{"id":"W3135085493","doi":"10.1137/21m1404569","title":"Emergent Behaviors of Rotation Matrix Flocks","year":2022,"lang":"en","type":"article","venue":"SIAM Journal on Applied Dynamical Systems","topic":"Nonlinear Dynamics and Pattern Formation","field":"Computer Science","cited_by":14,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Research Foundation of Korea; Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Covariant transformation; Lyapunov function; Dynamical systems theory; Exponential stability; Matrix (chemical analysis); Rotation (mathematics); Class (philosophy); Dynamical system (definition); Applied mathematics; Function (biology); Pure mathematics; Mathematical analysis; Computer science; Nonlinear system; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006592163,0.0001280585,0.0002128326,0.0001983052,0.0002722684,0.0001020186,0.000620878,0.00004347744,0.00004768687],"category_scores_gemma":[0.000003987043,0.000115751,0.0001080497,0.0003223181,0.00001352827,0.0001159338,0.0001601819,0.0004166848,0.00002762317],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002233621,"about_ca_system_score_gemma":0.00004763568,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001769081,"about_ca_topic_score_gemma":0.000001543314,"domain_scores_codex":[0.9980429,0.0001179223,0.0006306954,0.0001849481,0.000805666,0.0002178652],"domain_scores_gemma":[0.9990559,0.00003296907,0.0004579322,0.0002707222,0.00006209349,0.0001204018],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001286636,0.0007750012,0.001773738,0.0001076483,0.00009076983,0.00004837557,0.001101255,0.518242,0.0161135,0.437786,0.000617628,0.0232154],"study_design_scores_gemma":[0.0005707425,0.0003131132,0.00110726,0.00002157032,0.00001159794,0.0001898007,0.0002031303,0.994415,0.00006867425,0.001073529,0.001823726,0.0002018893],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.530366,0.00004956271,0.4658212,0.0002156897,0.001984716,0.0003664681,0.00002988435,0.00005409298,0.00111244],"genre_scores_gemma":[0.9979714,0.000006356933,0.001692993,0.00004403775,0.00009903211,0.0000348112,0.0000245453,0.00001259353,0.0001142049],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.476173,"threshold_uncertainty_score":0.4720188,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008395185974365855,"score_gpt":0.246919347133269,"score_spread":0.2385241611589032,"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."}}