{"id":"W2614091911","doi":"","title":"The majorization theorem and signless Dirichlet spectral radius of connected graphs.","year":2017,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Majorization; Spectral radius; Combinatorics; Dirichlet distribution; Eigenvalues and eigenvectors; Physics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004284175,0.0001048926,0.0001578555,0.00002998706,0.0007883033,0.00008766809,0.0003726317,0.00005611916,0.000009924468],"category_scores_gemma":[0.0003806119,0.00007614925,0.00005081835,0.00008945217,0.0003853024,0.00008945983,0.00006489709,0.0000960575,0.000002693352],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000007083628,"about_ca_system_score_gemma":0.00001325335,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008781066,"about_ca_topic_score_gemma":0.000006842039,"domain_scores_codex":[0.9993043,0.00008008559,0.0001996165,0.0001451788,0.0001190058,0.0001518436],"domain_scores_gemma":[0.9983268,0.0006063229,0.0002673578,0.0006729647,0.00008039946,0.00004620487],"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":[0.0000180943,0.00006250247,0.00209805,0.00001536677,0.00003474331,7.18707e-7,0.0002119066,1.002886e-7,0.001942856,0.994853,0.0003502863,0.0004124065],"study_design_scores_gemma":[0.0005113198,0.00003563528,0.009467449,0.00001621155,0.00003799113,0.000002934043,0.00009797907,0.00004285369,0.008914522,0.9805594,0.0002231084,0.00009057699],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9944135,0.00007973555,0.0000766375,0.0003963924,0.0003023601,0.0002682237,0.00000803181,0.00004164975,0.004413459],"genre_scores_gemma":[0.9996055,0.00005916282,0.0001554635,0.000009439912,0.000005799594,0.00002501705,0.000003283141,0.000014728,0.0001216113],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01429355,"threshold_uncertainty_score":0.6063071,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01970777913647579,"score_gpt":0.27927326883956,"score_spread":0.2595654897030842,"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."}}