Information flow in first-order potts model phase transition.

Phase transitions abound in nature and society, and, from species extinction to stock market collapse, their prediction is of widespread importance. In earlier work we showed that Global Transfer Entropy, a general measure of information flow, was found to peaks away from the transition on the disordered side for the Ising model, a canonical second order transition. Here we show that (a) global transfer entropy also peaks on the disordered side of the transition of finite first order transitions, such as ecology dynamics on coral reefs, which have latent heat and no correlation length divergence, and (b) analysis of information flow across state boundaries unifies both transition orders.

Decreased directed functional connectivity in the psychedelic state.

Neuroimaging studies of the psychedelic state offer a unique window onto the neural basis of conscious perception and selfhood. Despite well understood pharmacological mechanisms of action, the large-scale changes in neural dynamics induced by psychedelic compounds remain poorly understood. Using source-localised, steady-state MEG recordings, we describe changes in functional connectivity following the controlled administration of LSD, psilocybin and low-dose ketamine, as well as, for comparison, the (non-psychedelic) anticonvulsant drug tiagabine.

Solved problems for Granger causality in neuroscience: A response to Stokes and Purdon.

Granger-Geweke causality (GGC) is a powerful and popular method for identifying directed functional ('causal') connectivity in neuroscience. In a recent paper, Stokes and Purdon (2017b) raise several concerns about its use. They make two primary claims: (1) that GGC estimates may be severely biased or of high variance, and (2) that GGC fails to reveal the full structural/causal mechanisms of a system.

Global and local complexity of intracranial EEG decreases during NREM sleep.

Key to understanding the neuronal basis of consciousness is the characterization of the neural signatures of changes in level of consciousness during sleep. Here we analysed three measures of dynamical complexity on spontaneous depth electrode recordings from 10 epilepsy patients during wakeful rest (WR) and different stages of sleep: (i) Lempel-Ziv complexity, which is derived from how compressible the data are; (ii) amplitude coalition entropy, which measures the variability over time of the set of channels active above a threshold; (iii) synchrony coalition entropy, which measures the variability over time of the set of synchronous channels. When computed across sets of channels that are broadly distributed across multiple brain regions, all three measures decreased substantially in all participants during early-night non-rapid eye movement (NREM) sleep.

Detectability of Granger causality for subsampled continuous-time neurophysiological processes.

Background: Granger causality is well established within the neurosciences for inference of directed functional connectivity from neurophysiological data. These data usually consist of time series which subsample a continuous-time biophysiological process. While it is well known that subsampling can lead to imputation of spurious causal connections where none exist, less is known about the effects of subsampling on the ability to reliably detect causal connections which do exist.

Granger causality for state-space models.

Granger causality has long been a prominent method for inferring causal interactions between stochastic variables for a broad range of complex physical systems. However, it has been recognized that a moving average (MA) component in the data presents a serious confound to Granger causal analysis, as routinely performed via autoregressive (AR) modeling. We solve this problem by demonstrating that Granger causality may be calculated simply and efficiently from the parameters of a state-space (SS) model.

Information flow in a kinetic Ising model peaks in the disordered phase.

There is growing evidence that for a range of dynamical systems featuring complex interactions between large ensembles of interacting elements, mutual information peaks at order-disorder phase transitions. We conjecture that, by contrast, information flow in such systems will generally peak strictly on the disordered side of a phase transition. This conjecture is verified for a ferromagnetic 2D lattice Ising model with Glauber dynamics and a transfer entropy-based measure of systemwide information flow.

The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference.

Background: Wiener-Granger causality ("G-causality") is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond.

Granger causality analysis of fMRI BOLD signals is invariant to hemodynamic convolution but not downsampling.

Granger causality is a method for identifying directed functional connectivity based on time series analysis of precedence and predictability. The method has been applied widely in neuroscience, however its application to functional MRI data has been particularly controversial, largely because of the suspicion that Granger causal inferences might be easily confounded by inter-regional differences in the hemodynamic response function. Here, we show both theoretically and in a range of simulations, that Granger causal inferences are in fact robust to a wide variety of changes in hemodynamic response properties, including notably their time-to-peak.

Transfer entropy as a log-likelihood ratio.

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required.

Causal density and integrated information as measures of conscious level.

An outstanding challenge in neuroscience is to develop theoretically grounded and practically applicable quantitative measures that are sensitive to conscious level. Such measures should be high for vivid alert conscious wakefulness, and low for unconscious states such as dreamless sleep, coma and general anaesthesia. Here, we describe recent progress in the development of measures of dynamical complexity, in particular causal density and integrated information.

Behaviour of Granger causality under filtering: theoretical invariance and practical application.

Granger causality (G-causality) is increasingly employed as a method for identifying directed functional connectivity in neural time series data. However, little attention has been paid to the influence of common preprocessing methods such as filtering on G-causality inference. Filtering is often used to remove artifacts from data and/or to isolate frequency bands of interest.

Multivariate Granger causality and generalized variance.

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables but may occur among groups or "ensembles" of variables.

Granger causality and transfer entropy are equivalent for Gaussian variables.

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field.