Measuring directed interactions in the brain in terms of information flow is a promising approach, mathematically treatable and amenable to encompass several methods. In this chapter we propose some approaches rooted in this framework for the analysis of neuroimaging data. First we will explore how the transfer of information depends on the network structure, showing how for hierarchical networks the information flow pattern is characterized by exponential distribution of the incoming information and a fat-tailed distribution of the outgoing information, as a signature of the law of diminishing marginal returns. This was reported to be true also for effective connectivity networks from human EEG data. Then we address the problem of partial conditioning to a limited subset of variables, chosen as the most informative ones for the driver node.We will then propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion are associated to informational circuits present in the system, with an informational character (synergetic or redundant) which can be associated to the sign of the contribution. Applications are reported for EEG and fMRI data.
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