{"id":"W2532762607","doi":"10.48550/arxiv.1610.04769","title":"Optimal sampling rates for approximating analytic functions from pointwise samples","year":2016,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Statistical and numerical algorithms","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Air Force Office of Scientific Research; Natural Sciences and Engineering Research Council of Canada; Alfred P. Sloan Foundation","keywords":"Mathematics; Rate of convergence; Polynomial; Applied mathematics; Bounded function; Exponential polynomial; Pointwise; Equidistributed sequence; Minimax approximation algorithm; Discrete mathematics; Combinatorics; Exponential function; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00462616,0.0006312407,0.0008408993,0.0007421651,0.0003750496,0.001063255,0.001725468,0.0009695755,0.00100872],"category_scores_gemma":[0.02807477,0.0005439649,0.0005809402,0.0006197894,0.001620471,0.002241867,0.001742009,0.001517748,0.000397566],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009527961,"about_ca_system_score_gemma":0.000831409,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001679709,"about_ca_topic_score_gemma":0.001299856,"domain_scores_codex":[0.9983174,0.0006379096,0.00008474692,0.0002225787,0.0006023448,0.0001351063],"domain_scores_gemma":[0.9905298,0.00720426,0.0005320288,0.0008194682,0.0006996634,0.0002147592],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0007651272,0.0001103789,0.003095989,0.0002099718,0.00006107101,0.0001447102,0.0003504378,0.7972825,0.01996726,0.1005718,0.0005627602,0.07687803],"study_design_scores_gemma":[0.00001144699,0.00003991354,0.0001071996,0.000006980805,0.000003385692,0.00001680847,0.00001680185,0.9874986,0.004418163,0.007676049,0.0001979689,0.000006732667],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.04414067,0.0001841361,0.9547082,0.0001064834,0.00001355351,0.00003286861,0.00002158684,0.0001451482,0.0006473047],"genre_scores_gemma":[0.6411185,0.0003478678,0.3569832,0.00007365391,0.00003390477,0.000162533,0.0001214643,0.0001220542,0.001036714],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.00462616,"threshold_uncertainty_score":0.02446574,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2330395347571578,"score_gpt":0.2804201418276647,"score_spread":0.0473806070705069,"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."}}