A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations

A class of second order approximations, called the weighted and shifted Gr\"{u}nwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions. The stability and convergence of our difference schemes for space fractional diffusion equations with constant coefficients in one and two dimensions are theoretically established. Several numerical examples are implemented to testify the efficiency of the numerical schemes and confirm the convergence order, and the numerical results for variable coefficients problem are also presented.Comment: 24 Page

Genetically engineered mouse models for functional studies of SKP1-CUL1-F-box-protein (SCF) E3 ubiquitin ligases

The SCF (SKP1 (S-phase-kinase-associated protein 1), Cullin-1, F-box protein) E3 ubiquitin ligases, the founding member of Cullin-RING ligases (CRLs), are the largest family of E3 ubiquitin ligases in mammals. Each individual SCF E3 ligase consists of one adaptor protein SKP1, one scaffold protein cullin-1 (the first family member of the eight cullins), one F-box protein out of 69 family members, and one out of two RING (Really Interesting New Gene) family proteins RBX1/ROC1 or RBX2/ROC2/SAG/RNF7. Various combinations of these four components construct a large number of SCF E3s that promote the degradation of many key regulatory proteins in cell-context, temporally, and spatially dependent manners, thus controlling precisely numerous important cellular processes, including cell cycle progression, apoptosis, gene transcription, signal transduction, DNA replication, maintenance of genome integrity, and tumorigenesis. To understand how the SCF E3 ligases regulate these cellular processes and embryonic development under in vivo physiological conditions, a number of mouse models with transgenic (Tg) expression or targeted deletion of components of SCF have been established and characterized. In this review, we will provide a brief introduction to the ubiquitin-proteasome system (UPS) and the SCF E3 ubiquitin ligases, followed by a comprehensive overview on the existing Tg and knockout (KO) mouse models of the SCF E3s, and discuss the role of each component in mouse embryogenesis, cell proliferation, apoptosis, carcinogenesis, as well as other pathogenic processes associated with human diseases. We will end with a brief discussion on the future directions of this research area and the potential applications of the knowledge gained to more effective therapeutic interventions of human diseases

Ray-tracing-based reconstruction algorithms for digital breast tomosynthesis

As a breast-imaging technique, digital breast tomosynthesis has great potential to improve the diagnosis of early breast cancer over mammography. Ray-tracing-based reconstruction algorithms, such as ray-tracing back projection, maximum-likelihood expectation maximization (MLEM), ordered-subset MLEM (OS-MLEM), and simultaneous algebraic reconstruction technique (SART), have been developed as reconstruction methods for different breast tomosynthesis systems. This paper provides a comparative study to investigate these algorithms by computer simulation and phantom study. Experimental results suggested that, among the four investigated reconstruction algorithms, OS-MLEM and SART performed better in interplane artifact removal with a fast speed convergence

Structure and cultivation of the knowledge and abilities of students of higher vocational technical education

This paper puts forward the constitution module for the knowledge and ability structure that students of higher vocational education should have. It sets forth at the full some basic principles that the basic knowledge the students of higher vocational education should master ought to be limited to no more than enough for their future use while their special skills and knowledge should be advanced, practical and their humane knowledge should be rich and extensive. It also suggests certain measures for the cultivation of their comprehensive practical abilities and the dialectical relationship between knowledge and ability which leads to the conclusion that equal stress should be put on both of them