The intra-session reliability of functional connectivity during naturalistic viewing conditions.

Functional connectivity analysis is a common approach to the characterization of brain function. While studies of functional connectivity have predominantly focused on resting-state fMRI, naturalistic paradigms, such as movie watching, are increasingly being used. This ecologically valid, yet relatively unconstrained acquisition state has been shown to improve subject compliance and, potentially, enhance individual differences. However, unlike the reliability of resting-state functional connectivity, the reliability of functional connectivity during naturalistic viewing has not yet been fully established. The current study investigates the intra-session reliability of functional connectivity during naturalistic viewing sessions to extend its understanding. Using fMRI data of 24 subjects measured at rest as well as during six naturalistic viewing conditions, we quantified the split-half reliability of each condition, as well as cross-condition reliabilities. We find that intra-session reliability is relatively high for all conditions. While cross-condition reliabilities are higher for pairings of two naturalistic viewing conditions, split-half reliability is highest for the resting state. Potential sources of variability across the conditions, as well as the strengths and limitations of using intra-session reliability as a measure in naturalistic viewing, are discussed.

Identifying causal gateways and mediators in complex spatio-temporal systems.

Identifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Earth's climate to volcanic eruptions, extreme events or geoengineering. Here a data-driven approach is introduced based on a dimension reduction, causal reconstruction, and novel network measures based on causal effect theory that go beyond standard complex network tools by distinguishing direct from indirect pathways. Applied to a data set of atmospheric dynamics, the method identifies several strongly uplifting regions acting as major gateways of perturbations spreading in the atmosphere. Additionally, the method provides a stricter statistical approach to pathways of atmospheric teleconnections, yielding insights into the Pacific-Indian Ocean interaction relevant for monsoonal dynamics. Also for neuroscience or power grids, the novel causal interaction perspective provides a complementary approach to simulations or experiments for understanding the functioning of complex spatio-temporal systems with potential applications in increasing their resilience to shocks or extreme events.

Functional connectivity in resting-state fMRI: is linear correlation sufficient?

Functional connectivity (FC) analysis is a prominent approach to analyzing fMRI data, especially acquired under the resting state condition. The commonly used linear correlation FC measure bears an implicit assumption of Gaussianity of the dependence structure. If only the marginals, but not all the bivariate distributions are Gaussian, linear correlation consistently underestimates the strength of the dependence. To assess the suitability of linear correlation and the general potential of nonlinear FC measures, we present a framework for testing and estimating the deviation from Gaussianity by means of comparing mutual information in the data and its Gaussianized counterpart. We apply this method to 24 sessions of human resting state fMRI. For each session, matrix of connectivities between 90 anatomical parcel time series is computed using mutual information and compared to results from its multivariate Gaussian surrogate that conserves the correlations but cancels any nonlinearity. While the group-level tests confirmed non-Gaussianity in the FC, the quantitative assessment revealed that the portion of mutual information neglected by linear correlation is relatively minor-on average only about 5% of the mutual information already captured by the linear correlation. The marginality of the non-Gaussianity was confirmed in comparisons using clustering of the parcels-the disagreement between clustering obtained from mutual information and linear correlation was attributable to random error. We conclude that for this type of data, practical relevance of nonlinear methods trying to improve over linear correlation might be limited by the fact that the data are indeed almost Gaussian.

Partitioning networks into clusters and residuals with average association.

We investigate the problem of detecting clusters exhibiting higher-than-average internal connectivity in networks of interacting systems. We show how the average association objective formulated in the context of spectral graph clustering leads naturally to a clustering strategy where each system is assigned to at most one cluster. A residual set is formed of the systems that are not members of any cluster. Maximization of the average association objective leads to a discrete optimization problem, which is difficult to solve, but a relaxed version can be solved using an eigendecomposition of the connectivity matrix. A simple approach to extracting clusters from a relaxed solution is described and developed by applying a variance maximizing solution to the relaxed solution, which leads to a method with increased accuracy and sensitivity. Numerical studies of theoretical connectivity models and of synchronization clusters in a lattice of coupled Lorenz oscillators are conducted to show the efficiency of the proposed approach. The method is applied to an experimentally obtained human resting state functional magnetic resonance imaging dataset and the results are discussed.

Identification of nonlinear oscillatory activity embedded in broadband neural signals.

Oscillatory phenomena in the brain activity and their synchronization are frequently studied using mathematical models and analytic tools derived from nonlinear dynamics. In many experimental situations, however, neural signals have a broadband character and if oscillatory activity is present, its dynamical origin is unknown. To cope with these problems, a framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modelled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, further analysis using nonlinear approaches such as the phase synchronization analysis can potentially bring new information. For linear processes, however, standard approaches such as the coherence analysis are more appropriate and provide sufficient description of underlying interactions with smaller computational effort. The method is illustrated in a numerical example and applied to analyze experimentally obtained human EEG time series from a sleeping subject.

Phase synchronization analysis by assessment of the phase difference gradient.

Phase synchronization is an important phenomenon of nonlinear dynamics and has recently received much scientific attention. In this work a method for identifying phase synchronization epochs is described which focuses on estimating the gradient of segments of the generalized phase differences between phase slips in an experimental time series. In phase synchronized systems, there should be a zero gradient of the generalized phase differences even if the systems are contaminated by noise. A method which tests if the gradient of the generalized phase difference is statistically different from zero is reported. The method has been validated by numerical studies on model systems and by comparing the results to those published previously. The method is applied to cardiorespiratory time series from a human volunteer measured in clinical settings and compared to synchrogram analysis for the same data. Potential problems with synchrogram analysis of experimental data are discussed.

Detecting nonlinear oscillations in broadband signals.

A framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modeled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, it can be further analyzed using nonlinear approaches such as phase synchronization analysis. For linear processes standard approaches, such as the coherence analysis, are more appropriate. The method is illustrated in a numerical example and applied to analyze experimentally obtained human electroencephalogram time series from a sleeping subject.

Inferring the directionality of coupling with conditional mutual information.

Uncovering the directionality of coupling is a significant step in understanding drive-response relationships in complex systems. In this paper, we discuss a nonparametric method for detecting the directionality of coupling based on the estimation of information theoretic functionals. We consider several different methods for estimating conditional mutual information. The behavior of each estimator with respect to its free parameter is shown using a linear model where an analytical estimate of conditional mutual information is available. Numerical experiments in detecting coupling directionality are performed using chaotic oscillators, where the influence of the phase extraction method and relative frequency ratio is investigated.

Directionality of coupling from bivariate time series: how to avoid false causalities and missed connections.

We discuss some problems encountered in inference of directionality of coupling, or, in the case of two interacting systems, in inference of causality from bivariate time series. We identify factors and influences that can lead to either decreased test sensitivity or false detections and propose ways to cope with them in order to perform tests with high sensitivity and a low rate of false positive results.