Causal interactions and delays in a neuronal ensemble

We analyze a neural system which mimics a sensorial cortex, with different input characteristics, in presence of transmission delays. We propose a new measure to characterize collective behavior, based on the nonlinear extension of the concept of Granger causality, and an interpretation is given of the variation of the percentage of the causally relevant interactions with transmission delays.Comment: 7 pages, 3 figures. To appear in the AIP seminar notes of 9th Granada seminar on Computational Physics: Computational and Mathematical Modeling of Cooperative Behavior in Neural System

Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by mainly redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone

On the interpretability and computational reliability of frequency-domain Granger causality

This is a comment to the paper 'A study of problems encountered in Granger causality analysis from a neuroscience perspective'. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name 'causality', as nicely described in previous literature). On the other hand we think that the paper uses a formulation of Granger causality which is outdated (albeit still used), and in doing so it dismisses the measure based on a suboptimal use of it. Furthermore, since data from simulated systems are used, the pitfalls that are found with the used formulation are intended to be general, and not limited to neuroscience. It would be a pity if this paper, even written in good faith, became a wildcard against all possible applications of Granger Causality, regardless of the hard work of colleagues aiming to seriously address the methodological and interpretation pitfalls. In order to provide a balanced view, we replicated their simulations used the updated State Space implementation, proposed already some years ago, in which the pitfalls are mitigated or directly solved

Synergy and redundancy in the Granger causal analysis of dynamical networks

We analyze by means of Granger causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst we show that fully conditioned Granger causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. In cases when the number of samples is low, thus making the fully conditioned approach unfeasible, we show that partially conditioned Granger causality is an effective approach if the set of conditioning variables is properly chosen. We consider here two different strategies (based either on informational content for the candidate driver or on selecting the variables with highest pairwise influences) for partially conditioned Granger causality and show that depending on the data structure either one or the other might be valid. On the other hand, we observe that fully conditioned approaches do not work well in presence of redundancy, thus suggesting the strategy of separating the pairwise links in two subsets: those corresponding to indirect connections of the fully conditioned Granger causality (which should thus be excluded) and links that can be ascribed to redundancy effects and, together with the results from the fully connected approach, provide a better description of the causality pattern in presence of redundancy. We finally apply these methods to two different real datasets. First, analyzing electrophysiological data from an epileptic brain, we show that synergetic effects are dominant just before seizure occurrences. Second, our analysis applied to gene expression time series from HeLa culture shows that the underlying regulatory networks are characterized by both redundancy and synergy

Universality of the Tearing Phase in Matrix Models

The spontaneous symmetry breaking associated to the tearing of a random surface, where large dynamical holes fill the surface, was recently analized obtaining a non-universal critical exponent on a border phase. Here the issue of universality is explained by an independent analysis. The one hole sector of the model is useful to manifest the origin of the (limited) non-universal behaviour, that is the existence of two inequivalent critical points.Comment: 9 pages, 1 figure non include

The measure of randomness by leave-one-out prediction error in the analysis of EEG after laser painful stimulation in healthy subjects and migraine patients

Objective: We aimed to perform a quantitative analysis of event-related modulation of EEG activity, resulting from a not-warned and a warned paradigm of painful laser stimulation, in migraine patients and controls, by the use of a novel analysis, based upon a parametric approach to measure predictability of short and noisy time series. Methods: Ten migraine patients were evaluated during the not-symptomatic phase and compared to seven age and sex matched controls. The dorsum of the right hand and the right supraorbital zone were stimulated by a painful CO2 laser, in presence or in absence of a visual warning stimulus. An analysis time of 1 s after the stimulus was submitted to a time–frequency analysis by a complex Morlet wavelet and to a crosscorrelation analysis, in order to detect the development of EEG changes and the most activated cortical regions. A parametric approach to measure predictability of short and noisy time series was applied, where time series were modeled by leave-one-out (LOO) error. Results: The averaged laser-evoked potentials features were similar between the two groups in the alerted and not alerted condition. A strong reset of the beta rhythms after the painful stimuli was seen for three groups of electrodes along the midline in patients and controls: the predictability of the series induced by the laser stimulus changed very differently in controls and patients. The separation was more evident after the warning signal, leading to a separation with P-values of 0.0046 for both the hand and the face. Discussion: As painful stimulus causes organization of the local activity in cortex, EEG series become more predictable after stimulation. This phenomenon was less evident in migraine, as a sign of an inadequate cortical reactivity to pain. Significance: The LOO method enabled to show in migraine subtle changes in the cortical response to pain