Matrix-valued θ\theta-deformed bi-orthogonal polynomials, Non-commutative Toda theory and B\"acklund transformation

This paper is devoted to revealing the relationship between matrix-valued $\theta$-deformed bi-orthogonal polynomials and non-commutative Toda-type hierarchies. In this procedure, Wronski quasi-determinants are widely used and play the role of non-commutative $\tau$-functions. At the same time, B\"acklund transformations are realized by using a moment modification method and non-commutative $\theta$-deformed Volterra hierarchies are obtained, which contain the known examples of the Itoh-Narita-Bogoyavlensky lattices and the fractional Volterra hierarchy.Comment: 30 pages. Comments are welcom

SCOPE: Scalable Composite Optimization for Learning on Spark

Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to solve the large-scale composite optimization problems, which have shown better performance than traditional batch methods. However, most of these DSO methods are not scalable enough. In this paper, we propose a novel DSO method, called \underline{s}calable \underline{c}omposite \underline{op}timization for l\underline{e}arning~({SCOPE}), and implement it on the fault-tolerant distributed platform \mbox{Spark}. SCOPE is both computation-efficient and communication-efficient. Theoretical analysis shows that SCOPE is convergent with linear convergence rate when the objective function is convex. Furthermore, empirical results on real datasets show that SCOPE can outperform other state-of-the-art distributed learning methods on Spark, including both batch learning methods and DSO methods

RIdeogram : Drawing SVG graphics to visualize and map genome-wide data on the idiograms

Background. Owing to the rapid advances in DNA sequencing technologies, whole genome from more and more species are becoming available at increasing pace. For whole-genome analysis, idiograms provide a very popular, intuitive and effective way to map and visualize the genome-wide information, such asGCcontent, gene and repeat density, DNA methylation distribution, genomic synteny, etc. However, most available software programs and web servers are available only for a few model species, such as human, mouse and fly, or have limited application scenarios. As more and more non-model species are sequenced with chromosome-level assembly being available, tools that can generate idiograms for a broad range of species and be capable of visualizing more data types are needed to help better understanding fundamental genome characteristics. Results. The R package RIdeogram allows users to build high-quality idiograms of any species of interest. It can map continuous and discrete genome-wide data on the idiograms and visualize them in a heat map and track labels, respectively. Conclusion. The visualization of genome-wide data mapping and comparison allow users to quickly establish a clear impression of the chromosomal distribution pattern, thus making RIdeogram a useful tool for any researchers working with omics.</p

Preparation and properties of asphalt binders modified by THFS extracted from direct coal liquefaction residue

This paper aims to study the preparation and viscoelastic properties of asphalt binder modified by tetrahydrofuran soluble fraction (THFS) extracted from direct coal liquefaction residue. The modified asphalt binders, which blended with SK-90 (control asphalt binder) and 4%, 6%, 8% and 10% THFS (by weight of SK-90), were fabricated. The preparation process for asphalt binder was optimized in terms of the orthogonal array test strategy and gray correlation analysis results. The properties of asphalt binder were measured by applying Penetration performance grade and Superpave performance grade specifications. In addition, the temperature step and frequency sweep test in Dynamic Shear Rheometer were conducted to predict the rheological behavior, temperature and frequency susceptibility of asphalt binder. The test results suggested the optimal preparation process, such as 150 °C shearing temperature, 45 min shearing time and 4000 rpm shearing rate. Subsequently, the addition of THFS was beneficial in increasing the high-temperature properties but decreased the low-temperature properties and resistance to fatigue. The content analysis of THFS showed the percentage of 4~6% achieved a balance in the high-and-low temperature properties of asphalt binder. The asphalt binder with higher THFS content exhibited higher resistance to rutting and less sensitivity to frequency and temperature

The divergent restoration effects of Lactobacillus strains in antibiotic-induced dysbiosis

To evaluate functions of Lactobacillus strains, isolated from fermented food, in restoration of ampicillin-induced disruption based on mucosal barrier, gut microbial community and metabolome analyses, three Lactobacillus strains, L. plantarum CGMCC12436 (LacP), L. casei CGMCC 12,435 (LacC) and L. rhamnosus strain GG (LacG) were individually administered to ampicillin-pretreated mice. All three strains significantly restored concentrations of endotoxin and diamine oxidase to control levels. Linear discriminate analysis based on 16S rRNA sequencing of faecal bacteria revealed that the restoration of microbial communities by Lactobacillus strains was more effective than natural restoration. Correlation analysis between microbiota and metabolites indicated that, the higher level of acetate in LacC group was positively correlated with increased relative abundance of Citrobacter, Bifidobacterium and S24-7. Furthermore, LacC down-regulated the expression of NF-κB p65 and modulated the ampicillin-induced inflammatory responses. The LacC strain could particularly attenuate ampicillin-induced disruption by optimisation of microbial taxa and enhancement of acetate and butyrate production