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We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel-Granger causality to the multivariate case, here presented, shares the following features with the bivariate measures: (i) the nonlinearity of the regression model can be controlled(More)
We consider an extension of Granger causality to nonlinear bivariate time series. In this frame, if the prediction error of the first time series is reduced by including measurements from the second time series, then the second time series is said to have a causal influence on the first one. Not all the nonlinear prediction schemes are suitable to evaluate(More)
Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we(More)
We 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 the informational circuits present in the system, with an informational character which can be(More)
We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under estimation of causalities. Using the un-normalized version of the causality index, we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches(More)
A great improvement to the insight on brain function that we can get from fMRI data can come from effective connectivity analysis, in which the flow of information between even remote brain regions is inferred by the parameters of a predictive dynamical model. As opposed to biologically inspired models, some techniques as Granger causality (GC) are purely(More)
We consider kernel-based learning methods for regression and analyze what happens to the risk minimizer when new variables, statistically independent of input and target variables, are added to the set of input variables. This problem arises, for example, in the detection of causality relations between two time series. We find that the risk minimizer(More)
Recovering directed pathways of information transfer between brain areas is an important issue in neuroscience and helps to shed light on the brain function in several physiological and cognitive states. Granger causality (GC) analysis is a valuable tool to detect directed dynamical connectivity, and it is being increasingly used. Unfortunately, this(More)
We describe the multiresolution wavelet analysis of blood pressure waves in vasovagal syncope-affected patients compared with those in healthy people, using Haar and Gaussian bases. A comparison between scale-dependent and scale-independent measures discriminating the two classes of subjects is made. What emerges is a sort of equivalence between these two(More)
The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional(More)