{"id":"W2214938339","doi":"","title":"Jensen's inequality for nonconvex functions ∗","year":2004,"lang":"en","type":"article","venue":"University of Zagreb University Computing Centre (SRCE)","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Jensen's inequality; Combinatorics; Convex function; Regular polygon; Convex set; Lipschitz continuity; Euclidean space; Function (biology); Pure mathematics; Convex analysis; Convex optimization; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002594869,0.0001762303,0.000351753,0.0001185627,0.0005159837,0.000013141,0.0003754259,0.0001228566,0.0002128115],"category_scores_gemma":[0.000113029,0.0002175808,0.0002667964,0.0002810418,0.0001957316,0.0001144042,0.0002086651,0.0001414182,0.00003478819],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002182551,"about_ca_system_score_gemma":0.0001032959,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003397434,"about_ca_topic_score_gemma":0.0001692053,"domain_scores_codex":[0.9988854,0.00006762872,0.0002143636,0.0003168847,0.000200656,0.0003150479],"domain_scores_gemma":[0.9981997,0.0006899982,0.0002760771,0.0003882443,0.0002909857,0.0001550056],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"qualitative","study_design_scores_codex":[0.00009229154,0.0006347627,0.00004784072,0.0004290735,0.0001858372,0.00001741548,0.06534613,0.0004717331,0.000242208,0.9266404,0.005180164,0.0007121781],"study_design_scores_gemma":[0.007169879,0.0002356388,0.000548853,0.0004592519,0.0008038259,0.00001424913,0.8327655,0.007487299,0.0005205714,0.1303901,0.01851973,0.001085093],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5862942,0.000003615875,0.4094789,0.001017277,0.00006578621,0.0003454429,0.0001252874,0.0001511449,0.002518365],"genre_scores_gemma":[0.9464827,0.000004715268,0.04900107,0.00003406639,0.00004952714,3.025974e-11,0.00003614394,0.00001303672,0.004378747],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7962502,"threshold_uncertainty_score":0.8872686,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04610374017967079,"score_gpt":0.2606078208404912,"score_spread":0.2145040806608204,"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."}}