{"id":"W4403615949","doi":"10.1142/s0218127424501839","title":"Ulam’s Method for Computing Stationary Densities of Invariant Measures for Piecewise Convex Maps with Countably Infinite Number of Branches","year":2024,"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":"Concordia University; University of Prince Edward Island","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Piecewise; Regular polygon; Invariant (physics); Invariant measure; Mathematical analysis; Applied mathematics; Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0008547509,0.00009172453,0.0002733277,0.0001432948,0.00002521282,0.0000473702,0.0001098515,0.00004481951,0.00002338712],"category_scores_gemma":[0.0003440742,0.00006894204,0.00009332306,0.00005654118,0.0000558451,0.0001469402,0.00001642529,0.0000680845,3.531281e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002695825,"about_ca_system_score_gemma":0.0001148158,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007099291,"about_ca_topic_score_gemma":0.000006539214,"domain_scores_codex":[0.9988245,0.00003103772,0.0006259024,0.00008576534,0.0003610918,0.00007170267],"domain_scores_gemma":[0.9963728,0.001767466,0.0005026455,0.0000558249,0.001265515,0.00003578043],"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":[0.000474708,0.0001986031,0.0005602163,0.001462423,0.0008871372,0.00000499298,0.004866405,0.0001428501,0.003413657,0.9686031,0.0009153488,0.01847053],"study_design_scores_gemma":[0.0020571,0.0003170255,0.0006744444,0.001854996,0.0002819606,0.0003911425,0.002109883,0.1962062,0.005660539,0.7866544,0.003571813,0.0002206052],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09311776,0.0001580002,0.9049473,0.0008957057,0.0001944197,0.0002306718,0.0001892629,0.000007472445,0.0002593855],"genre_scores_gemma":[0.8247987,0.00004545061,0.1748044,0.00008219811,0.000119188,0.000007524868,0.0000198765,0.00001551335,0.000107123],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7316809,"threshold_uncertainty_score":0.2811375,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04085098098827634,"score_gpt":0.3710037235319689,"score_spread":0.3301527425436925,"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."}}