Memory and betweenness preference in temporal networks induced from time series

Area of Science:

• Complex systems analysis
• Network science
• Time series analysis

Background:

• Understanding memory effects in time series is crucial for characterizing dynamical systems.
• Traditional methods may not fully capture the complex temporal dependencies within signals.
• Temporal networks offer a novel framework for analyzing time-dependent data.

Purpose of the Study:

• To develop and apply a novel temporal network framework for analyzing memory effects in time series.
• To investigate the utility of memory entropy analysis in distinguishing various dynamical systems.
• To assess the potential of temporal network properties in characterizing physiological signals.

Main Methods:

• Construction of temporal networks by unfolding time series data into a topological dimension.
• Application of memory entropy analysis to quantify memory effects at different scales.
• Analysis of betweenness preference within the constructed temporal networks.
• Testing the methods on diverse time series including noise, autoregressive, periodic, and chaotic signals, as well as human cardiac data.

Main Results:

• Distinct patterns in entropy growth rates were observed for different time series dynamics.
• Chaotic time series exhibited exponential scaling in memory entropy analysis.
• The memory exponent successfully characterized bifurcation phenomena and differentiated healthy from pathological cardiac states.
• Betweenness preference analysis effectively characterized dynamical systems and separated distinct electrocardiogram recordings.

Conclusions:

• Temporal networks combined with memory entropy analysis provide a powerful tool for understanding memory effects in time series.
• This approach offers a new perspective for characterizing complex dynamical systems and physiological signals.
• The findings highlight the potential of network-based methods in advancing time series analysis and biomedical applications.