{"id":"W2001540634","doi":"10.1103/physreve.64.056203","title":"Interplays between Harper and Mathieu equations","year":2001,"lang":"en","type":"article","venue":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Science North","funders":"","keywords":"Mathieu function; Algebraic equation; Quadratic equation; Nonlinear system; Energy (signal processing); Mathematics; Physics; Applied mathematics; Mathematical physics; Mathematical analysis; Quantum mechanics; Geometry","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":[0.002780015,0.0005711722,0.0009074407,0.00181702,0.001079969,0.002873847,0.001484119,0.00171926,0.006751292],"category_scores_gemma":[0.008163782,0.000444038,0.0008952799,0.0008402626,0.003417758,0.006535054,0.002861168,0.002710804,0.0009826903],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001419144,"about_ca_system_score_gemma":0.0009224899,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001829834,"about_ca_topic_score_gemma":0.0009982251,"domain_scores_codex":[0.9981909,0.0005555866,0.0001144108,0.0001965797,0.0007799802,0.0001625727],"domain_scores_gemma":[0.9978597,0.001119687,0.000212527,0.0002414457,0.000418349,0.0001482304],"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":[0.00000234017,0.000002915201,0.00003846717,0.00001250394,0.00000166857,0.00002374572,0.00006019622,0.0005583522,0.0001559752,0.9972737,0.0003211318,0.0015488],"study_design_scores_gemma":[0.000005756448,0.000008899146,0.0001514426,0.00001311128,0.000002221333,0.00008525742,0.00003793145,0.01052625,0.0002024687,0.9855237,0.003429407,0.000013485],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09567042,0.01024991,0.5279855,0.01263369,0.001270845,0.0001478373,0.000269145,0.0003675676,0.3514052],"genre_scores_gemma":[0.8493545,0.006647385,0.08962874,0.002740947,0.001769958,0.0002136733,0.0001594577,0.0002612498,0.04922403],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006751292,"threshold_uncertainty_score":0.02258533,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01624516703280886,"score_gpt":0.3220714689431459,"score_spread":0.3058263019103371,"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."}}