{"id":"W2133442019","doi":"10.4007/annals.2006.164.603","title":"Combinatorics of random processes and sections of convex bodies","year":2006,"lang":"en","type":"article","venue":"Annals of Mathematics","topic":"Machine Learning and Algorithms","field":"Computer Science","cited_by":37,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of California, Davis; University of Alberta; Pacific Institute for the Mathematical Sciences; National Science Foundation","keywords":"Mathematics; Combinatorics; Regular polygon; Mixed volume; Convex body; Geometry; Convex hull","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001377323,0.0006031087,0.0007664177,0.002842462,0.001100476,0.003158815,0.000934633,0.000741802,0.005615732],"category_scores_gemma":[0.005687026,0.0005567383,0.00105653,0.001031875,0.004191451,0.004938531,0.002611173,0.001898573,0.0004794594],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001438064,"about_ca_system_score_gemma":0.0003589109,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004640294,"about_ca_topic_score_gemma":0.0003781471,"domain_scores_codex":[0.999036,0.0002983472,0.00005118395,0.0002333988,0.000254487,0.0001266618],"domain_scores_gemma":[0.9952627,0.002566701,0.000871814,0.0004709345,0.0003066311,0.0005212337],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000009710629,0.000006218044,0.0004579687,0.00001413903,0.000007406418,0.0000630973,0.00007342466,0.003027902,0.0004090261,0.9941874,0.0001615222,0.001582346],"study_design_scores_gemma":[0.000009253919,0.00001482699,0.000642667,0.0000119964,0.000007966445,0.0001271559,0.00005684781,0.02366024,0.0007138239,0.9733222,0.00142247,0.00001054711],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4860494,0.001165305,0.4733127,0.001759709,0.0001130903,0.00008159706,0.0002832939,0.0002420763,0.03699285],"genre_scores_gemma":[0.9583067,0.0006578494,0.02788496,0.0001618964,0.000245985,0.0001340021,0.0002727083,0.00009156521,0.01224431],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005615732,"threshold_uncertainty_score":0.01878655,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02637954132136015,"score_gpt":0.2831536717992701,"score_spread":0.25677413047791,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}