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We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex…
In this paper, we shall prove the uniform sharp $L^p$ decay estimates for a class of oscillatory integral operators with polynomial phases. By this one-dimensional result, we can use the rotation method to obtain uniform sharp $L^p$…
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. Keywords: Weil representation,…
In this paper, we present a novel estimation and control strategy to balance a formation of discrete-time oscillators on a circle. We consider the case in which each oscillator only gathers noisy proximity measurements, whose range is lower…
This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…
We consider the problem of an harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the…
Set-valued state estimation when in the presence of uncertainties in the model have been addressed in the literature essentially following three main approaches: i) interval arithmetic of the uncertain dynamics with the estimates; ii)…
The purpose of this note is to prove a stationary phase estimate well adapted to parameter dependent phases. In particular, no discussion is made on the positions (and behaviour) of critical points, no lower or upper bound on the gradient…
The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby…
We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of oscillatory Riemann-Hilbert problems associated with partial…
A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
This note formulates a deterministic recovery result for vectors $x$ from quadratic measurements of the form $(Ax)_i \overline{(Ax)_j}$ for some left-invertible $A$. Recovery is exact, or stable in the noisy case, when the couples $(i,j)$…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We consider nonlinear inverse problems described by operator equations in Banach spaces. Assuming conditional stability of the inverse problem, that is, assuming that stability holds on a closed, convex subset of the domain of the operator,…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
This mostly expository paper centers on recently proved conjectures in two areas: A) A conjecture of A. Oppenheim on the values of real indefinite quadratic forms at integral points. B) Conjectures of Dani, Raghunathan, and Margulis on…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
Phase aberrations, despite degrading ultrasound images, also encode valuable information about the spatial distribution of the speed of sound in tissue. In pulse-echo ultrasound, we can quantify them by exploiting speckle correlations.…