{"id":"W3127350324","doi":"10.48550/arxiv.1911.02974","title":"Cutoff for Random Walks on Upper Triangular Matrices","year":2019,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Graph theory and applications","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Combinatorics; Conjecture; Mathematics; Cutoff; Heisenberg group; Dihedral group; Abelian group; Cayley graph; Group (periodic table); Random walk; Graph; Physics; Statistics; Mathematical analysis; Quantum mechanics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0004223571,0.0003176423,0.0004973324,0.0002548876,0.0001746401,0.0000451307,0.0006818573,0.0003715533,0.0001490375],"category_scores_gemma":[0.0001302435,0.000324806,0.0005629889,0.0002420323,0.00007123885,0.00007113679,0.00024955,0.0003931854,0.0002225981],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007970231,"about_ca_system_score_gemma":0.00007133844,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001026947,"about_ca_topic_score_gemma":0.000004119318,"domain_scores_codex":[0.9985625,0.0001191018,0.00023343,0.0007292954,0.00006873313,0.0002869853],"domain_scores_gemma":[0.9972847,0.00108236,0.0003125937,0.001108534,0.0001157059,0.00009610828],"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":[0.0005141682,0.0001891783,0.0001272253,0.0002846639,0.0001841431,0.000009142806,0.0001115745,0.005297107,0.00003299477,0.9900186,0.003128405,0.0001027785],"study_design_scores_gemma":[0.002820951,0.00006031107,0.00003799778,0.000128492,0.0004496772,0.000001102763,0.0001422024,0.00814425,0.0002964716,0.9790522,0.008464581,0.0004017807],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8801765,0.00007931441,0.1031768,0.0001734871,0.0005372638,0.002803236,0.0002831104,0.0002899047,0.01248035],"genre_scores_gemma":[0.9865702,0.00009695123,0.001085477,0.00007716039,0.0001227596,0.00001668259,0.00006322128,0.0000493517,0.0119182],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1063937,"threshold_uncertainty_score":0.9999204,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1075488268547095,"score_gpt":0.2351928607429992,"score_spread":0.1276440338882897,"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."}}