{"id":"W2217630407","doi":"10.1007/s10107-016-0980-z","title":"Nearly convex sets: fine properties and domains or ranges of subdifferentials of convex functions","year":2016,"lang":"en","type":"article","venue":"Mathematical Programming","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Subderivative; Convex analysis; Monotone polygon; Regular polygon; Proper convex function; Convex set; Convex optimization; Convex function; Convex combination; Effective domain; Combinatorics; Pure mathematics; 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":[],"consensus_categories":[],"category_scores_codex":[0.0002444393,0.00009073742,0.0002872368,0.00008131672,0.00005652287,0.00005252295,0.0001719281,0.00004112697,0.0002121515],"category_scores_gemma":[0.0002741824,0.00004679894,0.00006004095,0.0002309746,0.0001543604,0.0001984869,0.00009840774,0.00002863315,0.00001194931],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000008500752,"about_ca_system_score_gemma":0.00003004468,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000578637,"about_ca_topic_score_gemma":0.00000411205,"domain_scores_codex":[0.99906,0.00005191932,0.0003662187,0.0001658902,0.0002268783,0.0001290302],"domain_scores_gemma":[0.9991729,0.0002562162,0.0001495634,0.0002033186,0.0001576737,0.00006028887],"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":[0.0001399316,0.001287763,0.002379827,0.001490005,0.0006198162,0.00000523473,0.004682979,0.00002944489,0.02370952,0.6169065,0.0002359732,0.348513],"study_design_scores_gemma":[0.01575404,0.003770322,0.01366595,0.00413284,0.001614597,0.0001731692,0.002395966,0.5869286,0.1565026,0.2047933,0.007225667,0.003042943],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04248397,0.00005917698,0.9554918,0.001518245,0.00002731026,0.0001945652,0.00000486466,0.0000526252,0.0001674044],"genre_scores_gemma":[0.9121487,0.000007866597,0.08711274,0.00002008087,0.00001084069,0.00002325904,0.00000123771,0.000005640477,0.0006696896],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8696647,"threshold_uncertainty_score":0.232291,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04564266979921341,"score_gpt":0.2512032887819591,"score_spread":0.2055606189827457,"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."}}