For optical waveguides with high index contrast and sharp corners, high order full-vectorial mode solvers are difficult to develop, due to the field singularities at the corners. A recently developed method (the so-called BIENtD method) based on boundary integral equations (BIEs) and Neumannto-Dirichlet (NtD) maps achieves high order of accuracy for dielectric waveguides. In this paper, we deve...

Stein’s method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the Berry-Essen Theorem is achieved. The approximation of the total number of points of a point processes is also considered. The results are applied to the excee...

High order finite difference methods obeying a summation-by-parts (SBP) rule are developed for equidistant grids. With curvilinear grids, a coordinate transformation operator that does not destroy the SBP property must be used. We show that it is impossible to construct such an operator without decreasing the order of accuracy of the method.

We present a novel and efficient method for solving the Poisson equation, the heat equation, and Stefan-type problems with Robin boundary conditions over potentially moving, arbitrarily-shaped domains. The method utilizes a level set framework, thus it has all of the benefits of a sharp, implicitly-represented interface such as the ease of handling complex topological changes. This method is st...

Background: Osteoporosis is a systemic skeletal disease characterized by low bone mineral density (BMD) and micro-architectural deterioration of bone tissue, leading to bone fragility and increased fracture risk. Since Panoramic image is a feasible and relatively routine imaging technique in dentistry; it could provide an opportunistic chance for screening osteoporosis. In this regard, numerous...

We propose a new ranking model for personalized local search. While local search verticals such as Google Local and Yahoo! Local incorporate physical proximity and public sentiment (reviews and ratings), their rankings reflect minimal personalization. We personalize local search by integrating Twitter social network structure and content analysis. Specifically, we infer sentiment for tweets by ...