There are many new applications of the centroidal Voronoi tessellations that come to life in recent years, along with more mathematical understandings and new algorithmic advances in their efficient computation. Some examples are presented in this paper as an illustration with an emphasis on the construction of ideal point distributions, best mode selections and optimal spatial partitions.

The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...

We present a new approach for aligning families of 2D gels. Instead of choosing one of the gels as reference and performing a pairwise alignment, we construct an ideal gel that is representative of the entire family and obtain a set of piecewise affine transformations that optimally align each gel of the family to the ideal gel. The coefficients defining the transformations as well as the ideal...

In this article, we study the jumping numbers of an ideal in the local ring at rational singularity on a complex algebraic surface. By understanding the contributions of reduced divisors on a fixed resolution, we are able to present an algorithm for finding of the jumping numbers of the ideal. This shows, in particular, how to compute the jumping numbers of a plane curve from the numerical data...

Clark and Lauderdale develop a novel approach for orienting Supreme Court opinions in unidimensional policy space. They argue that the most important portion of a Court’s opinion is not its judgment in favor of one party or another, but its reasoning, for it is this reasoning that becomes binding law and shapes the path of American legal development. The authors thus measure the policy orientat...

The contributions in this paper are in two folds. On the one hand, we propose a general approach for approximating ideal filters based on fractional calculus from the point of view of systems of fractional order. On the other hand, we suggest that the Paley and Wiener criterion might not be a necessary condition for designing physically realizable ideal filters. As an application of the present...

GIS-based multicriteria analysis (GIS-MCA) is a procedure for transforming and combining geographic data and value judgments (preferences) to evaluate a set of alternatives with respect to relevant criteria. Ideal Point Method (IPM) is one of the most often used GIS-MCA techniques. It has been applied in many research/planning areas including environmental planning, urban/regional planning, was...

We present detailed experimental studies of the temperature dependence of the plateau conductance of GaAs quantum point contacts in the temperature range from 0.3 K to 10 K. Due to a strong lateral confinement produced by a shallow-etching technique we are able to observe the following unexpected feature: a linear temperature dependence of the measured mid-plateau conductance. We discuss an int...

We )nd that adding certain amounts of inhibitory inputs to a neuron improves its capability of accurately decoding the input information. The optimal ratio r of inhibitory to excitatory inputs for decoding the input information from an observation of the e,erent interspike intervals is calculated. Surprisingly, the Fisher information could be zero for certain values of the ratio, seemingly impl...