Related papers: Graph Theoretic Framework of Dynamical Systems Thr…
We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…
Can the cross product be generalized? Why are the trace and determinant so important in matrix theory? What do all the coefficients of the characteristic polynomial represent? This paper describes a technique for `doodling' equations from…
This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends,…
For a given natural number $n$, the second part of Hilbert's 16th Problem asks whether there exists a finite upper bound for the maximum number of limit cycles that planar polynomial vector fields of degree $n$ can have. This maximum number…
We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…
These last years an increasing interest appeared for studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. One of the difficulties for understanding the dynamics of…
A family of polynomials linked to the set of the deltoid tangents and its associated algebraic hypersurfaces has been presented in recent years. In this paper we study some related maximising and free plane curves. We also analyse the…
The purpose of this paper is to develop a "calculus" on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new…
Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and…
The monograph is concerned with some key problems of the theory of nonlinear economic dynamics. The authors' concept consists in analyzing the problem of structural instability of economic systems within the framework of the synergetic…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in R^2 with a potential having a deep strict minimum on the graph, when the width of the well shrinks to zero. For a generic…
Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…
The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is established. An algorithm for constructing a Hamiltonian cycle…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…