Assessing cooperative behavior in dynamical networks with applications to brain data

Capturing the collective coherent spatiotemporal activity from measured data in large ensembles of coupled nonlinear sub-systems has revealed to be a key topic in many areas of applied sciences. Currently, this topic is addressed by considering multivariate time series analysis tools. They provide methods whose limiting factors are the amount and quality of data, or the restricted applicability to the class of narrow-band signals. In this study, we propose three new methods to infer cooperativeness from broad-band multivariate signals that also cope with the constraints due to amount and quality of data. Successfully, we validated all the methods on prototypical models of dynamical networks. Also, we tested their sensitiveness upon amount of data, endogenous and exogenous noises intensity, and number of sub-systems. The first two methods rely on statistical properties of the multivariate signals by using an entropy-like formula from the correlation matrix estimated from the data. They compute the amount of cooperativeness among the sub-systems by estimating the amount of shrinking of the network embedded space relative to the uncoupled case. The second method of them, based on the partial correlation matrix, may account for cooperation marginalizing third confounder systems. Furthermore, both methods may be applied to embedded and not embedded data, and may be used to estimate (partial) cooperativeness among communities of sub-systems. The third method follows a deterministic dynamical modeling approach. By means of a suitably decomposed identification of dynamical systems, it can detect interactions among signals both in strength and direction. The method allows the adaptability of the algorithmic setup on the specific applications, and provides a model of local behavior. In parallel to the methodological development, we applied the first method to two brain data sets in order to assess visual stimuli induced interhemispheric cooperativeness. According to the neuroscientist's interpretation, our results gave new insights about brain functioning. We have been able to assay flexible stimulus-dependent modulation (i.e. behavior) of neuronal cooperativeness over two brain spatial scales: macroscopic by analyzing EEG recordings, and mesoscopic by analyzing LFP recordings. The analysis on EEGs has extended previous results highlighting that the stimuli induced arrangement of cooperativeness goes beyond the one addressable by narrow-band analysis. The analysis on LFPs allowed us to describe a new kind of inter-hemispheric integration. We assayed that inter-hemispheric connections modulate in a flexible, stimulus-dependent way, the cooperation in neuronal populations likely to be involved in stimulus detection and/or categorization. Finally, contrary to current belief in neuroscience, our results showed that simple relations between frequencies and brain functions are unlikely to be true and that stimulus-driven cortical dynamics may change in a way still far from being fully understood.

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