{"id":"W2975384298","doi":"10.1561/9781680835939","title":"Higher-order Fourier Analysis and Applications","year":2019,"lang":"en","type":"book","venue":"now publishers, Inc. eBooks","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Fourier analysis; Generalization; Fourier transform; Fourier series; Order (exchange); Mathematics; Field (mathematics); Fourier inversion theorem; Algebraic number; Algebra over a field; Calculus (dental); Computer science; Pure mathematics; Mathematical analysis; Short-time Fourier transform","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005505029,0.0006294632,0.001061116,0.0008513877,0.0003623618,0.0006870535,0.0008154497,0.001048559,0.001219359],"category_scores_gemma":[0.00007663936,0.0005436483,0.0004052052,0.0002466726,0.0004186008,0.000283813,0.0005316816,0.0009527765,0.00004587253],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001473819,"about_ca_system_score_gemma":0.0003086557,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001563318,"about_ca_topic_score_gemma":0.00008405377,"domain_scores_codex":[0.9972328,0.00009873792,0.0006579309,0.0008760971,0.0006503011,0.0004841641],"domain_scores_gemma":[0.9963424,0.0006052642,0.0005522177,0.001846689,0.0004201945,0.0002331856],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00001376951,0.00002015125,0.0001387915,0.0002571838,0.002244322,0.000004216347,0.0002353278,6.546436e-7,0.000001431417,0.6511501,0.336122,0.009812064],"study_design_scores_gemma":[0.0002176943,0.00001698156,0.00005502354,0.00001979877,0.001444283,0.00000300274,0.00001587906,0.00001137983,0.000002590788,0.42717,0.570657,0.0003863139],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0001069822,0.0003430823,0.001648113,0.0001069394,0.0005844518,0.001016423,0.0001934866,0.0002213056,0.9957792],"genre_scores_gemma":[0.0005646853,0.00001439842,0.006965443,0.0005589146,0.0009700409,0.000188725,0.0003563442,0.0001591096,0.9902223],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.234535,"threshold_uncertainty_score":0.9997015,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01887474454343497,"score_gpt":0.2606792553054733,"score_spread":0.2418045107620383,"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."}}