Related papers: Electric currents in infinite networks
Graph auto-encoders have proved to be useful in network embedding task. However, current models only consider explicit structures and fail to explore the informative latent structures cohered in networks. To address this issue, we propose a…
We study transport processes on infinite metric graphs with non-constant velocities and matrix boundary conditions in the $\\mathrm{L}^{\infty}$-setting. We apply the theory of bi-continuous operator semigroups to obtain well-posedness of…
Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine,…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…
The electric and magnetic fields of an infinite straight wire carrying a steady current which is turned on abruptly are determined using Jefimenko's equations, starting from the standard assumption that the wire is electrically neutral in…
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…
We calculate effective impedances of infinite $LC$- and $CL$- ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves precise mathematical concepts. These concepts are related…
In recent years, attempts have been made to extend nonlinear small-gain theorems for input-to-state stability (ISS) from finite networks to countably infinite networks with finite indegrees. Under specific assumptions about the…
Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network…
We study the mechanism of topological superconductivity in a hierarchical chain of chiral non-linear sigma-models (models of current algebra) in one, two, and three spatial dimensions. The models have roots in the 1D Peierls-Frohlich model…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
We study mesoscopic transport in the Q1D wires and rings made of a 2D conductor of width W and length L >> W. Our aim is to compare an impurity-free conductor with grain boundaries with a grain-free conductor with impurity disorder. A…
A large number of complex systems, naturally emerging in various domains, are well described by directed networks, resulting in numerous interesting features that are absent from their undirected counterparts. Among these properties is a…
A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks…