{"id":"W2604480575","doi":"10.20382/jocg.v8i2a3","title":"Hyperplane separability and convexity of probabilistic point sets","year":2017,"lang":"en","type":"article","venue":"Journal of Computational Geometry (Carleton University)","topic":"Facility Location and Emergency Management","field":"Business, Management and Accounting","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Deutscher Akademischer Austauschdienst; National Science Foundation","keywords":"Mathematics; Convex hull; Combinatorics; Hyperplane; Probabilistic logic; Convexity; Separable space; Reduction (mathematics); Orthogonal convex hull; Regular polygon; Subspace topology; Point (geometry); Convex combination; Hull; Discrete mathematics; Convex body; Convex optimization; Mathematical analysis; Statistics; Geometry","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":[0.002426211,0.001333341,0.00253679,0.002290104,0.001739032,0.004379223,0.00347787,0.001408207,0.008779068],"category_scores_gemma":[0.02088688,0.001169854,0.002678516,0.003651775,0.0024328,0.007137982,0.006531646,0.004668002,0.002163332],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002894579,"about_ca_system_score_gemma":0.002161536,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00477537,"about_ca_topic_score_gemma":0.004103174,"domain_scores_codex":[0.9948853,0.0008654983,0.0003462772,0.001192877,0.002067803,0.0006422101],"domain_scores_gemma":[0.9858131,0.008543126,0.001464547,0.002498213,0.001148273,0.0005328258],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.001099629,0.0003118555,0.01159982,0.00045186,0.0002697782,0.0004258198,0.0008940565,0.5550818,0.005734676,0.1691586,0.01243545,0.2425367],"study_design_scores_gemma":[0.00004500666,0.00005293041,0.001221957,0.00002817294,0.00002475927,0.0001902113,0.0001406746,0.846934,0.004047681,0.1448089,0.002472045,0.00003363743],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05313753,0.0003106798,0.9381886,0.0006974981,0.00003698586,0.000223916,0.001210965,0.001405998,0.004787794],"genre_scores_gemma":[0.6240008,0.0003889118,0.3640352,0.0002334821,0.0001607568,0.0005274225,0.004980911,0.0004563056,0.005216195],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008779068,"threshold_uncertainty_score":0.02936894,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02299352665663522,"score_gpt":0.2301167273940917,"score_spread":0.2071232007374564,"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."}}