The perils of thresholding

Font-Clos, Francesc; Pruessner, Gunnar; Moloney, Nicholas R.; Deluca, Anna

doi:10.1088/1367-2630/17/4/043066

Cited by 24 publications

(27 citation statements)

References 27 publications

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“…More in general, we underline that particular attention needs to be taken when avalanches of activity -defined by thresholding-are inferred from a continuous time series of activity. Our findings, add to the recent literature warning on the "perils" associated with thresholding in timeseries [44] [45,46].…”

Section: Introductionsupporting

confidence: 81%

Time-series thresholding and the definition of avalanche size

et al. 2019

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Avalanches whose sizes and durations are distributed as power laws appear in many contexts, from physics to geophysics and biology. Here, we show that there is a hidden peril in thresholding continuous times series -either from empirical or synthetic data-for the identification of avalanches. In particular, we consider two possible alternative definitions of avalanche size used e.g. in the empirical determination of avalanche exponents in the analysis of neural-activity data. By performing analytical and computational studies of an Ornstein-Uhlenbeck process (taken as a guiding example) we show that (i) if relatively large threshold values are employed to determine the beginning and ending of avalanches and (ii) if -as sometimes done in the literature-avalanche sizes are defined as the total area (above zero) of the avalanche, then true asymptotic scaling behavior is not seen, instead the observations are dominated by transient effects. This problem -that we have detected in some recent works-leads to misinterpretations of the resulting scaling regimes.

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Section: Introductionsupporting

confidence: 81%

Time-series thresholding and the definition of avalanche size

et al. 2019

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“…Interestingly, these exponents are compatible with those found in rainfall, another natural system that has been shown to be compatible with SOC dynamics74, and cannot be explained by simple null models47. While the precise values of the exponents are not extremely relevant, one should take these with caution as thresholding is known to introduce in some cases finite size biases in the form of a second scaling region for short sizes which is only removed when the series is long enough75. In what follows we explore the emergence of classical linguistic laws in these acoustic signals.…”

Section: Resultssupporting

confidence: 60%

Emergence of linguistic laws in human voice

Torre

Luque

Lacasa

et al. 2017

Sci Rep

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Linguistic laws constitute one of the quantitative cornerstones of modern cognitive sciences and have been routinely investigated in written corpora, or in the equivalent transcription of oral corpora. This means that inferences of statistical patterns of language in acoustics are biased by the arbitrary, language-dependent segmentation of the signal, and virtually precludes the possibility of making comparative studies between human voice and other animal communication systems. Here we bridge this gap by proposing a method that allows to measure such patterns in acoustic signals of arbitrary origin, without needs to have access to the language corpus underneath. The method has been applied to sixteen different human languages, recovering successfully some well-known laws of human communication at timescales even below the phoneme and finding yet another link between complexity and criticality in a biological system. These methods further pave the way for new comparative studies in animal communication or the analysis of signals of unknown code.

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“…(25)- (29) in the next section, after introducing a voterlike family of models. We should mention that the existence of a double scaling is not new and has been reported previously, for example, in the family of Bessel processes [32] or in the birth-death process with population-proportional rates [33]. The latter case has a singularity of the type of Eq.…”

Section: Case Of Unbounded ∆mentioning

confidence: 54%

First-passage distributions for the one-dimensional Fokker-Planck equation

et al. 2018

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We present an analytical framework to study the first-passage (FP) and first-return (FR) distributions for the broad family of models described by the one-dimensional Fokker-Planck equation in finite domains, identifying general properties of these distributions for different classes of models. When in the Fokker-Planck equation the diffusion coefficient is positive (nonzero) and the drift term is bounded, as in the case of a Brownian walker, both distributions may exhibit a power-law decay with exponent −3/2 for intermediate times. We discuss how the influence of an absorbing state changes this exponent. The absorbing state is characterized by a vanishing diffusion coefficient and/or a diverging drift term. Remarkably, the exponent of the Brownian walker class of models is still found, as long as the departure and arrival regions are far enough from the absorbing state, but the range of times where the power law is observed narrows. Close enough to the absorbing point, though, a new exponent may appear. The particular value of the exponent depends on the behavior of the diffusion and the drift terms of the Fokker-Planck equation. We focus on the case of a diffusion term vanishing linearly at the absorbing point. In this case, the FP and FR distributions are similar to those of the voter model, characterized by a power law with exponent −2. As an illustration of the general theory, we compare it with exact analytical solutions and extensive numerical simulations of a two-parameter voter-like family models. We study the behavior of the FP and FR distributions by tuning the importance of the absorbing points throughout changes of the parameters. Finally, the possibility of inferring relevant information about the steady-sate probability distribution of a model from the FP and FR distributions is addressed.

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The perils of thresholding

Cited by 24 publications

References 27 publications

Time-series thresholding and the definition of avalanche size

Time-series thresholding and the definition of avalanche size

Emergence of linguistic laws in human voice

First-passage distributions for the one-dimensional Fokker-Planck equation

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