Abstract
Many complex systems in physics, biology and engineering are modeled as dynamical networks and described using multivariate time series analysis. Recent developments have shown that the emergent dynamics of a network system are significantly affected by interactions involving multiple network nodes which cannot be described using pairwise links. While these higher-order interactions can be probed using information-theoretic measures, a rigorous framework to describe them in the frequency domain is still lacking. This work presents an approach for the spectral decomposition of multivariate information measures, capable of identifying higher-order synergistic and redundant interactions between oscillatory processes. We show theoretically that synergy and redundancy can coexist at different frequencies among the output signals of a network system and can be detected only using the proposed spectral method. To demonstrate the broad applicability of the framework, we provide parametric and non-parametric data-efficient estimators for the spectral information measures, and employ them to describe multivariate interactions in three complex systems producing rich oscillatory dynamics, namely the human brain, a ring of electronic oscillators, and the global climate system. In these systems, we show that the use of our framework for the spectral decomposition of information measures reveals multivariate and higher-order interactions not detectable in the time domain. Our results are exemplary of how the frequency-specific analysis of multivariate dynamics can aid the implementation of assessment and control strategies in real-world network systems.
Highlights
T HE complexity of many physical, biological and technological systems originates from the richness of the structural and functional interactions among their constituent units
Collective phenomena in complex network systems often emerge from multiple links among many elementary subsystems that may occur through different mechanisms and can be detected only going beyond the framework of pairwise interactions
This work demonstrates that higher-order interactions in a multivariate set of dynamic processes can remain hidden if they are investigated exclusively in the time domain, and that such processes may display redundancy in a certain frequency range and synergy in another range
Summary
T HE complexity of many physical, biological and technological systems originates from the richness of the structural and functional interactions among their constituent units. There is mounting evidence that the overall interplay among the several units of a network system cannot be exhaustively described by combinations of pairwise couplings, and that higher-order interactions −i.e., interactions involving more than two units− are present and often play a crucial role for understanding the overall system behavior [4], [5]. In this context, novel approaches are under development to accommodate higher-order many body interactions into generalized network representations [6]. While these measures are generally defined in a model-free framework on the basis of the probability densities of the various available dynamic variables, it has been shown that for Gaussian processes they are fully dependent on the parameters of a linear Vector Autoregressive (VAR) model [11], [16]
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