Wavelet Galerkin method for fractional elliptic differential equations

Under the guidance of the general theory developed for classical partial differential equations (PDEs), we investigate the Riesz bases of wavelets in the spaces where fractional PDEs usually work, and their applications in numerically solving fractional elliptic differential equations (FEDEs). The technique issues are solved and the detailed algorithm descriptions are provided. Compared with the ordinary Galerkin methods, the wavelet Galerkin method we propose for FEDEs has the striking benefit of efficiency, since the condition numbers of the corresponding stiffness matrixes are small and uniformly bounded; and the Toeplitz structure of the matrix still can be used to reduce cost. Numerical results and comparison with the ordinary Galerkin methods are presented to demonstrate the advantages of the wavelet Galerkin method we provide.Comment: 20 pages, 0 figure

Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model

We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks. In an effort to reduce the setup assumptions required for efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle attacks, we consider a model, which we call the Authenticated Public-Key (APK) model. The APK model seems to significantly reduce the setup assumptions made by the CRS model (as no trusted party or honest execution of a centralized algorithm are required), and can be seen as a slightly stronger variation of the Bare Public-Key (BPK) model from \cite{CGGM,MR}, and a weaker variation of the registered public-key model used in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK model. Our main result is a constant-round concurrent non-malleable zero-knowledge argument of knowledge for any polynomial-time relation (associated to a language in $\mathcal{NP}$), under the (minimal) assumption of the existence of a one-way function family. Furthermore,We show time-efficient instantiations of our protocol based on known number-theoretic assumptions. We also note a negative result with respect to further reducing the setup assumptions of our protocol to those in the (unauthenticated) BPK model, by showing that concurrently non-malleable zero-knowledge arguments of knowledge in the BPK model are only possible for trivial languages

Resettable Zero Knowledge in the Bare Public-Key Model under Standard Assumption

In this paper we resolve an open problem regarding resettable zero knowledge in the bare public-key (BPK for short) model: Does there exist constant round resettable zero knowledge argument with concurrent soundness for $\mathcal{NP}$ in BPK model without assuming \emph{sub-exponential hardness}? We give a positive answer to this question by presenting such a protocol for any language in $\mathcal{NP}$ in the bare public-key model assuming only collision-resistant hash functions against \emph{polynomial-time} adversaries.Comment: 19 pag

Automatic Recognition of Sunspots in HSOS Full-Disk Solar Images

A procedure is introduced to recognise sunspots automatically in solar full-disk photosphere images obtained from Huairou Solar Observing Station, National Astronomical Observatories of China. The images are first pre-processed through Gaussian algorithm. Sunspots are then recognised by the morphological Bot-hat operation and Otsu threshold. Wrong selection of sunspots is eliminated by a criterion of sunspot properties. Besides, in order to calculate the sunspots areas and the solar centre, the solar limb is extracted by a procedure using morphological closing and erosion operations and setting an adaptive threshold. Results of sunspot recognition reveal that the number of the sunspots detected by our procedure has a quite good agreement with the manual method. The sunspot recognition rate is 95% and error rate is 1.2%. The sunspot areas calculated by our method have high correlation (95%) with the area data from USAF/NOAA.Comment: 9 pages, 6 figures, 2 tables, accepted for publication in PAS

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