{"id":"W4225573577","doi":"10.1016/j.acha.2023.02.002","title":"Generalized matrix spectral factorization with symmetry and applications to symmetric quasi-tight framelets","year":2023,"lang":"en","type":"preprint","venue":"Applied and Computational Harmonic Analysis","topic":"Fibroblast Growth Factor Research","field":"Biochemistry, Genetics and Molecular Biology","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Factorization; Constructive; Mathematics; Symmetry (geometry); Pure mathematics; Matrix decomposition; Mathematical proof; Spectral theorem; Algebra over a field; Matrix (chemical analysis); Quantum mechanics; Physics; Algorithm; Computer science; Eigenvalues and eigenvectors; Operator theory; Geometry","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001659845,0.0003316408,0.0004383967,0.0007874413,0.0001715158,0.0001641554,0.0002342489,0.0002715413,0.00001602966],"category_scores_gemma":[0.00001675146,0.0003129067,0.0001297077,0.001472798,0.00009370338,0.000004134581,0.0005033811,0.0002864151,0.00002150472],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004967483,"about_ca_system_score_gemma":0.0001523979,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008794304,"about_ca_topic_score_gemma":0.00003102782,"domain_scores_codex":[0.9978557,0.00005400715,0.0003311895,0.0009989577,0.0004478539,0.0003122936],"domain_scores_gemma":[0.9990028,0.00008104151,0.0001572868,0.0003526114,0.000170672,0.0002356552],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"observational","study_design_scores_codex":[0.001534793,0.001082796,0.07407761,0.001753868,0.03073218,0.00003414351,0.0007067604,0.578746,0.06625427,0.2220408,0.002828074,0.02020861],"study_design_scores_gemma":[0.006382286,0.001667316,0.684873,0.0001831382,0.007714835,0.0000477983,0.0006185047,0.1588188,0.0200197,0.1050722,0.008319284,0.006283068],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4714836,0.0005005836,0.5265898,0.0003270847,0.00002192824,0.0007131078,0.0002064081,0.00005239355,0.0001051118],"genre_scores_gemma":[0.9843349,0.0002270393,0.0109559,0.0001019329,0.0001911749,0.0003506034,0.003514686,0.0000514025,0.0002723188],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6107954,"threshold_uncertainty_score":0.9999323,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01649535775437217,"score_gpt":0.2909975018369894,"score_spread":0.2745021440826172,"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."}}