A Framework for the Time- and Frequency-Domain Assessment of High-Order Interactions in Brain and Physiological Networks

Understand

While the standard network description of complex systems is based on quantifying links between pairs of system units, higher-order interactions (HOIs) involving three or more units play a major role in governing the collective network behavior.

• This work introduces an approach to quantify pairwise and HOIs for multivariate rhythmic processes interacting across multiple time scales.
• We define the so-called O-information rate (OIR) as a new metric to assess HOIs for multivariate time series, and propose a framework to decompose it into measures quantifying Granger-causal and instantaneous influences, as well as to expand it in the frequency domain.
• The framework exploits the spectral representation of vector autoregressive and state-space models to assess synergistic and redundant interactions among groups of processes, both in specific bands and in the time domain after whole-band integration.