Related papers: An introduction to pointwise sparse domination
Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space…
The study of domination in graphs has led to a variety of domination problems studied in the literature. Most of these follow the following general framework: Given a graph $G$ and an integer $k$, decide if there is a set $S$ of $k$…
The paper introduces notions of robustness margins geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and in engineering, a theory of robustness for behaviors away from…
In this note we give simple proofs of several results involving maximal truncated Calde\'on-Zygmund operators in the general setting of rearrangement invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to…
Nous poursuivons l'\'etude d'un contr\^ole \'epars d'un op\'erateur singulier. Plus pr\'ecis\'ement nous expliquons comment on peut conserver certaines propri\'et\'es de l'op\'erateur initial \`a travers un tel contr\^ole et d\'ecrivons…
This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…
As AI models achieve remarkable capabilities across diverse domains, understanding what representations they learn and how they encode concepts has become increasingly important for both scientific progress and trustworthy deployment.…
Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are extremely sparse, which severely limits the applicability of both…
This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function, which can equip distributed networks with robust learning capability in the presence of impulsive interference. In order to…
Direction-of-arrival (DOA) estimation refers to the process of retrieving the direction information of several electromagnetic waves/sources from the outputs of a number of receiving antennas that form a sensor array. DOA estimation is a…
The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…
This is an expository paper on the helicoidal method, a tool designed for proving multiple vector-valued inequalities for operators in harmonic analysis, which is based on stopping times and localizations. As it turns out, the local…
In this paper, using a new technique from harmonic analysis called sparse domination, we characterize the positive Borel measures including forward, vanishing, and reverse Bergman Carleson measures. The main novelty of this paper is…
We prove a new type of pointwise estimate of the Kalamajska-Mazya-Shaposhnikova type, where sparse averaging operators replace the maximal operator. It allows us to extend the Gagliardo-Nirenberg interpolation inequality to all…
Pairwise debiasing is one of the most effective strategies in reducing position bias in learning-to-rank (LTR) models. However, limiting the scope of this strategy, are the underlying assumptions required by many pairwise debiasing…
In this paper we refine the recent sparse domination of the integrated $p = 2$ matrix weighted dyadic square function by T. Hytonen, S. Petermichl, and A. Volberg to prove a pointwise sparse domination of general matrix weighted dyadic…
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…
In this note, we show that if $T$ is a Calder\'on--Zygmund operator satisfying $T(1)=0$, then the usual sparse domination for $T$ can be sharpened by replacing local averages by local mean oscillations. As an application, we characterize…
Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…
Overparametrized Deep Neural Networks (DNNs) have demonstrated remarkable success in a wide variety of domains too high-dimensional for classical shallow networks subject to the curse of dimensionality. However, open questions about…