Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Hans Parshall"'
Publikováno v:
Applied and Computational Harmonic Analysis. 65:279-295
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 corresponding to the symmetry group of the underlying manifold. We derive the sam
We establish that if $d \geq 2k + 6$ and $q$ is odd and sufficiently large with respect to $\alpha \in (0,1)$, then every set $A\subseteq \mathbf{F}_q^d$ of size $|A| \geq \alpha q^d$ will contain an isometric copy of every spherical $(k+2)$-point co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74170673f40834296928c784524103f4
http://arxiv.org/abs/2301.11306
http://arxiv.org/abs/2301.11306
Autor:
Dustin G. Mixon, Hans Parshall
Publikováno v:
SIAM Journal on Discrete Mathematics. 35:234-249
For $d\in\{5,6\}$, we classify arrangements of $d + 2$ points in $\mathbf{RP}^{d-1}$ for which the minimum distance is as large as possible. To do so, we leverage ideas from matrix and convex analysis to determine the best possible codes that contain
Publikováno v:
Constructive Approximation. 53:381-402
We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish concerning the distribution of the singular values of random subensembles of Paley equiangular tight frames. Our analysis applies more generally to real equiangul
Autor:
Hans Parshall, Dustin G. Mixon
Publikováno v:
Experimental Mathematics. 31:474-485
How can we arrange $n$ lines through the origin in three-dimensional Euclidean space in a way that maximizes the minimum interior angle between pairs of lines? Conway, Hardin and Sloane (1996) produced line packings for $n \leq 55$ that they conjectu
Publikováno v:
Mosc. J. Comb. Number Theory 8, no. 2 (2019), 103-115
Let [math] be a finite field of order [math] . We prove that if [math] is even and [math] with [math] then ¶ F q = Δ ( E ) Δ ( E ) = { a b : a ∈ Δ ( E ) , b ∈ Δ ( E ) ∖ { 0 } } , ¶ where ¶ Δ ( E ) = { ∥ x − y ∥ : x , y ∈ E } ,
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 neural collapse also emerges empirically. By studying this model, we provid
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::163a76b979d3c98e067a795f7d7f06ac
http://arxiv.org/abs/2011.11619
http://arxiv.org/abs/2011.11619
Autor:
Hans Parshall
Publikováno v:
Proceedings of the American Mathematical Society. 145:2323-2334
We prove that, provided $d > k$, every sufficiently large subset of $\mathbf{F}_q^d$ contains an isometric copy of every $k$-simplex that avoids spanning a nontrivial self-orthogonal subspace. We obtain comparable results for simplices exhibiting sel
The Lov\'{a}sz theta number is a semidefinite programming bound on the clique number of (the complement of) a given graph. Given a vertex-transitive graph, every vertex belongs to a maximal clique, and so one can instead apply this semidefinite progr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::824f7a3e5da2914e6da89db37330a99e
http://arxiv.org/abs/1907.05971
http://arxiv.org/abs/1907.05971
Publikováno v:
2019 13th International conference on Sampling Theory and Applications (SampTA).
The line packing problem is concerned with the optimal packing of points in real or complex projective space so that the minimum distance between points is maximized. Until recently, all bounds on optimal line packings were known to be derivable from