Related papers: The twist for electrical networks and the inverse …
We provide a new solution to the classical black box problem (the discrete Calderon problem) in the theory of circular electrical networks. Our approach is based on the explicit embedding of electrical networks into non-negative…
In this paper we study the inverse Dirichlet-to-Neumann problem for certain cylindrical electrical networks. We define and study a birational transformation acting on cylindrical electrical networks called the electrical $R$-matrix. We use…
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 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…
The aim of this paper is to discuss a relationship between total positivity and planar directed networks. We show that the inverse boundary problem for these networks is naturally linked with the study of the totally nonnegative…
We study the optical response of the alternating twisted trilayer graphene by making use of a unitary transformation for the trilayer Hamiltonian and the Kubo formulation of linear response theory. The layer-resolved optical conductivities…
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…
The inverse problem of fractional Brownian motion and other Gaussian processes with stationary increments involves inverting an infinite hermitian positively definite Toeplitz matrix (a matrix that has equal elements along its diagonals).…
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 define and study the Pfaffian state on Riemann surfaces with arbitrary metrics and an inhomogeneous magnetic field and derive its universal transport coefficients. Following a path integral approach, we compute the generating functional…
The main purpose of this work is to study an inverse coefficient problem for the telegrapher's equations on a tree-shaped network. To analyze the stability for this inverse problem, Carleman estimate is established first. Based upon this…
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 review a resistor network approach to the numerical solution of the inverse problem of electrical impedance tomography (EIT). The networks arise in the context of finite volume discretizations of the elliptic equation for the electric…
This paper is devoted to the inverse design of strained graphene surfaces for the control of electrons in the semi-classical optical-like regime. Assuming that charge carriers are described by the Dirac equation in curved-space and…
A positive function (conductivity) on the edges of a graph induces the Dirichlet-to- Neumann map between boundary values of harmonic functions. The inverse conductivity problem is to find the conductivity from the Dirichlet-to-Neumann map.…
We study the inverse problem of recovering a tree graph together with the weights on its edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. We prove an explicit formula…
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…
We calculate the perpendicular electrical conductivity in twisted three-dimensional graphite (rotationally stacked graphite pieces) by using the effective continuum model and the recursive Green's function method. In the low twist angle…
We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors…
In this article we present a method to reconstruct the interconnectedness of dynamically related stochastic processes, where the interactions are bi-directional and the underlying topology is a tree. Our approach is based on multivariate…