Results 31 to 40 of about 57,263 (168)
Discrete Morse functions for graph configuration spaces
, 2012 We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice
A Sawicki +10 more
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Graph 4-braid groups and Massey products [PDF]
, 2014 We first show that the braid group over a graph topologically containing no $\Theta$-shape subgraph has a presentation related only by commutators. Then using discrete Morse theory and triple Massey products, we prove that a graph topologically contains ...
Hyo +3 more
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Discrete microlocal Morse theory
Journal of Pure and Applied AlgebraWe 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 CombinatoricsFor 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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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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A practical guide to characterising ecological coexistence. [PDF]
Biol Rev Camb Philos SocABSTRACT Coexistence is simultaneously one of the most fundamental concepts of ecology, and one of the most difficult to define. A particular challenge is that, despite a well‐developed body of research, several different schools of thought have developed over the past century, leading to multiple independent, and largely isolated, branches of ...
Clark AT +9 more
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Multiparameter discrete Morse theory
Journal of Applied and Computational TopologyThe 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 +2 more
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, 2011 We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works.
Bruggesser +6 more
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Smoothing discrete Morse theory [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2016 After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete Morse theory are equivalent, in the sense that every discrete Morse vector on some PL triangulation is also a PL handle vector, and conversely, every PL handle ...
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The Morse theory of \v{C}ech and Delaunay complexes
, 2016 Given a finite set of points in $\mathbb R^n$ and a radius parameter, we study the \v{C}ech, Delaunay-\v{C}ech, Delaunay (or Alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the \v{C}ech and Delaunay complexes as
Bauer, Ulrich, Edelsbrunner, Herbert
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