Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive ob...

Pseudo-Centroid Clustering replaces the traditional concept of a centroid expressed as a center of gravity with the notion of a pseudo-centroid (or a coordinate free centroid) which has the advantage of applying to clustering problems where points do not have numerical coordinates (or categorical coordinates that are translated into numerical form). Such problems, for which classical centroids ...

This work addresses the problem of detecting local centroid paths, paths within an area of interest on a spatial network that has the highest concentration of activities. The KMR algorithm [1] is used to do clustering on the spatial network, and a new measure of the density of activities on a path, Activity Coverage Rate (ACR), is introduced to locate each such path. We use experiment results t...

This paper compares five Doppler centroid estimation methods which are :energy balancing, matched-correlation , maximum likelihood, correlation Doppler estimator(CDE) and sign Doppler estimator (SDE). Their estimation performances in raw data domain and image domain are studied. The computer simulation results are presented. ERS-1 raw data are also used to test the performances of every method....

The volume enclosed by subdivision surfaces, such as Doo-Sabin, Catmull-Clark, and Loop has recently been derived. Moments of higher degree d are more challenging because of the growing number of coefficients in the d + 3-linear forms. We derive the intrinsic symmetries of the tensors, and thereby reduce the complexity of the problem. Our framework allows to compute the 4-linear forms that de...

In recent years we have seen a tremendous growth in the volume of text documents available on the Internet, digital libraries, news sources, and company-wide intranets. Automatic text categorization, which is the task of assigning text documents to pre-specified classes (topics or themes) of documents, is an important task that can help both in organizing as well as in finding information on th...

A new generalized unsupervised competitive learning rule is introduced for adaptive scalar quan-tization. The rule, called generalized Boundary Adaptation Rule (BAR r), minimizes r-th power law distortion D r in the high resolution case. It is shown by simulations that a fast version of BAR r outperforms generalized Lloyd I in minimizing D 1 (mean absolute error) and D 2 (mean squared error) di...

Abstract It has been a long-term effort to get higher energy resolution for experiment detector. Usually the can be converted from spatial though mechanical setup. To shrink pixel size of detector takes lot efforts, time and is limited by integrated circuit technology. So centroid algorithm widely used increase resolution. Through electron cloud diffusion, excited electrons are distributed amon...

The Gibbs Centroid Sampler is a software package designed for locating conserved elements in biopolymer sequences. The Gibbs Centroid Sampler reports a centroid alignment, i.e. an alignment that has the minimum total distance to the set of samples chosen from the a posteriori probability distribution of transcription factor binding-site alignments. In so doing, it garners information from the f...