Results 71 to 80 of about 121,870 (266)
Mathematics, 2023 In this paper, we introduce the concepts of Harary Laplacian-energy-like for a simple undirected and connected graph G with order n. We also establish novel matrix results in this regard. Furthermore, by employing matrix order reduction techniques, we derive upper and lower bounds utilizing existing graph invariants and vertex connectivity. Finally, we
Luis Medina +2 more
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Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley +1 more source
On the Eigenvalues and Energy of the Seidel and Seidel Laplacian Matrices of Graphs
Discrete Dynamics in Nature and SocietyLet SΓ be a Seidel matrix of a graph Γ of order n and let DΓ=diagn−1−2d1,n−1−2d2,…,n−1−2dn be a diagonal matrix with di denoting the degree of a vertex vi in Γ. The Seidel Laplacian matrix of Γ is defined as SLΓ=DΓ−SΓ.
J. Askari +2 more
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Some Properties of the Eigenvalues of the Net Laplacian Matrix of a Signed Graph
Discussiones Mathematicae Graph Theory, 2022 Given a signed graph Ġ, let AĠ and DG˙±D_{\dot G}^ \pm denote its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of Ġ is defined to be NG˙=DG˙±-AG˙{N_{\dot G}} = D_{\dot G}^ \pm - {A_{\dot
Stanić Zoran
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Composition‐Aware Cross‐Sectional Integration for Spatial Transcriptomics
Advanced Intelligent Discovery, EarlyView.Multi‐section spatial transcriptomics demands coherent cell‐type deconvolution, domain detection, and batch correction, yet existing pipelines treat these tasks separately. FUSION unifies them within a composition‐aware latent framework, modeling reads as cell‐type–specific topics and clustering in embedding space.
Qishi Dong +5 more
wiley +1 more source
On the Eigenvalues of General Sum-Connectivity Laplacian Matrix [PDF]
Journal of the Operations Research Society of China, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Deng, Hanyuan, Huang, He, Zhang, Jie
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Advanced Intelligent Systems, EarlyView.This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
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On Path Laplacian Eigenvalues and Path Laplacian Energy of Graphs
Journal of New Theory, 2018 We introduce the concept of Path Laplacian Matrix for a graph and explore the eigenvalues of this matrix. The eigenvalues of this matrix are called the path Laplacian eigenvalues of the graph.
Shridhar Chandrakant Patekar +1 more
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Advanced Intelligent Systems, EarlyView.This paper presents a high‐speed object pose estimation method that deconstructs objects into geometric components. Inspired by human cognitive generalization, it detects these primitives and infers the 6D pose from their stable spatial configuration.
Xuyang Li +6 more
wiley +1 more source
Bipartite subgraphs and the signless Laplacian matrix
Applicable Analysis and Discrete Mathematics, 2011 For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalized Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs.
Steve Kirkland, Debdas Paul
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