Breaking the scale invariance of the primordial power spectrum in Horava-Lifshitz Cosmology

We study the spectral tilt of primordial perturbations in Horava-Lifshitz cosmology. The uniform approximation, which is a generalization of the familiar Wentzel-Kramers-Brillouin (WKB) method, is employed to compute the spectral index both numerically and analytically in a closed form. We clarify how the spectral index depends on the inflation model and parameters in the modified dispersion relation.Comment: 5 pages, 2 figures, accepted for publication in Physical Review

Window effect in the power spectrum analysis of a galaxy redshift survey

We investigate the effect of the window function on the multipole power spectrum in two different ways. First, we consider the convolved power spectrum including the window effect, which is obtained by following the familiar (FKP) method developed by Feldman, Kaiser and Peacock. We show how the convolved multipole power spectrum is related to the original power spectrum, using the multipole moments of the window function. Second, we investigate the deconvolved power spectrum, which is obtained by using the Fourier deconvolution theorem. In the second approach, we measure the multipole power spectrum deconvolved from the window effect. We demonstrate how to deal with the window effect in these two approaches, applying them to the Sloan Digital Sky Survey (SDSS) luminous red galaxy (LRG) sample.Comment: 22 pages, 11 figures, references adde

First-order quantum correction to the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field

First-order quantum correction to the Larmor radiation is investigated on the basis of the scalar QED on a homogeneous background of time-dependent electric field, which is a generalization of a recent work by Higuchi and Walker so as to be extended for an accelerated charged particle in a relativistic motion. We obtain a simple approximate formula for the quantum correction in the limit of the relativistic motion when the direction of the particle motion is parallel to that of the electric field.Comment: 12 pages, 2 figures, accepted for publication in Physical Review

Quantum Larmor radiation in conformally flat universe

We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics (SQED). A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the SQED. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e^2\hbar is determined by a non-local integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D80 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a non-relativistic motion in a homogeneous electric field.Comment: 12 pages, 4 figure, accepted for publication in Physical Review

Statistical hypothesis test of factor loading in principal component analysis and its application to metabolite set enrichment analysis

Principal component analysis (PCA) has been widely used to visualize high-dimensional metabolomic data in a two- or three-dimensional subspace. In metabolomics, some metabolites (e.g. top 10 metabolites) have been subjectively selected when using factor loading in PCA, and biological inferences for these metabolites are made. However, this approach is possible to lead biased biological inferences because these metabolites are not objectively selected by statistical criterion. We proposed a statistical procedure to pick up metabolites by statistical hypothesis test of factor loading in PCA and make biological inferences by metabolite set enrichment analysis (MSEA) for these significant metabolites. This procedure depends on the fact that the eigenvector in PCA for autoscaled data is proportional to the correlation coefficient between PC score and each metabolite levels. We applied this approach for two metabolomic data of mice liver samples. 136 of 282 metabolites in first case study and 66 of 275 metabolites in second case study were statistically significant. This result suggests that to set the previously-determined number of metabolites is not appropriate because the number of significant metabolites is different in each study when using factor loading in PCA. Moreover, MSEA was performed for these significant metabolites and significant metabolic pathways can be detected. These results are acceptable when compared with previous biological knowledge. It is essential to select metabolites statistically for making unbiased biological inferences from metabolome data, when using factor loading in PCA. We proposed a statistical procedure to pick up metabolites by statistical hypothesis test of factor loading in PCA and make biological inferences by MSEA for these significant metabolites. We developed an R package mseapca to perform this approach. The “mseapca” package is publicity available on CRAN website

Statistical hypothesis testing of factor loading in principal component analysis and its application to metabolite set enrichment analysis

BACKGROUND: Principal component analysis (PCA) has been widely used to visualize high-dimensional metabolomic data in a two- or three-dimensional subspace. In metabolomics, some metabolites (e.g., the top 10 metabolites) have been subjectively selected when using factor loading in PCA, and biological inferences are made for these metabolites. However, this approach may lead to biased biological inferences because these metabolites are not objectively selected with statistical criteria. RESULTS: We propose a statistical procedure that selects metabolites with statistical hypothesis testing of the factor loading in PCA and makes biological inferences about these significant metabolites with a metabolite set enrichment analysis (MSEA). This procedure depends on the fact that the eigenvector in PCA for autoscaled data is proportional to the correlation coefficient between the PC score and each metabolite level. We applied this approach to two sets of metabolomic data from mouse liver samples: 136 of 282 metabolites in the first case study and 66 of 275 metabolites in the second case study were statistically significant. This result suggests that to set the number of metabolites before the analysis is inappropriate because the number of significant metabolites differs in each study when factor loading is used in PCA. Moreover, when an MSEA of these significant metabolites was performed, significant metabolic pathways were detected, which were acceptable in terms of previous biological knowledge. CONCLUSIONS: It is essential to select metabolites statistically to make unbiased biological inferences from metabolomic data when using factor loading in PCA. We propose a statistical procedure to select metabolites with statistical hypothesis testing of the factor loading in PCA, and to draw biological inferences about these significant metabolites with MSEA. We have developed an R package “mseapca” to facilitate this approach. The “mseapca” package is publicly available at the CRAN website