Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schr\"odinger Operator with only one Observation

This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain

A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and $a1 > a2$ . As a consequence of this inequality, uniqueness and Lip- schitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement

Homeomorphic Embedding for Online Termination of Symbolic Methods

Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems

Quantitative angiographic follow-up of the coronary wallstent in native vessels and bypass grafts (European experience - March 1986 to March 1990)

The coronary stent has been investigated as an adjunct to percutaneous transluminal coronary angioplasty to obviate the problems of early occlusion and late restenosis. From March 1986 to March 1990, 265 patients (308 lesions) were implanted with the coronary Wallstent in 6 European centers. For this study, the patients were analyzed accordin

A Mild Form of SLC29A3 Disorder: A Frameshift Deletion Leads to the Paradoxical Translation of an Otherwise Noncoding mRNA Splice Variant

We investigated two siblings with granulomatous histiocytosis prominent in the nasal area, mimicking rhinoscleroma and Rosai-Dorfman syndrome. Genome-wide linkage analysis and whole-exome sequencing identified a homozygous frameshift deletion in SLC29A3, which encodes human equilibrative nucleoside transporter-3 (hENT3). Germline mutations in SLC29A3 have been reported in rare patients with a wide range of overlapping clinical features and inherited disorders including H syndrome, pigmented hypertrichosis with insulin-dependent diabetes, and Faisalabad histiocytosis. With the exception of insulin-dependent diabetes and mild finger and toe contractures in one sibling, the two patients with nasal granulomatous histiocytosis studied here displayed none of the many SLC29A3-associated phenotypes. This mild clinical phenotype probably results from a remarkable genetic mechanism. The SLC29A3 frameshift deletion prevents the expression of the normally coding transcripts. It instead leads to the translation, expression, and function of an otherwise noncoding, out-of-frame mRNA splice variant lacking exon 3 that is eliminated by nonsense-mediated mRNA decay (NMD) in healthy individuals. The mutated isoform differs from the wild-type hENT3 by the modification of 20 residues in exon 2 and the removal of another 28 amino acids in exon 3, which include the second transmembrane domain. As a result, this new isoform displays some functional activity. This mechanism probably accounts for the narrow and mild clinical phenotype of the patients. This study highlights the ‘rescue’ role played by a normally noncoding mRNA splice variant of SLC29A3, uncovering a new mechanism by which frameshift mutations can be hypomorphic

Weakly Consistent Regularisation Methods for Ill-Posed Problems

This Chapter takes its origin in the lecture notes for a 9 h course at the Institut Henri Poincaré in September 2016. The course was divided in three parts. In the first part, which is not included herein, the aim was to first recall some basic aspects of stabilised finite element methods for convection-diffusion problems. We focus entirely on the second and third parts which were dedicated to ill-posed problems and their approximation using stabilised finite element methods. First we introduce the concept of conditional stability. Then we consider the elliptic Cauchy-problem and a data assimilation problem in a unified setting and show how stabilised finite element methods may be used to derive error estimates that are consistent with the stability properties of the problem and the approximation properties of the finite element space. Finally, we extend the result to a data assimilation problem subject to the heat equation

Genome-wide association and HLA fine-mapping studies identify risk loci and genetic pathways underlying allergic rhinitis

Allergic rhinitis is the most common clinical presentation of allergy, affecting 400 million people worldwide, with increasing incidence in westernized countries1,2. To elucidate the genetic architecture and understand the underlying disease mechanisms, we carried out a meta-analysis of allergic rhinitis in 59,762 cases and 152,358 controls of European ancestry and identified a total of 41 risk loci for allergic rhinitis, including 20 loci not previously associated with allergic rhinitis, which were confirmed in a replication phase of 60,720 cases and 618,527 controls. Functional annotation implicated genes involved in various immune pathways, and fine mapping of the HLA region suggested amino acid variants important for antigen binding. We further performed genome-wide association study (GWAS) analyses of allergic sensitization against inhalant allergens and nonallergic rhinitis, which suggested shared genetic mechanisms across rhinitis-related traits. Future studies of the identified loci and genes might identify novel targets for treatment and prevention of allergic rhinitis