Related papers: Recovering Conductances of Resistor Networks in a …

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) resistors. Generalizing work of Curtis, Ingerman, Morrow, Colin de Verdiere, Gitler, and Vertigan, we characterize…

In an alternating-current network, each edge has a complex "conductance" with positive real part. The response map is the linear map from the vector of voltages at a subset of "boundary nodes" to the vector of currents flowing into the…

The resolution matrix is a mathematical tool for analyzing inverse problems such as computational imaging systems. When treating network connectivity estimation as an inverse problem, the resolution matrix describes the degree to which…

We address the discrete inverse conductance problem for well-connected spider networks; that is, to recover the conductance function on a well-connected spider network from the Dirichlet-to-Neumann map. It is well-known that this inverse…

We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…

We discuss several parametrizations of the space of circular planar electrical networks. For any circular planar network we associate a canonical minimal network with the same response matrix, called a "standard" network. The conductances…

We give a derivation of conductivities in certain classes of graphs based on knowing certain subdeterminants of the response matrix, mainly utilizing the boundary edge and boundary spike formulas given in Curtis' and Morrow's book.

Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor…

For a connected graph $G$, its resistance distance matrix is denoted by $R(G)$. A graph is called resistance regular if all the row (or column) sums of $R(G)$ are equal. We provide a necessary and sufficient condition for a simple connected…

We show that the problem of recovering the topology and admittance of an electrical network from power and voltage data at all vertices is often ill-posed, and sometimes it even has multiple solutions. We reformulate the problem to seek for…

We study the inverse problem of determining the conductivity matrix of an electrical network from the prescribed knowledge of the magnitude of the induced current along the edges coupled with the imposed voltage or injected current on the…

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…

A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…

Recovery of the causal structure of dynamic networks from noisy measurements has long been a problem of interest across many areas of science and engineering. Many algorithms have been proposed, but there is little work that compares the…

We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of…

In this article, we present a method to reconstruct the topology of a partially observed radial network of linear dynamical systems with bi-directional interactions. Our approach exploits the structure of the inverse power spectral density…

In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…

This paper addresses the problem of finding an orientation and a minimum radius for directional antennas of a fixed angle placed at the points of a planar set S, that induce a strongly connected communication graph. We consider problem…

Coordinating multiple local power sources can restore critical loads after the major outages caused by extreme events. A radial topology is needed for distribution system restoration, while determining a good topology in real-time for…

Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…