{"id":"W2096220424","doi":"10.1007/s11228-004-7197-7","title":"Nonsmooth Analysis of Singular Values. Part I: Theory","year":2005,"lang":"en","type":"article","venue":"Set-Valued Analysis","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":109,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University; University of Waterloo","funders":"","keywords":"Subderivative; Mathematics; Simple (philosophy); Limiting; TRACE (psycholinguistics); Singular value; Mathematical analysis; Singular solution; Work (physics); Applied mathematics; Matrix (chemical analysis); Pure mathematics; Calculus (dental); Eigenvalues and eigenvectors; Regular polygon; Geometry; Philosophy; Physics","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":[0.002499003,0.0002809208,0.0009525121,0.001871815,0.0002001071,0.0001248567,0.001358879,0.0001123209,0.0009541748],"category_scores_gemma":[0.000123186,0.0002452323,0.001350749,0.01083778,0.0001578463,0.0004275902,0.0002510131,0.0001679065,0.00007826833],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005809985,"about_ca_system_score_gemma":0.00006742855,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004808078,"about_ca_topic_score_gemma":0.00003265322,"domain_scores_codex":[0.9968219,0.0006324454,0.0007016324,0.0007201604,0.0006746548,0.0004492144],"domain_scores_gemma":[0.9972589,0.0002813606,0.0003754828,0.001708233,0.0001924895,0.0001835397],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00005930585,0.0006803185,0.004473675,0.00004073429,0.05812826,0.00007060115,0.004701909,0.2483548,0.0004200498,0.5458328,0.0007991766,0.1364384],"study_design_scores_gemma":[0.0002898062,0.00004670507,0.00183511,0.000009684766,0.01612743,0.000002379525,0.0001284673,0.9621564,0.002110392,0.01371099,0.003151777,0.0004308867],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05617754,0.0007443528,0.9383847,0.0003382607,0.0001303906,0.0001130476,0.00004538376,0.0002076525,0.003858727],"genre_scores_gemma":[0.9446645,0.00003793106,0.05211852,0.0004012717,0.0001668517,0.000009525668,0.00006030535,0.00001612223,0.002525006],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8884869,"threshold_uncertainty_score":1,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01194793296660928,"score_gpt":0.2594108906264844,"score_spread":0.2474629576598751,"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."}}