Results 21 to 30 of about 1,393 (155)

Topology of matching complexes of complete graphs via discrete Morse theory [PDF]

Discrete Mathematics & Theoretical Computer Science
Bouc (1992) first studied the topological properties of $M_n$, the matching complex of the complete graph of order $n$, in connection with Brown complexes and Quillen complexes. Bj\"{o}rner et al. (1994) showed that $M_n$ is homotopically $(\nu_n-1)$
Anupam Mondal, Sajal Mukherjee, Kuldeep Saha   +2 more
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Adaptive Discrete Vector Field in Sensor Networks

Sensors, 2018
Homology groups are a prime tool for measuring the connectivity of a network, and their computation in a distributed and adaptive way is mandatory for their use in sensor networks.
Mengyi Zhang, Alban Goupil
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Discrete Morse Theory for Computing Zigzag Persistence [PDF]

Discrete & Computational Geometry, 2019
We introduce a theoretical and computational framework to use discrete Morse theory as an efficient preprocessing in order to compute zigzag persistent homology. From a zigzag filtration of complexes $(K_i)$, we introduce a zigzag Morse filtration whose complexes $(A_i)$ are Morse reductions of the original complexes $(K_i)$, and we prove that they ...
Maria, Clément, Schreiber, Hannah
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Decidability of the isomorphism and the factorization between minimal substitution subshifts

Discrete Analysis, 2022
Decidability of the isomorphism and the factorization between minimal substitution subshifts, Discrete Analysis 2022:7, 65 pp. Symbolic dynamics is the study of topological dynamical systems $(X,S)$ where $X$ is a shift-invariant space of singly or ...
Fabien Durand, Julien Leroy
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Automatic Detection of Cross-Shaped Targets for Laser Scan Registration

IEEE Access, 2018
Laser scan registration estimates a relative transformation to match one scan with another, based on the shape of the overlapping portions of the scans. The core and challenging problem of scan registration in a large-scale scene is, how to detect public
Cheng Yi, Hongwen Xing, Qiaoyun Wu, Yuan Zhang, Mingqiang Wei, Bo Wang, Laishui Zhou   +6 more
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Discrete microlocal Morse theory

Journal of Pure and Applied Algebra
We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category of sheaves on a poset with the Alexandrov topology. We prove that each bounded complex of sheaves on a finite poset
Adam Brown, Ondřej Draganov
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Existence of acyclic matching and Morse complex on transitive digraphs

AKCE International Journal of Graphs and Combinatorics
For any digraph, there exists a transitive closure. The transitive digraph is a discrete geometric object which has a close relationship with simplicial complex.
Chong Wang, Shiquan Ren
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Estimate of Number of Periodic Solutions of Second-Order Asymptotically Linear Difference System

Abstract and Applied Analysis, 2013
We investigate the number of periodic solutions of second-order asymptotically linear difference system. The main tools are Morse theory and twist number, and the discussion in this paper is divided into three cases. As the system is resonant at infinity,
Honghua Bin, Zhenkun Huang
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Multiparameter discrete Morse theory

Journal of Applied and Computational Topology
The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition to adapting the main definitions and results of Forman to this vectorial setting, we use concepts of ...
Guillaume Brouillette, Madjid Allili, Tomasz Kaczynski   +2 more
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Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems

Discrete Dynamics in Nature and Society, 2010
We consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case.
Bo Zheng
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