{"id":"W4390414797","doi":"10.1016/j.laa.2023.12.020","title":"On the stability of the principal ratio","year":2023,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Bounded function; Combinatorics; Multiplicative function; Spectral gap; Adjacency matrix; Eigenvalues and eigenvectors; Upper and lower bounds; Graph; Discrete mathematics; Measure (data warehouse); Graph energy; Line graph; Graph power; Mathematical analysis","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":[0.00252541,0.001110969,0.001522446,0.004066795,0.001904802,0.003732053,0.001801893,0.001534873,0.009189789],"category_scores_gemma":[0.01688084,0.0005842973,0.00100066,0.002258685,0.006611612,0.007665309,0.002793431,0.003501886,0.001279823],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001726925,"about_ca_system_score_gemma":0.000806944,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001217423,"about_ca_topic_score_gemma":0.0005272045,"domain_scores_codex":[0.9986265,0.000571459,0.00004617216,0.0003318108,0.0002617932,0.0001622986],"domain_scores_gemma":[0.9906262,0.006471239,0.0009005885,0.0003768536,0.0008776079,0.0007474126],"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":[0.0001068186,0.00002188056,0.0002212593,0.00005081297,0.00001356238,0.00004344068,0.000176873,0.002612777,0.000945986,0.9894945,0.001289368,0.005022892],"study_design_scores_gemma":[0.00001662936,0.00002117971,0.0001804365,0.00001187779,0.000007366966,0.00004857331,0.00005457537,0.01469824,0.0003328541,0.9836656,0.0009484547,0.00001415648],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5022724,0.01035871,0.3031237,0.0146167,0.001278413,0.00009240209,0.0005902341,0.0005745752,0.1670928],"genre_scores_gemma":[0.9687579,0.002897874,0.01298175,0.0007159659,0.001826415,0.0000920799,0.0002003958,0.0001994689,0.01232821],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009189789,"threshold_uncertainty_score":0.03074288,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05441369205311207,"score_gpt":0.3033575243069773,"score_spread":0.2489438322538652,"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."}}