Spectral Information Dynamics: a New Framework to Assess Multi-Order Interactions in Network Neuroscience and Physiology

Recent advances in signal processing and information theory are boosting the development of new approaches for the data-driven modelling of complex network systems. In the fields of Network Physiology and Network Neuroscience, where the signals of interest are rich of oscillatory content, the spectral representation of network systems is essential to ascribe interactions to specific oscillations with physiological meaning. This thesis introduces a coherent framework integrating several information dynamics approaches to quantify node-specific, pairwise and high-order interactions in network systems. A hierarchical organization of interactions of different order is established using measures of information rate to quantify the dynamics of each individual node of the network, the links between pairs of nodes, and the redundant/synergistic hyperlinks in groups of nodes. All measures are formulated in the time domain and then expanded to the spectral domain to obtain frequencyspecific information in the context of Gaussian data characterized by linear parametric models. The framework is first illustrated using simulation examples where the properties of the measures are displayed in benchmark simulated network systems. Then, it is applied to several representative datasets of multivariate time series in the context of Network Neuroscience and Network Physiology. The utilization of high-order measures of information rate with spectral meaning has been proven successful to highlight the respiratory-driven redundant nature of cardiovascular, cardiorespiratory and cerebrovascular interactions, as well as the overall prevalence of redundancy for high-order brain interactions together with the emergence of synergistic circuits not retrievable from a pairwise analysis.