{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006929467,0.00008974048,0.0002036131,0.0002039091,0.00003728448,0.00005428216,0.0001203693,0.00005448385,0.00002450423],"category_scores_gemma":[0.0008692235,0.00007176281,0.00005374527,0.00005573736,0.00005707252,0.0002139717,0.00003472985,0.0001014157,0.000001564576],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004529036,"about_ca_system_score_gemma":0.00006344273,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008966615,"about_ca_topic_score_gemma":0.000009693366,"domain_scores_codex":[0.998701,0.00005757397,0.0005504524,0.00008225028,0.0005404599,0.00006823627],"domain_scores_gemma":[0.9980895,0.0002855927,0.0004994227,0.00008188726,0.0009270647,0.000116554],"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":[0.0007450526,0.001365958,0.0005866142,0.000185562,0.0009167825,0.00002167238,0.01257459,0.0006275221,0.008052746,0.9437469,0.001611913,0.0295647],"study_design_scores_gemma":[0.003888031,0.0001969599,0.0007993777,0.0002456747,0.000184976,0.0007494372,0.001144701,0.08709407,0.0005041958,0.9048074,0.0001966542,0.0001885381],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1410329,0.0001916314,0.8547376,0.002811318,0.0002408282,0.0001965659,0.00003091967,0.000008601641,0.0007496446],"genre_scores_gemma":[0.988256,0.00003932386,0.01138061,0.00007400178,0.0001122868,0.000007302756,0.00001131397,0.000009149165,0.0001100443],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8472231,"threshold_uncertainty_score":0.2926402,"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."}}