Linking local and large-scale salient events with oscillatory and broadband arrhythmic activities in the resting...

Narrowband oscillations (NOs) and broadband arrhythmic activity (BAA) are valuable conceptualizations extensively used to interpret brain data, with NOs linked to communication and synchronization and BAA encompassing scale-free dynamics and neuronal avalanches. Although both frameworks offer critical insights into brain function, they have largely evolved in parallel, with limited integration and no unifying mechanistic account of how these dynamics interact to generate transient, salient events (SEs). This gap is particularly pressing given recent interest in how SEs-brief ( $\approx$ 100 ms) bursts of activity coordinated across brain regions-relate to large-scale brain function and cognition. To address this, we introduce a signal-level framework that links the Fourier spectral properties (oscillation-domain) of neural signals to the emergence of realistic SEs in the time-domain from NOs and BAA. Our approach is grounded in a novel concept-spectral group delay consistency (SGDC)-along with associated measures that quantify the temporal alignment of spectral components and capture the conditions under which NOs and BAA coalesce into transient, burst-like events. Unlike traditional power- or phase-based measures, or higher-order statistical metrics such as kurtosis and cokurtosis, SGDC provides a signal-level mechanistic account of how local and large-scale SEs emerge from the spectral structure of the underlying signals. Empirical validation is provided using source-reconstructed MEG data from a large cohort and a comprehensive array of features characterizing the statistical, spatiotemporal, and spectral properties of observed SEs. We found that the SEs identified in our empirical MEG dataset can be segregated based on their spectral signature in two main groups having different propagation patterns. Using generative models based on the SGDC mechanism, we provide a theoretical framework to interpret these experimental results showing that cluster 2 events are specifically related to the long-range spread of narrowband alpha bursts across the brain network (i.e., SNEs: salient network events), whereas cluster 1 events correspond to more short-lived and spatially localized fluctuations mainly promoted by the BAA (i.e., SLEs: salient local events). We also provide analytical arguments and numerical simulations showing that (a) high SGDC in specific narrow frequency bands, (b) transient cross-regional coherent Nos, and (c) BAA are all key ingredients for the emergence of realistic SNEs.