Results 21 to 30 of about 1,238,875 (302)
The treewidth of 2-section of hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Let $H=(V,F)$ be a simple hypergraph without loops. $H$ is called linear if $|f\cap g|\le 1$ for any $f,g\in F$ with $f\not=g$. The $2$-section of $H$, denoted by $[H]_2$, is a graph with $V([H]_2)=V$ and for any $ u,v\in V([H]_2)$, $uv\in E([H]_2)$ if ...
Ke Liu, Mei Lu
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Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks [PDF]
LOG IN, 2023 Our study reveals new theoretical insights into over-smoothing and feature over-correlation in graph neural networks. Specifically, we demonstrate that with increased depth, node representations become dominated by a low-dimensional subspace that depends
Andreas Roth, T. Liebig
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Tensor rank and other multipartite entanglement measures of graph states [PDF]
Physical Review A, 2022 Graph states play an important role in quantum information theory through their connection to measurement-based computing and error correction. Prior work has revealed elegant connections between the graph structure of these states and their multipartite
Louis Schatzki +3 more
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Perron-Frobenius theory and KMS states on higher-rank graph C*-Algebras
, 2019 In this thesis, we study the Perron-Frobenius theory for irreducible matrices and irreducible family of commuting matrices in detail. We then apply it to study the KMS states of the $C^*$-algebras of $ k $-graphs. To be more precise, we define the Toeplitz algebra $ \mathcal{T}C^{*}(\Lambda) $ and $C^*$-algebra $ C^{*}(\Lambda) $ for a $ k $-graph ...
Samandeep Singh
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Evaluation of Water Distribution Network Partitioning Methods Based on Graph Theory Using AHP [PDF]
آب و فاضلاب, 2020 The dramatic decline in renewable water resources, leakage and pollution in water distribution systems has led to a significant increase in the focus on leakage management and control approaches in most parts of the world.
Vida Dahrazma +1 more
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Современные информационные технологии и IT-образование, 2021 The theory discussed in the article refers to the theory of functional systems. This branch of mathematics explores functions defined on finite sets, as well as the composition of these functions.
Dmitriy Eremenko
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Exponential Graph Regularized Non-Negative Low-Rank Factorization for Robust Latent Representation
Mathematics, 2022 Non-negative matrix factorization (NMF) is a fundamental theory that has received much attention and is widely used in image engineering, pattern recognition and other fields.
Guowei Yang, Lin Zhang, Minghua Wan
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PLoS ONE, 2022 Organized into a global network of critical infrastructures, the oil & gas industry remains to this day the main energy contributor to the world's economy. Severe accidents occasionally occur resulting in fatalities and disruption.
Arnaud Mignan +4 more
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Lanczos method for spatio‐temporal graph convolutional networks to forecast expressway flow
IET Intelligent Transport Systems, 2023 Traffic forecasting has made pronounced progress with the development of graph convolution networks and the use of the topology of road networks. However, existing works face some limitations when it comes to modelling spatial dependencies.
Zhumei Gou, Yonggang Shen, Shuifu Chen
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A program for finding all KMS states on the Toeplitz algebra of a higher-rank graph [PDF]
Journal of operator theory, 2018 The Toeplitz algebra of a finite graph of rank k carries a natural action of the torus Tk, and composing with an embedding of R in Tk gives a dynamics on the Toeplitz algebra.
James Fletcher +2 more
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