{"id":"W3128277790","doi":"10.1093/imrn/rnab282","title":"Jensen’s Inequality for Separately Convex Noncommutative Functions","year":2021,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Probability measure; Jensen's inequality; Noncommutative geometry; Free probability; Combinatorics; Measure (data warehouse); Convex function; Regular polygon; Convex set; Convex analysis; Discrete mathematics; Pure mathematics; Convex optimization; Geometry","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":[0.003655094,0.000697039,0.0009104832,0.001561229,0.0009710268,0.001956643,0.001204598,0.000787026,0.004226591],"category_scores_gemma":[0.009743933,0.0004189001,0.001155865,0.001191279,0.003842469,0.004153671,0.001933778,0.002640754,0.0005415022],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002986009,"about_ca_system_score_gemma":0.001348402,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003536191,"about_ca_topic_score_gemma":0.002235097,"domain_scores_codex":[0.9961681,0.0007869571,0.0002152002,0.0006312703,0.001730275,0.0004682427],"domain_scores_gemma":[0.9912181,0.005491943,0.0005845117,0.0005414928,0.001724171,0.0004396729],"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":[0.00002236833,0.0000136332,0.0003640917,0.00004642589,0.00002100549,0.0001398962,0.0001303438,0.00398528,0.001709594,0.9890364,0.0008817529,0.003649183],"study_design_scores_gemma":[0.000009483796,0.00003705369,0.002038157,0.0000386075,0.00002333437,0.0001765903,0.00006999655,0.09262296,0.002345151,0.8988919,0.003712615,0.00003403125],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1900017,0.003467289,0.7097352,0.002578652,0.0003402098,0.00004839691,0.0005206757,0.0001671684,0.09314077],"genre_scores_gemma":[0.942431,0.001147192,0.04048938,0.0005709711,0.0004145675,0.00009879039,0.0002817114,0.0001208089,0.01444558],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004226591,"threshold_uncertainty_score":0.02166516,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.4451256689421778,"score_gpt":0.5562931392259455,"score_spread":0.1111674702837677,"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."}}