{"id":"W2065545157","doi":"10.4153/cjm-2015-002-6","title":"On Two-faced Families of Non-commutative Random Variables","year":2015,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Multiplicative function; Complement (music); Independence (probability theory); Random variable; Convolution (computer science); Operator (biology); Diagrammatic reasoning; Space (punctuation)","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":[0.001130614,0.0001562811,0.0005852632,0.0002907299,0.00007697411,0.00003945276,0.000368532,0.00006261416,0.00006004164],"category_scores_gemma":[0.001498414,0.0001202789,0.0001474174,0.0002579274,0.0001040429,0.00009355883,0.00001228536,0.0001976582,0.00001913577],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009842586,"about_ca_system_score_gemma":0.0008141202,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005553729,"about_ca_topic_score_gemma":0.001562452,"domain_scores_codex":[0.9985892,0.00006053153,0.0007635255,0.00007658246,0.0002947999,0.000215408],"domain_scores_gemma":[0.996641,0.001329157,0.0007724993,0.00030031,0.0004938271,0.0004632425],"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":[0.0002990018,0.000845315,0.0004329996,0.0009879917,0.000890284,0.000133979,0.05713394,0.004842939,0.0008346309,0.8241699,0.1074439,0.001985158],"study_design_scores_gemma":[0.009523234,0.0003482237,0.00003660379,0.0005711876,0.0003134056,0.0001619524,0.01249466,0.003366192,0.002414689,0.9683877,0.00208679,0.0002953827],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.880995,0.0002372739,0.08130261,0.0005070223,0.0002737916,0.0005704695,0.00007297484,0.00001361419,0.03602719],"genre_scores_gemma":[0.9205701,0.00001419468,0.07897615,0.00004975852,0.00007982428,0.00000780851,0.000001536941,0.00003060883,0.0002699971],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1442178,"threshold_uncertainty_score":0.4904831,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04766252686095643,"score_gpt":0.3113420427787768,"score_spread":0.2636795159178204,"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."}}