Complete sets of diagonal operators in quantum-statistical mechanics

Complete sets of diagonal operators, i.e. operators commuting with the hamiltonian of a physical system, are constructed. In terms of these sets all diagonal operators can be written as a series, the uniform convergence of which is studied for infinitely large systems. This uniform convergence is introduced as a possible criterion for ergodicity

The Influence of Age and Sex on Genetic Associations with Adult Body Size and Shape : A Large-Scale Genome-Wide Interaction Study

Genome-wide association studies (GWAS) have identified more than 100 genetic variants contributing to BMI, a measure of body size, or waist-to-hip ratio (adjusted for BMI, WHRadjBMI), a measure of body shape. Body size and shape change as people grow older and these changes differ substantially between men and women. To systematically screen for age-and/or sex-specific effects of genetic variants on BMI and WHRadjBMI, we performed meta-analyses of 114 studies (up to 320,485 individuals of European descent) with genome-wide chip and/or Metabochip data by the Genetic Investigation of Anthropometric Traits (GIANT) Consortium. Each study tested the association of up to similar to 2.8M SNPs with BMI and WHRadjBMI in four strata (men 50y, women 50y) and summary statistics were combined in stratum-specific meta-analyses. We then screened for variants that showed age-specific effects (G x AGE), sex-specific effects (G x SEX) or age-specific effects that differed between men and women (G x AGE x SEX). For BMI, we identified 15 loci (11 previously established for main effects, four novel) that showed significant (FDR= 50y). No sex-dependent effects were identified for BMI. For WHRadjBMI, we identified 44 loci (27 previously established for main effects, 17 novel) with sex-specific effects, of which 28 showed larger effects in women than in men, five showed larger effects in men than in women, and 11 showed opposite effects between sexes. No age-dependent effects were identified for WHRadjBMI. This is the first genome-wide interaction meta-analysis to report convincing evidence of age-dependent genetic effects on BMI. In addition, we confirm the sex-specificity of genetic effects on WHRadjBMI. These results may providefurther insights into the biology that underlies weight change with age or the sexually dimorphism of body shape.Peer reviewe

Lightness filtering in color images with respect to the gamut

When image processing operations are performed on color images, it is normal that the production of out-of-gamut pixels is not prevented. The gamut mapping may reduce the effect of the image processing algorithm. In this paper we propose a generic method that allows grey image processing for lightness processing on color images without exceeding the limits of the gamut of the technique or device. In the proposed method the lightness processing is a function of the color of the pixel in question, the desired lightness change and a maximum and minimum lightness change per pixel. This maximum and minimum depend on the position of the pixel in the gamut of the output device and the relation between the lightness change and the chroma change. The hue of all pixels is kept constant. The monotonic character of the lightness correction guarantees that all points that were different before the lightness correction, remain different. The results of the proposed method are shown for two greyvalue image processing algorithms: 1) sharpening and 2) contrast improvement using gamma manipulation. For these two applications the gamut-limiting process is only advisable when the limiting is applied to the lightness dimension, rather than the chroma dimension

Method for transforming a coloured image

The invention relates to a method of transforming a colour image, wherein for each separate pixel a measured level of lightness, a measured chroma and a measured colour is determined, followed by a predetermined adjustment in the three-dimensional level of lightness, chroma and colour, wherein a. for each separate pixel a direction of adjustment is determined by selection of a three-dimensional adjustment level for lightness, chroma and colour change, b. and in that at the three-dimensional adjustment level selected the maximum available lightness change is determined, whereafter c.; for each separate pixel the measured lightness level, the measured chroma and the measured colour is changed in the direction of the selected three-dimensional adjustment level in concurrence with a predetermined function, which at most amounts to the maximum available lightness change at the selected three-dimensional adjustment level.Applied Science

Estimators for Orientation and Anisotropy in Digitized Images

Applied Science

Estimators of 2D edge length and position, 3D surface area and position in sampled grey-valued images

Applied Science

An Estimator of Edge Length and Surface Area in Digitized 2D and 3D Images

Applied Science

Curvature and Bending Energy in Digitized 2D and 3D Images

Applied Science