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Unifying Pairwise Interactions in Complex Dynamics

by   Oliver M. Cliff, et al.

Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods – from correlation coefficients to causal inference – rely on distinct quantitative theories that remain largely disconnected. Here we introduce a library of 249 statistics for pairwise interactions and assess their behavior on 1053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights new commonalities between different mathematical formulations, providing a unified picture of a rich, interdisciplinary literature. We then show that leveraging many methods from across science can uncover those most suitable for addressing a given problem, yielding high accuracy and interpretable understanding. Our framework is provided in extendable open software, enabling comprehensive data-driven analysis by integrating decades of methodological advances.


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