12 citations · 22 across the 11 of their papers we have counts for
17 papers
The Erdős unit distance problem for small point sets
Boris Alexeev, Dustin G. Mixon, Hans Parshall
We improve the best known upper bound on the number of edges in a unit-distance graph on vertices for each . When , our bounds match the best kn…
Generalized point configurations in
Paige Bright, Xinyu Fang, Barrett Heritage +4
In this paper, we generalize \cite{IosevichParshall}, \cite{LongPaths} and \cite{cycles} by allowing the \emph{distance} between two points in a finite field vector space to be def…
Spherical Configurations over Finite Fields
Neil Lyall, Akos Magyar, Hans Parshall
We establish that if and is odd and sufficiently large with respect to , then every set of size will con…
Neural collapse with unconstrained features
Dustin G. Mixon, Hans Parshall, Jianzong Pi
Neural collapse is an emergent phenomenon in deep learning that was recently discovered by Papyan, Han and Donoho. We propose a simple "unconstrained features model" in which neura…
Lie PCA: Density estimation for symmetric manifolds
Jameson Cahill, Dustin G. Mixon, Hans Parshall
We introduce an extension to local principal component analysis for learning symmetric manifolds. In particular, we use a spectral method to approximate the Lie algebra correspondi…
Uniquely optimal codes of low complexity are symmetric
Emily J. King, Dustin G. Mixon, Hans Parshall +1
We formulate explicit predictions concerning the symmetry of optimal codes in compact metric spaces. This motivates the study of optimal codes in various spaces where these predict…