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Journal of Mathematical Analysis and Applications, 2012 We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott's computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines a continuous bundle of twisted higher-rank graph algebras over the dual group. We use this to show that for
Alex Kumjian, David Pask, Aidan Sims
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A Note on Brill–Noether Theory and Rank-Determining Sets for Metric Graphs [PDF]
International Mathematics Research Notices, 2012 We produce open subsets of the moduli space of metric graphs without separating edges where the dimensions of Brill-Noether loci are larger than the corresponding Brill-Noether numbers. These graphs also have minimal rank determining sets that are larger than expected, giving couterexamples to a conjecture of Luo.
Chang Mou Lim +2 more
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Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study [PDF]
Journal of High Energy Physics, 2020 We carry out a detailed exploration of the deformations of rank-two five-dimensional superconformal field theories (SCFTs) T X $$ {\mathcal{T}}_{\mathbf{X}} $$ , which are geometrically engineered by M-theory on the space transverse to isolated toric ...
Vivek Saxena
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Dilation Theory for Rank 2 Graph Algebras
, 2007 29 pages, 5 ...
Kenneth R. Davidson +2 more
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On the K-theory of higher rank graph C*-algebras
, 2004 Given a row-finite $k$-graph $ $ with no sources we investigate the $K$-theory of the higher rank graph $C^*$-algebra, $C^*( )$. When $k=2$ we are able to give explicit formulae to calculate the $K$-groups of $C^*( )$. The $K$-groups of $C^*( )$ for $k>2$ can be calculated under certain circumstances and we consider the case $k=3$. We prove that
D. Gwion Evans
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Asymptotic tensor rank of graph tensors: beyond matrix multiplication [PDF]
Computational Complexity, 2016 We present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on k vertices.
M. Christandl +2 more
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Identifying Influential Nodes Based on Evidence Theory in Complex Network [PDF]
EntropyInfluential node identification is an important and hot topic in the field of complex network science. Classical algorithms for identifying influential nodes are typically based on a single attribute of nodes or the simple fusion of a few attributes ...
Fu Tan +5 more
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On the K-theory of twisted higher-rank-graph C*-algebras [PDF]
, 2012 Alex Kumjian, David Pask, Aidan Sims
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Dilation theory for rank two graph algebras.
, 2010 An analysis is given of $*$-representations of rank 2 single vertex graphs. We develop dilation theory for the non-selfadjoint algebras $\A_\theta$ and $\A_u$ which are associated with the commutation relation permutation $\theta$ of a 2-graph and, more generally, with commutation relations determined by a unitary matrix $u$ in $M_m(\bC) \otimes M_n ...
Kenneth R. Davidson +2 more
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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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