{"id":"W1491439802","doi":"10.48550/arxiv.0907.3016","title":"Duality for Min-Max Orderings and Dichotomy for Min Cost Homomorphisms","year":2009,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Homomorphism; Duality (order theory); Mathematics; Combinatorics; Discrete mathematics; Mathematical economics","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":[0.001398341,0.0004303083,0.0007495382,0.0009944641,0.001359002,0.004302044,0.0009980786,0.0009668994,0.006552943],"category_scores_gemma":[0.006528939,0.000544425,0.001009085,0.001190575,0.002237148,0.006545364,0.00158621,0.004057235,0.0006608725],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002269587,"about_ca_system_score_gemma":0.0009501856,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006933004,"about_ca_topic_score_gemma":0.000813021,"domain_scores_codex":[0.998666,0.0003845754,0.0000721823,0.0003648967,0.0002617389,0.000250601],"domain_scores_gemma":[0.9942214,0.003982027,0.0004386622,0.0005485506,0.0003317577,0.0004776421],"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":[0.0001527592,0.0001245349,0.001061696,0.00007576148,0.00001357729,0.0000820409,0.0002892912,0.006820342,0.002358333,0.9716119,0.002318908,0.01509087],"study_design_scores_gemma":[0.00002261139,0.00002810401,0.0003377063,0.00001191093,0.000006599117,0.000101825,0.0001014169,0.02178141,0.001237116,0.974664,0.001696395,0.0000109314],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.4474643,0.0006600627,0.4853036,0.004469115,0.0001797097,0.00009995782,0.001339555,0.0005570517,0.0599266],"genre_scores_gemma":[0.9273013,0.0003618333,0.06207576,0.0004922279,0.0001930392,0.000135494,0.000854485,0.0001249647,0.008460903],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.006552943,"threshold_uncertainty_score":0.02192175,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08347775112373572,"score_gpt":0.3516827286564536,"score_spread":0.2682049775327178,"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."}}