Results 171 to 180 of about 521,410 (206)

Reconstruction of the vietoris topology from compacta in the space of closed subgroups

Ukrainian Mathematical Journal, 1990
See the review in Zbl 0702.22009.
A. Piskunov
semanticscholar   +2 more sources

Vietoris thickenings and complexes are weakly homotopy equivalent

Journal of Applied and Computational Topology, 2023
Characterizing the homotopy types of the Vietoris–Rips complexes $${{\,\textrm{VR}\,}}(X;r)$$ VR ( X ; r ) of a metric space X is in general a difficult problem. The Vietoris–Rips metric thickening $${{\,\textrm{VR}\,}}^m(X;r)$$ VR m ( X ; r ) , a metric
P. Gillespie
semanticscholar   +1 more source

Homotopy Types of Vietoris-Rips Complexes of Hypercube Graphs

Journal of Topology and Analysis (JTA), 2023
We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs at scale $3$. We represent the vertices in the hypercube graph $Q_m$ as the collection of all subsets of $[m]=\{1, 2, \ldots, m\}$ and equip $Q_m$ with the metric using ...
Ziqin Feng
semanticscholar   +1 more source

Vietoris–Rips Complexes of Torus Grids

Mediterranean Journal of Mathematics
We study the topology of Vietoris–Rips complexes of finite grids on the torus. Let Tn,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
Henry Adams, Adenike Yeside Adetowubo, Hector Barriga-Acosta, Ziqin Feng, John Sterling   +4 more
semanticscholar   +1 more source

The connectivity of Vietoris–Rips complexes of spheres

Journal of Applied and Computational Topology
We survey what is known and unknown about Vietoris–Rips complexes and thickenings of spheres. Afterwards, we show how to control the homotopy connectivity of Vietoris–Rips complexes of spheres in terms of coverings of spheres and projective spaces.
Henry Adams, Johnathan Bush, Žiga Virk
semanticscholar   +1 more source

Topology-based analysis and optimization for agent fleet behavior

Open Research Europe
We introduce novel topological methods for analyzing the behaviors and navigation of an agent fleet. Our goal is to understand and enhance the evolution of agent fleet behaviors to minimize unintended behaviors, such as collisions and deadlocks ...
Javier Perera-Lago, Víctor Toscano-Durán, Álvaro Torras-Casas, Rocío González-Díaz   +3 more
semanticscholar   +1 more source

Topology-Driven Clustering: Enhancing Performance with Betti Number Filtration

arXiv.org
Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges.
Arghya Pratihar, Kushal Bose, Swagatam Das   +2 more
semanticscholar   +1 more source

Persistent interaction topology in data analysis

Foundations of Data Science
Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields.
Jian Liu, Dong Chen, Guo-Wei Wei
semanticscholar   +1 more source

Regular Multimeasures in the Vietoris Topology

2022
Alina Gavriluţ, Endre Pap
openaire   +1 more source

Exceptional topology of non-Hermitian systems

Reviews of Modern Physics, 2021
Emil J Bergholtz, Jan Carl Budich, Flore K Kunst   +2 more
exaly