Information propagation in Gaussian processes on multilayer networks
arxiv(2024)
摘要
Complex systems with multiple processes evolving on different temporal scales
are naturally described by multilayer networks, where each layer represents a
different timescale. In this work, we show how the multilayer structure shapes
the generation and propagation of information between layers. We derive a
general decomposition of the multilayer probability for continuous stochastic
processes described by Fokker-Planck operators. In particular, we focus on
Gaussian processes, for which this solution can be obtained analytically. By
explicitly computing the mutual information between the layers, we derive the
fundamental principles that govern how information is propagated by the
topology of the multilayer network. In particular, we unravel how edges between
nodes in different layers affect their functional couplings. We find that
interactions from fast to slow layers alone do not generate information,
leaving the layers statistically independent even if they affect their
dynamical evolution. On the other hand, interactions from slow to fast nodes
lead to non-zero mutual information, which can then be propagated along
specific paths of interactions between layers. We employ our results to study
the interplay between information and instability, identifying the critical
layers that drive information when pushed to the edge of stability. Our work
generalizes previous results obtained in the context of discrete stochastic
processes, allowing us to understand how the multilayer nature of complex
systems affects their functional structure.
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