{"id":"W3003034242","doi":"10.48550/arxiv.2001.09320","title":"Sampling discretization of integral norms","year":2020,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba; University of Alberta","funders":"Generalitat de Catalunya; Natural Sciences and Engineering Research Council of Canada; Lomonosov Moscow State University; Centres de Recerca de Catalunya","keywords":"Discretization; Mathematics; Trigonometry; Subspace topology; Norm (philosophy); Applied mathematics; Conditional entropy; Probabilistic logic; Pure mathematics; Calculus (dental); Mathematical analysis; Principle of maximum entropy; 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":[0.0001800207,0.0002308238,0.0004962374,0.0001156972,0.00006021471,0.00002448671,0.000364348,0.0002428732,0.0003191181],"category_scores_gemma":[0.0004426792,0.0002178152,0.0002639414,0.0002698219,0.00008764211,0.00007122693,0.0004534942,0.000388775,0.00004486619],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007142036,"about_ca_system_score_gemma":0.00008118919,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000528009,"about_ca_topic_score_gemma":0.00001809684,"domain_scores_codex":[0.998927,0.000067136,0.0003437583,0.0004186093,0.00007350076,0.0001700011],"domain_scores_gemma":[0.99852,0.0003658111,0.0003497102,0.000530922,0.0001184432,0.0001151012],"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":[0.00004571411,0.00008971347,0.0004667818,0.0007551921,0.0001077229,0.00000790239,0.0002926765,0.003001402,0.0001336337,0.9944373,0.0005643494,0.00009762691],"study_design_scores_gemma":[0.0002506837,0.00004634037,0.0000857451,0.000292923,0.0002662371,0.000001183836,0.0002406292,0.03954941,0.0004312908,0.9581647,0.0003843427,0.0002865138],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2875336,0.00001250534,0.7013489,0.000110235,0.0002688021,0.0003134577,0.00007516478,0.0001154656,0.01022192],"genre_scores_gemma":[0.9915138,0.00003955621,0.007018885,0.00002255608,0.0001046028,8.837206e-7,0.00004281209,0.0000290652,0.001227852],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7039802,"threshold_uncertainty_score":0.8882245,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2476849876502652,"score_gpt":0.253877027335453,"score_spread":0.006192039685187806,"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."}}