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We consider parameter estimation of ordinary differential equation (ODE) models from noisy observations. For this problem, one conventional approach is to fit numerical solutions (e.g., Euler, Runge--Kutta) of ODEs to data. However, such a…

Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with support Oracle for compressed sensing sparse reconstructions, where the available…

We introduce an analytical framework to calculate the values of key observables in a strongly disordered discrete time crystal (DTC) without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement…

Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…

We study two numerical approximations of solutions of nonlocal diffusion evolution problems which are inspired in algorithms for computing the bilateral denoising filtering of an image, and which are based on functional rearrangements and…

In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this…

This paper addresses the problem of resilient state estimation and attack reconstruction for bounded-error nonlinear discrete-time systems with nonlinear observations/ constraints, where both sensors and actuators can be compromised by…

A considerable amount of research in harmonic analysis has been devoted to non-linear estimators of signals contaminated by additive Gaussian noise. They are implemented by thresholding coefficients in a frame, which provide a sparse signal…

We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…

This paper is concerned with the state estimation problem for two-dimensional systems with asynchronous multichannel delays and energy harvesting constraints. In the system, each smart sensor has a certain probability of harvesting energy…

This paper proposes a novel Distributed Unknown Input Observer (DUIO) framework for state estimation in large-scale systems subject to local unknown inputs. We consider systems where outputs are measured by a network of spatially…

We propose an unrolled algorithm approach for learning spatially adaptive parameter maps in the framework of convolutional synthesis-based $\ell_1$ regularization. More precisely, we consider a family of pre-trained convolutional filters…

Convolutional neural networks (CNN) have improved speech recognition performance greatly by exploiting localized time-frequency patterns. But these patterns are assumed to appear in symmetric and rigid kernels by the conventional CNN…

This paper revisits a classical scenario in communication theory: a waveform sampled at regular intervals is to be encoded so as to minimize distortion in its reconstruction, despite noise. This transformation must be online (causal), to…

Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…

It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikhonov regularization require heuristic parameter tuning, and…

A new adaptive observer is proposed for a certain class of nonlinear systems with bounded unknown input and parametric uncertainty. Unlike most existing solutions, the proposed approach ensures asymptotic convergence of the unknown…

The problem of estimating the shift (or, equivalently, the center of symmetry) of an unknown symmetric and periodic function $f$ observed in Gaussian white noise is considered. Using the blockwise Stein method, a penalized profile…