{"id":"W4213394396","doi":"10.48550/arxiv.1204.6624","title":"Theorems about Ergodicity and Class-Ergodicity of Chains with\\n Applications in Known Consensus Models","year":2012,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Complex Network Analysis Techniques","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Polytechnique Montréal","funders":"","keywords":"Ergodicity; Class (philosophy); Mathematics; Property (philosophy); Statistical physics; Limiting; Chain (unit); Consensus; Applied mathematics; Discrete mathematics; Mathematical economics; Computer science; Multi-agent system; Statistics; Physics; Artificial intelligence","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":[0.003624624,0.0008130005,0.0007027039,0.002672649,0.001336067,0.001981381,0.001426458,0.001292926,0.004456521],"category_scores_gemma":[0.02005108,0.0004315752,0.001645475,0.001428026,0.003958232,0.005441331,0.002369753,0.002660195,0.0004705714],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001982693,"about_ca_system_score_gemma":0.001147078,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002048582,"about_ca_topic_score_gemma":0.001625179,"domain_scores_codex":[0.9981566,0.0005121267,0.0001203804,0.0004989628,0.0004106249,0.0003011922],"domain_scores_gemma":[0.9825435,0.01190784,0.00201488,0.001394546,0.00131512,0.0008241061],"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":[0.00002680918,0.00002279609,0.0009711693,0.00006713819,0.00003235988,0.0001235375,0.0003175259,0.03389094,0.0009517972,0.9565096,0.0007771284,0.006309204],"study_design_scores_gemma":[0.0000124165,0.0000299336,0.0004271362,0.00003518929,0.0000231659,0.0001017025,0.00009532837,0.2329881,0.001163784,0.7630513,0.002043632,0.00002824221],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08451194,0.001049278,0.8976483,0.0009130205,0.0001137452,0.00006091495,0.0003731993,0.0002695482,0.01506003],"genre_scores_gemma":[0.9395629,0.001439631,0.05145636,0.0002438574,0.0004652909,0.0003212956,0.0004471769,0.0001396072,0.005923919],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004456521,"threshold_uncertainty_score":0.01916903,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0468254889528241,"score_gpt":0.1995479796458739,"score_spread":0.1527224906930498,"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."}}