1,721,013 research outputs found
Critical temperatures in driven binary mixtures with conserved and non-conserved dynamics
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Kernel-Granger causality and the analysis of dynamical networks
Full text linkWe 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 by choosing the kernel function and ii the problem of false causalities,
arising as the complexity of the model increases, is addressed by a selection strategy of the eigenvectors of a
reduced Gram matrix whose range represents the additional features due to the second time series. Moreover,
there is no a priori assumption that the network must be a directed acyclic graph. We apply the proposed
approach to a network of chaotic maps and to a simulated genetic regulatory network: it is shown that the
underlying topology of the network can be reconstructed from time series of node’s dynamics, provided that a
sufficient number of samples is available. Considering a linear dynamical network, built by preferential attachment
scheme, we show that for limited data use of the bivariate Granger causality is a better choice than
methods using L1 minimization. Finally we consider real expression data from HeLa cells, 94 genes and 48
time points. The analysis of static correlations between genes reveals two modules corresponding to wellknown
transcription factors; Granger analysis puts in evidence 19 causal relationships, all involving genes
related to tumor development
Granger causality for circular variables
No full textIn this Letter we discuss the use of Granger causality to the analyze systems of coupled circular variables,
by modifying a recently proposed method for multivariate analysis of causality. We show the application
of the proposed approach on several Kuramoto systems, in particular one living on networks built
by preferential attachment and a model for the transition from deeply to lightly anaesthetized states.
Granger causalities describe the flow of information among variables
Synergy as a warning sign of transitions : the case of the two-dimensional Ising model
Full text linkWe consider the formalism of information decomposition of target effects from multisource interactions, i.e., the problem of defining redundant and synergistic components of the information that a set of source variables provides about a target, and apply it to the two-dimensional Ising model as a paradigm of a critically transitioning system. Intuitively, synergy is the information about the target variable that is uniquely obtained by taking the sources together, but not considering them alone; redundancy is the information which is shared by the sources. To disentangle the components of the information both at the static level and at the dynamical one, the decomposition is applied respectively to the mutual information and to the transfer entropy between a given spin, target, and a pair of neighboring spins (taken as the drivers). We show that a key signature of an impending phase transition (approached from the disordered size) is the fact that the synergy peaks in the disordered phase, both in the static and in the dynamic case: The synergy can thus be considered a precursor of the transition. The redundancy, instead, reaches its maximum at the critical temperature. The peak of the synergy of the transfer entropy is far more pronounced than those of the static mutual information. We show that these results are robust with respect to the details of the information decomposition approach, as we find the same results using two different methods; moreover, with respect to previous literature rooted in the notion of global transfer entropy, our results demonstrate that considering as few as three variables is sufficient to construct a precursor of the transition, and provide a paradigm for the investigation of a variety of systems prone to crisis, such as financial markets, social media, or epileptic seizures
Kernel Method for Nonlinear Granger Causality
Full text linkImportant 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 generalize Granger causality to the nonlinear case using the
theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature
space of suitable kernel functions, assuming arbitrary degree of nonlinearity.We develop a new strategy to
cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces.
Applications to coupled chaotic maps and physiological data sets are presented
Causal Information Approach to Partial Conditioning in Multivariate Data Sets
Full text linkWhen evaluating causal influence from one time series to another in a multivariate data set it is necessary to take into account
the conditioning effect of the other variables. In the presence of many variables and possibly of a reduced number of samples, full
conditioning can lead to computational and numerical problems. In this paper, we address the problem of partial conditioning to
a limited subset of variables, in the framework of information theory. The proposed approach is tested on simulated data sets and
on an example of intracranial EEG recording from an epileptic subject. We show that, in many instances, conditioning on a small
number of variables, chosen as the most informative ones for the driver node, leads to results very close to those obtained with
a fully multivariate analysis and even better in the presence of a small number of samples. This is particularly relevant when the
pattern of causalities is sparse
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