following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

Abstract The topology of vector fields offers a well known way to show a “condensed” view of the stream line behavior of a vector field. The global structure of a field can be shown without time-consuming user interaction. With regard to large data visualization, one encounters a major drawback: the necessity to analyze a whole data set, even when interested in only a small region. We show that...

This paper studies the problem of designing a logical topology over a wavelength-routed all-optical network physical topology. The physical topology consists of the nodes and ber links in the network. On an all-optical network physical topology, we can set up lightpaths between pairs of nodes, where a lightpath represents a direct optical connection without any intermediate electronics. The set...

We continue our research plan of developing the theory small and locally spaces, proposing this as a realisation Grothendieck’s idea tame topology on level general topology. In paper, we develop Heyting spaces prove new version Esakia Duality for such spaces. To do this, notice that spectral may be seen sober with all smops compact introduce method standard spectralification. This helps to unde...

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

In this paper, Hidden Markov Models (HMMs) are utilized to represent motifs. Motifs are the preserved sites in the evolution process and are considered to represent the function or structure of proteins. It is compulsory to use direct periodic topology and the OR rule to represent motifs. The direct periodic topology is necessary to represent cyclic structures, such as global loops for helices....

Recent results from statistical physics show that large classes of complex networks, both manmade and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class of networks are said to have a small-world topology. In the context of communication networks, navigable small-world topologies, i.e. those which admit efficie...

Robustness and small-world effect are two crucial structural features of complex networks and have attracted increasing attention. However, little is known about the relation between them. Here we demonstrate that, there is a conflicting relation between robustness and small-world effect for a given degree sequence. We suggest that the robustness-oriented optimization will weaken the small-worl...