Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain.
Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy.
Phys Rev E. 2019 Jul;100(1-1):012133. doi: 10.1103/PhysRevE.100.012133.
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-from either 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 (1) if relatively large threshold values are employed to determine the beginning and ending of avalanches and (2) 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.
在从物理学到地球物理学和生物学的许多领域中，大小和持续时间呈幂律分布的雪崩现象随处可见。在这里，我们表明，对于识别雪崩，从经验或合成数据对连续时间序列进行阈值处理存在潜在危险。特别是，我们考虑了两种可能的替代定义的雪崩大小的使用，例如，在分析神经活动数据中经验确定雪崩指数时。通过对奥恩斯坦-乌伦贝克过程（作为指导示例）进行分析和计算研究，我们表明：（1）如果使用相对较大的阈值来确定雪崩的开始和结束；（2）如果-如文献中有时所做的那样-将雪崩大小定义为雪崩的总面积（高于零），则不会看到真正的渐近标度行为，而是观察结果受到瞬态效应的支配。我们在一些最近的研究中发现了这个问题，这导致了对所得到的标度区域的误解。
