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Nontrivial solutions of discrete Kirchhoff-type problems via Morse theory
Advances in Nonlinear Analysis, 2022 In this article, we study discrete Kirchhoff-type problems when the nonlinearity is resonant at both zero and infinity. We establish a series of results on the existence of nontrivial solutions by combining variational method with Morse theory.
Long Yuhua
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The Elser nuclei sum revisited [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Fix a finite undirected graph $\Gamma$ and a vertex $v$ of $\Gamma$. Let $E$ be the set of edges of $\Gamma$. We call a subset $F$ of $E$ pandemic if each edge of $\Gamma$ has at least one endpoint that can be connected to $v$ by an $F$-path (i.e., a ...
Darij Grinberg
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Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems
Advances in Difference Equations, 2007 An existence result of multiple periodic solutions to the asymptotically linear discrete Hamiltonian systems is obtained by using the Morse index theory.
Bo Zheng
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Merging Discrete Morse Vector Fields: A Case of Stubborn Geometric Parallelization
Algorithms, 2021 We address the basic question in discrete Morse theory of combining discrete gradient fields that are partially defined on subsets of the given complex. This is a well-posed question when the discrete gradient field V is generated using a fixed algorithm
Douglas Lenseth, Boris Goldfarb
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Combinatorial Topology of Toric arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We prove that the complement of a complexified toric arrangement has the homotopy type of a minimal CW-complex, and thus its homology is torsion-free.
Giacomo d'Antonio, Emanuele Delucchi
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Boundary Value Problem for a Second-Order Difference Equation with Resonance
Complexity, 2020 In this paper, we study the existence and multiplicity of nontrivial solutions of a second-order discrete boundary value problem with resonance and sublinear or superlinear nonlinearity.
Zhenguo Wang, Zhan Zhou
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Negative $q$-Stirling numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The notion of the negative $q$-binomial was recently introduced by Fu, Reiner, Stanton and Thiem. Mirroring the negative $q$-binomial, we show the classical $q$ -Stirling numbers of the second kind can be expressed as a pair of statistics on a subset of ...
Yue Cai, Margaret Readdy
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Line Structure Extraction from LiDAR Point Cloud Based on the Persistence of Tensor Feature
Applied Sciences, 2022 The LiDAR point cloud has been widely used in scenarios of automatic driving, object recognition, structure reconstruction, etc., while it remains a challenging problem in line structure extraction, due to the noise and accuracy, especially in data ...
Xuan Wang +3 more
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Graph skeletonization of high-dimensional point cloud data via topological method
Journal of Computational Geometry, 2022 Geometric graphs form an important family of hidden structures behind data. In this paper, we develop an efficient and robust algorithm to infer a graph skeleton of a high-dimensional point cloud dataset (PCD).
Lucas Magee, Yusu Wang
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Research on P System with Chain Structure and Application and Simulation in Arithmetic Operation
Discrete Dynamics in Nature and Society, 2015 Considering the advantages of distribution and maximum parallelism of membrane computing and availability of discrete Morse theory to deal with discrete structure, in this paper, combining discrete Morse theory and membrane computing, a novel membrane ...
Jing Luan, Zhong Yao
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