Motivation: Several recent studies attempted to establish measures for the similarity between genes that are based on the topological properties of metabolic networks. However, these approaches offer only a static description of the properties of interest and offer moderate (albeit significant) correlations with pertinent

The study is devoted to definition of generalized metrical and topological (informational entropy) characteristics of neural signals via their well-known theoretical models. We have shown that time dependence of action potential of neurons is scale invariant. Information and entropy of neural signals have constant values in case of self-similarity and self-affinity.

We use a semisupervised learning algorithm based on a topological data analysis approach to assign functional categories to yeast proteins using similarity graphs. This new approach to analyzing biological networks yields results that are as good as or better than state of the art existing approaches.

We show that every two-dimensional class of topological similarity, and hence every diagonal conjugacy class of pairs, is meager in the group of order preserving bijections of the rationals and in the group of automorphisms of the ordered rational Urysohn space.

Similarity is the assessment of deviation from equivalence. Spatial similarity is complex due to the numerous constraining properties of geographic objects and their embedding in space. Among these properties, the spatial relations between geographic objects—topological, directional, and metrical—are critical, because they capture the essence of a scene’s structure. These relations can be categ...

Spectral clustering has gained importance in recent years due to its ability to cluster complex data as it requires only pairwise similarity among data points with its ease of implementation. The central point in spectral clustering is the process of capturing pair-wise similarity. In the literature, many research techniques have been proposed for effective construction of affinity matrix with ...

Network self-similarity or fractality are widely accepted as an important topological property of metabolic networks; however, recent studies cast doubt on the reality of self-similarity in the networks. Therefore, we perform a comprehensive evaluation of metabolic network fractality using a box-covering method with an earlier version and the latest version of metabolic networks and demonstrate...

In order to extend classical models of computing with symbols we introduce a model for quantitative computation which is based on innnite-dimensional topological linear structures. In particular machines which operate on data taken from Hilbert spaces will be looked at. These Hilbert machines (and other topological linear machines) allow the adequate treatment of concepts like innniteness and s...

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, and similarity and diversit...

in this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. we also investigate effect to fuzzy soft connectedness. moreover, c_i-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.