Related papers: Electric currents in infinite networks
This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the…
Mesoscopic systems and large molecules are often modeled by graphs of one-dimensional wires, connected at vertices. In this paper we discuss the solutions of the Schr\"odinger equation on such graphs, which have been named "quantum…
In communication networks theory the concepts of networkness and network surplus have recently been defined. Together with transmission and betweenness centrality, they were based on the assumption of equal communication between vertices.…
The directed network model describing chiral edge states on the surface of a cylindrical 3D quantum Hall system is known to map to a one-dimensional quantum ferromagnetic spin chain. Using the spin wave expansion for this chain, we…
We study multiport networks, common in electrical engineering. They have boundary conditions different from electrical networks: the boundary vertices are split into pairs and the sum of the incoming currents is set to be zero in each pair.…
The network of networks(NON) research is focused on studying the properties of n interdependent networks which is ubiquitous in the real world. Identifying the influential nodes in the network of networks is theoretical and practical…
How do networks form and what is their ultimate topology? Most of the literature that addresses these questions assumes complete information: agents know in advance the value of linking to other agents, even with agents they have never met…
We consider an idealized network, formed by N neurons individually described by the FitzHugh-Nagumo equations and connected by electrical synapses. The limit for N to infinity of the resulting discrete model is thoroughly investigated, with…
We derive novel results on the ergodic theory of irreducible, aperiodic Markov chains. We show how to optimally steer the network flow to a stationary distribution over a finite or infinite time horizon. Optimality is with respect to an…
Network connectivity is usually addressed for convex domains where a direct line of sight exists between any two transmitting/receiving nodes. Here, we develop a general theory for the network connectivity properties across a small opening,…
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and…
A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on $X$ which is either observed directly or derived from a data set. For an electrical network there are two…
We develop a theory of graph algebras over general fields. This is modeled after the theory developed by Freedman, Lov\'asz and Schrijver in [22] for connection matrices, in the study of graph homomorphism functions over real edge weight…
The first three authors [European J. Combin. 33 (2012), 62--71] established a relationship between the transversal number and the domination number of uniform hypergraphs. In this paper, we establish a relationship between the total…
In this article we describe all possible infinite linear configurations that can be found in a shift of any set of positive upper Banach density. This simultaneously generalizes Szemer\'edi's theorem on arithmetic progressions and the…
In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…
Application of the Ramsey Infinite Theorem to the variational principles of physics is discussed. According to the Ramsey Infinite Theorem,there exists the infinite, monochromatic chain of the pathways (clique), which are completely built…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
We show that the two phases of the 4-dimensional compact U(1) lattice gauge theory are characterized by the existence or absence of an infinite current network, defining ``infinite'' on a finite lattice in a manner appropriate to the chosen…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…