{"id":"W2109513701","doi":"10.1093/imrn/rnt212","title":"Flow Polytopes of Signed Graphs and the Kostant Partition Function","year":2013,"lang":"en","type":"article","venue":"International Mathematics Research Notices","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":37,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Polytope; Partition (number theory); Combinatorics; Partition function (quantum field theory); Function (biology); Mathematics; Volume (thermodynamics); Library science; Humanities; Mathematical economics; Computer science; Art; Physics","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":[0.0004083574,0.0007005822,0.000473866,0.002661509,0.001042399,0.002284507,0.0007254547,0.0005694737,0.005183286],"category_scores_gemma":[0.002143076,0.000345324,0.000615799,0.0007806456,0.002817519,0.002413673,0.001172986,0.001586657,0.0005708464],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008539757,"about_ca_system_score_gemma":0.0003618109,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008034782,"about_ca_topic_score_gemma":0.0005526688,"domain_scores_codex":[0.9997,0.00006054806,0.00001120787,0.00005201095,0.00009867731,0.0000777013],"domain_scores_gemma":[0.9990231,0.0003737459,0.0002376589,0.00007042194,0.00008250704,0.0002125279],"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":[0.00002321641,0.00001616025,0.0004194796,0.00003486417,0.000005556476,0.00007687674,0.00008052311,0.006792147,0.001361436,0.987393,0.0006061085,0.003190699],"study_design_scores_gemma":[0.000017855,0.00002932293,0.001233479,0.00003547148,0.000007739437,0.000209824,0.00008881102,0.03783769,0.001007169,0.9567698,0.002739196,0.00002360135],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7573546,0.001492936,0.1447321,0.0008856612,0.0002781379,0.00007546824,0.0005200147,0.0001872201,0.09447391],"genre_scores_gemma":[0.9834983,0.0006621439,0.008580084,0.00009684813,0.0002526843,0.00008109445,0.0002559675,0.00008301542,0.006489946],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005183286,"threshold_uncertainty_score":0.01733983,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0907891771281897,"score_gpt":0.3891687069645437,"score_spread":0.298379529836354,"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."}}