{"id":"W2213502955","doi":"10.1142/s0218127415501126","title":"Stochastic Perturbations and Invariant Measures of Position Dependent Random Maps via Fourier Approximations","year":2015,"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; Invariant measure; Separable space; Fourier transform; Absolute continuity; Invariant (physics); Combinatorics; Measure (data warehouse); Kernel (algebra); Mathematical analysis; Mathematical physics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001451795,0.0007864839,0.0006547868,0.001487817,0.0006633992,0.00112404,0.001186076,0.0010219,0.001196378],"category_scores_gemma":[0.005224825,0.0004766481,0.0009740174,0.0004665336,0.002485074,0.00207552,0.00145796,0.001377098,0.0001934121],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001829167,"about_ca_system_score_gemma":0.0007795625,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002218136,"about_ca_topic_score_gemma":0.000871486,"domain_scores_codex":[0.9994221,0.0001890541,0.00002308021,0.00008653929,0.0002046076,0.00007473055],"domain_scores_gemma":[0.9985669,0.0006031664,0.0003106345,0.0001471477,0.0001686384,0.000203473],"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":[0.00009333017,0.00005315836,0.001011816,0.00005716073,0.00004865012,0.0003802738,0.0002411947,0.1200373,0.01110206,0.8630611,0.0004053784,0.003508497],"study_design_scores_gemma":[0.00001932178,0.00005952083,0.000761194,0.00001705516,0.00001338786,0.0001717704,0.00004808445,0.8310246,0.001776526,0.1653727,0.0006983418,0.00003745599],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5403815,0.0007432813,0.4449439,0.0008903743,0.0001592741,0.00008767493,0.0001335596,0.0002178225,0.01244272],"genre_scores_gemma":[0.9616332,0.0005243421,0.031103,0.0001003065,0.00009614166,0.0000988892,0.00009370126,0.00005747674,0.006292942],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002218136,"threshold_uncertainty_score":0.01327157,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05953040532993571,"score_gpt":0.3045716315568007,"score_spread":0.245041226226865,"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."}}