{"id":"W2070154657","doi":"10.4153/cmb-2010-067-5","title":"The Mean Width of Circumscribed Random Polytopes","year":2010,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":26,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Hungarian Scientific Research Fund","keywords":"Mathematics; Combinatorics; Polytope; Regular polygon; Convex body; Intersection (aeronautics); Infinity; Convex polytope; Mathematical analysis; Convex hull; Geometry; Convex set; Convex optimization","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"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":[0.003725252,0.0005409807,0.001254418,0.001876318,0.0007260958,0.002246769,0.001887403,0.0009137852,0.003055673],"category_scores_gemma":[0.01867584,0.0009204662,0.0006029828,0.0007800984,0.003001618,0.003417081,0.002172573,0.001976754,0.0003299262],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001748268,"about_ca_system_score_gemma":0.0005836872,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001072467,"about_ca_topic_score_gemma":0.0009393016,"domain_scores_codex":[0.9979774,0.0005106819,0.0001052594,0.0005354441,0.0005900587,0.0002811161],"domain_scores_gemma":[0.9824624,0.01132626,0.001856972,0.001349257,0.00142164,0.001583563],"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":[0.0005709864,0.0001423492,0.01230406,0.0003077871,0.0001331028,0.0002876782,0.0003652629,0.2554229,0.02107769,0.686364,0.001648737,0.02137544],"study_design_scores_gemma":[0.00003342814,0.0001466952,0.006634814,0.00009481313,0.00004150984,0.0003025164,0.0002098118,0.7417914,0.008354524,0.2401646,0.002139303,0.00008659616],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4997529,0.001200585,0.4898262,0.0004617907,0.00007550081,0.00005754929,0.0003925514,0.0002613526,0.007971578],"genre_scores_gemma":[0.9509736,0.0005052771,0.04542948,0.0001174591,0.00007692527,0.0001235295,0.0003477232,0.0001103721,0.002315712],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003725252,"threshold_uncertainty_score":0.01970124,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02257054007901126,"score_gpt":0.2643768186028396,"score_spread":0.2418062785238284,"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."}}