{"id":"W2071210623","doi":"10.1073/pnas.1221333110","title":"Insights into capacity-constrained optimal transport","year":2013,"lang":"en","type":"article","venue":"Proceedings of the National Academy of Sciences","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Uniqueness; Gravitational singularity; Dimension (graph theory); Topology (electrical circuits); Set (abstract data type); Symmetry (geometry); Identification (biology); Mathematical optimization; Mathematics; Computer science; Applied mathematics; Combinatorics; Mathematical analysis; Geometry; Biology","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":[0.0007375628,0.0001016002,0.0001930349,0.0002514482,0.0001761728,0.000021939,0.0006849205,0.00008127913,0.00007745853],"category_scores_gemma":[0.000984253,0.00006201056,0.00008753499,0.001049331,0.0008932463,0.0007401407,0.00005441581,0.000142702,0.000003594696],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002087253,"about_ca_system_score_gemma":0.00003641771,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002451183,"about_ca_topic_score_gemma":8.476717e-8,"domain_scores_codex":[0.9981737,0.000003883504,0.0004296552,0.0001761401,0.001068062,0.0001485937],"domain_scores_gemma":[0.9988183,0.0002431665,0.0003882596,0.000007209464,0.00050556,0.00003745931],"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":[0.000003321876,0.0000605823,0.0008727321,0.0003092214,0.000019838,2.641357e-9,0.001689771,0.00001517178,0.04918374,0.9470205,0.0006047497,0.0002204076],"study_design_scores_gemma":[0.0001229559,0.0000375078,0.006322658,0.00007604881,0.00001104197,0.000003040299,0.0008463213,0.0004407227,0.1316172,0.8602923,0.0001417112,0.00008847342],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9766481,0.00005185079,0.00002027231,0.001690551,0.00001425783,0.0001796831,0.000003688556,0.00001709077,0.02137452],"genre_scores_gemma":[0.9860347,0.00001013449,0.01335375,0.0001506302,0.0000549824,0.00001755267,5.837359e-8,0.000003745694,0.0003744589],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08672815,"threshold_uncertainty_score":0.3291203,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08091578762228711,"score_gpt":0.3167367510431097,"score_spread":0.2358209634208226,"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."}}