{"id":"W2010219188","doi":"10.4064/sm183-1-2","title":"Volume thresholds for Gaussian and spherical random polytopes and their duals","year":2007,"lang":"en","type":"article","venue":"Studia Mathematica","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Institut Henri Poincaré","keywords":"Dual polyhedron; Mathematics; Combinatorics; Polytope; Integer (computer science); Convex hull; Regular polygon; Gaussian; Volume (thermodynamics); Geometry; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003690337,0.0008778099,0.001656694,0.004436233,0.00107721,0.005099463,0.002467653,0.001736115,0.006579161],"category_scores_gemma":[0.02050888,0.0008706221,0.001201667,0.001669882,0.004418158,0.006335889,0.003430957,0.002686167,0.0005926255],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003495701,"about_ca_system_score_gemma":0.0007625373,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002130811,"about_ca_topic_score_gemma":0.001169222,"domain_scores_codex":[0.9981268,0.0005162805,0.00008325848,0.0002889305,0.0005296419,0.0004551379],"domain_scores_gemma":[0.9864572,0.008042371,0.002039649,0.0005398667,0.0009753072,0.001945593],"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":[0.00006635178,0.0000245651,0.0005858666,0.00004565604,0.00001676985,0.00004742897,0.0001073847,0.01585626,0.0004995434,0.979526,0.001015942,0.002208267],"study_design_scores_gemma":[0.00004470094,0.00004373191,0.001829871,0.0000587451,0.00002287038,0.000186934,0.0001957293,0.2169654,0.0006185126,0.7782761,0.001714684,0.00004282774],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6413357,0.003683256,0.2987413,0.005185854,0.0002337336,0.000136845,0.001251663,0.0005680306,0.04886367],"genre_scores_gemma":[0.9732357,0.001353518,0.01508807,0.0004493865,0.0003993452,0.0002365369,0.0007128914,0.0001997426,0.008324795],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006579161,"threshold_uncertainty_score":0.02536327,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04468507100330477,"score_gpt":0.3182087625411851,"score_spread":0.2735236915378803,"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."}}