{"id":"W2521932407","doi":"10.1016/j.jcta.2017.06.008","title":"Weighted lattice walks and universality classes","year":2017,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University; University of Waterloo; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche; Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Universality (dynamical systems); Random walk; Generating function; Combinatorics; Lattice (music); Algebraic number; Discrete mathematics; Mathematical analysis; Statistics","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":[],"consensus_categories":[],"category_scores_codex":[0.001804101,0.0002497142,0.0006788727,0.000092952,0.0005394062,0.0002806033,0.0007612797,0.0001731937,0.00005862387],"category_scores_gemma":[0.004346596,0.0002081077,0.0001503637,0.00007019687,0.0004316036,0.001515681,0.000286616,0.0004638784,0.000003045076],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009787862,"about_ca_system_score_gemma":0.0001247548,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003241992,"about_ca_topic_score_gemma":0.000001766837,"domain_scores_codex":[0.9981373,0.000279587,0.0006762121,0.0001610672,0.0004805847,0.0002652614],"domain_scores_gemma":[0.9953373,0.001416606,0.001722745,0.0007311968,0.0006003068,0.0001918109],"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":[0.0007322471,0.0001683684,0.0001319235,0.00009791055,0.0001409068,0.00006334989,0.0006326367,1.293758e-7,0.0002519648,0.9967071,0.0003893341,0.0006841028],"study_design_scores_gemma":[0.002248285,0.0004615999,0.0001237759,0.000151652,0.0001726532,0.0001551861,0.0007947854,0.000006374476,0.00200151,0.9833503,0.01031548,0.0002183987],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9666878,0.0002723478,0.003015754,0.001089785,0.0128607,0.000341076,0.00000864413,0.0000843048,0.01563961],"genre_scores_gemma":[0.9850664,0.000149308,0.01310977,0.00002328927,0.0008991111,0.000002034319,2.902642e-7,0.0000485048,0.0007013625],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01837855,"threshold_uncertainty_score":0.8486384,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02951541638307812,"score_gpt":0.3153242338792457,"score_spread":0.2858088174961675,"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."}}