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The minimum rank problem: A counterexample
Linear Algebra and its Applications, 2008 We provide a counterexample to a recent conjecture that the minimum rank of every sign pattern matrix can be realized by a rational matrix. We use one of the equivalences of the conjecture and some results from projective geometry. As a consequence of the counterexample, we show that there is a graph for which the minimum rank over the reals is ...
Kopparty, Swastik, Bhaskara Rao, K.P.S.
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Minimum Distance Tests and Estimates Based on Ranks
Revstat Statistical Journal, 2020 It is well known that the least squares estimate in classical linear regression model is very sensitive to violation of the assumptions, in particular normality of model errors.
Radim Navrátil
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Low frequency groans indicate larger and more dominant fallow deer (Dama dama) males. [PDF]
PLoS ONE, 2008 BACKGROUND: Models of honest advertisement predict that sexually selected calls should signal male quality. In most vertebrates, high quality males have larger body sizes that determine higher social status and in turn higher reproductive success ...
Elisabetta Vannoni, Alan G McElligott
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A note on the minimum skew rank of a graph [PDF]
, 2012 The minimum skew rank $mr^{-}(\mathbb{F},G)$ of a graph $G$ over a field $\mathbb{F}$ is the smallest possible rank among all skew symmetric matrices over $\mathbb{F}$, whose ($i$,$j$)-entry (for $i\neq j$) is nonzero whenever $ij$ is an edge in $G$ and ...
Bo Zhoub, R Esearch Article, Yanna Wanga
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Remote Sensing, 2019 A hyperspectral image (HSI) contains abundant spatial and spectral information, but it is always corrupted by various noises, especially Gaussian noise.
Xiangyang Kong +3 more
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Minimum vector rank and complement critical graphs [PDF]
The Electronic Journal of Linear Algebra, 2014 Given a graph G, a real orthogonal representation of G is a function from its set of vertices to R^d such that two vertices are mapped to orthogonal vectors if and only if they are not neighbors. The minimum vector rank of a graph is the smallest dimension d for which such a representation exists.
Li, Xiaowei +2 more
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Efficient Rank Reduction of Correlation Matrices [PDF]
, 2005 Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature.
Grubisic, Igor, Pietersz, Raoul
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Bounds on List Decoding of Rank-Metric Codes [PDF]
, 2012 So far, there is no polynomial-time list decoding algorithm (beyond half the minimum distance) for Gabidulin codes. These codes can be seen as the rank-metric equivalent of Reed--Solomon codes.
Wachter-Zeh, Antonia
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Lower Bounds in Minimum Rank Problems
Linear Algebra and its Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mitchell, Lon +2 more
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Minimum n-rank approximation via iterative hard thresholding [PDF]
Applied Mathematics and Computation, 2015 The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics such as image inpainting and video inpainting.
Zhang, Min, Yang, Lei, Huang, Zheng-Hai
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