时间序列阈值和雪崩大小的定义
Time-series thresholding and the definition of avalanche size
摘要：
雪崩的规模和持续时间分布的幂律出现在许多情况下。在这里，我们表明，有一个隐藏的危险阈值连续时间序列-无论是从经验或合成数据-雪崩的检测。特别是，我们考虑两种可能的替代定义雪崩的大小，例如，在经验确定雪崩指数的神经活动数据的分析。通过对Ornstein-Uhlenbeck过程的分析和计算研究，（作为一个指导性的例子），我们表明，如果（i）相对较大的阈值被用来确定雪崩的开始和结束，如果（ii）-有时在文献中做-雪崩的大小被定义为总面积（零以上）的雪崩，那么真正的渐近标度行为是看不到的，而是观察占主导地位的瞬态效应。这些可能会导致误解所产生的缩放制度，以及一个错误的普遍性类的分配。
英文摘要：
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.
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