4 papers
Nonlocal techniques for the analysis of deep ReLU neural network approximations
Cornelia Schneider, Mario Ullrich, Jan Vybiral
Recently, Daubechies, DeVore, Foucart, Hanin, and Petrova introduced a system of piece-wise linear functions, which can be easily reproduced by artificial neural networks with the…
Lower bounds on the minimal dispersion of point sets via cover-free families
Matěj Trödler, Jan Volec, Jan Vybíral
We elaborate on the intimate connection between the largest volume of an empty axis-parallel box in a set of points from and cover-free families from the extremal set…
Robust network formation with biological applications
Jan Haskovec, Jan Vybiral
We provide new results on the structure of optimal transportation networks obtained as minimizers of an energy cost functional consisting of a kinetic (pumping) and material (metab…
A tight lower bound on the minimal dispersion
Matěj Trödler, Jan Volec, Jan Vybíral
We give a new lower bound for the minimal dispersion of a point set in the unit cube and its inverse function in the high dimension regime. This is done by considering only a very…