{"id":"W2030421585","doi":"10.1016/s0024-3795(00)00305-0","title":"Optimizing quadratic forms of adjacency matrices of trees and related eigenvalue problems","year":2001,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Combinatorics; Permutation matrix; Adjacency matrix; Diagonal; Matrix (chemical analysis); Diagonal matrix; Quadratic equation; Tree (set theory); Permutation (music); Discrete mathematics; Circulant matrix; Graph","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":[0.002178698,0.0011373,0.001389671,0.001150657,0.0009004393,0.002262951,0.002104895,0.002008476,0.006156116],"category_scores_gemma":[0.01300196,0.001177907,0.0006591185,0.0016271,0.002209035,0.004852013,0.002055778,0.002142765,0.0007390283],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001386626,"about_ca_system_score_gemma":0.001305815,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002230796,"about_ca_topic_score_gemma":0.004038246,"domain_scores_codex":[0.9987193,0.0006031278,0.00003720832,0.0002689281,0.0002286041,0.0001428058],"domain_scores_gemma":[0.9940924,0.004152182,0.0004826402,0.0002999804,0.0005446176,0.0004281219],"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":[0.0001127355,0.0002249979,0.0007331492,0.0002121793,0.00004301189,0.0000826977,0.0002886081,0.3944614,0.002791653,0.5591841,0.007179318,0.03468617],"study_design_scores_gemma":[0.00001702593,0.00003388875,0.0002130915,0.00001052367,0.000006334849,0.00002824152,0.00006733178,0.4671102,0.0004491732,0.5313984,0.000648639,0.0000171845],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1386517,0.0006301068,0.8420945,0.00153091,0.0001474673,0.0001118353,0.0002316074,0.0002437832,0.01635804],"genre_scores_gemma":[0.7938565,0.001005743,0.1706009,0.0005168289,0.0003861302,0.0003471859,0.0005317164,0.0006714533,0.03208358],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006156116,"threshold_uncertainty_score":0.02059424,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02506848078688935,"score_gpt":0.2808369818325135,"score_spread":0.2557685010456242,"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."}}