Laplace's equation and the Dirichlet-Neumann map: a new mode for Mikhlin's method

Mikhlin's method for solving Laplace's equation in domains exterior to a number of closed contours is discussed with particular emphasis on the Dirichlet-Neutnann map. In the literature there already exit tyro computational modes for Mikhlin's method. Here a new mode is presented. The new mode is at least as stable as the previous modes. Furthermore, its computational complexity in the number of closed contours is better. As a result. highly. accurate solutions in domains exterior to tens of thousands of closed contours can be obtained on a simple workstation

Spectral bounds for the Neumann-Poincaré operator on planar domains with corners

The boundary double layer potential, or the Neumann-Poincaré operator, is studied on the Sobolev space of order 1/2 along the boundary, coinciding with the space of charges giving rise to double layer potentials with finite energy in the whole space. Poincaré’s program of studying the spectrum of the boundary double layer potential is developed in complete generality on closed Lipschitz hypersurfaces in euclidean space. Furthermore, the Neumann-Poincaré operator is realized as a singular integral transform bearing similarities to the Beurling-Ahlfors transform in 2 dimensions. As an application, in the case of planar curves with corners, bounds for the spectrum of the Neumann-Poincaré operator are derived from recent results in quasi-conformal mapping theory

The transmission problem on a three-dimensional wedge

We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the spectrum. This is carried out in two formulations leading to rather different spectral pictures. One formulation is in terms of square integrable boundary data, the other is in terms of finite energy solutions. We use the layer potential method, which requires the harmonic analysis of a non-commutative non-unimodular group associated with the wedge

The effect on melanoma risk of genes previously associated with telomere length.

Telomere length has been associated with risk of many cancers, but results are inconsistent. Seven single nucleotide polymorphisms (SNPs) previously associated with mean leukocyte telomere length were either genotyped or well-imputed in 11108 case patients and 13933 control patients from Europe, Israel, the United States and Australia, four of the seven SNPs reached a P value under .05 (two-sided). A genetic score that predicts telomere length, derived from these seven SNPs, is strongly associated (P = 8.92x10(-9), two-sided) with melanoma risk. This demonstrates that the previously observed association between longer telomere length and increased melanoma risk is not attributable to confounding via shared environmental effects (such as ultraviolet exposure) or reverse causality. We provide the first proof that multiple germline genetic determinants of telomere length influence cancer risk.This is the final version of the article. It first appeared from Oxford University Press via http://dx.doi.org/10.1093/jnci/dju26

Melanocortin-1 Receptor, Skin Cancer and Phenotypic Characteristics (M-SKIP) Project: Study Design and Methods for Pooling Results of Genetic Epidemiological Studies

Background: For complex diseases like cancer, pooled-analysis of individual data represents a powerful tool to investigate the joint contribution of genetic, phenotypic and environmental factors to the development of a disease. Pooled-analysis of epidemiological studies has many advantages over meta-analysis, and preliminary results may be obtained faster and with lower costs than with prospective consortia. Design and methods: Based on our experience with the study design of the Melanocortin-1 receptor (MC1R) gene, SKin cancer and Phenotypic characteristics (M-SKIP) project, we describe the most important steps in planning and conducting a pooled-analysis of genetic epidemiological studies. We then present the statistical analysis plan that we are going to apply, giving particular attention to methods of analysis recently proposed to account for between-study heterogeneity and to explore the joint contribution of genetic, phenotypic and environmental factors in the development of a disease. Within the M-SKIP project, data on 10,959 skin cancer cases and 14,785 controls from 31 international investigators were checked for quality and recoded for standardization. We first proposed to fit the aggregated data with random-effects logistic regression models. However, for the M-SKIP project, a two-stage analysis will be preferred to overcome the problem regarding the availability of different study covariates. The joint contribution of MC1R variants and phenotypic characteristics to skin cancer development will be studied via logic regression modeling. Discussion: Methodological guidelines to correctly design and conduct pooled-analyses are needed to facilitate application of such methods, thus providing a better summary of the actual findings on specific fields

Genome-wide meta-analysis identifies five new susceptibility loci for cutaneous malignant melanoma.

Thirteen common susceptibility loci have been reproducibly associated with cutaneous malignant melanoma (CMM). We report the results of an international 2-stage meta-analysis of CMM genome-wide association studies (GWAS). This meta-analysis combines 11 GWAS (5 previously unpublished) and a further three stage 2 data sets, totaling 15,990 CMM cases and 26,409 controls. Five loci not previously associated with CMM risk reached genome-wide significance (P < 5 × 10(-8)), as did 2 previously reported but unreplicated loci and all 13 established loci. Newly associated SNPs fall within putative melanocyte regulatory elements, and bioinformatic and expression quantitative trait locus (eQTL) data highlight candidate genes in the associated regions, including one involved in telomere biology.[Please see the Supplementary Note for acknowledgments.]This is the author accepted manuscript. The final version is available from NPG via http://dx.doi.org/10.1038/ng.337

Melanocortin-1 receptor, skin cancer and phenotypic characteristics (M-SKIP) project

Background: For complex diseases like cancer, pooled-analysis of individual data represents a powerful tool to investigate the joint contribution of genetic, phenotypic and environmental factors to the development of a disease. Pooled-analysis of epidemiological studies has many advantages over meta-analysis, and preliminary results may be obtained faster and with lower costs than with prospective consortia. Design and methods. Based on our experience with the study design of the Melanocortin-1 receptor (MC1R) gene, SKin cancer and Phenotypic characteristics (M-SKIP) project, we describe the most important steps in planning and conducting a pooled-analysis of genetic epidemiological studies. We then present the statistical analysis plan that we are going to apply, giving particular attention to methods of analysis recently proposed to account for between-study heterogeneity and to explore the joint contribution of genetic, phenotypic and environmental factors in the development of a disease. Within the M-SKIP project, data on 10,959 skin cancer cases and 14,785 controls from 31 international investigators were checked for quality and recoded for standardization. We first proposed to fit the aggregated data with random-effects logistic regression models. However, for the M-SKIP project, a two-stage analysis will be preferred to overcome the problem regarding the availability of different study covariates. The joint contribution of MC1R variants and phenotypic characteristics to skin cancer dev

Spectral super-resolution in metamaterial composites

We investigate the optical properties of periodic composites containing metamaterial inclusions in a normal material matrix. We consider the case where these inclusions have sharp corners, and following Hetherington and Thorpe, use analytic results to argue that it is then possible to deduce the shape of the corner (its included angle) by measurements of the absorptance of such composites when the scale size of the inclusions and period cell is much finer than the wavelength. These analytic arguments are supported by highly accurate numerical results for the effective permittivity function of such composites as a function of the permittivity ratio of inclusions to matrix. The results show that this function has a continuous spectral component with limits independent of the area fraction of inclusions, and with the same limits for both square and staggered square arrays.Comment: 17 pages, 6 figure