{"id":"W2341883566","doi":"10.1090/proc/13457","title":"On the volume of sections of a convex body by cones","year":2016,"lang":"en","type":"preprint","venue":"Proceedings of the American Mathematical Society","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche","keywords":"Intersection (aeronautics); Convex body; Regular polygon; Centroid; Mixed volume; Volume (thermodynamics); Mathematics; Combinatorics; Convex set; Pure mathematics; Convex geometry; Geometry; Convex hull; Convex optimization; Physics; Geography; Cartography","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001756218,0.001024582,0.0009472083,0.003595464,0.001044757,0.00274229,0.001679839,0.0006391287,0.006545593],"category_scores_gemma":[0.008567597,0.0004999409,0.001085126,0.001213989,0.005409732,0.004515797,0.003094517,0.002384451,0.0009777187],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001469507,"about_ca_system_score_gemma":0.0005715398,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001967713,"about_ca_topic_score_gemma":0.0009462725,"domain_scores_codex":[0.9990189,0.0002372521,0.00003010063,0.0002140573,0.0003298962,0.0001697202],"domain_scores_gemma":[0.9947461,0.002676985,0.0007999673,0.0003142341,0.0007840364,0.0006786765],"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":[0.00005721256,0.00001999183,0.001239832,0.00006870098,0.00002245518,0.00009686589,0.0003623218,0.008529522,0.00259695,0.9778451,0.001250376,0.007910466],"study_design_scores_gemma":[0.00001453907,0.00007598779,0.002776267,0.00005743824,0.00002812627,0.0002504852,0.0003462876,0.06488974,0.002709763,0.9235768,0.005242557,0.00003199],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4319584,0.002508879,0.4823694,0.001596367,0.000230839,0.00007331281,0.0006652808,0.0003122388,0.08028534],"genre_scores_gemma":[0.9383839,0.002200079,0.03840102,0.0002925704,0.0005458729,0.0001210051,0.0007305607,0.0004803132,0.01884457],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006545593,"threshold_uncertainty_score":0.0218972,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02971882007363265,"score_gpt":0.2939108424913819,"score_spread":0.2641920224177493,"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."}}