Jacobi-Predictor-Corrector Approach for the Fractional Ordinary Differential Equations

We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t. the Jacobi-weight function $\omega(s)=(1-s)^{\alpha-1}(1+s)^0$. This method has the computational cost O(N) and the convergent order $IN$, where $N$ and $IN$ are, respectively, the total computational steps and the number of used interpolating points. The detailed error analysis is performed, and the extensive numerical experiments confirm the theoretical results and show the robustness of this method.Comment: 24 pages, 5 figure

The asymmetric structure of the Galactic halo

Using the stellar photometry catalogue based on the latest data release (DR4) of the Sloan Digital Sky Survey (SDSS), a study of the Galactic structure using star counts is carried out for selected areas of the sky. The sample areas are selected along a circle at a Galactic latitude of +60$^\circ$, and 10 strips of high Galactic latitude along different longitudes. Direct statistics of the data show that the surface densities of $\ell$ from $180^{\circ}$ to $360^{\circ}$ are systematically higher than those of $\ell$ from $0^{\circ}$ to $180^{\circ}$, defining a region of overdensity (in the direction of Virgo) and another one of underdensity (in the direction of Ursa Major) with respect to an axisymmetric model. It is shown by comparing the results from star counts in the $(g-r)$ colour that the density deviations are due to an asymmetry of the stellar density in the halo. Theoretical models for the surface density profile are built and star counts are performed using a triaxial halo of which the parameters are constrained by observational data. Two possible reasons for the asymmetric structure are discussed.Comment: 17 pages, 7 figures, 5 tables, MNRAS accepte

Robust variable selection in partially varying coefficient single-index model

By combining basis function approximations and smoothly clipped absolute deviation (SCAD) penalty, this paper proposes a robust variable selection procedure for a partially varying coefficient single-index model based on modal regression. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. Furthermore, we also discuss the bandwidth selection and propose a modified expectation-maximization (EM)-type algorithm for the proposed estimation procedure. The finite sample properties of the proposed estimators are illustrated by some simulation examples.The research of Zhu is partially supported by National Natural Science Foundation of China (NNSFC) under Grants 71171075, 71221001 and 71031004. The research of Yu is supported by NNSFC under Grant 11261048

Role of noncoding RNA in vascular remodelling

Purpose of review: Noncoding RNAs (ncRNAs), such as microRNAs (miRNAs) and long noncoding RNAs (lncRNAs) are becoming fundamentally important in the pathophysiology relating to injury-induced vascular remodelling. We highlight recent studies that demonstrate the involvement of ncRNAs in vein graft disease, in in-stent restenosis and in pulmonary arterial hypertension, with a particular focus on endothelial cell and vascular smooth muscle cell function. We also briefly discuss the emerging role of exosomal-derived ncRNAs and how this mechanism impacts on vascular function. Recent findings: ncRNAs have been described as novel regulators in the pathophysiology of vascular injury, inflammation, and vessel wall remodelling. In particular, several studies have demonstrated that manipulation of miRNAs can reduce the burden of pathological vascular remodelling. Such studies have also shown that exosomal miRNA-mediated, cell-to-cell communication between endothelial cells and vascular smooth muscle cells is critical in the disease process. In addition to miRNAs, lncRNAs are emerging as regulators of vascular function in health and disease. Although lncRNAs are complex in both their sheer numbers and mechanisms of action, identifying their contribution to vascular disease is essential. Summary: Given the important roles of ncRNAs in vascular injury and remodelling together will their capacity for cell-to-cell communication, manipulating ncRNA might provide novel therapeutic interventions

Miraculous Survival of Three Trapping Miners by Drinking High Mineral Mine Water for 25

Little is known that how long a human been can survive a complete starvation. There were dozens of miners who lost their lives in a coal mine disaster at Qinglong,Guizhou,China in June 2009, only three of them were rescued 25 days later after they had been trapped in a coal mine 600 meters underground. They maintained their lives only by drinking mineral water in the mine, which created a miracle of life. We reported here on this life miracle in relation to high mineral mine water