Rational realization of maximum eigenvalue multiplicity of symmetric tree sign patterns

Atoshi Chowdhury; Leslie Hogben; Jude Melancon; Rana Mikkelson

doi:10.1016/j.laa.2006.02.017

Rational realization of maximum eigenvalue multiplicity of symmetric tree sign patterns

Linear Algebra and its Applications ◽

10.1016/j.laa.2006.02.017 ◽

2006 ◽

Vol 418 (2-3) ◽

pp. 380-393 ◽

Cited By ~ 2

Author(s):

Atoshi Chowdhury ◽

Leslie Hogben ◽

Jude Melancon ◽

Rana Mikkelson

Keyword(s):

Maximum Eigenvalue ◽

Sign Patterns ◽

Symmetric Tree

Download Full-text

Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns

Linear Algebra and its Applications ◽

10.1016/j.laa.2006.02.018 ◽

2006 ◽

Vol 418 (2-3) ◽

pp. 394-415 ◽

Cited By ~ 10

Author(s):

Luz Maria DeAlba ◽

Timothy L. Hardy ◽

Irvin Roy Hentzel ◽

Leslie Hogben ◽

Amy Wangsness

Keyword(s):

Maximum Eigenvalue ◽

Minimum Rank ◽

Sign Patterns ◽

Symmetric Tree

Download Full-text

Optimal topology for maximum eigenvalue using density-dependent material model

10.2514/6.1996-1627 ◽

1996 ◽

Cited By ~ 1

Author(s):

B. Wang ◽

C. Lu ◽

R. Yang

Keyword(s):

Material Model ◽

Optimal Topology ◽

Maximum Eigenvalue ◽

Density Dependent

Download Full-text

Sarnak’s conjecture for sequences of almost quadratic word growth

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2020.94 ◽

2020 ◽

pp. 1-56

Author(s):

REDMOND MCNAMARA

Keyword(s):

Box Dimension ◽

Multiplicative Functions ◽

Logarithmic Density ◽

Liouville Function ◽

Sign Patterns

Abstract We prove the logarithmic Sarnak conjecture for sequences of subquadratic word growth. In particular, we show that the Liouville function has at least quadratically many sign patterns. We deduce the main theorem from a variant which bounds the correlations between multiplicative functions and sequences with subquadratically many words which occur with positive logarithmic density. This allows us to actually prove that our multiplicative functions do not locally correlate with sequences of subquadratic word growth. We also prove a conditional result which shows that if the ( $\kappa -1$ )-Fourier uniformity conjecture holds then the Liouville function does not correlate with sequences with $O(n^{t-\varepsilon })$ many words of length n where $t = \kappa (\kappa +1)/2$ . We prove a variant of the $1$ -Fourier uniformity conjecture where the frequencies are restricted to any set of box dimension less than $1$ .

Download Full-text

Analysis of grid operation state based on improved maximum eigenvalue sample covariance matrix algorithm

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/09596518211001270 ◽

2021 ◽

pp. 095965182110012

Author(s):

Dinghui Wu ◽

Juan Zhang ◽

Bo Wang ◽

Tinglong Pan

Keyword(s):

Covariance Matrix ◽

Signal To Noise Ratio ◽

Poor Performance ◽

Sample Covariance Matrix ◽

Maximum Eigenvalue ◽

Signal To Noise ◽

Matrix Algorithm ◽

Sample Covariance ◽

Noise Ratio ◽

Application Fields

Traditional static threshold–based state analysis methods can be applied to specific signal-to-noise ratio situations but may present poor performance in the presence of large sizes and complexity of power system. In this article, an improved maximum eigenvalue sample covariance matrix algorithm is proposed, where a Marchenko–Pastur law–based dynamic threshold is introduced by taking all the eigenvalues exceeding the supremum into account for different signal-to-noise ratio situations, to improve the calculation efficiency and widen the application fields of existing methods. The comparison analysis based on IEEE 39-Bus system shows that the proposed algorithm outperforms the existing solutions in terms of calculation speed, anti-interference ability, and universality to different signal-to-noise ratio situations.

Download Full-text