Results 1 to 10 of about 332,055 (262)
A Minimum Rank Approach for Reduction of Environmental Noise in Near-Field Array Antenna Diagnosis [PDF]
Journal of Imaging, 2019 A method to filter out the contribution of interference sources in array diagnosis is proposed. The interference-affected near field measured on a surface is treated as a (complex-data) image.
Marco Donald Migliore +4 more
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Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph [PDF]
INFORMS Journal on Computing, 2022 The minimum rank of a graph G is the minimum of the ranks of all symmetric adjacency matrices of G. We present a new combinatorial bound for the minimum rank of an arbitrary graph G based on enumerating certain subsets of vertices of G satisfying matroid theoretic properties.
Illya V Hicks +2 more
exaly +3 more sources
On the Hardness of the Decoding and the Minimum Distance Problems for Rank Codes [PDF]
IEEE Transactions on Information Theory, 2016 In this paper we give a randomized reduction for the Rank Syndrome Decoding problem and Rank Minimum Distance problem for rank codes. Our results are based on an embedding from linear codes equipped with Hamming distance unto linear codes over an extension field equipped with the rank metric.
Philippe Gaborit, Gilles Zémor
exaly +4 more sources
ADMiRA: Atomic Decomposition for Minimum Rank Approximation [PDF]
IEEE Transactions on Information Theory, 2010 A short version (arXiv:0901.1898) will be presented at ISIT ...
Kiryung Lee, Yoram Bresler
exaly +3 more sources
Subgraph Complementation and Minimum Rank [PDF]
The Electronic Journal of Combinatorics, 2022 Any finite simple graph $G = (V,E)$ can be represented by a collection $\mathscr{C}$ of subsets of $V$ such that $uv\in E$ if and only if $u$ and $v$ appear together in an odd number of sets in $\mathscr{C}$. Let $c_2(G)$ denote the minimum cardinality of such a collection.
Calum Buchanan +2 more
openaire +3 more sources
Bounds on the Minimum Edge Dominating Energy in Terms of Some Parameters of a Graph [PDF]
Mathematics Interdisciplinary Research, 2023 The minimum edge dominating energy, denoted by $EE_{F}(G)$, is the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of graph $G$.
Fateme Movahedi
doaj +1 more source
Polytopes of Minimum Positive Semidefinite Rank [PDF]
Discrete & Computational Geometry, 2013 The positive semidefinite (psd) rank of a polytope is the smallest $k$ for which the cone of $k \times k$ real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals ...
João Gouveia +2 more
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State-independent quantum contextuality with projectors of nonunit rank
New Journal of Physics, 2021 Virtually all of the analysis of quantum contextuality is restricted to the case where events are represented by rank-one projectors. This restriction is arbitrary and not motivated by physical considerations.
Zhen-Peng Xu +2 more
doaj +1 more source
Maximum nullity and zero forcing of circulant graphs
Special Matrices, 2020 The zero forcing number of a graph has been applied to communication complexity, electrical power grid monitoring, and some inverse eigenvalue problems.
Duong Linh +4 more
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Reducing the rank of a matroid [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider the rank reduction problem for matroids: Given a matroid $M$ and an integer $k$, find a minimum size subset of elements of $M$ whose removal reduces the rank of $M$ by at least $k$. When $M$ is a graphical matroid this problem is the minimum $
Gwenaël Joret, Adrian Vetta
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