Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities

An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge was recently proposed by Kim et al. They achieved this by introducing off-shell Noether currents and potentials. In this paper, we construct the crucial off-shell Noether current by the variation of the Bianchi identity for the expression of motion equation, with the help of the property of Killing vector. Our Noether current, which contains an additional term that is just one half of the Lie derivative of a surface term with respect to the Killing vector, takes a different form in comparison with the one in their work. Then we employ the generalized formulation to calculate the quasi-local conserved charges for the most general charged spherically symmetric and the dyonic rotating black holes with AdS asymptotics in four-dimensional conformal Weyl gravity, as well as the charged spherically symmetric black holes in arbitrary dimensional Einstein-Gauss-Bonnet gravity coupled to Maxwell or nonlinear electrodynamics in AdS spacetime. Our results confirm those through other methods in the literature.Comment: 21 Pages, no figures, references adde

Off-shell Noether current and conserved charge in Horndeski theory

We derive the off-shell Noether current and potential in the context of Horndeski theory, which is the most general scalar-tensor theory with a Lagrangian containing derivatives up to second order while yielding at most to second-order equations of motion in four dimensions. Then the formulation of conserved charges is proposed on basis of the off-shell Noether potential and the surface term got from the variation of the Lagrangian. As an application, we calculate the conserved charges of black holes in a scalar-tensor theory with non-minimal coupling between derivatives of the scalar field and the Einstein tensor.Comment: 19 pages, no figures, to appear in PL

MAPPING GENES FOR QUANTITATIVE TRAITS USING SELECTED SAMPLES OF SIBLING PAIRS

One of the most important research areas in human genetics is the effort to map genes associated with complex diseases such as cancer, heart disease, and diabetes. The public health relevance of these kinds of work is that gene mapping will bring an understanding of genetic risk and protective factors, and a description of the interaction between environment and genetic variation. In the last ten years there has been a dramatic increase in the number of studies seeking to map genes for quantitative traits. This has caused an explosion of new work on statistical methods for human quantitative trait locus (QTL) mapping. However, little of that work has dealt with selected samples, which are more common than population samples for human studies. This dissertation focuses on sibling pairs and considers the most common types of selected sampling. I surveyed most QTL mapping methods in the literature to evaluate which are appropriate for selected samples, and also developed new statistics for selected samples. Using simulation and analytical approaches, I identified the most powerful statistics for each type of sampling considered. I then compared various sampling designs using the best statistic for each and gave guidelines for choosing appropriate and powerful designs under different scenarios