{"id":"W2016919634","doi":"10.1134/s1560354710040039","title":"Criteria for existence of a Hamiltonian structure","year":2010,"lang":"en","type":"article","venue":"Regular and Chaotic Dynamics","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Diagonalizable matrix; Hamiltonian (control theory); Mathematics; Hamiltonian system; Pure mathematics; Tensor (intrinsic definition); Mathematical physics; Physics; Eigenvalues and eigenvectors; Quantum mechanics; Mathematical optimization; Symmetric matrix","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":[0.001459182,0.0004258659,0.0005674742,0.001687518,0.001626341,0.001499519,0.0006955906,0.001586226,0.008451231],"category_scores_gemma":[0.01006863,0.0004846296,0.0004183761,0.0004662857,0.003245496,0.002256691,0.001908796,0.001314494,0.000948394],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007626165,"about_ca_system_score_gemma":0.001143319,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005045473,"about_ca_topic_score_gemma":0.0005135735,"domain_scores_codex":[0.9988441,0.0002499963,0.0001230355,0.0002274168,0.0003485924,0.0002067629],"domain_scores_gemma":[0.990168,0.004832124,0.001170833,0.0004573519,0.001977023,0.001394686],"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":[0.0001418538,0.00008627632,0.003406367,0.0001712022,0.00002062573,0.0006713974,0.0004441398,0.004898512,0.01219309,0.9700328,0.002382801,0.005550922],"study_design_scores_gemma":[0.0001315281,0.0002134287,0.004262294,0.0001093143,0.00002054287,0.0007919485,0.0007274262,0.05435733,0.01152835,0.9188592,0.008923635,0.00007515425],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6394809,0.0009578641,0.2726059,0.003097941,0.0003368164,0.0003937772,0.001671193,0.0004891372,0.08096652],"genre_scores_gemma":[0.9539236,0.0001955104,0.04091972,0.000196177,0.0001592313,0.0002554305,0.0007744674,0.00007950833,0.003496385],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008451231,"threshold_uncertainty_score":0.02827215,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005689193416774989,"score_gpt":0.2445369322139472,"score_spread":0.2388477387971722,"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."}}