6 papers
On volume vectors determined by hypergraphs in thin subsets of Euclidean space
Tainara Borges, Ben Foster, Yumeng Ou +2
Generalizing the Falconer distance problem, the authors of this paper recently established the first non-trivial dimensional threshold for any distance graph in high enough of a di…
Falconer-type results for any finite graph with multiple pins
Tainara Borges, Ben Foster, Yumeng Ou +2
A generalization of the celebrated Falconer distance problem asks for a graph , with vertex set and edge set , how large the…
Quantifying Extrinsic Curvature in Neural Manifolds
Francisco Acosta, Sophia Sanborn, Khanh Dao Duc +2
The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In…
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…
Distinct Angles and Angle Chains in Three Dimensions
Ruben Ascoli, Livia Betti, Jacob Lehmann Duke +6
In 1946, Erdős posed the distinct distance problem, which seeks to find the minimum number of distinct distances between pairs of points selected from any configuration of poin…
A Mattila-Sjölin theorem for triangles
Eyvindur Ari Palsson, Francisco Romero Acosta
We show for a compact set , , that if the Hausdorff dimension of is larger than , then the set of congruence classes of triang…