{"id":"W1778352006","doi":"10.1007/978-3-642-31155-0_19","title":"Minimum Convex Partitions and Maximum Empty Polytopes","year":2012,"lang":"en","type":"book-chapter","venue":"Lecture notes in computer science","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Combinatorics; Mathematics; Convex body; Partition (number theory); Regular polygon; Convex polytope; Dimension (graph theory); Polytope; Upper and lower bounds; Convex hull; Unit cube; Convex set; General position; Polyhedron; Approximation algorithm; Steiner tree problem; Discrete mathematics; Convex optimization; Geometry; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0005936228,0.0003695834,0.0003522229,0.0006441394,0.0003296323,0.000468768,0.001064906,0.0002154166,0.00004880729],"category_scores_gemma":[0.00005131726,0.0003531224,0.00007679948,0.0004728581,0.0004816855,0.000797949,0.0008254144,0.000414881,0.00006384733],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001053972,"about_ca_system_score_gemma":0.000322088,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000863993,"about_ca_topic_score_gemma":0.00002702393,"domain_scores_codex":[0.9974439,0.00003240459,0.0003887698,0.0009793947,0.0006400121,0.0005154988],"domain_scores_gemma":[0.9983539,0.000358284,0.0001794759,0.00067837,0.0001931579,0.0002368058],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000003918134,0.00004022046,0.0001208284,0.00003179057,0.00001377735,0.00002607362,0.0006708483,0.008651863,0.000281556,0.05946079,0.0001102261,0.9305881],"study_design_scores_gemma":[0.0005038294,0.0002386649,0.001877997,0.0002517114,0.0000258181,0.0003060441,3.778004e-7,0.3361822,0.002688199,0.635965,0.02069206,0.001268106],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0004545952,0.001980522,0.9921358,0.001393685,0.001540703,0.0002598824,0.00000801809,0.0001087294,0.002118116],"genre_scores_gemma":[0.5815974,0.0002245825,0.4126275,0.003114761,0.001397997,0.00002002404,0.0000278471,0.00003548688,0.0009542885],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.92932,"threshold_uncertainty_score":0.9998921,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0200805532088027,"score_gpt":0.2471383111693847,"score_spread":0.227057757960582,"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."}}