Related papers: On an inverse problem for tree-like networks of el…

This paper revisits the classical problem "Can we hear the density of a string?", which can be formulated as an inverse spectral problem for a Sturm-Liouville operator. Based on inverting a sequence of trace formulas, we propose a new…

We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, being measured in the direction to a specific boundary…

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [arXiv: 1908.10529] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio…

In this paper we study the inverse problem of determining the residual stress in Man's model using tomographic data. Theoretically, the tomographic data is obtained at zero approximation of geometrical optics for Man's residual stress…

Study of a simple single-trace transmission example shows how an extended source formulation of full-waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via…

An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…

We introduce the graph theoretical parameter of edge treewidth. This parameter occurs in a natural way as the tree-like analogue of cutwidth or, alternatively, as an edge-analogue of treewidth. We study the combinatorial properties of…

Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…

In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric…

In this article we study the inverse problem of determining a semilinear term appearing in an elliptic equation from boundary measurements. Our main objective is to develop flexible and general theoretical results that can be used for…

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…

The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

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…

This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…

Some data analysis problems require the computation of (regularised) inverse traces, i.e. quantities of the form $\Tr (q \bI + \bL)^{-1}$. For large matrices, direct methods are unfeasible and one must resort to approximations, for example…

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using…

We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…

Let G be an undirected graph on n vertices and let S(G) be the set of all real symmetric n x n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The inverse inertia problem for G…

This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…