Wavefront sensing systems measure the slope or curvature of a surface by calculating the centroid displacement of two focal spot images. Accurately finding the centroid of each focal spot determines the measurement results. This paper studied several widely used centroid-finding techniques and observed that thresholding is the most critical factor affecting the centroid-finding accuracy. Since ...

The capabilities of evolutionary algorithms (EAs) in solving nonlinear and non-convex optimization problems are significant. Differential evolution (DE) is an effective population-based EA, which has emerged as very competitive. Since its inception in 1995, multiple variants of DE have been proposed with higher performance. Among these DE variants, opposition-based differential evolution (ODE) ...

Given a set V of n points in the plane, no three of them being collinear, a convex inclusion chain of V is an ordering of the points of V such that no point belongs to the convex hull of the points preceding it in the ordering. We call k-set of the convex inclusion chain, every k-set of an initial subsequence of at least k points of the ordering. We show that the number of such k-sets (without ...

In a number of estimation problems in bioinformatics, accuracy measures of the target problem are usually given, and it is important to design estimators that are suitable to those accuracy measures. However, there is often a discrepancy between an employed estimator and a given accuracy measure of the problem. In this study, we introduce a general class of efficient estimators for estimation p...

Let S be a set of points in IR d , each with a weight that is not known precisely, only known to fall within some range. What is the locus of the centroid of S? We prove that this locus is a convex polytope, the projection of a zonotope in IR d+1. We derive complexity bounds and algorithms for the construction of these \centroid polytopes".

The asymmetric unit of the title compound, C(9)H(7)N(3)O(2), is composed of two independent mol-ecules. The crystal structure is stabilized by C-H⋯O and C-H⋯N hydrogen bonds, forming a three-dimensional network. The crystal structure also features pyrazine-pyrazine π-π inter-actions [centroid-centroid distance = 3.6994 (5) Å] and also pyridine-pyrazine π-π inter-actions [centroid-centroid dista...

In its crystal structure, the title compound, C(9)H(7)NO(3), forms π-stacked dimers, with a centroid-centroid distance of 3.475 (5) Å between the benzenoid and the 2,4 dicarbonyl oxazine rings. These dimers then form staircase-like linear chains through further π-stacking between the benzenoid rings [centroid-centroid distance of 3.761 (2) Å]. The methyl-H atoms are disordered due to rotation a...

The paper is devoted to the dissipative Schrödinger-Poisson system. We indicate conditions in terms of the Schrödinger-Poisson data which guarantee the uniqueness of the solution. Moreover, it is shown that if the system is sufficiently small shrunken, then it always admits a unique solution.

Pediatric ocular trauma is a commonly seen in patients with maxillofacial trauma.[1] It often results in phthisis bulbi, a small, shrunken, non-functional eye. Therapeutic options are limited in phthisical eyes and provide only symptomatic relief. Majority of patients with phthisis bulbi eventually become blind resulting in aesthetic disfigurement of face resulting in psychological and emotiona...