{"id":"W2560269824","doi":"10.1016/j.jde.2017.02.038","title":"A Lie systems approach to the Riccati hierarchy and partial differential equations","year":2017,"lang":"en","type":"article","venue":"Journal of Differential Equations","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal; Université du Québec à Trois-Rivières","funders":"Narodowe Centrum Nauki; Lady Margaret Hall, University of Oxford; Agence Nationale de la Recherche","keywords":"Mathematics; Riccati equation; Algebraic Riccati equation; Ordinary differential equation; Hierarchy; Mathematical analysis; Partial differential equation; Linear-quadratic regulator; Superposition principle; Differential equation; Applied mathematics; Pure mathematics; Optimal control; Mathematical optimization","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":[0.0001772321,0.0001702893,0.0003008215,0.000103467,0.001144758,0.00077855,0.0004913067,0.000044344,0.00009566724],"category_scores_gemma":[0.0001057105,0.0001121625,0.0001946255,0.00006837984,0.0001057635,0.0002379961,0.0001569953,0.0003043702,0.00001872779],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002160188,"about_ca_system_score_gemma":0.0001126284,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001683108,"about_ca_topic_score_gemma":0.000006335655,"domain_scores_codex":[0.9986048,0.0001162998,0.0005102286,0.0001639282,0.000347351,0.0002574464],"domain_scores_gemma":[0.998414,0.0001842067,0.0005383152,0.000447942,0.0001889577,0.0002265767],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0000942319,0.001664314,0.003953919,0.00004944651,0.0009638955,0.000002362501,0.003744772,0.002309599,0.00258525,0.9708828,0.002846352,0.01090308],"study_design_scores_gemma":[0.008661145,0.001064523,0.1372086,0.0004815362,0.002640374,0.00004064783,0.005231385,0.7992774,0.0009821469,0.01990477,0.02261043,0.001897074],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1800732,0.00005855486,0.815835,0.0009223244,0.0009898475,0.0002960792,0.0001086735,0.000006719111,0.0017096],"genre_scores_gemma":[0.995903,0.00000395459,0.000367646,0.00001281856,0.002795358,0.0000250694,0.00002819059,0.00001784248,0.0008461343],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.950978,"threshold_uncertainty_score":0.8804666,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03706124426680404,"score_gpt":0.2932889732509356,"score_spread":0.2562277289841316,"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."}}