{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.01157111,0.001740158,0.003044328,0.004495336,0.002521408,0.005102884,0.00532642,0.004208326,0.007023007],"category_scores_gemma":[0.08121312,0.002008684,0.002275452,0.002607686,0.009425692,0.01159626,0.006894655,0.01001814,0.0007906932],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002052225,"about_ca_system_score_gemma":0.001825572,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009195113,"about_ca_topic_score_gemma":0.001043419,"domain_scores_codex":[0.9936023,0.002649378,0.0002897597,0.0009200814,0.00172386,0.0008145917],"domain_scores_gemma":[0.9009734,0.07902825,0.00472234,0.005846965,0.006003316,0.003425685],"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":[0.0001123382,0.0000938611,0.0005742922,0.0001372891,0.00005768053,0.00008903013,0.000194145,0.02256859,0.001552101,0.9677523,0.001245978,0.005622297],"study_design_scores_gemma":[0.00002769689,0.00002377122,0.0002810607,0.00004683691,0.00002743552,0.00008552234,0.00005185313,0.1670506,0.0007195782,0.8310879,0.0005534855,0.00004439355],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1394244,0.003387123,0.8251018,0.003228876,0.0004605142,0.00009215688,0.0002506912,0.0003774474,0.02767691],"genre_scores_gemma":[0.8443188,0.002382419,0.1371259,0.00127141,0.001273042,0.0003876698,0.0005255938,0.0006615212,0.01205377],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01157111,"threshold_uncertainty_score":0.0611946,"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."}}