Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obl...

Making an extensive use of small transfinite topological dimension trind, we ascribe to every metric space X an ordinal number (or −1 or Ω) tHD(X), and we call it the transfinite Hausdorff dimension of X. This ordinal number shares many common features with Hausdorff dimension. It is monotone with respect to subspaces, it is invariant under bi-Lipschitz maps (but in general not under homeomorph...

J.M. Aarts introduced and studied a new dimension function, Hind, in 1975 and obtained several results on this function. In this paper, a new local inductive dimension function called local huge inductive dimension function denoted by locHind is introduced and studied. Furthermore, an effort is made to introduce and study dimension functions for fuzzy topological spaces. It has been possible to...

A simple topological graph T = (V (T), E(T)) is a drawing of a graph in the plane where every two edges have at most one common point (an endpoint or a crossing) and no three edges pass through a single crossing. Topological graphs G and H are isomorphic if H can be obtained from G by a homeomorphism of the sphere, and weakly isomorphic if G and H have the same set of pairs of crossing edges. W...

1. INTRODUCTION. The concept of dimension has many aspects and meanings within mathematics, and there are a number of very different definitions of what the dimension of a set should be. The simplest case is that of R d : in order to distinguish points in R d , we need d different (real) coordinates, so R d has dimension d as a (real) vector space. Similarly, a d-dimensional manifold is a space...

With industrial modelling tools, topological structures and free form surfaces are often managed separately, and patches used for embedding are limited to dimension 2. A new approach is to combine topology structures of any dimension with embedding of same dimension, and use topological operations to modify the shape and the properties of surfaces and volumes. The use of Chains of map as topolo...