{"id":"W4390092862","doi":"10.48550/arxiv.2312.13201","title":"On Kemeny's constant and stochastic complement","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Gruppo Nazionale per il Calcolo Scientifico; Division of Mathematical Sciences; Istituto Nazionale di Alta Matematica \"Francesco Severi\"","keywords":"Constant (computer programming); Complement (music); Markov chain; Combinatorics; Mathematics; Kronecker delta; Discrete mathematics; Computation; Matrix (chemical analysis); Algorithm; Computer science; Statistics; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002406705,0.0002252028,0.0002640677,0.0001667365,0.0001836556,0.00002911973,0.0002913769,0.0001205028,0.0001059606],"category_scores_gemma":[0.000063541,0.0002488532,0.00009711248,0.0001891087,0.0001710183,0.00002473815,0.0005311635,0.0003394148,0.0001090483],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006817,"about_ca_system_score_gemma":0.00004117402,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002061385,"about_ca_topic_score_gemma":0.00004265713,"domain_scores_codex":[0.9989159,0.00007436293,0.000166729,0.0005685812,0.00006013632,0.0002143342],"domain_scores_gemma":[0.9984245,0.0006345328,0.0001616352,0.0006165234,0.00005374091,0.000109085],"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":[0.00002845148,0.00008512568,0.00005711014,0.00008243498,0.0000922754,0.00002979899,0.0001003297,0.008308067,0.00001104983,0.9902,0.0009768998,0.00002847461],"study_design_scores_gemma":[0.0003670025,0.00003980111,0.0001001969,0.0001591399,0.0001458254,0.000001246234,0.0002813831,0.009702096,0.00001216974,0.9888725,0.00007731099,0.000241378],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8974069,0.00001255217,0.09666397,0.000181451,0.0001930486,0.0008637849,0.000270227,0.0003487816,0.004059256],"genre_scores_gemma":[0.997965,0.00002846517,0.0002702832,0.0000445806,0.00002186511,0.000005116638,0.00003114931,0.00002741397,0.001606149],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.100558,"threshold_uncertainty_score":0.9999964,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2179687238825011,"score_gpt":0.2488843195492434,"score_spread":0.03091559566674232,"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."}}