Fluctuation Scaling and 1/f Noise

Kendal, Wayne S.

doi:10.5963/jbap0202002

Cited by 14 publications

(9 citation statements)

References 26 publications

(44 reference statements)

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“…Power laws such as the electrophysiological power spectrum arise from a large /f 1 χ number of physical sources (Kendal, W.S., 2013). In neural electrophysiology, aspects of the power spectral slope have been attributed to shot and brownian noise (Mandelbrot, B.B.…”

Section: Steeper Slope May Reflect Increased Inhibitory Conductancementioning

confidence: 99%

Aperiodic neural activity is a better predictor of schizophrenia than neural oscillations

Rosen

Belger

et al. 2017

Preprint

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Schizophrenia has been associated with separate irregularities in several neural oscillatory frequency bands, including theta, alpha, and gamma. Our multivariate classification suggests that instead of irregularities in many frequency bands, schizophrenia-related EEG differences may better be explained by an overall shift in neural noise, reflected by a change in the 1/f slope of the power spectrum. Significance statementUnderstanding the neurobiological origins of schizophrenia, and identifying reliable biomarkers, are both of critical importance in improving treatment of that disease. While we lack predictive biomarkers, numerous studies have observed disruptions to neural oscillations in schizophrenia patients. This literature has, in part, lead to schizophrenia being characterized as disease of disrupted neural coordination. We report however that changes to background noise (i.e., 1/f noise) are a substantially better predictor of schizophrenia than oscillatory power. The observed alterations in neural noise are consistent with inhibitory neuron dysfunctions associated with schizophrenia, allowing for a direct link between noninvasive EEG and neurobiological deficits.

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Section: Steeper Slope May Reflect Increased Inhibitory Conductancementioning

confidence: 99%

Aperiodic neural activity is a better predictor of schizophrenia than neural oscillations

Rosen

Belger

et al. 2017

Preprint

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“…In fact, Taylor's power law is one of over 100 power laws discovered in physics, economics, social science and biology. Power laws are extensively studied in physics, and in particular, in the studies of phase transitions in thermodynamics and complex systems where the emergence of power law is associated with phase transitions (Kendal , ; Eisler et al . ; Ma ).…”

Section: Introductionmentioning

confidence: 99%

Power law analysis of the human microbiome

Sam

2015

Molecular Ecology

147

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Taylor's (1961, Nature, 189:732) power law, a power function (V = am(b) ) describing the scaling relationship between the mean and variance of population abundances of organisms, has been found to govern the population abundance distributions of single species in both space and time in macroecology. It is regarded as one of few generalities in ecology, and its parameter b has been widely applied to characterize spatial aggregation (i.e. heterogeneity) and temporal stability of single-species populations. Here, we test its applicability to bacterial populations in the human microbiome using extensive data sets generated by the US-NIH Human Microbiome Project (HMP). We further propose extending Taylor's power law from the population to the community level, and accordingly introduce four types of power-law extensions (PLEs): type I PLE for community spatial aggregation (heterogeneity), type II PLE for community temporal aggregation (stability), type III PLE for mixed-species population spatial aggregation (heterogeneity) and type IV PLE for mixed-species population temporal aggregation (stability). Our results show that fittings to the four PLEs with HMP data were statistically extremely significant and their parameters are ecologically sound, hence confirming the validity of the power law at both the population and community levels. These findings not only provide a powerful tool to characterize the aggregations of population and community in both time and space, offering important insights into community heterogeneity in space and/or stability in time, but also underscore the three general properties of power laws (scale invariance, no average and universality) and their specific manifestations in our four PLEs.

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“…A restrictive view of TL limits its application to apparently random variability without dominating systematic trends, that is, to what is sometimes called 'fluctuation scaling.' A broader view of TL, adopted here, includes applications of TL to nonnegative quantities that may change deterministically, for example, in purely mathematical structures (Kendal and Jørgensen 2011;Kendal 2013;Cohen 2013, Kendal andJørgensen 2015;Xiao, Locey, and White 2015;Cohen 2016) or that may fluctuate apparently chaotically or randomly to some extent while dominated by systematic trends (Cohen, Xu, and Brunborg 2013;Bohk, Rau, and Cohen 2015). We discuss some unanswered questions raised by this broader view of TL in the concluding section 4.2 on future research.…”

Section: Introductionmentioning

confidence: 99%

Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data

Cohen¹,

Bohk

Rau

2018

DemRes

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Fluctuation Scaling and 1/f Noise

Abstract: Tweedie convergence theorem provides a generally applicable explanation for the origin of these scaling relationships, and can provide insight into processes like self-organized criticality and multifractality.

Cited by 14 publications

References 26 publications

Aperiodic neural activity is a better predictor of schizophrenia than neural oscillations

Aperiodic neural activity is a better predictor of schizophrenia than neural oscillations

Power law analysis of the human microbiome

Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data

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