The formulation of quantum statistical mechanics based on the path centroid variable in Feynman path integration is generalized to a phase space perspective, thereby including the momentum as an independent dynamical variable. By virtue of this approach, operator averages and imaginary time correlation functions can be expressed in terms of an averaging over the multidimensional phase space cen...

(a) The medians intersect in a point interior to the triangle, called the centroid, which divides each of the medians in the ratio 2 : 1. (b) The medians form a new triangle, called the median triangle. (c) The area of the median triangle is 3/4 of the area of the given triangle in which the medians were constructed. (d) The median triangle of the median triangle is similar to the given triangl...

In this paper we present a technique for shape similarity estimation and apply it to content-based indexing and retrieval over large image databases. This technique is based on wavelet decomposition and uses polygonal approximation. It uses simple features (aspect ratio, angles, distances from the centroid, distance ratios and relative positions) extracted at high curvature points. The experime...

Using random projection, a method to speed up both kernel k-means and centroid initialization with k-means++ is proposed. We approximate the matrix distances in lower-dimensional space Rd before clustering motivated by upper error bounds. With projections, previous work on bounds for dot products an improved bound methods are considered k-means. The complexities Lloyd’s algorithm known be O(nkD...

Information on the energy of 5d levels of Ce ions coordinated by CO3 22 , SO4 22 , PO4 32 , BO3 32 , and SiO4 42 ionic complexes or by neutral water molecules in oxide compounds will be presented and systematically analyzed. The average energy of the 5d configuration of excited Ce is shifted towards lower energy relative to the free ion value. This centroid shift depends on the binding strength...

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...