Related papers: Mixed norm spaces and rearrangement invariant esti…
We investigate the relationship between the compactness of embeddings of Sobolev spaces built upon rearrangement-invariant spaces into rearrangement-invariant spaces endowed with $d$-Ahlfors measures under certain restriction on the speed…
Magnetic resonance imaging (MRI) is mainly limited by long scanning time and vulnerable to human tissue motion artifacts, in 3D clinical scenarios. Thus, k-space undersampling is used to accelerate the acquisition of MRI while leading to…
We propose neural network layers that explicitly combine frequency and image feature representations and show that they can be used as a versatile building block for reconstruction from frequency space data. Our work is motivated by the…
In this work, we prove uniform continuity bounds for entropic quantities related to the sandwiched R\'enyi divergences such as the sandwiched R\'enyi conditional entropy. We follow three different approaches: The first one is the "almost…
We study moduli spaces of twisted maps to a smooth pair in arbitrary genus, and give geometric explanations for previously known comparisons between orbifold and logarithmic Gromov--Witten invariants. Namely, we study the space of twisted…
A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement- invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in…
To accelerate MRI, the field of compressed sensing is traditionally concerned with optimizing the image quality after a partial undersampling of the measurable $\textit{k}$-space. In our work, we propose to change the focus from the quality…
In this paper we investigate the mapping properties in Lebesgue-type spaces of certain generalized Radon transforms defined by integration over curves.
Given a set of points \F in a high dimensional space, the problem of finding a union of subspaces \cup_i V_i\subset \R^N that best explains the data \F increases dramatically with the dimension of \R^N. In this article, we study a class of…
We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis. As an application, uniform estimates for the expected value of averages of order…
Multimodal machine learning has gained significant attention in recent years due to its potential for integrating information from multiple modalities to enhance learning and decision-making processes. However, it is commonly observed that…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
This paper contains some estimates for the {\it integral-uniform} norm and the uniform norm of a wide class of random polynomials. The family of integral-uniform norms introduced by Kasin and Tzafriri is a natural generalization of the…
We make four contributions to the theory of optimal subspace packings and equi-isoclinic subspaces: (1) a new lower bound for block coherence, (2) an exact count of equi-isoclinic subspaces of even dimension $r$ in $\mathbb{R}^{2r+1}$ with…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
We study the optimal domain for the Hardy operator considered with values in a rearrangement invariant space. In particular, this domain can be represented as the space of integrable functions with respect to a vector measure defined on a…
The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number…
Undersampled inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined linear or non-linear reconstruction problems. There are now a myriad of techniques to design decoders…
We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization…