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This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all…
This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under…
Topological dynamical systems $(X,T)$ are actions $T \times X \to X$, given as $(t, x) \to tx$, on a compact, Hausdorff topological space $X$ with $T$ as an acting group or monoid. We take up the property of topological transitivity…
Work in progress concerning alternative formalizations of arithmetic.
This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…
This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.
This work continues the author's article in Rus. J. Nonlinear Dynamics (2010, v.6, No.4) and contains applications of the Boolean functions method to investigation of the admissible regions and the phase topology of three algebraically…
A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial 1-complexes, or graphs, very much in the spirit of Stallings. A number of classical, as well as some new results about…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
In this paper, we review multi-agent collective behavior algorithms in the literature and classify them according to their underlying mathematical structure. For each mathematical technique, we identify the multi-agent coordination tasks it…
We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
The group of extensions (as in the title), endowed with something like a connection at Archimedean infinity, is isomorphic to the ad\'ele-class group of $\Q$: which is a topological group with interesting Haar measure.}
This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Through this method, old and new bounds are derived and numerical examples are provided, showing how former results…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
In this note we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten for superstring perturbation theory in arXiv:1209.5461. We intend to make the construction…
This paper clarifies the main research methods and ideas of the thesis [1,2,4]. The special calculation process is also realized by corresponding computer algorithm. Finally, we introduce zero rows sum case and give the corresponding…