{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001357341,0.0004921601,0.0004598693,0.001187228,0.0007747661,0.001309903,0.0007070518,0.0007196615,0.003164742],"category_scores_gemma":[0.004988434,0.0002597678,0.0006208465,0.001010956,0.002739802,0.004002104,0.001159077,0.001329663,0.0003456105],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008824171,"about_ca_system_score_gemma":0.0003388423,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006685969,"about_ca_topic_score_gemma":0.0004679481,"domain_scores_codex":[0.999155,0.0002594553,0.00003020663,0.0001927836,0.0002068714,0.0001556268],"domain_scores_gemma":[0.9970683,0.001703122,0.000423614,0.0002461226,0.0003431564,0.0002156773],"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":[0.00002219275,0.00001396254,0.0005400283,0.00003616479,0.000009550647,0.00008053438,0.0002124714,0.004638506,0.002763934,0.9833265,0.0005998192,0.007756306],"study_design_scores_gemma":[0.000004991456,0.00002544823,0.0004852875,0.00001300628,0.000005835058,0.0001582327,0.0001097784,0.04107103,0.001636126,0.9545979,0.00187911,0.00001318806],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.404967,0.001413432,0.5552389,0.001493953,0.00006003099,0.0000435612,0.0002313854,0.0001558885,0.03639598],"genre_scores_gemma":[0.9580366,0.0005600055,0.03725611,0.0001382577,0.0001002042,0.00004465866,0.00009110767,0.00006464027,0.00370844],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.003164742,"threshold_uncertainty_score":0.0105871,"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."}}