Synchronization as adjustment of information rates: Detection from bivariate time series

Abstract

An information-theoretic approach for studying synchronization phenomena in experimental bivariate time series is presented. "Coarse-grained" information rates are introduced and their ability to indicate generalized synchronization as well as to establish a "direction of information flow" between coupled systems, i.e., to discern the driving from the driven (response) system, is demonstrated using numerically generated time series from unidirectionally coupled chaotic systems. The method introduced is then applied in a case study of electroencephalogram recordings of an epileptic patient. Synchronization events leading to seizures have been found on two levels of organization of brain tissues and "directions of information flow" among brain areas have been identified. This allows localization of the primary epileptogenic areas, also confirmed by magnetic resonance imaging and pasitron emission tomography scans.

Delayed mutual information infers patterns of synaptic connectivity in a proprioceptive neural network

“…Timedelayed mutual information quantifies the co-dependence between variables by considering shared previous information content as a function of time (Nichols et al 2005;Palus et al 2001;Vastano and Harry 1988). Here we analyse the delayed mutual information (DMI) estimated from a large multivariate neurobiological data set obtained by Angarita-Jaimes et al (2012), Kondoh et al (1995), Newland and Kondoh (1997a,b) and Vidal-Gadea et al (2010) from a neural network that produces and controls movements of the hind leg of an insect, the desert locust.…”

Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique

“…According to this concept, Porta et al [8] exploited the definition of conditional entropy [9] to measure causality in bivariate systems as the amount of information carried by one process when the past of the * Author to whom correspondence should be addressed: luca.faes@unitn.it other process is known. Further developing this idea through independent approaches, Schreiber [10] and Palus et al [11] defined the concepts of transfer entropy and conditional mutual information, which have been shown to be equivalent later on [12]. These measures allow us to quantify the amount of information exchanged between two systems separately for both directions and, when desired, conditional to common signals.…”

“…The assessment of causality based on information transfer is framed in different terms with respect to the Granger approach, the first involving the concept of uncertainty and the second the concept of predictability. Nevertheless, the relation between transfer entropy and Granger causality is known [11,13], and analytical equivalence has been very recently demonstrated [14], bridging information-theoretic approaches to the classical predictability-based approaches for the evaluation of causality.…”

Nonlinear cardio-respiratory interactions revealed by time-phase bispectral analysis

“…Using the same method one could equally well analyse the combinatorial frequencies responsible for the influence of cardiac on the respiratory system. In fact, using newly developed algorithms for analysis of the direction of coupling (Schreiber 2000, Rosenblum and Pikovsky 2001, Rosenblum et al 2002, Paluš et al 2001, it has already been shown (Stefanovska 2002, Paluš and) that the two systems are bidirectionally coupled. The effect of respiratory system is, however, dominant (i.e.…”

“…The interactions can be detected by analysis of recorded time series, and their strength and direction can also be determined (Schreiber 2000, Rosenblum and Pikovsky 2001, Paluš et al 2001, Rosenblum et al 2002, Paluš and Stefanovska 2003. The next logical step in studying interactions among the coupled oscillators must be to determine the nature of the couplings from the time series.…”