Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Adamaszek, Michal"'
Autor:
Adamaszek, Michał, Adams, Henry
We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs at small scale parameters. In more detail, let $Q_n$ be the vertex set of the hypercube graph with $2^n$ vertices, equipped with the shortest path metric. Equivalently, $Q_
Externí odkaz:
http://arxiv.org/abs/2103.01040
Autor:
Adamaszek, Michal, Adams, Henry, Gasparovic, Ellen, Gommel, Maria, Purvine, Emilie, Sazdanovic, Radmila, Wang, Bei, Wang, Yusu, Ziegelmeier, Lori
We study Vietoris-Rips complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips complexes. We also provide g
Externí odkaz:
http://arxiv.org/abs/1712.06224
Publikováno v:
SIAM J. Appl. Algebra Geom. 2 (4), 597-619 (2018)
Given a sample of points $X$ in a metric space $M$ and a scale $r>0$, the Vietoris-Rips simplicial complex $\mathrm{VR}(X;r)$ is a standard construction to attempt to recover $M$ from $X$ up to homotopy type. A deficiency of this approach is that $\m
Externí odkaz:
http://arxiv.org/abs/1706.04876
Publikováno v:
Journal of Topology and Analysis 11 (2019), 661-690
For $X$ a metric space and $r>0$ a scale parameter, the Vietoris-Rips complex $VR_<(X;r)$ (resp. $VR_\leq(X;r)$) has $X$ as its vertex set, and a finite subset $\sigma\subseteq X$ as a simplex whenever the diameter of $\sigma$ is less than $r$ (resp.
Externí odkaz:
http://arxiv.org/abs/1704.04956
Publikováno v:
Discrete & Computational Geometry 58(3):526-542 (2017)
The Rips complex at scale r of a set of points X in a metric space is the abstract simplicial complex whose faces are determined by finite subsets of X of diameter less than r. We prove that for X in the Euclidean 3-space R^3 the natural projection m
Externí odkaz:
http://arxiv.org/abs/1602.04131
Autor:
Adamaszek, Michal
In this work we study simplicial complexes associated to graphs and their homotopical and combinatorial properties. The main focus is on the family of flag complexes, which can be viewed as independence complexes and clique complexes of graphs. In th
Externí odkaz:
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.560420
Publikováno v:
Advances in Applied Mathematics 83 (2017), 1-23
For X a finite subset of the circle and for 0 < r <= 1 fixed, consider the function f_r : X -> X which maps each point to the clockwise furthest element of X within angular distance less than 2 pi r. We study the discrete dynamical system on X genera
Externí odkaz:
http://arxiv.org/abs/1511.07832
Autor:
Adamaszek, Michal
We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. The proof uses th
Externí odkaz:
http://arxiv.org/abs/1508.02426
Autor:
Adamaszek, Michal, Hladký, Jan
Publikováno v:
Mathematika 62 (2016) 909-928
We prove that among all flag triangulations of manifolds of odd dimension 2r-1 with sufficiently many vertices the unique maximizer of the entries of the f-, h-, g- and gamma-vector is the balanced join of r cycles. Our proof uses methods from extrem
Externí odkaz:
http://arxiv.org/abs/1503.05961
Autor:
Adamaszek, Michal, Adams, Henry
Publikováno v:
Pacific Journal of Mathematics 290-1 (2017), 1-40
Given a metric space X and a distance threshold r>0, the Vietoris-Rips simplicial complex has as its simplices the finite subsets of X of diameter less than r. A theorem of Jean-Claude Hausmann states that if X is a Riemannian manifold and r is suffi
Externí odkaz:
http://arxiv.org/abs/1503.03669