Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems

For a strongly elliptic second-order operator $A$ on a bounded domain $\Omega\subset \mathbb{R}^n$ it has been known for many years how to interpret the general closed $L_2(\Omega)$-realizations of $A$ as representing boundary conditions (generally nonlocal), when the domain and coefficients are smooth. The purpose of the present paper is to extend this representation to nonsmooth domains and coefficients, including the case of H\"older $C^{\frac32+\varepsilon}$-smoothness, in such a way that pseudodifferential methods are still available for resolvent constructions and ellipticity considerations. We show how it can be done for domains with $B^\frac32_{p,2}$-smoothness and operators with $H^1_q$-coefficients, for suitable $p>2(n-1)$ and $q>n$. In particular, Kre\u\i{}n-type resolvent formulas are established in such nonsmooth cases. Some unbounded domains are allowed.Comment: 62 page

Refining the impact of TCF7L2 gene variants on type 2 diabetes and adaptive evolution

To access publisher full text version of this article. Please click on the hyperlink in Additional Links fieldWe recently described an association between risk of type 2diabetes and variants in the transcription factor 7-like 2 gene (TCF7L2; formerly TCF4), with a population attributable risk (PAR) of 17%-28% in three populations of European ancestry. Here, we refine the definition of the TCF7L2 type 2diabetes risk variant, HapB(T2D), to the ancestral T allele of a SNP, rs7903146, through replication in West African and Danish type 2 diabetes case-control studies and an expanded Icelandic study. We also identify another variant of the same gene, HapA, that shows evidence of positive selection in East Asian, European and West African populations. Notably, HapA shows a suggestive association with body mass index and altered concentrations of the hunger-satiety hormones ghrelin and leptin in males, indicating that the selective advantage of HapA may have been mediated through effects on energy metabolism

EuReCa ONE—27 Nations, ONE Europe, ONE Registry A prospective one month analysis of out-of-hospital cardiac arrest outcomes in 27 countries in Europe

AbstractIntroductionThe aim of the EuReCa ONE study was to determine the incidence, process, and outcome for out of hospital cardiac arrest (OHCA) throughout Europe.MethodsThis was an international, prospective, multi-centre one-month study. Patients who suffered an OHCA during October 2014 who were attended and/or treated by an Emergency Medical Service (EMS) were eligible for inclusion in the study. Data were extracted from national, regional or local registries.ResultsData on 10,682 confirmed OHCAs from 248 regions in 27 countries, covering an estimated population of 174 million. In 7146 (66%) cases, CPR was started by a bystander or by the EMS. The incidence of CPR attempts ranged from 19.0 to 104.0 per 100,000 population per year. 1735 had ROSC on arrival at hospital (25.2%), Overall, 662/6414 (10.3%) in all cases with CPR attempted survived for at least 30 days or to hospital discharge.ConclusionThe results of EuReCa ONE highlight that OHCA is still a major public health problem accounting for a substantial number of deaths in Europe.EuReCa ONE very clearly demonstrates marked differences in the processes for data collection and reported outcomes following OHCA all over Europe. Using these data and analyses, different countries, regions, systems, and concepts can benchmark themselves and may learn from each other to further improve survival following one of our major health care events