{"id":"W2113490539","doi":"10.48550/arxiv.1007.1852","title":"A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases","year":2010,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Basis (linear algebra); Riesz representation theorem; Mathematics; Hilbert space; Sampling (signal processing); Basis function; Separable space; Extension (predicate logic); Nyquist–Shannon sampling theorem; Applied mathematics; Function (biology); M. Riesz extension theorem; Vector-valued function; Pure mathematics; Algorithm; Mathematical optimization; Computer science; Mathematical analysis; Geometry; Computer vision","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004160084,0.0009429897,0.0009048889,0.001511118,0.0005660858,0.001693439,0.00127625,0.001230457,0.002980659],"category_scores_gemma":[0.009038267,0.0003721503,0.001197059,0.001023355,0.002937466,0.002433611,0.003117242,0.002095829,0.0005829014],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007886998,"about_ca_system_score_gemma":0.000732421,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007616677,"about_ca_topic_score_gemma":0.0005373606,"domain_scores_codex":[0.9983324,0.0004707316,0.00008371718,0.0003239857,0.0006530184,0.0001361757],"domain_scores_gemma":[0.9967997,0.001667618,0.0003027212,0.0006185661,0.0004513604,0.0001600577],"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":[0.00006172428,0.00001559483,0.000331953,0.0001100528,0.00003748172,0.0001666206,0.0001445163,0.03733594,0.01084409,0.9254205,0.001120588,0.02441108],"study_design_scores_gemma":[0.00002724977,0.0001242124,0.000417026,0.0000424895,0.0000278851,0.0004269981,0.00006066278,0.4243823,0.008182921,0.5584267,0.007834873,0.00004664605],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.00869412,0.0002679843,0.9877397,0.0002189781,0.00005118123,0.00002328473,0.00008217719,0.00008793612,0.002834581],"genre_scores_gemma":[0.5583346,0.001726635,0.4285216,0.0008149827,0.0005982898,0.0002627894,0.0005316808,0.000301126,0.008908344],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004160084,"threshold_uncertainty_score":0.02200091,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.239083765065653,"score_gpt":0.2862367018186233,"score_spread":0.04715293675297036,"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."}}