A new study sheds light on the causal timescales of complex systems. The research, conducted by Luka V. Petrović, Anatol Wegner and Ingo Scholtes, introduces a new information-theoretic measure called “temporal path entropy” to detect the timescales at which the causal influences occur in temporal networks. The results of the study have important implications for the analysis of temporal networks, which can provide valuable insights into the dynamics of complex systems.
The research of dynamic complex systems has advanced in recent years, moving beyond static graph representations. The study of temporal networks has revealed that the interplay between temporal and topological patterns can yield valuable insights into the behaviour of complex systems. In particular, the statistics of time-respecting paths can be affected by the interplay between the temporal and topological patterns, impacting the analysis of accessibility, reachability, spreading, clustering, centralities, and visualization.
The authors first analyzed the behaviour of temporal path entropy in synthetically generated temporal networks with known causal timescales. They then compared the behaviour of the measure in two real-world networks with information about the ground truth timescales and two real-world networks without such information. The results showed that the temporal path entropy decreases in accordance with the planted timescale at which the interactions cause one another.
The study compared the histogram of causal inter-event times with the temporal path entropy at different timescales of the temporal network. The results showed that the increased number of causal interactions increases the difference in temporal path entropy between the original and the shuffled network. The authors concluded that the temporal path entropy can capture the causal timescales in both synthetic and empirical temporal networks.
The temporal path entropy measure allows system-relevant timescales to be inferred from the temporal networks themselves, which is crucial for the analysis of temporal networks where inherent timescales are unavailable and hard to measure. The results of the study have important implications for the analysis of temporal networks, as they provide a way to detect the timescales at which the causal influences occur in these networks. This can provide valuable insights into the dynamics of complex systems, helping researchers and practitioners to better understand and analyze these systems.
Source : Petrovi'c, L.V., Wegner, A., & Scholtes, I. (2023). Higher-Order Patterns Reveal Causal Timescales of Complex Systems https://doi.org/10.48550/arXiv.2301.11623