{"id":"W2074430489","doi":"10.1109/cdc.2014.7039449","title":"Stability of dynamical systems on a graph","year":2014,"lang":"en","type":"article","venue":"","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Adjacency matrix; Eigenvalues and eigenvectors; Topology (electrical circuits); Scalar (mathematics); Graph energy; Mathematics; Dynamical systems theory; Exponential stability; Graph theory; Stability (learning theory); Interconnection; Adjacency list; Graph; Lyapunov function; Discrete mathematics; Applied mathematics; Pure mathematics; Computer science; Line graph; Voltage graph; Algorithm; Combinatorics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002017245,0.00008949878,0.0002193234,0.00002141295,0.00002651709,0.00001449308,0.00009283381,0.00002772238,0.0002211143],"category_scores_gemma":[0.00000529177,0.0000624929,0.0001002342,0.00007458177,0.00004215138,0.00002414652,0.00001869913,0.0000665909,0.00003879474],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000008589665,"about_ca_system_score_gemma":0.000007303653,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009944066,"about_ca_topic_score_gemma":0.000005269768,"domain_scores_codex":[0.9992252,0.00007619766,0.0002468753,0.0001636643,0.0001440331,0.0001440366],"domain_scores_gemma":[0.9994574,0.0001140409,0.0000678807,0.0002518465,0.00003650767,0.00007233984],"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":[0.00001108979,0.0001523276,0.04297253,0.0000287944,0.00001777025,3.94281e-8,0.00001977429,0.0001100153,0.0007184918,0.9549762,0.00008151845,0.0009114431],"study_design_scores_gemma":[0.002108733,0.0009879724,0.0315265,0.0001987156,0.00004687977,9.014169e-7,0.001074025,0.8853931,0.002944283,0.06990214,0.00499665,0.0008200707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8629251,0.000004106843,0.05800128,0.00003273518,0.0001811059,0.0001385305,0.00002039544,0.00002448045,0.07867231],"genre_scores_gemma":[0.9996924,6.700037e-8,0.00003846807,0.000008241488,0.0001039822,0.00001136685,0.000009441928,0.000006775987,0.0001292289],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8852831,"threshold_uncertainty_score":0.2548386,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009039440903022607,"score_gpt":0.2201804175180611,"score_spread":0.2111409766150384,"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."}}