{"id":"W4403128855","doi":"10.1515/crelle-2024-0071","title":"A geometric approach to apriori estimates for optimal transport maps","year":2024,"lang":"en","type":"article","venue":"Journal für die reine und angewandte Mathematik (Crelles Journal)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs; Simons Foundation; National Science Foundation","keywords":"Apriori algorithm; A priori and a posteriori; Computer science; Data mining; Geography; Mathematics; Association rule learning","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":[0.003566837,0.001408723,0.0009974289,0.004466404,0.001144252,0.002550465,0.001728921,0.001613375,0.007367708],"category_scores_gemma":[0.009372358,0.000757508,0.00163728,0.001021334,0.003956518,0.006012169,0.005208562,0.004468255,0.0008073505],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002416297,"about_ca_system_score_gemma":0.0006854851,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001068425,"about_ca_topic_score_gemma":0.0008348504,"domain_scores_codex":[0.9988797,0.0003928864,0.00004248449,0.0002096572,0.0003622696,0.0001129649],"domain_scores_gemma":[0.9962795,0.001859391,0.0004912715,0.0003778453,0.0006547317,0.0003372794],"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":[0.00001304251,0.00001079826,0.0002456943,0.00003527683,0.000009107251,0.00005028272,0.00006529564,0.007381948,0.000939757,0.9879341,0.0007707991,0.00254379],"study_design_scores_gemma":[0.000006851127,0.00004043474,0.0004452049,0.00003304011,0.000013085,0.0001108773,0.00006164963,0.09679912,0.001119185,0.8965026,0.00484959,0.0000185],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0619323,0.002226751,0.8867925,0.004102283,0.0002699707,0.00007074313,0.0002481193,0.000227993,0.04412945],"genre_scores_gemma":[0.7967034,0.00259487,0.1627497,0.001117815,0.001121158,0.0003195886,0.0004896941,0.00061268,0.03429106],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007367708,"threshold_uncertainty_score":0.02464741,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04150167073401071,"score_gpt":0.3313682592047952,"score_spread":0.2898665884707845,"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."}}