Related papers: On Weak Observability For Evolution Systems with S…
We address the inverse problem of reconstructing both the structure and dynamics of a network from mean-field measurements, which are linear combinations of node states. This setting arises in applications where only a few aggregated…
We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the…
Compressed sensing (CS) is a powerful tool for reducing the amount of data to be collected while maintaining high spatial resolution. Such techniques work well in practice and at the same time are supported by solid theory. Standard CS…
Two-points nonlocal problem for the first order differential evolution equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified in assumption that the…
Generative adversarial networks (GANs) learn a deep generative model that is able to synthesise novel, high-dimensional data samples. New data samples are synthesised by passing latent samples, drawn from a chosen prior distribution,…
We use the method of similar operators to study a mixed problem for a differential equation with an involution and an operator-valued potential function. The differential operator defined by the equation is transformed into a similar…
This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic…
The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and…
Minimum phase functions are fundamental in a range of applications, including control theory, communication theory and signal processing. A basic mathematical challenge that arises in the context of geophysical imaging is to understand the…
The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to…
Quantum process tomography provides a means of measuring the evolution operator for a system at a fixed measurement time $t$. The problem of using that tomographic snapshot to predict the evolution operator at other times is generally…
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…
With advances in Generative Adversarial Networks (GANs) leading to dramatically-improved synthetic images and video, there is an increased need for algorithms which extend traditional forensics to this new category of imagery. While GANs…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…