Hasson Uri, Iacovacci Jacopo, Davis Ben, Flanagan Ryan, Tagliazucchi Enzo, Laufs Helmut, Lacasa Lucas
Center for Mind and Brain Sciences, University of Trento, Trento, Italy.
Center for Practical Wisdom, The University of Chicago, Chicago, USA.
Sci Rep. 2018 Feb 23;8(1):3557. doi: 10.1038/s41598-018-21785-0.
We explore a combinatorial framework which efficiently quantifies the asymmetries between minima and maxima in local fluctuations of time series. We first showcase its performance by applying it to a battery of synthetic cases. We find rigorous results on some canonical dynamical models (stochastic processes with and without correlations, chaotic processes) complemented by extensive numerical simulations for a range of processes which indicate that the methodology correctly distinguishes different complex dynamics and outperforms state of the art metrics in several cases. Subsequently, we apply this methodology to real-world problems emerging across several disciplines including cases in neurobiology, finance and climate science. We conclude that differences between the statistics of local maxima and local minima in time series are highly informative of the complex underlying dynamics and a graph-theoretic extraction procedure allows to use these features for statistical learning purposes.
我们探索了一个组合框架，该框架能有效地量化时间序列局部波动中最小值和最大值之间的不对称性。我们首先将其应用于一系列合成案例来展示其性能。我们在一些典型动力学模型（有相关性和无相关性的随机过程、混沌过程）上获得了严格的结果，并对一系列过程进行了广泛的数值模拟，结果表明该方法能正确区分不同的复杂动力学，且在几种情况下优于现有技术指标。随后，我们将此方法应用于多个学科中出现的实际问题，包括神经生物学、金融和气候科学中的案例。我们得出结论，时间序列中局部最大值和局部最小值的统计差异能高度反映复杂的潜在动力学，并且一种基于图论的提取程序允许将这些特征用于统计学习目的。
