Related papers: On sparse interpolation and the design of determin…
In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vall\'ee Poussin filters. These polynomials can be an useful device for many theoretical and…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
We introduce and study the unconstrained polarization (or Chebyshev) problem which requires to find an $N$-point configuration that maximizes the minimum value of its potential over a set $A$ in $p$-dimensional Euclidean space. This problem…
Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive…
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved…
We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical…
The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there…
Sparsity, defined as the presence of missing or zero values in a dataset, often poses a major challenge while operating on real-life datasets. Sparsity in features or target data of the training dataset can be handled using various…
The calibration of modern radio interferometers is a significant challenge, specifically at low frequencies. In this perspective, we propose a novel iterative calibration algorithm, which employs the popular sparse representation framework,…
We present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C$^1$ continuity and its partial derivatives are analytically…
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…
A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic…
Graph-based methods play an important role in unsupervised and semi-supervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semi-supervised learning and…