A combinatorial framework to quantify peak/pit asymmetries in complex dynamics

Scientific Reports
Uri HassonLucas Lacasa

Abstract

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.

References

May 1, 1995·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·S D FormanD C Noll
Mar 26, 2008·Proceedings of the National Academy of Sciences of the United States of America·Lucas LacasaJuan Carlos Nuño
Jul 4, 2009·NeuroImage·Douglas N Greve, Bruce Fischl
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B LuqueJ Luque
Aug 18, 2010·Journal of Neural Transmission·Mehran AhmadlouAnahita Adeli
Nov 10, 2010·Frontiers in Human Neuroscience·Ali Mazaheri, Ole Jensen
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lucas Lacasa, Raul Toral
Feb 27, 2013·Proceedings of the National Academy of Sciences of the United States of America·Xiao Liu, Jeff H Duyn
Jun 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ángel M NúñezAlberto Robledo
Oct 22, 2015·Scientific Reports·Lucas LacasaVito Latora
May 14, 2016·Physical Review. E·Jacopo Iacovacci, Lucas Lacasa

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Citations

Jul 13, 2021·Chaos·Avraam CharakopoulosIoannis Sarris
Aug 10, 2019··Jinghuai GaoZhiguo Wang

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Methods Mentioned

BETA
feature extraction
PCA

Software Mentioned

ΔVGA
ncdf4
epi
reg
AVA
FAST FMRIB Automated Segmentation Tool
FSL
R

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