{"id":"W2790565012","doi":"","title":"Rank of the Hermitian-adjacency matrix of a mixed graph in terms of matching number.","year":2018,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Graph theory and applications","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Hermitian matrix; Adjacency matrix; Rank (graph theory); Combinatorics; Matching (statistics); Graph; Matrix (chemical analysis); Discrete mathematics; Pure mathematics; Statistics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009303055,0.0006573128,0.0005336244,0.002733904,0.0006319474,0.002009196,0.00114607,0.0008130749,0.01171408],"category_scores_gemma":[0.005337805,0.0003169916,0.0003188766,0.001031231,0.001622569,0.003257191,0.001050405,0.001032815,0.001506463],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005695145,"about_ca_system_score_gemma":0.0005270279,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004573115,"about_ca_topic_score_gemma":0.000954498,"domain_scores_codex":[0.9993136,0.0002363304,0.0000332209,0.0001376604,0.0001671012,0.0001120949],"domain_scores_gemma":[0.9950728,0.002187394,0.0009132567,0.0004779046,0.00066176,0.0006868951],"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":[0.000190578,0.00008853618,0.001908225,0.0001396934,0.00004465822,0.0002107272,0.0002107075,0.007237116,0.007903568,0.9606463,0.006454697,0.01496523],"study_design_scores_gemma":[0.00002325006,0.00006443173,0.002401599,0.00004986187,0.00002639534,0.0005183994,0.0001694053,0.09061428,0.003142553,0.8985938,0.004332746,0.00006335614],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6547411,0.001942976,0.2663643,0.002402951,0.0004837728,0.00008937716,0.002072683,0.0008372928,0.07106557],"genre_scores_gemma":[0.9651453,0.000429639,0.02123755,0.0002103829,0.0002856924,0.00007585561,0.00048364,0.0001463676,0.01198557],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01171408,"threshold_uncertainty_score":0.03918749,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01640992588016643,"score_gpt":0.2986308202271762,"score_spread":0.2822208943470098,"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."}}