{"id":"W1811034619","doi":"10.48550/arxiv.math/0411565","title":"Noncommutative continuous Bernoulli shifts","year":2004,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Free probability; Noncommutative geometry; Commutative property; Bernoulli's principle; Pure mathematics; Logarithm; Algebraic number; Type (biology); Von Neumann algebra; Algebra over a field; Von Neumann architecture; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007104764,0.0004246313,0.0003348463,0.0006422899,0.000559532,0.001214058,0.0006740964,0.0004480855,0.003746058],"category_scores_gemma":[0.001813507,0.0002002348,0.0004695056,0.0004558573,0.002504913,0.001956568,0.001311773,0.0009676024,0.0004923907],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007755306,"about_ca_system_score_gemma":0.0005458635,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006010812,"about_ca_topic_score_gemma":0.0004138176,"domain_scores_codex":[0.9992334,0.0001368267,0.00004059482,0.0001933758,0.000289429,0.0001063899],"domain_scores_gemma":[0.9990687,0.0002481982,0.0001797445,0.0001483933,0.0002001435,0.0001550014],"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":[0.00000897771,0.000008962263,0.0001795905,0.00001097671,0.000003425136,0.0000638895,0.000140961,0.001115204,0.001778089,0.9943552,0.0001399858,0.002194767],"study_design_scores_gemma":[0.00001133554,0.0000553532,0.0005292859,0.00001052704,0.000008045785,0.0002811679,0.0001089186,0.02590621,0.00322427,0.9599806,0.009861471,0.00002282248],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3957676,0.001139124,0.5205647,0.001037472,0.0006779009,0.00006571058,0.0001533466,0.0002269265,0.08036727],"genre_scores_gemma":[0.9436007,0.0005394025,0.03421712,0.000237609,0.0002970509,0.00006849373,0.00006093627,0.00004674155,0.02093196],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003746058,"threshold_uncertainty_score":0.01253182,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1166193513063247,"score_gpt":0.3966469919397727,"score_spread":0.280027640633448,"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."}}