{"id":"W2172758441","doi":"10.1016/j.aam.2015.09.015","title":"The logarithmic Minkowski inequality for non-symmetric convex bodies","year":2015,"lang":"en","type":"article","venue":"Advances in Applied Mathematics","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":29,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Logarithm; Minkowski space; Regular polygon; Inequality; Minkowski addition; Minkowski's theorem; Minkowski inequality; Pure mathematics; Convex body; Mixed volume; Mathematical analysis; Combinatorics; Rearrangement inequality; Linear inequality; Mathematical physics; Geometry; Convex optimization","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":[0.002684862,0.0003220044,0.0006425327,0.0002753707,0.0001997248,0.00009952633,0.0005773018,0.0001345268,0.00000562733],"category_scores_gemma":[0.005626121,0.0002230244,0.0001015597,0.0007938141,0.0002009819,0.0002061957,0.0001605762,0.0002279497,0.00002947279],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001304333,"about_ca_system_score_gemma":0.0001077123,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005562159,"about_ca_topic_score_gemma":0.00007866118,"domain_scores_codex":[0.99753,0.0000253831,0.0009877861,0.0003218547,0.0005203409,0.0006146483],"domain_scores_gemma":[0.9927381,0.005810751,0.0004824838,0.0005958964,0.0002580673,0.0001147419],"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":[0.00005575223,0.000218181,0.00007452048,0.001426271,0.00002440759,0.000001610962,0.002440971,0.00002108619,0.000009196807,0.9834213,0.001698075,0.01060864],"study_design_scores_gemma":[0.001170123,0.00008632267,0.000008648531,0.00006685335,0.00003348447,0.000005664939,0.007074017,0.001739195,0.0007013911,0.956833,0.03196878,0.0003125009],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04023978,0.01038869,0.7197713,0.001122029,0.001780739,0.005945827,0.0001565495,0.0005201052,0.220075],"genre_scores_gemma":[0.6911279,0.0009035153,0.3045142,0.0002093109,0.0002929216,0.001282232,0.00001720756,0.00009480666,0.00155796],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6508881,"threshold_uncertainty_score":0.9094672,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0756796761499367,"score_gpt":0.3564699797214048,"score_spread":0.2807903035714681,"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."}}