Time-series thresholding and the definition of avalanche size

Abstract

Avalanches whose sizes and durations are distributed as power laws appear in many contexts. Here, we show that there is a hidden peril in thresholding continuous times series --either from empirical or synthetic data-- for the detection 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 if (i) relatively large threshold values are employed to determine the beginning and ending of avalanches and if (ii) --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. These can induce misinterpretations of the resulting scaling regimes as well as to a wrong assignation of universality classes.

arXiv comment4 figures, 6 pages. Accepted to be published in PRE

References in corpus (28)

• Power laws, Pareto distributions and Zipf's law
• Are biological systems poised at criticality?
• Modeling Cascading Failures in the North American Power Grid
• Unified Scaling Law for Earthquakes
• Colloquium: Criticality and dynamical scaling in living systems
• Paths to Self-Organized Criticality
• Percolation on sparse networks
• Self-Organized Branching Processes: A Mean-Field Theory for Avalanches
• Critical brain networks
• Beyond power laws: Universality in the average avalanche shape
• A Complexity View of Rainfall
• Experiments in vortex avalanches
• Power-law statistics and universal scaling in the absence of criticality
• Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization
• Avalanche and spreading exponents in systems with absorbing states
• Dynamics of a ferromagnetic domain wall and the Barkhausen effect
• Self-organized criticality in X-ray flares of gamma-ray burst afterglows
• Self-organization without conservation: Are neuronal avalanches generically critical?
• Inhibition causes ceaseless dynamics in networks of excitable nodes
• Self-Organized Bistability Associated With First-Order Phase Transitions
• The average shape of a fluctuation: universality in excursions of stochastic processes
• Avalanche shape and exponents beyond mean-field theory
• Neutral theory and scale-free neural dynamics
• The effect of thresholding on temporal avalanche statistics
• A simple unified view of branching process statistics: random walks in balanced logarithmic potentials
• First-passage distributions for the one-dimensional Fokker-Planck equation
• The perils of thresholding
• Mapping multiplicative to additive noise

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• Spatial-temporal analysis of neural desynchronization in sleep-like states reveals critical dynamics
• Sampling effects and measurement overlap can bias the inference of neuronal avalanches
• Percolation theory of self-exciting temporal processes
• Effect of thresholding on avalanches and their clustering for interfaces with long-range elasticity
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