{"id":"W1679530233","doi":"10.48550/arxiv.0805.4256","title":"Monotone Linear Relations: Maximality and Fitzpatrick Functions","year":2008,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":48,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Monotonic function; Monotone polygon; Affine transformation; Linear operators; Skew; Regular polygon; Discrete mathematics; Graph; Operator (biology); Linear map; Pure mathematics; Combinatorics; Computer science; Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.0001950832,0.0002044601,0.0002545647,0.0002363935,0.000330083,0.00008323465,0.0004180946,0.0002153209,0.0001037016],"category_scores_gemma":[0.0001444265,0.000204278,0.0001470561,0.0005630463,0.000051806,0.0003134783,0.0007770525,0.000404784,0.0003597947],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000669935,"about_ca_system_score_gemma":0.0001666201,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001791643,"about_ca_topic_score_gemma":0.00001025252,"domain_scores_codex":[0.9984375,0.00009667993,0.0003979381,0.0006395371,0.0002584858,0.0001699114],"domain_scores_gemma":[0.9985498,0.0001035243,0.0002354382,0.0007142251,0.0002782687,0.0001186965],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.000008421579,0.0002452124,0.8704338,0.00003896301,0.0002789443,0.00001472616,0.0006814583,0.1140829,0.00001475274,0.009156052,0.003735238,0.001309507],"study_design_scores_gemma":[0.0002296002,0.00001779238,0.5106601,0.00001707873,0.00007034364,0.0000102869,0.00001166726,0.4806655,0.00001575371,0.001761875,0.006220174,0.0003197687],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1312916,0.0003604342,0.8610035,0.004427281,0.0004085694,0.0002170912,0.00002974941,0.0002559496,0.002005827],"genre_scores_gemma":[0.9233004,0.001226753,0.0667627,0.0006443918,0.0002869567,0.00006791872,0.0002134353,0.00001965605,0.007477746],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7942408,"threshold_uncertainty_score":0.8330213,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04762173557120956,"score_gpt":0.2623533702017976,"score_spread":0.214731634630588,"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."}}