On subfields of the Hermitian function fields involving the involution automorphism

A function field over a finite field is called maximal if it achieves the Hasse-Weil bound. Finding possible genera that maximal function fields achieve has both theoretical interest and practical applications to coding theory and other topics. As a subfield of a maximal function field is also maximal, one way to find maximal function fields is to find all subfields of a maximal function field. Due to the large automorphism group of the Hermitian function field, it is natural to find as many subfields of the Hermitian function field as possible. In literature, most of papers studied subfields fixed by subgroups of the decomposition group at one point (usually the point at infinity). This is because it becomes much more complicated to study the subfield fixed by a subgroup that is not contained in the decomposition group at one point. In this paper, we study subfields of the Hermitian function field fixed by subgroups that are not contained in the decomposition group of any point except the cyclic subgroups. It turns out that some new maximal function fields are found

RTeQTL: Real-Time Online Engine for Expression Quantitative Trait Loci Analyses

Our database tool, called Real-Time Engine for Expression Quantitative Trait Loci Analyses (RTeQTL), can efficiently provide eQTL association results that are not available in existing eQTL databases browsers. These functions include (i) single SNP (single-nucleotide polymorphism) and (ii) two-SNP conditional eQTL effects on gene expression regardless of the magnitude of P-values. The database is based on lymphoblastoid cell lines from >900 samples with global gene expression and genome-wide genotyped and imputed SNP data. The detailed result for any pairs of gene and SNPs can be efficiently computed and browsed online, as well as downloaded in batch mode. This is the only tool that can assess the independent effect of a disease- or trait-associated SNP on gene expression conditioning on other SNPs of interest, such as the top eQTL of the same gene. It is also useful to identify eQTLs for candidate genes, which are often missed in existing eQTL browsers, which only store results with genome-wide significant P-value. Additional analyses stratifying by gender can also be easily achieved by this tool. Database URL: http://eqtl.rc.fas.harvard.edu

Transportation inequalities: From Poisson to Gibbs measures

We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality for the Gibbs measure on $\mathbb{N}^{\Lambda}$ or the continuum Gibbs measure on the configuration space.Comment: Published in at http://dx.doi.org/10.3150/00-BEJ268 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm