{"id":"W2138305655","doi":"10.1007/s00526-014-0795-9","title":"Dual potentials for capacity constrained optimal transport","year":2014,"lang":"en","type":"article","venue":"Calculus of Variations and Partial Differential Equations","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Duality (order theory); Mathematics; Lagrange multiplier; Combinatorics; Strong duality; Regular polygon; Function (biology); Convex optimization; Dual (grammatical number); Linear programming; Weak duality; Transportation theory; Mathematical optimization; Optimization problem; Geometry","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":[0.0004058583,0.0001610197,0.0003653158,0.0001572745,0.0002827058,0.00003858664,0.00008460104,0.0001139173,0.0002060773],"category_scores_gemma":[0.001344796,0.0001479819,0.0001613707,0.0002076487,0.0001370199,0.000135119,0.00002103754,0.000074626,0.000001917275],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001086909,"about_ca_system_score_gemma":0.00006304455,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007485074,"about_ca_topic_score_gemma":0.00003046765,"domain_scores_codex":[0.9986466,0.00007132442,0.0006026059,0.0002197039,0.0002077049,0.000252118],"domain_scores_gemma":[0.9981202,0.001063987,0.0002294442,0.0001851276,0.0002941731,0.0001070554],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00002292225,0.0001797412,0.00001140601,0.0001390628,0.00008507753,1.055686e-7,0.0006009855,0.0001051309,0.001436163,0.9962876,0.00005507771,0.00107669],"study_design_scores_gemma":[0.004357079,0.0006973433,0.001427568,0.00009811838,0.001289017,0.00000907295,0.0004072069,0.8610585,0.009181874,0.118812,0.001889593,0.0007726724],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07966445,0.00001398912,0.9186679,0.0002296522,0.0002102268,0.0003469764,0.0004764322,0.00004402641,0.0003463602],"genre_scores_gemma":[0.99269,0.000005369632,0.006560293,0.00002116725,0.0002344068,0.00009390937,0.0001389284,0.00001548667,0.0002404264],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9130256,"threshold_uncertainty_score":0.6034528,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07084169491532805,"score_gpt":0.3070029880930585,"score_spread":0.2361612931777305,"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."}}