The effect of thresholding on temporal avalanche statistics

Laurson, Lasse; Illa, Xavier; Alava, Mikko J.

doi:10.1088/1742-5468/2009/01/p01019

Cited by 40 publications

(60 citation statements)

References 42 publications

(69 reference statements)

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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: 82%

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: 82%

Time-series thresholding and the definition of avalanche size

et al. 2019

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“…a noise whose amplitude changes with the dynamical variable (the degree of freedom). Let us cite two specific examples from the literature to illustrate our point: in [22], Laurson et al apply thresholds to Brownian excursion, but since noise is additive in Brownian motion, the asymptotic exponent of −3 2 is recovered at any threshold level. On the other hand, Larremore et al [23] apply thresholds to networks of excitable nodes and critical branching processes, i.e.…”

Section: Summary and Discussionmentioning

confidence: 99%

The perils of thresholding

et al. 2015

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The thresholding of time series of activity or intensity is frequently used to define and differentiate events. This is either implicit, for example due to resolution limits, or explicit, in order to filter certain small scale physics from the supposed true asymptotic events. Thresholding the birth-death process, however, introduces a scaling region into the event size distribution, which is characterized by an exponent that is unrelated to the actual asymptote and is rather an artefact of thresholding. As a result, numerical fits of simulation data produce a range of exponents, with the true asymptote visible only in the tail of the distribution. This tail is increasingly difficult to sample as the threshold is increased. In the present case, the exponents and the spurious nature of the scaling region can be determined analytically, thus demonstrating the way in which thresholding conceals the true asymptote. The analysis also suggests a procedure for detecting the influence of the threshold by means of a data collapse involving the threshold-imposed scale.

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“…This method works well if the signal to noise ratio is high, but can induce spurious effects otherwise 15 . Our thin films have a correspondingly weak signal, thus making the use of V th inappropriate.…”

Section: V(t/t) ¬ 4 T/t(1 ¬ T/t) V(t/t) ¬ 4 T/t(1 ¬ T/t) V(t/t)/v Maxmentioning

confidence: 99%

Universality beyond power laws and the average avalanche shape

et al. 2011

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The study of critical phenomena and universal power laws has been one of the central advances in statistical mechanics during the second half of the past century, explaining traditional thermodynamic critical points 1 , avalanche behaviour near depinning transitions 2,3 and a wide variety of other phenomena 4 . Scaling, universality and the renormalization group claim to predict all behaviour at long length and timescales asymptotically close to critical points. In most cases, the comparison between theory and experiments has been limited to the evaluation of the critical exponents of the power-law distributions predicted at criticality. An excellent area for investigating scaling phenomena is provided by systems exhibiting crackling noise, such as the Barkhausen effect in ferromagnetic materials 5 . Here we go beyond powerlaw scaling and focus on the average functional form of the noise emitted by avalanches-the average temporal avalanche shape 4 . By analysing thin permalloy films and improving the data analysis methods, our experiments become quantitatively consistent with our calculation for the multivariable scaling function in the presence of a demagnetizing field and finite field-ramp rate.The average temporal avalanche shape has been measured for earthquakes 6 and for dislocation avalanches in plastically deformed metals 7,8 , but the primary experimental and theoretical focus has always been Barkhausen avalanches in magnetic systems 5,6,[9][10][11] . Theory and experiment agreed well for avalanche sizes and durations, but the strikingly asymmetric shapes found experimentally in ribbons 11 disagreed sharply with the theoretical predictions, for which the asymmetry in the scaling shapes under time reversal was at most very small 4,6 . (We note that the relevant models are not microscopically time-reversal invariant; temporal symmetry is thus emergent.) Doubts about universality 4 were resolved when eddy currents were shown to be responsible for the asymmetry, at least on short timescales 12 , but the exact form of the asymptotic universal scaling function of the Barkhausen avalanche shape still remained elusive.Here, we report an experimental study of Barkhausen noise in permalloy thin films, where a careful study of the average avalanche shapes leads to symmetric shapes, undistorted by eddy currents (which are suppressed by the sample geometry). We provide a quantitative explanation of the experimental results by solving exactly the mean-field theories for two general models of magnetic reversal: a domain-wall dynamics model 13 Time-series data (jagged line) are traditionally separated into avalanches using a threshold V th set above the instrumental noise (dotted blue line)-here breaking one avalanche into a few pieces. We instead do an optimal Wiener deconvolution (smoothed red curve, see text), allowing the use of a zero threshold (solid black line), which avoids distortions of the average shape and also gives more decades of size and duration scaling. Averaging over all avalanches with this duratio...

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The effect of thresholding on temporal avalanche statistics

Cited by 40 publications

References 42 publications

Time-series thresholding and the definition of avalanche size

Time-series thresholding and the definition of avalanche size

The perils of thresholding

Universality beyond power laws and the average avalanche shape

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