{"id":"W2045301394","doi":"10.1016/j.difgeo.2012.09.003","title":"Geometric affine symplectic curve flows in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math>","year":2012,"lang":"lv","type":"article","venue":"Differential Geometry and its Applications","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Symplectic geometry; Mathematics; Affine transformation; Equivariant map; Invariant (physics); Ordinary differential equation; Hamiltonian (control theory); Affine geometry of curves; Mathematical analysis; Pure mathematics; Differential equation; Mathematical physics; Affine combination","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":["metaepi_narrow","sts","scholarly_communication","research_integrity","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.000839769,0.0007799384,0.0003972363,0.0007780621,0.001470706,0.001180568,0.001307848,0.00133295,0.2106747],"category_scores_gemma":[0.000303072,0.001335461,0.001160662,0.002232874,0.0006017642,0.001100842,0.001397103,0.001441753,0.00190923],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001691363,"about_ca_system_score_gemma":0.0007182514,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001201757,"about_ca_topic_score_gemma":0.0003228479,"domain_scores_codex":[0.993435,0.0002262558,0.001480505,0.001415822,0.001306186,0.002136206],"domain_scores_gemma":[0.9949456,0.0009800085,0.001167331,0.001735464,0.0001426137,0.001028943],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.0005517319,0.0009406156,0.0001137218,0.0007708584,0.001302909,0.00008596852,0.001008017,0.0004246293,0.002115596,0.9621301,0.02567195,0.004883847],"study_design_scores_gemma":[0.004782188,0.001335306,0.002206923,0.0007381731,0.002594108,0.0005272962,0.00220457,0.2229114,0.7403038,0.0003258339,0.01940351,0.002666852],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8004016,0.001449442,0.003373923,0.0003988908,0.001462532,0.00009903258,0.001076067,0.0001166344,0.1916219],"genre_scores_gemma":[0.9887677,0.0008700967,0.001049022,0.0003049012,0.003584279,0.001313945,0.003021762,0.0004139898,0.0006742474],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9618043,"threshold_uncertainty_score":0.9999635,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01747645983924156,"score_gpt":0.2482047654179096,"score_spread":0.2307283055786681,"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."}}