Optimal regularity of minimal graphs in the hyperbolic space

We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $\Omega\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal regularity $f\in C^{\frac{1}{n+1}}(\bar{\Omega})$. We can improve the H\"older exponent for $f$ if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.Comment: Accepted by Calc. Var. Partial Differential Equation

Prediction-error of Prediction Error (PPE)-based Reversible Data Hiding

This paper presents a novel reversible data hiding (RDH) algorithm for gray-scaled images, in which the prediction-error of prediction error (PPE) of a pixel is used to carry the secret data. In the proposed method, the pixels to be embedded are firstly predicted with their neighboring pixels to obtain the corresponding prediction errors (PEs). Then, by exploiting the PEs of the neighboring pixels, the prediction of the PEs of the pixels can be determined. And, a sorting technique based on the local complexity of a pixel is used to collect the PPEs to generate an ordered PPE sequence so that, smaller PPEs will be processed first for data embedding. By reversibly shifting the PPE histogram (PPEH) with optimized parameters, the pixels corresponding to the altered PPEH bins can be finally modified to carry the secret data. Experimental results have implied that the proposed method can benefit from the prediction procedure of the PEs, sorting technique as well as parameters selection, and therefore outperform some state-of-the-art works in terms of payload-distortion performance when applied to different images.Comment: There has no technical difference to previous versions, but rather some minor word corrections. A 2-page summary of this paper was accepted by ACM IH&MMSec'16 "Ongoing work session". My homepage: hzwu.github.i

New Insights on Low Energy πN\pi N Scattering Amplitudes

The $S$- and $P$- wave phase shifts of low-energy pion-nucleon scatterings are analysed using Peking University representation, in which they are decomposed into various terms contributing either from poles or branch cuts. We estimate the left-hand cut contributions with the help of tree-level perturbative amplitudes derived in relativistic baryon chiral perturbation theory up to $\mathcal{O}(p^2)$. It is found that in $S_{11}$ and $P_{11}$ channels, contributions from known resonances and cuts are far from enough to saturate experimental phase shift data -- strongly indicating contributions from low lying poles undiscovered before, and we fully explore possible physics behind. On the other side, no serious disagreements are observed in the other channels.Comment: slightly chnaged version, a few more figures added. Physical conclusions unchange

Nonlinear transport theory for hybrid normal-superconducting devices

We report a theory for analyzing nonlinear DC transport properties of mesoscopic or nanoscopic normal-superconducting (N-S) systems. Special attention was paid such that our theory satisfies gauge invariance. At the linear transport regime and the sub-gap region where the familiar scattering matrix theory has been developed, we provide confirmation that our theory and the scattering matrix theory are equivalent. At the nonlinear regime, however, our theory allows the investigation of a number of important problems: for N-S hybrid systems we have derived the general nonlinear current-voltage characteristics in terms of the scattering Green's function, the second order nonlinear conductance at the weakly nonlinear regime, and nonequilibrium charge pile-up in the device which defines the electrochemical capacitance coefficients

miR-1258: a novel microRNA that controls TMPRSS4 expression is associated with malignant progression of papillary thyroid carcinoma

Background: MicroRNA-1258 (miR-1258) has been shown to play an anti-cancer role in a variety of cancers, but its relationship with papillary thyroid cancer (PTC) has not been reported. The emphasis of this research was to reveal the biological function of miR-1258 in PTC and its potential mechanisms. Material and methods: We measured miR-1258 expression in PTC cells and the transfection efficiency of miR-1258 mimic and miR-1258 inhibitor by quantitative real-time PCR (qRT-PCR) assay. Cell Counting Kit-8 assay (CCK8) and Transwell experiments were conducted to examine the influences of altering miR-1258 expression on the viability, migration, and invasion of PTC cells. Bioinformatics prediction and dual-luciferase experiment were performed to verify the target gene of miR-1258. Finally, we carried out a rescue assay to verify whether the regulation of miR-1258 on the biological behaviour of PTC cells needs to be achieved by regulating TMPRSS4. Results: The outcomes revealed that miR-1258 was lowly expressed in PTC cell lines and miR-1258 showed the lowest expression in KTC-1 and the highest expression in B-CPAP among all tested PTC cell lines. Overexpression of miR-1258 inhibited KTC-1 cell viability and ability to migrate and invade, whereas inhibition of miR-1258 in B-CPAP cells has the opposite effect. Furthermore, we affirmed that miR-1258 can directly target TMPRSS4, and miR-1258 can reduce the biological malignant behaviour of PTC cells via regulation of TMPRSS4. Conclusion: Taken together, our research raised the possibility that miR-1258 was an anti-oncogene, which exerts its anti-cancer function by targeting TMPRSS4. Hence, it may be possible to treat PTC by targeting the miR-1258/TMPRSS4 axis in the future.

Blow-up sets of Ricci curvatures of complete conformal metrics

A version of the singular Yamabe problem in smooth domains in a closed manifold yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study the blow-up phenomena of Ricci curvatures of these metrics on domains whose boundary is close to a certain limit set of a lower dimension. We will characterize the blow-up set according to the Yamabe invariant of the underlying manifold. In particular, we will prove that all points in the lower dimension part of the limit set belong to the blow-up set on manifolds not conformally equivalent to the standard sphere and that all but one point in the lower dimension part of the limit set belong to the blow-up set on manifolds conformally equivalent to the standard sphere. In certain cases, the blow-up set can be the entire manifold. We will demonstrate by examples that these results are optimal