4 citations · 7 across the 9 of their papers we have counts for
13 papers
Polynomial potential minimization on the unit circle
Josiah Park
In the following, we study the minimization of polynomial potentials on the unit circle, where the potentials take the form \[ f(t) = \sum_{i=1}^n b_i x^{2i}, \quad b_i \i…
Optimal Measures for Multivariate Geometric Potentials
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of p…
Optimizers of three-point energies and nearly orthogonal sets
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
This paper is devoted to spherical measures and point configurations optimizing three-point energies. Our main goal is to extend the classic optimization problems based on pairs of…
Grassmannian packings: Trust-region stochastic tuning for matrix incoherence
Josiah Park, Carlos Saltijeral, Ming Zhong
We provide a new numerical procedure for constructing low coherence matrices, Trust-Region Stochastic Tuning for Matrix Incoherence (TRSTMI) and detail the results of experiments w…
Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation
Josiah Park, Stephan Wojtowytsch
In this article, we prove approximation theorems in classes of deep and shallow neural networks with analytic activation functions by elementary arguments. We prove for both real a…
Neural Network Approximation of Refinable Functions
Ingrid Daubechies, Ronald DeVore, Nadav Dym +6
In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approxi…
Potential theory with multivariate kernels
Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin +3
In the present paper we develop the theory of minimization for energies with multivariate kernels, i.e. energies, in which pairwise interactions are replaced by interactions betwee…
Energy on spheres and discreteness of minimizing measures
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal meas…
Optimal measures for p-frame energies on spheres
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
We provide new answers about the placement of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the -frame energies, i.e. energie…
Frame Potentials and Orthogonal Vectors
Josiah Park
An extension is given of a recent result of Glazyrin, showing that an orthonormal basis joined with the vectors , where min…
Lattices from tight frames and vertex transitive graphs
Lenny Fukshansky, Deanna Needell, Josiah Park +1
We show that real tight frames that generate lattices must be rational, and use this observation to describe a construction of lattices from vertex transitive graphs. In the case o…
Repeated minimizers of -frame energies
Alexey Glazyrin, Josiah Park
For a collection of unit vectors , define the -frame energy of as the quantity . In this…
Balian-Low Theorems in Several Variables
Michael Northington, Josiah Park
Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on . Here we extend these results to a multivariable setting…