Possible Realization and Protection of Valley-Polarized Quantum Hall Effect in Mn/WS2

By using the first-principles calculations and model analyses, we found that the combination of defected tungsten disulfide monolayer and sparse manganese adsorption may give a KK` valley spin splitting up to 210 meV. This system also has a tunable magnetic anisotropy energy, a clean band gap, and an appropriate band alignment, with the Fermi level sitting right above the top of valence bands at the K-valleys. Therefore, it can be used for the realization of the valley-polarized anomalous Hall effect and for the exploration of other valley related physics without using optical methods. A protective environment can be formed by covering it with a hexagonal BN layer, without much disturbance to the benign properties of Mn/WS2.Comment: 16 pages, 4 figure

Power partitions and saddle-point method

For $k\geqslant 1$, denote by $p_k(n)$ the number of partitions of an integer $n$ into $k$-th powers. In this note, we apply the saddle-point method to provide a new proof for the well-known asymptotic expansion of $p_k(n)$. This approach turns out to significantly simplify those of Wright (1934), Vaughan (2015) and Gafni (2016).Comment: An error in the proof of Lemma 2.3 has been correcte

Robust Bayesian Variable Selection for Gene-Environment Interactions

Gene-environment (G×E) interactions have important implications to elucidate the etiology of complex diseases beyond the main genetic and environmental effects. Outliers and data contamination in disease phenotypes of G×E studies have been commonly encountered, leading to the development of a broad spectrum of robust penalization methods. Nevertheless, within the Bayesian framework, the issue has not been taken care of in existing studies. We develop a robust Bayesian variable selection method for G×E interaction studies. The proposed Bayesian method can effectively accommodate heavy-tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. In particular, the spike-and-slab priors have been imposed on both individual and group levels to identify important main and interaction effects. An efficient Gibbs sampler has been developed to facilitate fast computation. The Markov chain Monte Carlo algorithms of the proposed and alternative methods are efficiently implemented in C++