{"id":"W2891872939","doi":"10.1080/00150517.2019.12427620","title":"Connection Coefficients for Higher-order Bernoulli and Euler Polynomials: A Random Walk Approach","year":2019,"lang":"en","type":"article","venue":"˜The œFibonacci quarterly","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"","keywords":"Connection (principal bundle); Bernoulli's principle; Euler's formula; Random walk; Order (exchange); Mathematics; Bernoulli polynomials; Difference polynomials; Mathematical analysis; Orthogonal polynomials; Physics; Geometry; Statistics; Thermodynamics","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":[0.0005301014,0.0002175325,0.0003714623,0.00006448121,0.0002607704,0.000140588,0.0002217698,0.0001170346,0.00007447506],"category_scores_gemma":[0.00001771033,0.0001516673,0.0001325897,0.0002095769,0.0000543737,0.0001046752,0.00001962509,0.0001246562,0.00009120305],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002787139,"about_ca_system_score_gemma":0.00002487091,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006419457,"about_ca_topic_score_gemma":0.00002072545,"domain_scores_codex":[0.9986364,0.00007942297,0.0003878766,0.0003798619,0.0002043662,0.0003121018],"domain_scores_gemma":[0.9980161,0.001115753,0.0002048179,0.0004777309,0.0001115069,0.00007407191],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.009118214,0.00568599,0.004434574,0.003111284,0.002046432,0.000003928521,0.0307982,0.0004121846,0.01557653,0.5550681,0.1664867,0.2072579],"study_design_scores_gemma":[0.08325227,0.002623796,0.003670557,0.0001510157,0.001302656,0.0001228173,0.01080707,0.07710134,0.0003151761,0.175819,0.642301,0.002533328],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.850386,0.0004231886,0.1344445,0.001072504,0.000734249,0.004755666,0.00007993156,0.000223017,0.007880891],"genre_scores_gemma":[0.9900225,0.000008269588,0.003918746,0.0001315785,0.0002611305,0.0005286225,0.00003014474,0.00005175549,0.00504727],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4758142,"threshold_uncertainty_score":0.6184813,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02342298290797652,"score_gpt":0.2816549580877409,"score_spread":0.2582319751797644,"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."}}