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Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...
We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of pos ...
We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...
This letter investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs enjoy, by design, ...
We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient di ...
This paper proposes a computational approach to form-find pin-jointed bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet structural and geometrical constraints via gradient-based optimizati ...
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrain ...
The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...
Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and of ...
We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a cont ...
