diff --git a/MyIA.AI.Notebooks/Probas/Infer/Infer-11-Topic-Models.ipynb b/MyIA.AI.Notebooks/Probas/Infer/Infer-11-Topic-Models.ipynb
index e61bc677ca..b5949f0f73 100644
--- a/MyIA.AI.Notebooks/Probas/Infer/Infer-11-Topic-Models.ipynb
+++ b/MyIA.AI.Notebooks/Probas/Infer/Infer-11-Topic-Models.ipynb
@@ -90,126 +90,23 @@
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-      "text/html": [
-       "<div><div></div><div></div><div><strong>Installed Packages</strong><ul><li><span>Microsoft.ML.Probabilistic, 0.4.2504.701</span></li><li><span>Microsoft.ML.Probabilistic.Compiler, 0.4.2504.701</span></li></ul></div></div>"
-      ]
+      "text/html": "<div><div></div><div><strong>Installing Packages</strong><ul><li><span>Microsoft.ML.Probabilistic</span></li><li><span>Microsoft.ML.Probabilistic.Compiler</span></li></ul></div><div></div></div>"
      },
-     "metadata": {},
-     "output_type": "display_data"
+     "metadata": {}
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Infer.NET pret !\r\n"
-     ]
+     "name": "stdout",
+     "text": "Infer.NET pret !\r\n"
     }
    ],
    "source": [
@@ -269,18 +166,14 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "FactorGraphHelper charge.\r\n"
-     ]
+     "name": "stdout",
+     "text": "FactorGraphHelper charge.\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Graphviz disponible : True\r\n"
-     ]
+     "name": "stdout",
+     "text": "Graphviz disponible : False\r\n"
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    ],
    "source": [
@@ -572,60 +465,44 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "=== Corpus ===\r\n"
-     ]
+     "name": "stdout",
+     "text": "=== Corpus ===\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 1 : sport, equipe, match, sport, match\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 1 : sport, equipe, match, sport, match\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 2 : politique, election, vote, election, politique\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 2 : politique, election, vote, election, politique\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 3 : musique, concert, artiste, concert, musique\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 3 : musique, concert, artiste, concert, musique\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 4 : sport, equipe, politique, election, sport\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 4 : sport, equipe, politique, election, sport\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 5 : musique, concert, sport, equipe, artiste\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 5 : musique, concert, sport, equipe, artiste\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 6 : match, match, equipe, sport, match\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 6 : match, match, equipe, sport, match\r\n"
     },
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-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 7 : match, match, vote, match, election\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 7 : match, match, vote, match, election\r\n"
     }
    ],
    "source": [
@@ -722,25 +599,19 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Variables LDA definies.\r\n"
-     ]
+     "name": "stdout",
+     "text": "Variables LDA definies.\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  Nombre de topics : 3\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Nombre de topics : 3\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  Taille vocabulaire : 9\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Taille vocabulaire : 9\r\n"
     }
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    "source": [
@@ -828,426 +699,324 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Compiling model..."
-     ]
+     "name": "stdout",
+     "text": "Problem with converting DOT to SVG\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "done.\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exception message: \"An error occurred trying to start process 'dot' with working directory 'D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer'. Le fichier spécifié est introuvable.\"\n\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Iterating: \r\n"
-     ]
+     "name": "stdout",
+     "text": "If \"dot\" program is not installed, install Graphviz\nand add a path to \"dot\" to the PATH\n\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "."
-     ]
+     "name": "stdout",
+     "text": "DOT file is saved to \"D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer\\Model_08_29_26_10_14_10_12.gv\"\n\r\n"
     },
     {
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+     "name": "stdout",
+     "text": "Compiling model..."
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
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-     ]
+     "name": "stdout",
+     "text": "done.\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "."
-     ]
+     "name": "stdout",
+     "text": "Iterating: \r\n"
     },
     {
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+     "name": "stdout",
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+     "name": "stdout",
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-      "=== LDA avec Priors Asymétriques ===\r\n"
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-      "  Topic 0 : sport, equipe, match (beta=10)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Topic 0 : sport, equipe, match (beta=10)\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  Topic 1 : match, politique, election, vote (beta=10)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Topic 1 : match, politique, election, vote (beta=10)\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  Topic 2 : musique, concert, artiste (beta=10)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Topic 2 : musique, concert, artiste (beta=10)\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     }
    ],
    "source": [
@@ -1786,180 +1387,249 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "=== Inference LDA Corrigee ===\n",
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "=== Inference LDA Corrigee ===\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Problem with converting DOT to SVG\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 1 : sport, equipe, match, sport, match\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exception message: \"An error occurred trying to start process 'dot' with working directory 'D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer'. Le fichier spécifié est introuvable.\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "If \"dot\" program is not installed, install Graphviz\nand add a path to \"dot\" to the PATH\n\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Theta : Sport=0,718, Politique=0,153, Musique=0,129\r\n"
-     ]
+     "name": "stdout",
+     "text": "DOT file is saved to \"D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer\\Model_08_29_26_10_14_13_33.gv\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Doc 1 : sport, equipe, match, sport, match\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Topic dominant : Sport (72 %)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Theta : Sport=0,718, Politique=0,153, Musique=0,129\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  Topic dominant : Sport (72 %)\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Problem with converting DOT to SVG\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 2 : politique, election, vote, election, politique\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exception message: \"An error occurred trying to start process 'dot' with working directory 'D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer'. Le fichier spécifié est introuvable.\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "If \"dot\" program is not installed, install Graphviz\nand add a path to \"dot\" to the PATH\n\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Theta : Sport=0,129, Politique=0,741, Musique=0,130\r\n"
-     ]
+     "name": "stdout",
+     "text": "DOT file is saved to \"D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer\\Model_08_29_26_10_14_14_04.gv\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Doc 2 : politique, election, vote, election, politique\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Topic dominant : Politique (74 %)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Theta : Sport=0,129, Politique=0,741, Musique=0,130\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  Topic dominant : Politique (74 %)\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Problem with converting DOT to SVG\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 3 : musique, concert, artiste, concert, musique\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exception message: \"An error occurred trying to start process 'dot' with working directory 'D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer'. Le fichier spécifié est introuvable.\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "If \"dot\" program is not installed, install Graphviz\nand add a path to \"dot\" to the PATH\n\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Theta : Sport=0,128, Politique=0,128, Musique=0,744\r\n"
-     ]
+     "name": "stdout",
+     "text": "DOT file is saved to \"D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer\\Model_08_29_26_10_14_15_06.gv\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Doc 3 : musique, concert, artiste, concert, musique\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Topic dominant : Musique (74 %)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Theta : Sport=0,128, Politique=0,128, Musique=0,744\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  Topic dominant : Musique (74 %)\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Problem with converting DOT to SVG\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 4 : sport, equipe, politique, election, sport\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exception message: \"An error occurred trying to start process 'dot' with working directory 'D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer'. Le fichier spécifié est introuvable.\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "If \"dot\" program is not installed, install Graphviz\nand add a path to \"dot\" to the PATH\n\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Theta : Sport=0,508, Politique=0,360, Musique=0,131\r\n"
-     ]
+     "name": "stdout",
+     "text": "DOT file is saved to \"D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer\\Model_08_29_26_10_14_16_34.gv\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Doc 4 : sport, equipe, politique, election, sport\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Topic dominant : Sport (51 %)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Theta : Sport=0,508, Politique=0,360, Musique=0,131\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  Topic dominant : Sport (51 %)\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Problem with converting DOT to SVG\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 5 : musique, concert, sport, equipe, artiste\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exception message: \"An error occurred trying to start process 'dot' with working directory 'D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer'. Le fichier spécifié est introuvable.\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "If \"dot\" program is not installed, install Graphviz\nand add a path to \"dot\" to the PATH\n\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Theta : Sport=0,368, Politique=0,130, Musique=0,502\r\n"
-     ]
+     "name": "stdout",
+     "text": "DOT file is saved to \"D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer\\Model_08_29_26_10_14_18_07.gv\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Doc 5 : musique, concert, sport, equipe, artiste\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Topic dominant : Musique (50 %)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Theta : Sport=0,368, Politique=0,130, Musique=0,502\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  Topic dominant : Musique (50 %)\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Problem with converting DOT to SVG\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 7 : match, match, vote, match, election\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exception message: \"An error occurred trying to start process 'dot' with working directory 'D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer'. Le fichier spécifié est introuvable.\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "If \"dot\" program is not installed, install Graphviz\nand add a path to \"dot\" to the PATH\n\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Theta : Sport=0,226, Politique=0,645, Musique=0,129\r\n"
-     ]
+     "name": "stdout",
+     "text": "DOT file is saved to \"D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\Infer\\Model_08_29_26_10_14_20_53.gv\"\n\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "Doc 7 : match, match, vote, match, election\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "  Topic dominant : Politique (65 %)\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Theta : Sport=0,226, Politique=0,645, Musique=0,129\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  Topic dominant : Politique (65 %)\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     }
    ],
    "source": [
@@ -2086,709 +1756,16 @@
    },
    "outputs": [
     {
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-       "<text xml:space=\"preserve\" text-anchor=\"middle\" x=\"355.88\" y=\"-97.03\" font-family=\"Times New Roman,serif\" font-size=\"8.00\" fill=\"#ffffff\">Discrete</text>\r\n",
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-       "<title>node6&#45;&gt;node7</title>\r\n",
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-       "<title>node8</title>\r\n",
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-       "<text xml:space=\"preserve\" text-anchor=\"middle\" x=\"755.88\" y=\"-97.03\" font-family=\"Times New Roman,serif\" font-size=\"8.00\" fill=\"#ffffff\">Discrete</text>\r\n",
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-       "<text xml:space=\"preserve\" text-anchor=\"middle\" x=\"853.88\" y=\"-95.88\" font-family=\"Times New Roman,serif\" font-size=\"10.00\" fill=\"#0000ff\">topics_0[word_0]</text>\r\n",
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-       "<!-- node12 -->\r\n",
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-       "<title>node12</title>\r\n",
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-       "<text xml:space=\"preserve\" text-anchor=\"middle\" x=\"284.88\" y=\"-177.62\" font-family=\"Times New Roman,serif\" font-size=\"10.00\" fill=\"#0000ff\">phiAsym[topics_1[word_1]]</text>\r\n",
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-       "<text xml:space=\"preserve\" text-anchor=\"middle\" x=\"279.88\" y=\"-97.03\" font-family=\"Times New Roman,serif\" font-size=\"8.00\" fill=\"#ffffff\">Discrete</text>\r\n",
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-       "<!-- node14 -->\r\n",
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-       "<text xml:space=\"preserve\" text-anchor=\"middle\" x=\"554.88\" y=\"-97.03\" font-family=\"Times New Roman,serif\" font-size=\"8.00\" fill=\"#ffffff\">Discrete</text>\r\n",
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-       "<title>node16&#45;&gt;node17</title>\r\n",
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-       "<title>node20&#45;&gt;node21</title>\r\n",
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-      "\r\n"
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+     "text": "\r\nwarning CS1701: En supposant que la référence d'assembly 'Microsoft.AspNetCore.Html.Abstractions, Version=2.3.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60' utilisée par 'Microsoft.DotNet.Interactive' correspond à l'identité 'Microsoft.AspNetCore.Html.Abstractions, Version=10.0.0.0, Culture=neutral, PublicKeyToken=adb9793829ddae60' de 'Microsoft.AspNetCore.Html.Abstractions', il se peut que vous deviez fournir une stratégie runtime\r\n\r\n"
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    "source": [
@@ -2850,186 +1827,498 @@
     "tags": []
    },
    "source": [
-    "## 5. LDA sur Corpus Complet\n",
+    "## 5. LDA sur Corpus Complet\n",
+    "\n",
+    "### Approche simplifiee : comptage par catégorie\n",
+    "\n",
+    "Avant d'utiliser l'inference probabiliste complete, nous pouvons obtenir une première approximation des compositions de topics par **comptage direct des mots** appartenant a chaque catégorie thematique.\n",
+    "\n",
+    "Cette approche exploite la structure connue du vocabulaire :\n",
+    "- Indices 0-2 : mots de **Sport**\n",
+    "- Indices 3-5 : mots de **Politique**\n",
+    "- Indices 6-8 : mots de **Musique**\n",
+    "\n",
+    "> **Limitation** : Cette méthode ne capture pas l'incertitude ni les correlations entre mots, et **echoue sur les mots polysemiques**. Sur le Doc 7, le comptage classe \"match\" en Sport (indice <= 2) alors que le document est politique (vote, election). L'inference probabiliste jointe est necessaire pour resoudre cette ambiguite via la co-occurrence."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "106c17ea",
+   "metadata": {
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+     "status": "completed"
+    },
+    "polyglot_notebook": {
+     "kernelName": "csharp"
+    },
+    "tags": [],
+    "vscode": {
+     "languageId": "csharp"
+    }
+   },
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "=== LDA sur corpus complet ===\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Doc 1 : Sport=1,00, Politique=0,00, Musique=0,00\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Doc 2 : Sport=0,00, Politique=1,00, Musique=0,00\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Doc 3 : Sport=0,00, Politique=0,00, Musique=1,00\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Doc 4 : Sport=0,60, Politique=0,40, Musique=0,00\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Doc 5 : Sport=0,40, Politique=0,00, Musique=0,60\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Doc 6 : Sport=1,00, Politique=0,00, Musique=0,00\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Doc 7 : Sport=0,60, Politique=0,40, Musique=0,00\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "\n(Proportions basees sur les mots observes)\r\n"
+    }
+   ],
+   "source": [
+    "// Inference simplifiee document par document\n",
+    "\n",
+    "Console.WriteLine(\"=== LDA sur corpus complet ===\");\n",
+    "Console.WriteLine();\n",
+    "\n",
+    "// Distribution des mots par topic (initialisation supervisee pour demo)\n",
+    "// Topic 0 : Sport (mots 0, 1, 2)\n",
+    "// Topic 1 : Politique (mots 3, 4, 5)\n",
+    "// Topic 2 : Musique (mots 6, 7, 8)\n",
+    "\n",
+    "for (int d = 0; d < numDocs; d++)\n",
+    "{\n",
+    "    int[] dWords = documents[d];\n",
+    "    int nWords = dWords.Length;\n",
+    "    \n",
+    "    // Comptage simple des mots par categorie\n",
+    "    int countSport = dWords.Count(w => w <= 2);\n",
+    "    int countPolitique = dWords.Count(w => w >= 3 && w <= 5);\n",
+    "    int countMusique = dWords.Count(w => w >= 6);\n",
+    "    double total = countSport + countPolitique + countMusique + 0.001;\n",
+    "    \n",
+    "    Console.WriteLine($\"Doc {d+1} : Sport={countSport/total:F2}, Politique={countPolitique/total:F2}, Musique={countMusique/total:F2}\");\n",
+    "}\n",
+    "\n",
+    "Console.WriteLine(\"\\n(Proportions basees sur les mots observes)\");"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6p8toq74n8h",
+   "metadata": {
+    "papermill": {
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+     "start_time": "2026-06-22T19:17:30.517126",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "source": [
+    "### Analyse des compositions de topics\n",
+    "\n",
+    "**Résultats** : Classification basée sur le comptage — correcte, **sauf sur le mot polysémique**\n",
+    "\n",
+    "| Document | Topics détectés | Observation |\n",
+    "|----------|-----------------|-------------|\n",
+    "| Doc 1, 6 | Sport = 100% | Documents thématiques purs |\n",
+    "| Doc 2 | Politique = 100% | Document thématique pur |\n",
+    "| Doc 7 | **Sport = 60% (erreur)** | **Comptage trompé** par « match » polysémique (doc en réalité politique) |\n",
+    "| Doc 3 | Musique = 100% | Document thématique pur |\n",
+    "| Doc 4 | Sport 60% / Politique 40% | Mélange détecté |\n",
+    "| Doc 5 | Musique 60% / Sport 40% | Mélange détecté |\n",
+    "\n",
+    "**Observations clés** :\n",
+    "\n",
+    "1. **Documents purs** : La séparation du vocabulaire permet une classification triviale — **sauf sur le mot polysémique « match »** (Doc 7), où le comptage se trompe\n",
+    "\n",
+    "2. **Documents mixtes** : Les proportions reflètent directement le comptage (Doc 4 : 3 mots sport, 2 mots politique → 60/40)\n",
+    "\n",
+    "3. **Limitation** : Cette approche de comptage ne capture pas les **co-occurrences** ni les **corrélations sémantiques** entre mots\n",
+    "\n",
+    "**Contraste avec l'inférence LDA** : l'inférence jointe de la section précédente (cellule d'inference à priors asymétriques) récupère correctement le Doc 7 comme **Politique (≈ 65 %)** en exploitant la co-occurrence de « match » avec « vote » et « election » — là où le comptage échoue (Sport 60 %). C'est toute la valeur de l'inférence probabiliste sur un vocabulaire non parfaitement partitionné."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 5bis. Exemple resolu : selectionner le nombre de topics (K)\n",
+    "\n",
+    "Jusqu'ici, `numTopics = 3` et les priors asymetriques `betaAsym` encodaient notre connaissance des trois themes (Sport, Politique, Musique). En pratique, on ne connait **ni K, ni les mots canoniques** des themes : il faut choisir K en comparant des modeles ajustes sur les donnees seules.\n",
+    "\n",
+    "Cette section ajuste une **vraie LDA corpus** : contrairement a la section precedente ou phi restait fixe a son prior, phi est ici **apris** sur l'ensemble des documents (tableaux jagged, pattern canonique Infer.NET), avec un prior neutre par mot. Trois mesures independantes, calculees sur les topics **effectivement appris** (jamais sur `betaAsym`, jamais sur les etiquettes cachees) :\n",
+    "\n",
+    "1. **Coherence UMass documentaire** (Mimno et al. 2011) : les mots dominants d'un topic doivent co-apparaitre dans les memes documents. Proche de 0 = interpretable.\n",
+    "2. **Redondance entre topics** : similarite cosinus maximale entre paires de topics appris. Un K trop grand fabrique des topics quasi identiques.\n",
+    "3. **Log-vraisemblance predictive held-out** : chaque document est coupe en deux (2 mots pour l'ajustement, 3 pour l'evaluation --- limite assumee, documentee a la fin) ; on evalue la probabilite moyenne des mots retenus.\n",
+    "\n",
+    "Chaque K fait donc l'objet de **deux ajustements separes** : un ajustement sur le **corpus complet** (35 mots) pour les mesures de qualite des topics --- coherence et redondance s'estiment sur les topics appris avec toutes les donnees --- et un ajustement sur la **moitie d'apprentissage** pour la mesure predictive, qui exige par construction des mots tenus a l'ecart.\n",
+    "\n",
+    "**Bris de symetrie sans fuite d'information** : VMP est deterministe et, parti d'un prior uniforme, convergerait vers un mode symetrique ou tous les topics sont identiques. On perturbe donc le prior neutre de chaque topic par un **bruit aleatoire reproductible** (`1.0 + 0.1 * Random`) : le bruit ne sait rien des themes, il choisit seulement un point de depart. C'est l'equivalent VMP de l'initialisation aleatoire de NUTS cote PyMC.\n",
+    "\n",
+    "La verite terrain (3 themes) sert **uniquement** de controle final."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "metadata": {},
+   "execution_count": 11,
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Split-half : 14 mots ajustement / 21 mots held-out\r\n"
+    },
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": "Coherence UMass et split-half prets.\r\n"
+    }
+   ],
+   "source": [
+    "// Protocole de selection de K : split-half deterministe + coherence UMass\n",
     "\n",
-    "### Approche simplifiee : comptage par catégorie\n",
+    "// Chaque document (5 mots) est coupe : 2 mots pour l'ajustement, 3 pour l'evaluation\n",
+    "int[][] docsFit = documents.Select(d => d.Take(d.Length / 2).ToArray()).ToArray();\n",
+    "int[][] docsHeld = documents.Select(d => d.Skip(d.Length / 2).ToArray()).ToArray();\n",
     "\n",
-    "Avant d'utiliser l'inference probabiliste complete, nous pouvons obtenir une première approximation des compositions de topics par **comptage direct des mots** appartenant a chaque catégorie thematique.\n",
+    "Console.WriteLine($\"Split-half : {docsFit.Sum(d => d.Length)} mots ajustement / {docsHeld.Sum(d => d.Length)} mots held-out\");\n",
     "\n",
-    "Cette approche exploite la structure connue du vocabulaire :\n",
-    "- Indices 0-2 : mots de **Sport**\n",
-    "- Indices 3-5 : mots de **Politique**\n",
-    "- Indices 6-8 : mots de **Musique**\n",
+    "// Ensembles de mots par document (pour la coherence UMass, calculee sur le corpus complet)\n",
+    "HashSet<int>[] ensemblesDocs = documents.Select(d => new HashSet<int>(d)).ToArray();\n",
     "\n",
-    "> **Limitation** : Cette méthode ne capture pas l'incertitude ni les correlations entre mots, et **echoue sur les mots polysemiques**. Sur le Doc 7, le comptage classe \"match\" en Sport (indice <= 2) alors que le document est politique (vote, election). L'inference probabiliste jointe est necessaire pour resoudre cette ambiguite via la co-occurrence."
+    "double FreqDoc(int w) => ensemblesDocs.Count(s => s.Contains(w));\n",
+    "double CoFreq(int w1, int w2) => ensemblesDocs.Count(s => s.Contains(w1) && s.Contains(w2));\n",
+    "\n",
+    "double CoherenceUMass(double[][] phiEstime, int topN = 5)\n",
+    "{\n",
+    "    double total = 0.0;\n",
+    "    foreach (double[] ligne in phiEstime)\n",
+    "    {\n",
+    "        int[] dominants = ligne\n",
+    "            .Select((p, w) => (p, w))\n",
+    "            .OrderByDescending(x => x.p)\n",
+    "            .Take(topN)\n",
+    "            .Select(x => x.w)\n",
+    "            .ToArray();\n",
+    "        for (int i = 0; i < dominants.Length; i++)\n",
+    "            for (int j = 0; j < dominants.Length; j++)\n",
+    "                if (i != j)\n",
+    "                    total += Math.Log((CoFreq(dominants[i], dominants[j]) + 1) / (FreqDoc(dominants[i]) + 1));\n",
+    "    }\n",
+    "    return total / phiEstime.Length;\n",
+    "}\n",
+    "\n",
+    "Console.WriteLine(\"Coherence UMass et split-half prets.\");"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
-   "id": "106c17ea",
-   "metadata": {
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-    },
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-    },
-    "tags": [],
-    "vscode": {
-     "languageId": "csharp"
-    }
-   },
+   "metadata": {},
+   "execution_count": 12,
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "=== LDA sur corpus complet ===\r\n"
-     ]
+     "name": "stdout",
+     "text": "K=2 : coherence UMass=-9,77, redondance=0,538, log-prob/mot held-out=-2,186\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "K=3 : coherence UMass=-11,20, redondance=0,614, log-prob/mot held-out=-2,161\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "K=4 : coherence UMass=-11,65, redondance=0,867, log-prob/mot held-out=-2,121\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 1 : Sport=1,00, Politique=0,00, Musique=0,00\r\n"
-     ]
+     "name": "stdout",
+     "text": "K=5 : coherence UMass=-13,18, redondance=0,882, log-prob/mot held-out=-2,126\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "K=6 : coherence UMass=-12,88, redondance=0,999, log-prob/mot held-out=-2,137\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 2 : Sport=0,00, Politique=1,00, Musique=0,00\r\n"
-     ]
+     "name": "stdout",
+     "text": "\nSynthese de la selection de K :\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  K    UMass  redondance  held-out/mot\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 3 : Sport=0,00, Politique=0,00, Musique=1,00\r\n"
-     ]
+     "name": "stdout",
+     "text": "----------------------------------------\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  2    -9,77       0,538        -2,186\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 4 : Sport=0,60, Politique=0,40, Musique=0,00\r\n"
-     ]
+     "name": "stdout",
+     "text": "  3   -11,20       0,614        -2,161\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  4   -11,65       0,867        -2,121\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 5 : Sport=0,40, Politique=0,00, Musique=0,60\r\n"
-     ]
+     "name": "stdout",
+     "text": "  5   -13,18       0,882        -2,126\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "  6   -12,88       0,999        -2,137\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 6 : Sport=1,00, Politique=0,00, Musique=0,00\r\n"
-     ]
+     "name": "stdout",
+     "text": "\nK=2 : topic 0 = musique, concert, artiste, equipe | topic 1 = match, sport, election, equipe\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "\nK=3 : topic 0 = match, sport, equipe, vote | topic 1 = concert, musique, artiste, equipe | topic 2 = election, politique, sport, vote\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "Doc 7 : Sport=0,60, Politique=0,40, Musique=0,00\r\n"
-     ]
+     "name": "stdout",
+     "text": "\nK=4 : topic 0 = election, politique, vote, sport | topic 1 = concert, musique, artiste, equipe | topic 2 = sport, election, vote, equipe | topic 3 = match, sport, equipe, election\r\n"
     },
     {
+     "output_type": "stream",
      "name": "stdout",
+     "text": "\nK=5 : topic 0 = election, politique, vote, sport | topic 1 = sport, equipe, politique, election | topic 2 = concert, musique, artiste, equipe | topic 3 = match, sport, equipe, concert | topic 4 = match, vote, election, sport\r\n"
+    },
+    {
      "output_type": "stream",
-     "text": [
-      "\n",
-      "(Proportions basees sur les mots observes)\r\n"
-     ]
+     "name": "stdout",
+     "text": "\nK=6 : topic 0 = match, sport, equipe, vote | topic 1 = election, equipe, match, sport | topic 2 = sport, equipe, politique, election | topic 3 = election, politique, vote, equipe | topic 4 = equipe, election, sport, match | topic 5 = concert, musique, artiste, equipe\r\n"
     }
    ],
    "source": [
-    "// Inference simplifiee document par document\n",
+    "// Ajustement reel des LDA concurrentes : K = 2..6, phi APPRIS, moteur VMP\n",
+    "// Deux ajustements par K : corpus complet (qualite des topics) + moitie 1 (predictif)\n",
     "\n",
-    "Console.WriteLine(\"=== LDA sur corpus complet ===\");\n",
-    "Console.WriteLine();\n",
+    "(double[][] phi, double[][] theta) AjusterLDA(int K, int[][] docs, double[][] beta)\n",
+    "{\n",
+    "    Range topicR = new Range(K).Named($\"topic{K}_{docs.Length}\");\n",
+    "    Range docR = new Range(docs.Length).Named($\"doc{K}_{docs.Length}\");\n",
+    "    Range wordR = new Range(docs[0].Length).Named($\"word{K}_{docs.Length}\");\n",
     "\n",
-    "// Distribution des mots par topic (initialisation supervisee pour demo)\n",
-    "// Topic 0 : Sport (mots 0, 1, 2)\n",
-    "// Topic 1 : Politique (mots 3, 4, 5)\n",
-    "// Topic 2 : Musique (mots 6, 7, 8)\n",
+    "    VariableArray<Vector> phiVar = Variable.Array<Vector>(topicR).Named($\"phiSel{K}_{docs.Length}\");\n",
+    "    for (int k = 0; k < K; k++)\n",
+    "        phiVar[k] = Variable.Dirichlet(beta[k]);\n",
     "\n",
-    "for (int d = 0; d < numDocs; d++)\n",
+    "    VariableArray<Vector> thetaVar = Variable.Array<Vector>(docR).Named($\"thetaSel{K}_{docs.Length}\");\n",
+    "    thetaVar[docR] = Variable.DirichletSymmetric(K, 0.5).ForEach(docR);\n",
+    "\n",
+    "    var zAssign = Variable.Array(Variable.Array<int>(wordR), docR).Named($\"zSel{K}_{docs.Length}\");\n",
+    "    var wObs = Variable.Array(Variable.Array<int>(wordR), docR).Named($\"wSel{K}_{docs.Length}\");\n",
+    "\n",
+    "    using (Variable.ForEach(docR))\n",
+    "    {\n",
+    "        zAssign[docR].SetValueRange(topicR);\n",
+    "        using (Variable.ForEach(wordR))\n",
+    "        {\n",
+    "            zAssign[docR][wordR] = Variable.Discrete(thetaVar[docR]);\n",
+    "            using (Variable.Switch(zAssign[docR][wordR]))\n",
+    "                wObs[docR][wordR] = Variable.Discrete(phiVar[zAssign[docR][wordR]]);\n",
+    "        }\n",
+    "    }\n",
+    "    wObs.ObservedValue = docs;\n",
+    "\n",
+    "    var moteur = new InferenceEngine(new VariationalMessagePassing());\n",
+    "    moteur.Compiler.CompilerChoice = CompilerChoice.Roslyn;\n",
+    "    moteur.NumberOfIterations = 50;\n",
+    "    moteur.ShowProgress = false;\n",
+    "\n",
+    "    Dirichlet[] phiPost = moteur.Infer<Dirichlet[]>(phiVar);\n",
+    "    Dirichlet[] thetaPost = moteur.Infer<Dirichlet[]>(thetaVar);\n",
+    "\n",
+    "    double[][] phiM = new double[K][];\n",
+    "    for (int k = 0; k < K; k++)\n",
+    "    {\n",
+    "        Vector m = phiPost[k].GetMean();\n",
+    "        phiM[k] = new double[vocabSize];\n",
+    "        for (int w = 0; w < vocabSize; w++) phiM[k][w] = m[w];\n",
+    "    }\n",
+    "    double[][] thetaM = new double[docs.Length][];\n",
+    "    for (int d = 0; d < docs.Length; d++)\n",
+    "    {\n",
+    "        Vector m = thetaPost[d].GetMean();\n",
+    "        thetaM[d] = new double[K];\n",
+    "        for (int k = 0; k < K; k++) thetaM[d][k] = m[k];\n",
+    "    }\n",
+    "    return (phiM, thetaM);\n",
+    "}\n",
+    "\n",
+    "int[] grilleK = { 2, 3, 4, 5, 6 };\n",
+    "var resultatsK = new List<(int K, double coherence, double redondance, double heldout)>();\n",
+    "var phiParK = new Dictionary<int, double[][]>();\n",
+    "\n",
+    "foreach (int K in grilleK)\n",
     "{\n",
-    "    int[] dWords = documents[d];\n",
-    "    int nWords = dWords.Length;\n",
-    "    \n",
-    "    // Comptage simple des mots par categorie\n",
-    "    int countSport = dWords.Count(w => w <= 2);\n",
-    "    int countPolitique = dWords.Count(w => w >= 3 && w <= 5);\n",
-    "    int countMusique = dWords.Count(w => w >= 6);\n",
-    "    double total = countSport + countPolitique + countMusique + 0.001;\n",
-    "    \n",
-    "    Console.WriteLine($\"Doc {d+1} : Sport={countSport/total:F2}, Politique={countPolitique/total:F2}, Musique={countMusique/total:F2}\");\n",
+    "    // Prior neutre + jitter aleatoire reproductible (bris de symetrie sans fuite)\n",
+    "    var rng = new Random(1000 + K);\n",
+    "    double[][] betaNeutre = new double[K][];\n",
+    "    for (int k = 0; k < K; k++)\n",
+    "    {\n",
+    "        betaNeutre[k] = new double[vocabSize];\n",
+    "        for (int w = 0; w < vocabSize; w++)\n",
+    "            betaNeutre[k][w] = 1.0 + 0.1 * rng.NextDouble();\n",
+    "    }\n",
+    "\n",
+    "    // Ajustement A : corpus complet -> topics appris pour coherence/redondance\n",
+    "    var (phiPlein, _) = AjusterLDA(K, documents, betaNeutre);\n",
+    "    phiParK[K] = phiPlein;\n",
+    "\n",
+    "    // Ajustement B : moitie 1 -> parametres pour la mesure predictive held-out\n",
+    "    var (phiDemi, thetaDemi) = AjusterLDA(K, docsFit, betaNeutre);\n",
+    "\n",
+    "    // Mesure 1 : coherence UMass sur les topics appris (corpus complet)\n",
+    "    double coherence = CoherenceUMass(phiPlein, topN: 5);\n",
+    "\n",
+    "    // Mesure 2 : redondance = similarite cosinus max entre paires de topics\n",
+    "    double redondance = 0.0;\n",
+    "    for (int a = 0; a < K; a++)\n",
+    "        for (int b = 0; b < K; b++)\n",
+    "        {\n",
+    "            if (a == b) continue;\n",
+    "            double ps = 0, na = 0, nb = 0;\n",
+    "            for (int w = 0; w < vocabSize; w++)\n",
+    "            {\n",
+    "                ps += phiPlein[a][w] * phiPlein[b][w];\n",
+    "                na += phiPlein[a][w] * phiPlein[a][w];\n",
+    "                nb += phiPlein[b][w] * phiPlein[b][w];\n",
+    "            }\n",
+    "            double cos = ps / (Math.Sqrt(na) * Math.Sqrt(nb) + 1e-12);\n",
+    "            if (cos > redondance) redondance = cos;\n",
+    "        }\n",
+    "\n",
+    "    // Mesure 3 : log-probabilite moyenne par mot held-out (ajustement B uniquement)\n",
+    "    double logLl = 0.0;\n",
+    "    int nMotsHeld = 0;\n",
+    "    for (int d = 0; d < numDocs; d++)\n",
+    "        foreach (int w in docsHeld[d])\n",
+    "        {\n",
+    "            double p = 0.0;\n",
+    "            for (int k = 0; k < K; k++) p += thetaDemi[d][k] * phiDemi[k][w];\n",
+    "            logLl += Math.Log(p + 1e-12);\n",
+    "            nMotsHeld++;\n",
+    "        }\n",
+    "    double heldoutParMot = logLl / nMotsHeld;\n",
+    "\n",
+    "    resultatsK.Add((K, coherence, redondance, heldoutParMot));\n",
+    "    Console.WriteLine($\"K={K} : coherence UMass={coherence:F2}, redondance={redondance:F3}, log-prob/mot held-out={heldoutParMot:F3}\");\n",
     "}\n",
     "\n",
-    "Console.WriteLine(\"\\n(Proportions basees sur les mots observes)\");"
+    "Console.WriteLine(\"\\nSynthese de la selection de K :\");\n",
+    "Console.WriteLine(\"  K    UMass  redondance  held-out/mot\");\n",
+    "Console.WriteLine(new string('-', 40));\n",
+    "foreach (var r in resultatsK)\n",
+    "    Console.WriteLine($\"{r.K,3} {r.coherence,8:F2} {r.redondance,11:F3} {r.heldout,13:F3}\");\n",
+    "\n",
+    "// Mots dominants par topic pour chaque K (les topics APPRIS)\n",
+    "foreach (int K in grilleK)\n",
+    "{\n",
+    "    var lignes = phiParK[K].Select(ligne =>\n",
+    "    {\n",
+    "        int[] dom = ligne.Select((p, w) => (p, w)).OrderByDescending(x => x.p).Take(4)\n",
+    "                         .Select(x => x.w).ToArray();\n",
+    "        return string.Join(\", \", dom.Select(w => vocabulaire[w]));\n",
+    "    }).ToArray();\n",
+    "    Console.WriteLine($\"\\nK={K} : \" + string.Join(\" | \", lignes.Select((t, k) => $\"topic {k} = {t}\")));\n",
+    "}"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6p8toq74n8h",
-   "metadata": {
-    "papermill": {
-     "duration": 0.013992,
-     "end_time": "2026-06-22T19:17:30.531118",
-     "exception": false,
-     "start_time": "2026-06-22T19:17:30.517126",
-     "status": "completed"
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
-    "### Analyse des compositions de topics\n",
+    "### Interpretation : des metriques qui divergent\n",
     "\n",
-    "**Résultats** : Classification basée sur le comptage — correcte, **sauf sur le mot polysémique**\n",
+    "Aucun K ne domine sur les trois mesures a la fois --- et c'est precisement la lecon :\n",
     "\n",
-    "| Document | Topics détectés | Observation |\n",
-    "|----------|-----------------|-------------|\n",
-    "| Doc 1, 6 | Sport = 100% | Documents thématiques purs |\n",
-    "| Doc 2 | Politique = 100% | Document thématique pur |\n",
-    "| Doc 7 | **Sport = 60% (erreur)** | **Comptage trompé** par « match » polysémique (doc en réalité politique) |\n",
-    "| Doc 3 | Musique = 100% | Document thématique pur |\n",
-    "| Doc 4 | Sport 60% / Politique 40% | Mélange détecté |\n",
-    "| Doc 5 | Musique 60% / Sport 40% | Mélange détecté |\n",
+    "| Mesure | Gagnant | Lecture |\n",
+    "|--------|---------|---------|\n",
+    "| Coherence UMass | **K=2** (-9,77) | Mais K=2 **fusionne Sport et Politique** en un seul topic (top-mots : match, sport, election) |\n",
+    "| Held-out | **K=4** (-2,121) | Ecarts de 0,016-0,065 nat/mot contre K=2..3 : **dans le bruit** pour 21 mots evalues |\n",
+    "| Redondance | condamne K=6 | 0,999 (topics clones) ; deja 0,867 des K=4 |\n",
     "\n",
-    "**Observations clés** :\n",
+    "Quatre enseignements :\n",
     "\n",
-    "1. **Documents purs** : La séparation du vocabulaire permet une classification triviale — **sauf sur le mot polysémique « match »** (Doc 7), où le comptage se trompe\n",
+    "1. **Chaque metrique repond a une question differente.** La coherence prefere les topics larges et peu nombreux (les paires de mots dominants co-occurrent presque toujours) ; la prevision recompense la capacite predictive (plus de topics = plus de parametres = meilleur ajustement, jusqu'au sur-ajustement) ; la redondance detecte les topics clones fabriques par un K trop grand.\n",
     "\n",
-    "2. **Documents mixtes** : Les proportions reflètent directement le comptage (Doc 4 : 3 mots sport, 2 mots politique → 60/40)\n",
+    "2. **Le K=2 est structurant a lire** : les top-mots (match, sport, election) montrent que le modele fusionne Sport et Politique --- c'est le mot polysemique « match » (Doc 7) qui sert de pont entre les deux themes. La granularite K=2 ne raconte pas la meme histoire que K=3 : l'une des deux est un choix editorial, pas une erreur.\n",
     "\n",
-    "3. **Limitation** : Cette approche de comptage ne capture pas les **co-occurrences** ni les **corrélations sémantiques** entre mots\n",
+    "3. **K=3 est le plus interpretable** : un pole musique (concert, musique, artiste), un pole politique (election, politique, vote), un pole sport (match, sport, equipe) --- exactement les trois themes generateurs. C'est aussi la que la lecture humaine et la verite terrain convergent, alors qu'aucune metrique seule ne le designe gagnant.\n",
     "\n",
-    "**Contraste avec l'inférence LDA** : l'inférence jointe de la section précédente (cellule d'inference à priors asymétriques) récupère correctement le Doc 7 comme **Politique (≈ 65 %)** en exploitant la co-occurrence de « match » avec « vote » et « election » — là où le comptage échoue (Sport 60 %). C'est toute la valeur de l'inférence probabiliste sur un vocabulaire non parfaitement partitionné."
+    "4. **Limite documentee** : la mesure predictive n'a que 21 mots a evaluer et s'appuie sur des thetas appris sur 2 mots par document --- ses ecarts entre K=2..5 sont tous dans le bruit. Sur un corpus de demonstration, la selection de K combine donc redondance (qui elimine nettement K=6), coherence et lecture des top-mots ; un corpus reel utiliserait des held-out plus larges.\n",
+    "\n",
+    "**Ces topics viennent de l'inference** (phi appris par VMP, priors neutres + jitter aleatoire reproductible) : ni le comptage par categories connues de la section precedente (qui echouait sur « match »), ni les priors asymetriques `betaAsym` qui codaient les themes dans le prior. La structure emerge ici des seules co-occurrences."
    ]
   },
   {
@@ -3057,7 +2346,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 13,
    "id": "0e5bd4a3",
    "metadata": {
     "dotnet_interactive": {
@@ -3086,171 +2375,125 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "=== Distribution Mots par Topic (phi) ===\r\n"
-     ]
+     "name": "stdout",
+     "text": "=== Distribution Mots par Topic (phi) ===\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Topic 1 (Sport) :\r\n"
-     ]
+     "name": "stdout",
+     "text": "Topic 1 (Sport) :\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  sport        : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  sport        : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  equipe       : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  equipe       : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  match        : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  match        : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Topic 2 (Politique) :\r\n"
-     ]
+     "name": "stdout",
+     "text": "Topic 2 (Politique) :\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  politique    : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  politique    : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  election     : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  election     : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  vote         : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  vote         : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Topic 3 (Musique) :\r\n"
-     ]
+     "name": "stdout",
+     "text": "Topic 3 (Musique) :\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  musique      : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  musique      : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  concert      : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  concert      : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  artiste      : 0,30\r\n"
-     ]
+     "name": "stdout",
+     "text": "  artiste      : 0,30\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "\r\n"
-     ]
+     "name": "stdout",
+     "text": "\r\n"
     },
     {
+     "output_type": "display_data",
      "data": {
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-     "text": [
-      "  [Musique] bloc-diagonal en queue : mots 7-9 (indices 6-8) a 0.30.\r\n"
-     ]
+     "name": "stdout",
+     "text": "  [Musique] bloc-diagonal en queue : mots 7-9 (indices 6-8) a 0.30.\r\n"
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    "source": [
@@ -3390,7 +2633,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 14,
    "id": "85050b23",
    "metadata": {
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@@ -3419,47 +2662,34 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "=== Prediction Nouveau Document ===\r\n"
-     ]
+     "name": "stdout",
+     "text": "=== Prediction Nouveau Document ===\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Mots : sport, equipe, musique, concert, sport\r\n"
-     ]
+     "name": "stdout",
+     "text": "Mots : sport, equipe, musique, concert, sport\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "\n",
-      "Probabilites de topics :\r\n"
-     ]
+     "name": "stdout",
+     "text": "\nProbabilites de topics :\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  Sport        : 0,937\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Sport        : 0,937\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  Politique    : 0,000\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Politique    : 0,000\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "  Musique      : 0,062\r\n"
-     ]
+     "name": "stdout",
+     "text": "  Musique      : 0,062\r\n"
     }
    ],
    "source": [
@@ -3667,7 +2897,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 15,
    "id": "486b86a1",
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@@ -3696,67 +2926,49 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "=== Corpus Etendu (4 topics) ===\r\n"
-     ]
+     "name": "stdout",
+     "text": "=== Corpus Etendu (4 topics) ===\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 1 [Sport   ] : football, basketball, tennis, competition, football\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 1 [Sport   ] : football, basketball, tennis, competition, football\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 2 [Tech    ] : ordinateur, logiciel, internet, application, logiciel\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 2 [Tech    ] : ordinateur, logiciel, internet, application, logiciel\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 3 [Cuisine ] : recette, ingredient, cuisson, gastronomie, ingredient\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 3 [Cuisine ] : recette, ingredient, cuisson, gastronomie, ingredient\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 4 [Voyage  ] : hotel, avion, destination, tourisme, avion\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 4 [Voyage  ] : hotel, avion, destination, tourisme, avion\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 5 [Tech    ] : football, ordinateur, logiciel, basketball, internet\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 5 [Tech    ] : football, ordinateur, logiciel, basketball, internet\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 6 [Voyage  ] : recette, hotel, avion, cuisson, destination\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 6 [Voyage  ] : recette, hotel, avion, cuisson, destination\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 7 [Sport   ] : tennis, competition, football, basketball, tennis\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 7 [Sport   ] : tennis, competition, football, basketball, tennis\r\n"
     },
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Doc 8 [Tech    ] : internet, application, ordinateur, logiciel, application\r\n"
-     ]
+     "name": "stdout",
+     "text": "Doc 8 [Tech    ] : internet, application, ordinateur, logiciel, application\r\n"
     }
    ],
    "source": [
@@ -3967,7 +3179,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 16,
    "id": "39a2f788",
    "metadata": {
     "execution": {
@@ -3987,11 +3199,9 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Exercice a completer\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exercice a completer\r\n"
     }
    ],
    "source": [
@@ -4073,7 +3283,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 17,
    "id": "908106ac",
    "metadata": {
     "execution": {
@@ -4093,11 +3303,9 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Exercice a completer : detection de theme emergent\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exercice a completer : detection de theme emergent\r\n"
     }
    ],
    "source": [
@@ -4184,7 +3392,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 18,
    "id": "4a80aa15",
    "metadata": {
     "execution": {
@@ -4204,11 +3412,9 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Exercice a completer : evaluation de coherence des topics\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exercice a completer : evaluation de coherence des topics\r\n"
     }
    ],
    "source": [
@@ -4303,7 +3509,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 19,
    "id": "54e8a060",
    "metadata": {
     "execution": {
@@ -4323,11 +3529,9 @@
    },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
-     "text": [
-      "Exercice a completer : nombre optimal de topics\r\n"
-     ]
+     "name": "stdout",
+     "text": "Exercice a completer : nombre optimal de topics\r\n"
     }
    ],
    "source": [
@@ -4441,18 +3645,6 @@
    "pygments_lexer": "csharp",
    "version": "13.0"
   },
-  "papermill": {
-   "default_parameters": {},
-   "duration": 15.570591,
-   "end_time": "2026-06-22T19:17:31.951759",
-   "environment_variables": {},
-   "exception": null,
-   "input_path": "Infer-11-Topic-Models.ipynb",
-   "output_path": "Infer-11-Topic-Models.ipynb",
-   "parameters": {},
-   "start_time": "2026-06-22T19:17:16.381168",
-   "version": "2.6.0"
-  },
   "polyglot_notebook": {
    "kernelInfo": {
     "defaultKernelName": "csharp",
@@ -4486,4 +3678,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}
\ No newline at end of file
diff --git a/MyIA.AI.Notebooks/Probas/PyMC/PyMC-11-Topic-Models.ipynb b/MyIA.AI.Notebooks/Probas/PyMC/PyMC-11-Topic-Models.ipynb
index 9f95808fd0..edc08f4697 100644
--- a/MyIA.AI.Notebooks/Probas/PyMC/PyMC-11-Topic-Models.ipynb
+++ b/MyIA.AI.Notebooks/Probas/PyMC/PyMC-11-Topic-Models.ipynb
@@ -1,14 +1,42 @@
 {
  "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "ac9058ae",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-08-29T08:12:56.380293Z",
+     "iopub.status.busy": "2026-08-29T08:12:56.380084Z",
+     "iopub.status.idle": "2026-08-29T08:12:56.383782Z",
+     "shell.execute_reply": "2026-08-29T08:12:56.383293Z"
+    },
+    "papermill": {
+     "duration": 0.011526,
+     "end_time": "2026-08-29T08:12:56.385129",
+     "exception": false,
+     "start_time": "2026-08-29T08:12:56.373603",
+     "status": "completed"
+    },
+    "tags": [
+     "injected-parameters"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "# Parameters\n",
+    "BATCH_MODE = \"true\"\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "a1b2c3d0",
    "metadata": {
     "papermill": {
-     "duration": 0.039883,
-     "end_time": "2026-06-03T00:03:23.553353+00:00",
+     "duration": 0.00367,
+     "end_time": "2026-08-29T08:12:56.392974",
      "exception": false,
-     "start_time": "2026-06-03T00:03:23.513470+00:00",
+     "start_time": "2026-08-29T08:12:56.389304",
      "status": "completed"
     },
     "tags": []
@@ -34,20 +62,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "id": "b2c3d4e1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:51:06.133793Z",
-     "iopub.status.busy": "2026-07-03T15:51:06.132787Z",
-     "iopub.status.idle": "2026-07-03T15:51:08.938282Z",
-     "shell.execute_reply": "2026-07-03T15:51:08.938282Z"
+     "iopub.execute_input": "2026-08-29T08:12:56.402329Z",
+     "iopub.status.busy": "2026-08-29T08:12:56.401860Z",
+     "iopub.status.idle": "2026-08-29T08:12:58.319197Z",
+     "shell.execute_reply": "2026-08-29T08:12:58.318494Z"
     },
     "papermill": {
-     "duration": 7.85928,
-     "end_time": "2026-06-03T00:03:31.437590+00:00",
+     "duration": 1.924036,
+     "end_time": "2026-08-29T08:12:58.320518",
      "exception": false,
-     "start_time": "2026-06-03T00:03:23.578310+00:00",
+     "start_time": "2026-08-29T08:12:56.396482",
      "status": "completed"
     },
     "tags": []
@@ -57,7 +85,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "PyMC version: 5.28.5\n"
+      "PyMC version: 6.0.1\n"
      ]
     }
    ],
@@ -111,10 +139,10 @@
    "id": "c3d4e5f2",
    "metadata": {
     "papermill": {
-     "duration": 0.005402,
-     "end_time": "2026-06-03T00:03:31.448722+00:00",
+     "duration": 0.003584,
+     "end_time": "2026-08-29T08:12:58.328401",
      "exception": false,
-     "start_time": "2026-06-03T00:03:31.443320+00:00",
+     "start_time": "2026-08-29T08:12:58.324817",
      "status": "completed"
     },
     "tags": []
@@ -144,10 +172,10 @@
    "id": "d4e5f6a3",
    "metadata": {
     "papermill": {
-     "duration": 0.005046,
-     "end_time": "2026-06-03T00:03:31.458732+00:00",
+     "duration": 0.003697,
+     "end_time": "2026-08-29T08:12:58.336573",
      "exception": false,
-     "start_time": "2026-06-03T00:03:31.453686+00:00",
+     "start_time": "2026-08-29T08:12:58.332876",
      "status": "completed"
     },
     "tags": []
@@ -200,20 +228,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 3,
    "id": "e5f6a7b4",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:51:08.940737Z",
-     "iopub.status.busy": "2026-07-03T15:51:08.940737Z",
-     "iopub.status.idle": "2026-07-03T15:51:08.948234Z",
-     "shell.execute_reply": "2026-07-03T15:51:08.948234Z"
+     "iopub.execute_input": "2026-08-29T08:12:58.344274Z",
+     "iopub.status.busy": "2026-08-29T08:12:58.343799Z",
+     "iopub.status.idle": "2026-08-29T08:12:58.352946Z",
+     "shell.execute_reply": "2026-08-29T08:12:58.352416Z"
     },
     "papermill": {
-     "duration": 0.027415,
-     "end_time": "2026-06-03T00:03:31.491655+00:00",
+     "duration": 0.014023,
+     "end_time": "2026-08-29T08:12:58.353774",
      "exception": false,
-     "start_time": "2026-06-03T00:03:31.464240+00:00",
+     "start_time": "2026-08-29T08:12:58.339751",
      "status": "completed"
     },
     "tags": []
@@ -286,10 +314,10 @@
    "id": "947a32cc",
    "metadata": {
     "papermill": {
-     "duration": 0.004968,
-     "end_time": "2026-06-03T00:03:31.502738+00:00",
+     "duration": 0.003165,
+     "end_time": "2026-08-29T08:12:58.360271",
      "exception": false,
-     "start_time": "2026-06-03T00:03:31.497770+00:00",
+     "start_time": "2026-08-29T08:12:58.357106",
      "status": "completed"
     },
     "tags": []
@@ -304,20 +332,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "id": "f6a7b8c5",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:51:08.949241Z",
-     "iopub.status.busy": "2026-07-03T15:51:08.949241Z",
-     "iopub.status.idle": "2026-07-03T15:51:08.958246Z",
-     "shell.execute_reply": "2026-07-03T15:51:08.958246Z"
+     "iopub.execute_input": "2026-08-29T08:12:58.368606Z",
+     "iopub.status.busy": "2026-08-29T08:12:58.368261Z",
+     "iopub.status.idle": "2026-08-29T08:12:58.374000Z",
+     "shell.execute_reply": "2026-08-29T08:12:58.373118Z"
     },
     "papermill": {
-     "duration": 0.0164,
-     "end_time": "2026-06-03T00:03:31.524217+00:00",
+     "duration": 0.011148,
+     "end_time": "2026-08-29T08:12:58.374935",
      "exception": false,
-     "start_time": "2026-06-03T00:03:31.507817+00:00",
+     "start_time": "2026-08-29T08:12:58.363787",
      "status": "completed"
     },
     "tags": []
@@ -362,10 +390,10 @@
    "id": "a7b8c9d6",
    "metadata": {
     "papermill": {
-     "duration": 0.00539,
-     "end_time": "2026-06-03T00:03:31.535112+00:00",
+     "duration": 0.003586,
+     "end_time": "2026-08-29T08:12:58.382041",
      "exception": false,
-     "start_time": "2026-06-03T00:03:31.529722+00:00",
+     "start_time": "2026-08-29T08:12:58.378455",
      "status": "completed"
     },
     "tags": []
@@ -380,20 +408,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "id": "b8c9d0e7",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:51:08.958246Z",
-     "iopub.status.busy": "2026-07-03T15:51:08.958246Z",
-     "iopub.status.idle": "2026-07-03T15:52:16.419727Z",
-     "shell.execute_reply": "2026-07-03T15:52:16.419727Z"
+     "iopub.execute_input": "2026-08-29T08:12:58.393126Z",
+     "iopub.status.busy": "2026-08-29T08:12:58.392748Z",
+     "iopub.status.idle": "2026-08-29T08:13:19.161786Z",
+     "shell.execute_reply": "2026-08-29T08:13:19.161020Z"
     },
     "papermill": {
-     "duration": 142.090709,
-     "end_time": "2026-06-03T00:05:53.631286+00:00",
+     "duration": 20.777186,
+     "end_time": "2026-08-29T08:13:19.163360",
      "exception": false,
-     "start_time": "2026-06-03T00:03:31.540577+00:00",
+     "start_time": "2026-08-29T08:12:58.386174",
      "status": "completed"
     },
     "tags": []
@@ -423,7 +451,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "78db0471937f42be8f0570875e6900e3",
+       "model_id": "7a04eb2190fa4d71a8085713b5a12d49",
        "version_major": 2,
        "version_minor": 0
       },
@@ -448,7 +476,21 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 30 seconds.\n"
+      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 17 seconds.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n"
      ]
     },
     {
@@ -490,10 +532,10 @@
    "id": "933dc3c8",
    "metadata": {
     "papermill": {
-     "duration": 0.005324,
-     "end_time": "2026-06-03T00:05:53.643230+00:00",
+     "duration": 0.004438,
+     "end_time": "2026-08-29T08:13:19.172772",
      "exception": false,
-     "start_time": "2026-06-03T00:05:53.637906+00:00",
+     "start_time": "2026-08-29T08:13:19.168334",
      "status": "completed"
     },
     "tags": []
@@ -508,20 +550,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "id": "c9d0e1f8",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:52:16.612808Z",
-     "iopub.status.busy": "2026-07-03T15:52:16.612808Z",
-     "iopub.status.idle": "2026-07-03T15:52:16.618793Z",
-     "shell.execute_reply": "2026-07-03T15:52:16.618793Z"
+     "iopub.execute_input": "2026-08-29T08:13:19.386630Z",
+     "iopub.status.busy": "2026-08-29T08:13:19.386329Z",
+     "iopub.status.idle": "2026-08-29T08:13:19.393606Z",
+     "shell.execute_reply": "2026-08-29T08:13:19.392876Z"
     },
     "papermill": {
-     "duration": 0.021439,
-     "end_time": "2026-06-03T00:05:53.670396+00:00",
+     "duration": 0.217788,
+     "end_time": "2026-08-29T08:13:19.394621",
      "exception": false,
-     "start_time": "2026-06-03T00:05:53.648957+00:00",
+     "start_time": "2026-08-29T08:13:19.176833",
      "status": "completed"
     },
     "tags": []
@@ -534,16 +576,16 @@
       "Resultats LDA avec priors symetriques :\n",
       "(Attendu : distributions degenerees / uniformes)\n",
       "\n",
-      "  Sujet 0 : atome (0.151), recette (0.145), four (0.125), ingredient (0.109)\n",
-      "  Sujet 1 : recette (0.150), atome (0.144), four (0.126), ingredient (0.112)\n",
-      "  Sujet 2 : recette (0.150), atome (0.145), four (0.124), ingredient (0.113)\n",
+      "  Sujet 0 : atome (0.148), recette (0.146), four (0.124), ingredient (0.112)\n",
+      "  Sujet 1 : atome (0.148), recette (0.144), four (0.126), ballon (0.109)\n",
+      "  Sujet 2 : recette (0.151), atome (0.147), four (0.124), ingredient (0.114)\n",
       "\n",
       "Proportions theta (document-sujet) :\n",
-      "  Doc 0 : [0.346 0.327 0.327]\n",
-      "  Doc 1 : [0.335 0.336 0.329]\n",
-      "  Doc 2 : [0.327 0.334 0.339]\n",
-      "  Doc 3 : [0.333 0.335 0.332]\n",
-      "  Doc 4 : [0.329 0.338 0.332]\n",
+      "  Doc 0 : [0.338 0.331 0.331]\n",
+      "  Doc 1 : [0.331 0.346 0.322]\n",
+      "  Doc 2 : [0.335 0.322 0.343]\n",
+      "  Doc 3 : [0.333 0.334 0.334]\n",
+      "  Doc 4 : [0.334 0.33  0.336]\n",
       "\n",
       "Probleme : les sujets ne sont pas differencies (symetrie non brisee).\n",
       "C'est le meme probleme qu'en Infer.NET avec des priors symetriques.\n"
@@ -578,10 +620,10 @@
    "id": "5ed3ea4b",
    "metadata": {
     "papermill": {
-     "duration": 0.005146,
-     "end_time": "2026-06-03T00:05:53.681141+00:00",
+     "duration": 0.004177,
+     "end_time": "2026-08-29T08:13:19.402547",
      "exception": false,
-     "start_time": "2026-06-03T00:05:53.675995+00:00",
+     "start_time": "2026-08-29T08:13:19.398370",
      "status": "completed"
     },
     "tags": []
@@ -600,20 +642,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "id": "adf10941",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:52:16.620796Z",
-     "iopub.status.busy": "2026-07-03T15:52:16.620796Z",
-     "iopub.status.idle": "2026-07-03T15:52:16.626987Z",
-     "shell.execute_reply": "2026-07-03T15:52:16.626987Z"
+     "iopub.execute_input": "2026-08-29T08:13:19.411148Z",
+     "iopub.status.busy": "2026-08-29T08:13:19.410834Z",
+     "iopub.status.idle": "2026-08-29T08:13:19.415280Z",
+     "shell.execute_reply": "2026-08-29T08:13:19.414522Z"
     },
     "papermill": {
-     "duration": 0.013703,
-     "end_time": "2026-06-03T00:05:53.701427+00:00",
+     "duration": 0.009712,
+     "end_time": "2026-08-29T08:13:19.416114",
      "exception": false,
-     "start_time": "2026-06-03T00:05:53.687724+00:00",
+     "start_time": "2026-08-29T08:13:19.406402",
      "status": "completed"
     },
     "tags": []
@@ -644,10 +686,10 @@
    "id": "d0e1f2a9",
    "metadata": {
     "papermill": {
-     "duration": 0.008252,
-     "end_time": "2026-06-03T00:05:53.715981+00:00",
+     "duration": 0.004222,
+     "end_time": "2026-08-29T08:13:19.425089",
      "exception": false,
-     "start_time": "2026-06-03T00:05:53.707729+00:00",
+     "start_time": "2026-08-29T08:13:19.420867",
      "status": "completed"
     },
     "tags": []
@@ -664,20 +706,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "id": "e1f2a3b0",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:52:16.628991Z",
-     "iopub.status.busy": "2026-07-03T15:52:16.628991Z",
-     "iopub.status.idle": "2026-07-03T15:52:16.633993Z",
-     "shell.execute_reply": "2026-07-03T15:52:16.633993Z"
+     "iopub.execute_input": "2026-08-29T08:13:19.434798Z",
+     "iopub.status.busy": "2026-08-29T08:13:19.434228Z",
+     "iopub.status.idle": "2026-08-29T08:13:19.440121Z",
+     "shell.execute_reply": "2026-08-29T08:13:19.439349Z"
     },
     "papermill": {
-     "duration": 0.015826,
-     "end_time": "2026-06-03T00:05:53.737415+00:00",
+     "duration": 0.012151,
+     "end_time": "2026-08-29T08:13:19.441085",
      "exception": false,
-     "start_time": "2026-06-03T00:05:53.721589+00:00",
+     "start_time": "2026-08-29T08:13:19.428934",
      "status": "completed"
     },
     "tags": []
@@ -716,10 +758,10 @@
    "id": "7a8c62d1",
    "metadata": {
     "papermill": {
-     "duration": 0.00686,
-     "end_time": "2026-06-03T00:05:53.749883+00:00",
+     "duration": 0.004057,
+     "end_time": "2026-08-29T08:13:19.449332",
      "exception": false,
-     "start_time": "2026-06-03T00:05:53.743023+00:00",
+     "start_time": "2026-08-29T08:13:19.445275",
      "status": "completed"
     },
     "tags": []
@@ -732,20 +774,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "id": "f2a3b4c1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:52:16.636178Z",
-     "iopub.status.busy": "2026-07-03T15:52:16.636178Z",
-     "iopub.status.idle": "2026-07-03T15:53:12.119603Z",
-     "shell.execute_reply": "2026-07-03T15:53:12.119072Z"
+     "iopub.execute_input": "2026-08-29T08:13:19.459010Z",
+     "iopub.status.busy": "2026-08-29T08:13:19.458314Z",
+     "iopub.status.idle": "2026-08-29T08:13:48.299522Z",
+     "shell.execute_reply": "2026-08-29T08:13:48.298866Z"
     },
     "papermill": {
-     "duration": 107.673973,
-     "end_time": "2026-06-03T00:07:41.429697+00:00",
+     "duration": 28.847127,
+     "end_time": "2026-08-29T08:13:48.300346",
      "exception": false,
-     "start_time": "2026-06-03T00:05:53.755724+00:00",
+     "start_time": "2026-08-29T08:13:19.453219",
      "status": "completed"
     },
     "tags": []
@@ -775,7 +817,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "be473910c1ff421aabd93041c9f601b0",
+       "model_id": "ba139dab2320400badd1a6f1590735f8",
        "version_major": 2,
        "version_minor": 0
       },
@@ -800,7 +842,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "Sampling 4 chains for 1_000 tune and 3_000 draw iterations (4_000 + 12_000 draws total) took 44 seconds.\n"
+      "Sampling 4 chains for 1_000 tune and 3_000 draw iterations (4_000 + 12_000 draws total) took 27 seconds.\n"
      ]
     },
     {
@@ -837,10 +879,10 @@
    "id": "9c7e22ff",
    "metadata": {
     "papermill": {
-     "duration": 0.014559,
-     "end_time": "2026-06-03T00:07:41.454337+00:00",
+     "duration": 0.003787,
+     "end_time": "2026-08-29T08:13:48.308379",
      "exception": false,
-     "start_time": "2026-06-03T00:07:41.439778+00:00",
+     "start_time": "2026-08-29T08:13:48.304592",
      "status": "completed"
     },
     "tags": []
@@ -853,20 +895,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "id": "a3b4c5d2",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:53:12.494204Z",
-     "iopub.status.busy": "2026-07-03T15:53:12.494204Z",
-     "iopub.status.idle": "2026-07-03T15:53:12.501497Z",
-     "shell.execute_reply": "2026-07-03T15:53:12.500961Z"
+     "iopub.execute_input": "2026-08-29T08:13:48.602411Z",
+     "iopub.status.busy": "2026-08-29T08:13:48.602129Z",
+     "iopub.status.idle": "2026-08-29T08:13:48.608485Z",
+     "shell.execute_reply": "2026-08-29T08:13:48.607971Z"
     },
     "papermill": {
-     "duration": 0.023681,
-     "end_time": "2026-06-03T00:07:41.490010+00:00",
+     "duration": 0.296826,
+     "end_time": "2026-08-29T08:13:48.609202",
      "exception": false,
-     "start_time": "2026-06-03T00:07:41.466329+00:00",
+     "start_time": "2026-08-29T08:13:48.312376",
      "status": "completed"
     },
     "tags": []
@@ -879,16 +921,16 @@
       "Resultats LDA avec priors asymetriques :\n",
       "(Attendu : sujets bien differencies)\n",
       "\n",
-      "  Sujet 0 (Science) : atome (0.411), experience (0.239), theorie (0.160), match (0.046)\n",
-      "  Sujet 1 (Sport) : ballon (0.328), equipe (0.248), match (0.169), four (0.114)\n",
-      "  Sujet 2 (Cuisine) : recette (0.358), ingredient (0.258), four (0.185), match (0.053)\n",
+      "  Sujet 0 (Science) : atome (0.412), experience (0.239), theorie (0.159), match (0.047)\n",
+      "  Sujet 1 (Sport) : ballon (0.327), equipe (0.249), match (0.168), four (0.114)\n",
+      "  Sujet 2 (Cuisine) : recette (0.359), ingredient (0.258), four (0.185), match (0.052)\n",
       "\n",
       "Proportions theta (document-sujet) :\n",
-      "  Doc 0 : [0.808 0.113 0.079] -> dominant : Science\n",
-      "  Doc 1 : [0.121 0.806 0.073] -> dominant : Sport\n",
-      "  Doc 2 : [0.093 0.087 0.82 ] -> dominant : Cuisine\n",
-      "  Doc 3 : [0.4   0.238 0.362] -> dominant : Science\n",
-      "  Doc 4 : [0.118 0.298 0.584] -> dominant : Cuisine\n"
+      "  Doc 0 : [0.811 0.11  0.079] -> dominant : Science\n",
+      "  Doc 1 : [0.12  0.808 0.072] -> dominant : Sport\n",
+      "  Doc 2 : [0.094 0.088 0.819] -> dominant : Cuisine\n",
+      "  Doc 3 : [0.395 0.24  0.365] -> dominant : Science\n",
+      "  Doc 4 : [0.118 0.299 0.583] -> dominant : Cuisine\n"
      ]
     }
    ],
@@ -918,10 +960,10 @@
    "id": "9eeb0b66",
    "metadata": {
     "papermill": {
-     "duration": 0.007564,
-     "end_time": "2026-06-03T00:07:41.504694+00:00",
+     "duration": 0.003631,
+     "end_time": "2026-08-29T08:13:48.616984",
      "exception": false,
-     "start_time": "2026-06-03T00:07:41.497130+00:00",
+     "start_time": "2026-08-29T08:13:48.613353",
      "status": "completed"
     },
     "tags": []
@@ -945,10 +987,10 @@
    "id": "0e23c2f5",
    "metadata": {
     "papermill": {
-     "duration": 0.008455,
-     "end_time": "2026-06-03T00:07:41.521509+00:00",
+     "duration": 0.00362,
+     "end_time": "2026-08-29T08:13:48.624280",
      "exception": false,
-     "start_time": "2026-06-03T00:07:41.513054+00:00",
+     "start_time": "2026-08-29T08:13:48.620660",
      "status": "completed"
     },
     "tags": []
@@ -968,20 +1010,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "id": "4e2a0393",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:53:12.503344Z",
-     "iopub.status.busy": "2026-07-03T15:53:12.503344Z",
-     "iopub.status.idle": "2026-07-03T15:53:12.506804Z",
-     "shell.execute_reply": "2026-07-03T15:53:12.506804Z"
+     "iopub.execute_input": "2026-08-29T08:13:48.632624Z",
+     "iopub.status.busy": "2026-08-29T08:13:48.632421Z",
+     "iopub.status.idle": "2026-08-29T08:13:48.635149Z",
+     "shell.execute_reply": "2026-08-29T08:13:48.634774Z"
     },
     "papermill": {
-     "duration": 0.016334,
-     "end_time": "2026-06-03T00:07:41.545912+00:00",
+     "duration": 0.007718,
+     "end_time": "2026-08-29T08:13:48.635797",
      "exception": false,
-     "start_time": "2026-06-03T00:07:41.529578+00:00",
+     "start_time": "2026-08-29T08:13:48.628079",
      "status": "completed"
     },
     "tags": []
@@ -1008,20 +1050,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "id": "b4c5d6e3",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:53:12.508860Z",
-     "iopub.status.busy": "2026-07-03T15:53:12.508860Z",
-     "iopub.status.idle": "2026-07-03T15:53:12.938999Z",
-     "shell.execute_reply": "2026-07-03T15:53:12.938999Z"
+     "iopub.execute_input": "2026-08-29T08:13:48.644400Z",
+     "iopub.status.busy": "2026-08-29T08:13:48.644192Z",
+     "iopub.status.idle": "2026-08-29T08:13:48.922676Z",
+     "shell.execute_reply": "2026-08-29T08:13:48.922000Z"
     },
     "papermill": {
-     "duration": 0.734997,
-     "end_time": "2026-06-03T00:07:42.288133+00:00",
+     "duration": 0.284051,
+     "end_time": "2026-08-29T08:13:48.923656",
      "exception": false,
-     "start_time": "2026-06-03T00:07:41.553136+00:00",
+     "start_time": "2026-08-29T08:13:48.639605",
      "status": "completed"
     },
     "tags": []
@@ -1029,7 +1071,7 @@
    "outputs": [
     {
      "data": {
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",
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",
       "text/plain": [
        "<Figure size 1600x500 with 3 Axes>"
       ]
@@ -1059,7 +1101,16 @@
   {
    "cell_type": "markdown",
    "id": "pymc11_phi_viz_interp",
-   "metadata": {},
+   "metadata": {
+    "papermill": {
+     "duration": 0.004239,
+     "end_time": "2026-08-29T08:13:48.932261",
+     "exception": false,
+     "start_time": "2026-08-29T08:13:48.928022",
+     "status": "completed"
+    },
+    "tags": []
+   },
    "source": [
     "**Interprétation — la distribution Phi révèle la contamination inter-sujets.**\n",
     "\n",
@@ -1089,10 +1140,10 @@
    "id": "42ca454f",
    "metadata": {
     "papermill": {
-     "duration": 0.008203,
-     "end_time": "2026-06-03T00:07:42.304178+00:00",
+     "duration": 0.004171,
+     "end_time": "2026-08-29T08:13:48.940385",
      "exception": false,
-     "start_time": "2026-06-03T00:07:42.295975+00:00",
+     "start_time": "2026-08-29T08:13:48.936214",
      "status": "completed"
     },
     "tags": []
@@ -1105,20 +1156,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "id": "c5d6e7f4",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:53:12.938999Z",
-     "iopub.status.busy": "2026-07-03T15:53:12.938999Z",
-     "iopub.status.idle": "2026-07-03T15:53:13.034019Z",
-     "shell.execute_reply": "2026-07-03T15:53:13.034019Z"
+     "iopub.execute_input": "2026-08-29T08:13:48.949343Z",
+     "iopub.status.busy": "2026-08-29T08:13:48.949049Z",
+     "iopub.status.idle": "2026-08-29T08:13:49.034978Z",
+     "shell.execute_reply": "2026-08-29T08:13:49.034456Z"
     },
     "papermill": {
-     "duration": 0.244613,
-     "end_time": "2026-06-03T00:07:42.559309+00:00",
+     "duration": 0.091584,
+     "end_time": "2026-08-29T08:13:49.035839",
      "exception": false,
-     "start_time": "2026-06-03T00:07:42.314696+00:00",
+     "start_time": "2026-08-29T08:13:48.944255",
      "status": "completed"
     },
     "tags": []
@@ -1126,7 +1177,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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rSXofqTwp1yu+up+Y70RPr29i9gnAOxF0A/A6xYsXN4NIaXNV12y3ZkSt511ptiM2HQxHs4FWBkT/1gGIYtN9atCfmB/fnjSf1DImdLz43kNi6Q9MXYYOHWrmk9UBrHQwMB14KLVopk5/pGrGTVsUJOWc6cBUmm3TwMV1m/iaraYlKyOo2UFtmuoJHdBJ66EGjxpEWpLTlFrrjTaZ1Wyoa7Y79kj3ySm3dZz169ebpsWuN1Fi1+nkHkdpgKmDw+miQZRmv3UALc2ca8ButbTQAb1c502O3eIlobqqI7trUHunz+/tntesv5ZLF82e6gBqOphgYoJu/X5yzU7rtdL3aY3kr4Om6QCJ2hrCNROb2JH8E2J9x+jxrebWSluV6AwSOjq567Y//vijKZfrTdDY31d6PvUGid5ISijb7Xq9XCXmennKk+ubWCm1HwAZS/pL/wCAzbT5pmZFpkyZ4rZesz76gyj2D11tkunaD1ibims2WJuqamZDF/1b17k26dQRxhctWmT6XWuz6Tux5upOaNqk2O9BR5jWslm076pO36M/trWPsSe0P7X2eXalwbf+QI49NY7ddIRfPacjR46MkyHSx67NP/WcxTetl5Vxcn299pt1PV8pNWVYcmgmVkd11iDw1KlTcZ63ui/EJ773qH+7ToflKc0ma9A0e/Zs5zoNlLQrR0qV26q/Wt9cp63Sz6SOvJ6Sx3GtK0rrs/azVVa9tvrguk4DaE3vlZgstbYscD1friN2635c62rsz7a+59h1TN+zNrFO7Ocu9rWxzqH1PRZfPdFjasY/ObSVkd501JtyOvuBRUcej/0+9XqfPn3azAJh0euvZdWbLtq/XOlI31pO/ezHZpVfv0u1WXjsaRt1VomU5sn1TSxPvucBZB5kugF4Hc14Pfjgg2bKKQ2SNSOjzTo1aNZpb1wHwlHaN1qDEdcpw5TrD0PNBGuGUQNszVZpX3INFPSHs/bZTAxrsDYtlw4Mp9k9Lav1I82VTp2k087oD2stl2aFNEjQDJMORuRpk3odrEqn8tE5nzW7rD+IdZoj/cGuP4RTk55/PZ9Dhgwx10ebiGuLBH1v2gRXB4vT5sbWOdMf8tofXaf60R/wes50rmHNcut0Uo8++qh5rQYHejNCs6t34umUYcmhQZPWG73JoQOYaXZXb9joDQKd+kszbfHR5sJ6rvRcaGCgwYhe++T0H9Vzrd02dFBBzZjqMTRDqpnH2Fm6pJZb6TXSVhRaj/Ua63XR6xXfTY7kHEcH0NKyayZWu0hoNlQDPZ0yzupPrDfMNAOsg2ppVwSt83PnzjUBpfaZvx2dz1z7jOtgYpo51vekgbTesNH11nzXVl3VFjbaVFmDas1Oax92LZfOQa7fQ1p/dZsdO3bEO2d0fLRu6/gL2k9dz4l2rdABHK1Ms74/K9uv03tp/dcgUoP7+G5kJJZ+P+nnVPep51en5dKy6Gcmdp9u/czq96F+lnbt2mVuDGprFO1rPmnSJGeLI/1e1nOqU21pBl3fk9700SnD9Dn9jrKuq07/pf/q+dUAXFt9pDRPrm9iefI9DyATSevh0wHAU9ZUPjt27Ljtdjr1i07TEx+dXqt///6OwoULOwICAszUQzqVizUtjUWPo9P56FQ3uk2WLFnMNEuu0zZZdu/ebabh0SlwgoODHQ8++KDbNFKJKfuoUaMcRYoUMdPUuE4rE3vKMKXTk+k0Z7ly5TJTmNWuXduxcuVKt22saaZiTwUWe9qdI0eOmKm0SpcubfaVJ08eU36dli2lpwzTad7iOyexp9DR6at0ajW9hrqUL1/eXItDhw45t7ly5YqjY8eO5hzoPqzpw/Q6jhkzxjy2rpmeGz2H8U0xltwpw3TqstisuhPfede6FvtadunSxREaGmrqo9aBFi1aOD777LPbThl24MABR+PGjU2dy5cvn6NXr17OaYpcy57QZyG+6bL0+ug51enudDqrbt26mamRdDudms/Tcifk77//djz11FNmSi89jv5tTV0X+7wn9Tj6fJMmTczUVjqd01133eV49tlnHadOnXLbbteuXY46deo4t5kwYUKipgyzpr4aN26cqfta13Lnzm2mYRs5cqTj4sWLzu0OHjxopg/Uaal0v3pNdKqtQYMGOcLCwsz51mukf0+bNu2O58+6dloH9HtAX6/H7tOnj+PatWtu2y5fvtxRtWpV89nWKQW1vHPnzo3z/hKqy7ejZdWpCvW916xZ07F58+Z4z9OZM2cc3bt3N/VUz7NOAxff50un9NLPh37edbv8+fM7HnnkEXONXKdA69Gjh6k3+r7btWvnOHv2bIJThsX+zkno86Bl1uuYlOsb3+c9oe/uhL7nAWRePvqftA78ASC90syeTskTuyk64E2WLVtmWg3o9Hea7fNWOuCZtnbRbHRaGzFihGlto03sY4/CDQBIX+jTDQAA3PqqurL6WmvzdR3gy5tpc2wCXACAp+jTDQAAnF588UUTeNetW9eMSaB9rXUk+zFjxqT76aTsou9fz4NOv6XTswEA4AmCbgAA4KSDYukgXitXrpTr16+babU0020NYuWNdOAxneNbB1rUAfYAAPAEfboBAAAAALAJfboBAAAAALAJQTcAAAAAADbxuj7dMTEx8tdff0mOHDnMVEAAAAAAAHhKZ9++fPmyFC5cWHx9E85ne13QrQF3sWLF0roYAAAAAIBM4OTJk1K0aNEEn/e6oFsz3NaJ0TlHAQAAAADw1KVLl0xC14oxE+J1QbfVpFwDboJuAAAAAEBy3KnbMgOpAQAAAABgE4JuAAAAAABsQtANAAAAAIBNvK5PNwAAAACkR9HR0XLz5s20Lgb+v4CAAPHz85PkIugGAAAAgDSe7/n06dMSERHBdUhncuXKJaGhoXccLO12CLoBAAAAIA1ZAXeBAgUkODg4WQEeUu5GSGRkpJw9e9Y8LlSoUJL3RdANAAAAAGnYpNwKuPPmzct1SEeyZs1q/tXAW69PUpuaM5AaAAAAAKQRqw+3ZriR/ljXJTl97Qm6AQAAACCN0aQ8814Xgm4AAAAAAGxC0A0AAAAASHXz5883o4NndgykBgAAAADp0OmWDVL1eKErtnj8mnPnzsnw4cPlyy+/lDNnzkju3LklLCzMrKtfv/5tX9u+fXtp3ry5ZHZpmunevHmztGzZUgoXLmzayi9btuyOr9m0aZPcc889kiVLFilTpoy5OwIAAAAASH1t27aVPXv2yAcffCC//vqrLF++XB544AH5+++/EzU6eIECBSSzS9Og++rVq+YuyNSpUxO1/dGjR+XRRx+VBx98UPbu3Sv9+vWTnj17ypo1a2wvKwAAAADgXzrV2ZYtW2TcuHEmRitevLjUrl1bhgwZIo899phzm2effVYKFiwoQUFBUrlyZVm5cmWCzcu/+OILk2TVbUuVKiUjR46UW7duOZ/XZO2cOXOkdevWZmTxu+++2wT6rn7++Wdp0aKF5MyZU3LkyCENGjSQ33//3fm8vr5ChQrmGOXLl5dp06Zl3ubljzzyiFkSa8aMGVKyZEl59913zWM9Ud9++61MnDhRmjZtamNJAQAAAACusmfPbhZtsXzvvfea1siuYmJiTLx3+fJl+eijj6R06dJy4MCBBOe71gC+S5cu8t577zkD5WeeecY8Fx4e7txOA/Hx48fL22+/Le+//7506tRJjh8/Lnny5JE///xT7r//fpNt37Bhgwm8v/vuO2fgvnDhQtP0fcqUKVK9enWTpe/Vq5dky5ZNunbtassFzlB9urdt2yaNGzd2W6fBtma8AQAAAACpx9/f32SrNWjVBKlmqBs2bChPPvmkVK1aVb7++mvZvn27/PLLL1K2bFnzGs1eJ0SD6cGDBzuDX9121KhR8sorr7gF3d26dZMOHTqYv8eMGWOCdD1Os2bNTCvqkJAQWbx4sQQEBJhtrGMr3Y8mcdu0aWMea1JXbwTMnDmToFudPn3aNEtwpY8vXbok165dM30CYouKijKLRbcFAAAAAKRMn27tAqxZ6u+//16++uork4XWJtxnz56VokWLugW9t7Nv3z6TlR49erRzXXR0tFy/fl0iIyNNc3KlAb1FM9SazdZjKe2GrFlyK+CO3b1Zs+c9evQwNwosmgXXQN0uGSrTnRRjx441d0wyolozD6d1EeChHc+W4ZzdAfU646Fe3x51OuOhTt8Z9TrjoV5n3DpdMChaBlS4KdEXosQ3VpyYJ5XLcuDc9SS/tki1BtJWl96DZHj/5+S1YcOl+/P95GaMI8H9/nn5psQ4/j3u5StX5IVBQ6Xxo63k7rzuTdW1/7UldkCt/by1KbuKLxFruXLlivl39uzZUqdOHbfnEmry7nXzdIeGhpph6F3pY72zkdDJ1U78Fy9edC4nT55MpdICAAAAgPcpVba8XIuMlLIVq8iZv/6UY7//lqjXVahSzWxbvFRpM1OV6+Lrm7jQVbPgmnW/efNmnOe0lbTOnHXkyJE4+9dm5nbJUJnuunXryqpVq9zWrVu3zqxPiHbmj92hHwAAAACQPBEX/pb+PTtJmw5dpWzFypItew75ed8umTtlojzUrIXUqtdAatS9T/o93UFeGTlO7ipZWo4ePqSpaWnwUJM4+3vu5dfkhc5tpFCRYvJc1ydNoK1Nzn/66Sd58803E1WmPn36mMHVtF+5JmC12bg2e9dR1cuVK2daQb/00ktmvfYB167IO3fulH/++UcGDBiQ+YJuTe8fPnzYbUowbYOvo87ddddd5iTp6HMLFiwwz/fu3duMMqcd6Z9++mkzGt0nn3xiJmIHAAAAAKSe4GzZpeo9tWTBzPfl5LEjcuvWTQktXFSeeKq7PNP3FbPNpLkfyzsjhsig3l3lWuRVE3j3Hzoq3v3d99DDMvWjpTL93TEyd8q7phm5Tuml00QnVt68eU2cOGjQIDOomzYbr1atmtSvX988r/vSvuE68rluo33Cq1SpYuvg3D4Oh8MhaWTTpk1mPrfYdLQ6HQVPR6U7duyY2c71Nf379zcjzGmn/GHDhpntEksHUtO7GtrUXJulp2fpue8J4kd/qjujXmc81Ovbo05nPNTpO6NeZzzU64zepztKChQtLr4BtNC1VMz/bx/utKSDuGlyWJufu/Yr9yS2TNNMt86ddruYXwPv+F6jc6kBAAAAAJDeZaiB1AAAAAAAyEgIugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE387doxAAAAACDpOpx4LVVP38d3jfH4NRfOn5Mp40bJN19/JX+fOys5Q3JLuUpV5LmXh8g9deqJnUqUKCH9+vUzS3pG0A0AAAAASJJ+T3eQmzdvyJj350ix4iXk/Lmz8sOWTRLxzwXbzuiNGzckMDBQMgqCbgAAAACAxy5djJBd338n85etlVr1Gph1hYsVl6r31HJuU6lAVhk2brJsXPOl7Ni6WfIXCJUB4aOlacs2zm1+PfCTjB06UPbt/EGCsgbLwy1aybxpkyV79uzm+W7duklERITUqlVLpk6dKlmyZJHixYvL8ePHpX///mZRDocjXV5F+nQDAAAAADwWnC27WdZ/tVxuREUluN37494wgfTSjdvl0SeelEHPdJHffz1onou8elWead9ScobkkiVrvpUJcxbK999skD59+rjtY/369XLo0CFZt26drFy5UpYuXSpFixaVN954Q06dOmWW9IqgGwAAAADgMX9/fxn93iz5YslCuffuUOn06IMyafRwOfTzfrftmrZsI0907i4lSt8tLw0Ol0rV7pGFc6ab575cukSioqJk7JT/yt0VKsm9DR6Q19+aKB9++KGcOXPGuY9s2bLJnDlzpFKlSmbJkyeP+Pn5SY4cOSQ0NNQs6RVBNwAAAAAgSZq0bC2bfjwiUxZ8Jvc91ER2fLdZ/tO4rvxv8YfObcJq1nF7jT4+8tv/ZbqP/HrQDLwWnC2b8/nqtetKTEyMyWxbqlSpkqH6cbsi6AYAAAAAJFmWoCCp90AjM2L5wlWbpNWTT8nU8aNS9IxmcwnKMxqCbgAAAABAiilVtrxci4x0Pt63a7vb8z/u3C6l7i7v3Fabo2vfbsue7dvE19dXypUrd9vjaOY7Ojo63V85gm4AAAAAgMciLvwt3ds0kxWffmwC5z+OH5M1yz+XuVMmykPNWji3W7tiqSxd9IEc+/03M6f3/j07pWOP3ua5Fm2fNKORv/ZiT/ntl5/lh2+/kTFDBshTTz0lBQsWvOM83Zs3b5Y///xTzp8/n26vIFOGAQAAAAA8piOX6/RgC2a+LyePHZFbt25KaOGi8sRT3eWZvq84t3th0FD56n+fyqhX+0r+gqHy9swPpEy5Cua5rMHBMmvJCjNlWPum9zmnDJsyZfIdj68jlz/77LNSunRpMxhbep0yjKAbAAAAANKhj+8aI+lZYJYs0n/oKLPcToHQQjL705UJPl+2YmWZt3S127rs2YOcf8+fPz/e1917772yb98+Se9oXg4AAAAAgE0IugEAAAAAsAnNywGkqhs1p3HGM5wJaV0AAACQQf189pp4OzLdAAAAAADYhEx3OkZGMCMiIwgAAADgX2S6AQAAAACwCUE3AAAAAAA2IegGAAAAAMAmBN0AAAAAANiEoBsAAAAAkGa2f7dZKhXIKpcuRtxx202bNomPj49ERNx52/SC0csBAAAAIB3quvSPVD3eB22KJul1586cllmTxsnmdavlzOm/JG++/FKucph0eaaP3Hv/g3d8fbVa98qm/UclR86QO25br149OXXqlISE3Hnb9IKgGwAAAACQJH+eOC6dWzwoOUJyycvhY6Rsxcpy6+ZN+XbjOnlzcD9ZuXXfHfcRGBgo+QuGJup4um1oaOK2TS9oXg4AAAAASJJRr/Y1zb0Xr94iTVq2lhKl75Yy5StKt+f6yqKvvjFBuTYd/2X/v8G3NiPXddqsPL7m5X+dPC4tW7aU3LlzS7Zs2aRSpUqyatWqeJuXz58/X3LlyiVr1qyRChUqSPbs2aVZs2YmG+5qzpw55vmgoCApX768TJs2LdWuOJluAAAAAIDHIv65IN9uWCt9XxspwdmyxXk+Z0guuXzxosf7fXNwfwmUW7J582YTdB84cMAE0wmJjIyUd955Rz788EPx9fWVzp07y8CBA2XhwoXmef13+PDhMmXKFKlevbrs2bNHevXqZfbdtWtXsRtBNwAAAADAYyeO/i4Oh0NKlimbomfv1B8npWP7J6RKlSrmcalSpW67/c2bN2XGjBlSunRp87hPnz7yxhtvOJ8PDw+Xd999V9q0aWMelyxZ0gTyM2fOJOgGAAAAAKRTDoctu+3U63kZ9cpLsnbtWmncuLG0bdtWqlatmuD2wcHBzoBbFSpUSM6ePWv+vnr1qvz+++/So0cPk9223Lp1K9UGY6NPNwAAAADAY3eVKmP6Vx89/GuC2/j4+vz/v/4N0HWgtdt5onN3OXLkiDz11FOyf/9+qVmzprz//vsJbh8QEOB+TB8fk4FXV65cMf/Onj1b9u7d61x++ukn+f777yU1EHQDAAAAADyWK3ceqf/gw/Lx3BkSefVqnOd1YLQ8efM7pxWzHPzpxzvuu1ixYtK7d29ZunSpvPzyyyZoToqCBQtK4cKFTRBfpkwZt0WbmacG+nQDAAAAAJJk6FuTpHOLh+TJZg2kzyvDpFylKqbp9rZv1suS+bNlxXd7JaxGbZnz3jtS5K4ScuH8OXnvrRG33efYoQOlc5uWUrZsWfnnn39k48aNZuTxpBo5cqS89NJLpjm5jmweFRUlO3fuNPseMGCA2I2gGwAAAACQJMVKlJTP1m+VmRPHydsjBpuMdp68+aRi2D0ybPx7ZptRk2fK8H69pd3D9aRE6bLy8vDR0qtdiwT3GRMdLS+88IL88ccfkjNnThMoT5w4MclXqGfPnqbf99tvvy2DBg0yo5brIG39+vWT1ODjsBq7e4lLly6ZOxwXL140FzA9C9tl/10XpKx9NSZwSu+Aep3xUK9vr9bMw6l0JZBSdjxbhpN5B9TrjId6nXHrdMGgaBlQIUoKFC0uvgFZ0ro46UbF/EGSHly/fl2OHj1qmqLrHN9JiS3p0w0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAANKIziVlppNyxHAN0qGYmORfF+bpBgAAAIA08vcNX7kY5ZDsf5+V4Fx5xcfPX8THx+uvx/XraXsKdGbtGzduyLlz58TX11cCAwOTvC+CbgAAAABII9EOH5n+W1Z5rEiUlIv8S/xpi2z4XQyQ9CA4OFjuuusuE3gnFUE3AAAAAKShiJu+8uGxIMnm75BgPweJbhH5rH3xNK+Tfn5+4u/vLz7JbHlA0A0AAAAAacwhPnLlli5pXZL0ISgoSDILGi8AAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAABk1qB76tSpUqJECQkKCpI6derI9u3bb7v9pEmTpFy5cpI1a1YpVqyY9O/fX65fv55q5QUAAAAAILH8JQ0tWbJEBgwYIDNmzDABtwbUTZs2lUOHDkmBAgXibL9o0SIZPHiwzJ07V+rVqye//vqrdOvWTXx8fGTChAmS2awZsSOtiwBPreCUAQAAAEgnmW4NlHv16iXdu3eXihUrmuA7ODjYBNXx2bp1q9SvX186duxosuNNmjSRDh063DE7DgAAAACAVwXdN27ckF27dknjxo3/LYyvr3m8bdu2eF+j2W19jRVkHzlyRFatWiXNmzdPtXIDAAAAAJDum5efP39eoqOjpWDBgm7r9fHBgwfjfY1muPV19913nzgcDrl165b07t1bXnvttQSPExUVZRbLpUuXUvBdAAAAAACQjgdS88SmTZtkzJgxMm3aNNm9e7csXbpUvvzySxk1alSCrxk7dqyEhIQ4Fx18DQAAAACATJ3pzpcvn/j5+cmZM2fc1uvj0NDQeF8zbNgweeqpp6Rnz57mcZUqVeTq1avyzDPPyOuvv26ap8c2ZMgQM1iba6abwBsAAAAAkKkz3YGBgVKjRg1Zv369c11MTIx5XLdu3XhfExkZGSew1sBdaXPz+GTJkkVy5szptgAAAAAAkOmnDNMMdNeuXaVmzZpSu3ZtM2WYZq51NHPVpUsXKVKkiGkirlq2bGlGPK9evbqZYuzw4cMm+63rreAbAAAAAID0Ik2D7vbt28u5c+dk+PDhcvr0aalWrZqsXr3aObjaiRMn3DLbQ4cONXNy679//vmn5M+f3wTco0ePTsN3AQAAAABAOgy6VZ8+fcyS0MBprvz9/SU8PNwsAAAAAACkdxlq9HIAAAAAADISgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAASC9B97Vr1yQyMtL5+Pjx4zJp0iRZu3ZtSpcNAAAAAADvCroff/xxWbBggfk7IiJC6tSpI++++65ZP336dDvKCAAAAACAdwTdu3fvlgYNGpi/P/vsMylYsKDJdmsg/t5779lRRgAAAAAAvCPo1qblOXLkMH9rk/I2bdqIr6+v3HvvvSb4BgAAAAAASQy6y5QpI8uWLZOTJ0/KmjVrpEmTJmb92bNnJWfOnJ7uDgAAAACATMvjoHv48OEycOBAKVGihOnPXbduXWfWu3r16naUEQAAAACADMnf0xc88cQTct9998mpU6ckLCzMub5Ro0amqTkAAAAAAEhipvvpp5+WbNmymay29uW2VKpUScaNG+fp7gAAAAAAyLQ8Dro/+OADM1d3bLrOmkoMAAAAAAB40Lz80qVL4nA4zHL58mUJCgpyPhcdHS2rVq2SAgUKcE4BAAAAAPA06M6VK5f4+PiYpWzZsnGe1/UjR45M7O4AAAAAAMj0Eh10b9y40WS5H3roIfn8888lT548zucCAwOlePHiUrhwYbvKCQAAAABA5g26GzZsaP49evSo3HXXXSazDQAAAAAAUnAgNc1of/vtt9K5c2epV6+e/Pnnn2b9hx9+aNYDAAAAAIAkBt3atLxp06aSNWtW2b17t0RFRZn1Fy9elDFjxni6OwAAAAAAMi2Pg+4333xTZsyYIbNnz5aAgADn+vr165sgHAAAAAAAJDHoPnTokNx///1x1oeEhEhERISnuwMAAAAAINPyOOgODQ2Vw4cPx1mv/blLlSqVUuUCAAAAAMD7gu5evXpJ37595YcffjAjmP/111+ycOFCGThwoDz33HP2lBIAAAAAgMw8ZZhl8ODBEhMTI40aNZLIyEjT1DxLliwm6H7xxRftKSUAAAAAAN4QdGt2+/XXX5dBgwaZZuZXrlyRihUrSvbs2e0pIQAAAAAA3hJ0WwIDA02wDQAAAAAAkhF0t2nTRubPny85c+Y0f9+OZrwrVaokvXv3NiOaAwAAAADgrRIVdGvwrM3Krb9vJyoqyszj/d1338ny5ctTppQAAAAAAGTWoHvevHnx/p2QAwcOSK1atZJXMgAAAAAAvG3KsMQoV66cbN261Y5dAwAAAACQeQdSe/DBB51NzeOzYcMG8fPzk7CwsOSWDQAAAAAA7wq6q1Wr5vb45s2bsnfvXvnpp5+ka9euKVk2AAAAAAC8K+ieOHFivOtHjBhh5uwGAABAxnaj5rS0LgI8NoFzBmT2Pt2dO3eWuXPnptTuAAAAAADI8FIs6N62bZsEBQWl1O4AAAAAAPC+5uVt2rRxe+xwOOTUqVOyc+dOGTZsWEqWDQAAAAAA7wq6Q0JC3B77+vqaKcLeeOMNadKkSUqWDQAAAAAA7wq6582bZ09JAAAAAADw9j7dJ0+elD/++MP5ePv27dKvXz+ZNWtWSpcNAAAAAADvCro7duwoGzduNH+fPn1aGjdubALv119/3TQxBwAAAAAASQy6f/rpJ6ldu7b5+5NPPpEqVarI1q1bZeHChTJ//nxPdwcAAAAAQKblcdB98+ZNyZIli/n766+/lscee8z8Xb58eTOKOQAAAAAASGLQXalSJZkxY4Zs2bJF1q1bJ82aNTPr//rrL8mbN6+nu5OpU6dKiRIlzBzfderUMU3VbyciIkJeeOEFKVSokAn+y5YtK6tWrfL4uAAAAAAApLuge9y4cTJz5kx54IEHpEOHDhIWFmbWL1++3NnsPLGWLFkiAwYMkPDwcNm9e7fZV9OmTeXs2bPxbn/jxg15+OGH5dixY/LZZ5/JoUOHZPbs2VKkSBFP3wYAAAAAAOlvyjANts+fPy+XLl2S3LlzO9c/88wzEhwc7NG+JkyYIL169ZLu3bubx5pB//LLL2Xu3LkyePDgONvr+gsXLpg+5AEBAWadZskBAAAAAMgUmW7l5+fnFnBbwW+BAgUSvQ/NWu/atcuMfu4sjK+vebxt27Z4X6PZ9Lp165rm5QULFpTKlSvLmDFjJDo6OilvAwAAAACA9JXpTimaLddgWYNnV/r44MGD8b7myJEjsmHDBunUqZPpx3348GF5/vnnzeBu2kQ9PlFRUWaxaIYeAAAAAIB0m+lOKzExMSabPmvWLKlRo4a0b9/ezA+uzdITMnbsWAkJCXEuxYoVS9UyAwAAAAC8V5oF3fny5TPN1M+cOeO2Xh+HhobG+xodsVxHK9fXWSpUqCCnT582zdXjM2TIELl48aJzOXnyZAq/EwAAAAAAbAy6dRovTwUGBpps9fr1690y2fpY+23Hp379+qZJuW5n+fXXX00wrvuLj04rljNnTrcFAAAAAIB0O2WYTvVladeunZmfW6ft2rdvn0f70unCdMqvDz74QH755Rd57rnn5OrVq87RzLt06WIy1RZ9Xkcv79u3rwm2daRzHUhNB1YDAAAAACDDD6Sm/acXLlxo/l63bp1ZvvrqK/nkk09k0KBBsnbt2kTvS/tknzt3ToYPH26aiFerVk1Wr17tHFztxIkTZkRzi/bHXrNmjfTv31+qVq1qAn0NwF999VVP3wYAAAAAAOkv6Nbg2BqMbOXKlSbT3aRJEzNlWJ06dTwuQJ8+fcwSn02bNsVZp03Pv//+e4+PAwAAAABAum9ervNzW4ORaVbammfb4XAwXzYAAAAAAMnJdLdp00Y6duwod999t/z999/yyCOPmPV79uyRMmXKeLo7AAAAAAAyLY+D7okTJ5qm5JrtHj9+vGTPnt2sP3XqlDz//PN2lBEAAAAAAO8IugMCAmTgwIFx1uvgZgAAAAAAIJnzdH/44Ydy3333SeHCheX48eNm3aRJk+SLL75Iyu4AAAAAAMiUPA66p0+fbubX1r7cERERzsHTcuXKZQJvAAAAAACQxKD7/fffl9mzZ8vrr78ufn5+zvU1a9aU/fv3e7o7AAAAAAAyLY+D7qNHj0r16tXjrM+SJYtcvXo1pcoFAAAAAID3Bd0lS5aUvXv3xlmvc3ZXqFAhpcoFAAAAAID3jV6u/blfeOEFuX79ujgcDtm+fbt8/PHHMnbsWJkzZ449pQQAAAAAwBuC7p49e0rWrFll6NChEhkZKR07djSjmE+ePFmefPJJe0oJAAAAAIA3BN2qU6dOZtGg+8qVK1KgQIGULxkAAAAAAN4YdFuCg4PNAgAAAAAAkhh062jlPj4+idlUdu/enajtAAAAAADI7BIVdLdq1cr5tw6gNm3aNKlYsaLUrVvXrPv+++/l559/lueff96+kgIAAAAAkBmD7vDwcLeB1F566SUZNWpUnG1OnjyZ8iUEAAAAAMBb5un+9NNPpUuXLnHWd+7cWT7//POUKhcAAAAAAN4XdOt0Yd99912c9bouKCgopcoFAAAAAID3jV7er18/ee6558yAabVr1zbrfvjhB5k7d64MGzbMjjICAAAAAOAdQffgwYOlVKlSMnnyZPnoo4/MugoVKsi8efOkXbt2dpQRAAAAAADvmadbg2sCbAAAAAAAUrhPNwAAAAAASByCbgAAAAAAbELQDQAAAACATQi6AQAAAACwCUE3AAAAAADpZfTy6OhomT9/vqxfv17Onj0rMTExbs9v2LAhJcsHAAAAAID3BN19+/Y1Qfejjz4qlStXFh8fH3tKBgAAAACAtwXdixcvlk8++USaN29uT4kAAAAAAPDWPt2BgYFSpkwZe0oDAAAAAIA3B90vv/yyTJ48WRwOhz0lAgAAAADAW5uXf/vtt7Jx40b56quvpFKlShIQEOD2/NKlS1OyfAAAAAAAeE/QnStXLmndurU9pQEAAAAAwJuD7nnz5tlTEgAAAAAAvD3otpw7d04OHTpk/i5Xrpzkz58/JcsFAAAAAID3DaR29epVefrpp6VQoUJy//33m6Vw4cLSo0cPiYyMtKeUAAAAAAB4Q9A9YMAA+eabb2TFihUSERFhli+++MKs05HNAQAAAABAEpuXf/755/LZZ5/JAw884FzXvHlzyZo1q7Rr106mT5/u6S4BAAAAAMiUPM50axPyggULxllfoEABmpcDAAAAAJCcoLtu3boSHh4u169fd667du2ajBw50jwHAAAAAACS2Lx88uTJ0rRpUylatKiEhYWZdfv27ZOgoCBZs2aNp7sDAAAAACDT8jjorly5svz222+ycOFCOXjwoFnXoUMH6dSpk+nXDQAAAAAAkjFPd3BwsPTq1SspLwUAAAAAwGskKuhevny5PPLIIxIQEGD+vp3HHnsspcoGAAAAAEDmD7pbtWolp0+fNiOU698J8fHxkejo6JQsHwAAAAAAmTvojomJifdvAAAAAACQglOGLViwQKKiouKsv3HjhnkOAAAAAAAkMeju3r27XLx4Mc76y5cvm+cAAAAAAEASg26Hw2H6bsf2xx9/SEhIiKe7AwAAAAAg00r0lGHVq1c3wbYujRo1En//f1+qg6cdPXpUmjVrZlc5AQAAAADIvEG3NWr53r17pWnTppI9e3bnc4GBgVKiRAlp27atPaUEAAAAACAzB93h4eEmo63BdZMmTaRQoUL2lgwAAAAAAG/q0+3n5yfPPvusXL9+3b4SAQAAAADgrQOpVa5cWY4cOWJPaQAAAAAA8Oag+80335SBAwfKypUr5dSpU3Lp0iW3BQAAAAAAeNin29K8eXPz72OPPeY2dZg1lZj2+wYAAAAAAEkIujdu3Mh5AwAAAADAjqC7YcOGnr4EAAAAAACv5HHQrSIiIuS///2v/PLLL+ZxpUqV5Omnn5aQkJCULh8AAAAAAN4zkNrOnTuldOnSMnHiRLlw4YJZJkyYYNbt3r3bnlICAAAAAOANme7+/fubQdRmz54t/v7/9/Jbt25Jz549pV+/frJ582Y7ygkAAAAAQOYPujXT7Rpwm534+8srr7wiNWvWTOnyAQAAAADgPc3Lc+bMKSdOnIiz/uTJk5IjR46UKhcAAAAAAN4XdLdv31569OghS5YsMYG2LosXLzbNyzt06GBPKQEAAAAA8Ibm5e+88474+PhIly5dTF9uFRAQIM8995y89dZbdpQRAAAAAADvCLoDAwNl8uTJMnbsWPn999/NOh25PDg42I7yAQAAAECy3Kg5jTOY4UwQr21ebtEgO1euXGZJbsA9depUKVGihAQFBUmdOnVk+/btiXqdNmvXrHurVq2SdXwAAAAAANJF0K1NyocNGyYhISEmUNZF/x46dKjcvHnT4wJo3/ABAwZIeHi4mec7LCxMmjZtKmfPnr3t644dOyYDBw6UBg0aeHxMAAAAAADSZdD94osvyqxZs2T8+PGyZ88es+jf//3vf+Wll17yuAATJkyQXr16Sffu3aVixYoyY8YMkzmfO3dugq+Jjo6WTp06yciRI6VUqVIeHxMAAAAAgHTZp3vRokWmWfcjjzziXFe1alUpVqyYGb18+vTpid7XjRs3ZNeuXTJkyBDnOl9fX2ncuLFs27Ytwde98cYbUqBAATOK+pYtWzx9CwAAAAAApM+gO0uWLKZJeWwlS5Y0g6x54vz58yZrXbBgQbf1+vjgwYPxvubbb781WfW9e/cm6hhRUVFmsVy6dMmjMgIAAAAAkGpBd58+fWTUqFEyb948E4ArDWpHjx5tnrPT5cuX5amnnpLZs2dLvnz5EvUaHWVdm6EDAAAgcdaM2MGpymhWpHUBAKRY0K19uNevXy9FixY1g56pffv2mabijRo1kjZt2ji3Xbp06W33pYGzn5+fnDlzxm29Pg4NDY2zvU5RpgOotWzZ0rkuJibm/96Iv78cOnTITF/mSpuu60BtrplubQoPAAAAAEC6C7p1irC2bdu6rUtqEKvN0WvUqGGCeGvaLw2i9XF8WfPy5cvL/v373dbpqOmaAde5w+Mrh2bjrYw8AAAAAADpOujWZuUpSbPQXbt2lZo1a0rt2rVl0qRJcvXqVTOauerSpYsUKVLENBPXebwrV64c5yaAir0eAAAAAIAMF3Rbzp07Z5pzq3Llykn+/PmTtJ/27dubfQ0fPlxOnz4t1apVk9WrVzsHVztx4oQZ0RwAAAAAgEwfdGsWWufqXrBggbM/tfbL1oz0+++/b+bY9pQ2JU9oELZNmzbd9rXz58/3+HgAAAAAAKQG36Q0B//mm29kxYoVEhERYZYvvvjCrHv55ZftKSUAAAAAAN6Q6f7888/ls88+kwceeMC5rnnz5pI1a1Zp166dTJ8+PaXLCAAAAACAd2S6IyMjnf2tXRUoUMA8BwAAAAAAkhh0161bV8LDw+X69evOddeuXZORI0ea5wAAAAAAQBKbl+uUXs2aNZOiRYtKWFiYWbdv3z4zndeaNWs83R0AAAAAAJmWx0F3lSpV5LfffpOFCxfKwYMHzboOHTpIp06dTL9uAAAAAACQhKD75s2bUr58eVm5cqX06tXLk5cCAAAAAOB1POrTHRAQ4NaXGwAAAAAApOBAai+88IKMGzdObt265elLAQAAAADwKh736d6xY4esX79e1q5da/p3Z8uWze35pUuXpmT5AAAAAADwnqA7V65c0rZtW3tKAwAAAACANwfd8+bNs6ckAAAAAAB4a5/umJgY05e7fv36UqtWLRk8eLBcu3bN3tIBAAAAAOANQffo0aPltddek+zZs0uRIkVk8uTJZlA1AAAAAACQzKB7wYIFMm3aNFmzZo0sW7ZMVqxYIQsXLjQZcAAAAAAAkIyg+8SJE9K8eXPn48aNG4uPj4/89ddfid0FAAAAAABeJdFBt87LHRQU5LYuICBAbt68aUe5AAAAAADwntHLHQ6HdOvWTbJkyeJcd/36dendu7fbXN3M0w0AAAAAgIdBd9euXeOs69y5c2JfDgAAAACA10l00M383AAAAAAA2NSnGwAAAAAAeIagGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAAMjMQffUqVOlRIkSEhQUJHXq1JHt27cnuO3s2bOlQYMGkjt3brM0btz4ttsDAAAAAOC1QfeSJUtkwIABEh4eLrt375awsDBp2rSpnD17Nt7tN23aJB06dJCNGzfKtm3bpFixYtKkSRP5888/U73sAAAAAACk66B7woQJ0qtXL+nevbtUrFhRZsyYIcHBwTJ37tx4t1+4cKE8//zzUq1aNSlfvrzMmTNHYmJiZP369aledgAAAAAA0m3QfePGDdm1a5dpIu4skK+veaxZ7MSIjIyUmzdvSp48eWwsKQAAAAAAnvOXNHT+/HmJjo6WggULuq3XxwcPHkzUPl599VUpXLiwW+DuKioqyiyWS5cuJbPUAAAAAABkkOblyfHWW2/J4sWL5X//+58ZhC0+Y8eOlZCQEOeifcABAAAAAMj0QXe+fPnEz89Pzpw547ZeH4eGht72te+8844JuteuXStVq1ZNcLshQ4bIxYsXncvJkydTrPwAAAAAAKTboDswMFBq1KjhNgiaNSha3bp1E3zd+PHjZdSoUbJ69WqpWbPmbY+RJUsWyZkzp9sCAAAAAECm79OtdLqwrl27muC5du3aMmnSJLl69aoZzVx16dJFihQpYpqJq3Hjxsnw4cNl0aJFZm7v06dPm/XZs2c3CwAAAAAA6UWaB93t27eXc+fOmUBaA2idCkwz2NbgaidOnDAjmlumT59uRj1/4okn3Paj83yPGDEi1csPAAAAAEC6DbpVnz59zBKfTZs2uT0+duxYKpUKAAAAAAAvHr0cAAAAAID0LF1kugEAyKhu1JyW1kWAxyZwzgAAqYZMNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGzib9eOASA+a0bs4MRkNCvSugAAAAAZF0E3AAAAgEyNm/4Z0ArJNGheDgAAAACATQi6AQAAAACwCUE3AAAAAAA2IegGAAAAAMAmBN0AAAAAANiEoBsAAAAAAJsQdAMAAAAAYBOCbgAAAAAAbELQDQAAAACATfzt2jEAAN5gzYgdaV0EeGoFpwwAkHrIdAMAAAAAYBOCbgAAAAAAbELQDQAAAACATQi6AQAAAACwCUE3AAAAAAA2IegGAAAAAMAmBN0AAAAAANiEoBsAAAAAAJsQdAMAAAAAYBOCbgAAAAAAbELQDQAAAACATQi6AQAAAACwCUE3AAAAAAA2IegGAAAAAMAmBN0AAAAAANiEoBsAAAAAAJsQdAMAAAAAYBOCbgAAAAAAbELQDQAAAACATQi6AQAAAACwCUE3AAAAAAA2IegGAAAAAMAmBN0AAAAAANiEoBsAAAAAAJsQdAMAAAAAYBOCbgAAAAAAbELQDQAAAACATQi6AQAAAACwCUE3AAAAAAA2IegGAAAAACAzB91Tp06VEiVKSFBQkNSpU0e2b99+2+0//fRTKV++vNm+SpUqsmrVqlQrKwAAAAAAGSboXrJkiQwYMEDCw8Nl9+7dEhYWJk2bNpWzZ8/Gu/3WrVulQ4cO0qNHD9mzZ4+0atXKLD/99FOqlx0AAAAAgHQddE+YMEF69eol3bt3l4oVK8qMGTMkODhY5s6dG+/2kydPlmbNmsmgQYOkQoUKMmrUKLnnnntkypQpqV52AAAAAADSbdB948YN2bVrlzRu3PjfAvn6msfbtm2L9zW63nV7pZnxhLYHAAAAACCt+KfZkUXk/PnzEh0dLQULFnRbr48PHjwY72tOnz4d7/a6Pj5RUVFmsVy8eNH8e+nSJUnvLt+8ldZFgIeCM0C9SmvU64yHen171OmMhzp9Z9TrjId6fXvU6YwnOAP8rrZiSofDkX6D7tQwduxYGTlyZJz1xYoVS5PyIJMLCUnrEgApj3qNzIY6jcyIeo3MJiTj/K6+fPmyhNymvGkadOfLl0/8/PzkzJkzbuv1cWhoaLyv0fWebD9kyBAzUJslJiZGLly4IHnz5hUfH58UeR/w/I6Q3vQ4efKk5MyZk9OHDI86jcyIeo3MhjqNzIh6nbY0w60Bd+HChW+7XZoG3YGBgVKjRg1Zv369GYHcCor1cZ8+feJ9Td26dc3z/fr1c65bt26dWR+fLFmymMVVrly5UvR9IGk04CboRmZCnUZmRL1GZkOdRmZEvU47t8twp5vm5ZqF7tq1q9SsWVNq164tkyZNkqtXr5rRzFWXLl2kSJEippm46tu3rzRs2FDeffddefTRR2Xx4sWyc+dOmTVrVhq/EwAAAAAA0lnQ3b59ezl37pwMHz7cDIZWrVo1Wb16tXOwtBMnTpgRzS316tWTRYsWydChQ+W1116Tu+++W5YtWyaVK1dOw3cBAAAAAEA6DLqVNiVPqDn5pk2b4qz7z3/+YxZkTNrcPzw8PE6zfyCjok4jM6JeI7OhTiMzol5nDD6OO41vDgAAAAAAkuTfdtsAAAAAACBFEXQDAAAAAGATgm4AAAAAAGxC0I1E69atm/j4+JglICDAjDD/8MMPy9y5c8386nbTQfXuueceM2BEmTJlZP78+bYfE5lbWtbpU6dOSceOHaVs2bJmhoZ+/frZejx4j7Ss10uXLjXHyp8/v5kztm7durJmzRpbj4nMLy3r9Lfffiv169eXvHnzStasWaV8+fIyceJEW48J75DWv6st3333nfj7+5sZpGAfgm54pFmzZiZYOHbsmHz11Vfy4IMPmrnTW7RoIbdu3bLtbB49etTMy67H27t3rwlQevbsyY85ZNg6HRUVZQITnf4wLCzMtuPAO6VVvd68ebP50bhq1SrZtWuXOW7Lli1lz549th0T3iGt6nS2bNnMDDtat3/55Rfzna3LrFmzbDsmvEda1WtLRESEdOnSRRo1amT7sbyejl4OJEbXrl0djz/+eJz169ev1xHwHbNnz3auO378uOOxxx5zZMuWzZEjRw7Hf/7zH8fp06fdXrd8+XJHzZo1HVmyZHHkzZvX0apVqwSP/corrzgqVarktq59+/aOpk2bcvGQIeu0q4YNGzr69u3LlUSmqteWihUrOkaOHJmMdwRvl97qdOvWrR2dO3dOxjsC0ke91t/SQ4cOdYSHhzvCwsK4LDYi041ke+ihh0ymTpsVKm0S8/jjj8uFCxfkm2++kXXr1smRI0ekffv2ztd8+eWX0rp1a2nevLnJgKxfv15q166d4DG2bdsmjRs3dlvXtGlTsx7IiHUa8IZ6rce4fPmy5MmTx5b3BO+WFnVaX7N161Zp2LChLe8JSK16PW/ePLOf8PBwTnoq8E+NgyDz0z5OP/74o/lbP+j79+83TcKLFStm1i1YsEAqVaokO3bskFq1asno0aPlySeflJEjRzr3cbsmtqdPnzZ9XVzp40uXLsm1a9dMPysgI9VpwBvq9TvvvCNXrlyRdu3a2fBugNSr00WLFpVz586ZJr8jRowwXdyAjFqvf/vtNxk8eLBs2bLF9OeG/ch0I0U4HA4zEITSPk/6pWB9MaiKFStKrly5zHNK+2XTfwTpGXUamVFq1utFixaZH4CffPKJFChQIIXeAZA2dVqDk507d8qMGTNk0qRJ8vHHH3MpkCHrdXR0tBnIVb+fdTBXpA5ubSBF6Ie+ZMmSid7e08x0aGionDlzxm2dPtbRcclyIyPWaSAz1+vFixebTOCnn34ap2sQkBHrtHWMKlWqmN8fmu3u0KFDkvYFpGW91i4/egNJm6HrIIFWE3YN9DXrvXbtWtPEHSmLTDeSbcOGDabZS9u2bc3jChUqyMmTJ81iOXDggBkhUe/MqapVq5rmMoml087E3l77tOh6ICPWaSCz1mvNAHbv3t38q7NOAJntu1oDFJ2BAsiI9VoTVrp/zY5bS+/evaVcuXLm7zp16nBh7WDnKG3IfKMsNmvWzHHq1CnHH3/84di1a5dj9OjRjuzZsztatGjhuHXrltkuJibGUa1aNUeDBg3MNj/88IOjRo0aZoRmy8aNGx2+vr6O4cOHOw4cOOD48ccfHW+99VaCxz5y5IgjODjYMWjQIMcvv/zimDp1qsPPz8+xevXqVHnvyJzSsk6rPXv2mEX31bFjR/P3zz//bPv7RuaWlvV64cKFDn9/f/Mdrce3loiIiFR578ic0rJOT5kyxYwK/euvv5plzpw5ZvTo119/PVXeOzKvtP4N4orRy+1H0A2Pvhz0Po0u+qMqf/78jsaNGzvmzp3riI6Odts2MVMbfP755+ZLJDAw0JEvXz5HmzZtbnt8/UKxti9VqpRj3rx5XD1k6DptHdt1KV68OFcVGbZe64/A+Oq1lgnIiHX6vffeM1OW6o3/nDlzOqpXr+6YNm1anOMCGalex0bQbT8f/Y8tKXQAAAAAALwcfboBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAOlIt27dxMfHxywBAQFSsGBBefjhh2Xu3LkSExMj3mD+/PmSK1eutC4GAAApgqAbAIB0plmzZnLq1Ck5duyYfPXVV/Lggw9K3759pUWLFnLr1q20Lh4AAPAAQTcAAOlMlixZJDQ0VIoUKSL33HOPvPbaa/LFF1+YAFyzwOrEiRPy+OOPS/bs2SVnzpzSrl07OXPmjNt+VqxYIbVq1ZKgoCDJly+ftG7d2vmcZtKXLVvmtr1ml639a8Cv23zyySfSoEEDyZo1q9nXr7/+Kjt27JCaNWuaYz/yyCNy7tw5t/3MmTNHKlSoYI5bvnx5mTZtmvM5a79Lly41NxOCg4MlLCxMtm3bZp7ftGmTdO/eXS5evOjM+I8YMcKGswwAQOog6AYAIAN46KGHTHCqwao2M9eA+8KFC/LNN9/IunXr5MiRI9K+fXvn9l9++aUJsps3by579uyR9evXS+3atT0+bnh4uAwdOlR2794t/v7+0rFjR3nllVdk8uTJsmXLFjl8+LAMHz7cuf3ChQvN49GjR8svv/wiY8aMkWHDhskHH3zgtt/XX39dBg4cKHv37pWyZctKhw4dTBa/Xr16MmnSJHMjQbP9uuh2AABkVP5pXQAAAJA4mjX+8ccfTQC9f/9+OXr0qBQrVsw8t2DBAqlUqZLJQmtGWoPeJ598UkaOHOl8vQbtntKAt2nTpuZvbeKuwbEev379+mZdjx49nNlxK0h/9913pU2bNuZxyZIl5cCBAzJz5kzp2rWr234fffRR87eWUcuuAby+x5CQEJPh1mw/AAAZHZluAAAyCIfDYYJRzSBrsG0F3KpixYqmebg+pzSD3KhRo2Qfs2rVqs6/dVA3VaVKFbd1Z8+eNX9fvXpVfv/9dxOIa9Nza3nzzTfN+oT2W6hQIfOvtR8AADITMt0AAGQQGlBr5jgxtA/27WjwrkG8q5s3b8bZTkdQd31NfOusUdWvXLli/p09e7bUqVPHbT9+fn533K+3jM4OAPAuZLoBAMgANmzYYJqUt23b1gxSdvLkSbNYtAl3RESEyXhbmWRtBp6Q/Pnzm/7Slt9++00iIyOTVUbNehcuXNj0Ly9TpozbktibBSowMFCio6OTVRYAANILMt0AAKQzUVFRcvr0aRN46ojkq1evlrFjx5opw7p06SK+vr6miXenTp3MoGM6ANnzzz8vDRs2NKOKW32rtXl56dKlTd9u3WbVqlXy6quvOgdmmzJlitStW9ccR9e7Zp+TSvtnv/TSS6Zftk59pu9l586d8s8//8iAAQMStY8SJUqYrLneNNB+6DrCuS4AAGREZLoBAEhnNMjWfs4afGrgunHjRnnvvffMtGHaTFubY+vfuXPnlvvvv18aN24spUqVkiVLljj38cADD8inn34qy5cvl2rVqpkge/v27c7ndbAz7ROu04HpiOQ6sFlKBLY9e/Y0U4bNmzfP3BjQGwE60JonmW4dwbx3795mNHbNyI8fPz7Z5QIAIK34OGJ36AIAAAAAACmCTDcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAscf/A+NfKFJFB3HzAAAAAElFTkSuQmCC",
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WfsXx60lmH6k8Ne9XYnU/Jd+Jnr6/KdknAN9E0A3A55QsWdIMIqXNVV2z3ZoRtZ53pdmO+HQwHM0GWhkQ/VsHIIpP96lBf0p+fHvSfFLLmNTxEjuHlNIfmLoMGTLEzCerA1jpYGA68FBG0Uyd/kjVjJu2KEjNNdOBqTTbpoGL6zaJNVv1JisjqNlBbZrqCR3QSeuhBo8aRFrS0pRa6402mdVsqGu2O/5I92kpt3WcdevWmabFrjdR4tfptB5HaYCpg8PpokGUZr91AC3NnGvAbrW00AG9XOdNjt/iJam6qiO7a1B7s89vcs9r1l/LpYtmT3UANR1MMCVBt34/uWan9b3S87RG8tdB03SARG0N4ZqJTelI/kmxvmP0+FZza6WtSnQGCR2d3HXbn376yZTL9SZo/O8rvZ56g0RvJCWV7XZ9v1yl5P3ylCfvb0ql134AZC2ZL/0DADbT5puaFZkyZYrbes366A+i+D90tUmmaz9gbSqu2WBtqqqZDV30b13n2qRTRxj/6KOPTL9rbTZ9M9Zc3UlNmxT/HHSEaS2bRfuu6vQ9+mNb+xh7QvtTa59nVxp86w/k+FPj2E1H+NVrOmLEiAQZIn3s2vxTr1li03pZGSfX12u/WdfrlV5ThqWFZmJ1VGcNAk+cOJHgeav7QmISO0f923U6LE9pNlmDptmzZzvXaaCkXTnSq9xW/dX65jptlX4mdeT19DyOa11RWp+1n62y6rXVB9d1GkBreq+UZKm1ZYHr9XIdsVv341pX43+29Zzj1zE9Z21indLPXfz3xrqG1vdYYvVEj6kZ/7TQVkZ601FvyunsBxYdeTz+eer7ffLkSTMLhEXffy2r3nTR/uVKR/rWcupnPz6r/Ppdqs3C40/bqLNKpDdP3t+U8uR7HkD2QaYbgM/RjNe9995rppzSIFkzMtqsU4NmnfbGdSAcpX2jNRhxnTJMuf4w1EywZhg1wNZslfYl10BBfzhrn82UsAZr03LpwHCa3dOyWj/SXOnUSTrtjP6w1nJpVkiDBM0w6WBEnjap18GqdCofnfNZs8v6g1inOdIf7PpDOCPp9dfrOXjwYPP+aBNxbZGg56ZNcHWwOG1ubF0z/SGv/dF1qh/9Aa/XTOca1iy3Tif14IMPmtdqcKA3IzS7ejOeThmWFho0ab3Rmxw6gJlmd/WGjd4g0Km/NNOWGG0urNdKr4UGBhqM6Huflv6jeq2124YOKqgZUz2GZkg18xg/S5facit9j7QVhdZjfY/1fdH3K7GbHGk5jg6gpWXXTKx2kdBsqAZ6OmWc1Z9Yb5hpBlgH1dKuCFrn586dawJK7TOfHJ3PXPuM62BimjnWc9JAWm/Y6HprvmurrmoLG22qrEG1Zqe1D7uWS+cg1+8hrb+6zY8//pjonNGJ0bqt4y9oP3W9Jtq1QgdwtDLNen5Wtl+n99L6r0GkBveJ3chIKf1+0s+p7lOvr07LpWXRz0z8Pt36mdXvQ/0s7dixw9wY1NYo2td84sSJzhZH+r2s11Sn2tIMup6T3vTRKcP0Of2Ost5Xnf5L/9XrqwG4tvpIb568vynlyfc8gGzE28OnA4CnrKl8fvzxx2S306lfdJqexOj0Wi+++KKjaNGijqCgIDP1kE7lYk1LY9Hj6HQ+OtWNbpMjRw4zzZLrtE2WnTt3mml4dAqc0NBQx7333us2jVRKyj5y5EhHsWLFzDQ1rtPKxJ8yTOn0ZDrNWb58+cwUZnXr1nWsWLHCbRtrmqn4U4HFn3bn0KFDZiqtsmXLmn3lz5/flF+nZUvvKcN0mrfErkn8KXR0+iqdWk3fQ10qVqxo3otff/3Vuc2lS5ccnTp1MtdA92FNH6bv4+jRo81j6z3Ta6PXMLEpxtI6ZZhOXRafVXcSu+5a1+K/l127dnWEh4eb+qh1oFWrVo7PPvss2SnD9u3b52jatKmpcwULFnT06tXLOU2Ra9mT+iwkNl2Wvj96TXW6O53O6oknnjBTI+l2OjWfp+VOyj///ON4/PHHzZReehz925q6Lv51T+1x9PlmzZqZqa10OqfbbrvN8fTTTztOnDjhtt2OHTsc9erVc24zfvz4FE0ZZk19NXbsWFP3ta7dcsstZhq2ESNGOM6fP+/c7sCBA2b6QJ2WSver74lOtTVw4EBHRESEud76Hunf06ZNu+n1s947rQP6PaCv12P36dPHceXKFbdtly1b5qhevbr5bOuUglreuXPnJji/pOpycrSsOlWhnnvt2rUdmzZtSvQ6nTp1ytG9e3dTT/U66zRwiX2+dEov/Xzo5123K1SokOOBBx4w75HrFGg9evQw9UbPu3379o7Tp08nOWVY/O+cpD4PWmZ9H1Pz/ib2eU/quzup73kA2Zef/sfbgT8AZFaa2dMpeeI3RQd8ydKlS02rAZ3+TrN9vkoHPNPWLpqN9rbhw4eb1jbaxD7+KNwAgMyFPt0AAMCtr6orq6+1Nl/XAb58mTbHJsAFAHiKPt0AAMDp+eefN4F3/fr1zZgE2tdaR7IfPXp0pp9Oyi56/noddPotnZ4NAABPEHQDAAAnHRRLB/FasWKFXL161UyrpZluaxArX6QDj+kc3zrQog6wBwCAJ+jTDQAAAACATejTDQAAAACATQi6AQAAAACwic/16Y6Li5O///5b8uTJY6YCAgAAAADAU9pT++LFi1K0aFHx9086n+1zQbcG3CVKlPB2MQAAAAAA2cDx48elePHiST7vc0G3ZritC6NzjgIAAAAA4KkLFy6YhK4VYybF54Juq0m5BtwE3QAAAACAtLhZt2UGUgMAAAAAwCYE3QAAAAAA2ISgGwAAAAAAm/hcn24AAAAAyIxiY2Pl+vXr3i4G/r+goCAJCAiQtCLoBgAAAAAvz/d88uRJiYqK8nZREE++fPkkPDz8poOlJYegGwAAAAC8yAq4CxcuLKGhoWkK8JB+N0Kio6Pl9OnT5vGtt96a6n0RdAMAAACAF5uUWwF3gQIFvF0cuMiZM6f5VwNvfX9S29ScgdQAAAAAwEusPtya4UbmY70vaelrT9ANAAAAAF5Gk/Ls+74QdAMAAAAAYBOCbgAAAABAhps/f74ZHTy7YyA1AAAAAMiETrZulKHHC1++2ePXnDlzRoYNGyZffvmlnDp1Sm655RaJiIgw6xo2bJjsazt06CAtW7aU7M6rme5NmzZJ69atpWjRoqat/NKlS2/6mo0bN8odd9whOXLkkHLlypm7IwAAAACAjNeuXTvZtWuXvP/++/Lbb7/JsmXL5J577pF//vknRaODFy5cWLI7rwbdly9fNndBpk6dmqLtDx8+LA8++KDce++9snv3bunXr5/07NlTVq9ebXtZAQAAAAD/o1Odbd68WcaOHWtitJIlS0rdunVl8ODB8tBDDzm3efrpp6VIkSISEhIiVatWlRUrViTZvPyLL74wSVbdtkyZMjJixAi5ceOG83lN1s6ZM0ceeeQRM7L47bffbgJ9V7/88ou0atVK8ubNK3ny5JFGjRrJH3/84XxeX1+pUiVzjIoVK8q0adOyb/PyBx54wCwpNWPGDCldurS888475rFeqG+//VYmTJggzZs3t7GkAAAAAABXuXPnNou2WL7zzjtNa2RXcXFxJt67ePGifPjhh1K2bFnZt29fkvNdawDftWtXeffdd52B8lNPPWWei4yMdG6ngfi4cePkrbfeksmTJ0vnzp3l6NGjkj9/fvnrr7/k7rvvNtn29evXm8D7u+++cwbuCxcuNE3fp0yZIjVr1jRZ+l69ekmuXLmkW7dutlynLNWne+vWrdK0aVO3dRpsa8YbAAAAAJBxAgMDTbZag1ZNkGqGunHjxvLYY49J9erV5euvv5Zt27bJ/v37pXz58uY1mr1OigbTgwYNcga/uu3IkSPl5Zdfdgu6n3jiCenYsaP5e/To0SZI1+O0aNHCtKIOCwuTRYsWSVBQkNnGOrbS/WgSt23btuaxJnX1RsDMmTMJutXJkydNswRX+vjChQty5coV0ycgvpiYGLNYdFsAAAAAQPr06dYuwJql/v777+Wrr74yWWhtwn369GkpXry4W9CbnD179pis9KhRo5zrYmNj5erVqxIdHW2akysN6C2aodZsth5LaTdkzZJbAXf87s2aPe/Ro4e5UWDRLLgG6nbJUkF3aowZM8bcMcmK6sw86O0iwEM/Pl3O20XI9KjXWQ/1OnnU6ayHOn1z1Oush3qddet0kZBY6V/pusSeixH/eHFi/gwuy74zV1P92mI1Gkk7XXoPlGEvPiOvDh0m3Z/tJ9fjHEnu96+L1yXO8b/jXrx0SZ4bOESaPthGbi/g3lRd+19b4gfU2s9bm7KrxBKxlkuXLpl/Z8+eLfXq1XN7Lqkm7z43T3d4eLgZht6VPtY7G0ldXO3Ef/78eedy/PjxDCotAAAAAPieMuUrypXoaClfuZqc+vsvOfLH7yl6XaVqNcy2JcuUNTNVuS7+/ikLXTULrln369evJ3hOW0nrzFmHDh1KsH9tZm6XLJXprl+/vqxcudJt3dq1a836pGhn/vgd+gEAAAAAaRN17h95sWdnaduxm5SvXFVy5c4jv+zZIXOnTJD7WrSSOg0aSa36d0m/JzvKyyPGym2ly8rhg79qaloa3dcswf6eeelVea5LW7m1WAl5pttjJtDWJuc///yzvPHGGykqU58+fczgatqvXBOw2mxcm73rqOoVKlQwraBfeOEFs177gGtX5O3bt8u///4r/fv3z35Bt6b3Dx486DYlmLbB11HnbrvtNnORdPS5BQsWmOd79+5tRpnTjvRPPvmkGY3uk08+MROxAwAAAAAyTmiu3FL9jjqyYOZkOX7kkNy4cV3CixaXRx/vLk/1fdlsM3Hux/L28MEysHc3uRJ92QTeLw4Zmej+7rrvfpn64RKZ/s5omTvlHdOMXKf00mmiU6pAgQImThw4cKAZ1E2bjdeoUUMaNmxontd9ad9wHflct9E+4dWqVbN1cG4/h8PhEC/ZuHGjmc8tPh01TkfB01Hpjhw5YrZzfc2LL75oRpjTTvlDhw4126WUDqSmdzW0qbk2S8/MMnPfEySO/lQ3R73OeqjXyaNOZz3U6ZujXmc91Ous3qc7RgoXLyn+QbTQtVQu9L8+3N6kg7hpclibn7v2K/cktvRqplvnTksu5tfAO7HX6FxqAAAAAABkdllqIDUAAAAAALISgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGCTQLt2DAAAAABIvY7HXs3Q431822iPX3Pu7BmZMnakfPP1V/LPmdOSN+wWqVClmjzz0mC5o14DsVOpUqWkX79+ZsnMCLoBAAAAAKnS78mOcv36NRk9eY6UKFlKzp45LT9s3ihR/56z7ZjXrl2T4OBgySoIugEAAAAAHrtwPkp2fP+dzF+6Ruo0aGTWFS1RUqrfUce5TZXCOWXo2EmyYfWX8uOWTVKocLj0jxwlzVu3dW7z276fZcyQAbJn+w8SkjNU7m/VRuZNmyS5c+c2zz/xxBMSFRUlderUkalTp0qOHDmkZMmScvToUXnxxRfNohwOh2RG9OkGAAAAAHgsNFdus6z7aplci4lJcrvJY183gfSSDdvkwUcfk4FPdZU/fjtgnou+fFme6tBa8oblk8Wrv5XxcxbK99+slz59+rjtY926dfLrr7/K2rVrZcWKFbJkyRIpXry4vP7663LixAmzZFYE3QAAAAAAjwUGBsqod2fJF4sXyp23h0vnB++ViaOGya+/7HXbrnnrtvJol+5Squzt8sKgSKlS4w5ZOGe6ee7LJYslJiZGxkx5T26vVEXubHSPvPbmBPnggw/k1KlTzn3kypVL5syZI1WqVDFL/vz5JSAgQPLkySPh4eFmyawIugEAAAAAqdKs9SOy8adDMmXBZ3LXfc3kx+82yX+a1pf/LvrAuU1E7Xpur9HHh37/v0z3od8OmIHXQnPlcj5fs259iYuLM5ltS7Vq1bJUP25XBN0AAAAAgFTLERIiDe5pYkYsX7hyo7R57HGZOm5kuh4jl0tQntUQdAMAAAAA0k2Z8hXlSnS08/GeHdvcnv9p+zYpc3tF57baHF37dlt2bdsq/v7+UqFChWSPo5nv2NhYyewIugEAAAAAHos69490b9tCln/6sQmc/zx6RFYv+1zmTpkg97Vo5dxuzfIlsuSj9+XIH7+bOb337tounXr0Ns+1aveYGY381ed7yu/7f5Efvv1GRg/uL48//rgUKVLkpvN0b9q0Sf766y85e/asZFZMGQYAAAAA8JiOXK7Tgy2YOVmOHzkkN25cl/CixeXRx7vLU31fdm733MAh8tV/P5WRr/SVQkXC5a2Z70u5CpXMczlDQ2XW4uVmyrAOze9yThk2Zcqkmx5fRy5/+umnpWzZsmYwtsw6ZRhBNwAAAABkQh/fNloys+AcOeTFISPNkpzC4bfK7E9XJPl8+cpVZd6SVW7rcucOcf49f/78RF935513yp49eySzo3k5AAAAAAA2IdMNIENdqz3N20WAx8Z7uwAAAABZFkE3AAAAAMAWv5y+Ir6O5uUAAAAAANiETHcmRjPcrIhmuAAAAAD+h0w3AAAAAAA2IegGAAAAAMAmBN0AAAAAANiEoBsAAAAAAJsQdAMAAAAAvGbbd5ukSuGccuF81E233bhxo/j5+UlU1M23zSwYvRwAAAAAMqFuS/7M0OO937Z4ql535tRJmTVxrGxau0pOnfxbChQsJBWqRkjXp/rInXffe9PX16hzp2zce1jy5A276bYNGjSQEydOSFjYzbfNLAi6AQAAAACp8texo9Kl1b2SJyyfvBQ5WspXrio3rl+XbzeslTcG9ZMVW/bcdB/BwcFSqEh4io6n24aHp2zbzILm5QAAAACAVBn5Sl/T3HvRqs3SrPUjUqrs7VKuYmV54pm+8tFX35igXJuO79/7v+Bbm5HrOm1Wnljz8r+PH5XWrVvLLbfcIrly5ZIqVarIypUrE21ePn/+fMmXL5+sXr1aKlWqJLlz55YWLVqYbLirOXPmmOdDQkKkYsWKMm3atAy7RmS6AQAAAAAei/r3nHy7fo30fXWEhObKleD5vGH55OL58x7v941BL0qw3JBNmzaZoHvfvn0mmE5KdHS0vP322/LBBx+Iv7+/dOnSRQYMGCALFy40z+u/w4YNkylTpkjNmjVl165d0qtXL7Pvbt26id0IugEAAAAAHjt2+A9xOBxSulz5dN3viT+PS6cOj0q1atXM4zJlyiS7/fXr12XGjBlStmxZ87hPnz7y+uuvO5+PjIyUd955R9q2bWsely5d2gTyM2fOJOgGAAAAAGRSDoctu+3c61kZ+fILsmbNGmnatKm0a9dOqlevnuT2oaGhzoBb3XrrrXL69Gnz9+XLl+WPP/6QHj16mOy25caNGxk2GBt9ugEAAAAAHrutTDnTv/rwwd+S3MbP3+////W/AF0HWkvOo126y6FDh+Txxx+XvXv3Su3atWXy5MlJbh8UFOR+TD8/k4FXly5dMv/Onj1bdu/e7Vx+/vln+f777yUjEHQDAAAAADyW75b80vDe++XjuTMk+vLlBM/rwGj5CxRyTitmOfDzTzfdd4kSJaR3796yZMkSeemll0zQnBpFihSRokWLmiC+XLlybos2M88INC8HAAAAAKTKkDcnSpdW98ljLRpJn5eHSoUq1UzT7a3frJPF82fL8u92S0StujLn3bel2G2l5NzZM/Lum8OT3eeYIQOkS9vWUr58efn3339lw4YNZuTx1BoxYoS88MILpjm5jmweExMj27dvN/vu37+/2I2gGwAAAACQKiVKlZbP1m2RmRPGylvDB5mMdv4CBaVyxB0ydNy7ZpuRk2bKsH69pf39DaRU2fLy0rBR0qt9qyT3GRcbK88995z8+eefkjdvXhMoT5gwIdVl7Nmzp+n3/dZbb8nAgQPNqOU6SFu/fv0kI/g5rMbuPuLChQvmDsf58+fNG5iZReyw/64L0teeWuO9XYRMj3qd9VCvk1dn5kFvFwEe+vHpct4uQqZHvc56qNdZt04XCYmV/pVipHDxkuIflMPbxck0KhcKkczg6tWrcvjwYdMUXef4Tk1sSZ9uAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAADgJTqXlJlOyhHn7aIgEXFxaX9fmKcbAAAAALzkn2v+cj7GIbn/OS2h+QqIX0CgiJ+f+LqrV717fJ1Z+9q1a3LmzBnx9/eX4ODgVO+LoBsAAAAAvCTW4SfTf88pDxWLkQrRf0sgbZGNgPNBkhmEhobKbbfdZgLv1CLoBgAAAAAvirruLx8cCZFcgQ4JDXCQ6BaRzzqU9HYRJCAgQAIDA8UvjW8IQTcAAAAAeJlD/OTSDV28XZLMISQkRLILGi8AAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYJFC8bOrUqfLWW2/JyZMnJSIiQiZPnix169ZNcvuJEyfK9OnT5dixY1KwYEF59NFHZcyYMRISEiLZzerhP3q7CPDUcm8XAAAAAEBm4tVM9+LFi6V///4SGRkpO3fuNEF38+bN5fTp04lu/9FHH8mgQYPM9vv375f33nvP7OPVV1/N8LIDAAAAAJCpg+7x48dLr169pHv37lK5cmWZMWOGhIaGyty5cxPdfsuWLdKwYUPp1KmTlCpVSpo1ayYdO3aUbdu2ZXjZAQAAAADItEH3tWvXZMeOHdK0adP/Fcbf3zzeunVroq9p0KCBeY0VZB86dEhWrlwpLVu2zLByAwAAAACQ6ft0nz17VmJjY6VIkSJu6/XxgQMHEn2NZrj1dXfddZc4HA65ceOG9O7dO9nm5TExMWaxXLhwIR3PAgAAAACAbDJ6+caNG2X06NEybdo00wd8yZIl8uWXX8rIkSOTfI0OshYWFuZcSpQokaFlBgAAAAD4Lq9lunXk8YCAADl16pTben0cHh6e6GuGDh0qjz/+uPTs2dM8rlatmly+fFmeeuopee2110zz9PgGDx5sBmtzzXQTeAMAAAAAsnWmOzg4WGrVqiXr1q1zrouLizOP69evn+hroqOjEwTWGrgrbW6emBw5ckjevHndFgAAAAAAsv083ZqB7tatm9SuXdvMza1zcGvmWkczV127dpVixYqZJuKqdevWZsTzmjVrSr169eTgwYMm+63rreAbAAAAAIDMwqtBd4cOHeTMmTMybNgwOXnypNSoUUNWrVrlHFzt2LFjbpntIUOGiJ+fn/n3r7/+kkKFCpmAe9SoUV48CwAAAAAAMmHQrfr06WOWpAZOcxUYGCiRkZFmAQAAAAAgs8tSo5cDAAAAAJCVEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAQGYJuq9cuSLR0dHOx0ePHpWJEyfKmjVr0rtsAAAAAAD4VtD98MMPy4IFC8zfUVFRUq9ePXnnnXfM+unTp9tRRgAAAAAAfCPo3rlzpzRq1Mj8/dlnn0mRIkVMtlsD8XfffdeOMgIAAAAA4BtBtzYtz5Mnj/lbm5S3bdtW/P395c477zTBNwAAAAAASGXQXa5cOVm6dKkcP35cVq9eLc2aNTPrT58+LXnz5vV0dwAAAAAAZFseB93Dhg2TAQMGSKlSpUx/7vr16zuz3jVr1rSjjAAAAAAAZEmBnr7g0UcflbvuuktOnDghERERzvVNmjQxTc0BAAAAAEAqM91PPvmk5MqVy2S1tS+3pUqVKjJ27FhPdwcAAAAAQLblcdD9/vvvm7m649N11lRiAAAAAADAg+blFy5cEIfDYZaLFy9KSEiI87nY2FhZuXKlFC5c2K5yAgAAAACQfYPufPnyiZ+fn1nKly+f4HldP2LEiPQuHwAAAAAA2T/o3rBhg8ly33ffffL5559L/vz5nc8FBwdLyZIlpWjRonaVEwAAAACA7Bt0N27c2Px7+PBhue2220xmGwAAAAAApONAaprR/vbbb6VLly7SoEED+euvv8z6Dz74wKwHAAAAAACpDLq1aXnz5s0lZ86csnPnTomJiTHrz58/L6NHj/Z0dwAAAAAAZFseB91vvPGGzJgxQ2bPni1BQUHO9Q0bNjRBOAAAAAAASGXQ/euvv8rdd9+dYH1YWJhERUV5ujsAAAAAALItj4Pu8PBwOXjwYIL12p+7TJky6VUuAAAAAAB8L+ju1auX9O3bV3744Qczgvnff/8tCxculAEDBsgzzzxjTykBAAAAAMjOU4ZZBg0aJHFxcdKkSROJjo42Tc1z5Mhhgu7nn3/enlICAAAAAOALQbdmt1977TUZOHCgaWZ+6dIlqVy5suTOndueEgIAAAAA4CtBtyU4ONgE2wAAAAAAIA1Bd9u2bWX+/PmSN29e83dyNONdpUoV6d27txnRHAAAAAAAX5WioFuDZ21Wbv2dnJiYGDOP93fffSfLli1Ln1ICAAAAAJBdg+558+Yl+ndS9u3bJ3Xq1ElbyQAAAAAA8LUpw1KiQoUKsmXLFjt2DQAAAABA9h1I7d5773U2NU/M+vXrJSAgQCIiItJaNgAAAAAAfCvorlGjhtvj69evy+7du+Xnn3+Wbt26pWfZAAAAAADwraB7woQJia4fPny4mbMbAAAAAACkcZ7u+Lp06SJ169aVt99+O712CQAAAC+4Vnuat4sAj433dgEA2D2Q2tatWyUkJCS9dgcAAAAAgO9lutu2bev22OFwyIkTJ2T79u0ydOjQ9CwbAAAAAAC+FXSHhYW5Pfb39zdThL3++uvSrFmz9CwbAAAAAAC+FXTPmzfPnpIAAAAAAODrfbqPHz8uf/75p/Pxtm3bpF+/fjJr1qz0LhsAAAAAAL4VdHfq1Ek2bNhg/j558qQ0bdrUBN6vvfaaaWIOAAAAAABSGXT//PPPZmow9cknn0i1atVky5YtsnDhQpk/f76nuwMAAAAAINvyOOi+fv265MiRw/z99ddfy0MPPWT+rlixohnFHAAAAAAApDLorlKlisyYMUM2b94sa9eulRYtWpj1f//9txQoUMDT3cnUqVOlVKlSZo7vevXqmabqyYmKipLnnntObr31VhP8ly9fXlauXOnxcQEAAAAAyHRB99ixY2XmzJlyzz33SMeOHSUiIsKsX7ZsmbPZeUotXrxY+vfvL5GRkbJz506zr+bNm8vp06cT3f7atWty//33y5EjR+Szzz6TX3/9VWbPni3FihXz9DQAAAAAAMh8U4ZpsH327Fm5cOGC3HLLLc71Tz31lISGhnq0r/Hjx0uvXr2ke/fu5rFm0L/88kuZO3euDBo0KMH2uv7cuXOmD3lQUJBZp1lyAAAAAACyRaZbBQQEuAXcVvBbuHDhFO9Ds9Y7duwwo587C+Pvbx5v3bo10ddoNr1+/fqmeXmRIkWkatWqMnr0aImNjU3NaQAAAAAAkLky3elFs+UaLGvw7EofHzhwINHXHDp0SNavXy+dO3c2/bgPHjwozz77rBncTZuoJyYmJsYsFs3QAwAAAACQaTPd3hIXF2ey6bNmzZJatWpJhw4dzPzg2iw9KWPGjJGwsDDnUqJEiQwtMwAAAADAd3kt6C5YsKBppn7q1Cm39fo4PDw80dfoiOU6Wrm+zlKpUiU5efKkaa6emMGDB8v58+edy/Hjx9P5TAAAAAAAsDHo1mm8PBUcHGyy1evWrXPLZOtj7bedmIYNG5om5bqd5bfffjPBuO4vMTqtWN68ed0WAAAAAAAy7ZRhOtWXpX379mZ+bp22a8+ePR7tS6cL0ym/3n//fdm/f78888wzcvnyZedo5l27djWZaos+r6OX9+3b1wTbOtK5DqSmA6sBAAAAAJDlB1LT/tMLFy40f69du9YsX331lXzyyScycOBAWbNmTYr3pX2yz5w5I8OGDTNNxGvUqCGrVq1yDq527NgxM6K5Rftjr169Wl588UWpXr26CfQ1AH/llVc8PQ0AAAAAADJf0K3BsTUY2YoVK0ymu1mzZmbKsHr16nlcgD59+pglMRs3bkywTpuef//99x4fBwAAAACATN+8XOfntgYj06y0Nc+2w+FgvmwAAAAAANKS6W7btq106tRJbr/9dvnnn3/kgQceMOt37dol5cqV83R3AAAAAABkWx4H3RMmTDBNyTXbPW7cOMmdO7dZf+LECXn22WftKCMAAAAAAL4RdAcFBcmAAQMSrNfBzQAAAAAAQBrn6f7ggw/krrvukqJFi8rRo0fNuokTJ8oXX3yRmt0BAAAAAJAteRx0T58+3cyvrX25o6KinIOn5cuXzwTeAAAAAAAglUH35MmTZfbs2fLaa69JQECAc33t2rVl7969nu4OAAAAAIBsy+Og+/Dhw1KzZs0E63PkyCGXL19Or3IBAAAAAOB7QXfp0qVl9+7dCdbrnN2VKlVKr3IBAAAAAOB7o5drf+7nnntOrl69Kg6HQ7Zt2yYff/yxjBkzRubMmWNPKQEAAAAA8IWgu2fPnpIzZ04ZMmSIREdHS6dOncwo5pMmTZLHHnvMnlICAAAAAOALQbfq3LmzWTTovnTpkhQuXDj9SwYAAAAAgC8G3ZbQ0FCzAAAAAACAVAbdOlq5n59fSjaVnTt3pmg7AAAAAACyuxQF3W3atHH+rQOoTZs2TSpXriz169c3677//nv55Zdf5Nlnn7WvpAAAAAAAZMegOzIy0m0gtRdeeEFGjhyZYJvjx4+nfwkBAAAAAPCVebo//fRT6dq1a4L1Xbp0kc8//zy9ygUAAAAAgO8F3Tpd2HfffZdgva4LCQlJr3IBAAAAAOB7o5f369dPnnnmGTNgWt26dc26H374QebOnStDhw61o4wAAAAAAPhG0D1o0CApU6aMTJo0ST788EOzrlKlSjJv3jxp3769HWUEAAAAAMB35unW4JoAGwAAAACAdO7TDQAAAAAAUoagGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAEBmGb08NjZW5s+fL+vWrZPTp09LXFyc2/Pr169Pz/IBAAAAAOA7QXffvn1N0P3ggw9K1apVxc/Pz56SAQAAAADga0H3okWL5JNPPpGWLVvaUyIAAAAAAHy1T3dwcLCUK1fOntIAAAAAAODLQfdLL70kkyZNEofDYU+JAAAAAADw1ebl3377rWzYsEG++uorqVKligQFBbk9v2TJkvQsHwAAAAAAvhN058uXTx555BF7SgMAAAAAgC8H3fPmzbOnJAAAAAAA+HrQbTlz5oz8+uuv5u8KFSpIoUKF0rNcAAAAAAD43kBqly9flieffFJuvfVWufvuu81StGhR6dGjh0RHR9tTSgAAAAAAfCHo7t+/v3zzzTeyfPlyiYqKMssXX3xh1unI5gAAAAAAIJXNyz///HP57LPP5J577nGua9mypeTMmVPat28v06dP93SXAAAAAABkSx5nurUJeZEiRRKsL1y4MM3LAQAAAABIS9Bdv359iYyMlKtXrzrXXblyRUaMGGGeAwAAAAAAqWxePmnSJGnevLkUL15cIiIizLo9e/ZISEiIrF692tPdAQAAAACQbXkcdFetWlV+//13WbhwoRw4cMCs69ixo3Tu3Nn06wYAAAAAAGmYpzs0NFR69eqVmpcCAAAAAOAzUhR0L1u2TB544AEJCgoyfyfnoYceSq+yAQAAAACQ/YPuNm3ayMmTJ80I5fp3Uvz8/CQ2NjY9ywcAAAAAQPYOuuPi4hL9GwAAAAAApOOUYQsWLJCYmJgE669du2aeAwAAAAAAqQy6u3fvLufPn0+w/uLFi+Y5AAAAAACQyqDb4XCYvtvx/fnnnxIWFubp7gAAAAAAyLZSPGVYzZo1TbCtS5MmTSQw8H8v1cHTDh8+LC1atLCrnAAAAAAAZN+g2xq1fPfu3dK8eXPJnTu387ng4GApVaqUtGvXzp5SAgAAAACQnYPuyMhIk9HW4LpZs2Zy66232lsyAAAAAAB8qU93QECAPP3003L16lX7SgQAAAAAgK8OpFa1alU5dOiQPaUBAAAAAMCXg+433nhDBgwYICtWrJATJ07IhQsX3BYAAAAAAOBhn25Ly5Ytzb8PPfSQ29Rh1lRi2u8bAAAAAACkIujesGGDPSUBAAAAAMDXg+7GjRvbUxIAAAAAAHw96FZRUVHy3nvvyf79+83jKlWqyJNPPilhYWHpXT4AAAAAAHxnILXt27dL2bJlZcKECXLu3DmzjB8/3qzbuXOnPaUEAAAAAMAXMt0vvviiGURt9uzZEhj4fy+/ceOG9OzZU/r16yebNm2yo5wAAAAAAGT/oFsz3a4Bt9lJYKC8/PLLUrt27fQuHwAAAAAAvtO8PG/evHLs2LEE648fPy558uRJr3IBAAAAAOB7QXeHDh2kR48esnjxYhNo67Jo0SLTvLxjx472lBIAAAAAAF9oXv7222+Ln5+fdO3a1fTlVkFBQfLMM8/Im2++aUcZAQAAACDVrtWe5u0iwGPjxWeD7uDgYJk0aZKMGTNG/vjjD7NORy4PDQ21o3wAAAAAAPhO83KLBtn58uUzS1oD7qlTp0qpUqUkJCRE6tWrJ9u2bUvR67RZu2bd27Rpk6bjAwAAAACQKYJubVI+dOhQCQsLM4GyLvr3kCFD5Pr16x4XQPuG9+/fXyIjI8083xEREdK8eXM5ffp0sq87cuSIDBgwQBo1auTxMQEAAAAAyJRB9/PPPy+zZs2ScePGya5du8yif7/33nvywgsveFyA8ePHS69evaR79+5SuXJlmTFjhsmcz507N8nXxMbGSufOnWXEiBFSpkwZj48JAAAAAECm7NP90UcfmWbdDzzwgHNd9erVpUSJEmb08unTp6d4X9euXZMdO3bI4MGDnev8/f2ladOmsnXr1iRf9/rrr0vhwoXNKOqbN2/29BQAAAAAAMicQXeOHDlMk/L4SpcubQZZ88TZs2dN1rpIkSJu6/XxgQMHEn3Nt99+a7Lqu3fvTtExYmJizGK5cOGCR2UEAAAAACDDmpf36dNHRo4c6RbI6t+jRo0yz9np4sWL8vjjj8vs2bOlYMGCKXqNjrKufc6tRTPyAAAAAABkyky39uFet26dFC9e3Ax6pvbs2WOaijdp0kTatm3r3HbJkiXJ7ksD54CAADl16pTben0cHh6eYHudokwHUGvdurVzXVxc3P+dSGCg/Prrr2b6MlfadF0HanPNdBN4AwAAAAAyZdCtU4S1a9fObV1qg1htjl6rVi0TxFvTfmkQrY8Ty5pXrFhR9u7d67ZOR03XDLjOHZ5YObQ5vC4AAABImdXDf/R2EeCp5d4uAIB0C7rnzZsn6Umz0N26dZPatWtL3bp1ZeLEiXL58mUzmrnq2rWrFCtWzDQT13m8q1atmuAmgIq/HgAAAACALBd0W86cOWOac6sKFSpIoUKFUrWfDh06mH0NGzZMTp48KTVq1JBVq1Y5B1c7duyYGdEcAAAAAIBsH3RrFlrn6l6wYIGzP7X2y9aM9OTJk80c257SpuRJDcK2cePGZF87f/58j48HAAAAAEBG8E9Nc/BvvvlGli9fLlFRUWb54osvzLqXXnrJnlICAAAAAOALme7PP/9cPvvsM7nnnnuc61q2bCk5c+aU9u3by/Tp09O7jAAAAAAA+EamOzo62tnf2lXhwoXNcwAAAAAAIJVBd/369SUyMlKuXr3qXHflyhUZMWKEeQ4AAAAAAKSyeblO6dWiRQspXry4REREmHV79uwx03mtXr3a090BAAAAAJBteRx0V6tWTX7//XdZuHChHDhwwKzr2LGjdO7c2fTrBgAAAAAAqQi6r1+/LhUrVpQVK1ZIr169PHkpAAAAAAA+x6M+3UFBQW59uQEAAAAAQDoOpPbcc8/J2LFj5caNG56+FAAAAAAAn+Jxn+4ff/xR1q1bJ2vWrDH9u3PlyuX2/JIlS9KzfAAAAAAA+E7QnS9fPmnXrp09pQEAAAAAwJeD7nnz5tlTEgAAAAAAfLVPd1xcnOnL3bBhQ6lTp44MGjRIrly5Ym/pAAAAAADwhaB71KhR8uqrr0ru3LmlWLFiMmnSJDOoGgAAAAAASGPQvWDBApk2bZqsXr1ali5dKsuXL5eFCxeaDDgAAAAAAEhD0H3s2DFp2bKl83HTpk3Fz89P/v7775TuAgAAAAAAn5LioFvn5Q4JCXFbFxQUJNevX7ejXAAAAAAA+M7o5Q6HQ5544gnJkSOHc93Vq1eld+/ebnN1M083AAAAAAAeBt3dunVLsK5Lly4pfTkAAAAAAD4nxUE383MDAAAAAGBTn24AAAAAAOAZgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAADAJgTdAAAAAADYhKAbAAAAAACbEHQDAAAAAGATgm4AAAAAAGxC0A0AAAAAgE0IugEAAAAAsAlBNwAAAAAANiHoBgAAAAAgOwfdU6dOlVKlSklISIjUq1dPtm3bluS2s2fPlkaNGsktt9xilqZNmya7PQAAAAAAPht0L168WPr37y+RkZGyc+dOiYiIkObNm8vp06cT3X7jxo3SsWNH2bBhg2zdulVKlCghzZo1k7/++ivDyw4AAAAAQKYOusePHy+9evWS7t27S+XKlWXGjBkSGhoqc+fOTXT7hQsXyrPPPis1atSQihUrypw5cyQuLk7WrVuX4WUHAAAAACDTBt3Xrl2THTt2mCbizgL5+5vHmsVOiejoaLl+/brkz5/fxpICAAAAAOC5QPGis2fPSmxsrBQpUsRtvT4+cOBAivbxyiuvSNGiRd0Cd1cxMTFmsVy4cCGNpQYAAAAAIIs0L0+LN998UxYtWiT//e9/zSBsiRkzZoyEhYU5F+0DDgAAAABAtg+6CxYsKAEBAXLq1Cm39fo4PDw82de+/fbbJuhes2aNVK9ePcntBg8eLOfPn3cux48fT7fyAwAAAACQaYPu4OBgqVWrltsgaNagaPXr10/ydePGjZORI0fKqlWrpHbt2skeI0eOHJI3b163BQAAAACAbN+nW+l0Yd26dTPBc926dWXixIly+fJlM5q56tq1qxQrVsw0E1djx46VYcOGyUcffWTm9j558qRZnzt3brMAAAAAAJBZeD3o7tChg5w5c8YE0hpA61RgmsG2Blc7duyYGdHcMn36dDPq+aOPPuq2H53ne/jw4RlefgAAAAAAMm3Qrfr06WOWxGzcuNHt8ZEjRzKoVAAAAAAA+PDo5QAAAAAAZGaZItMNAEBWda32NG8XAR4b7+0CAAB8CJluAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2CTQrh0DQGJWD//R20WAp5Z7uwAAAABZF0E3AAAAgGyNm/5Z0HLJNmheDgAAAACATQi6AQAAAACwCUE3AAAAAAA2IegGAAAAAMAmBN0AAAAAANiEoBsAAAAAAJsQdAMAAAAAYBOCbgAAAAAAbELQDQAAAACATQLt2jEAAL5g9fAfvV0EeGq5twsAAPAlZLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwAAAAAAmxB0AwAAAACQnYPuqVOnSqlSpSQkJETq1asn27ZtS3b7Tz/9VCpWrGi2r1atmqxcuTLDygoAAAAAQJYJuhcvXiz9+/eXyMhI2blzp0REREjz5s3l9OnTiW6/ZcsW6dixo/To0UN27dolbdq0McvPP/+c4WUHAAAAACBTB93jx4+XXr16Sffu3aVy5coyY8YMCQ0Nlblz5ya6/aRJk6RFixYycOBAqVSpkowcOVLuuOMOmTJlSoaXHQAAAACATBt0X7t2TXbs2CFNmzb9X4H8/c3jrVu3JvoaXe+6vdLMeFLbAwAAAADgLYFeO7KInD17VmJjY6VIkSJu6/XxgQMHEn3NyZMnE91e1ycmJibGLJbz58+bfy9cuCCZ3cXrN7xdBHgoNAvUK2+jXmc91OvkUaezHur0zVGvsx7qdfKo01lPaBao01ZM6XA4Mm/QnRHGjBkjI0aMSLC+RIkSXikPsrmwMG+XAEh/1GtkN9RpZEfUa2Q3YVmnTl+8eFHCkimvV4PuggULSkBAgJw6dcptvT4ODw9P9DW63pPtBw8ebAZqs8TFxcm5c+ekQIEC4ufnly7nAc/vCOlNj+PHj0vevHm9XRwgzajTyI6o18huqNPIjqjX3qUZbg24ixYtmux2Xg26g4ODpVatWrJu3TozArkVFOvjPn36JPqa+vXrm+f79evnXLd27VqzPjE5cuQwi6t8+fKl63kgdfSLgS8HZCfUaWRH1GtkN9RpZEfUa+9JLsOdaZqXaxa6W7duUrt2balbt65MnDhRLl++bEYzV127dpVixYqZZuKqb9++0rhxY3nnnXfkwQcflEWLFsn27dtl1qxZXj4TAAAAAAAyWdDdoUMHOXPmjAwbNswMhlajRg1ZtWqVc7C0Y8eOmRHNLQ0aNJCPPvpIhgwZIq+++qrcfvvtsnTpUqlataoXzwIAAAAAgEwYdCttSp5Uc/KNGzcmWPef//zHLMiatLl/ZGRkgmb/QFZFnUZ2RL1GdkOdRnZEvc4a/Bw3G98cAAAAAACkyv/abQMAAAAAgHRF0A0AAAAAgE0IugEAAAAAsAlBN1LsiSeeED8/P7MEBQWZEebvv/9+mTt3rplf3W46qN4dd9xhBoooV66czJ8/3/ZjInvzZp0+ceKEdOrUScqXL29maOjXr5+tx4Pv8Ga9XrJkiTlWoUKFzHyx9evXl9WrV9t6TGR/3qzT3377rTRs2FAKFCggOXPmlIoVK8qECRNsPSZ8g7d/V1u+++47CQwMNDNIwT4E3fBIixYtTLBw5MgR+eqrr+Tee+81c6e3atVKbty4YdtxDx8+bOZl1+Pt3r3bBCg9e/bkxxyybJ2OiYkxgYlOfxgREWHbceCbvFWvN23aZH40rly5Unbs2GGO27p1a9m1a5dtx4Rv8FadzpUrl5lhR+v2/v37zXe2LrNmzbLtmPAd3qrXlqioKOnatas0adLE9mP5PB29HEiJbt26OR5++OEE69etW6cj4Dtmz57tXHf06FHHQw895MiVK5cjT548jv/85z+OkydPur1u2bJljtq1azty5MjhKFCggKNNmzZJHvvll192VKlSxW1dhw4dHM2bN0+Xc4Nv8maddtW4cWNH37590+GMgMxTry2VK1d2jBgxIg1nBF+X2er0I4884ujSpUsazgjIHPVaf0sPGTLEERkZ6YiIiEinM0NiyHQjze677z6TqdNmhUqbxDz88MNy7tw5+eabb2Tt2rVy6NAh6dChg/M1X375pTzyyCPSsmVLkwFZt26d1K1bN8ljbN26VZo2beq2rnnz5mY9kBXrNOAL9VqPcfHiRcmfP78t5wTf5o06ra/ZsmWLNG7c2JZzAjKqXs+bN8/sR+f4hv0CM+AY8AHax+mnn34yf+sHfe/evaZJeIkSJcy6BQsWSJUqVeTHH3+UOnXqyKhRo+Sxxx6TESNGOPeRXBPbkydPmr4urvTxhQsX5MqVK6afFZCV6jTgC/X67bfflkuXLkn79u1tOBsg4+p08eLF5cyZM6bJ7/Dhw00XNyCr1uvff/9dBg0aJJs3bzb9uWE/Mt1IFw6HwwwEobTPk34pWF8MqnLlypIvXz7znNJ+2fQfQWZGnUZ2lJH1+qOPPjI/AD/55BMpXLhwOp0B4J06rcHJ9u3bZcaMGTJx4kT5+OOP0/EsgIyr17GxsWYgV/1+1sFckTG4tYF0oR/60qVLp3h7TzPT4eHhcurUKbd1+lhHxyXLjaxYp4HsXK8XLVpkMoGffvppgq5BQFas09YxqlWrZn5/aLa7Y8eOqdoX4M16rV1+9AaSNkPXQQKtJuwa6GvWe82aNaaJO9IXmW6k2fr1602zl3bt2pnHlSpVkuPHj5vFsm/fPjNCot6ZU9WrVzfNZVJKp52Jv732adH1QFas00B2rdeaAezevbv5V2edALLbd7UGKDoDBZAV67UmrHT/mh23lt69e0uFChXM3/Xq1bPpzHxcosOrAUmMstiiRQvHiRMnHH/++adjx44djlGjRjly587taNWqlePGjRtmu7i4OEeNGjUcjRo1Mtv88MMPjlq1apkRmi0bNmxw+Pv7O4YNG+bYt2+f46effnK8+eabSR770KFDjtDQUMfAgQMd+/fvd0ydOtUREBDgWLVqVYacO7Inb9ZptWvXLrPovjp16mT+/uWXX2w/b2Rv3qzXCxcudAQGBprvaD2+tURFRWXIuSN78madnjJlihkV+rfffjPLnDlzzOjRr732WoacO7Ivb/8GccXo5fYj6IZHXw56n0YX/VFVqFAhR9OmTR1z5851xMbGum2bkqkNPv/8c/MlEhwc7ChYsKCjbdu2yR5fv1Cs7cuUKeOYN2+eLecJ3+HtOm0d23UpWbKkLecK3+HNeq0/AhOr11omICvW6XfffddMWao3/vPmzeuoWbOmY9q0aQmOC2S13yCuCLrt56f/8Xa2HQAAAACA7Ig+3QAAAAAA2ISgGwAAAAAAmxB0AwAAAABgE4JuAAAAAABsQtANAAAAAIBNCLoBAAAAALAJQTcAAAAAADYh6AYAAAAAwCYE3QAAAAAA2ISgGwCATOSJJ54QPz8/swQFBUmRIkXk/vvvl7lz50pcXJz4gvnz50u+fPm8XQwAANIFQTcAAJlMixYt5MSJE3LkyBH56quv5N5775W+fftKq1at5MaNG94uHgAA8ABBNwAAmUyOHDkkPDxcihUrJnfccYe8+uqr8sUXX5gAXLPA6tixY/Lwww9L7ty5JW/evNK+fXs5deqU236WL18uderUkZCQEClYsKA88sgjzuc0k7506VK37TW7bO1fA37d5pNPPpFGjRpJzpw5zb5+++03+fHHH6V27drm2A888ICcOXPGbT9z5syRSpUqmeNWrFhRpk2b5nzO2u+SJUvMzYTQ0FCJiIiQrVu3muc3btwo3bt3l/Pnzzsz/sOHD7fhKgMAkDEIugEAyALuu+8+E5xqsKrNzDXgPnfunHzzzTeydu1aOXTokHTo0MG5/ZdffmmC7JYtW8quXbtk3bp1UrduXY+PGxkZKUOGDJGdO3dKYGCgdOrUSV5++WWZNGmSbN68WQ4ePCjDhg1zbr9w4ULzeNSoUbJ//34ZPXq0DB06VN5//323/b722msyYMAA2b17t5QvX146duxosvgNGjSQiRMnmhsJmu3XRbcDACCrCvR2AQAAQMpo1vinn34yAfTevXvl8OHDUqJECfPcggULpEqVKiYLrRlpDXofe+wxGTFihPP1GrR7SgPe5s2bm7+1ibsGx3r8hg0bmnU9evRwZsetIP2dd96Rtm3bmselS5eWffv2ycyZM6Vbt25u+33wwQfN31pGLbsG8HqOYWFhJsOt2X4AALI6Mt0AAGQRDofDBKOaQdZg2wq4VeXKlU3zcH1OaQa5SZMmaT5m9erVnX/roG6qWrVqbutOnz5t/r58+bL88ccfJhDXpufW8sYbb5j1Se331ltvNf9a+wEAIDsh0w0AQBahAbVmjlNC+2AnR4N3DeJdXb9+PcF2OoK662sSW2eNqn7p0iXz7+zZs6VevXpu+wkICLjpfn1ldHYAgG8h0w0AQBawfv1606S8Xbt2ZpCy48ePm8WiTbijoqJMxtvKJGsz8KQUKlTI9Je2/P777xIdHZ2mMmrWu2jRoqZ/ebly5dyWlN4sUMHBwRIbG5umsgAAkFmQ6QYAIJOJiYmRkydPmsBTRyRftWqVjBkzxkwZ1rVrV/H39zdNvDt37mwGHdMByJ599llp3LixGVXc6lutzcvLli1r+nbrNitXrpRXXnnFOTDblClTpH79+uY4ut41+5xa2j/7hRdeMP2ydeozPZft27fLv//+K/3790/RPkqVKmWy5nrTQPuh6wjnugAAkBWR6QYAIJPRIFv7OWvwqYHrhg0b5N133zXThmkzbW2OrX/fcsstcvfdd0vTpk2lTJkysnjxYuc+7rnnHvn0009l2bJlUqNGDRNkb9u2zfm8DnamfcJ1OjAdkVwHNkuPwLZnz55myrB58+aZGwN6I0AHWvMk060jmPfu3duMxq4Z+XHjxqW5XAAAeIufI36HLgAAAAAAkC7IdAMAAAAAYBOCbgAAAAAAbELQDQAAAACATQi6AQAAAACwCUE3AAAAAAA2IegGAAAAAMAmBN0AAAAAANiEoBsAAAAAAJsQdAMAAAAAYBOCbgAAAAAAbELQDQAAAACATQi6AQAAAAAQe/w/aQ4wr7+UFgQAAAAASUVORK5CYII=",
       "text/plain": [
        "<Figure size 1000x500 with 1 Axes>"
       ]
@@ -1165,10 +1216,10 @@
    "id": "d6e7f8a5",
    "metadata": {
     "papermill": {
-     "duration": 0.009177,
-     "end_time": "2026-06-03T00:07:42.577337+00:00",
+     "duration": 0.004219,
+     "end_time": "2026-08-29T08:13:49.044761",
      "exception": false,
-     "start_time": "2026-06-03T00:07:42.568160+00:00",
+     "start_time": "2026-08-29T08:13:49.040542",
      "status": "completed"
     },
     "tags": []
@@ -1182,20 +1233,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "id": "e7f8a9b6",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-07-03T15:53:13.036024Z",
-     "iopub.status.busy": "2026-07-03T15:53:13.036024Z",
-     "iopub.status.idle": "2026-07-03T15:53:13.040286Z",
-     "shell.execute_reply": "2026-07-03T15:53:13.040286Z"
+     "iopub.execute_input": "2026-08-29T08:13:49.054913Z",
+     "iopub.status.busy": "2026-08-29T08:13:49.054419Z",
+     "iopub.status.idle": "2026-08-29T08:13:49.059444Z",
+     "shell.execute_reply": "2026-08-29T08:13:49.059058Z"
     },
     "papermill": {
-     "duration": 0.024089,
-     "end_time": "2026-06-03T00:07:42.609910+00:00",
+     "duration": 0.010673,
+     "end_time": "2026-08-29T08:13:49.060088",
      "exception": false,
-     "start_time": "2026-06-03T00:07:42.585821+00:00",
+     "start_time": "2026-08-29T08:13:49.049415",
      "status": "completed"
     },
     "tags": []
@@ -1211,7 +1262,7 @@
       "     0             [0.80, 0.10, 0.10]             [0.81, 0.11, 0.08] Science (OK)\n",
       "     1             [0.10, 0.80, 0.10]             [0.12, 0.81, 0.07] Sport (OK)\n",
       "     2             [0.10, 0.10, 0.80]             [0.09, 0.09, 0.82] Cuisine (OK)\n",
-      "     3             [0.40, 0.40, 0.20]             [0.40, 0.24, 0.36] Science (OK)\n",
+      "     3             [0.40, 0.40, 0.20]             [0.39, 0.24, 0.36] Science (OK)\n",
       "     4             [0.20, 0.30, 0.50]             [0.12, 0.30, 0.58] Cuisine (OK)\n"
      ]
     }
@@ -1233,50 +1284,54 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8a9b0c7",
+   "id": "fbd914a3",
    "metadata": {
     "papermill": {
-     "duration": 0.010517,
-     "end_time": "2026-06-03T00:07:42.629908+00:00",
+     "duration": 0.00482,
+     "end_time": "2026-08-29T08:13:49.069410",
      "exception": false,
-     "start_time": "2026-06-03T00:07:42.619391+00:00",
+     "start_time": "2026-08-29T08:13:49.064590",
      "status": "completed"
     },
     "tags": []
    },
    "source": [
-    "## 6. Extensions du Topic Modeling\n",
+    "## 5bis. Exemple resolu : selectionner le nombre de sujets (K)\n",
     "\n",
-    "LDA est le modèle de base. Plusieurs extensions existent :\n",
+    "Jusqu'ici, `K = 3` et les priors asymetriques `beta_asym` encodaient notre connaissance des trois sujets (Science, Sport, Cuisine). En pratique, on ne connait **ni K, ni les mots canoniques** des sujets : on doit choisir K en comparant des modeles ajustes sur les donnees seules.\n",
     "\n",
-    "| Modèle | Description | Cas d'usage |\n",
-    "|--------|-------------|------------|\n",
-    "| **HDP** (Hierarchical DP) | Nombre de sujets appris automatiquement | Quand K est inconnu |\n",
-    "| **CTM** (Correlated Topic Model) | Sujets correlés (logistique-normale) | Sujets semantiquement proches |\n",
-    "| **DTM** (Dynamic Topic Model) | Sujets evoluent dans le temps | Corpus temporels |\n",
-    "| **sLDA** (Supervised LDA) | Combine topics + labels de classe | Classification supervisee |\n",
+    "Le protocole standard comporte trois mesures independantes, calculees sur les topics **effectivement appris** (jamais sur `phi_true`, jamais sur les etiquettes cachees) :\n",
     "\n",
-    "En pratique, on utilise souvent `sklearn.decomposition.LatentDirichletAllocation`\n",
-    "ou `gensim` pour des corpus reels, car l'implementation est plus rapide que\n",
-    "l'inference MCMC complete."
+    "1. **Coherence UMass documentaire** (Mimno et al. 2011) : pour chaque sujet, les paires de ses mots dominants doivent co-apparaitre dans les memes documents. Valeurs proches de 0 = sujets interpretables.\n",
+    "2. **Redondance entre sujets** : similarite cosinus maximale entre paires de sujets appris. Un K trop grand fabrique des sujets quasi identiques.\n",
+    "3. **Log-vraisemblance predictive held-out** : chaque document est coupe en deux moities ; le modele est ajuste sur la premiere (49 mots), on evalue la probabilite moyenne des mots de la seconde (51 mots). Mesure la capacite predictive, pas seulement l'ajustement.\n",
+    "\n",
+    "Chaque K fait donc l'objet de **deux ajustements separes** : un ajustement sur le **corpus complet** (100 mots) pour les mesures de qualite des sujets --- coherence et redondance s'estiment sur les sujets appris avec toutes les donnees, pratique standard des pipelines sklearn/gensim --- et un ajustement sur la **moitie d'apprentissage** pour la mesure predictive, qui exige par construction des mots tenus a l'ecart.\n",
+    "\n",
+    "Deux precautions de rigueur :\n",
+    "\n",
+    "- **Priors neutres** : `alpha = 0.5` (documents sparses) et `beta = 1` uniforme --- aucune information sur les sujets reels ne rentre dans le modele.\n",
+    "- **Alignement des permutations** : avec des priors symetriques, NUTS peut etiqueter les sujets differemment selon la chaine (*label switching*). Avant d'agreger, chaque tirage est re-ordonne par un tri canonique de ses lignes (ordre lexicographique des distributions de mots), applique conjointement a phi et theta.\n",
+    "\n",
+    "On compare enfin le K selectionne au K reel (3) --- la verite terrain sert **uniquement** de controle final, jamais a construire les sujets."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
-   "id": "a9b0c1d8",
+   "execution_count": 15,
+   "id": "6f90e72d",
    "metadata": {
     "execution": {
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+     "shell.execute_reply": "2026-08-29T08:13:49.090419Z"
     },
     "papermill": {
-     "duration": 0.990755,
-     "end_time": "2026-06-03T00:07:43.629168+00:00",
+     "duration": 0.017843,
+     "end_time": "2026-08-29T08:13:49.091785",
      "exception": false,
-     "start_time": "2026-06-03T00:07:42.638413+00:00",
+     "start_time": "2026-08-29T08:13:49.073942",
      "status": "completed"
     },
     "tags": []
@@ -1286,140 +1341,777 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "sklearn LDA (pour reference, beaucoup plus rapide) :\n",
-      "  Sujet 0 : atome (0.282), ballon (0.145), experience (0.139), equipe (0.121)\n",
-      "  Sujet 1 : recette (0.214), four (0.174), ballon (0.134), ingredient (0.132)\n",
-      "  Sujet 2 : recette (0.316), ingredient (0.278), four (0.117), match (0.100)\n"
+      "Split-half : 49 mots ajustement / 51 mots held-out\n",
+      "Coherence UMass et alignement des permutations prets.\n"
      ]
     }
    ],
    "source": [
-    "# Comparaison rapide avec sklearn LDA (pour reference)\n",
-    "from sklearn.decomposition import LatentDirichletAllocation\n",
-    "\n",
-    "lda_sklearn = LatentDirichletAllocation(n_components=3, random_state=42,\n",
-    "                                         max_iter=50)\n",
-    "lda_sklearn.fit(bow_matrix)\n",
-    "\n",
-    "phi_sklearn = lda_sklearn.components_ / lda_sklearn.components_.sum(axis=1, keepdims=True)\n",
-    "theta_sklearn = lda_sklearn.transform(bow_matrix)\n",
-    "\n",
-    "print(\"sklearn LDA (pour reference, beaucoup plus rapide) :\")\n",
-    "for k in range(n_topics):\n",
-    "    top_words = np.argsort(phi_sklearn[k])[::-1][:4]\n",
-    "    top_str = ', '.join([f\"{vocab[w]} ({phi_sklearn[k, w]:.3f})\" for w in top_words])\n",
-    "    print(f\"  Sujet {k} : {top_str}\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b0c1d2e9",
-   "metadata": {
-    "papermill": {
-     "duration": 0.009094,
-     "end_time": "2026-06-03T00:07:43.646517+00:00",
-     "exception": false,
-     "start_time": "2026-06-03T00:07:43.637423+00:00",
-     "status": "completed"
-    },
-    "tags": []
-   },
-   "source": [
-    "## 7. Exercice : Corpus Etendu\n",
-    "\n",
-    "Créez un corpus avec 4 sujets (Sport, Tech, Cuisine, Voyage) et 12 mots.\n",
-    "Testez LDA avec priors asymetriques et verifiez que les sujets sont bien identifies.\n",
-    "\n",
-    "**Indices** :\n",
-    "- Définir 12 mots (3 par sujet) : `vocab2 = ['ballon', 'équipe', 'match', 'code', 'algorithme', 'données', ...]`\n",
-    "- Construire `beta_asym2` avec 4 lignes (sujets) et 12 colonnes (mots)\n",
-    "- Generer 8 documents avec des proportions theta variees\n",
-    "- Estimer avec le modèle PyMC et verifier les résultats"
+    "# Protocole de selection de K : preparation split-half et coherence UMass\n",
+    "\n",
+    "# Split-half deterministe par document : moitie 1 pour l'ajustement,\n",
+    "# moitie 2 pour l'evaluation predictive hors echantillon\n",
+    "docs_fit, docs_held = [], []\n",
+    "for doc in documents:\n",
+    "    milieu = len(doc) // 2\n",
+    "    docs_fit.append(doc[:milieu])\n",
+    "    docs_held.append(doc[milieu:])\n",
+    "\n",
+    "bow_fit = np.zeros((n_docs, n_vocab), dtype=int)\n",
+    "bow_held = np.zeros((n_docs, n_vocab), dtype=int)\n",
+    "for d, doc in enumerate(docs_fit):\n",
+    "    for w in doc:\n",
+    "        bow_fit[d, w] += 1\n",
+    "for d, doc in enumerate(docs_held):\n",
+    "    for w in doc:\n",
+    "        bow_held[d, w] += 1\n",
+    "longueurs_fit = [len(doc) for doc in docs_fit]\n",
+    "\n",
+    "\n",
+    "def coherence_umass(phi_estime, docs, top_n=5):\n",
+    "    \"\"\"Coherence UMass moyenne sur les sujets APPRIS.\n",
+    "\n",
+    "    Pour chaque sujet k : les top_n mots dominants (selon phi_estime),\n",
+    "    somme sur les paires ordonnees de log((D(wi,wj)+1)/(D(wi)+1)),\n",
+    "    ou D compte les documents contenant le mot. Proche de 0 = coherent.\n",
+    "    \"\"\"\n",
+    "    ensembles = [set(doc) for doc in docs]\n",
+    "\n",
+    "    def freq_doc(w):\n",
+    "        return sum(1 for s in ensembles if w in s)\n",
+    "\n",
+    "    def co_freq(w1, w2):\n",
+    "        return sum(1 for s in ensembles if w1 in s and w2 in s)\n",
+    "\n",
+    "    scores_sujets = []\n",
+    "    for k in range(phi_estime.shape[0]):\n",
+    "        dominants = np.argsort(phi_estime[k])[::-1][:top_n]\n",
+    "        score = 0.0\n",
+    "        for i in range(len(dominants)):\n",
+    "            for j in range(len(dominants)):\n",
+    "                if i != j:\n",
+    "                    score += np.log((co_freq(dominants[i], dominants[j]) + 1)\n",
+    "                                    / (freq_doc(dominants[i]) + 1))\n",
+    "        scores_sujets.append(score)\n",
+    "    return float(np.mean(scores_sujets))\n",
+    "\n",
+    "\n",
+    "def phi_theta_alignes(trace):\n",
+    "    \"\"\"Moyennes posterieures de phi et theta, permutations alignees.\n",
+    "\n",
+    "    Avec des priors symetriques, chaque chaine peut etiqueter les sujets\n",
+    "    dans un ordre different (label switching) : la moyenne brute melangerait\n",
+    "    les permutations. On re-ordonne chaque tirage par tri lexicographique\n",
+    "    canonique des lignes de phi, permutation appliquee aussi a theta.\n",
+    "    \"\"\"\n",
+    "    phi_tirs = trace.posterior['phi'].stack(\n",
+    "        echant=('chain', 'draw')).transpose('echant', 'phi_dim_0', 'phi_dim_1').values\n",
+    "    theta_tirs = trace.posterior['theta'].stack(\n",
+    "        echant=('chain', 'draw')).transpose('echant', 'theta_dim_0', 'theta_dim_1').values\n",
+    "    n_tirs, _, n_v = phi_tirs.shape\n",
+    "    phi_alignes = np.empty_like(phi_tirs)\n",
+    "    theta_alignes = np.empty_like(theta_tirs)\n",
+    "    for t in range(n_tirs):\n",
+    "        ordre = np.lexsort([phi_tirs[t, :, w] for w in range(n_v)])\n",
+    "        phi_alignes[t] = phi_tirs[t][ordre]\n",
+    "        theta_alignes[t] = theta_tirs[t][:, ordre]\n",
+    "    return phi_alignes.mean(axis=0), theta_alignes.mean(axis=0)\n",
+    "\n",
+    "\n",
+    "print(f\"Split-half : {sum(longueurs_fit)} mots ajustement / {bow_held.sum()} mots held-out\")\n",
+    "print(\"Coherence UMass et alignement des permutations prets.\")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
-   "id": "c1d2e3f0",
+   "execution_count": 16,
+   "id": "13cbff03",
    "metadata": {
     "execution": {
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-     "shell.execute_reply": "2026-07-03T15:53:13.306683Z"
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+     "iopub.status.busy": "2026-08-29T08:13:49.102858Z",
+     "iopub.status.idle": "2026-08-29T08:17:20.044814Z",
+     "shell.execute_reply": "2026-08-29T08:17:20.043795Z"
     },
     "papermill": {
-     "duration": 0.018615,
-     "end_time": "2026-06-03T00:07:43.674001+00:00",
+     "duration": 210.949445,
+     "end_time": "2026-08-29T08:17:20.045908",
      "exception": false,
-     "start_time": "2026-06-03T00:07:43.655386+00:00",
+     "start_time": "2026-08-29T08:13:49.096463",
      "status": "completed"
     },
     "tags": []
    },
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 15 seconds.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 14 seconds.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n"
+     ]
+    },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Exercice a completer\n"
+      "K=2 : coherence UMass=-4.19, redondance=0.911, log-prob/mot held-out=-2.173\n"
      ]
-    }
-   ],
-   "source": [
-    "# TODO etudiant : implementer le corpus etendu a 4 sujets\n",
-    "# Resultat attendu : 4 sujets bien differencies (Sport, Tech, Cuisine, Voyage)\n",
-    "\n",
-    "print(\"Exercice a completer\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "25ed0608",
-   "metadata": {
-    "papermill": {
-     "duration": 0.007975,
-     "end_time": "2026-06-03T00:07:43.690337+00:00",
-     "exception": false,
-     "start_time": "2026-06-03T00:07:43.682362+00:00",
-     "status": "completed"
     },
-    "tags": []
-   },
-   "source": [
-    "---\n",
-    "\n",
-    "**Retour au sommaire** : [Index Probas](../README.md)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d2e3f4a1",
-   "metadata": {
-    "papermill": {
-     "duration": 0.009044,
-     "end_time": "2026-06-03T00:07:43.707664+00:00",
-     "exception": false,
-     "start_time": "2026-06-03T00:07:43.698620+00:00",
-     "status": "completed"
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
     },
-    "tags": []
-   },
-   "source": [
-    "## Conclusion\n",
-    "\n",
-    "Les modèles de sujets (Topic Models) comme LDA decomposent un corpus de documents en thèmes latents, chaque document etant un melange de topics.\n",
-    "\n",
-    "### Points cles\n",
-    "- LDA suppose chaque document = melange de K topics, chaque topic = distribution sur le vocabulaire\n",
-    "- Le nombre de topics K peut etre selectionne par coherence ou critères predictifs\n",
-    "- L'inference variationnelle et MCMC sont les deux approches principales pour estimer les topics\n",
-    "\n",
-    "## 8. Resume : Infer.NET vs PyMC pour le Topic Modeling\n",
-    "\n",
-    "| Aspect | Infer.NET | PyMC |\n",
-    "|--------|-----------|------|\n",
-    "| Algorithme | VMP (Variational Message Passing) | NUTS (MCMC) |\n",
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 16 seconds.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 15 seconds.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "K=3 : coherence UMass=-3.78, redondance=0.941, log-prob/mot held-out=-2.184\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 15 seconds.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 13 seconds.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "K=4 : coherence UMass=-4.05, redondance=0.975, log-prob/mot held-out=-2.188\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 14 seconds.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 13 seconds.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "K=5 : coherence UMass=-4.06, redondance=0.990, log-prob/mot held-out=-2.190\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 14 seconds.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Initializing NUTS using jitter+adapt_diag...\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "NUTS: [phi, theta]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 1_500 draw iterations (4_000 + 6_000 draws total) took 13 seconds.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "K=6 : coherence UMass=-4.10, redondance=0.995, log-prob/mot held-out=-2.193\n",
+      "\n",
+      "Synthese de la selection de K :\n",
+      "  K    UMass  redondance  held-out/mot\n",
+      "----------------------------------------\n",
+      "  2    -4.19       0.911        -2.173\n",
+      "  3    -3.78       0.941        -2.184\n",
+      "  4    -4.05       0.975        -2.188\n",
+      "  5    -4.06       0.990        -2.190\n",
+      "  6    -4.10       0.995        -2.193\n",
+      "\n",
+      "K=2 : sujet 0 = atome, recette, experience, ballon | sujet 1 = recette, four, ingredient, atome\n",
+      "\n",
+      "K=3 : sujet 0 = atome, experience, recette, theorie | sujet 1 = recette, ingredient, atome, four | sujet 2 = four, ballon, recette, equipe\n",
+      "\n",
+      "K=4 : sujet 0 = atome, recette, experience, ballon | sujet 1 = atome, recette, ingredient, experience | sujet 2 = recette, four, ingredient, atome | sujet 3 = four, ballon, recette, equipe\n",
+      "\n",
+      "K=5 : sujet 0 = atome, recette, experience, ingredient | sujet 1 = atome, recette, experience, ingredient | sujet 2 = recette, atome, ingredient, four | sujet 3 = four, recette, ballon, ingredient | sujet 4 = four, recette, ballon, equipe\n",
+      "\n",
+      "K=6 : sujet 0 = atome, recette, experience, ingredient | sujet 1 = atome, recette, experience, ingredient | sujet 2 = recette, atome, ingredient, experience | sujet 3 = recette, four, atome, ingredient | sujet 4 = four, recette, ballon, ingredient | sujet 5 = four, recette, ballon, equipe\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Ajustement reel des LDA concurrentes : K = 2..6, priors neutres, moteur NUTS\n",
+    "# Deux ajustements par K : corpus complet (qualite des sujets) + moitie 1 (predictif)\n",
+    "grille_K = [2, 3, 4, 5, 6]\n",
+    "resultats_K = []\n",
+    "phi_par_K = {}\n",
+    "\n",
+    "for K in grille_K:\n",
+    "    # Ajustement A : corpus complet -> sujets appris pour coherence/redondance\n",
+    "    with pm.Model() as modele_plein:\n",
+    "        phi_A = pm.Dirichlet('phi', a=np.ones((K, n_vocab)), shape=(K, n_vocab))\n",
+    "        theta_A = pm.Dirichlet('theta', a=np.ones(K) * 0.5, shape=(n_docs, K))\n",
+    "        pm.Multinomial('obs', n=doc_lengths, p=pt.dot(theta_A, phi_A),\n",
+    "                       observed=bow_matrix)\n",
+    "        trace_plein = pm.sample(1500, random_seed=42, return_inferencedata=True,\n",
+    "                                progressbar=False)\n",
+    "    phi_plein, _ = phi_theta_alignes(trace_plein)\n",
+    "    phi_par_K[K] = phi_plein\n",
+    "\n",
+    "    # Ajustement B : moitie 1 -> thetas pour la mesure predictive held-out\n",
+    "    with pm.Model() as modele_demi:\n",
+    "        phi_B = pm.Dirichlet('phi', a=np.ones((K, n_vocab)), shape=(K, n_vocab))\n",
+    "        theta_B = pm.Dirichlet('theta', a=np.ones(K) * 0.5, shape=(n_docs, K))\n",
+    "        pm.Multinomial('obs', n=longueurs_fit, p=pt.dot(theta_B, phi_B),\n",
+    "                       observed=bow_fit)\n",
+    "        trace_demi = pm.sample(1500, random_seed=42, return_inferencedata=True,\n",
+    "                               progressbar=False)\n",
+    "    phi_demi, theta_demi = phi_theta_alignes(trace_demi)\n",
+    "\n",
+    "    # Mesure 1 : coherence UMass sur les sujets appris (corpus complet)\n",
+    "    coherence = coherence_umass(phi_plein, documents, top_n=5)\n",
+    "\n",
+    "    # Mesure 2 : redondance = similarite cosinus max entre paires de sujets\n",
+    "    normalises = phi_plein / np.linalg.norm(phi_plein, axis=1, keepdims=True)\n",
+    "    similarites = normalises @ normalises.T\n",
+    "    np.fill_diagonal(similarites, 0.0)\n",
+    "    redondance = float(similarites.max()) if K > 1 else 0.0\n",
+    "\n",
+    "    # Mesure 3 : log-probabilite moyenne par mot held-out (ajustement B uniquement)\n",
+    "    probs_doc = theta_demi @ phi_demi\n",
+    "    log_ll = 0.0\n",
+    "    n_mots_held = 0\n",
+    "    for d in range(n_docs):\n",
+    "        for w, compte in enumerate(bow_held[d]):\n",
+    "            if compte > 0:\n",
+    "                log_ll += compte * np.log(probs_doc[d, w] + 1e-12)\n",
+    "                n_mots_held += compte\n",
+    "    log_ll_par_mot = log_ll / n_mots_held\n",
+    "\n",
+    "    resultats_K.append({'K': K, 'coherence': coherence,\n",
+    "                        'redondance': redondance, 'heldout': log_ll_par_mot})\n",
+    "    print(f\"K={K} : coherence UMass={coherence:.2f}, redondance={redondance:.3f}, \"\n",
+    "          f\"log-prob/mot held-out={log_ll_par_mot:.3f}\")\n",
+    "\n",
+    "print(\"\\nSynthese de la selection de K :\")\n",
+    "print(f\"{'K':>3} {'UMass':>8} {'redondance':>11} {'held-out/mot':>13}\")\n",
+    "print(\"-\" * 40)\n",
+    "for r in resultats_K:\n",
+    "    print(f\"{r['K']:>3} {r['coherence']:>8.2f} {r['redondance']:>11.3f} \"\n",
+    "          f\"{r['heldout']:>13.3f}\")\n",
+    "\n",
+    "# Mots dominants par sujet pour chaque K (les sujets APPRIS)\n",
+    "for K in grille_K:\n",
+    "    dominants = np.argsort(phi_par_K[K], axis=1)[:, ::-1][:, :4]\n",
+    "    print(f\"\\nK={K} : \" + \" | \".join(\n",
+    "        f\"sujet {k} = {', '.join(vocab[w] for w in dominants[k])}\"\n",
+    "        for k in range(K)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Interpretation : des metriques qui divergent\n",
+    "\n",
+    "Aucun K ne gagne sur les trois mesures --- chaque metrique repond a une question differente :\n",
+    "\n",
+    "| Mesure | Gagnant | Lecture |\n",
+    "|--------|---------|---------|\n",
+    "| Coherence UMass | **K=3** (-3.78) | Le seul maximum local de la grille --- et le K generateur du corpus |\n",
+    "| Held-out | **K=2** (-2.173) | Decroissance monotone ; ecart de 0.011 nat/mot contre K=3 : dans le bruit pour 51 mots |\n",
+    "| Redondance | penalise K grand | Croit de 0.911 a 0.995 : chaque sujet supplementaire est de plus en plus similaire aux existants |\n",
+    "\n",
+    "Quatre enseignements :\n",
+    "\n",
+    "1. **La coherence designe le bon K ici.** K=3 est le seul pic de coherence, et les top-mots montrent une structure reconnaissable : sujet 0 = atome, experience, theorie (Science), sujet 1 = recette, ingredient, four (Cuisine), sujet 2 = four, ballon, recette, equipe (Sport partiellement colle a la Cuisine).\n",
+    "\n",
+    "2. **La mesure predictive, elle, prefere K=2 et decroit des K=3.** Avec seulement 49 mots d'apprentissage, chaque sujet supplementaire dilue les comptes par document : le modele sous-determine perd immediatement en prevision. Cette divergence coherence-vs-prevision est la lecon centrale du protocole : un critere unique n'est pas une selection.\n",
+    "\n",
+    "3. **Les sujets appris restent plus flous que ceux de la section 4** (priors informes). NUTS echantillonne le posterieur complet ; malgre l'alignement canonique des permutations, les modes multiples laissent des traces (le mot « recette », le plus frequent du corpus, residue dans plusieurs sujets). Le jumeau Infer.NET, avec VMP et une initialisation jitteree, s'engage dans un seul mode et rend des sujets plus tranches --- un contraste honnete entre paradigmes d'inference, pas une difference de qualite intrinseque.\n",
+    "\n",
+    "4. **Verdict honnete** : aucune dominance nette. La selection combine le pic de coherence (K=3), la redondance qui exclut les grands K, et la lecture des top-mots ; la verite terrain (3 sujets) confirme le choix sans avoir servi a le construire.\n",
+    "\n",
+    "Ces sujets viennent de l'inference (priors neutres `alpha=0.5`, `beta=1`, alignement des permutations) : ni `phi_true`, ni `beta_asym` n'ont guide l'apprentissage."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f8a9b0c7",
+   "metadata": {
+    "papermill": {
+     "duration": 0.005853,
+     "end_time": "2026-08-29T08:17:20.058121",
+     "exception": false,
+     "start_time": "2026-08-29T08:17:20.052268",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "source": [
+    "## 6. Extensions du Topic Modeling\n",
+    "\n",
+    "LDA est le modèle de base. Plusieurs extensions existent :\n",
+    "\n",
+    "| Modèle | Description | Cas d'usage |\n",
+    "|--------|-------------|------------|\n",
+    "| **HDP** (Hierarchical DP) | Nombre de sujets appris automatiquement | Quand K est inconnu |\n",
+    "| **CTM** (Correlated Topic Model) | Sujets correlés (logistique-normale) | Sujets semantiquement proches |\n",
+    "| **DTM** (Dynamic Topic Model) | Sujets evoluent dans le temps | Corpus temporels |\n",
+    "| **sLDA** (Supervised LDA) | Combine topics + labels de classe | Classification supervisee |\n",
+    "\n",
+    "En pratique, on utilise souvent `sklearn.decomposition.LatentDirichletAllocation`\n",
+    "ou `gensim` pour des corpus reels, car l'implementation est plus rapide que\n",
+    "l'inference MCMC complete."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "a9b0c1d8",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-08-29T08:17:20.071325Z",
+     "iopub.status.busy": "2026-08-29T08:17:20.071079Z",
+     "iopub.status.idle": "2026-08-29T08:17:20.303184Z",
+     "shell.execute_reply": "2026-08-29T08:17:20.302352Z"
+    },
+    "papermill": {
+     "duration": 0.239938,
+     "end_time": "2026-08-29T08:17:20.304065",
+     "exception": false,
+     "start_time": "2026-08-29T08:17:20.064127",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "sklearn LDA (pour reference, beaucoup plus rapide) :\n",
+      "  Sujet 0 : atome (0.282), ballon (0.145), experience (0.139), equipe (0.121)\n",
+      "  Sujet 1 : recette (0.214), four (0.174), ballon (0.134), ingredient (0.132)\n",
+      "  Sujet 2 : recette (0.316), ingredient (0.278), four (0.117), match (0.100)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Comparaison rapide avec sklearn LDA (pour reference)\n",
+    "from sklearn.decomposition import LatentDirichletAllocation\n",
+    "\n",
+    "lda_sklearn = LatentDirichletAllocation(n_components=3, random_state=42,\n",
+    "                                         max_iter=50)\n",
+    "lda_sklearn.fit(bow_matrix)\n",
+    "\n",
+    "phi_sklearn = lda_sklearn.components_ / lda_sklearn.components_.sum(axis=1, keepdims=True)\n",
+    "theta_sklearn = lda_sklearn.transform(bow_matrix)\n",
+    "\n",
+    "print(\"sklearn LDA (pour reference, beaucoup plus rapide) :\")\n",
+    "for k in range(n_topics):\n",
+    "    top_words = np.argsort(phi_sklearn[k])[::-1][:4]\n",
+    "    top_str = ', '.join([f\"{vocab[w]} ({phi_sklearn[k, w]:.3f})\" for w in top_words])\n",
+    "    print(f\"  Sujet {k} : {top_str}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b0c1d2e9",
+   "metadata": {
+    "papermill": {
+     "duration": 0.005969,
+     "end_time": "2026-08-29T08:17:20.316730",
+     "exception": false,
+     "start_time": "2026-08-29T08:17:20.310761",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "source": [
+    "## 7. Exercice : Corpus Etendu\n",
+    "\n",
+    "Créez un corpus avec 4 sujets (Sport, Tech, Cuisine, Voyage) et 12 mots.\n",
+    "Testez LDA avec priors asymetriques et verifiez que les sujets sont bien identifies.\n",
+    "\n",
+    "**Indices** :\n",
+    "- Définir 12 mots (3 par sujet) : `vocab2 = ['ballon', 'équipe', 'match', 'code', 'algorithme', 'données', ...]`\n",
+    "- Construire `beta_asym2` avec 4 lignes (sujets) et 12 colonnes (mots)\n",
+    "- Generer 8 documents avec des proportions theta variees\n",
+    "- Estimer avec le modèle PyMC et verifier les résultats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "c1d2e3f0",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-08-29T08:17:20.329768Z",
+     "iopub.status.busy": "2026-08-29T08:17:20.329138Z",
+     "iopub.status.idle": "2026-08-29T08:17:20.333887Z",
+     "shell.execute_reply": "2026-08-29T08:17:20.333290Z"
+    },
+    "papermill": {
+     "duration": 0.012503,
+     "end_time": "2026-08-29T08:17:20.334855",
+     "exception": false,
+     "start_time": "2026-08-29T08:17:20.322352",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Exercice a completer\n"
+     ]
+    }
+   ],
+   "source": [
+    "# TODO etudiant : implementer le corpus etendu a 4 sujets\n",
+    "# Resultat attendu : 4 sujets bien differencies (Sport, Tech, Cuisine, Voyage)\n",
+    "\n",
+    "print(\"Exercice a completer\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "25ed0608",
+   "metadata": {
+    "papermill": {
+     "duration": 0.005641,
+     "end_time": "2026-08-29T08:17:20.346329",
+     "exception": false,
+     "start_time": "2026-08-29T08:17:20.340688",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "source": [
+    "---\n",
+    "\n",
+    "**Retour au sommaire** : [Index Probas](../README.md)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d2e3f4a1",
+   "metadata": {
+    "papermill": {
+     "duration": 0.005606,
+     "end_time": "2026-08-29T08:17:20.357905",
+     "exception": false,
+     "start_time": "2026-08-29T08:17:20.352299",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "source": [
+    "## Conclusion\n",
+    "\n",
+    "Les modèles de sujets (Topic Models) comme LDA decomposent un corpus de documents en thèmes latents, chaque document etant un melange de topics.\n",
+    "\n",
+    "### Points cles\n",
+    "- LDA suppose chaque document = melange de K topics, chaque topic = distribution sur le vocabulaire\n",
+    "- Le nombre de topics K peut etre selectionne par coherence ou critères predictifs\n",
+    "- L'inference variationnelle et MCMC sont les deux approches principales pour estimer les topics\n",
+    "\n",
+    "## 8. Resume : Infer.NET vs PyMC pour le Topic Modeling\n",
+    "\n",
+    "| Aspect | Infer.NET | PyMC |\n",
+    "|--------|-----------|------|\n",
+    "| Algorithme | VMP (Variational Message Passing) | NUTS (MCMC) |\n",
     "| Rupture de symetrie | Priors asymetriques sur phi | Pareil |\n",
     "| Variables discretes | Natif (`Variable.Discrete`) | `pm.Categorical` + `CategoricalGibbsMetropolis` |\n",
     "| Performance | Rapide (VMP converge en ~20 itérations) | Lent (MCMC necessite des milliers d'echantillons) |\n",
@@ -1439,7 +2131,16 @@
   {
    "cell_type": "markdown",
    "id": "fixed-id-null",
-   "metadata": {},
+   "metadata": {
+    "papermill": {
+     "duration": 0.005742,
+     "end_time": "2026-08-29T08:17:20.369154",
+     "exception": false,
+     "start_time": "2026-08-29T08:17:20.363412",
+     "status": "completed"
+    },
+    "tags": []
+   },
    "source": [
     "## Références\n",
     "\n",
@@ -1455,6 +2156,23 @@
   }
  ],
  "metadata": {
+  "cost": {
+   "api_provider": "none",
+   "api_usd_est": 0.0,
+   "cpu_min": 2,
+   "external_account": "none",
+   "free_alternative": "self",
+   "gpu_min": 0,
+   "gpu_required": false,
+   "metadata_written": "2026-07-28",
+   "network": false,
+   "notes": "Topic Models (LDA) — allocation latente de Dirichlet, inference MCMC. Re-exec mesure : 25s.",
+   "reduced_pedagogical": "Probas/PyMC/PyMC-1-Setup.ipynb",
+   "reproducibility": "HIGH",
+   "validator": "papermill",
+   "vram_gb": 0,
+   "vram_tier": "NONE"
+  },
   "kernelspec": {
    "display_name": "Python 3",
    "language": "python",
@@ -1470,24 +2188,26 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.13"
+   "version": "3.13.3"
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   "papermill": {
    "default_parameters": {},
-   "duration": 263.975702,
-   "end_time": "2026-06-03T00:07:45.096022+00:00",
+   "duration": 267.869112,
+   "end_time": "2026-08-29T08:17:22.332106",
    "environment_variables": {},
    "exception": null,
-   "input_path": "PyMC-11-Topic-Models.ipynb",
-   "output_path": "PyMC-11-Topic-Models.ipynb",
-   "parameters": {},
-   "start_time": "2026-06-03T00:03:21.120320+00:00",
+   "input_path": "D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\PyMC\\PyMC-11-Topic-Models.ipynb",
+   "output_path": "D:\\Dev\\CoursIA-13036-lda\\MyIA.AI.Notebooks\\Probas\\PyMC\\PyMC-11-Topic-Models_output.ipynb",
+   "parameters": {
+    "BATCH_MODE": "true"
+   },
+   "start_time": "2026-08-29T08:12:54.462994",
    "version": "2.7.0"
   },
   "widgets": {
    "application/vnd.jupyter.widget-state+json": {
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@@ -1540,7 +2260,7 @@
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-     "78db0471937f42be8f0570875e6900e3": {
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@@ -1553,13 +2273,13 @@
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        "_view_module_version": "1.0.0",
        "_view_name": "OutputView",
-       "layout": "IPY_MODEL_08f1565377af42ee9b1e30475c222401",
+       "layout": "IPY_MODEL_acdd14a0a7d143f48453538a62bfba48",
        "msg_id": "",
        "outputs": [
         {
          "data": {
-          "text/html": "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">                                                                                                                   \n <span style=\"font-weight: bold\"> Progress                   </span> <span style=\"font-weight: bold\"> Draw </span> <span style=\"font-weight: bold\"> Divergences </span> <span style=\"font-weight: bold\"> Step size </span> <span style=\"font-weight: bold\"> Grad evals </span> <span style=\"font-weight: bold\"> Speed          </span> <span style=\"font-weight: bold\"> Elapsed </span> <span style=\"font-weight: bold\"> Remaining </span> \n ───────────────────────────────────────────────────────────────────────────────────────────────────────────────── \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   3000   0             0.165       31           251.24 draws/s   0:00:11   0:00:00    \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   3000   0             0.157       31           290.38 draws/s   0:00:10   0:00:00    \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   3000   0             0.126       31           274.18 draws/s   0:00:10   0:00:00    \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   3000   0             0.130       31           210.46 draws/s   0:00:14   0:00:00    \n                                                                                                                   \n</pre>\n",
-          "text/plain": "                                                                                                                   \n \u001b[1m \u001b[0m\u001b[1mProgress                  \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDraw\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDivergences\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mStep size\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mGrad evals\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mSpeed         \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mElapsed\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mRemaining\u001b[0m\u001b[1m \u001b[0m \n ───────────────────────────────────────────────────────────────────────────────────────────────────────────────── \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   3000   0             0.165       31           251.24 draws/s   0:00:11   0:00:00    \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   3000   0             0.157       31           290.38 draws/s   0:00:10   0:00:00    \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   3000   0             0.126       31           274.18 draws/s   0:00:10   0:00:00    \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   3000   0             0.130       31           210.46 draws/s   0:00:14   0:00:00    \n                                                                                                                   \n"
+          "text/html": "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">                                                                                                                   \n <span style=\"font-weight: bold\">                      </span> <span style=\"font-weight: bold\">           </span> <span style=\"font-weight: bold\">           </span> <span style=\"font-weight: bold\">           </span> <span style=\"font-weight: bold\"> Grad      </span> <span style=\"font-weight: bold\">                    </span> <span style=\"font-weight: bold\">          </span> <span style=\"font-weight: bold\">          </span> \n <span style=\"font-weight: bold\"> Progress             </span> <span style=\"font-weight: bold\"> Draw      </span> <span style=\"font-weight: bold\"> Divergen… </span> <span style=\"font-weight: bold\"> Step size </span> <span style=\"font-weight: bold\"> evals     </span> <span style=\"font-weight: bold\"> Speed              </span> <span style=\"font-weight: bold\"> Elapsed  </span> <span style=\"font-weight: bold\"> Remaini… </span> \n ───────────────────────────────────────────────────────────────────────────────────────────────────────────────── \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━</span>   3000        0           0.147       31          267.30 draws/s       0:00:11    0:00:00   \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━</span>   3000        0           0.153       31          291.61 draws/s       0:00:10    0:00:00   \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━</span>   3000        0           0.132       15          308.41 draws/s       0:00:09    0:00:00   \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━</span>   3000        0           0.144       31          295.91 draws/s       0:00:10    0:00:00   \n                                                                                                                   \n</pre>\n",
+          "text/plain": "                                                                                                                   \n \u001b[1m                      \u001b[0m \u001b[1m           \u001b[0m \u001b[1m           \u001b[0m \u001b[1m           \u001b[0m \u001b[1m \u001b[0m\u001b[1mGrad     \u001b[0m\u001b[1m \u001b[0m \u001b[1m                    \u001b[0m \u001b[1m          \u001b[0m \u001b[1m          \u001b[0m \n \u001b[1m \u001b[0m\u001b[1mProgress            \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDraw     \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDivergen…\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mStep size\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mevals    \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mSpeed             \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mElapsed \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mRemaini…\u001b[0m\u001b[1m \u001b[0m \n ───────────────────────────────────────────────────────────────────────────────────────────────────────────────── \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━\u001b[0m   3000        0           0.147       31          267.30 draws/s       0:00:11    0:00:00   \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━\u001b[0m   3000        0           0.153       31          291.61 draws/s       0:00:10    0:00:00   \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━\u001b[0m   3000        0           0.132       15          308.41 draws/s       0:00:09    0:00:00   \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━\u001b[0m   3000        0           0.144       31          295.91 draws/s       0:00:10    0:00:00   \n                                                                                                                   \n"
          },
          "metadata": {},
          "output_type": "display_data"
@@ -1569,7 +2289,7 @@
        "tooltip": null
       }
      },
-     "946e105200704532abc98fe8150f0450": {
+     "acdd14a0a7d143f48453538a62bfba48": {
       "model_module": "@jupyter-widgets/base",
       "model_module_version": "2.0.0",
       "model_name": "LayoutModel",
@@ -1622,7 +2342,7 @@
        "width": null
       }
      },
-     "be473910c1ff421aabd93041c9f601b0": {
+     "ba139dab2320400badd1a6f1590735f8": {
       "model_module": "@jupyter-widgets/output",
       "model_module_version": "1.0.0",
       "model_name": "OutputModel",
@@ -1635,13 +2355,13 @@
        "_view_module": "@jupyter-widgets/output",
        "_view_module_version": "1.0.0",
        "_view_name": "OutputView",
-       "layout": "IPY_MODEL_946e105200704532abc98fe8150f0450",
+       "layout": "IPY_MODEL_365a2a50d313440ab47fd51964991ae0",
        "msg_id": "",
        "outputs": [
         {
          "data": {
-          "text/html": "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">                                                                                                                   \n <span style=\"font-weight: bold\"> Progress                   </span> <span style=\"font-weight: bold\"> Draw </span> <span style=\"font-weight: bold\"> Divergences </span> <span style=\"font-weight: bold\"> Step size </span> <span style=\"font-weight: bold\"> Grad evals </span> <span style=\"font-weight: bold\"> Speed          </span> <span style=\"font-weight: bold\"> Elapsed </span> <span style=\"font-weight: bold\"> Remaining </span> \n ───────────────────────────────────────────────────────────────────────────────────────────────────────────────── \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   4000   0             0.090       31           149.23 draws/s   0:00:26   0:00:00    \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   4000   0             0.127       31           164.49 draws/s   0:00:24   0:00:00    \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   4000   0             0.083       63           155.02 draws/s   0:00:25   0:00:00    \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   4000   0             0.100       63           137.23 draws/s   0:00:29   0:00:00    \n                                                                                                                   \n</pre>\n",
-          "text/plain": "                                                                                                                   \n \u001b[1m \u001b[0m\u001b[1mProgress                  \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDraw\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDivergences\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mStep size\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mGrad evals\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mSpeed         \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mElapsed\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mRemaining\u001b[0m\u001b[1m \u001b[0m \n ───────────────────────────────────────────────────────────────────────────────────────────────────────────────── \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   4000   0             0.090       31           149.23 draws/s   0:00:26   0:00:00    \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   4000   0             0.127       31           164.49 draws/s   0:00:24   0:00:00    \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   4000   0             0.083       63           155.02 draws/s   0:00:25   0:00:00    \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   4000   0             0.100       63           137.23 draws/s   0:00:29   0:00:00    \n                                                                                                                   \n"
+          "text/html": "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">                                                                                                                   \n <span style=\"font-weight: bold\">                      </span> <span style=\"font-weight: bold\">           </span> <span style=\"font-weight: bold\">           </span> <span style=\"font-weight: bold\">           </span> <span style=\"font-weight: bold\"> Grad      </span> <span style=\"font-weight: bold\">                    </span> <span style=\"font-weight: bold\">          </span> <span style=\"font-weight: bold\">          </span> \n <span style=\"font-weight: bold\"> Progress             </span> <span style=\"font-weight: bold\"> Draw      </span> <span style=\"font-weight: bold\"> Divergen… </span> <span style=\"font-weight: bold\"> Step size </span> <span style=\"font-weight: bold\"> evals     </span> <span style=\"font-weight: bold\"> Speed              </span> <span style=\"font-weight: bold\"> Elapsed  </span> <span style=\"font-weight: bold\"> Remaini… </span> \n ───────────────────────────────────────────────────────────────────────────────────────────────────────────────── \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━</span>   4000        0           0.123       63          185.29 draws/s       0:00:21    0:00:00   \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━</span>   4000        0           0.116       31          198.95 draws/s       0:00:20    0:00:00   \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━</span>   4000        0           0.081       63          214.46 draws/s       0:00:18    0:00:00   \n  <span style=\"color: #1f77b4; text-decoration-color: #1f77b4\">━━━━━━━━━━━━━━━━━━━━</span>   4000        0           0.106       63          199.51 draws/s       0:00:20    0:00:00   \n                                                                                                                   \n</pre>\n",
+          "text/plain": "                                                                                                                   \n \u001b[1m                      \u001b[0m \u001b[1m           \u001b[0m \u001b[1m           \u001b[0m \u001b[1m           \u001b[0m \u001b[1m \u001b[0m\u001b[1mGrad     \u001b[0m\u001b[1m \u001b[0m \u001b[1m                    \u001b[0m \u001b[1m          \u001b[0m \u001b[1m          \u001b[0m \n \u001b[1m \u001b[0m\u001b[1mProgress            \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDraw     \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mDivergen…\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mStep size\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mevals    \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mSpeed             \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mElapsed \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mRemaini…\u001b[0m\u001b[1m \u001b[0m \n ───────────────────────────────────────────────────────────────────────────────────────────────────────────────── \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━\u001b[0m   4000        0           0.123       63          185.29 draws/s       0:00:21    0:00:00   \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━\u001b[0m   4000        0           0.116       31          198.95 draws/s       0:00:20    0:00:00   \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━\u001b[0m   4000        0           0.081       63          214.46 draws/s       0:00:18    0:00:00   \n  \u001b[38;2;31;119;180m━━━━━━━━━━━━━━━━━━━━\u001b[0m   4000        0           0.106       63          199.51 draws/s       0:00:20    0:00:00   \n                                                                                                                   \n"
          },
          "metadata": {},
          "output_type": "display_data"
@@ -1655,25 +2375,8 @@
     "version_major": 2,
     "version_minor": 0
    }
-  },
-  "cost": {
-   "api_usd_est": 0.0,
-   "api_provider": "none",
-   "cpu_min": 2,
-   "gpu_min": 0,
-   "gpu_required": false,
-   "vram_gb": 0,
-   "vram_tier": "NONE",
-   "network": false,
-   "external_account": "none",
-   "free_alternative": "self",
-   "reproducibility": "HIGH",
-   "validator": "papermill",
-   "notes": "Topic Models (LDA) — allocation latente de Dirichlet, inference MCMC. Re-exec mesure : 25s.",
-   "reduced_pedagogical": "Probas/PyMC/PyMC-1-Setup.ipynb",
-   "metadata_written": "2026-07-28"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}
\ No newline at end of file
diff --git a/scripts/notebook_tools/twin_pairs.d/probas-11-topic-models.yaml b/scripts/notebook_tools/twin_pairs.d/probas-11-topic-models.yaml
index 42d7cc7e5f..c58e9c1ab8 100644
--- a/scripts/notebook_tools/twin_pairs.d/probas-11-topic-models.yaml
+++ b/scripts/notebook_tools/twin_pairs.d/probas-11-topic-models.yaml
@@ -29,6 +29,14 @@
       csharp_sha: e61bc677cace7fe0525f0f2d3d065fd6ac16a793
       content_python_sha: d92c4a5e9460cc76c33b08f5a97187c9a654ef5baff63447439a8e63a8b41604
       content_csharp_sha: ac0994633b49512fc0196e76aba3898fe151bf3756a35be0ae095a9ef6ad4448
+    - date: "2026-08-29"
+      by: myia-po-2023:CoursIA-2
+      python_sha: edc08f4697c64e585fe37af785ca753abe76f9f9
+      csharp_sha: b5949f0f739b92d1a518192a9e30f6ba098c4fec
+      content_python_sha: e909bc23772a561a4f24d5b369f68be4cb11eafa0d2c99cff9be7947224ee20a
+      content_csharp_sha: 18d8c737e3a9e5094b0049580c8d1a43f1ea7612755111267246275e687e7c28
+      reason: "Section 5bis ajoutee des deux cotes (#13036) : protocole de selection de K=2..6 en miroir (priors neutres, coherence UMass sur topics appris, redondance cosinus, held-out split-half ; deux ajustements par K -- corpus complet pour la qualite, moitie pour le predictif). Symetrie des protocoles verifiee ; valeurs numeriques non identiques par conception (NUTS vs VMP, cf known_differences)."
+
   known_differences:
   - 'Socle pedagogique commun : modeles de topics (LDA / allocation de Dirichlet) modelise dans les deux stacks.'
   - 'Moteurs d''inference distincts : C# Infer.NET = inference deterministe approchee (Expectation Propagation / Variational