In this paper, we consider the problem of inserting points in a square grid, which has many background applications, including halftone in reprographic and image processing. We consider an online version of this problem, i.e., the points are inserted one at a time. The objective is to assign the points as uniform as possible. Precisely speaking, after each insertion, the gap ratio should be as ...

A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges to line segments that avoid grid points but the extremes. Additionally G is said to be properly embeddable in the grid if it is grid locatable and the segments representing edges do not cross each other. We study the area needed to obtain those representations for some gra...

Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an equidistantly spaced grid. They have compact support of the size determined by the order of the underlying interpolating polynomial that is used to generate IS...

Virtual synchronous machines are inverters with a control algorithm that causes them to behave towards the power grid like generators. A popular way realize such synchronverters. Their has evolved over time, but all different formulations in literature share same “basic algorithm”. We investigate equilibrium points and stability of synchronverter described by this basic algorithm, when connecte...

In this, paper we present a probabilistic approach to analysis and prediction of protein structure. We argue that this approach provides a flexible and convenient mechanism to perform general scientific data analysis in molecular biology. We apply our approach to an important problem in molecular biology-predicting the secondary structure of proteins-and obtain experimental results comparable t...

An adaptive remeshing procedure based on a cell volume deformation method is presented. Starting with an initial grid, this method offers direct cell volume control through the specification of the transformation Jacobian. Grid points are moved with appropriate grid velocities so that the specified cell volume distribution can be achieved at the end of the grid movement without adding or removi...