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

Effect of spin relaxations on the spin mixing conductances for a bilayer structure

The spin current can result in a spin-transfer torque in the normal-metal(NM)|ferromagnetic-insulator(FMI) or normal-metal(NM)|ferromagnetic-metal(FMM) bilayer. In the earlier study on this issue, the spin relaxations were ignored or introduced phenomenologically. In this paper, considering the FMM or FMI with spin relaxations described by a non-Hermitian Hamiltonian, we derive an effective spin-transfer torque and an effective spin mixing conductance in the non-Hermitian bilayer. The dependence of the effective spin mixing conductance on the system parameters (such as insulating gap, \textit{s-d} coupling, and layer thickness) as well as the relations between the real part and the imaginary part of the effective spin mixing conductance are given and discussed. We find that the effective spin mixing conductance can be enhanced in the non-Hermitian system. This provides us with the possibility to enhance the spin mixing conductance

High-resolution mapping of heteroduplex DNA formed during UV-induced and spontaneous mitotic recombination events in yeast.

In yeast, DNA breaks are usually repaired by homologous recombination (HR). An early step for HR pathways is formation of a heteroduplex, in which a single-strand from the broken DNA molecule pairs with a strand derived from an intact DNA molecule. If the two strands of DNA are not identical, there will be mismatches within the heteroduplex DNA (hetDNA). In wild-type strains, these mismatches are repaired by the mismatch repair (MMR) system, producing a gene conversion event. In strains lacking MMR, the mismatches persist. Most previous studies involving hetDNA formed during mitotic recombination were restricted to one locus. Below, we present a global mapping of hetDNA formed in the MMR-defective mlh1 strain. We find that many recombination events are associated with repair of double-stranded DNA gaps and/or involve Mlh1-independent mismatch repair. Many of our events are not explicable by the simplest form of the double-strand break repair model of recombination