Community structure and multi-modal oscillations in complex networks

On developing a framework for detection of oscillations in data

Oscillation is a phenomenon very commonly observed in systems, ranging from simple ones to complex distributed network. Several techniques have been proposed in the literature for detecting oscillations to study their importance in domains ranging from physiology to climate studies. However, there is a lack of a common framework accommodative of important features of data such as non-stationarity, intermittent oscillations, measurement noise, multimodal oscillations, and the like. In this article, we outline a framework that addresses these challenges, the results of which can then be analyzed along with appropriate knowledge about the underlying system. We present results of an extensive simulation study that establishes the robustness and reliability of the proposed technique and demonstrate its applicability to real datasets in climate and in industrial datasets.

Resting-state temporal synchronization networks emerge from connectivity topology and heterogeneity

Spatial patterns of coherent activity across different brain areas have been identified during the resting-state fluctuations of the brain. However, recent studies indicate that resting-state activity is not stationary, but shows complex temporal dynamics. We were interested in the spatiotemporal dynamics of the phase interactions among resting-state fMRI BOLD signals from human subjects. We found that the global phase synchrony of the BOLD signals evolves on a characteristic ultra-slow (<0.01Hz) time scale, and that its temporal variations reflect the transient formation and dissolution of multiple communities of synchronized brain regions. Synchronized communities reoccurred intermittently in time and across scanning sessions. We found that the synchronization communities relate to previously defined functional networks known to be engaged in sensory-motor or cognitive function, called resting-state networks (RSNs), including the default mode network, the somato-motor network, the visual network, the auditory network, the cognitive control networks, the self-referential network, and combinations of these and other RSNs. We studied the mechanism originating the observed spatiotemporal synchronization dynamics by using a network model of phase oscillators connected through the brain’s anatomical connectivity estimated using diffusion imaging human data. The model consistently approximates the temporal and spatial synchronization patterns of the empirical data, and reveals that multiple clusters that transiently synchronize and desynchronize emerge from the complex topology of anatomical connections, provided that oscillators are heterogeneous.

The spontaneous or resting-state activity of the brain is organized into multiple spatial patterns of correlated activity. These patterns have been associated with functional interacting brain networks. Recent studies show that the correlations among brain regions are not stationary, but evolve over time, and have refocused the study of spontaneous brain activity on characterizing these time-varying functional interactions. In this article, we show that the synchrony between the BOLD activities of different brain regions displays global slow fluctuations that reflect the dynamical association and dissociation of functional synchronized clusters. Using a network of anatomically connected phase oscillators, we show that transiently synchronized patterns emerge from the interplay between nonlinear dynamics and the complex, but static, network topology. Our results suggest that the brain constantly explores its dynamical repertoire during rest, which allows for an all-around visitation of functional states.