{"id":"W2040926607","doi":"10.1007/s11117-012-0192-6","title":"Generalized positive sets and abstract monotonicity","year":2012,"lang":"en","type":"article","venue":"Positivity","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Centre de Recherches Mathématiques","keywords":"Monotonic function; Mathematics; Monotone polygon; Operator theory; Potential theory; Banach space; Pure mathematics; Duality (order theory); Regular polygon; Discrete mathematics; Subderivative; Relation (database); Mathematical analysis; Convex optimization; Computer science","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00207228,0.0008778475,0.001034738,0.001443165,0.001254315,0.002542346,0.001232035,0.001242042,0.005968153],"category_scores_gemma":[0.008131344,0.0006510823,0.0009736973,0.001260614,0.006053051,0.00555796,0.003056259,0.003504712,0.0003758073],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001149459,"about_ca_system_score_gemma":0.0005386981,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007942735,"about_ca_topic_score_gemma":0.0008576146,"domain_scores_codex":[0.9988865,0.0005364378,0.00004271754,0.0001871692,0.0002610059,0.00008614355],"domain_scores_gemma":[0.9969617,0.002058369,0.0002317896,0.0002461083,0.0003209777,0.0001810547],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000010202,0.000006436444,0.00005060623,0.00003282995,0.000006903202,0.00003490529,0.00009105751,0.001439146,0.0003642978,0.9934382,0.0007919842,0.003733434],"study_design_scores_gemma":[0.000002994975,0.000002846974,0.00005734427,0.000007082075,0.00000249919,0.00003077537,0.00001940828,0.003862202,0.00008737555,0.994429,0.001495105,0.000003374851],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1330999,0.008200293,0.7132963,0.008033039,0.0005350583,0.00006068319,0.0002742588,0.0001767782,0.1363237],"genre_scores_gemma":[0.902801,0.004135656,0.06053607,0.001407242,0.0008775102,0.0001887054,0.0002026339,0.0002154317,0.0296358],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005968153,"threshold_uncertainty_score":0.01996547,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01486627257183556,"score_gpt":0.2619785330958381,"score_spread":0.2471122605240026,"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."}}