{"id":"W3208171027","doi":"10.1016/j.laa.2024.03.013","title":"Deletion-contraction for a unified Laplacian and applications","year":2024,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Mathematics; Laplace operator; Conjecture; Laplacian matrix; Vertex (graph theory); Eigenvalues and eigenvectors; Interlacing; Laplacian smoothing; Contraction (grammar); Graph; Spanning tree; Discrete mathematics; Computer science; Artificial intelligence; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0002258129,0.0001468412,0.0001483437,0.0001119518,0.0004416861,0.00009547709,0.0000957979,0.0001062484,0.00002888382],"category_scores_gemma":[0.00003856097,0.0001400882,0.00005966142,0.0003324071,0.00006864292,0.0001431107,0.00002620337,0.0001350224,0.00004782477],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001285637,"about_ca_system_score_gemma":0.00002941413,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001911496,"about_ca_topic_score_gemma":0.000007738529,"domain_scores_codex":[0.9990921,0.00001911093,0.0002620965,0.0003774318,0.00007637181,0.0001728675],"domain_scores_gemma":[0.9987999,0.0006897529,0.00005639649,0.00024961,0.00009272228,0.0001116753],"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":[0.000005808816,0.00006048712,0.00000573541,0.0001790224,0.00003409773,9.390023e-8,0.00009717599,8.892362e-7,0.001897079,0.9837523,0.0006570752,0.0133103],"study_design_scores_gemma":[0.0001500576,0.00001780999,0.00004105716,0.0000176557,0.0001023245,0.0000140253,0.0001286006,0.002801039,0.0007641666,0.6697608,0.3260654,0.0001371269],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03860876,0.004018144,0.9376549,0.005265942,0.00008318841,0.006603661,0.0005559141,0.0009743548,0.006235193],"genre_scores_gemma":[0.9708442,0.000620474,0.01323388,0.0002395137,0.0006319694,0.01202235,0.000208176,0.00006496873,0.002134449],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9322355,"threshold_uncertainty_score":0.5712631,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0262838352694974,"score_gpt":0.3130012834160383,"score_spread":0.2867174481465409,"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."}}