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

Area of Science:

• Complex Systems Analysis
• Data Science
• Time Series Analysis

Background:

• Time series data often exhibit complex dynamics that are challenging to quantify.
• Existing methods may not fully capture the asymmetries present in local fluctuations.

Purpose of the Study:

• To develop and validate a combinatorial framework for quantifying asymmetries between minima and maxima in time series.
• To demonstrate the framework's ability to distinguish diverse complex dynamics and outperform current metrics.

Main Methods:

• Development of a combinatorial framework to analyze local fluctuations.
• Application to synthetic datasets and canonical dynamical models (stochastic, chaotic).
• Validation through extensive numerical simulations and real-world data from neurobiology, finance, and climate science.

Main Results:

• The framework rigorously quantifies asymmetries in time series fluctuations.
• It successfully distinguishes between different complex dynamics, including stochastic and chaotic processes.
• Performance was superior to state-of-the-art metrics in several benchmark cases.

Conclusions:

• Asymmetries between local maxima and minima are highly informative of underlying complex dynamics.
• A graph-theoretic approach enables the use of these features for statistical learning.
• The methodology offers a powerful new tool for analyzing complex time series data across disciplines.