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Graph Theory versus Minimum Rank for Index Coding [PDF]
2014 IEEE International Symposium on Information Theory, 2014 We obtain novel index coding schemes and show that they provably outperform all previously known graph theoretic bounds proposed so far. Further, we establish a rather strong negative result: all known graph theoretic bounds are within a logarithmic factor from the chromatic number.
Karthikeyan Shanmugam +2 more
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A dual graph construction for higher-rank graphs, and 𝐾-theory for finite 2-graphs [PDF]
Proceedings of the American Mathematical Society, 2005 Given a k k -graph Λ \Lambda and an element p p of N k \mathbb {N}^k , we define the dual k k -graph, p Λ p\Lambda .
Stephen Allen, David Pask, Aidan Sims
core +10 more sources
Real and complex K-theory for higher rank graph algebras arising from cube complexes [PDF]
Annals of K-TheoryUsing the Evans spectral sequence and its counter-part for real $K$-theory, we compute both the real and complex $K$-theory of several infinite families of $C^*$-algebras based on higher-rank graphs of rank $3$ and $4$. The higher-rank graphs we consider arise from double-covers of cube complexes. By considering the real and complex $K$-theory together,
Jeffrey L. Boersema, Alina Vdovina
semanticscholar +5 more sources
Feature Construction Using Network Control Theory and Rank Encoding for Graph Machine Learning [PDF]
IEEE Open Journal of Control SystemsIn this article, we utilize the concept of average controllability in graphs, along with a novel rank encoding method, to enhance the performance of Graph Neural Networks (GNNs) in social network classification tasks. GNNs have proven highly effective in
Anwar Said +5 more
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THE K-THEORY OF THE -ALGEBRAS OF 2-RANK GRAPHS ASSOCIATED TO COMPLETE BIPARTITE GRAPHS [PDF]
Journal of the Australian Mathematical Society, 2021 AbstractUsing a result of Vdovina, we may associate to each complete connected bipartite graph$\kappa $a two-dimensional square complex, which we call a tile complex, whose link at each vertex is$\kappa $. We regard the tile complex in two different ways, each having a different structure as a$2$-rank graph.
Sam A. Mutter
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Structure theory and stable rank for C*-algebras of finite higher-rank graphs [PDF]
Proceedings of the Edinburgh Mathematical Society, 2021 AbstractWe study the structure and compute the stable rank of$C^{*}$-algebras of finite higher-rank graphs. We completely determine the stable rank of the$C^{*}$-algebra when the$k$-graph either contains no cycle with an entrance or is cofinal. We also determine exactly which finite, locally convex$k$-graphs yield unital stably finite$C^{*}$-algebras ...
David Pask, Adam Sierakowski, Aidan Sims
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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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$C^{\star}$-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory [PDF]
Publicacions Matemàtiques, 2023 We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action on the product of trees defines a $k$-dimensional cube complex, which induces a higher-rank graph.
Sam A. Mutter +2 more
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K-theory and homotopies of 2-cocycles on higher-rank graphs [PDF]
Pacific Journal of Mathematics, 2015 This paper continues our investigation into the question of when a homotopy $ = \{ _t\}_{t \in [0,1]}$ of 2-cocycles on a locally compact Hausdorff groupoid $\mathcal{G}$ gives rise to an isomorphism of the $K$-theory groups of the twisted groupoid $C^*$-algebras: $K_*(C^*(\mathcal{G}, _0)) \cong K_*(C^*(\mathcal{G}, _1)).$ In particular, we ...
Elizabeth Gillaspy
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Remote Sensing, 2020 The accuracy of anomaly detection in hyperspectral images (HSIs) faces great challenges due to the high dimensionality, redundancy of data, and correlation of spectral bands.
Shangzhen Song +3 more
doaj +2 more sources