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 often rich of oscillatory content, the spectral representation of network systems is essential to ascribe the analyzed interactions to specific oscillations with physiological meaning. In this context, the present work formalizes a coherent framework which integrates several information dynamics approaches to quantify node-specific, pairwise and higher-order interactions in network systems. The framework establishes a hierarchical organization of interactions of different order using measures of entropy rate, mutual information rate and O-information rate, to quantify respectively the dynamics of individual nodes, the links between pairs of nodes, and the redundant/synergistic hyperlinks between groups of nodes. All measures are formulated in the time domain, and then expanded to the spectral domain to obtain frequency-specific information. The practical computation of all measures is favored presenting a toolbox that implements their parametric and non-parametric estimation, and includes approaches to assess their statistical significance. The framework is illustrated first using theoretical examples where the properties of the measures are displayed in benchmark simulated network systems, and then applied to representative examples of multivariate time series in the context of Network Neuroscience and Network Physiology.

翻译：近年来，信号处理与信息论的最新进展正推动复杂网络系统数据驱动建模方法的发展。在网络生理学与网络神经科学领域，由于所关注的信号通常富含振荡成分，网络系统的谱表示对于将分析所得的交互作用归因于具有生理意义的特定振荡至关重要。在此背景下，本文形式化了一个统一的理论框架，融合多种信息动力学方法，用于量化网络系统中的节点特异性、成对交互及高阶交互作用。该框架利用熵率、互信息率和O信息率分别量化单个节点的动力学、节点对间的连接以及节点群组间的冗余/协同超连接，建立了不同阶次交互的层级组织。所有度量指标均在时域中定义，随后拓展至谱域以获取频率特异性的信息。通过提供实现参数与非参数估计的工具箱（包含统计显著性评估方法），本文促进了上述度量指标的实际计算。该框架首先通过理论示例在基准模拟网络系统中展示度量特性，继而应用于网络神经科学和网络生理学领域的代表性多变量时间序列分析案例中。