{"id":"W2164206522","doi":"10.1109/isit.2003.1228475","title":"Invariance of stationary and ergodic properties of a quantum source under memoryless transformations","year":2003,"lang":"en","type":"article","venue":"","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Ergodicity; Ergodic theory; Tensor product; TRACE (psycholinguistics); Quantum; Lattice (music); Mathematics; Product (mathematics); Pure mathematics; Discrete mathematics; Physics; Quantum mechanics; Philosophy","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":[0.0002959596,0.00009847627,0.0002450648,0.00004428162,0.00003907695,0.000006857832,0.000082603,0.00003831622,0.0001229695],"category_scores_gemma":[0.0002272098,0.00007507666,0.00004401937,0.0001399408,0.0002000073,0.0001499604,0.0000101644,0.00006739629,0.000004064895],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001196539,"about_ca_system_score_gemma":0.00004324428,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005407875,"about_ca_topic_score_gemma":0.000002934534,"domain_scores_codex":[0.9991207,0.00008747202,0.0003952338,0.00009079953,0.0001940334,0.0001117321],"domain_scores_gemma":[0.9992253,0.0003503888,0.000116479,0.0001876832,0.00008445666,0.00003565594],"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":[0.00001150556,0.0002004644,0.00000824298,0.0005869573,0.00003102016,9.693287e-8,0.002552327,0.00006817253,0.01177195,0.9846672,0.00004469688,0.00005730871],"study_design_scores_gemma":[0.0002497207,0.00003829883,0.00003089483,0.00009345898,0.00003124398,0.00000511994,0.002219669,0.001990287,0.1011839,0.8940611,0.00001175741,0.0000845023],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6241369,0.00007270858,0.3654099,0.0001045056,0.00001589523,0.0002645611,0.000004515226,0.00003345804,0.009957586],"genre_scores_gemma":[0.9860595,0.00001162071,0.01361798,0.00003078972,0.000004148679,0.00001268589,5.365769e-7,0.00001453585,0.0002481408],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3619227,"threshold_uncertainty_score":0.3061537,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06873870750750498,"score_gpt":0.2882958438627446,"score_spread":0.2195571363552397,"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."}}