{"id":"W2035380905","doi":"10.1007/s00222-010-0242-2","title":"Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation","year":2010,"lang":"en","type":"article","venue":"Inventiones mathematicae","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":291,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Alfred P. Sloan Foundation; John D. and Catherine T. MacArthur Foundation; National Science Foundation","keywords":"Mathematics; Ode; Nonlinear Schrödinger equation; Fourier transform; Mathematical analysis; Sobolev space; Hamiltonian (control theory); Mathematical physics; Hamiltonian system; Nonlinear system; Invariant (physics); Torus; Breather; Conservation law; Schrödinger equation; Pure mathematics; Geometry; Quantum mechanics; Physics","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":[0.0002861191,0.0003079039,0.0002925969,0.0004270566,0.0006849993,0.0006327815,0.0003991043,0.0006461695,0.001313774],"category_scores_gemma":[0.001064139,0.0002054278,0.0003244182,0.0003219205,0.001489006,0.0009199099,0.001027159,0.0008294691,0.0001465576],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008970714,"about_ca_system_score_gemma":0.0006693425,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00620807,"about_ca_topic_score_gemma":0.003284708,"domain_scores_codex":[0.9998986,0.0000210998,0.00000380399,0.00001053455,0.00003754206,0.00002846874],"domain_scores_gemma":[0.9997821,0.00007768419,0.00004663157,0.00002102728,0.00003262416,0.00003984283],"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":[0.0002445571,0.00006642741,0.002132893,0.0001339188,0.00002291088,0.001037933,0.001445004,0.1365483,0.06798808,0.7779882,0.001498453,0.01089342],"study_design_scores_gemma":[0.00007079155,0.0001404101,0.001580962,0.00001665872,0.00000982839,0.000298953,0.0003712016,0.8004922,0.007569653,0.1882578,0.001136396,0.00005510245],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9375623,0.0001300724,0.04580622,0.001128822,0.00004116826,0.00002651639,0.00005776802,0.000115466,0.01513163],"genre_scores_gemma":[0.9832775,0.0001402646,0.01177856,0.0000927793,0.00002083754,0.00002646889,0.00004073602,0.0000292887,0.004593405],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00620807,"threshold_uncertainty_score":0.01234388,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06514502211597445,"score_gpt":0.313971349122923,"score_spread":0.2488263270069485,"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."}}