{"id":"W1921063444","doi":"10.1090/s0002-9947-03-03196-9","title":"Non-crossing cumulants of type B","year":2003,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":56,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Cumulant; Mathematics; Free probability; Type (biology); Convolution (computer science); Multiplicative function; Pure mathematics; Combinatorics; Level crossing; Mathematical analysis; Statistics","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":[],"consensus_categories":[],"category_scores_codex":[0.0002799044,0.0001123105,0.0003850631,0.00001504378,0.0001916001,0.0000141921,0.0002424087,0.00003457247,0.0001570482],"category_scores_gemma":[0.0000836438,0.00007497652,0.0004134411,0.0006222832,0.0006506633,0.00004167494,0.000008144043,0.0001315302,0.000009074005],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002085319,"about_ca_system_score_gemma":0.00006114506,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002570079,"about_ca_topic_score_gemma":0.000001203504,"domain_scores_codex":[0.9990444,0.00003825306,0.0003999491,0.0001206458,0.0002324519,0.0001643708],"domain_scores_gemma":[0.9986054,0.0004367285,0.0003416373,0.0004804058,0.00008997311,0.00004581536],"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":[0.0003542757,0.01218956,0.004975784,0.007139516,0.003485975,0.000001356681,0.03996221,0.003078031,0.1803575,0.7172124,0.01388006,0.01736334],"study_design_scores_gemma":[0.002497364,0.000302659,0.002122369,0.0004000029,0.001214291,0.00005081786,0.00638777,0.01428702,0.09977441,0.8702602,0.00195771,0.0007453223],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6894361,0.00001722895,0.3074084,0.0001485306,0.00003593102,0.0002934801,0.00001231325,0.00002865836,0.00261937],"genre_scores_gemma":[0.9077437,0.00001829339,0.09179192,0.00002862347,0.000007457802,0.00001267338,1.980282e-7,0.00001747724,0.000379689],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2183076,"threshold_uncertainty_score":0.3057454,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03280128051427411,"score_gpt":0.3283894165260562,"score_spread":0.2955881360117821,"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."}}