Zobrazeno 1 - 10
of 345
pro vyhledávání: '"MIXON, DUSTIN G."'
Autor:
Alexeev, Boris, Mixon, Dustin G.
We correct errors that appear throughout "The vicious neighbour problem" by Tao and Wu. We seek to solve the following problem. Suppose $N$ nerds are distributed uniformly at random in a square region. At 3:14pm, every nerd simultaneously snipes thei
Externí odkaz:
http://arxiv.org/abs/2409.06068
Autor:
Alexeev, Boris, Mixon, Dustin G.
For a uniformly distributed population, we show that with high probability, any majority-minority voting district containing a fraction of the population necessarily exhibits a tiny Polsby-Popper score.
Externí odkaz:
http://arxiv.org/abs/2408.05832
We consider the coding problem in the Stiefel manifold with chordal distance. After considering various low-dimensional instances of this problem, we use Rankin's bounds on spherical codes to prove upper bounds on the minimum distance of a Stiefel co
Externí odkaz:
http://arxiv.org/abs/2407.01813
We describe a flexible technique that constructs tight fusion frames with prescribed transitive symmetry. Applying this technique with representations of the symmetric and alternating groups, we obtain several new infinite families of equi-isoclinic
Externí odkaz:
http://arxiv.org/abs/2406.19542
We prove the existence of a positive semidefinite matrix $A \in \mathbb{R}^{n \times n}$ such that any decomposition into rank-1 matrices has to have factors with a large $\ell^1-$norm, more precisely $$ \sum_{k} x_k x_k^*=A \quad \implies \quad \sum
Externí odkaz:
http://arxiv.org/abs/2405.06154
Autor:
Qaddura, Yousef, Mixon, Dustin G.
Given a real inner product space $V$ and a group $G$ of linear isometries, we construct a family of $G$-invariant real-valued functions on $V$ that we call coorbit filter banks, which unify previous notions of max filter banks and finite coorbit filt
Externí odkaz:
http://arxiv.org/abs/2403.14042
Consider the quotient of a Hilbert space by a subgroup of its automorphisms. We study whether this orbit space can be embedded into a Hilbert space by a bilipschitz map, and we identify constraints on such embeddings.
Externí odkaz:
http://arxiv.org/abs/2305.17241
In 1992, Godsil and Hensel published a ground-breaking study of distance-regular antipodal covers of the complete graph that, among other things, introduced an important connection with equi-isoclinic subspaces. This connection seems to have been ove
Externí odkaz:
http://arxiv.org/abs/2212.12617
Autor:
Mixon, Dustin G., Qaddura, Yousef
Given a real inner product space V and a group G of linear isometries, max filtering offers a rich class of G-invariant maps. In this paper, we identify nearly sharp conditions under which these maps injectively embed the orbit space V/G into Euclide
Externí odkaz:
http://arxiv.org/abs/2212.11156
Autor:
Mixon, Dustin G., Packer, Daniel
Given a finite-dimensional real inner product space V and a finite subgroup G of linear isometries, max filtering affords a bilipschitz Euclidean embedding of the orbit space V/G. We identify the max filtering maps of minimum distortion in the settin
Externí odkaz:
http://arxiv.org/abs/2212.05104