{ "cells": [ { "cell_type": "markdown", "id": "a1b2c3d4", "metadata": {}, "source": [ "## Yeast gene trees in BHV space\n", "\n", "One of the biggest challenges in phylogenetics is that different data sets based on different genes can yield different phylogenetic trees. In an article published in *Nature* in 2003, Rokas et al. found that when data sets contain a small number of genes, it is exceedingly likely that the resulting trees will have conflicting topologies. One possible resolution to this is doing a majority-rule tree; another possibility is to adopt a Bayesian posterior over possible trees. Here, we use the geomstats implementation of BHV space (Billera et al. 2001) to look at how the trees differ based on gene sets considered, and how as the gene sets become larger and larger the resulting trees converge to both the Frechet mean of the single-gene trees and the all-gene tree.\n", "\n", "We will be working in BHV(8), with 8 leaves. Each leaf represents one of the 8 yeast species from Rokas et al. 2003:\n", "* *S. cerevisiae* (Scer), *S. paradoxus* (Spar), *S. mikatae* (Smik),\n", "* *S. kudriavzevii* (Skud), *S. bayanus* (Sbay), *S. castellii* (Scas),\n", "* *S. kluyveri* (Sklu), and *C. albicans* (Calb, outgroup).\n", "\n", "The data we have provided in `datasets/data/yeast/yeast_concatenated.fasta` is concatenated alignment of all 106 considered genes (127026 basepairs). We then divide this concatenated gene situation into 106 equal-sized windows (of around 1198 basepairs each). **Note: These windows do not exactly correspond to genes (gene boundaries do not agree with our fixed window size). We use 'single-gene' for the plot!** (If you want true single-gene trees, feel free to get the alignment partitions from the authors of the paper, or get the individual sequences from the National Center for Biotechnology Information.) We build one Neighbor-Joining tree (using the biopython python package) for each window, giving us 106 trees that live in BHV(8). Each tree represents the inferred phylogenetic relationships for the 8 yeast species considering the alignment in that window. These trees will likely disagree, as different windows and different genes capture different evolutionary signals, which can lead to different inferred topologies. This is also what Rokas et al. quantified in their paper. We then increase our window size to yield 15 windows building more trees. We hopefully show that these are converging to a stable representation of what should be the underlying species tree. We confirm this by finding the Fréchet mean of the single-gene trees, and the variance around that mean. Then we find the Fréchet mean of the multi-gene trees and find the variance around that. We then plot everything using MultiDimensional Scaling to put it in 2d, and we indeed see convergence. Hoorah!\n", "\n", "**Data note:**\n", "We have provided for you the processed data in `data/yeast/yeast_concatenated.fasta`. Some species of scientists appear to be allergic to Python, so in order to get this data, we use the `phangorn` R package. If you are desperate to have the R code to get it yourself, please see the code below the References section at the very bottom of this notebook." ] }, { "cell_type": "markdown", "id": "b2c3d4e5", "metadata": {}, "source": [ "## 0. Imports" ] }, { "cell_type": "code", "execution_count": 1, "id": "c3d4e5f6", "metadata": {}, "outputs": [], "source": [ "from collections import Counter\n", "\n", "import matplotlib.pyplot as plt\n", "from sklearn.manifold import MDS\n", "\n", "import geomstats.backend as gs\n", "import geomstats.datasets.utils as data_utils\n", "from geomstats.learning.frechet_mean import FrechetMean\n", "from geomstats.metric_geometry.bhv_space import TreeSpace\n", "\n", "gs.random.seed(66)" ] }, { "cell_type": "code", "execution_count": 2, "id": "1eec808c", "metadata": {}, "outputs": [], "source": [ "def count_and_plot_topologies(trees, tree_str, n_common=5):\n", " \"\"\"Count and plot the k most common different topologies.\n", "\n", " Parameters\n", " ----------\n", " trees : list of Tree\n", " Trees to look at.\n", " tree_str : str\n", " Just for printing/plotting convenience.\n", " n_common : int\n", " Max number of most common topologies to plot\n", " \"\"\"\n", " all_topologies = [tree.topology.topology_key() for tree in trees]\n", " unique_topologies = set(all_topologies)\n", "\n", " counts = Counter(all_topologies)\n", " print(f\"{len(unique_topologies)} unique topologies across {tree_str} trees\")\n", " print(\"Top 5 (topology_id, count):\")\n", " trees_to_plot = []\n", " for i, (topology_key, count) in enumerate(counts.most_common(n_common)):\n", " print(f\"\\ttopology #{i + 1}: {count}\")\n", " trees_to_plot.append(single_gene_trees[all_topologies.index(topology_key)])\n", "\n", " _, axes = plt.subplots(1, len(trees_to_plot), figsize=(n_common, n_common // 2 + 1))\n", " axes = axes.flatten()\n", " for i, tree in enumerate(trees_to_plot):\n", " tree.plot(root_id=0, ax=axes[i])\n", " plt.suptitle(\"Top 5 single-gene yeast phylogenetic tree topologies in BHV(8)\")\n", " plt.tight_layout()\n", " plt.show()" ] }, { "cell_type": "markdown", "id": "87c82170", "metadata": {}, "source": [ "## 1. Load data" ] }, { "cell_type": "code", "execution_count": 3, "id": "ba463f71", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Built 106 'single-gene' trees in BHV(8)\n", "Example: (({0, 1}|{2, 3, 4, 5, 6, 7}, {0, 1, 2}|{3, 4, 5, 6, 7}, {0, 1, 2, 3}|{4, 5, 6, 7}, {0, 1, 2, 3, 4, 5}|{6, 7}, {0, 1, 2, 3, 4}|{5, 6, 7});[0.02698943 0.01330342 0.01215568 0.02141068 0.05232679])\n", "\n", "9 unique topologies across single-gene trees\n", "Top 5 (topology_id, count):\n", "\ttopology #1: 36\n", "\ttopology #2: 30\n", "\ttopology #3: 13\n", "\ttopology #4: 12\n", "\ttopology #5: 8\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "single_gene_trees = data_utils.load_yeast(n_windows=106)\n", "print(f\"Built {len(single_gene_trees)} 'single-gene' trees in BHV(8)\")\n", "print(f\"Example: {single_gene_trees[0]}\\n\")\n", "count_and_plot_topologies(single_gene_trees, \"single-gene\", n_common=5)" ] }, { "cell_type": "markdown", "id": "4509e7a2", "metadata": {}, "source": [ "### Great, let's make some multi-gene trees!\n", "We expect there will be more agreement among these." ] }, { "cell_type": "code", "execution_count": 4, "id": "65b35d2d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Built 15 'multi-gene' trees in BHV(8)\n", "Example: (({0, 1}|{2, 3, 4, 5, 6, 7}, {0, 1, 2, 5, 6, 7}|{3, 4}, {0, 1, 2}|{3, 4, 5, 6, 7}, {0, 1, 2, 3, 4, 5}|{6, 7}, {0, 1, 2, 3, 4}|{5, 6, 7});[0.01956877 0.00959495 0.01005255 0.01562352 0.06409424])\n", "\n", "3 unique topologies across multi-gene trees\n", "Top 5 (topology_id, count):\n", "\ttopology #1: 7\n", "\ttopology #2: 7\n", "\ttopology #3: 1\n" ] }, { "data": { "image/png": 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8dj4TIXf/PCuew/0z3UGwuZlacQUoBixQXJTJnSNuXlwsEydOlOeee87cNH///XenfNjHPWbMGHPxDxkyxPiu8eX37NnTzENqSI6Mu8+vFeBoHyexBcQjWfPD4otvP6HUveRem/zL3/z+xGSH41jkiZJ3PwdWIFxS8uP++zivwM3O/TNZZDnnKCnJhXgfbvT2m6CvcM+es34DsQnuv4FNj31eUnutJATnxlNWH3Ngve6NjBIvdubMGTl+/LiZ++R8pn0skNB7uUb5fOs7UrNucrN1n0sUKj7Xmks2rZMnTzayy/VNLA7KC3EdKcWb6zYxKlasaOJweKBsEyfJusWa5Z6CTqyadaz9QVyLJ1BCkHsUCRgxYoQ5r8R82bHG6h7jwXlh7b3//vvNPZP7JPdM5guFzlNJDOszvP39ycqO8eZkoDFz0u2LHTs3TjrpZHY8LfDWc55ueElxzWIlSS42LLJPPfWUeXCS0e5efPFFozUT9MfOLjUwdmsxsuPNDY05Yu6sfG13rOfYHaABe/pu8Ob7+S6OJ9jUE1zAyYXPZCdAoJsnrEUrITh3CD3ng0A6gk8RfHuwlLdzRGolFi8UGRQM+27V07ipB8GDoD4C6Z5//nkjuwnNjzf4Wsbhsccek06dOhlLCrslrFEE+vni2uQ4/uZmb1dE3H8HgW/WTtiuINohQDA5WGNAsUko6y0lKfgs3ARVcsPztSLirtRZv4GNjj1rwI4ly6m9VhKCc4jFxR1rt+vtOszmBEsE6yXzlpzPtI8FEnovn4ssWXKZmnWTAHVPgfLu42Ojw4NgZTYk7777rrFOsvlhAxIIVKtWzVgZSKV1t2glB5QsFBoSE1hPUUYIzkcZ8zQ/7ko+liyUCcuCZAflB2sdiqrdQmZ9RkIy4QmfXZXcLBgQmqa7ucl63Q47U7vQYfpjR1q6dGkzecnF+p7kpO3ijmDnxULK5PmiOBmFXLgBbtq0yeV5bzJ/yKbggsSU5UnjtaKZubjdX7MWOHYx7pH43FjdMwH4LnYqzLun73KPkvYGPpPfzjn09JneLKxo3SyAmLS5CNx3+d7OkXWDcFdU2GkkBi4nvpMbu91l4m718QYyGFCE7LAgoOCRZZQScIEwxqefftoo0Oywk8rU8fbaRHaB6zAx2UVRx5WA65MF09N5SK6ShbuQ65HrxtPn8bBM9cnZbbJzwz2UksJeyT3nXDNly5Y15zyh32Ap96m9VhIaG+eSOXR393GukRPOmx0shfasqtOnTxsLDRY3FE3ceGSTcJz9+1DqcH+zVqMIJzQfZKkg89YmEbBuUmPCypjhO/jNyKe9eBYy66lwlzvM5datWz2uizw8uSqZP+TdcmUk5cZPT9auXWv+9UWZCKweWDReffVV87lYR9zXC6wxwBzasWTQ3bvAueQ5FEjOnR0y6VAuk3P/8JklBPMWZmJ2ndzMuRmwA3nnnXeMiZbUJTtoSqRevvLKK+aHsOvFn5rUzRqB5oLAD45/H2sGPnLeh9/T3QfvDlYEKzebk4zvjh0wn8UCklpIC0MjZ/EjLZDdG2Pmt0FiuzEWYlJFERTcQ2iszA07CeaSOX3kkUcSfD+fTYofaX8oV/jBmR+ewyRq/+4uXboY8xznBp8fGjcmTHy8pBqyW+CGlxz4vaTFkr7Hjh1BZIFDHvAlkrqVlILJjQhZItaBc+LuE/Z2jkghZoHHosFFw86exZXx2Tl58qRZmNkN8R5uEliZsIDYd7N8LnLHuEhFYy7t+f2e4CLGZ0yaIfPPos33s/Cl1OLGjQGluX///uZ3e1OsyttrE3Mw84uCQ9wKv5NUSktZscsP6ZPUD+BmxXyz0HMDw9LEPLvHHiQFuymsIIyRDQHyi7sIdwo3df61ahVYiiZj4HjkFlnzZL0jnoUdIKZjlFrONTdQLEMsvlwHCZGSc46Sy7WPZZVzw02Y30MMEoqBFc+T2muFsbHmoTBijscMznMUi+J8sT7yHVxDpNKyvnKe3BUG5AmFG8sw84Jscu5ZMyywFnAMc4erCWWQz0OJwjSfkBLMfJECzIYCRYF1CQvEgAEDzLpEeQMLxsqYmTfWIzZHHIdcJOWGY81FqWEt4PejGPNb2HzNmjXLyDOKFDdi1jcUNeaWMSBDyI+lgKc3GzZscMb0sSlE3pAL1t7kWhM9wfrDvZa55FzbrcIWzAUyhGKBLFqw2WENHDRokFHaWCs4f4QDELdH2QD3c89nEJuDguI1Dh9lx1jpgg8//LCJAicljojiF154wXHhwgWX4/javn37mihgIszJ3CCqnHSupCDquGnTpiYLhPcR6UtkNZ9lj8BOCLIqiMomjYg0MVKq7rvvPseOHTuSzI4hIt3TPLhH0G/YsMFEl5MlQCQxn096KJ9JKmpi7wUyf8hwYX7J+GCOevbs6Vi1apXDG0g1JcuI30d6Lp/Xtm1bE7Vvhwh+IsbJPmCsROtzHojc37Jli/M4xkimQFKZCHD48GGTZkZkNueH309KHqmlZ86c8Wr8pAQyV6SJJoQ3c7Rp0yaTjUI693XXXWfSinft2uWS6YFsIrNEkZO1wmeRwsvrVgYLkO3RsWNHR65cuUyWQVKXjjVnROgjN5wL0vlIIbRjRdm7p6Zb2Qv2tE4LZJXXGLcnPJ0Xb69Nfue9995rfifXFvNHGiHfR9qj+xh79+5tUkI516SFcm299dZbKf59ZLwxb8gNn8ln87f7+xk7mRdkRdgzAzz9drI/SLkmdZLzQMYFqZv2NFRPJHTOrbHbU63tcI137tzZZIDwG1ir+D57WmRqrxVkgLRXZJux2NcRMm66detmfiefizwzVvv6aP0GMqRIwybLhblhjSAF3x3SafkN1vVGxgwp1HY8pegCGYxcq6wxvJ/1e8mSJfG+g9RcMmmsdZnrn/nh2k0sUwWYr5dfftn8Vt5vpY+TTmplYVKy4LbbbjMyxTGcH7Jb7KnCyc2OSc51m1R2TM6cOU12IGtEQvdMTzAGT/NuwRx4yuSxQ8o+8+z+vVw7yA7rI7KGjHLuf/rpp3hpuGQzsWa4Zy4mRYqVkNSQ2ISGKtS24CZvT0FLL44fP25uEIwhGHjqqafMQnfkyBFHsJKQ4uYLBg4caK4hlN30wKr14OnGoQQnSSlSgQDpz5RAQBFW0pa9e/caxSyhNF1voJYISqaVnu8tPnPHKOJiWsQUj4nL8muSefHyyy+7pKClBQRyEeyG6RQfKe6mTz75xJjKMXMGMpjyCMbC1IvpNqXBm6EKfuvt27cb+cJdZq8i6yswrxNvg2kfczrnBFMupu7klGJWlJTEL+D2wXXJOoZLCjeWvZq1kjZwv8Ktxb2DwPfkBnHjUsKVR1B2slwxvowJUf4DHyMLN/5HTg6xJh9//HG6KAH47vArE7CIL5XYA4J1uaDT4qblS6xANfzH1OxQXMFPzOJMHEaySyN7CXEVxBow/wQQckMgtkHPh5LWsFEi5oT4H9ZQgreJj3GPJ1TSBjbJrL9sQqitlBzILKVMBvE3ySUD5pBkv0tRFEVRFCWV+L6Cj6IoiqIoiheoEqIoiqIoil9QJURRFEVRFL+gSoiiKIqiKH5BlRBFURRFUfyCKiGKoiiKovgFVUIURVEURfELqoQoiqIoiuIXVAlRFEVRFMUvqBKiKIqiKIpfUCVEURRFURS/oEqIoiiKoih+QZUQRVEURVH8giohiqIoiqL4BVVCFEVRFEXxC6qEKIqiKIriF1QJURRFURTFL6gSoiiKoiiKX1AlRFEURVEUv6BKiKIoiqIofkGVEEVRFEVR/IIqIYqiKIqi+AVVQhRFURRF8QuqhCiKoiiK4hdUCVEURVEUxS+oEqIoiqIoil9QJURRFEVRFL+gSoiiKIqiKH5BlRBFURRFUfyCKiGKoiiKovgFVUIURVEURfELqoQoiqIoiuIXVAlRFEVRFMUvqBKiKIqiKIpfUCVEURRFURS/oEqIoiiKoih+IcI/X6sEMg6HQ87HOeRSnEOyZMog0ZkySIYMGfw9LCXMUDlUVI5CH1VCFCcXrlyV9ccuyurD5+XEpavO53NlySi1Y6Olau5IiYpQ45mStqgcKipH4YMqIYph26lLMmn7Kbn8/7rHsrHfy2/Dv5TTRw5KvlLlpfUzb0m5OtdLu5IxUiomi86akiaoHCoqR+GFbmsVs/CP2/qfAvLnzEny64cvy833PSH9Rs6TEjUbyLB+XeTw3j3mOI5XFF+jcqioHIUfqoSEOZi+sYA4bM/9NuIbqXNnd6nb7m7JV6qc3PHs25Izf2FZPn6oOY7jeZ+iqBwqgYSuZ8GHKiFhDjEglgUErly+JPs2r5OyDW5yOa7s9TfJrnUrzf85fsOxi+k9VCWEUTlUVI7CE1VCwjz7gCBUO+dOHJOrcXGSPU+sy/PZc8fK6aOHnH+vOnzevF9RVA6VQEDXs+BElZAwhjRcexaMK24puQ6HS5ou77sQp0qIonKoBAa6ngUnqoSEMdQBcSdrrtySMVMmOWOzesCZ40eMNcTORVVCFJVDJUDQ9Sw4USUkjKEQmTsRmbNIoYrVZcuKhS7P/7t8oRSrXtfluUgP71cUlUPFH+h6FpxonZAwhkqoFCJzd8nc0P1hGftKXylSsboUq1ZXfp84XE4c2CP1O/RyHsP7olQJUVQOlQBB17PgRJWQMIYYDyqhzt171uX5ai3aydmTx2Xu4I9MsbL8pStIr4Gj5LpCRZ3H1ImN1lLuisqhEjDoehacZHBoioOEe179lxuPuaTpJgYOGCq3962cW0u4KyqHSkCh61nwoTEhYQ69YCjFnpzojvYlY1QBUVQOlYBD17PgQy0hiseeHZ7InPGaAlJSe8coaYTKoaJyFF6oEqK4mDKphLrKQxddYkCq5ImUqExqPFPSFpVDReUofFAlRIkHYUJbduySUeMmyP29ekqh2DwahKr4RQ6nzpgtu/cfkN49e5hsLHvBPEXxVo7mLFosf27cJH0efEDlKMDQ7BglHiz0kRg8zp/WC1bxqxxGOK5IpkvnJJpoaEVJoRxldsRJhgtnVY4CEL2yFUVRFEXxC6qEKIqiKIriF1QJURRFURTFL2hMiOLCsmXL5NixY3L69Gnz94IFCyQqKkoKFiwotWrV0tlS0pyzZ8/K4sWL5cqVK7Jz5045c+aM/Prrr+Y1ZBBZVBQlNFAlRHFhxYoVcvLkSWcWwqZNm+Tq1atSpEgRVUKUdOHUqVOyfPlyI4NWQefVq1eb/+fNm1eVEEUJIdQdo7jQqFEj86+1+KOA2J9XlLQGS0fx4sVdnkMeIyMjpUaNGnoCFCWEUCVEcaFmzZqSPXt259/sRvPlyyfly5fXmVLSjZtuusmpCFtyiCKMIqIoSuigSojiQkREhNx4443Ov7kR3HzzzVokSklXSpQo4WINyZIli9SrV0/PgqKEGBoToni0hsyfP1/Onz8vuXPnViuI4jdryA8//GD+r1YQJSWxRT/99JNcvHjRPC5duiSffPKJee2GG26QOnXq6KQGAGoJUTxaQ1BErMVfS2Ur/rKG5MiRw8ifWkGU5JI5c2Y5fvy4UUZQQrDq8n8edlef4l/UEqLEgwv0+iY3S7a8+aV8lcrmb1VElPQGuevcvaccO3VK4jJlVjlUkkV0dLQ0aNBAlixZ4qJ0ZMuWzbnJUvyPNrBTXLqXrj92UVZ76KJbOzZaquaOlCjt4aGkMSqHiq84d+6cccFQc8bitttuU8taAKHumCBh0aJFcscdd0ihQoWMVWLy5MnO1y5fviz9+/eXqlWrGi2fY3r27Cn79u1z+YyHHnpISpcubXYIsbGx0rZtW/nrr7/Ma9tOXZIvNx6TuXvPGgXkyqWLMrDLTfJCrVjZtH6deZ7XOY7vd3988803Lt/FzuPDDz+UcuXKmYyGokWLyjvvvON8vVevXh4/p3Llymk+l0rKUTlUgomsWbMaa4gF66MWXQwsVAkJoiqS1atXly+++MKjtr9mzRp55ZVXzL8TJ06Uf/75R9q0aeNyXO3atWXo0KGyefNmmTlzplEUbr31Vtly/LyM23pKLv9n/JDpn70uOWILuLyf1zkO+Jz9+/c7H/fcc4/LsY8//rgMGTLEKCIoOlOnTnXZfXz22Wcu79+9e7cJgu3UqZOvpkxJA1QOlWDj+uuvl4wZr93qyPwj5k0JHPRsBAmYEHl4ImfOnDJ79myX5z7//HNz09+1a5cUK1bMPPfggw+6BP299dZbRrH5fskGyVm4pPO1v5fMkS3LFkj3D4fKP0vmunyu5VnNmiNGChRwVVIsUHK+/vpr2bBhQ4KZNYyZhwWWHYLI7r333iTnQvEfKodKMFpDsMhu2bJFrSABiFpCQhSr9HquXLkS3NFizShUrIRky1fY+fzpo4dk4ptPSee3vpIsUdEJfn6/fv1MCe26desaV4xVWRWwepQqVUp++eUXKVmypFF47r//ftOTJiG+++47adasWbxKmUpwo3Ko+Bssvnd06CR9n+kvlySjZsYEGGoJCUEuXLggzz//vHTr1k1iYmJcXvvqq6/kueeeM0pIhQoV5OFvxktE5izOi3X8//pJ/Y73SJFKNeT4vl0eP795n+elRsObpGulfDJv3jx5+umn5ciRI/Lyyy+b17dt22Yaj40bN06GDx8ucXFx8uSTT0rHjh3N8e7gjpk+fbqMHDkyTeZD8Q8qh4o/0QDn4EAtISEGQapdunQxlgkUDne6d+8uf/zxhyxcuFBKlSkj3zzVWy5fvGBeWzp6sFw8e1puuveJRL/jlvufltyVakuFqtWNAvLGG2/IgAEDnK/z3eTlo4BQFIiiU1g6KID2999/x/u8YcOGGYvNnXfe6ZM5UPyPyqGSGBrgrFioJSTEFv7OnTvL9u3bjcXB3Qpij8UoW7asVKhZV4rkyysb50+TGi3by7aVi2XX+tXySoP/3DPwZY/mUv22DtL5jS9dnr8Y55DoCDHR5xQAOnjwoOTPn980ICP4Cz+sRcWKFc2/xKjY40Swvnz//fdy9913m9LcSvCjcqh4G+BMDFiHDh0SDLTnGGLFnnjiCRNov2rVKpdAezZVxLzh6n3ttddMoP3cdX/LxB1nnfFr9kD7/f9sTDDQvmXLls7X7PFqVqD9rFmzTKA9WYi4GbH+2gPt33vvPeffpAQzdg20TxpVQkJs4Sf4CotDnjx5knxPRAYuU4fEXbpo/r7j2XekeZ8XnK+fOnxAhvbtLF3fGyxFq9SO9/7ITBnMv1hWoqKinPEnVFnlIty6datJCQaydcA95gOLzL///iv33Xdfqn6/Erxy6Lh8SeUwzNAAZ8VClZAg4cyZM+ZmbYG1Y+3atSatlbogxFuweyAYlBiMAwcOmON4HQsDcRpjxowxwZ/0UFi2bJlxg0RkiZTyjZqaY3MVLOLynZFZs137jCIlJGf+Qub/mxfONMGrlWvXk7058suCBQvkpZdeMpk3VodTvoNc/N69e8unn35q3DN9+/aV5s2bu1hHADdN/fr1pUqVKmk8g0ogyWGTJk2M9WzFihUyevToa3LYuJk5VuVQ8XWA890fD08y0L7PQw+aQHo2RKxnVlqvPdAeawnWW9a4Dz74wMi1JzTQ3ntUCQkSMEPSzdbiqaeeMv9SnwMz5M8//2z+rlGjhsv72I2SG3/48GGZMGGCKRiGuRNXDaWLn/7wazmYJ5/X48gYESHLx30vMz95VT52XDUXJzEhKBnOYzJmNBcuFzbfTYEgdj4fffRRvIWFMWHKVEJfDqnXYCkhb7/9tmmQiNmbDKuXv/pBdueK9XocKofhgwY4hzZatj1EwfpA/MXGjRtN3Q52CigelSpVMlVJCxcubHYWRJBTCdVeqCwxcMBQub1v5dxawl1JEgKUCUbetGmTsaBgHSlSpIiRQeKELN+7ymH4wjo0adIkj4HpuPeIq2Atw+rqHufGRubQoUMmw+79AQNk7b+75OGhv0rmyChZMmqQrJ81WR4cMlUyZspksv0+aF1b+o2aJ4XKV433XY9XzS3RERnNZomNFZ8NWEUGDx5s5Niy5GLtIyaFQozutZDeffdd8xlUrNY4t6RRS0gIKh4s+CgemM65aAmksisedugF065kjAnQ8ravZPuSMaqAKMlWPJo2bWqUYPegP5VDxRMa4BweqBISAooHJc8ti4eleBBjkZDi4U6pmCzSqXSMTNruWrrdncwZrykgJWM0i0VJveKhcqj4MsA5iwmU10D7YEOVkBBTPFjwWfyTUjw8KSK4WDYcuyirPHTRrRMbLVXyREpUJi0to/yneJD1hBymVPFQOQxPfBXgTEouzTj37t0r77//vmSJjNIA5yBDY0KCXPHAr47FIyWKR0IQ/b1lxy4ZNW6C3N+rpxSKzeOzz1ZCQ/HA4sEu1VI8UDpSqngkJodTZ8yW3fsPSO+ePSQq07VOy0rwQ3yHPcDZwgpwJkvFE1hFKH5IvAWtIFavXm3qiFCfiCD4dn2fk3+jyeSLLyeeYkL+XjJXZn7xlpzcs0Pk/wPt+VwC7e2N7vg+Au2pFWIPtLdnxxBDQo0kAu0feOABH81U6KNKSADDImzFePBA8ciRI4czuNSXioc7lF0nhffRRx/1yhSqhJfigZsPGfS14uHOtGnTzDXw8MMPp9l3KKGzUZs5b4GszVlBMkRk9qiIuKOB9v5H3TEBrHhg8Th9+rRRPFjw01rxUJSkFI9bbrnFKB4J1WtQFH+l8U6cONG4eGq3yCMbpLAG2gcJqoQEiOJhd7VYiodl4i5atKgqHkq6Kh4s5lS9VcVDCXSOHj0qo0aNMmUIKONOleaKpy5poH2QoEpIgCkeVoyHKh5KekD1XHtwqaV44K9Xi4cS6CCz48ePN2snsRyW61gD7YMHVUL8oHhYMR4oHtmzZ3fGeASC4kEjKMppW9Hoe/bsMeO87rrr0tT3r6S/4mG5WlA8yEgIFMWD64RsB8aFLDLeHTt2mNdQkDJnxt+vhDPIyPLly2X27NlSpkwZad++velf5V4DqU6+aKkdGyVzFi2WPzdukj4PPqABzgGGKiF+UjwsiwcdIP2teNgZMmSIKadtMXnyZPMvaXB9+vTx48iUtFA8yDRA8UDJDBQIiv7hhx9cnrP+RlEiC0IJX5BdUnfXrVtnmmUSp2T1efEE62tmR5xkuHDWVERVAgtVQtJI8cCCgInb3eLBI9AUDzvUGlm5cmW856m6qgQXwaR42CH4muuFbDB3GLcSvrCWUh/k4MGD0q5dO6lWrZq/h6SkElVC0ljxCFSLR0I0btzY5N6T7mZBd9x69er5dVyK94oHCgdyGEyKhx3qM2DtID3Xgp0u48+bN69fx6b4D1x0KCDQq1cv45pTgh9VQnykeBBciv/arngQ45GYmTAQoQAajZnolsrvA0yeKCJKYCseKL9YPlA8KJoUTIqHO3R4XrRokdMaglLcpEkTfw9L8RN//vmn6dCMXFPOnUBUJTRQJSSFiocV4xEKiocnawhKCFAiWa0gwaN4cKNGDoNR8UjMGoKbUK0g4QfK59y5c2Xp0qVSo0YNadWqlUslUyX40bOZjGh9y9ViVzysGI9gVzzcrSG0rKYhWa1atdQKEoCKB//S5CuUFA9P1hCyH/idagUJ7wJk9Ihp0KBBULi0lTBUQlASzsc55FKcw3RSjPaixwQZIFSBRJlISvHA1UJfAHoG2INLQ0nxcP/tNzZtLscvXJE61zc2f+vF73sZtFKiSYlNSJa4AdtjPCzFAysBcmjvXRFqZMqUSRrf3FT2Hz4iWXPlVjkM8wJkSmgS1ErIhStXZf2xi7LaQ9fX2rHRUjV3pMkV97TwDx061CgV9p4UluJhuVosxcMeXBqqikf8+XSIVG8pg7eel1xZLiY6n+FMSmUQSDEkBZqus7jA3BUPy9XC3wUKFAgLxSPenEaVFilaWgauP+bVnCqhW4BMCU2C9kreduqSfLnxmAz5ebZ89khXeefWKvJCrVjZOH+auRnM3XvWvM5xnhQQAt5I8zpy5IiJ8aA7It0Pv/vuOxMEVbZsWdPR8amnnjJ+yBIlSgSUAvLuu+9K3bp1zYWaL18+ufPOO437xA7dKCtUqGAUKUz1zZo1kxUrVnj8vK0nL0qNm5pLvfxZZcnMX1xee6F5DfN8dOZMZnfP4/nnn4/3GTS8I2WOokHcNGl+Zx+L9V77g7GFmwzaFRBA3lA0UDpYfAcMGCDjxo0zu8EbbrjBdO986KGHjKISSAqIr2WQTUCT5i2MnA38aZyLUvd+q1rySJU8LnKoMhhacP6XLVsmI0eONBu+++67TxWQMCAoLSEs6uO2njINii5dOCcFy1WW2m26yohn73U57vJVMcd1Kh1jyvhaCggmPntxLnpmBJvFY+HChabdNDcBghJfeukl4zflRmbd2Inr+OKLL0x7atxPn3zyiTmGnQbFx+zz+fgbA8SRSNfJZo88L/Xa9TBH3FEih1Qu6Hoz/Pjjj01ra26g9evXN/7cbdu2OV9/5pln4nVCxQLA+MNJBt0VEDh8+LB88MEH5jyivKF4IIeBpHCktQzCK+99KAfPxyUpg4Ac3lW5YFjLYDgXIPMGNpqk9LK+s+YjD1999ZVRYBs2bCjVq1f32fiVMFJCMNVO2n5t8YfyjZqZR0JwHMd3LSTy09DvXaqBAgLZs2dPKV68eMArHnZmzJjh8jfKFbtRanxYFSW7desWb5G2LD0svtZ8fjljqSwe8bX0/XGW2c17IjJrNsmRN7/5/+JzItWjsjpfO378uLz88ssydepU5+cCN1ILYm/s8TcsNtysvvnmGwkXGexbObds+nOtmSd3UHxvv/32oNr5+UoG4ffVf8gXn33qtQzCrMNXpWy+q8Y1E24yGEqkVQEy1vb9+/eb2D+7wg/u9wHFfwTPXff/wVfM7jI5cPzQmYs9Ch7aMdkgwaSAeIL4FUho90xmxaBBg0z/F/sOYOWe4/LT8w9Jm/7vuSzw7iz64XN54+ZyMrDLTTJr0Mfyx4HTztfIYCCVjngarElUvCSXn3L1CYEFil0yu/5wkcE5m3Z6VECshTiYFBBfyuC5c+ekS7duyZLB+UM+lvMXL8mGYxfDUgZDBc7X4MGDTcYhBch8WQEVaxxWLvcA8ejoaFMLSQkMIoLNZ0iwWkqILl9HYuWMXLxwwfjaUT4stm/fHtQ3AOaF2BViBqinYAcTZ5cuXcxCT1YFi7VVb4H3vfjc01Ksel2pdNNtCX5+o64PSqGKVSU6Ry7Zs3GNzPz8bXnmwG5ZPH64ucAxeXMDeOedd0xcDTcZdqXNmzc3O15qjdjBPDpixAiPPv1QlsFdGXJI6TJl+BBzwz5x4oQxQ1s7NM5R1qz/WZjCQQbhiSeekIJV6iRbBo/t2yV53xpoGpSFkwwGKwsWLDCWqDp16qRbATJcO7ShsFtDUDq1CWLgEFRKCCmQ9mC15HApIko6dunmbGDEIkSMCDcCgk6DGQJAuaAXL14c7zUafq1du9YE4LLj4GInMBCz+fjJU2Tz8kXSb9S8RD+/cY///OjEPkTH5JIRz/aWvYc+liL5Y83iT2DlwIEDjb8fSK8jvmH+/PnSokULl88j95+dP26wYCM1Mnjqisi9d3V1yiA3bvzWyCFWAnZo4SaD3ITmzZ8vdw+bnSIZbPnYq3KhfK6wksFgBBknhsiyUJAMkB4FyFB6sIbQcRe4xiwlSAkMgkoJoQZDargY55Do///FlCFHA+cRzJA5wUJOiWtM0O5wwdPqmgfFfsj6wSf/wgsvyLx58+XYnh3yRpMyLu8huLJEzQby4OApHr+zaNVrF/Ff/2wxSog1h/bmYgQdstvdtWuXRzN469atzQ0i2PClDGJFYvcX7CWoUyeD82Tb1q0plsGju7fLxbjSYSWDwQhKAPKO4k3mF/+mVwEyrCEovXynWkECj6BSQigClRoiU/n+QIILisV/0qRJxsxZsmRJr9+HFQie7d9fIm/s6PL6Z51vlFZPvykVb3TdOdrZ99d682+xwoWcFzmQnmndhNj5sPMl4NcOri92pty0ghGVQd/KIO6Q7r16y4gt1+JJkiuDMXnzm+s6nGQw2CAWb82aNc5eVPyL25G4oPQogog1hOwszrtaQQKPoFJCqEJJwSK7OfziuTNmN2RxfO8u2ff3eskac53kKvjfroz3RYWQEkJqJPn0U6ZMMTvpAwcOmOfxhWNyJCXt7bffljZt2phdInEwpKdhBu3UqZN5/fC+PVK4aDGJiyQO4b+5yVWgiOQufG3h3rlupexev1pK1W0kUdljZM/GP+TXj16Raje3lLIlrx1DcF/btm3l8ccfN4GHBPqyy6U+BKZ4O99//70Zz223Jez/D2RUBn0ng9ZN6fjhg1KoSFm5GpU9WTJYsUlLKVG8mLmuw0kGg61aMNlS9pgMID5o7NixphZTWisijO/Ozl3k7IVLcjlDJonQCtABRVApIQgrFRMpAmWxd9M6Gfzgnc6/f/34FfNvrTvukk6vf+F8vk5sdEiVHv/666/Nv3RKdU+TJMqcktd//fWX/PDDD2Y3SOAtEeG8TmrihAkTzHzE1rlZThQon+D3RGTJIn/OmixzBw2QK5cvyXUFi0jddnfLay/0d5nP4cOHy5NPPmn8u2Qa0euDFE57ABh+ewqaWeMLRlQGUyeD+OdpSoeVgvcTkIvCUqB+HtlnU0K8kcEb73nU5boOFxkMpmrBEXJVfvvtN+drnBfOARAPxf/T6jx4Ht85rbwbYGRwWNuRIMHUtdh4zOsUSZYn4gCp0RCOpZ7ZgZA5sH79enNDIHiPTr9Vq1Y1NRQyZonS+UwmKoPJh50vNTmQQ2I0CETESoEc0hfksiODymGQFeuj9s0/K5fKouFfyt7N6+T0kYPS46MfpPLNt5tjMmcUqe44IkumjDF/58+f37jGWH94YDGzV98lWJg1CqWUYmLvv/++lC9f3qX67ujRo03aNdlObKqwtFGYzlMF6Fatbpe/l8xzGZNVfffEftfU7f79+8t7773n8hzKKnVtaJ1Af6eOHTuawnvWWF5//fV434ubyV4MUwkxSwigSLQrGeOsVukN7UvGhJUCgl6JyZsFn8Zn3AAI0iMoi/RJ926rOp/JQ2XQO1B4idFADqmQilyicFCQCgXEnjbLXljlMPSqBa+WvNL0rnukfunCiabFagXo8CXoLCHumnhiFhE0cRSQkv9fLjvUwbTNgs+D1GP89CgdFABiF5KYO0rnM/nonMUH87rd8kbqMYGiyCGPpHoF6ZwGrxWQvknuVgdrHU6uJZq1jBRulBOr+q47FDjDmjJnzhyXCtAvTVwk3z3W3Vl915MlpFG3B6Vx94c9jo/qu4ULF45XfTcxcHGTbkyGmBa/C3FLiAV9OBAcKiau8uCTxFdcJU+kRGUKbQsIF+KGDRvMok9gIKnHpCli5k5OKXqdz+Sjc3YN9jH79u0zdUKwvGGOJv4DkzpymJweODqnoVktmHW6Tr7ogKoAPW/Ix5IrfyGp2qyNNHyhv1xfJKfH6rvUk0GW6UuEG8kTWn03DJUQQHNFsKmYeCHOYWowkK5HtHwoBaG6Q7XXzZs3G8WDtDMCu8gOYMdADYaUFv6xz+eWHbtk1LgJcn+vnlIo9rqQns/UEK4yCGS7WJY3Ak1JhUTp4EH2SUp/v31Op86YLbv3H5DePXuExZyGarVgNoqcT2/On1aADi+CWgmxQLCjI3j4eyRpB+W9t2zZYhZ8AqUIOKUuA+mPaOtRUVE+nc9IDCjnT+vCn4w5C3UZtDIaLMsb1g8sb8gfGSlUHvZlDybmNMJxRTJdOuesMqsEZ7Vg3oeSzjWSFFoBOrwI8SUzuGFHsGPHDrPgk1lAgScqPNLmGv86tRAUJa1B7uyWNxQNLG4UCONf7cMRHviyWnBCaAXo8EOVkABUPGhpjX+dHSf+SNLD6tWrZ8zcZLkoSlqDpY2MFhQPMlywxBFjhMWDmKNg7nOjBF61YK0AHb6oEhIgkM1i+deJDCffnDoeKB5kF6gvXElruBFQwwMFGMsbsUdkVVGMDMubva6DEn6kZbXg1FbfhZKFC0qFSlHxXEZaATqwUSXEj1C/g2wCFA8K8GDWpn4C7cfpdaAVHZX0AMsbMojljawEFn56bKAAkyapKGldLTil1XepxspmLaHxuaMVoAOPoK0TEqyQWmYVcNq6davZfdJdlAWf6oD2Ak7+gL4aWGJIUWOsBB5ycRMESwt2JTRA2bAsb4cOHTK7Tdws1JQhDdGfljeUop9++sm4gCh4hiwih0C/F8ao+IdArxa8Y88+Gb0/g0imCLSSgBufEh+1hKRzAScC/FhYcbG0aNHCaPFJFXBKT7j5YIa3sLqdqlUmNLqZWqXTd+7caVK5UXwJdEYRDpRzjEKEldDqMQKWTPpbSQ93ArlaMFmD48ePl1xlqsjpsg0DbnyKZ1QJSSOwcFDsxirgxKKaN29eady4sbF6uJdODxToOIrJ0x2agSnBBwovizOKByneyCWuvjvvvNO4/iwLQyBB1hd9QVatWuXstGuaLcbGuvQSUfwDBeU6lY4JqIrVK1eulOnTpxv5aN/uNtl93hFQ41MSRpUQH4O/0jJzU/6XAk6Yj3mQXhvoAabUeihWrJiJUeEGwHix1qBAKcEBFgRSaS3LG241ylDfeuut5lwik4EOyjot4C0lhH9RkAP9+gkXAqWyLXJBhdNly5aZRnbIOCnkpTJLQIxPSRqNCfEBpNFaBZz279/vLOCE4pGc0umBArVJ7NYQItdVCQlsWIyRPcvyRlExSl5bFUwJ5As2pk2bZna4QIDsww8/rEpIgMqeP6oFY+WbPHmycTHi2m7QoEGC45uzaLH8uXGT9HnwAS3AGGCoJSSF4KMmWtu9gBM7OEqop7R0eqBYQ0jNJECQ36QKSOBCuXSrpgxpi1g5sHagAKemdHogwLVkuWTUChK4+KNaMCm7o0ePNqm8d911l3EtJja+zI44yXDhrFbeDUCC906ZBhCNz4KXUAVIXrcXcKKgEzfs1q1bG8tHKBVwog8NQV4JdbBU0lbBTawMP1YOK7WbuCOCNZE/MkfIYgo2y1tisSH8Hm40GguiWKBsU1OEoHnSd3E1KsFLyLpj+Fn0OqDUMJX+KLST2K6QlMXvvvvOZK3YU1H5HDIJrNLpVgEny8wdiqXTnXN35apkiciY5NwpvpFBwKIxceJE6dChg7P+AbDgWpY3Mq34HKxUyCCWt1Asna5yqLhDMT0sIBRz7N69u9cB/gsWLJA1a9bIU089pZMaYESEYh477aZXewhGopBN1dyR8dKxiOmgKA7/stCTycL/LTP3qVOnTOn0UC/glJK5U3w3j8geCgg3XxZMTMxY3pBBXsMSR9Dw7bffbmp6sBCHIiqHiiew/k2aNMlsFHHBhJLlOZwJKUvItlOX5NGX35A/5/4qh3dskcyR0VK8el1p+dirEluijDMtizx3orst3yIFuiibbtUloGwwSghCbpVO93cBp6Sg4iAPgkqBcb/66qvGRO/OQw89JIMGDZJPPvlEnnjiCefcNb/lZtm2eqnLsdVuvVO6vjfYZe42/zZb3njjDaOkUeMElw03Txg2bJjce++9HsdIjEmoKnAWzCOpgbOHfCob5nmWQ3cZBJSNUaNGudTGwCWD5Y05QwYpnY4yHMioHCq+hlvU0qVLZc6cOeY6oHR7cmPu1BISuESE0uJPAZ1/Vy2V6zv3liKVa8rVuCsy84t35Ps+neTJCYslS3Q2kzfOceS5F8wcZywgpNLadTF2nF27dpXSpUsHTAGnpGB38N5775miU0B2S9u2beWPP/5wMesTTb5ixQopVKhQvLljBuq2u1uaP9Lf+Ro3UAvm7tVBI+SXt5+W9959xxS5Yt5wEViwQ2nZsqXL2PDbWjfTUMY+jyhzCcmhRGdzyiCKCIqjuwICBJYS9Y/7L1hQOVR8CdcE9T8IUL7hhhs0QDkEiQgV8y27Txb/3l+OdXmt4+sD5e2mFU2Pg5K1G5rnOI7jr84fKedOHvdYWZIbZrAoIHDHHXe4/E2zJ3aly5cvdyohBDE++uijMnPmTNMN1X3uIHNUtOTI6/mmF3flikwd8JK0ePxV6XX/g06Xgj1oEOuR3UxKCfh58+aZeJtQxn0ek5JDSwbbxJyVkcN/8PyZ/x9/FEyoHCq+gvo2BMdjJUSuatWqpZMbgoSEgx//e0KV8S6cPmX+jc7pGsDE8ZElKxvXi6eqkVSXDFbI2iF4C1fT9ddf79xR3H333fLss8+6WEbc527d9Any5i3l5ZOOjWXaJ/+Ti2fPOF/b99efcurQfrkqGaV6zZpmp467B19tQgwfPtzELnTs2FFCmcRkMCE55Pidl7OYhnGk1rorvdT94BwGKyqHSkrBHY5rl6SAbt26qQISwgS9JQR3AAGACb027eNXpUSN+lKgTMV4r2cpU1P6tbnFxHqgdZMhQ2wIFwCZB8EGbhGUDnbQ3NQI4iKAEd5//33jR33ssccSnLsat3WU3IWLSfY8+eTg1r9k5udvyf5/Nsp9X483rx/bu9P8O/fbAdKp/5vyYOMq8vHHH5uS7pQGpziWO8TbsIiEchBZYjKYlBz+ezlSHn/8cSODHEdQtCWHuAWDcd5UDpXUQENFUnDZOBFfRqVpJXQJeiWEFEh7BoKdn9/rL/u3bJKHv//F4+u8j0p/FNqh1gK9KXgEK7hF1q5da25gEyZMkHvuuUcWLlxo3EufffaZybiwB9eyE79om7t67e92/p+bZd6ipeSLHs1k7+Z1UrhidXH8f8zCzfc9KaWatJbKVXObmBriAMaNG2cCXu1QSpm0ZqwhoUxiMpiUHNplkHNDoC8Pe8xOsKFyqKQUCj+OGTPGBGCzeUlNCQSsiMTAkd6OYm8lIQAl3u0WYcV/BL0SQg0GT/z8/vOyedFMeXDIz5Izf8ILOqWG07PSX1qCImUFppJOTMlrlA8KWbG7IL3Tbip/4blnJCb/J9L/1zUeP69QxWqSKSKzHN21zSghVqxIvlLlnHOXKzLSNEQjf9+dIUOGSI0aNUwzslAmIRn0Vg5DSQZB5VBJCevWrZOff/7ZFKjr1KlTqpsrYlmkpo494JueWKDF7wKHoF/6KALlLngs/JvmT5MHBk+W3IWLJ/p+eh2EKswFuwBiQZo1a+byGlkXd3XrLhkatk/w/bhk4q5cdiofKCIRWSLl8M5/pUTNBmbu6N9Adgc9ctyreo4dO1beffddCXXcZTC5chjKMuiNHHa6q6tkuiHhmCGVw9DCaoxp/xuLLY+aNWuaoHlfJAXgknbvxgwoN2zSlMAg6JUQqlBSBMoyh095r78Jrrz7k+ESmTW7nD5y0DwflT3GZH7Y4X00WwoFXnzxRRMkSj0TYloITCU3fsaMGaZ5mb2BGWWPsYRs3fKP1G8byyogR/fskLXTJ0j5xs0kW67ccnDb3zLt4/9JoQpVpXiN+uZ9UdlzSL0O98icbz6QwoWLys7oyvLhhx+a19i52MGkSkwDVQ1DHXcZTI4chpIMJkcOrV0qSuyWvzdL4/bX3KBHd29XOQxxcJEQt2ZVpv7ll1+MG5n+QKTh+rIek3s3Zj67UaNGqbayKL4j6JUQhIoqlHP3XssiWDFuqPl38AN3uhzX8bWBUrtNV5fnaOccyAXIkgOFwNhpklFBtgUNzFj4mzdvbl5nJ0p8BnVDMEnyd/58+aRe/myy6kwGyZQ5i2z9fZEsGTVILp07a1wHFW5oLk0ffFYy2nYltz/xmmSKiJARL/WRYRfPG98qKbju5ZNJyW3fvr3XZZVDSQaTI4ehJIPeyCEN97jhYHqnEjHKMC7EG4rnlsVH4lQOQxzi1ShyaCkjWExx5bZr187Iiq8hpgRriNWNGVdhvXr1fP49SphXTKVGw5cbjyWaImmHJZ8SF30r5w7pMuRW3xsWfRQQdp0UYCNOg5LgZMvo3PkGnceEIfMM+UMOkUd2oQQFYnqn+RhKmM5feDB37lxZsmSJ0zLBGoS1lEagaQXK7qeffmq+kwKLWFuUwCHoLSGAIkEZbKtapTe0LxkTsgoIkeDWbpNqsFgjMEtWr17d7E7t6Nz5Bp1HV1jwsbhheUMBQREh4JAdL4HS7g33dP5CH9yzdteI9RxKQlqCNQT3IPKoVpDAIyQsIe59OxKziNC3AwWkpK1vRyiAlYMmZygf+NpZ5NltYvUgKyYpk384z50vCfd55IZiKcC4Xki1RAZRgL3pexPu8xfKXaOpH2P1mLKTMWNG6du3r8c6Q74a1+mLl+XkmXOSJ1eMdgUPMEJKCQHMuhuOXZRVHjqY4n+vkidSojKFhgWEU0cpdhZ9Oq0S54HCwaKPAoL/MzmE09ylJeE2j+xmLQV469atxsROkTzcLWRNJTfmJdzmL1y6HlMugJgQ9wwWCkPeeuutpmGjP8al+JeQU0Is+FkUgaIGAymQZCCESgAgwVzsNHnQmwVzIztNlA9f7CaYuy07dsmocRPk/l49pVBsnpCZu/QklGWQ30bwKe4WFGCyHTB5WwqwL7IP+I6pM2bL7v0HpHfPHiE1f+HWNbpt8ewy4rNrVZup0UFtIdxzWMc8nVPtxhw+hERMiCcQbKpQhkoRKLIIKI3ObpO+Npgw8a1TZ4GLmb99OXeRfNz507rwp3IeQ0kGgaqTZDcghxTAo/cS2QcoH3nz5vX5/EU4rkimS+ckWnesQd01esL2M9Ll0WekXO6sXimS2o05fAih5TE0OXDggFnw8afSV4Ry3tRhqFKlSlD2FVGCUwFG8bUUYG4i7GYpPEa2lS8VYCV0u0b/sue89M0ZLVERSSsh2o05fFAlJACh1wtKB4s+Jm96iVjulnz58vl7eEqYgKUDdwuyiAWErslY3lCA6YyshC8p7RpNrE+dfNHJVoLpTZXSruBrp4+X7LljpXyjpqbuUWS27B67gp86csissRRgTKivTLh0BU9PVAkJELioCOpD8fj777+NP5yALTrUUszJF2WMFcUbBZgYD+Rw3759ZsGtWrWqWZy1m6mS2q7RBBvXjo3yyiWj3ZjDA1VC/Awl1Nlt4menzDWWjqZNm5rqgVhA0pvly5eb1ErGAvRzIGqdXTDZDkpoKsCkdaN4kOXC3yjAlNUuV65cuivA7HgpaEXWDcXNkMVp06aZ12rVqqXKUIh0jU4K7cYcHqgS4gdIpd24caNZ9Cmgw00eEzc3eW72/swAQAmh2Jnl52ec3JQIFFMlJPQUYGQQBZj6HrGxsaaiJAowqZP+grEsW7bMeR2ws7aakNF7Ri0y4dE1WrsxhweqhKQTLKB0m2XR37x5s7OEeocOHZwl1AMBmjux67TaX1v/8rwS/Fg9hJBDenaQSosCjLvFKqHub1DEqXeDgm5VEOBfxso4lfDsGp1UN+Yu3XuIXN8uwfdrN+bAJDDufCEMxXmsCpL8nzoe9C4g0JT6HoEG1g5cMJjEgZsSO2RMo0pwwuKNwoEcYtlCAaZOAw0GUYDdS6gHAnRU/eGHH5x/a/fT8OoanZyu4IAMFylYQKLLlTPj0m7MwYMqIWkAizzWDhb97du3G7OiVUGSiyoQdpsJgUWGYFjLB88NjBtCII9Z8QxuNZRf5NDqIYRFC2uCew+hQIOGZlhDUJ5Au5+GV9fopLoxJzUu7QoePIRsxdT0hmncs2ePc7eJ2ZCS1Sz4KCDJLaHuTwgI/Oijj0wVTCw3jz76qCohQdxDCPlDDlNSQt2f4L60rCHa/TSwCNSux+cvx8nn64+YtFvxQtbDpaN6IKOWkCQgJoKFO6HFG1OhVUL9yJEjxsVSv359425Jq4ZM6WENwWpDcGDDhg2D6sYVqlArIaEsFRRg0mmtEupWD6E2bdoYBcQXJdT9ZQ2hIittCrT7aWARiF2PuQ4WzJklF7bvlywN7vD6faHcUT0YCCtLSFJdHj2Zs7///ntjCiRt1m4psEqo//vvv+bmQAl1FA9fl1D31zydvRwna9dvkJrVqkrWiIyqiPhJBq16CT///LP06tXLBI9acHO2SqjTQ4gbtlXUzt1nHrQNGg8dlaMnT0nZUiW0+2kAEihdj9ks/vLLL0YRb9WqleQuVy0gxqUkTVgoISnppkhg5nfffWd86ewkqcxHBUmrhDpFnbghsOCTXeDrDpD+QLtOBt7cUiZ91KhR5oaMrLVu3TpeDyGCS3mNYNNgV4BB5TC48HfXY6yEkydPNm7wtm3bGkU8EMaleEfIKyFo6s++/5ksHTtMju+/FuSWr1QFafrg01K+UTOnRoxpsdT/a8SYs4cOHWqUDmt6CI7CMkIBMSwjuCvIGgkW3n33XRNx/vjjj8unn35qnmNnbc9AgKJVakuf4TNcntu5bqXM+vId2b1hjURFZpZaNWrI9OnTTe8aItYJXPXE77//LnXr1pVwx9ot/jZmqKwY51kO3WUQSFHl/LDIAgoGCjEKMD2ELAU4mHoIqRyGLv7oGo1Vevz48UYhp9wB7kdP45qzaLH8uXGT9HnwAW3KGWBEhEOXx+yxhaTFYy9LnqKlzPNrpo6WH5/sKf1GzZP8pSsYkx3HdSodI8WyZpSRI0e6KCCWsHfp0iUoS6ivXLlSBg0aZJQnd1q2bCmvDfxWpu44bXy7RJW7KyBD+90lN937uLTp/65EZM4sJU5ud+64iRkhgt3OK6+8InPmzJE6depIuGPvNJozX+JyaMkgigjZAT/99JNTAbFMzigfZAjkz59fgg2Vw9AmvbtGE4RN6i4ZVKzNVPlNaFyZHXGS4cJZ7cYcgESEQ5fHik1auLzW4tGXZMX4YbJr/Sqz+APHcXz0islyeP/eeJ+He4YbQLApIMQNdO/eXQYPHixvvfVWvNcjsmSRxeeySva8nhuS/frRK9KwywNGCbG4kLG0ODJdqy1B1o+9giULA/ELmlETv9NoUnJoyeBdBRwybPBgFwXEWkwvXboUlAqIyqHiS7BWs1lkA9StWzcTi6cEJxnDrcvj1bg4WTdzklw6f06KVXN1FXD86ZgCCfrVSX0MNvr27WsCtdwrDFosWLBQ/ndzRfnwzvoy8c0n5cyxw87X+P/uDasle+688nWv2+XtZpVk0P1tZMvq5cbX6gkUELKEcPWEO4l1Gk1IDjl+7aGzHjOysMzhojl37pwEGyqHiq/AHUk3W6uWiCogwU1EuHR5PLBlk3zd6za5cumiZInOJj0+Gib5S8WvApqzakN56K5WZkfP7o0UXB78n2ZewQSmyjVr1hgzuCdwxWSr11IyxxaW43t3yeyv35UhD7WXR0fMkYgskXJsz05z3JxvB8jtT7wmhcpXkTW/jJUhD3eQQpMXS+3b6sS7URLMSwllirKFMwl1GvVGDvdkjDHxO9aCa8kgD1wywRYErXKo+ArW4R9//NH8e88995gS/0pwExEuXR7zligj/UbNlwtnTsmGuVNl/Kv95IEhU+LdAJxdHrNkMXU+grXWBztmglBnzZqV4E2rTcfOsmP9MfN/Wm4XrlRdPmhVS/76bbZUadpaHI5rc1i/fU+p07ab+X+hCtVk6++/ybzxP8mzt9Z26YZJsbaZM2fK2LFjJdxJqNOoN3L4X6fRjJI1a1bzCEYXDKgcKr5sbIgFBFcMltZgSgxQwswd46nLY0TmLJK3WCkpUqmGtOz3ihQoV1mWjhzk8f1Edwc7q1evNsG1tWvXNsXHeNATZuDAgeb/xBu4z1NMbAHJVbCIHN29zfydI++1G18+N0UttmRZOXFgb7x5IqOI+hQUyQp3Euo06q0choIMgsqh4gsolcD6QoLAvffeqwpICBERLl0e4+FwyJXLF33a5TGQoLga9UzscPFSU6J///4mwDbL/1s6LM6eOCYnD+5zKh/XFSpmFJPDO/91Oe7Irq1SvmFTl3nC/cAi0bNnz4BsiBaQMpiIHIaCDILKoZJaiDHDAsK6wvoS6H2PlOQREQ5dHmd+/paUa9RUchUoLBfPnjEBgdtWL5F7vxgT773ednkMdKieSQ0JO9Q4wVLB85T5fvKppyTPLZ0kR6EScnz/Hpn5xduSNVduqXxzK3M88R439Owrc779QAqWqywFyxETMkYO7/hXHvlkmMs8zZs3zzTru++++9L9twZLp1Fv5TBUZDApOaxcubIJ9n7++eel4G09JKZISTm+T+VQ+Y8DBw6YGBBkhiBU5EkJLSLCocsjWR5jX+lr2kvTWrpA2Upm4S/b4KZ47/W2y2MwgrXi2LFjJrWNLr9rVq+WgzNnybkzZ4z1o1TdRtL1vcESmS278z2Nuz9sgihJ1T138oRRRu77apzcVruSyzwRkErNEMrXK547jXorh6Esg4ArkNTKr776yvyLIjJ/4UNy9sxplUPFJcZsxIgRpvtzjx49TGyUEnqEbMXUQO3y6A+OHj1qsmRosmfVO6lVq5bZoVLvQ+cpbVAZ/A+yeujqS28PlA6ULFyDVB6m3DwxMCqHir2DMu0KCMimDkhKMsJIZZ8xY4aprYNLh4rXpUuXNq8hd+XLx8+OVNKfkLSEBGqXx/SEFONNmzYZ5YOKglzEVExF+XDPtAjneUpLwl0GgYUfxYNeN/yfjAYqviKL9p1tVESGsJ8r5Ro0BR0zZoxJ86cSKgURU2pxo6u0fZ/9999/m3/ZiKkSEhiErCUk0Lo8pgecSszbKB5WS3cK+aD14yYhKyYhwmme0ptwm1sWfxZ75HDr1q3mJkL8BwowTR8TczWF21yFO3R/zp49u7P/EW5iesFgsejcuXOia5Y3UDwRBdh+myPA9cknnwyqnkuhTMgrIeHQTZGCVmTCsOMkkIvgLZqboXzgT/WWUJ8nfxIOc8sNBcXjzz//NKbwIkWKGMUDBSQ5u9lwmCvlmrV2wIABZr3q3bu3cddNmjTJbJjat2/vkxYZpPZ+/vnnTiXEBNvfcEOCTTeV9CcslBB/dnlMy9+yc+dOs+ize2D3iXkRxYMme6lp6c5nb9mxS0aNmyD39+ophWLzBO08BRqhJIOAv50W6ijAFCZjd0krdZSP1BaTYq6mzpgtu/cfkN49ewT9XCmuYK2dMGGCOadYQ6gIzObpjjvuSNX65ckagnyCWkECj5CNCQmELo9pARcq5kUuKrR8KrredNNNZuHnQvbVPEWyBpw/rQu/jwkFGUQ5IMXbcvuhiGA+79ixo1GEU2tCt89VhOOKZLp0TrufhiAEynOOkSfWNWKEaPngSwUEsHxYSsj111+vbpgAI4iXwvCBzIItW7aYRZ9/MVNWqlRJ2rZtK8WKFdPdoZIu4GLB1cKCTjXemJgYs6ize82VK5eeBcVryNIjXshuiMetTEYM9UB8pcgCLmlikVCcGzRooGcpwFAlJIChpoeVWUDDJpo13XbbbVK1atWga2KmBCfcJChChxzi9uNvUmvJcCG11te7ViV0QFbooUQLAyoIR9vcae5ZKxZk8pFOW6BAAZ+Oo2PX7nL4+ElxZI40f6tbL3BQJSQAg7VY7Fn0yZWPjIw06YzEemjHSCU9m4VZbr8TJ05I3rx55ZZbbjFuP6pXKkpigcXrj100XaTdA4sp4Fc1d6T89ttvLu8hHZeAVNx5vmoaGn8cESKHj7mMI5TS4YMVVUICBLJacLeQ5XLhwgUpUaKEtGvXzlyY6dmLhTgTbkCMB/bu3WusMJg0Mb8roQvBzf/8849RPKjVgEncSq0l0yW9do9WzAnNyogVIOaEIGzArO5LU72Ser7++mvzYNOEbSNPyfJy8wNPS/lGzVyOQxF49JGH5feJw6VN17vlthsbGvdIuXLlUlQN9bXXXpPXX3/d5TlqILF2Wanee//9R2YMfEO2rVkqjqtXJX+pCtLt/SFy4lIRmbxqs7zTqrbHz6YTeKdOnZI9JiX5hFV2TKCBsoFZEuWD+h4ElrLTxOpBbw1/8MEHHxjfrDtkOvTp08cvY1LSt6IuN3pkkIq6WOLSG25mP/zwg8fXSK288cYb031MSsJMnTrVxKlFFigm03edldVTR8tvw7+UfqPmSf7SFZzHbZw/TeZ++4GcPX5UbuzZVz579TkplYpaLygh1BSZM2eO8znGcToypykQeGT3dvmyZwup27a7VG/ZzrRKOLT9HylSuaZkzx0rV+Pi5NzxI3JHiRxSPMe1cQwaNMisgSgyvgr0VxJHtxTpDDoffk92m6Q2svssW7asNGnSxKTW+iI3PjWw8121alW8592bkCnhU1E3vcHqgssHhcgdArKVwIKUWqtFQd7iIi0efUlWjB8mu9avciohJw/tl5/ff156fzlWhj3WzVhMsFSktk0GVjF7/AjjGL7xmPn8WV++Y6wxtz3xP+fruYuUcP4/Y6ZMkj1vfll8TqR6yWvjoE7JXXfdpQpIOqJKSDqBS4OdJsoHO0/cG+zosHwEkpujcePG5sZERo4Fu+H69ev7dVxK2lXU7dChgwk2DRQ3B+NAKZ82bZrzOQJgUUCITVECD2IvqHKLdWH9nJ/l0vlzUqxaXfMaa8nYl/sY64fdMsLxFKWrky/llUvJFqQEu7VGdXnqVbmcOZ/5zr8Wz5Yb7+kn3/fpJPv+3iDXFS4mN937uFS++XaXz7DGkWH3JhMH9eWXX6ZiJpTkEhirTojChUAaGos+vnZ86iykrVq1MjEfgRihnTNnTrMbXr16tTN6ne64/jDLK2lXUbdevXrJrqibnjC2hQsXOq0hXEsoJkrgwTrx85LV8kH3FqbjdpbobNLjo2GSv9S1BnGLhg2UjBER0rDrg/HeS1Xc2rFRKVoLUTqGDx9uYkoOHjwob731ltxz+83y2Ljf5OqVy3Lp3FlZOHSg3NrnBWn5+Kvyz9J5MuKZXnL/oElSqnajeONYN2SIicFjvVPSD1VC0ii4E42aB0GemLcpwkNqbTD0K8AaghIClNtWK0joVNQlpiK1FXX9YQ3BHahWkMCENNzIwqWk36j5cuHMKdkwd6qMf7WfPDBkily5cEGWjBok/UbO86hoEKxKBWEK+CUXyhVYsLZWr1tfSpUuLWt+GSPVW7Qzz1e6qaU07vGw+X+h8lVl17qVsmL8D/GUkMOnzpoaJa+88koKZkBJDaqE+Agi+WlRzm6THgjcvLkwsCqQWhuIVo/ErCHsLmhCxvjVChJ8FXV5UGcmLSrqpqc1ZNasWebaUitI4EIdkIjMWSRvsVLm7yKVasiejWtl6chBEluyrJw9dkTev72G83hcNtM++Z8sGTlI+v+6xrQw8EUF4cxRWaVAmUpydNc2yZort7G+5CtVzuWY2JLlZOfa5fHeu37OVFOMr2fPnqkfiJIsVAnxAnznEydONJUhMdfZoXKk1bQLszcVTKlkitslpS2oA4Fbb73V1Ieg5LESGNCbZe7cuaY8ul2hsCrqogDj9rMq6rZp0yaoK+piDcFyQxyLWkECFwqRxcPhkCuXL0rNVp2lTH1XN9rQvp2lZqtOUrtNN/M3PZR8gePKJZP9UqJmA6MUFalUUw7v2OpyzJFdWyVXwaLx3rtqyghpdccdqe53pCSfsFRCEqvk5w67sNGjR5u0QXaWBPBZTbtQPqijQY47uzYeobBYMj9RMbmky70PiGS61tshWG9koSCDVofaESNGGIUYuSOoOdQr6jJHNeo1kEpxDjl35WqSc6T4hzdfeUkuVWwsEXkKysWzZ2TdzEmybfUSufeLMZItV27zsJMxIrNkz5NPYkuUMYXDaEyYEp555hmTmYOizWaQmJBLZ09LrdZ3mdcJhB31/ANSstb1UqpOIxMT8teimfLAoMkun3Nk1zbZsWaZfPnmr6mYBSWlhJUS4k0lP3u6GIsgKVtWoSTKCaOQUMYa5YSmXZ07dzauC3+n1vpjfpT0meOTJ0+aADyUX1i+fLlx+SGXoVhRV+UwuEABmD6ijxw6cMDU4ihQtpJRQMo2uCnJ99aJjU6xYrlnzx7p2rWrWZexYFD4bNj0hbI9+zVLR+VbWsmdLw6QBUM/k6kDXpTY4qWl+4ChxlJiZ/WUkRJbsJCJ21PSn7ApVmZV0CMdy2LB95/KzC/eNlHbdzz7tmTOKNKuZIwpoMO0zJgxQ37//XeXz6F6aaNGjYxrhtiJYCI1FQZzFSwip/fv0gqDPpZBdzls3/9tpwwCLr7vvvvOWD3slyrnjSj+9K6o6wtUDkOPnfsOyOj9Io6M3u1rUTvQtVNbJ8Qdq16J+zWWIA6HZM6YQfpW8e04FO+JCJfFnwp6dm1r98Y/5PeJP0qBspWdzyG4HNepdIxsWjTLmSHiDp1DgzXeg2Jk7hUGrfmhwuA397U2FQabPfycs8JgxP+n52bLV1hemrXBY4VBe6S64p0MepJDuwwWjnSY+SU2xw47R9x+WECCFZXD0AGLxOgRIyRb8fJytnzjeDKeEO1Lxvj8xs/nocR7utY845DMm36TK2VuFQmywO1QIeRVPzRjdp92gbx47oyMeelhaf/KxxId42rNsCr5rV633uV5UhpZ/Kk0SRZMsGJVGLQeOa7L45wfe4XBQhWqmeqCFW641ZQ4dq0wmFVy5c1n3q8VBlMmg4nJoSWDK9f+GU8BQQ6xiJB2S9n/YEXlMDQgVu7HH3807pD772xplGcsyonB651Lx0jJVJRsTwysiN6Oo0VsBrm8f7sMGzbMlFNQ0p+IcKnkZ2fKe/2lQuPmJmp73pCP472H45vd84iUzHjOFEsi6M96YB4P5uBTrTAYGDKYlBxyfFTJKvLoo6VM6qBdBnlAoFQ4TQkqh8EPTQ7HjBljAkMpdY51uFTUNRcLFUh/P3hWTl0Rl7gnYkCq5ImUqExpu/9FEbHGscpD/JV9HMXvvdfEXA0dOtSk6AZqAb9QJXhXMS9gx0gAoB0it/f9tV76/jgr0feuP3lVGlYKrvoeSaEVBgNDBr2VQ1NNslJuvzUzTCtUDoMfLHE0j6PwHd1m7QoxLhFKsZfOfEEGfv2ttO98l5QpUdxkwaTnemqNg4qscxYtlj83bpI+Dz4QbxzU0rnXTREJ5o1msBHSSggpkHYN+MSBvfLLgJek91djJXNk4imMqankF6hohUH/y2By5DAUZRBUDoMbWgDghqUWTbt27RLMDDQ3+ssXJVtGZNh/nn/GkdkRJxkunE1wHCQZoIjgWkIRufvuu10a4ylpR0grIdRgsLN38zo5c+ywfNG9mUv1PnLEl4/9Tt5cvtfEPVj4qpJfoKIVBtNfBpMrh6Eug6ByGDxQo2bq1KkmO5AaHYFe/j85UADwnnvukZ9++kl++OEH6d69u+norKQtEeFUya9MvRvl8bGLXJ4b/9pjEluirDTp1c9FAfFlJb9A5ejBA1ph0A/VJJMjh6Eug1R73b7lb5XDIID6NDNnzpS6desaa1YouaotKDyJO2bkyJHGKtKtWzcpXry4v4cV0oS0EkKFRYKQLHN4ZLbsUqCMa9n1LNFZJWvO6+I9n5pKfoEKFQZZPMiqWLZsmYwbN04unqHCYGfzulYYTHsZTI4chqIMWnJIOXayEajDQ5O6a3KolS4DlUWLFsn8+fNNbZpmzZqFpAJiQbXhHj16mKBbrCIE3RL7oqQNIa2EcKFQhXLu3mvtwJNDair5BWJwJP03WPCpO0HGDz7Q2rVry+uDRsiOmGLmOK0w6HtUBv+DTr40RVy8eLF8++23JtMMOSRQ9Y0hI7XSZYCuHfPmzTPnjEaItAsIlXUxMcj0oRorGzW669Kvyb1vmOIbQr5ianIr6KVVJT9/wCJPEBl+3IMHD0qOHDmML5cS31YaWjjPT3oR7nNM3xurySPpxvjZ6c5MwTKr6F+4z1EgYq8aTUNLijQmB2rcfPbZZybIs1Spax12/cWCBQuMDD711FPJVpwJwt20aZMJwqUvk+JbQtoSkrIKemlTyS89Fw4KCNHYjAuHv+lt07RpU9Prxj2QLNzmxx+E4xzbmzxSUTM6OlqqV69ulA9PnUrDcY4CPVbnl19+MetIq1atpE6dOhKOkPnTvn170xqBTuoUq0SGFd8R8kqIvYKep74d7hX0WNjSqpJfWnL69GnTTZVF4/jx46a2BH53Fn572/dwnR9/Ew5zjMJLV2kUDxQQFBEUX0zZ5cuXT7K4WjjMUTDA7n/y5MnmHLL7D+b2AL6AjVubNm2MIkJmEHJNszzFN4SFEpLcCnrBtFuh8iSLPv+itWPibtu2ralimBzfbSjOT6ARqnOMiwVXCwowHVVjYmKM6R7XX65cuZL1WaE6R8EC3cEpQsZ6gvJILRDlWmwXQf0oImQIYRG54YYbdGp8QMjHhHiCn0wRKGowkAKZ3pX8UgsdVVnwsXxQwpsW7pgIq1SpYiK7fTE/W3bsklHjJsj9vXpKodg8QTU/wUCwyyDj3759u1GA6aXE3xUqVDDxRvj/fVE/gs+cOmO27N5/QHr37BF0cxRscGMlI2Tnzp3SuXNnKVu2bIo+Z+XKlcYFh8UA2UAesMYSh0Zwa3pBFuDcuXPNOIiJO3r0qFOpwkKckjgVZPK3334zmUKNGzeWW265RWUylYSNJcQOCxlVKIOpCBQLBKWSUT6I+YiMjDRmUhZ9lBBfz08k95Dzp3XhTyOCUQaBtFpLASbwkPLWLMQs6tmyZfP5HEU4rkimS+f8WnEzHLh48aKpjUEWHbUxSpYsmeLPIhaNNcpSGFFWuXmTCZWeSgi/adWqVS7PEajPWFCIUqKE8JvIEMIiMmvWLKPgtGzZUhWRVBBkS2D4ceDAAbPb5OJBsy9RooTx05IuxoWgKOkRI/DPP/8Y5YOmZcR24PbD+kami1onggs2NKTpW64ysuioh4GlgEyWokWLpurzsRCghFhGduvf9HZfoPSQzUJsC65rayzILwXXUgPuRjK7CN5lPlu3bu20/pENhnKu14V3qBISgKBsbNiwwSgf7EwwZVLTA6tHqDUzUwKXI0eOGMVj3bp15qZVuHBhkymB2w9LnBKcsIPnvGLxyJcvn6kMiluXkuW+sKpiYUBW9u3b51RArPIA6Q1WCzZwFigG9erV84nVjjWZjSBBvCgid955pykCiQuIjBpN5/UOVUICBC7WXbt2mcUBzZ3dJz7ZJk2amGp9CTWJUhRfwmKK/CGHyCOptSymWD3y58+vkx0CgacEEbO+4H7hZoyVoFevXh5Tp1MCN3oy87CuWLCO+WMNwyKB/FqKCGOg6quvwCWOZWXChAkmKJsH4K5UJcQ7VAnxM+xA2Gmy6GMOxVeJ9o6PnSyD9IYOklxIlvly8ODBZlHBR0ywmhJ6WBV1sbxhgcOXzvnu0KGDCTZNKrXW1yB/3MBQiHggi++//76RQ/zv4Z4ymhpwpxHHACgixPhwXftKAbFbQ1BaCQhFkfWHFcSTNcRXVhA7BLuisK9YscL53LZt28zanlR5BEWVEL/Aorp161az6ONrZ3FFkDF1E/PhT1+iydq4cMH5NzckCKVumUrCFXVZpO0Vdf0BGV64fyxFGCyZtCqsKimDDQ/ri+Um4f9Tpkwxbl5cM76CzyU2BAsB8uRPSy7WkAIFCpj4Ol9aQSxQ3O0KiP15rSeSNGoJSUcoImZlFlBcjJ1CixYtjNmO3UIgQKYDbazdwZyqBD8JVdTlvOP2CwRlEwsg7p/Vq1e73CzZrVP0TEkY5ut8nEMuxTlMB2caKFqbGhQ5evfYqzLwGhsN5po6GL6E4OW4TJmlWMlScu7KVZexpCf83o5de8j+Q4clQ2S0+duX41iyZIn5167cAcq9uxKS2PkJV1QJSQcfLLnyLPqY6NjJWT52gsACTQCxxBAdT56/dbFipfG1uVbxb0Xd3Llze11R1x+wi2YRt2dYMN5Au14CBXrvrD92UVZ7KPBGE8+quSNN0KT9JonFCXcbip0vu8S6jiWPyOaT8caSHuX2489JdpH1x3w+DjKKUO5Y57Fw4+aysmRYR8kg8+b8RIVpGnpYFitLDzBvs+ATBIbZmwqmmCW5oQe6SZmdst0a0rdvX2PSVIKLhCrqIofJrajrD3799VdnnQdcBQ8//HDAj9kfbDt1yZS6/23MUFkxbpgc37/LPJ+vVAVp+uDTUr5RM1PqPt++9bL7j2Xm/CMH3Bx9bfmyxmIvu7/g+09l5hdvS8OuD8odz75txkKfIKrjphXWOKZ/9YHMHTTA5bXseWLlpdmb0mQcxDCx2UThx7pEkPfSZcvl7PnzkrdYKenw6mdSuFJ1c+wLtTxv7D744AN59tlnJVxQS4gPwayJHxDlgx4aWbNmNRc8j2C6iWMNYdEnQJAMnWAau3Ktoi6KB/5/q6IupnYscL6oqJue1hBLCVErSMI3W6vpX858haTFYy9LnqLXinCtmTpafnyyp/QbNU/yl64g+wpUlS6PNkqzm799LBa7N/4hv0/8UQqUrex8DgWF4+gTlBZjcR8Hv/2+r8c7X8/w//EpaTEOUnaxLLF+9u/fX+o0biLdPxsl2XLnlaO7d0hUjv+SDV6ctcHlvf8smSsT3njCBISHE6qEeAkWDXYOmLHtYEjC5GY17cL9QtMuIs7xtQdrai2FhegaSWS5Elj1YzwF+qVnRd30LDZFlg5WRY0FiQ8mfnb71s22YpMWLq+3ePQlWTF+mOxav8rciDmO4+nN42vTv/tY4OK5MzLmpYel/Ssfy7whH7scn1Zj8TSOjJkySY68ntPL02ocZHMVLlJUrn/2I6dV6LpCxVyOcR/TpoUzpHTdxlKoWAkJJ8JSCUlucNDSpUtl9uzZRqno2rWreY7ofRQTlA+KOrFgNmrUyKSi8f9gn59SFSrJY89VkCwRGX0eyKUkXwZRbqnrsHv3bqNgWDUIQrmirgko7NZDLl25auYqOtO14D/lGsQYJNRt+GpcnKyf87NcOn9OilX7rzoox9McsE6+6DQfy5T3+kuFxs2lTP0m8ZSQtBqLp3Ec2bVd3rm1ikRkiZSiVWoZ5Sx3kRJpOo6ff/5Zqt/QVIY901u2r14mMfkKSINOvaVe+7s9Hn/66CH5a/Fs6fT6F2lyfgKZsFJCUhIchEkbBQTwq7PYE4DEgwWRwC5M3ezYgn2B1OCpwJxjYjvobIrFDX7//Xfj+rNX1K1Tp46xerhb6oIRlUPvFDRkyJ0DWzbJ171ukyuXLkqW6GzS46Nhkr+Ua0YR3Ylrx0b5bL3yNJZ1MyfJvr/WS98fZyX6Xl+OxdM4ilatJZ3f/ELyFistZ44dNsrQ1/feLk+MWyzZcuVOszkhLmTL1m3SuPvDcnPvJ2T3hj9k6oAXJSJLFqnV+q54x6+ZOkYis2aXyre08vlYAp2wUULwEz783Msy+1vPQUpz956VRfvPugQqoXSQQ28XclwUZIo0b97cmLuJ+wh2iF/p+9SzMnvmDLl88UK8AKpHqnguFR9uAVTpESznLoPIHAGaRN9boIzwwDJH6jRxO4GQWptaGcSH/uu06RrE5wVYhuxKrEXeEmWk36j5cuHMKdkwd6qMf7WfPDBkiosiwvvo4EwDxbQYy4kDe+WXAS9J76/GSubIxGOQfDkWT3NCUK6dYtXqyIA2dWXNL2Pkhh6PpMk4rI1DoYo1pEW/l83fhSpUk4Pb/pLl44Z5VEJW/zxSatzWwcyXr8cS6ISFEmIFKl11JByk5B6oFHHigIwePdolpQ3YdRKlH+yLvgXpmvUbNpIC1a+XXp+PluxJBFBxWcRsWSrPP/pQ2AVQ+SNYjj4fWDzcoaiYr+s6+FMGcWVqEJ/34MbzRETmLGYTAUUq1ZA9G9fK0pGDpN3LH7kcd9Hc5NJmLHs3rzNWhy+6N3NxD+1Ys0yWj/1O3ly+18Rp+HosCc2JHaxDBcpUkqO7tsV7zZdzkr9AQclXqpzLc/lKlpONc3+Jd+z2Ncvk8I5/pet7g9NkLIFOyP9M90ClxIKU7IFKZ38dKQ5bxUYLsg3wyxcvXlxCgbfffU+y5CkgHV//3PlcUgFUw9+ZJE1uujlFrbDDkZQGy91wdY8sX77c4zEEqFLoLhSUYQ3iSz7EEXmFwyFXLl+remwn0tv3p2AsZerdKI+PXeTy3PjXHpPYEmWlSa9+LgqIL8fizZzgpjq0/R8pUdO1iJgvxwHXN2ooK//61+W5Izu3Sq6C8TsUr5oyQgpXrC4Fy1VJk7EEOiGvhLgHKiUVpAQcX/qGlpLj+C5jCaHQEz0WUEDwxfP/UGHilJ+lUJ0mMuI57wOoNi+eLV0G/qe1K2kTLHcxTzETgEpdGYJOkUMeBEUTqIosBkql3dSgQXzJh0Bm4ojs7oeZn78l5Ro1lVwFCsvFs2dMXMa21Uvk3i/GuLyX90X58CbnPpbIbNmlQJmKLsdkic4qWXNeF+95X47F05xM++R/UuHGWyVXgSJy5tgRmT/kY7l49nQ8l4iv5+SZJ5+U6xs1kvnffSJVm7eVPf+fquxukbpw5rSsnz1VWj31epqNJdAJaSXEPVDJ2yAlOJ27mHRrXD1ecFAoZYrwW3bv2G4eyQ2gyln/1pCai7QiNcFyG0+LPNSuncc5DqW51yC+5MO5J5CZWDYLZGnsK33l9JGDEpU9RgqUrWQUkLINbnJ5b53YaJ/KjqexeIsvx+JpHCcP7pPRLzwk504ck2zX5ZGiVWvLIz/MkOsKFU3TOcFdOmDoaPng9Vdk3uCPjHW59TNvSc3bO7oc9+fMScb2Wb1F+zQbS6AT0kqIe6CSt0FKkFBwUCgJB/ODy6lwpeQHUJ3NkCWsgqcCLVgulORQg/hSBplUBDJbVrYO//ss0eORGBKvquSOTPOxuPPg4CnpMhb3cdjjLNJ7Tvp0aSeOqk0SnBOo16GneaT1WAKZ4HcopyJQKbEgJSs4KNTnh7gETwFUJw9cSwf1FEBVt12PsJgfX+CLYLlQJ6EgPm9kMFzmyBOkcpNJlRx1tH3JmDTpURIoYwmUccQfi8OvYwlkQvrXJhWoZAUpJRQgGOrBQcxP8Rr15MiOlAVQhfr8pHewnCc5DIc5JogvpTIYLnOUEGRQkUlFH5TE4PXOpWOkZBr2awmUsQTKOKyxNIw8LY4rlz0rIg6HeWTOkPZjCVRCWgmxApXsQUoEah3bu1N2rV8tI57t7TFIKVyCg5iflvc8Irs2rDYBVEd2bZO10yeYAKoGnXt7DKCydqDhMD9pIYPJkcNwmWOC+FIig+E0R0nd6Cg73qxwtniyxt8837dK7nS5wQXKWAJlHMRubVw0Uwr8NV+aehhLTOYMErdpidQ89VdYKiAhHxPiHqjkbZBSuAQH8fs63NJQ9n84zHS59D6AyhEW8xNqwXKBCkF87w8ZIR+++ZoG8aUQTPiU+qbSJnFEuKiwEKGgpbcMBcpYAmEcpNLT+6h371ZSNF9Wc027j2Xm3ij5feliub5u7ZDIdksuGRzu1bhCsEbDlxuPJRocZMcKDkqLJk+BBk3PpkybLlsK1ZEMmTJzx0z6TQ6HOOIuS7Xjm6Rl05uDtkFfeqIymDiHDx+WMRMmyenad0iGCC/73TiuisTFSascp6VqBdd4EkUJBOLi4uSrr74yXcitnmOeOHPmjAwcONAo482auQathwOhfZcNsEClQGv3/t1338nfG9ZLvSynvd4ZcFz1q4dlzYplMnz4cHMBKYmjMpgwdJ4ePHiwZLx6RW4rkNnr6zRDhoySf/96mThmlMybN89k2ChKILF27Vqzzt58882JHpc9e3Zp0KCBrFixwtQBCjdC+04bgIFKgQB9SAYNGmQsIffff780rV4+WfNze/3qcs8995gL7Ntvv5Vdu3al19CDFpXB+LvEmTNnmsZ85cuXN3JYo2jeZMlhrzuayy233CKLFy+WESNGyLlz59LyFCqK11BMcOHChVKlShUpUKBAksc3bNhQIiIi5Lfffgu7WQ55d4y7WZw2yas8dDDFV1clT6REZQpdvYzd4oIFC4ygs/DfeeedEhUVleL5wQrCTYQy9jT0q1+/fljEMKSGcJdBYLdndQW+9dZbjRnaLjfJnSOKnU2YMEEyZ84snTp1ksKFC6f7b1IUO8uWLTPd1/v27St58nhuAOrO4sWLZf78+fLoo4/KddddFzYTGlZKiAU/2d/BW+kNu0QW6u3btxvzYOPGjRP8zcmZH3a0c+bMMT1OKleuLG3atDFlxpXECUcZBKxm48aNM/9HYShWzLVPUUrn6OTJk+ZzDxw4YBr71apVKyzmUwk8aKdAjEeFChXkjjvu8Pp9ly5dks8//1xKly5tNojhQlgqIeEGbdJZoHG/0Pk2LRrP4dunB0jOnDmlc+fOJhhLUSxYZvB5szssWrSodOzY0fjCfW0CnzFjhqxevVpq1Kght99+u7GOKEp6ghsGa3O/fv3Mepgcfv/9dyPDjzzyiMTGxko4oEpIiC/8tIGfPn268Uuy80zuRZHcLIexY8eaBn9o8hUrujarUsITdngoqCiq119/vTRt2jRNs6oICPz111+NIoxCHE6mbcX/FmesIDVr1jRdrpNLXFycfPHFF1KwYEEju+GAKiEhClaPadOmmQW5Tp065oIg8Ck9TJHccDZt2mSCrbjhhEK7eSVlHDlyxCimuEtw1eGySw9wy/C958+fl/bt20vZsmXT5XuV8AZL38qVK+Xxxx+XbNmypegz1q5dK1OmTJEHHnhAChUqJKGOKiEhyPHjx80CzA2gdevWUr169XS3wBAjwgVZvHhx4wLyteldCXxQRFlMY2JizK4uvc3LKCCTJk2SLVu2yI033ihNmjRRhVhJ04BrrCBsvpJKy00qgeDrr782VusePf6rDhyqqBISYrDgTpw40VTeY+H3Jj0srdi5c6eJRcESgiuIWAAl9GERJViZDIFKlSoZC0hkpH86g6IQ458n66BMmTLGKhKOVSmVtIEyBbly5TJrHC5AKqRiBbFnHaZUgR83bpwphVCiRAnj5kGWU2pdCWRUCQkREFAConiUK1dO2rVrl+oLwdfpmLiE6tatq1kLIQxp22RhoYBS/ZEYkEDIUvn333+Nco4yhHKOz11RUsPZs2flo48+MhYLio1R9wb3c6NGjXyyng+miF/GjFKyZEljWSb1vFevXiF30tRZHwJgdh45cqRRQDADdunSJSAUEMiRI4f07NnTKB8EyGIeJ1BRCT2oF0MRPAKU2cFhlg4EBQSwgjz44IPGCkKl4D/++MPfQ1KCHOLfUBZOnDhhMlqQ9dy5c5vnfBHTly9fPpPZSP0QMr9Y50MRtYQEEQg3QolGbC3u+/fvN/EfXBDEXpBjHqhgqiRolWwFdqNWER/M9/wOLTIVHLAYsgu00rCRS4Lx2AlyDnG9oXwGIizmKMNkjZHBQBqvFbDNb+I64kaiKEmBsk1vGHdwO999990pTg/fs2eP2VS6Kx2slxQyCzXUEhJEEDXNLm7JkiXmb3Zz/J01a1azywtkBQQoYUx5btLQMDX+9ddf5nluXkOGDDEmcyXwwb32zTffmO6gWLWwbnFjx9qFBSRQFRBA4aCAFHEqf/75p3z//fdmJ4vywbWEHLILVZSkSKhfEfEbqbEAxsXFmevK/TNCtT+SWkKCBASQ/HEyXyzzMjdtKkNSITI90m99BQv+5MmTjRJC/Mo///zj3EH07t3b38NTEgGLFS4XQNkgxsJKv0XJDCYsK+KFCxeMVQcrI1YdridKyStKYuzbt89spuzUrl3bxL6ltkjekSNHTGAq1hbLvUOW2ZNPPhlyJ0UtIUHC5s2bnQoIoIDQr4VdXTApIGAFBxLMZSkgVkyBNsMLbMg0sXZoBB2jgNx3331Bp4AAwalYEMk4wARuLfb8RnajipIYdssEa9pdd91lSiL4okpv3rx5TZ0Q+nHZN2+hiCohAQCL37krV+XExTjzr3tgk5X5YocbATEW+LiDES4oLCF2kyP/X7RoUYrmSEk9Sc0xuzKUYfvzuC5ICw9WKGp29OjReBk+uGrcURkMb9zP/9mz55wKQ58+fUyvGF8SERFhrCrdu3c3FYattT7U5DC4ttAhBt1C1x+7KKs9dAutHRstVXNHSlRERrPIcwOwg+BhTqZPhl1bDhaI+MYX7/6btm7dasycVqVAb+dISTnezjEdmD0xb948qVatmjEXBxsUU/MEdUUo8keKpMpgeJPw+c8rNdp2l2aViku2LGnXo6hMmTImIHXvoSOy8tD5kFsLVQnxE9tOXZJJ20/J5asiJw/tlxmfvSF/L50rVy5ekLzFSkmHVz+TElWqS7uSMTJ16lSX95J+SxYCj2Dtz0JmAuCHR+mwp+1yY6CBkzVHb91WS07s3x3vMxp0ulc6vvSBmaNSMdq5NyVYc3zkgGcZPFGpuizaf1aa5rlWQMkORZqKFCliOuEGa0Vc4j9wCSKHKPqWiR1XE7UZClSpozIYxnhzffy7+WSar0HHMmaVGedzyVs3lQ+5tVADU/0k2OO2nhKMaOdPnZCBXW+R0nUaSf1O90r23Hnl6O4dcl2hopKnaEnBWVFw/5+S7fxxU30SCwE7zkCpv+ALrFx7lJH169eb4j/lGzV1ztGZ40fEYfPRH9z6l3z3SEd5YNBkKVWnkZmjTqWD7+ILFDk8l4QMAnOc/Z8lUilfjCmeRDyFv6qgphWYuw8dOmRik3B1lrv+Fll6MYfKYJiS3Osjrdagbbb7RSiuhaqE+MG09+XGY8YCAjMGviE71/4uD33/S4LvyZxRpG/l3EFpavPFHLkzdcBL8tdvs+SZKb87lbFwmyNfzrE3Mhhuc6wyGN4EyvVxIQzWwuAYZQiBb9EuUJsXzpTClWrIiOd6y1tNK8rArjfL7xN/dHkPx284FpqR0d7MkZ0rly/J2unjpU7bbi7WoHCbI1/OsTcyGG5zrDIY3gTK9bE+DNZCVULS2e1AUJGdY3t3yorxwyRv0VLS+8sxUr9DL5k64EVZ88sYl+NWHT4f9FHQKZ0jO5vmT5MLp09K7TZd470WLnPk6zn2VgbDZY5VBsObQLk+HGGyFmpgajpyPs7hEtUMjqtXjZbdot/L5u9CFarJwW1/yfJxw6RW67ucx/G+C3EOiY4InVgQb+fIzqrJI6Rcw6YSExu/O3C4zJGv59hbGQyXOVYZDG8C5fo4HyZroVpC0pFLcfE10xx580u+UuVcnstXspycPLAn3rEXPbw/HObI4vi+3fLv74ukbrseCR4TDnPk6zlOjgyGwxyrDIY3gXJ9XAqTtVCVkHQkS6b4WmnxGvXkyA7XnilHdm6VXAWLxjs20sP7w2GOLFb/PMpEppdv3DzBY8Jhjnw9x8mRwXCYY5XB8CZQro8sYbIWqhKSjkRnymAKy9hp1P1h2bVhtcz/7hM5smubrJ0+wQQ9Nejs2kOF90UFiVD5eo6A+g1ceJg/MyVQpj5c5sjXc+ytDIbLHKsMhjeBcn1Eh8laqEpIOkIEM5Xt7BStXFN6fPiDrJs5ST7rfKPMG/yRtH7mLal5e0eX4+rERodUbZDkzBH8u2KhnDiwR2q37Z7ge8Nljnw9x97KYLjMscpgeBMo10eGMFkLtU5IOpNU3rc7iFFEkOV9pxadI51jf6MyGN4Eyvm/ECDjSEuCY5QhBIJBad3k6KjtS8YEjUD5Ap0jnWN/ozIY3gTK+Y8KkHGkJWoJCYDeMQlB5TsEqmQQleD1JTpHOsf+RmUwvAmU878tQMaRFqgS4kcwtVHZbpWHroj49KrkiZSoTMGj0aYFOkc6x/5GZTC8CZTzfyFAxuFrVAkJAKhsR2EZ8rpJqyKqOViCitILnSOdY3+jMhjeBMr5dwTIOHyFKiGKoiiKoviF4LPdKIqiKIoSEqgSoiiKoiiKX1AlRFEURVEUv6BKiKIoiqIofkGVEEVRFEVR/IIqIYqiKIqi+AVVQhRFURRF8QuqhCiKoiiK4hdUCVEURVEUxS+oEqIoiqIoil9QJURRFEVRFL+gSoiiKIqiKH5BlRBFURRFUfyCKiGKoiiKovgFVUIURVEURfELqoQoiqIoiuIXVAlRFEVRFMUvqBKiKIqiKIpfUCVEURRFURS/oEqIoiiKoih+QZUQRVEURVHEH/wf6OlB30sJBGsAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "multi_gene_trees = data_utils.load_yeast(n_windows=15)\n", "print(f\"Built {len(multi_gene_trees)} 'multi-gene' trees in BHV(8)\")\n", "print(f\"Example: {multi_gene_trees[0]}\\n\")\n", "count_and_plot_topologies(multi_gene_trees, \"multi-gene\", n_common=5)" ] }, { "cell_type": "markdown", "id": "1d56cf7d", "metadata": {}, "source": [ "## 2. Let's calculate a mean!" ] }, { "cell_type": "markdown", "id": "0d3d87a9", "metadata": {}, "source": [ "First just of the single-gene boys." ] }, { "cell_type": "code", "execution_count": 5, "id": "53421d63", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average distance from mean: 0.0244\n" ] } ], "source": [ "bhv8 = TreeSpace(n_labels=8)\n", "mean_estimator = FrechetMean(\n", " bhv8, sample_method=\"stochastic\", max_iter=10000, epsilon=1e-4\n", ")\n", "mean_estimator = mean_estimator.fit(single_gene_trees)\n", "single_gene_mean = mean_estimator.estimate_\n", "\n", "print(\n", " f\"Average distance from mean: {bhv8.metric.dist(single_gene_trees, single_gene_mean).mean():0.4f}\"\n", ")" ] }, { "cell_type": "markdown", "id": "52bb702f", "metadata": {}, "source": [ "Now the multi-gene boys." ] }, { "cell_type": "code", "execution_count": 6, "id": "fb6225af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average distance from mean: 0.0113\n" ] } ], "source": [ "mean_estimator = FrechetMean(\n", " bhv8, sample_method=\"stochastic\", max_iter=10000, epsilon=1e-4\n", ")\n", "mean_estimator = mean_estimator.fit(multi_gene_trees)\n", "multi_gene_mean = mean_estimator.estimate_\n", "\n", "print(\n", " f\"Average distance from mean: {bhv8.metric.dist(multi_gene_trees, multi_gene_mean).mean():0.4f}\"\n", ")" ] }, { "cell_type": "markdown", "id": "b238262b", "metadata": {}, "source": [ "Are they the same?" ] }, { "cell_type": "code", "execution_count": 7, "id": "c88bfc61", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Single- and multi-gene means are same topology.\n" ] } ], "source": [ "_, axes = plt.subplots(1, 2, figsize=(5, 3))\n", "single_gene_mean.plot(root_id=0, ax=axes[0])\n", "axes[0].set_title(\"single-gene mean\")\n", "multi_gene_mean.plot(root_id=0, ax=axes[1])\n", "axes[1].set_title(\"multi-gene mean\")\n", "plt.suptitle(\n", " f\"Dist. between mean trees: {bhv8.metric.dist(single_gene_mean, multi_gene_mean):0.4f}\"\n", ")\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "if single_gene_mean.topology.topology_key() == multi_gene_mean.topology.topology_key():\n", " print(\"Single- and multi-gene means are same topology.\")\n", "else:\n", " print(\"Single- and multi-gene means are NOT same topology.\")" ] }, { "cell_type": "markdown", "id": "05b9caae", "metadata": {}, "source": [ "## 3. Some visualisation with multi-dimensional scaling (MDS)\n", "\n", "We embed all trees (106 single-gene trees + 15 multi-gene trees + Fréchet single-gene mean + Fréchet multi-gene mean) into two dimensions using metric MDS with the distance matrix. " ] }, { "cell_type": "markdown", "id": "fabed1c8", "metadata": {}, "source": [ "### Distance matrix" ] }, { "cell_type": "code", "execution_count": 8, "id": "f9fa10b1", "metadata": {}, "outputs": [], "source": [ "all_trees = single_gene_trees + multi_gene_trees + [single_gene_mean, multi_gene_mean]\n", "n_single, n_multi, n_all = len(single_gene_trees), len(multi_gene_trees), len(all_trees)\n", "\n", "# dist_matrix = bhv8.metric.dist(all_trees, all_trees)\n", "dist_matrix = gs.zeros((n_all, n_all))\n", "for i, tree in enumerate(all_trees):\n", " dist_matrix[i, :] = bhv8.metric.dist(tree, all_trees)" ] }, { "cell_type": "markdown", "id": "65d5a013", "metadata": {}, "source": [ "### MDS plotting" ] }, { "cell_type": "code", "execution_count": 17, "id": "b4ccfb7a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "coords = MDS(\n", " n_components=2, metric=\"precomputed\", random_state=66, init=\"random\", n_init=1\n", ").fit_transform(dist_matrix)\n", "\n", "single_coords = coords[:n_single]\n", "multi_coords = coords[n_single : n_single + n_multi]\n", "single_mean_coord = coords[-2]\n", "multi_mean_coord = coords[-1]\n", "\n", "fig, ax = plt.subplots(figsize=(7, 6))\n", "\n", "\n", "sc = ax.scatter(\n", " single_coords[:, 0],\n", " single_coords[:, 1],\n", " color=\"lightblue\",\n", " s=35,\n", " label=\"single-gene trees\",\n", ")\n", "ax.scatter(\n", " multi_coords[:, 0],\n", " multi_coords[:, 1],\n", " marker=\"^\",\n", " s=250,\n", " color=\"pink\",\n", " edgecolors=\"k\",\n", " zorder=5,\n", " label=\"multi-gene trees\",\n", ")\n", "ax.scatter(\n", " *single_mean_coord,\n", " marker=\"*\",\n", " s=350,\n", " color=\"blue\",\n", " edgecolors=\"k\",\n", " zorder=6,\n", " label=\"single-gene Fréchet mean\",\n", ")\n", "ax.scatter(\n", " *multi_mean_coord,\n", " marker=\"*\",\n", " s=350,\n", " color=\"magenta\",\n", " edgecolors=\"k\",\n", " zorder=7,\n", " label=\"multi-gene Fréchet mean\",\n", ")\n", "\n", "ax.legend(fontsize=9, loc=\"lower left\")\n", "ax.set_title(\"BHV(8): yeast phylogenetic trees\")\n", "ax.set_xlabel(\"MDS1\")\n", "ax.set_ylabel(\"MDS2\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d8829594", "metadata": {}, "source": [ "## 4. Convergence: dare we do something quantitative\n", "\n", "We will divvy up the basepairs into an increasing number of genes. Then with that increasing information we will build NJ trees and measure the variance of these trees (as the average of squared distance from their Fréchet mean). We will hopefully show that the tree estimate stabilises (decreasing variance) as the number of genes included in the calculation grows." ] }, { "cell_type": "code", "execution_count": null, "id": "f3a4b5c6", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "window_counts = [106, 50, 40, 30, 20, 5, 1]\n", "dists_from_single_mean = []\n", "variances = []\n", "for k in window_counts:\n", " trees = data_utils.load_yeast(n_windows=k)\n", " mean_tree = mean_estimator.fit(trees).estimate_\n", "\n", " dist_from_single_mean = bhv8.metric.dist(single_gene_mean, trees).mean()\n", " dists_from_single_mean.append(dist_from_single_mean)\n", "\n", " variance = bhv8.metric.squared_dist(mean_tree, trees).mean()\n", " variances.append(variance)\n", "\n", "num_genes = [106 / k for k in window_counts]\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))\n", "ax1.plot(num_genes, variances, c=\"blue\")\n", "ax2.plot(num_genes, dists_from_single_mean, c=\"orange\")\n", "\n", "ax1.set_xlabel(\"Number of 'genes' in tree\")\n", "ax2.set_xlabel(\"Number of 'genes' in tree\")\n", "ax1.set_ylabel(\"BHV variance\")\n", "ax2.set_ylabel(\"Dist to single-gene Fréchet mean\")\n", "ax1.set_yscale(\"log\")\n", "ax2.set_yscale(\"log\")\n", "ax1.grid(True)\n", "ax2.grid(True)\n", "plt.suptitle(\"More genes in tree computation converge toward species tree in BHV space\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "bfb1c7ee", "metadata": {}, "source": [ "### References\n", "Rokas, A., Williams, B., King, N. et al. Genome-scale approaches to resolving incongruence in molecular phylogenies. Nature 425, 798–804 (2003). https://doi.org/10.1038/nature02053\n", "\n", "Billera, Louis J., Susan P. Holmes, and Karen Vogtmann. \"Geometry of the space of phylogenetic trees.\" Advances in Applied Mathematics 27.4 (2001): 733-767. https://doi.org/10.1006/aama.2001.0759\n" ] }, { "cell_type": "markdown", "id": "60032d7f", "metadata": {}, "source": [ "### R code\n", "Here is the R code. Put it in an appropriately named file in the notebooks directory and run it by `Rscript save_yeast_fasta.R`.\n", "\n", "```\n", "# Run once to export the Rokas et al. 2003 yeast gene alignments from the\n", "# phangorn R package as a FASTA file.\n", "\n", "# Install phangorn if needed:\n", "# install.packages(\"phangorn\", repos = \"https://cloud.r-project.org\")\n", "library(phangorn)\n", "\n", "data(yeast)\n", "\n", "outdir <- \"../datasets/data/yeast\"\n", "dir.create(outdir, showWarnings = FALSE)\n", "\n", "# single concatenated phyDat\n", "cat(\"Detected: single concatenated phyDat\\n\")\n", "cat(\"Sequences:\", length(yeast), \"\\n\")\n", "cat(\"Total sites:\", attr(yeast, \"nr\"), \"\\n\")\n", "cat(\"Species:\", paste(names(yeast), collapse = \", \"), \"\\n\\n\")\n", "\n", "out_path <- file.path(outdir, \"yeast_concatenated.fasta\")\n", "write.phyDat(yeast, file = out_path, format = \"fasta\")\n", "cat(sprintf(\"Wrote concatenated alignment to %s\\n\", out_path))\n", "```" ] } ], "metadata": { "backends": [ "numpy" ], "kernelspec": { "display_name": "geomstats", "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": "3.14.0" } }, "nbformat": 4, "nbformat_minor": 5 }