{"id":"W2732939482","doi":"10.1007/s12220-017-9883-3","title":"Weighted Moser–Onofri–Beckner and Logarithmic Sobolev Inequalities","year":2017,"lang":"en","type":"article","venue":"Journal of Geometric Analysis","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"Pacific Institute for the Mathematical Sciences; University of British Columbia","funders":"Simons Foundation; Pacific Institute for the Mathematical Sciences; National Science Foundation","keywords":"Mathematics; Logarithm; Sobolev inequality; Differential geometry; Euclidean space; Sobolev space; Euclidean geometry; Pure mathematics; Constant (computer programming); Fourier analysis; Inequality; Combinatorics; Set (abstract data type); Mathematical analysis; Fourier transform; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009961806,0.0001629844,0.0007331299,0.002378619,0.0003466641,0.0002818013,0.0004248663,0.0001004018,0.0004026712],"category_scores_gemma":[0.00289249,0.0001263524,0.000431916,0.001353371,0.0001157222,0.000380443,0.0001286193,0.0002495585,0.00001562686],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005516385,"about_ca_system_score_gemma":0.00006563169,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001209077,"about_ca_topic_score_gemma":0.0001053417,"domain_scores_codex":[0.9981561,0.000110736,0.0008105485,0.0001514979,0.0005508446,0.0002202138],"domain_scores_gemma":[0.9968139,0.0005493132,0.001449249,0.0005041876,0.0005132217,0.0001701296],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.0006373081,0.004379952,0.5746281,0.0007649547,0.06620763,0.0005797006,0.004530014,0.0006959119,0.002354425,0.1476397,0.01491191,0.1826705],"study_design_scores_gemma":[0.006566054,0.001072797,0.4835213,0.0002320079,0.0404579,0.0001771116,0.001897536,0.05041749,0.003383659,0.4044912,0.006004726,0.001778222],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8598107,0.000365317,0.1376089,0.000617501,0.0001649318,0.00007540206,0.00002373346,0.00001484111,0.001318718],"genre_scores_gemma":[0.9838179,0.000177104,0.01331101,0.00002683866,0.0003199998,0.000001647892,0.000004134563,0.000016643,0.00232474],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2568515,"threshold_uncertainty_score":0.51525,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08215651454688938,"score_gpt":0.3655747035980454,"score_spread":0.283418189051156,"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."}}