{"id":"W2749842824","doi":"10.1007/s10959-018-0834-0","title":"Lumpings of Algebraic Markov Chains Arise from Subquotients","year":2018,"lang":"en","type":"article","venue":"Journal of Theoretical Probability","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"Natural Sciences and Engineering Research Council of Canada; Research Grants Council, University Grants Committee","keywords":"Markov chain; Algebraic number; Chain (unit); Class (philosophy); Random walk; Markov process; Function (biology); Operator (biology); Space (punctuation)","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":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.002033004,0.0002232476,0.0007712392,0.00008221258,0.00006200766,0.00002075708,0.0006327036,0.0001709817,0.0006187601],"category_scores_gemma":[0.01217116,0.0001687547,0.0003098594,0.0002178804,0.001544633,0.0001785559,0.000208353,0.0004204388,0.00001389302],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001579274,"about_ca_system_score_gemma":0.00009903726,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002310245,"about_ca_topic_score_gemma":0.000001292003,"domain_scores_codex":[0.9970277,0.0003033436,0.001412169,0.0002249845,0.000723794,0.0003079845],"domain_scores_gemma":[0.9951892,0.001887239,0.001092039,0.0006807694,0.0009325752,0.0002181281],"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":[0.0003830473,0.0008836334,0.00072429,0.0001607374,0.00008879192,0.000004961475,0.0007958687,7.575517e-7,0.0009946759,0.9949338,0.0003042402,0.0007251626],"study_design_scores_gemma":[0.0008377687,0.000633815,0.0003409,0.0002175608,0.0001201859,0.00001400877,0.00006599531,0.0003346524,0.01163334,0.985602,0.00004796991,0.0001518444],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9487368,0.00002987654,0.04772295,0.0003392649,0.0008437122,0.0003128054,0.00001353921,0.00002719942,0.001973782],"genre_scores_gemma":[0.9071559,0.000003585226,0.09238634,0.00003908795,0.0003632783,0.00000242654,4.92781e-7,0.00002887585,0.00002003373],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04466338,"threshold_uncertainty_score":0.9961497,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02771897176531937,"score_gpt":0.309859077855048,"score_spread":0.2821401060897286,"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."}}