相关论文: Circular Planar Electrical Networks I: The Electri…
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 construct a compactification of the space of circular planar electrical networks studied by Curtis-Ingerman-Morrow and De Verdiere-Gitler-Vertigan, using cactus networks. We embed this compactification as a linear slice of the totally…
We consider the problem of recovering the topology and the edge conductance value, as well as characterizing a set of electrical networks that satisfy the limitedly available Thevenin impedance measurements. The measurements are obtained…
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…
We refine the result of T. Lam \cite{L} on embedding the space $E_n$ of electrical networks on a planar graph with $n$ boundary points into the totally non-negative Grassmannian $\mathrm{Gr}_{\geq 0}(n-1,2n)$ by proving first that the image…
This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize descriptions of combinatorial features of graphic…
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…
Exceptional points (EPs) with their intriguing spectral topology have attracted considerable attention in a broad range of physical systems, with potential sensing applications driving much of the present research in this field. Here we…
Curtis-Ingerman-Morrow characterize response matrices for circular planar electrical networks as symmetric square matrices with row sums zero and non-negative circular minors. In this paper, we study this positivity phenomenon more closely,…
Using the generalized Temperley trick, we demonstrate the explicit embedding of circular electrical networks into totally non-negative Grassmannians. Building on this result, we show that the effective resistances between boundary nodes of…
We study a new invariant of circular planar electrical networks, well known to phylogeneticists: the circular split system. We use our invariant to answer some open questions about levels of complexity of networks and their related…
Existing network embedding approaches tackle the problem of learning low-dimensional node representations. However, networks can also be seen in the light of edges interlinking pairs of nodes. The broad goal of this paper is to introduce…
This paper presents a unified algebraic, topological, and logical framework for electrical one-port networks based on \v{S}are's $m$-theory. Within this formalism, networks are represented by $m$-words (jorbs) over an ordered alphabet,…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
The response matrix of a resistor network is the linear map from the potential at the boundary vertices to the net current at the boundary vertices. For circular planar resistor networks, Curtis, Ingerman, and Morrow have given a necessary…
The present paper is the continuity of the previous papers "Non-linear field theory" I and II. Here on the basis of the electromagnetic representation of Dirac's electron theory we consider the geometrical distribution of the…
We propose a new approach to studying electrical networks interpreting the Ohm law as the operator which solves certain Local Yang-Baxter equation. Using this operator and the medial graph of the electrical network we define a vertex…
Starting with an experimentally observed networks of actin bundles, we model their network structure in terms of edges and nodes. We then compute and discuss the main electrical parameters, considering the bundles as electrical wires. A set…
This paper introduces E(n) Equivariant Message Passing Cellular Networks (EMPCNs), an extension of E(n) Equivariant Graph Neural Networks to CW-complexes. Our approach addresses two aspects of geometric message passing networks: 1)…
Electrical circuits offer a unique platform to explore physical phenomena, from topology to non-Hermitian effects. Investigations of the fundamental properties of this metamaterial platform are crucial to distinguish observed/measured…