Zobrazeno 1 - 10
of 98
pro vyhledávání: '"Knudson, Kevin"'
Autor:
Johnson, Lacey, Knudson, Kevin
A classical result in Morse theory is the determination of the homotopy type of the loop space of a manifold. In this paper, we study this result through the lens of discrete Morse theory. This requires a suitable simplicial model for the loop space.
Externí odkaz:
http://arxiv.org/abs/2407.12156
We develop a discrete Morse theory for open simplicial complexes $K=X\setminus T$ where $X$ is a simplicial complex and $T$ a subcomplex of $X$. A discrete Morse function $f$ on $K$ gives rise to a discrete Morse function on the order complex $S_K$ o
Externí odkaz:
http://arxiv.org/abs/2402.12116
Autor:
Knudson, Kevin P.
Publikováno v:
Algorithms 13 (7) (2020), 172
We define the notion of an approximate triangulation for a manifold $M$ embedded in euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertices lie in $M$ and use persistent homology to find a complex in the fam
Externí odkaz:
http://arxiv.org/abs/2006.13993
Autor:
Johnson, Lacey, Knudson, Kevin
In the study of smooth functions on manifolds, min-max theory provides a mechanism for identifying critical values of a function. In this paper we introduce a discretized version of this theory associated to a discrete Morse function on a (regular) c
Externí odkaz:
http://arxiv.org/abs/1811.00719
Autor:
Blanchard, Eion, Knudson, Kevin
In recent decades, state legislatures have often drawn U.S. Congressional voting districts that look---to the human eye---to be rather twisted. In this paper, we propose a method to measure how much districts "meander" via a computation of the medial
Externí odkaz:
http://arxiv.org/abs/1805.08208
Autor:
Knudson, Kevin, Wang, Bei
Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and MacPherson. We desc
Externí odkaz:
http://arxiv.org/abs/1801.03183
Autor:
Knudson, Kevin
Publikováno v:
Math Horizons, 2020 Nov 01. 28(2), 15-17.
Externí odkaz:
https://www.jstor.org/stable/48664924
Autor:
Sjoberg, Laura, Knudson, Kevin
We use the theory of persistent homology to analyze a data set arising from the study of various aspects of democracy. Our results show that most "mature" democracies look more or less the same, in the sense that they form a single connected componen
Externí odkaz:
http://arxiv.org/abs/1506.01104
Autor:
Knudson, Kevin P.
We show that the group $H_2(\slzti;\zz)$ is not finitely generated, answering a question mentioned by Bux and Wortman in \cite{bux}.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/0808.1239
Suppose $M$ is a finite simplicial complex and that for $0=t_0,t_1,...,t_r=1$ we have a discrete Morse function $F_{t_i}:M\to \zr$. In this paper, we study the births and deaths of critical cells for the functions $F_{t_i}$ and present an algorithm f
Externí odkaz:
http://arxiv.org/abs/0808.0051