSGEELWRJE21jMYx0iRLDgghhBC1iSRNtYxGr8eqNNjt9poORQghhBB/IUlTLZMUMYAR57qzKbBfTYcihBBCiL+QpKmWMZkMABQUFddwJEIIIeqysjyNdr2orLs35Vpy4Kuvvip3AzfeeKPTolTi8kICvQE4l5hRs4EIIYSokwwGAxqNhpSUFPz9/av8fWy1mVKK4uJiUlJS0Gq1GI3Gq6qvXElTeZcn12g0nDhxgsaNG5frvOtZA08dT/scxzf7GEo9dl3/ZRdCCFF+Op2OBg0aEB8fX+PrGtUWrq6uhIWFodVe3Q22ci9umZiYSEBAQJnKenh4lDug6139BkH0c00HID0xGd/gwBqOSAghRF3j7u5Os2bNsFgsNR1KjdPpdOj1+koZhChXyjV+/Phy3Wr7xz/+gaenZ5nLb926lREjRhASEoJGo2HdunVOxydMmIBGo3Hahg4desV63377bRo1aoTZbKZ79+789ttvZY6purl6eZKlSoYP449E13A0Qggh6iqdTofZbL7utwu3KytDuZKmpUuXlmv0aNGiRfj5+ZW5fF5eHu3bt+ftt9++ZJmhQ4eSkJDg2JYvX37ZOleuXMnMmTN59tln2bt3L+3bt2fIkCEkJyeXOa7qlm0o6eO0UzE1HIkQQgghLqhV754bNmwYw4YNu2wZk8lEUFBQmet84403mDRpEvfddx8A7777Lt9++y0ffvghTz/99FXFW1WK3HwhK428c3E1HYoQQggh/lCupGnmzJllLvvGG2+UO5iy2Lx5MwEBAdSrV48bbriBF198EV9f34uWLS4uZs+ePcyePduxT6vVMmjQIHbu3HnJNoqKiigqKnJ8zs7OrrwLKAOtbwBkHceaklit7QohhBDi0sqVNO3bt69M5arqia+hQ4dy++23Ex4eTkxMDP/85z8ZNmwYO3fuRKfTlSqfmpqKzWYjMNB5MnVgYCDHjh27ZDvz5s1j7ty5lR5/WbkEh8Ip0Oek1lgMQgghhHBWrqRp06ZNVRVHmdx1112OP7dt25Z27drRpEkTNm/ezMCBAyutndmzZzuNqmVnZxMaGlpp9V9JvfBwLNs0FBXKApdCCCFEbXFVc5oyMzNZsmQJR48eBaB169bcf//9eHl5VUpwV9K4cWP8/Pw4efLkRZMmPz8/dDodSUlJTvuTkpIuOy/KZDJhMpkqPd6yCukeSeT8bqDVcovFitFQq6aeCSGEENelCq/ytHv3bpo0acKbb75Jeno66enpvPHGGzRp0oS9e/dWZoyXFB8fT1paGsHBwRc9bjQa6dy5Mxs3bnTss9vtbNy4kcjIyGqJsSIC/LwxmY3Y7YrzSZk1HY4QQgghuIqk6bHHHuOWW27h9OnTrFmzhjVr1hAbG8vNN9/MjBkzKlRnbm4uUVFRREVFARAbG0tUVBRxcXHk5uby5JNP8uuvv3L69Gk2btzIrbfeStOmTRkyZIijjoEDB7Jw4ULH55kzZ7J48WI++ugjjh49ypQpU8jLy3M8TVcbaTQawkJKJrefOZdWw9EIIYQQAq7i9tzu3btZvHgxev2fVej1embNmkWXLl0qXOeAAQMcny/MKxo/fjyLFi3iwIEDfPTRR2RmZhISEsLgwYN54YUXnG6lxcTEkJr65wTqMWPGkJKSwpw5c0hMTKRDhw6sX7++1OTw2maUazz+AUfJ+fVn6N6ipsMRQgghrnsVTpo8PT2Ji4sjIiLCaf/Zs2cr/PqU/v37X/atzD/88MMV67jYe3amTZvGtGnTKhRTTQkxWWhizONYfGxNhyKEEEIIruL23JgxY5g4cSIrV67k7NmznD17lhUrVvDAAw8wduzYyozxumQICCn5Q0btXblcCCGEuJ5UeKTp9ddfR6PRMG7cOKxWKwAGg4EpU6Ywf/78SgvweuXRIAwOgjk/vaZDEUIIIQRXkTQZjUYWLFjAvHnziIkpeUdakyZNcHV1rbTgrmf+TZpgBbysuSilqmzBUCGEEEKUzVUvAOTq6krbtm0rIxbxFyGtIogD6mmLyUhNx8f/4q+KEUIIIUT1uKqkqbCwkAMHDpCcnIzdbnc6dsstt1xVYNc7Nx8f8pQeN42Vs4ej8enf87LlC4ss7Nx7ki7twvFwM1dTlEIIIcT1o8JJ0/r16xk3bpzT4/0XaDQabDbbVQUmIF3vRVZRLrbzl39x77bfj/PCfz7HOzWWs+Zgpk26mTE3d0Onq/A8fyGEEEL8TYW/VR955BFGjx5NQkICdrvdaZOEqXKsjxjDxMSOnLBe/LU0aRm5PPXch3w3Zw4v2Dcw1vMcSZn5/PO1Lxh+/5ts332imiMWQgghrl0VHmlKSkpi5syZtX6RyLosrL4fAHHnS68K/vVXWzm49D1GG+Jx8ypJUruMG8+/i+vz36UbOBFzjnEzFjG4f3vefOZuzCZDtcYuhBBCXGsqPNJ0xx13sHnz5koMRfzdhVep/D1pOnrwON4fP8ttpjO4aW3YA0Kp/+hc6t9yJ/fd2ZctK2fzWjd4PeAI+375neVf/VoT4QshhBDXlAqPNC1cuJDRo0fzyy+/0LZtWwwG55GMRx999KqDu9410ufxpv8hSDwOTHHs3/vJx3TSWcjSuRHxyGy8uvVFo/0z//XQWmmddRS7MZe3Ag/y3GfujL2lh4w2CSGEEFehwknT8uXL+fHHHzGbzWzevNlpHSGNRiNJUyUIru+PiymXQruWomILJqOBwiILHjF7QA/afiPx7tG/1Hk6d08az19K3OuzcT9zgsHWaFZ+s4vxo3pX/0UIIYQQ14gK357717/+xdy5c8nKyuL06dPExsY6tlOnTlVmjNetwKZNsCswa+2cjzkDwHebDvBUUgs+sreh49i7L3muwT+IkElPAjDQNYU1n35DUbG1WuIWQgghrkUVTpqKi4sZM2YMWq081l5VtAYjWRoXAM4fiwZg+Ve/UqB01L/pDgweF3+q7gKXpq1w7RCJTgODLcf4/NvfqjxmIYQQ4lpV4Yxn/PjxrFy5sjJjEReRaypJjDLPnObEqQR+P3AKrVbD6OFdy3R+4JhJAPR3TWXdx1/JaJMQQghRQRWe02Sz2Xj11Vf54YcfaNeuXamJ4G+88cZVByfA6ukHKYkUJsSz68MlvB1wkKMh3Qjyv/wo0wXm8Oa4du5D/O7fsGelsvr73dx9a48qjloIIYS49lQ4aTp48CAdO3YE4NChQ07H5OWylUfvHwwph7CmJuKRnURjYz5+zX3KVUf9SU/yc4Mo9r39Hckfb+SOm7pgNFz1aweFEEKI60q5vznnzJnDrbfeyqZNm6oiHvE3bqGNSDhgojgthXbmbGxKQ/u7/1GuOvTePoy9vQ9vL/+Fc4kZrP1hD2Nu7l5FEQshhBDXpnLPaYqPj2fYsGE0aNCAKVOmsH79eoqLi6siNgEE9B/C/YkdibOUvIQ3JaA5Zr+ActdjNhl4aGxfBrim8O3yryo7TCGEEOKaV+6k6cMPPyQxMZHly5fj4eHB9OnT8fPzY9SoUfzvf/8jPT29KuK8bjUI9sGAnYGuJS9GDh95Z4XrGlJ4gFk+MfTLPcDp+NIvWhZCCCHEpVXo6TmtVkufPn149dVXiY6OZteuXXTv3p333nuPkJAQ+vbty+uvv865c+fKVe/WrVsZMWIEISEhaDQa1q1b5zhmsVh46qmnaNu2LW5uboSEhDBu3DjOnz9/2Tqfe+45NBqN0xYREVGRy64RLmYjg/0L8dJZydG60LD/wArXFXDjLQB0M2eyZcu+ygpRCCGEuC5UyiJLLVu2ZNasWWzfvp24uDjGjx/PL7/8wvLly8tVT15eHu3bt+ftt98udSw/P5+9e/fyzDPPsHfvXtasWUN0dDS33HLLFett3bo1CQkJjm3btm3liqumTTIfBUDfsDkaXcUncJsahJPv7odeo4j/ZXPlBCeEEEJcJyr9EaqAgAAmTpzIxIkTy33usGHDGDZs2EWPeXl5sWHDBqd9CxcupFu3bsTFxREWFnbJevV6PUFBQeWOp7bw+8cjZG77kXZPvXDVdbl3jMT+y9d4nj9Kbn4h7q7mSohQCCGEuPaVO2m6/fbbr1zpH0nKjTfeyIgRIyoUWFlkZWWh0Wjw9va+bLkTJ04QEhKC2WwmMjKSefPmXTbJKioqoqioyPE5Ozu7skKukAbDb6fB8Cv3e1nU7zuQs798TWdTBtt+i2Zo//aVUq8QQghxrSv37TkvL68rbi4uLpw4cYIxY8YwZ86cqoibwsJCnnrqKcaOHYunp+cly3Xv3p1ly5axfv16Fi1aRGxsLH369CEnJ+eS58ybN8/pekJDQ6viEmqEW8v2WHRG6uksHNy4pabDEUIIIeoMjVJKVVXl33zzDQ8//DBxcXHlPlej0bB27VpGjhxZ6pjFYmHUqFHEx8ezefPmyyZNf5eZmUnDhg154403LnkL8WIjTaGhoWRlZZWrrdoqas4MTMd381lxC55f/UGlLUa6/KtfiT6ViL+PB/6+HgT4ehLk70XThgHo9bpKaUMIIYSoTNnZ2Xh5eZXpO77Cc5qWL1/O2LFjL3rsySef5LXXXqN379506dKlok1clMVi4c477+TMmTP8/PPP5U5ivL29ad68OSdPnrxkGZPJhMlkutpQa60m9z3CLQ8tJDZPx5jj52jTosFV1/nBii28uPBrALqb0wnUFZNt15Nt15PhVZ+RI3ox5ubuZX79ixBCCFHbVPjpuSlTpvD999+X2v/YY4/xySefACUJypo1ayoe3d9cSJhOnDjBTz/9hK+vb7nryM3NJSYmhuDg4EqLq67xCG9Cs04lc5k27jhy1fV9+eNeR8J0640dmdDYypR6p3nK9yQv+R/jP/pN2Fa/y7i7ZvPgP5exY++lE1YhhBCitqpw0vTpp58yduxYp8f3H3nkET7//PMKv2IlNzeXqKgooqKiAIiNjSUqKoq4uDgsFgt33HEHu3fv5tNPP8Vms5GYmEhiYqLTiuQDBw5k4cKFjs9PPPEEW7Zs4fTp0+zYsYPbbrsNnU53yVGy68UNPVsC8POOo1dVzy+/H2fFfxbR0pjDfaP78N85d9Pt1pvw6N4f19ad0PsF4aK1M8w9mQX+Bxh8dAX/eHQRG7dffbImhBBCVKcK354bPnw477zzDrfccgsbNmxgyZIlfPnll2zatInmzZtXqM7du3czYMAAx+eZM2cCMH78eJ577jm++qrk9R8dOnRwOm/Tpk30798fgJiYGFJT/1ztOj4+nrFjx5KWloa/vz+9e/fm119/xd/fv0IxXiv6NNDzjG80hUknSc24H796HuWu4+CxeF575i3mekWj12lofNOjaDQafIffBcNLyiilKDi2n4wN68jetRm9jz/2FA0Llv7IDT1bysudhRBC1BlXtU7T3XffTWZmJr169cLf358tW7bQtGnTCtfXv39/LjcvvSxz1k+fPu30ecWKFRWO51rm4+VGT5cMCuxatmw/xKibIwHIzS/kP4t/IC0jl7mPjaSel9tFzz8dn8qsWf/HMx6HMGvtuLTthmt4i1LlNBoNri074NqyA4HZGfgmpWF+aAkHjsWzY89JenVpVqXXKYQQQlSWciVNF0Z+/s7f359OnTrxzjvvOPa98cYbVxeZqFLmRs0pNLrjUpzLiZ83wc2R7D10hsde+Ay3lNN4aS3ccTye/70xmfpB9ZzO3RUVwxP/XsIzpr3U01kwhDYh9LEX0egv/9dJ71mPAM963DWiO599sZXlS7+kV5cnqvIyhRBCiEpTrqRp376Lv6+sadOmZGdnO47LLZfaT6PVom/VBaI2Yzi1nzeX/MDC/21kqPk80wJOA/BNdhajHipk2X8mE9GkZOL8iq938X9vfsa/6x0h1FCItp4/DWf/B52La5nbntDVh8Hb95GccJj9R0bTvlXDqrhEIYQQolKVK2mq6ARvUTuFDRjE+ajNdNCnMnHpj4AGr6590CSkofJzudk9CZ+C3dwztZC3XrqfH385zHdrN/LfgEPU01nQefvS8J//weDjV652G7RtS45eUU+Xx5rFn9L+zX9WzQUKIYQQlajS3z0n6g73dt2woyVEX0RzD8XUx+7h1sGdsGbfSf7R/Zx7ay49XTLw0e5jymMLybIb0GCkqH4zTCYLobNeweAbUO529Z71MPS4EbXze8Jjt3PyTDJNG5a/HiGEEKI6lWvJgQMHDmC328tc/vDhw1it1nIHJaqHzsUVY/O2ACy6uwW3Du4ElCQ1nt370/CZBWjdPIgw5fIv3+MEuigWvTSBfq++RaO5b1coYbqgyd0TsaGhozmLLxbLZH0hhBC1X7mSpo4dO5KWllbm8pGRkRV6hYqoPsGjxmFq2BS/Ro1KHXNt0Y5Gz7+L3i+I8JbNWP7BLIb2a4vWaEJrLvscposx+Aeh2vYGwO/gT5xPyryq+oQQQoiqVq7bc0opnnnmGVxdy/aF+ddFJ0Xt5N6+O+7tu1/yuKl+Q8JffI+UVUvw0eVXatvNx03i1JO/EGlOZ8Wytcx86r5KrV8IIYSoTOVKmvr27Ut0dHSZy0dGRuLi4lLuoETtovf2JXjSrEqv1xTamKImHTDFRBG/5Wf2Dr+BTm3kSTpxfbiw7tylnjYuLLKQk1dIcbEVf18PjAaZgipETdOosqwYeZ0rzxuQRfkUxscy9821LN91Hj8fD75aPJ2QQO+aDkuIS7LZ7CSnZXM+KZNzSRmcT8okOS2b7NwCcnILyckrJC8nH7PZiL+/N4F+ngT6euLl6cL5pExOx6dyOj6V2LOpmAsyCTJZQW8EvR6N3gBWC5rCPEx2CweKPClQOjQaDY38XQkJ8iEwOAAPdzO5+UXk5hWSl1dIcWEB4Y1CGNCzFb26NMPDzVzT3VRjrFYbSanZJCRnUlBkoV1EKF4e1fOP92KLlZS0HJLTsklOyyE1PQe7Uhj0upLNoMPNxUT7VqEVeguDqBrl+Y6XpKkMJGmqWnn5RYyaspBjMQm0ahbCF+9MxdXFVNNhieucUoqUtByOxiRwLOY8x2ISiDkZj+X8GXzJx19XTICuiAB9EQszwsmwGwEY6xHPOK94LEpDhs1Aus1Iut1Arl2Pv66IV9KbkWU3AHC3Rzz3esVfMoaHk9oSrzyxWG2MdE/gQe8zZNr05CsdZo0ds8aGWWNHq4GX0pqxrcAXvU5L1/bh9OrcDD8fDzzczHi4m/FwM6PRaMgvLKagoJi8giKKiq0E+nkSHupPSIA3Ol3JNFebzc6puGQOHT/H0ZPncXUx0a1DYzq1bojZZKj6zv8bpRRpmbmcPZ/O2YSSLS0jl7w/EsecvCJycgtITs0iITUbu13RyJBHR1M20RYPDA2b06NLc3p0bEKn1g3x8rz0FBOlFOmZeSQkZ3IuKZOE5JItLTOXrJwCsnIKyMvOxZabg91mBasFZbWB3YrRVsTxYncsf0wXHuSaTHtTNsVK69jylY7oYncswU3o0rkFPTo2Iay+L9l/1J2dU0B27oWtkNz8QnJyC8kvKMZmt2Oz2bHblePPVpsdq9WGxWrDbleYTQY83My4uZpwdzPj7eFCg2AfwkJ8CAvxJTTEt9qSyLpCkqZKJklT1YtPTGfKpJe5S3eU3yNu4Y2XJ6HVVvh90kKUS2Z2PqfjU4k5k8zRk+c5euI8R0+dJz2zZB7fYNdk7vA4T4i+EN1F7qb90uFerPWb4eFuJix2BwG/rbtkW/si78enQ1caNfDDdd8GCjZ/jd1SXPLla7GgMRjRurqhc/Mg5KGncWnYlNSMXBI/Xoh+57cXrVOh4csuD7NhTxynzqZwq3sCPcwZZNoN5Nl15CsdeXY9CjBr7PwvuwFQciGdTJkE6otIVq5o/EPQu7hiPxdDmMrGQ2tlaXaYo53G5iJCmzaiTcdWdO/YmM5tGuHmWvofODabnbjzaSgFvt5ueHq4lGvR48SULPYdPvPHFsfhE+fILyimsSGPAa6pBOiK8NJacdNacdPacNXYcNPamJ/elO0Fvhj0Om4KKOAh7V4ACuxaDhV7cKDQi6PF7hR4BBDcKJRm4YGEhfiSmpHDmfhUzpxNpiDhHF7WHAL0RfjrivHXFbEoM5wCpQPgAa8zjPJIuGTsD6V0wuIVgL+vB7dqTxKZdfFFoS1Kw1MprThaXDLi1N2cTjNjHh5aK+4aG25aK+5aG65aK24aG5MSO1D8RzL2kNdpBrslowE0GoX2j5+mBkWR0vJwUjuSbCWjjb1d0uhgyiLBaibRZiLRasZaL4gunVsQ2akJPTs1KzW6b7PZSc/KI+58GvF/JKrxiRm4uZpoEhZA4zB/mjQMwK+e+zWxmLUkTZVMkqaqp5Ti8GP3oks8zcEiD84Nm8Zjk4fXdFiiligqtpKWkUtqRg4Wqw2/eu741nPHzcVUrl/axRYrR0+eZ++hM+w/epbYuGSyzp/HozCTEH0hoYYCGhvyaGzIZ05qBCdtHjRq4McdfpkMSP6lpBI3T8zBoRj9gzD4BaL3D8KjSx8MPiUvAbcX5mO3WFBFhVgzUrFmpmHJSMWem43eNxD39t3Qe/tWqB9seTlYUhKxFxWgNbuiNbugNbui0evRuZV8+Z45l0ri/MfwTIm9ZD3PuN+G3sUVo0HPoISNdFUXH+2yomV1l0dIzy1mV1QMj2t20taUwxmLCweLPDli8cLSoDmtO7chOMCb6JgEjpw8z9nYePrpzwOQZdeTixFcPdB4+hDcJJw2EaG0bVGfVs3qo9dpORR9riRBOnKG2MPH8c09T0tjLi2NOXyUHcqBIi80Gg3DAgp4xBB1yeuyDrmXwBFj8fNxx5IYT/Kn75B3dD8qP6dU2edSm7Or0AeAke4JDHdLIkhfhF5T+itxffsJGBuE4+XhQvjxTfjs/b7kgE7v2DQ6HVqzK6EzX8Slccl7OAtjj5N3aDf24mKUpQhlKcaamU7u4X3YstJZ3elhth2MJy0jl2lux+jOpUcdj9/5Anh4o9NqCNi2Ao+j2y5ZNm7cfLKUkdy8IkJ2raLhub1Oxy1Kw7Fid/YXefJ1bhAe/v7odDqsBfnYC/PRFBfhrbMQrC8kSFdU8l99Ef9OjaDoj+QxSFeI3s2NJi2b0rVdOJ3bNqJDqzBczMZS8RQWWUjNyCEtI5e0jFyKLTZ6dGyC92VG/KqTJE2VTJKm6lEUH8uJ2ZPQWQr5PjeAsIef5o6butV0WKIa2O12zpxL41RcCqfPpRJ3Lo0z59I4m5BOZlomQcWpuGuteGqtaCj5Is6yGyjQmdF51iMkNJg2LRrQ9o+tQXA9ElOyORWXzKm4FE6dTeHgsbMcPh5PYbENgH4uqUyvdwoX7cXXnrOOeICmo+7GxWzEkpZMUXws5oZNK5zwVKei+FgKTh7Fnp+LLT8Xe34etvxcQKE1uxJw14NozSW3aNK/+5zcA7+Tfy4Oe1oiGrsNfAJxb9YKl8Yt8BlyO1qzK3abjRNP3Y89PqZUe/EWM+tyg/g2LwgAd42VVfV3XzS2LJuen/P9eD+rEQABBgv9zMm0MObSwpCHn975qevkDkMJGfMAYfX90KQnkvHjWgx+gei8fdC5uKF1dS8ZmXNxQ+/tUzIv7C+U3U7R2RjyD+8j7/BeCk6fwJaWRPQtT3MkQ3E2IZ2+BUfpcO6PJMRgxBBYvyQp9g3E4BuAV7+bHG8+sOXngbKjdXFDU8HRcKUU1rRkDH6Bjn2ZW7+n4MRhdO6e6Nw80Ll6oHVzR+daco3mhk0d12bNysBekA9aLRqtBjTakg1QxYUYAoLRaEuSm9z9v5F/bD+W5PNYkhMoSozHnpMJgB24O7ErWdaSsvP8jtDBnH3RmIsMrnzVdSqn4lKIOZPMZMsOupgzSbCaOFzkwZFiD6KtXth9grDZ7BRYFRaLlWKLFT9rNvV0xXhprXhrLeg1iv0Wb+q3a8dNA9ozuE8bfOu5V6gvK4MkTZVMkqbqk7tvJ3GvzEKDYllWKF0emcnom7rWdFiiEtjt9pK5J3klE6bjEzPYfySOA0fOkHY8mvrWNBoYCgjWFfFboTcb8ksWTw3WFfJhcNQl6/0hz5//ZjT545Mi0pxBknLBV1NIsL6Q+vqS/zY15PNuZkMOGMLo2DqMgYFWOu/+BLRa9H5BmIIbYAwOw9ywKaZGzTDVb4TWeH3NrVM2K/bi4su+S9KanUn+sf3kH40i68BubOdOo0FxxhzCwcj7aNk0mFbN6mNe/yGqsABLVgbFWRlYszMhNxON3U6UR0veSmvI+eRMGhnyWBR48M8YNBqMDRrj1qItLs1b49aqIwa/oEq9TnthPhqj2ZH0FCedw5KahDGoAfp6fhVOhuoCpRSWpHPkHdqDJfk8Lrfex9GT59HrdLh88SZE70FjckHn7oExsD7GwPoYAkIwN2yKe8dIRz2xzz5MQfRBNJROIU4Wu/JIcjvH54+D9pZKhqEk2d6U78eKvFBaNg0hJNCbkABvggO8CQn0plmjQJo2CsSg11VNZ/yhSpOm1atX88ILLxAVFQXA008/TfPmzWnfvj1t2rTBZLr2fslI0lS9Ur9ZQconCwH4JLs+rSfP4O6RkVc4S9QG55My+W7TfmLOJJOamUt6Ri4FmSVfmFn5FpKsJb8f9Ni5xzOeCGMuzY15uGptTvWcCWpPxg33EhbiS4CrFrXoaQye3ujcPUGrxZadiSUrA1t2BpYugznUsB8Ho+M5f/QYTxesv2R8ul7DaTbtaTQaDfbCAizpKRgDgkuNToiys+Vmkx99AFVchGfkwMuWtVuKKYo7hdbsgql+Q9IycikqLEJ9sRBzeHNcmrTCHN7sqhfPFRVjtxSj0enLnDTa8vMoOHGYgugD5EcfIP/EYSguQgWEop3+BgaDDqNeR/H7z0J2Bnqveug8vLFbisg7uBusFo7qgph5phEAWhT/9D1OitVEis3IGYsr8XjgG9qAVs3r07JpCIN7tyY0pHJHe6s0abr55psZNGgQM2bMAMDDwwObzUZhYSE6nY6WLVuydetWvL29Kxp/rSNJU/VLXfs/Ula+D8CCjHAiJz/I+FG9aziq2sdqtZGcluN4wichOZOM7HxCg31o2jCQpo0CqOflVqUxZGXn893mA3z9w+9oju+jt0saDfQFeGuteOksGP6YI7I535dX0pthNOrxdjPykdvPjjqU0YRrk5aYGzbFGNQAlyYRuDRrU6b2ld3muBVREHOM8+/NpzglAaN/EKagBhiDGmAIaoCpfiPM4c2vu9EjIaqLslqxFeShNRiumPjaCvLJ3bcDvWc9MvzCiY5JJOX0adp//XKpshk2A7EWVz7JbsBjcx9hcJ+y/W4oqypNmsLDw/n2229p1aoVUJI0RUVFodPpOHjwIM899xyjR4/m6aefrvgV1DKSNNWMtG9XcvTLNTxwNIRCpePf00bwwF39ajqsUmw2O7sPxvLtz/vZsO0wfvU8eO6xkXRu06hK2lNKEXUkjs+/+Y1dm3aSU2AhxVaSCNTXF/Cw92mSrCbirWbOWl3IdfGhfkRzxtzakxsiWzoeK78a2bkF/LTtCN9tPsDWXccottjw1Fr4LHjPRZ8uw+SCqUNPQh7+t+OR9cSlb2Jq2BSXpq0wNWjkSHyEENcnW242WTt+wpqaRHHyeYriTlGccBZUybzDlcE3M/nphyp9Lb8qTZrMZjMxMTHUr18fAG9vb/bu3Uvjxo0BWLFiBW+99Rbbt2+vYPi1jyRNNcdutfDGhz+x8H8bAVj2+gP07xFRw1GVOHMulaWrtrFr8y5aF54hSF/IwsyS/w+0Wg2T7urHYxOHVNq6NhlZeaz+fjdffb2N0NSjDHJNJcKUy6rc+vzo0o5gf2+a1tMzLubjUudm2fT8kBfAHtdmDL11IGNu7lbuiZcFhcV8t+kA3/28j+z9u+lpSsZLa+X5tBZENAnm1hs7cmPqL3j4++PasgN6bx/0nvXQeXrL6I4QokLsRYUUnT1F4ZmTePUaVCW3bqs0aWrQoAErV66kV69eABQWFmIwGNDpSv6VeOzYMSIjI8nIyCh34Fu3buW1115jz549JCQksHbtWkaOHOk4rpTi2WefZfHixWRmZtKrVy8WLVpEs2bNLlvv22+/zWuvvUZiYiLt27fnrbfeolu3sj+VJUlTzXv2P1+Q/OOXuPnUY97Hb5Z5YmBBYckifpW9+u43G6NY+ca7jDSeppUpFwAFJE6Yzze7z7Ju/W4me51hv1crZv1rIg3r+xF9KoETsUlExyai02p4+N6BBPl7XbEti9XGR6u3s/5/n3OjLo5IlwzHLS+l0eIzfAxB/5ha8tluI2vrD1hSEig6d4bC+NMUJ5xFY7MAsDy7Pv/LDsVo0HH70C5MGz+QBkE+l20/MSWL/63ZzvavN9CHM/R2ScdLZ3Uc1zz1LhEdK3e4XAghqkt5vuPL/TKjG264gSVLljiSJrPZebl+rVaLxWIpb7UA5OXl0b59e+6//35uv/32UsdfffVV/u///o+PPvqI8PBwnnnmGYYMGcKRI0dKxXHBypUrmTlzJu+++y7du3fnv//9L0OGDCE6OpqAgIAKxSmq30OtdWT+Hku6NZ5PV25kwj2Dr3jOll3RPP7icnLzi/j0vw/SuW2jq46jqNjK/LfWYvx5Jf/0SARKFhZ0adkB716DaNGzIzcM7c1o72S8t+1iqC2J/z1+kiSbiYb6AsIN+TTVKOamteC7TQdY8Ow99Opy6aR/y65oXliwjttydvKCR6pjv75BY3wG3IRXrxudHoHXaHV497/JqQ5ls5K7dwdpP6yhU4ubiPrhCAeOxbN7/Ub+9fN6GgwaxtRxg5yGvFPSczhy4jyrv99N/PYtjHU/ywj3v6x14+aJd+QAPCMH4tqy5VX2qhBC1A3lHmk6ePAgXbt25ZVXXmH69Omlji9dupQ333yTAwcOXF1gGo3TSJNSipCQEB5//HGeeOIJALKysggMDGTZsmXcddddF62ne/fudO3alYULS57GstvthIaG8sgjj5R53pWMNNU8ZbWwf8poTDmpfFkYyqSliy95e6nYYuXN977hh9U/cMpSMgk6OMCLbz+ciY93xSdFnz2fxr/+/R6jMzfT1FiyUrT34FH4jbzXsYbLBZaUROLeeYnio6VXA7ZrtDxlvIVDMYlotRoeu38IU8fd4FgBvbDIws69J/l03U5+2n4EgFmBcfQ3JODVfzi+Q0dhbnT50dUr+X1/LMn/eZLGxYmcKnZlZX4Ynt36kZGZQ3ZsDEnZxST/MU9qkGsKj/vEoLRaPLsPwHvAzbi17ohGJy+QFULUfVW+TtMXX3zB3XffTd++fZkyZQpdu3ZFr9ezbds2Hn30UR577DGeeuqpCl8AlE6aTp06RZMmTdi3bx8dOnRwlOvXrx8dOnRgwYIFpeooLi7G1dWVL774wuk23/jx48nMzOTLL78sUyySNNUOWbu3c/71p7AoDd+2GcfsZyaVKhN3Lo1n57zLyIytBOsL+an9eH46nII2IZbOrUN5ecHsck2Ettns/Lb/FN/8vJ+vNuzDlp/LO8GH8HfTE/bIHDw69bzkuUopMjd+SfJXy9G7uuPSsAmmsMaYQpuga9KG5976mp+//4UHvM6wv8mN9BvYjY3bjnAmKorWpLCzwIcUXBk3qhfT7uiGS2EWLo0rZz6XsttIXb2MlG9WoCkqACDVasRTZ8GoUXyeE8Imj050bRfO+Fu6Ehi9Fe8BN5dKDoUQoq6r0ttzAHfccQdNmjThscceY/To0Y7XGCilGDFiBDNnzqxItZeVmFhyKyQwMNBpf2BgoOPY36WmpmKz2S56zrFjxy7ZVlFREUVFRY7P2dkXXyFVVC+vLr2Ia9wOw6kDBO3+isMnbqJ1s5IHEootVpZ/9Su/LP2Yqa7HcDPasJncmH5bR27vkkTxh9+QlXic9z5oxcMP3nbZdoqKrew7fIYfthzk2JattCuO4+uc+uTYDXRs3YTGD44nuFHoFRMIjUZDvUEjqTdo5EWPv/L0nfye+D3uiem0il/Dvvc2cq85Cz/vktvbwxrqCJ/9DE0bXfj7G1yu/rpsbFod/qMn4jNsNGnfriT125X4UQiAMph44I5ePHvfX0aS2zSutLaFEKKuqvD4eseOHdm8eTNxcXEcOHCA3NxcWrduTdu2bTl06BBt2tTdiaHz5s1j7ty5NR2GuIjmU5/ixOP30sMlg49fW8SL7z7P+i0H+eC91dyYv5/H3dMA0IZH0PTxlzD4BdIsPJ+Dq9/HLzsZr+8/YFuHlvTu/ueITVGxlUPR8ezce5Ko3YcpPnGQCF0m/VzSudNUDCYIaNmS5mPupWenppXyyP4F7Z6Yw6lXnsYv5Rw3upXMWVIGI+6tOtK5fXfqNajaV3bo3D0JGDMJ3+FjKIg5hjEwBENAyDW9IrIQQlTUVU9KCAsLIywsjJycHJYvX84DDzzAnj17sFqtVz65HIKCSpbRT0pKIjj4z39xJyUlOd2u+ys/Pz90Oh1JSUlO+5OSkhz1Xczs2bOdRsuys7MJDQ29iuhFZTHVb4hLvxEUb/mSPmm7uPHuV+mRvY9nPc5jdFUoNPjcPJbAuyaj0Zf89da5uBLxzOucmHU/ncxZrJ7/EkmTp3Pk5Hn2HT7DoePnCLZnM9v3BAMNBeD9Z3t2gwnPrn0YO2QUri2aV/71NAinxWtLSfv2c+yF+bi17YprRLtqf0Rf5+6Je3t5z58QQlzOVSdNW7duZcmSJaxevRpXV1f69OnD7t0Xf1Hj1QgPDycoKIiNGzc6kqTs7Gx27drFlClTLnqO0Wikc+fObNy40TGnyW63s3HjRqZNm3bJtkwm0zX5OphrRaNxD7HtyFHeOGQkxpJKPx8tRo3C1LIjIeMfvegkaXNoY4ImPUnq+/O4zRjLrnfnklnkwd7cEABs3t6EGUrm9hAYinfbzri17YJ7hx5oTRd/MrOyaM2u+I+aUKVtCCGEuHoVSpoSExNZtmwZS5YsISEhgVtvvZXPP/+cwYMHc+zYMdatW1ehYHJzczl58qTjc2xsLFFRUfj4+BAWFsaMGTN48cUXadasmWPJgZCQEKdJ3gMHDuS2225zJEUzZ85k/PjxdOnShW7duvHf//6XvLw87rvvvgrFKGqezs2Dbq+9S7v/rKGXm5kH7+iBa/Ip3DtGOubXXYz/DcPJPLAX668/EOmSQZMAV3rfMZaOrRvSsL4v+Yd2Y2rYDL2nd/VdjBBCiDqj3EnTiBEj2LhxIwMGDOC5555j5MiRuLn9+Rj35b60rmT37t0MGDDA8fnCLbLx48ezbNkyZs2aRV5eHpMnTyYzM5PevXuzfv16pzWaYmJiSE39cz2bMWPGkJKSwpw5c0hMTKRDhw6sX7++1ORwUbe4mI38519/WWaiQdnegt7k4Vmk1Q9Bo9fTsGUHXCPaO465te1a2WEKIYS4hpR7yQGtVsvdd9/NjBkz6NKlS6njhw8fpl27dthstoucXTfJkgNCCCHEtak83/HlfkRmx44duLi4cMMNN9CiRQuef/55YmJiKhysEEIIIURdUO6kqUePHixevJiEhASeeuopfvzxR5o3b06PHj146623Sj2pJoQQQghxLajQiuB/Fx0dzZIlS/j4449JSkpCo9HI7TkhhBBC1HpVenvuYlq0aMGrr75KfHw8a9asYfjw4ZVRrRBCCCFErVEpI03XOhlpEkIIIa5N1T7SJIQQQghxrZOkSQghhBCiDCRpEkIIIYQoA0mahBBCCCHKQJImIYQQQogykKRJCCGEEKIMJGkSQgghhCgDSZqEEEIIIcpAkiYhhBBCiDKQpEkIIYQQogwkaRJCCCGEKANJmoQQQgghykCSJiGEEEKIMpCkSQghhBCiDOpc0tSoUSM0Gk2pberUqRctv2zZslJlzWZzNUcthBBCiLpOX9MBlNfvv/+OzWZzfD506BA33ngjo0ePvuQ5np6eREdHOz5rNJoqjVEIIYQQ1546lzT5+/s7fZ4/fz5NmjShX79+lzxHo9EQFBRU1aEJIYQQ4hpW527P/VVxcTGffPIJ999//2VHj3Jzc2nYsCGhoaHceuutHD58+LL1FhUVkZ2d7bQJIYQQ4vpWp5OmdevWkZmZyYQJEy5ZpkWLFnz44Yd8+eWXfPLJJ9jtdnr27El8fPwlz5k3bx5eXl6OLTQ0tAqiF0IIIURdolFKqZoOoqKGDBmC0Wjk66+/LvM5FouFli1bMnbsWF544YWLlikqKqKoqMjxOTs7m9DQULKysvD09LzquIUQQghRO2RnZ+Pl5VWm7/g6N6fpgjNnzvDTTz+xZs2acp1nMBjo2LEjJ0+evGQZk8mEyWS62hCFEEIIcQ2ps7fnli5dSkBAAMOHDy/XeTabjYMHDxIcHFxFkQkhhBDiWlQnkya73c7SpUsZP348er3zYNm4ceOYPXu24/Pzzz/Pjz/+yKlTp9i7dy//+Mc/OHPmDA888EB1hy2EEEKIOqxO3p776aefiIuL4/777y91LC4uDq32z1wwIyODSZMmkZiYSL169ejcuTM7duygVatW1RmyEEIIIeq4Oj0RvLqUZ5KYEEIIIeqO8nzH18nbc0IIIYQQ1U2SJiGEEEKIMpCkSQghhBCiDCRpEkIIIYQoA0mahBBCCCHKQJImIYQQQogykKRJCCGEEKIMJGkSQgghhCgDSZqEEEIIIcpAkiYhhBBCiDKQpEkIIYQQogwkaRJCCCGEKANJmoQQQgghykCSJiGEEEKIMpCkSQghhBCiDCRpEkIIIYQoA0mahBBCCCHKQJImIYQQQogyqFNJ03PPPYdGo3HaIiIiLnvOqlWriIiIwGw207ZtW7777rtqilYIIYQQ15I6lTQBtG7dmoSEBMe2bdu2S5bdsWMHY8eOZeLEiezbt4+RI0cycuRIDh06VI0RCyGEEOJaUOeSJr1eT1BQkGPz8/O7ZNkFCxYwdOhQnnzySVq2bMkLL7xAp06dWLhwYTVGLIQQQohrQZ1Lmk6cOEFISAiNGzfmnnvuIS4u7pJld+7cyaBBg5z2DRkyhJ07d1Z1mEIIIYS4xuhrOoDy6N69O8uWLaNFixYkJCQwd+5c+vTpw6FDh/Dw8ChVPjExkcDAQKd9gYGBJCYmXradoqIiioqKHJ+zsrIAyM7OroSrEEIIIURtceG7XSl1xbJ1KmkaNmyY48/t2rWje/fuNGzYkM8//5yJEydWWjvz5s1j7ty5pfaHhoZWWhtCCCGEqD1ycnLw8vK6bJk6lTT9nbe3N82bN+fkyZMXPR4UFERSUpLTvqSkJIKCgi5b7+zZs5k5c6bjs91uJz09HV9fXzQaTYXjzc7OJjQ0lLNnz+Lp6VnhekTZSZ9XP+nz6id9Xr2kv6tfVfa5UoqcnBxCQkKuWLZOJ025ubnExMRw7733XvR4ZGQkGzduZMaMGY59GzZsIDIy8rL1mkwmTCaT0z5vb++rDdfB09NT/kerZtLn1U/6vPpJn1cv6e/qV1V9fqURpgvq1ETwJ554gi1btnD69Gl27NjBbbfdhk6nY+zYsQCMGzeO2bNnO8pPnz6d9evX85///Idjx47x3HPPsXv3bqZNm1ZTlyCEEEKIOqpOjTTFx8czduxY0tLS8Pf3p3fv3vz666/4+/sDEBcXh1b7Zx7Ys2dPPvvsM/7973/zz3/+k2bNmrFu3TratGlTU5cghBBCiDqqTiVNK1asuOzxzZs3l9o3evRoRo8eXUURlY/JZOLZZ58tdetPVB3p8+onfV79pM+rl/R39astfa5RZXnGTgghhBDiOlen5jQJIYQQQtQUSZqEEEIIIcpAkiYhhBBCiDKQpKkavf322zRq1Aiz2Uz37t357bffajqkOmHevHl07doVDw8PAgICGDlyJNHR0U5lCgsLmTp1Kr6+vri7uzNq1KhSC5vGxcUxfPhwXF1dCQgI4Mknn8RqtTqV2bx5M506dcJkMtG0aVOWLVtW1ZdX682fPx+NRuO03pn0d+U7d+4c//jHP/D19cXFxYW2bduye/dux3GlFHPmzCE4OBgXFxcGDRrEiRMnnOpIT0/nnnvuwdPTE29vbyZOnEhubq5TmQMHDtCnTx/MZjOhoaG8+uqr1XJ9tY3NZuOZZ54hPDwcFxcXmjRpwgsvvOD0Kg3p86uzdetWRowYQUhICBqNhnXr1jkdr87+XbVqFREREZjNZtq2bct3331XsYtSolqsWLFCGY1G9eGHH6rDhw+rSZMmKW9vb5WUlFTTodV6Q4YMUUuXLlWHDh1SUVFR6qabblJhYWEqNzfXUeahhx5SoaGhauPGjWr37t2qR48eqmfPno7jVqtVtWnTRg0aNEjt27dPfffdd8rPz0/Nnj3bUebUqVPK1dVVzZw5Ux05ckS99dZbSqfTqfXr11fr9dYmv/32m2rUqJFq166dmj59umO/9HflSk9PVw0bNlQTJkxQu3btUqdOnVI//PCDOnnypKPM/PnzlZeXl1q3bp3av3+/uuWWW1R4eLgqKChwlBk6dKhq3769+vXXX9Uvv/yimjZtqsaOHes4npWVpQIDA9U999yjDh06pJYvX65cXFzUe++9V63XWxu89NJLytfXV33zzTcqNjZWrVq1Srm7u6sFCxY4ykifX53vvvtO/etf/1Jr1qxRgFq7dq3T8erq3+3btyudTqdeffVVdeTIEfXvf/9bGQwGdfDgwXJfkyRN1aRbt25q6tSpjs82m02FhISoefPm1WBUdVNycrIC1JYtW5RSSmVmZiqDwaBWrVrlKHP06FEFqJ07dyqlSv7n1Wq1KjEx0VFm0aJFytPTUxUVFSmllJo1a5Zq3bq1U1tjxoxRQ4YMqepLqpVycnJUs2bN1IYNG1S/fv0cSZP0d+V76qmnVO/evS953G63q6CgIPXaa6859mVmZiqTyaSWL1+ulFLqyJEjClC///67o8z333+vNBqNOnfunFJKqXfeeUfVq1fP8TO40HaLFi0q+5JqveHDh6v777/fad/tt9+u7rnnHqWU9Hll+3vSVJ39e+edd6rhw4c7xdO9e3f14IMPlvs65PZcNSguLmbPnj0MGjTIsU+r1TJo0CB27txZg5HVTVlZWQD4+PgAsGfPHiwWi1P/RkREEBYW5ujfnTt30rZtWwIDAx1lhgwZQnZ2NocPH3aU+WsdF8pcrz+jqVOnMnz48FJ9Iv1d+b766iu6dOnC6NGjCQgIoGPHjixevNhxPDY2lsTERKf+8vLyonv37k597u3tTZcuXRxlBg0ahFarZdeuXY4yffv2xWg0OsoMGTKE6OhoMjIyqvoya5WePXuyceNGjh8/DsD+/fvZtm2b48Xw0udVqzr7tzJ/10jSVA1SU1Ox2WxOXyAAgYGBJCYm1lBUdZPdbmfGjBn06tXLsbJ7YmIiRqOx1PsB/9q/iYmJF+3/C8cuVyY7O5uCgoKquJxaa8WKFezdu5d58+aVOib9XflOnTrFokWLaNasGT/88ANTpkzh0Ucf5aOPPgL+7LPL/Q5JTEwkICDA6bher8fHx6dcP5frxdNPP81dd91FREQEBoOBjh07MmPGDO655x5A+ryqVWf/XqpMRfq/Tq0ILsTUqVM5dOgQ27Ztq+lQrllnz55l+vTpbNiwAbPZXNPhXBfsdjtdunTh5ZdfBqBjx44cOnSId999l/Hjx9dwdNemzz//nE8//ZTPPvuM1q1bExUVxYwZMwgJCZE+F5ckI03VwM/PD51OV+rpoqSkJIKCgmooqrpn2rRpfPPNN2zatIkGDRo49gcFBVFcXExmZqZT+b/2b1BQ0EX7/8Kxy5Xx9PTExcWlsi+n1tqzZw/Jycl06tQJvV6PXq9ny5Yt/N///R96vZ7AwEDp70oWHBxMq1atnPa1bNmSuLg44M8+u9zvkKCgIJKTk52OW61W0tPTy/VzuV48+eSTjtGmtm3bcu+99/LYY485Rlelz6tWdfbvpcpUpP8laaoGRqORzp07s3HjRsc+u93Oxo0biYyMrMHI6galFNOmTWPt2rX8/PPPhIeHOx3v3LkzBoPBqX+jo6OJi4tz9G9kZCQHDx50+h9ww4YNeHp6Or6sIiMjneq4UOZ6+xkNHDiQgwcPEhUV5di6dOnCPffc4/iz9Hfl6tWrV6llNI4fP07Dhg0BCA8PJygoyKm/srOz2bVrl1OfZ2ZmsmfPHkeZn3/+GbvdTvfu3R1ltm7disVicZTZsGEDLVq0oF69elV2fbVRfn6+0wveAXQ6HXa7HZA+r2rV2b+V+rum3FPHRYWsWLFCmUwmtWzZMnXkyBE1efJk5e3t7fR0kbi4KVOmKC8vL7V582aVkJDg2PLz8x1lHnroIRUWFqZ+/vlntXv3bhUZGakiIyMdxy88Aj948GAVFRWl1q9fr/z9/S/6CPyTTz6pjh49qt5+++3r9hH4v/vr03NKSX9Xtt9++03p9Xr10ksvqRMnTqhPP/1Uubq6qk8++cRRZv78+crb21t9+eWX6sCBA+rWW2+96OPZHTt2VLt27VLbtm1TzZo1c3o8OzMzUwUGBqp7771XHTp0SK1YsUK5urpeF4+//9348eNV/fr1HUsOrFmzRvn5+alZs2Y5ykifX52cnBy1b98+tW/fPgWoN954Q+3bt0+dOXNGKVV9/bt9+3al1+vV66+/ro4ePaqeffZZWXKgLnjrrbdUWFiYMhqNqlu3burXX3+t6ZDqBOCi29KlSx1lCgoK1MMPP6zq1aunXF1d1W233aYSEhKc6jl9+rQaNmyYcnFxUX5+furxxx9XFovFqcymTZtUhw4dlNFoVI0bN3Zq43r296RJ+rvyff3116pNmzbKZDKpiIgI9f777zsdt9vt6plnnlGBgYHKZDKpgQMHqujoaKcyaWlpauzYscrd3V15enqq++67T+Xk5DiV2b9/v+rdu7cymUyqfv36av78+VV+bbVRdna2mj59ugoLC1Nms1k1btxY/etf/3J6dF36/Ops2rTpor+7x48fr5Sq3v79/PPPVfPmzZXRaFStW7dW3377bYWuSaPUX5Y/FUIIIYQQFyVzmoQQQgghykCSJiGEEEKIMpCkSQghhBCiDCRpEkIIIYQoA0mahBBCCCHKQJImIYQQQogykKRJCCGEEKIMJGkSQgghhCgDSZqEEHXShAkTGDlyZLW3u2zZMjQaDRqNhhkzZlRavf3793fUGxUVVWn1CiEqj76mAxBCiL/TaDSXPf7ss8+yYMECauqFBp6enkRHR+Pm5lZpda5Zs4aYmBi6detWaXUKISqXJE1CiFonISHB8eeVK1cyZ84coqOjHfvc3d1xd3evidCAkqQuKCioUuv08fEhOzu7UusUQlQuuT0nhKh1goKCHJuXl5cjSbmwubu7l7o9179/fx555BFmzJhBvXr1CAwMZPHixeTl5XHffffh4eFB06ZN+f77753aOnToEMOGDcPd3Z3AwEDuvfdeUlNTyx1zo0aNeOGFFxg7dixubm7Ur1+ft99+23FcKcVzzz1HWFgYJpOJkJAQHn300Qr3kRCi+knSJIS4Znz00Uf4+fnx22+/8cgjjzBlyhRGjx5Nz5492bt3L4MHD+bee+8lPz8fgMzMTG644QY6duzI7t27Wb9+PUlJSdx5550Vav+1116jffv27Nu3j6effprp06ezYcMGAFavXs2bb77Je++9x4kTJ1i3bh1t27attGsXQlQ9uT0nhLhmtG/fnn//+98AzJ49m/nz5+Pn58ekSZMAmDNnDosWLeLAgQP06NGDhQsX0rFjR15++WVHHR9++CGhoaEcP36c5s2bl6v9Xr168fTTTwPQvHlztm/fzptvvsmNN95IXFwcQUFBDBo0CIPBQFhYmMxfEqKOkZEmIcQ1o127do4/63Q6fH19nUZzAgMDAUhOTgZg//79bNq0yTFHyt3dnYiICABiYmLK3X5kZGSpz0ePHgVg9OjRFBQU0LhxYyZNmsTatWuxWq3lbkMIUXNkpEkIcc0wGAxOnzUajdO+C0/l2e12AHJzcxkxYgSvvPJKqbqCg4MrNbbQ0FCio6P56aef2LBhAw8//DCvvfYaW7ZsKRW3EKJ2kqRJCHHd6tSpE6tXr6ZRo0bo9Vf/6/DXX38t9blly5aOzy4uLowYMYIRI0YwdepUIiIiOHjwIJ06dbrqtoUQVU9uzwkhrltTp04lPT2dsWPH8vvvvxMTE8MPP/zAfffdh81mK3d927dv59VXX+X48eO8/fbbrFq1iunTpwMli2IuWbKEQ4cOcerUKT755BNcXFxo2LBhZV+WEKKKSNIkhLhuhYSEsH37dmw2G4MHD6Zt27bMmDEDb29vtNry/3p8/PHH2b17Nx07duTFF1/kjTfeYMiQIQB4e3uzePFievXqRbt27fjpp5/4+uuv8fX1rezLEkJUEY2qqSV1hRCiDlq2bBkzZswgMzPTaX+jRo2YMWPGVb1a5fTp04SHh7Nv3z46dOhwVXEKISqfjDQJIUQ5ZWVl4e7uzlNPPVVpdQ4bNozWrVtXWn1CiMonE8GFEKIcRo0aRe/evYGSW26V5YMPPqCgoACAsLCwSqtXCFF55PacEEIIIUQZyO05IYQQQogykKRJCCGEEKIMJGkSQgghhCgDSZqEEEIIIcpAkiYhhBBCiDKQpEkIIYQQogwkaRJCCCGEKANJmoQQQgghykCSJiGEEEKIMvh/ebjYaA9/mkcAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(6,2.75))\n", "ax.plot(intervals_1D, deltaG_1D, c='fessa0', label='1D', linestyle='-')\n", "ax.plot(intervals_2D, deltaG_2D, c='fessa6', label='2D', linestyle='--')\n", "plt.legend()\n", "ax.set_ylim(5,20)\n", "ax.set_title(r'Convergence of $\\Delta G$')\n", "ax.set_ylabel(r'$\\Delta G$ [kJ/mol]')\n", "ax.set_xlabel('Time [ps]')\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "graph_mlcolvar_test_2.5", "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": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 2 }