46 citations · 413 across the 115 of their papers we have counts for
6 papers · 1 filter
VC-Dimension and Distance Chains in
Ruben Ascoli, Livia Betti, Justin Cheigh +8
Given a domain and a collection of functions , the Vapnik-Chervonenkis (VC) dimension of measures its complexity in an appropriate s…
Fractal dimension, approximation and data sets
L. Betti, I. Chio, J. Fleischman +13
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Princi…
Nonempty interior of configuration sets via microlocal partition optimization
Allan Greenleaf, Alex Iosevich, Krystal Taylor
We prove new results of Mattila-Sjölin type, giving lower bounds on Hausdorff dimensions of thin sets ensuring that various -point configuration sets, genera…
Pinned simplices and connections to product of sets on paraboloids
Alex Iosevich, Quy Pham, Thang Pham +1
In this paper we obtain improved dimensional thresholds for dot product sets corresponding to compact subsets of a paraboloid. As a direct application of these estimates, we obtain…
Dot products in and the Vapnik-Chervonenkis dimension
A. Iosevich, B. McDonald, M. Sun
Given a set , where is the field with elements. Consider a set of "classifiers" , where if…
Uniform distribution and geometric incidence theory
A. Gafni, A. Iosevich, E. Wyman
A celebrated unit distance conjecture due to Erd\H os says that that the unit distances cannot arise more than times (for any ) among points in the Euclidean…