INTRODUCTION Many applications in science and business such as signal analysis or costumer segmentation deal with large amounts of data which are usually high dimensional in the feature space. As a part of preprocessing and exploratory data analysis, visualization of the data helps to decide which kind of method probably leads to good results. Since the visual assessment of a feature space that...

A typical formation shape control problem involves point agents sensing relative positions, i.e. orientations and distances, of their neighbors and then moving so that these relative positions achieve some prespecified values. Such a procedure, requiring as it does sensing of orientations, implicitly presupposes that all agents have a shared understanding of the common orientations. On the othe...

This study develops an equation for describing three-dimensional membrane transformation through proliferation of its component cells regulated by morphogen density distributions on the membrane. The equation is developed in a two-dimensional coordinate system mapped on the membrane, referred to as the membrane coordinates. When the membrane expands, the membrane coordinates expand in the same ...

The major signal processing challenges in wireless CDMA systems stem from time-varying multipath propagation effects , multiaccess interference (MAI), and the complexity of the DSP algorithms. We propose a framework based on canonical multipath-Doppler coordinates for addressing these issues in an integrated fashion. The canonical coordinates are derived from a fundamental characterization of c...

The principles behind the detailed results of a light-front mean field theory of finite nuclei are elucidated by deriving the nucleon mode equation using a simple general argument, based on the idea that a static source in equal time coordinates corresponds to a moving source in light front coordinates. This idea also allows us to solve several simple toy model examples: scalar field in a box, ...

A new class of twistor-like string models in four-dimensional space-time extended by the addition of six tensorial central charge (TCC) coordinates z mn is studied. The Hamiltonian of tensionless string in the extended space-time is derived and its symmetries are investigated. We establish that the string constraints reduce the number of independent TCC coordinates z mn to one real effective co...

Transformations between group coordinates of three–dimensional conformal σ–models in the flat background and their flat, i.e. Riemannian coordinates enable to find general dilaton fields for three–dimensional flat σ–models. By the Poisson–Lie transformation we can get dilatons for the dual σ–models in a curved background. Unfortunately, in some cases the dilatons depend on inadmissible auxiliar...

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic p...

We describe G-Space (Geodesic Space), a straightforward linear time layout algorithm that draws undirected graphs based purely on their topological features. The algorithm is divided into two phases. The first phase is an embedding of the graph into a 2-D plane using geodesic distances as coordinates. These coordinates are computed with the same process used by HDE (High-Dimensional Embedding) ...