A supersolutions perspective on hypercontractivity

The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quantity which generates a hypercontractivity inequality. Our abstract argument applies to a general Markov semigroup whose generator is a diffusion and satisfies a curvature condition.Comment: 7 page

尿中Nerve Growth Factorは、過活動膀胱症状を呈する患児の治療効果の予測因子になる

Objective: To assess urinary nerve growth factor (NGF) in children with overactive bladder (OAB) and to investigate the relationship between urinary NGF/creatinine (Cr) levels and OAB. Patients and methods: Thirty-five children (27 boys and 8 girls) with OAB and 11 children (6 boys and 5 girls) without OAB or any other urinary symptoms, who served as controls, were included in this study. Urinary NGF levels were measured using enzyme-linked immunosorbent assay. The total urinary NGF levels were adjusted with the concentration of urinary creatinine (NGF/Cr level). Refractory OAB was defined as little improvement in OAB symptoms despite at least 3 months of urotherapy and anticholinergic agent treatment. Urinary NGF/Cr was compared between the children with OAB and the controls. The relationship between urinary NGF/Cr and treatment outcomes was also evaluated. Results: Urinary NGF/Cr was significantly higher in the children with OAB when compared with those in the control group (0.65 ± 0.82 vs 0.11 ± 0.09, P = .0007). Improvement of OAB symptoms was observed in 26 out of 35 children (74%). The remaining 9 children showed refractory OAB symptoms (the refractory group). Urinary NGF/Cr was significantly higher in the refractory group than in the improved group (1.28 ± 1.34 vs 0.44 ± 0.39, P = .027). Conclusion: Urinary NGF/Cr was significantly higher in the children with OAB than in the controls, and was significantly higher in the refractory group than in the improved group. Urinary NGF/Cr could not only be a potential biomarker for children with OAB, but also a predictor of therapeutic efficacy in children with OAB.博士（医学）・乙第1454号・令和2年3月16日Copyright © 2017 Elsevier Inc. All rights reserved