{"id":"W3000458209","doi":"10.4153/s0008439521000254","title":"Log-concavity and log-convexity of moments of averages of i.i.d. random variables","year":2021,"lang":"en","type":"preprint","venue":"Canadian Mathematical Bulletin","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Carnegie Mellon University; Simons Foundation","keywords":"Sequence (biology); Mathematics; Convexity; Combinatorics; Order (exchange); Logarithmically convex function; Conjecture; Moment (physics); Regular polygon; Random variable; Integer (computer science); Statistics; Convex optimization; Convex set; Physics; Computer science; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001134638,0.0003955457,0.001739858,0.0002459824,0.0000775478,0.00002627059,0.0005083185,0.0005821528,0.005884812],"category_scores_gemma":[0.002714842,0.0003472991,0.0003222322,0.0001149282,0.0007663813,0.00001947767,0.0005817015,0.0005239943,0.000005811455],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007097298,"about_ca_system_score_gemma":0.000391,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001749522,"about_ca_topic_score_gemma":0.0004354563,"domain_scores_codex":[0.9972283,0.0003139278,0.001221827,0.0004470563,0.0003977737,0.0003911577],"domain_scores_gemma":[0.9959075,0.001724094,0.0007119823,0.0009630664,0.0003189282,0.0003743566],"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":[0.0001849147,0.0004466684,0.002073091,0.02761914,0.001388131,0.00008531574,0.006578687,0.00003775583,0.0006355496,0.9542742,0.005809746,0.0008668435],"study_design_scores_gemma":[0.001127255,0.00005119922,0.0004919272,0.001447522,0.0003376792,0.00002097286,0.0003960804,0.0001434687,0.004080555,0.9911187,0.0004273701,0.0003572451],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9855239,0.0006317482,0.00249215,0.0003467833,0.0002517427,0.0007998217,0.000492807,0.00001982828,0.009441195],"genre_scores_gemma":[0.9853336,0.0000964811,0.01395958,0.00007749148,0.00003950677,0.00002420782,0.00002202794,0.00004463629,0.0004024574],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03684457,"threshold_uncertainty_score":0.9998979,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02457038436184648,"score_gpt":0.2624130755961095,"score_spread":0.237842691234263,"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."}}