{"id":"W2012929078","doi":"10.1239/aap/1418396236","title":"On Random Disc Polygons in Smooth Convex Discs","year":2014,"lang":"en","type":"article","venue":"Advances in Applied Probability","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"European Social Fund; Division of Mathematical Sciences; National Institutes of Health; Magyar Tudományos Akadémia; Hungarian Scientific Research Fund; European Commission; Fields Institute for Research in Mathematical Sciences","keywords":"Mathematics; Polygon (computer graphics); Intersection (aeronautics); Regular polygon; Combinatorics; Convexity; Convex polygon; Context (archaeology); Perimeter; Planar; Geometry; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00162896,0.0002391053,0.000552397,0.0001793094,0.00005721619,0.000026864,0.000279212,0.0000981144,0.00008207002],"category_scores_gemma":[0.001937938,0.00018838,0.00006348851,0.0006577351,0.0001772934,0.0001706591,0.00008361068,0.000309128,0.00002194696],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001156392,"about_ca_system_score_gemma":0.00003154645,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003513974,"about_ca_topic_score_gemma":0.0005851301,"domain_scores_codex":[0.9980414,0.0001236211,0.0006303253,0.0004756781,0.0002908976,0.0004380576],"domain_scores_gemma":[0.9970975,0.002122486,0.0001576922,0.0005330184,0.00002651328,0.00006282383],"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":[0.0003530234,0.0004178158,0.002074223,0.0005291869,0.00000303249,8.311785e-7,0.0005521173,0.0003211584,0.00001385138,0.9738036,0.00002879287,0.02190236],"study_design_scores_gemma":[0.002133076,0.0000699155,0.0009442222,0.00006560364,0.000005796805,4.70315e-7,0.0001858168,0.0002791913,0.0002343665,0.9899089,0.00592596,0.0002466266],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7502974,0.0006580198,0.02944131,0.0005580881,0.0003474682,0.00197526,0.00003553389,0.0002035857,0.2164834],"genre_scores_gemma":[0.9936025,0.00007170312,0.005700275,0.0001536572,0.00004699574,0.000288455,0.000009239498,0.00001967439,0.0001074814],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2433051,"threshold_uncertainty_score":0.7681913,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02330651058950534,"score_gpt":0.3060172886548267,"score_spread":0.2827107780653214,"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."}}