{"id":"W3000446254","doi":"10.1137/19m130889x","title":"Multi-Marginal Optimal Transportation Problem for Cyclic Costs","year":2021,"lang":"en","type":"preprint","venue":"SIAM Journal on Mathematical Analysis","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; University of Alberta","keywords":"Lebesgue measure; Absolute continuity; Lebesgue integration; Mathematics; Scalar (mathematics); Measure (data warehouse); Identity (music); Transportation theory; Combinatorics; Marginal distribution; Function (biology); Continuous function (set theory); Discrete mathematics; Pure mathematics; Mathematical analysis; Geometry; Computer science; Physics; Statistics; Random variable","routes":{"ca_aff":true,"ca_fund":true,"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":[0.002127653,0.001037594,0.001703106,0.0009344336,0.001068062,0.001831651,0.002420354,0.002900034,0.007618841],"category_scores_gemma":[0.005962892,0.0006652967,0.00152497,0.001359844,0.002119973,0.00349412,0.002326116,0.002335007,0.0004050319],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004386591,"about_ca_system_score_gemma":0.001986614,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.006338994,"about_ca_topic_score_gemma":0.004939157,"domain_scores_codex":[0.9990643,0.000349005,0.00003848787,0.0002114418,0.0001109436,0.0002258453],"domain_scores_gemma":[0.9976688,0.00129674,0.0002746027,0.0001585065,0.0002174446,0.000383883],"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":[0.0002692578,0.0001090469,0.0006766647,0.0001714892,0.00008508039,0.0001988019,0.0001366968,0.4810166,0.0009110257,0.5048482,0.002582184,0.008994958],"study_design_scores_gemma":[0.00003164564,0.00004272303,0.0002339146,0.00002051563,0.0000188336,0.00004978924,0.00006450954,0.8141297,0.0003414439,0.1834606,0.001583655,0.00002266831],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2688851,0.0008151729,0.7079804,0.00276688,0.0001386527,0.000133423,0.0007598805,0.0001944974,0.01832586],"genre_scores_gemma":[0.8832657,0.0004505953,0.1000188,0.000219677,0.00009001848,0.0002679336,0.0004505812,0.0001281295,0.01510862],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007618841,"threshold_uncertainty_score":0.03182709,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07999252461769027,"score_gpt":0.379594385363366,"score_spread":0.2996018607456757,"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."}}