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

TL;DR

This paper introduces a combinatorial framework that effectively quantifies asymmetries between local minima and maxima in time series, aiding in distinguishing complex dynamics across various scientific fields.

Contribution

It presents a novel combinatorial method that outperforms existing metrics in analyzing asymmetries in local fluctuations of time series data.

Findings

Successfully distinguishes different complex dynamics in synthetic data

Outperforms state-of-the-art metrics in several cases

Reveals that asymmetries are highly informative of underlying dynamics

Abstract

We explore a combinatorial framework which efficiently quantifies the asymmetries between minima and maxima in local fluctuations of time series. We firstly 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.