Statistical properties of the method of regularization with periodic Gaussian reproducing kernel

The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel regularization. We show in the white noise model setting, that in function spaces of very smooth functions, such as the infinite-order Sobolev space and the space of analytic functions, the method under consideration is asymptotically minimax; in finite-order Sobolev spaces, the method is rate optimal, and the efficiency in terms of constant when compared with the minimax estimator is reasonably high. The smoothing parameters in the periodic Gaussian regularization can be chosen adaptively without loss of asymptotic efficiency. The results derived in this paper give a partial explanation of the success of the Gaussian reproducing kernel in practice. Simulations are carried out to study the finite sample properties of the periodic Gaussian regularization.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000045

Genome-wide high-resolution mapping of UV-induced mitotic recombination events in Saccharomyces cerevisiae.

In the yeast Saccharomyces cerevisiae and most other eukaryotes, mitotic recombination is important for the repair of double-stranded DNA breaks (DSBs). Mitotic recombination between homologous chromosomes can result in loss of heterozygosity (LOH). In this study, LOH events induced by ultraviolet (UV) light are mapped throughout the genome to a resolution of about 1 kb using single-nucleotide polymorphism (SNP) microarrays. UV doses that have little effect on the viability of diploid cells stimulate crossovers more than 1000-fold in wild-type cells. In addition, UV stimulates recombination in G1-synchronized cells about 10-fold more efficiently than in G2-synchronized cells. Importantly, at high doses of UV, most conversion events reflect the repair of two sister chromatids that are broken at approximately the same position whereas at low doses, most conversion events reflect the repair of a single broken chromatid. Genome-wide mapping of about 380 unselected crossovers, break-induced replication (BIR) events, and gene conversions shows that UV-induced recombination events occur throughout the genome without pronounced hotspots, although the ribosomal RNA gene cluster has a significantly lower frequency of crossovers

K-essence Explains a Lorentz Violation Experiment

Recently, a state of the art experiment shows evidence for Lorentz violation in the gravitational sector. To explain this experiment, we investigate a spontaneous Lorentz violation scenario with a generalized scalar field. We find that when the scalar field is nonminimally coupled to gravity, the Lorentz violation induces a deformation in the Newtonian potential along the direction of Lorentz violation.Comment: 8 pages, the final version, discussion and references adde