{"id":"W4221166264","doi":"10.1007/s00245-022-09937-1","title":"Transport Type Metrics on the Space of Probability Measures Involving Singular Base Measures","year":2023,"lang":"en","type":"article","venue":"Applied Mathematics & Optimization","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche","keywords":"Mathematics; Probability measure; Measure (data warehouse); Lebesgue measure; Geodesic; Absolute continuity; Wasserstein metric; Metric space; Metric (unit); Base (topology); Type (biology); Pure mathematics; Combinatorics; Discrete mathematics; Mathematical analysis; Lebesgue integration","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":[0.001539046,0.001425257,0.001112589,0.004704642,0.001313322,0.004572542,0.001139855,0.001750046,0.005446079],"category_scores_gemma":[0.005654586,0.0005374349,0.00111426,0.001785837,0.002863648,0.005472647,0.002512987,0.00225776,0.0007563723],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002250399,"about_ca_system_score_gemma":0.0009696706,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001221591,"about_ca_topic_score_gemma":0.0008673927,"domain_scores_codex":[0.99913,0.0002601971,0.00005087593,0.0001479765,0.0003070615,0.000103974],"domain_scores_gemma":[0.9966242,0.0009349795,0.000691058,0.0002429197,0.0006958363,0.0008109728],"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":[0.00002605095,0.000012364,0.0003242422,0.00003314909,0.00001560459,0.0001311529,0.00007699893,0.003250828,0.001136329,0.9921875,0.0006762272,0.00212951],"study_design_scores_gemma":[0.00001196501,0.00004557127,0.0008904327,0.00002716515,0.00001414836,0.0003276424,0.0000760547,0.03850737,0.0006481404,0.9566749,0.002749055,0.00002745267],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4436122,0.005123322,0.479616,0.00346263,0.000802389,0.0001148096,0.001081586,0.000387397,0.06579959],"genre_scores_gemma":[0.9289666,0.002902422,0.02897455,0.0003949065,0.0008789282,0.00007404776,0.0007316768,0.0002240976,0.03685291],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005446079,"threshold_uncertainty_score":0.01821893,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07840090355786736,"score_gpt":0.2677687391888136,"score_spread":0.1893678356309463,"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."}}