Journal ArticleDOI
Finding Topology in a Factory: Configuration Spaces
Aaron Abrams,Robert Ghrist +1 more
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In this paper, the topology in a factory is described as a configuration space in the form of a topology, where the configuration space is composed of a set of configuration spaces.Abstract:
(2002). Finding Topology in a Factory: Configuration Spaces. The American Mathematical Monthly: Vol. 109, No. 2, pp. 140-150.read more
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Journal ArticleDOI
An introduction to right-angled Artin groups
TL;DR: Recently, right-angled Artin groups have attracted much attention in geometric group theory as mentioned in this paper, and they have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications.
Journal ArticleDOI
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
John Crisp,Bert Wiest +1 more
TL;DR: In this paper, it was shown that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and that the Euler characteristic −1 surface group (given by the relation x 2 y 2 = z 2 ) never embeds in a right-angle Artin group.
Book ChapterDOI
Persistent homology for random fields and complexes
TL;DR: In this paper, the authors discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes, and discuss how these are related to understanding more about manifold learning from random point cloud data.
Journal ArticleDOI
Discrete Morse theory and graph braid groups
Daniel Farley,Lucas Sabalka +1 more
TL;DR: In this article, a discrete version of Morse theory is applied to the configuration space of n points on, denoted U C n, and the braid group of on n strands is defined.
Journal ArticleDOI
Coordinating Multiple Droplets in Planar Array Digital Microfluidic Systems
Eric J. Griffith,Srinivas Akella +1 more
TL;DR: A general-purpose system that uses simple algorithms and yet is versatile is described that has been able to successfully coordinate hundreds of droplets simultaneously and perform one or more chemical analyses in parallel.
References
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Book
Robot Motion Planning
TL;DR: This chapter discusses the configuration space of a Rigid Object, the challenges of dealing with uncertainty, and potential field methods for solving these problems.
Book
Braids, Links, and Mapping Class Groups
TL;DR: Artin's braid group has been studied extensively in the literature as discussed by the authors, where structural and algebraic properties of the braid groups of two manifolds of two different scales have been studied.
Book
The complexity of robot motion planning
TL;DR: John Canny resolves long-standing problems concerning the complexity of motion planning and, for the central problem of finding a collision free path for a jointed robot in the presence of obstacles, obtains exponential speedups over existing algorithms by applying high-powered new mathematical techniques.
Journal ArticleDOI
Robot navigation functions on manifolds with boundary
Daniel E. Koditschek,Elon Rimon +1 more
TL;DR: In this paper, a class of scalar valued analytic maps on analytic manifolds with boundary is constructed on an arbitrary sphere world, a compact connected subset of Euclidean n-space whose boundary is formed from the disjoint union of a finite number of (n - l)-spheres.
Journal ArticleDOI
On the self‐linking of knots
Raoul Bott,Clifford Henry Taubes +1 more
TL;DR: In this paper, a subcomplex F of the de Rham complex of parametrized knot space is described, which is combinatorial over a number of universal "Anomaly Integrals".