noise in spectral fluctuations of complex networks

Bin, Ye; Li, Huijun; Ma, Xiaoping

doi:10.1016/j.physa.2010.07.023

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…It is well known that most disturbances in the battery usage environments follow the characteristics of

noise [37] , [38] . In order to stimulate more dynamic characteristics and protect the battery, a nondestructive

noise signal is superimposed to the input current, where the

noise is optimized by the

index [39] .…”

Section: Battery Test Platformmentioning

confidence: 99%

Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion

Podlubný

et al. 2020

Journal of Advanced Research

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Graphical abstract The fractional-order modeling with structure identification, parameter estimation and the ability of revealing natures of battery are considered. The correlative information criterion is proposed based on the 1/ f noise assisted I/O data, which is adept in evaluating the reliability of model structure and adaptiveness of model parameters. Experimental results validate the above conclusions.

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“…It is well known that most disturbances in the battery usage environments follow the characteristics of

noise [37] , [38] . In order to stimulate more dynamic characteristics and protect the battery, a nondestructive

noise signal is superimposed to the input current, where the

noise is optimized by the

index [39] .…”

Section: Battery Test Platformmentioning

confidence: 99%

Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion

Podlubný

et al. 2020

Journal of Advanced Research

View full text Add to dashboard Cite

show abstract

Random-matrix spectra as a time series

2013

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Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding possible artifacts introduced by standard unfolding techniques. The fluctuation modes are scale invariant and follow different power laws for Poisson and Gaussian ensembles, which already during the unfolding allows to distinguish the two cases.PACS numbers: 05.45. Tp,05.45.Mt,02.50.Sk The study of spectral fluctuations within the framework of Random Matrix Theory (RMT) is a standard tool in the statistical study of quantum chaos in the excitation spectra of quantum systems [1][2][3][4]. Recently, the approach has found new applications in many fields, such as in the study of eigenspectra of adjacency matrices of networks [5][6][7], and eigenspectra of empirical correlation matrices in finance [8][9][10], the climate [11], electro-and magnetoencephalography [12][13][14], and in complex systems [15]. The interest of the approach lies in the fact that the level density fluctuations ρ(E) = ρ(E) − ρ(E) around the smooth global density ρ(E) are universal and indicate the underlying symmetry class of the system [2,16]. On the other hand, the global level density ρ(E) is system dependent, and an unfolding procedure needs to be performed, to separate the global and the fluctuating parts [1]. The unfolding is straightforward if an analytical formula is known to describe the global level density ρ(E) for the system under study, such as e.g. the gaussian and semicircle distributions for Possion and GOE matrix ensembles from RMT [2], or the MarchenkoPastur distribution for the Laguerre ensemble of random Wishart correlation matrices [17]. However, such analytical formulae are formally only adequate in the asymptotic limit for spectra with an infinite number of levels. Often, an analytical form for ρ(E) is unknown, as is the case for adjacency matrices [5]. In practical cases, having finite, albeit large matrices, the usual approach is then to project the sequence of ordered eigenvalues into unfolded values E(n) → N [E(n)], using a smooth (often polynomial) approximation N (E) to the accumulated density , 5, 20]. After unfolding, the short-range and long-range correlations can be quantified using standard fluctuations measures such as the Nearest-Neighbour Spacing (NNS) distribution, number variance Σ 2 and ∆ 3 . In a recent approach, the unfolded fluctuations of the accumulated level density function N (E) = N (E) − N (E) (also called δ n function) *

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noise in spectral fluctuations of complex networks

Cited by 2 publications

References 11 publications

Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion

Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion

Random-matrix spectra as a time series

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