{"id":"W2582814303","doi":"10.1016/j.laa.2017.01.034","title":"Minimising the largest mean first passage time of a Markov chain: The influence of directed graphs","year":2017,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"","keywords":"Markov chain; Mathematics; Upper and lower bounds; Combinatorics; Continuous-time Markov chain; Stationary distribution; Matrix (chemical analysis); Markov chain mixing time; Term (time); Directed graph; Markov model; Balance equation; Discrete mathematics; Statistics; 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":[0.003133723,0.001076085,0.001825255,0.001770383,0.0007032061,0.001997111,0.002288593,0.001825065,0.001784988],"category_scores_gemma":[0.02504576,0.0008940814,0.001040967,0.00123464,0.002489208,0.003306694,0.001902107,0.002051698,0.0002440829],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001728814,"about_ca_system_score_gemma":0.001844176,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004317452,"about_ca_topic_score_gemma":0.003732612,"domain_scores_codex":[0.9984776,0.000729702,0.000052136,0.0003362688,0.0002652453,0.0001390154],"domain_scores_gemma":[0.9704706,0.02584514,0.001135,0.0007226557,0.001046972,0.0007796342],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001454285,0.00006654687,0.001026577,0.0003442313,0.0001484786,0.0001410601,0.0001699564,0.7727631,0.005298515,0.1981094,0.001437673,0.02034897],"study_design_scores_gemma":[0.000007214384,0.00002068816,0.000147514,0.00001434695,0.00002009994,0.00002079916,0.00001096658,0.9308445,0.0007081146,0.06774395,0.0004485957,0.00001319314],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08809698,0.001955545,0.9022087,0.001231805,0.0001562088,0.000039263,0.0001218055,0.000255984,0.005933661],"genre_scores_gemma":[0.9140058,0.002112583,0.0762797,0.0002895044,0.0003932054,0.0001222438,0.0001712961,0.0003426974,0.006282929],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004317452,"threshold_uncertainty_score":0.01657295,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01839238917672945,"score_gpt":0.2725671525234428,"score_spread":0.2541747633467134,"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."}}