{"id":"W2036346468","doi":"10.1016/j.cam.2012.02.034","title":"Variance bounds and existence results for randomly shifted lattice rules","year":2012,"lang":"en","type":"article","venue":"Journal of Computational and Applied Mathematics","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"Fonds Wetenschappelijk Onderzoek; Canada Research Chairs; University of New South Wales","keywords":"Mathematics; Hypercube; Lattice (music); Fourier series; Dimension (graph theory); Upper and lower bounds; Variance (accounting); Applied mathematics; Integrable system; Fourier transform; Convergence (economics); Numerical integration; Mathematical analysis; Pure mathematics; Combinatorics","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":[0.001446222,0.0001633174,0.0004195597,0.00008564598,0.000129847,0.00009096089,0.00009383199,0.00007397278,0.00001174286],"category_scores_gemma":[0.0008639169,0.0001179324,0.00007059269,0.00008150886,0.0000897461,0.0002468961,0.00002832644,0.0001326089,0.000003814551],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001963932,"about_ca_system_score_gemma":0.00003412658,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":1.498067e-7,"about_ca_topic_score_gemma":1.603955e-7,"domain_scores_codex":[0.9984345,0.00002193847,0.0009116309,0.0001017038,0.0003496138,0.0001806233],"domain_scores_gemma":[0.9961556,0.00260716,0.0007268543,0.00008690012,0.0002794274,0.0001441083],"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":[0.0001659415,0.0002557686,0.000002124334,0.0005017316,0.00004857721,2.483168e-7,0.002193005,0.000006814562,0.0001025315,0.995053,0.0007342726,0.0009360112],"study_design_scores_gemma":[0.002344718,0.0000729215,0.0001002181,0.0001408819,0.00009790521,0.0001205698,0.0004411949,0.0130772,0.0002498656,0.9819459,0.001269831,0.0001388202],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.1854355,0.0001539136,0.8071495,0.0008940775,0.00008572893,0.0004466807,0.00002651024,0.00002629565,0.005781873],"genre_scores_gemma":[0.07303516,0.00001581935,0.9263611,0.000126826,0.0001910247,0.00001839918,0.00001043782,0.00001679331,0.000224383],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.1192117,"threshold_uncertainty_score":0.4809143,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05299034154029196,"score_gpt":0.3157593038069262,"score_spread":0.2627689622666343,"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."}}