{"id":"W1491943380","doi":"10.3934/dcds.2017163","title":"Uniformly expanding Markov maps of the real line: Exactness and infinite mixing","year":2017,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Ministero dell’Istruzione, dell’Università e della Ricerca; Division of Mathematical Sciences; York University; Istituto Nazionale di Alta Matematica \"Francesco Severi\"","keywords":"Mixing (physics); Class (philosophy); Markov chain; Characterization (materials science); Markov process; Finite set","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":[0.000586544,0.0002144264,0.0005844866,0.00003561654,0.0003904514,0.0003018197,0.0003544202,0.0001542743,0.000004679135],"category_scores_gemma":[0.0004459684,0.0001329816,0.0001057449,0.00004335742,0.0002894353,0.0001514965,0.0003424736,0.0001893401,5.910373e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001683819,"about_ca_system_score_gemma":0.00001363043,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003392772,"about_ca_topic_score_gemma":0.00007942848,"domain_scores_codex":[0.9985512,0.00008438755,0.0005598509,0.0002558313,0.0002617505,0.000286959],"domain_scores_gemma":[0.9982197,0.000418622,0.0005285363,0.0006450727,0.00006742452,0.0001206668],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00008258013,0.0001108576,0.04906467,0.002372433,0.0002028742,0.00002045306,0.001105159,0.000003091359,0.002609955,0.9374365,0.0001063024,0.006885086],"study_design_scores_gemma":[0.005521204,0.0005603757,0.084728,0.007567134,0.0008351555,0.0002788993,0.006538707,0.4673051,0.0003128049,0.4226872,0.001278962,0.002386482],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9819919,0.0001048212,0.003168059,0.0001765676,0.0002211376,0.0004778727,0.0001005515,0.00003124645,0.0137278],"genre_scores_gemma":[0.9980621,0.00007190354,0.0003361707,0.000009319262,0.00007127682,0.00002078988,0.000007040991,0.00002712389,0.001394319],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5147493,"threshold_uncertainty_score":0.5422831,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02102647764575485,"score_gpt":0.2902669457808801,"score_spread":0.2692404681351253,"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."}}