{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002584184,0.00006279883,0.0002459959,0.00006433605,0.00002983201,0.00001093814,0.0001723672,0.00002604949,0.000002088373],"category_scores_gemma":[0.000192382,0.00005161063,0.00003417024,0.0001646121,0.00007667825,0.00007817171,0.00005891188,0.00004490927,4.98024e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":7.644471e-7,"about_ca_system_score_gemma":0.00002699623,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004653148,"about_ca_topic_score_gemma":0.000002284018,"domain_scores_codex":[0.9993834,0.00001805752,0.0002853713,0.00007577788,0.0001608017,0.00007654088],"domain_scores_gemma":[0.9989604,0.000294478,0.0002726933,0.0001665796,0.0002889752,0.00001682009],"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":[0.00002862792,0.003871766,0.008927342,0.01790625,0.000279745,0.000006797247,0.03119498,0.001859291,0.002793509,0.9190261,0.007460807,0.006644788],"study_design_scores_gemma":[0.001972185,0.0006031424,0.00235539,0.0006809639,0.00005148021,0.00003406321,0.0007360188,0.08229942,0.2169406,0.6925482,0.001415167,0.0003634198],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6709493,0.002357123,0.3178123,0.001308428,0.0001431696,0.0002239143,0.00001433533,0.00008337183,0.007108073],"genre_scores_gemma":[0.9798816,0.00009851294,0.01971526,0.00001364758,0.00001147423,0.000002148242,6.744805e-7,0.00000406816,0.0002725593],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3089324,"threshold_uncertainty_score":0.2104621,"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."}}