{"id":"W4412767601","doi":"10.23952/jano.7.2025.2.04","title":"Calculus rules of generalized proper $\\epsilon$-subdifferential for vector valued mappings and applications","year":2025,"lang":"en","type":"article","venue":"Journal of Applied and Numerical Optimization","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Subderivative; Calculus (dental); Mathematics; Pure mathematics; Geometry; Medicine; Regular polygon; Orthodontics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001659623,0.00009388806,0.0002695033,0.0001919007,0.0001163282,0.00007331503,0.0001571678,0.00005561855,0.00001105681],"category_scores_gemma":[0.00002758985,0.00007337955,0.00006918553,0.0003013699,0.00005023119,0.0001534926,0.00005485861,0.00005750418,2.546494e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001831708,"about_ca_system_score_gemma":0.00006260946,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002924813,"about_ca_topic_score_gemma":7.733291e-8,"domain_scores_codex":[0.9991384,0.00002249227,0.0004344571,0.0001592078,0.0001562318,0.0000892518],"domain_scores_gemma":[0.9991314,0.00006516991,0.0003323454,0.00009372542,0.000312606,0.00006476049],"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":[0.0001617382,0.0001794373,0.00005000949,0.00007405188,0.000173802,1.815831e-7,0.0002279303,0.2164036,0.001634604,0.7714983,0.0002495339,0.009346799],"study_design_scores_gemma":[0.001086223,0.00005843863,0.0005080749,0.00001398645,0.00009840567,0.000002640583,0.00001734604,0.9902052,0.0005649421,0.006295695,0.001059232,0.00008986062],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0007642757,0.0001117438,0.9974649,0.001044691,0.00005625194,0.0002353952,0.000004333801,0.00001200265,0.0003063975],"genre_scores_gemma":[0.2380061,0.0001342761,0.7613471,0.0002882956,0.00006375081,0.00003644964,0.00001485733,0.000006663358,0.0001025264],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.7738016,"threshold_uncertainty_score":0.2992331,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007807725067741243,"score_gpt":0.2367515569242589,"score_spread":0.2289438318565176,"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."}}