{"id":"W2149690228","doi":"10.1142/s021812740902297x","title":"INVARIANT MEASURES FOR HIGHER DIMENSIONAL MARKOV SWITCHING POSITION DEPENDENT RANDOM MAPS","year":2009,"lang":"en","type":"article","venue":"International Journal of Bifurcation and Chaos","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Prince Edward Island","funders":"","keywords":"Mathematics; Markov chain; Generalization; Position (finance); Invariant (physics); Invariant measure; Dimension (graph theory); Matrix (chemical analysis); Variable-order Markov model; Transformation (genetics); Discrete mathematics; Combinatorics; Pure mathematics; Markov model; Mathematical analysis; Statistics; Ergodic theory","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":[0.0007014989,0.0001045062,0.0002001797,0.00014622,0.00005890235,0.0000904986,0.0001550543,0.00006167882,0.00006459715],"category_scores_gemma":[0.0002783361,0.00008072802,0.0001118203,0.00003211444,0.00001240021,0.0001880239,0.00001733429,0.0001130696,0.000002096633],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005720612,"about_ca_system_score_gemma":0.00003365227,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002219935,"about_ca_topic_score_gemma":0.000002678973,"domain_scores_codex":[0.9987352,0.00003799423,0.0005249077,0.0001010234,0.0005031203,0.00009768856],"domain_scores_gemma":[0.9985833,0.0003217869,0.0004208226,0.00006961307,0.0005242163,0.00008025875],"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":[0.001809337,0.00106749,0.0001703958,0.00007589493,0.0005270351,0.0000478398,0.001043907,0.00007922132,0.04192014,0.8677621,0.005882221,0.07961437],"study_design_scores_gemma":[0.004135674,0.0002326139,0.001997182,0.0002589605,0.00009909074,0.0003609386,0.00008698257,0.007574533,0.001460028,0.9816836,0.001914462,0.0001960105],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3877837,0.0003566824,0.5734991,0.03371662,0.001582242,0.0006206488,0.00005836597,0.00003760178,0.002344988],"genre_scores_gemma":[0.9861344,0.0000345571,0.0124385,0.0006856078,0.0003716423,0.000005113911,0.00001228222,0.000009481775,0.0003084245],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5983507,"threshold_uncertainty_score":0.3291993,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0259779099239044,"score_gpt":0.3089032198781281,"score_spread":0.2829253099542237,"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."}}