In 2001, Bertalmio, et. al. drew an analogy between the image intensity function for the image inpainting problem and the stream function in a two-dimensional (2D) incompressible fluid. An approximate solution to the inpainting problem is obtained by numerically approximating the steady state solution of the 2D NSE vorticity transport equation, and simultaneously solving the Poisson problem bet...

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

In 2001, Bertalmio, et. al. drew an analogy between the image intensity function for the image inpainting problem and the stream function in a two-dimensional (2D) incompressible fluid. An approximate solution to the inpainting problem is obtained by numerically approximating the steady state solution of the 2D NSE vorticity transport equation, and simultaneously solving the Poisson problem bet...

The objective is to evaluate carotid arterial elasticity in patients with obstructive sleep apnea hypopnea syndrome (OSAHS) by two-dimensional speckle tracking imaging (2D-STI).Sixty-two hospitalized patients with OSAHS and 20 healthy subjects were studied. The OSAHS patients were divided into 3 subgroups: a mild group, a moderate group, and severe group. All subjects underwent complete left co...

We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix renormalization group (CTMRG) method, and its upper bound is surveyed. The variational approach is a way of applying the density matrix renormalization group m...

The non-differentiability and implicit definition of boundary of production possibility set (PPS) in data envelopment analysis (DEA) are two important difficulties for obtaining directional characteristics, including different elasticity measures and marginal rates of substitution. Also, imposing weight restrictions in DEA models have some shortcomings and misunderstandings. In this paper we ut...

The protein folding problem in the HP-model is NP-hard in both 2D and 3D [4, 6]. The problem is to put a sequence, consisting of two characters H and P, on a d-dimensional grid to have the maximal number of HH contacts. We design a 2 1− 1 d log n) time algorithm for ddimensional protein folding in the HP-model. In particular, our algorithm has O(2 √ n log ) and O(2 2 3 log ) computational time ...