{"id":"W4225853730","doi":"10.22215/etd/2021-14924","title":"Applications of Optimal Mass Transportation in Geometric and Functional Inequalities","year":2021,"lang":"en","type":"dissertation","venue":"","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematical proof; Mass transportation; Inequality; Sobolev space; Mathematics; Work (physics); Sobolev inequality; Applied mathematics; Pure mathematics; Calculus (dental); Mathematical optimization; Mathematical analysis; Geometry; Engineering; Mechanical engineering","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002674419,0.001461351,0.0009638352,0.00236917,0.001492057,0.001966855,0.001336308,0.001623214,0.007144883],"category_scores_gemma":[0.006032682,0.0005074493,0.002087292,0.001799062,0.004755793,0.004227109,0.003158108,0.00402593,0.0006642086],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003845239,"about_ca_system_score_gemma":0.001435391,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003932326,"about_ca_topic_score_gemma":0.002238968,"domain_scores_codex":[0.998629,0.0006461547,0.00006451766,0.0002433246,0.0003043049,0.0001127173],"domain_scores_gemma":[0.9980958,0.001230472,0.0001636621,0.0001556312,0.0002565891,0.00009771845],"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":[0.000004304265,0.00000542148,0.00004897729,0.00004466915,0.0000057714,0.00001665378,0.00004074028,0.007776499,0.0001591553,0.9871999,0.0006666989,0.004031102],"study_design_scores_gemma":[0.000003366725,0.00002030393,0.00009776915,0.00005673531,0.000008761192,0.00003466325,0.00003818114,0.03086765,0.0002634375,0.9585676,0.01003286,0.000008629928],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.008614164,0.00593026,0.9185341,0.005190932,0.0005878222,0.00004427694,0.0001257708,0.00006862536,0.06090395],"genre_scores_gemma":[0.5988854,0.01731573,0.338203,0.002021547,0.002748515,0.0003691084,0.0002975692,0.0003868334,0.03977231],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.007144883,"threshold_uncertainty_score":0.02789932,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02660485536552345,"score_gpt":0.2833990977887582,"score_spread":0.2567942424232347,"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."}}