Identifying causal gateways and mediators in complex spatio-temporal systems

J.R. received support by the German National Academic Foundation (Studienstiftung), a Humboldt University Postdoctoral Fellowship, and the German Federal Ministry of Science and Education (Young Investigators Group CoSy-CC2, grant no. 01LN1306A). J.F.D. thanks the Stordalen Foundation and BMBF (project GLUES) for financial support. D.H. has been funded by grant ERC-CZ CORES LL-1201 of the Czech Ministry of Education. M.P. and N.J. received funding from the Czech Science Foundation project No. P303-14-02634S and from the Czech Ministry of Education, Youth and Sports, project No. DAAD-15-30. J.H. was supported by the Czech Science Foundation project GA13-23940S and Czech Health Research Council project NV15-29835A. We thank Mary Lindsey from the National Oceanic and Atmospheric Administration for her kind help with Fig. 4e. NCEP Reanalysis data provided by NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their web site at http://www.esrl.noaa.gov/psd/.Peer reviewedPublisher PD

Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations

The mechanisms of seizure emergence, and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are two of the most important unresolved issues in modern epilepsy research. Our study shows that the transition to seizure is not a sudden phenomenon,but a slow process characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by the synchronous synaptic input from IEDs. IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either anti-seizure or pro-seizure effects. We show that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence

Detecting couplings between interacting oscillators with time-varying basic frequencies: Instantaneous wavelet bispectrum and information theoretic approach

In the natural world, the properties of interacting oscillatory systems are not constant, but evolve or fluctuating continuously in time. Thus, the basic frequencies of the interacting oscillators are time varying, which makes the system analysis complex. For studying their interactions we propose a complementary approach combining wavelet bispectral analysis and information theory. We show how these methods uncover the interacting properties and reveal the nature, strength, and direction of coupling. Wavelet bispectral analysis is generalized as a technique for detecting instantaneous phase-time dependence for the case of two or more coupled nonlinear oscillators whereas the information theory approach can uncover the directionality of coupling and extract driver-response relationships in complex systems. We generate bivariate time-series numerically to mimic typical situations that occur in real measured data, apply both methods to the same time-series and discuss the results. The approach is applicable quite generally to any system of coupled nonlinear oscillators

Enhanced Monte Carlo Singular System Analysis and detection of period 7.8 years oscillatory modes in the monthly NAO index and temperature records

International audienceAn extension of the Monte Carlo Singular System Analysis (MC SSA) is described, based on evaluating and testing regularity of dynamics of the SSA modes against the colored noise null hypothesis, in addition to the test based on variance (eigenvalues). The application of the regularity index, computed from a coarse-grained estimation of mutual information, enhances the test sensitivity and reliability in detection of relatively more regular dynamical modes than those obtained by decomposition of colored noises, in particular, in detection of irregular oscillations embedded in red noise. This enhanced MC SSA is successfully applied in detection of period 7.8 years oscillatory modes in records of monthly average near-surface air temperature from several European locations, as well as in the monthly North Atlantic Oscillation index

Chaotic Measures and Real-World Systems

. Direct estimation of the largest Lyapunov exponent as a measure of exponential divergence of nearby trajectories is well established in the case of deterministic dynamical systems. Questions are naturally raised about applicability of Lyapunov exponents and other "chaotic measures" when analyzing data from real-world systems, which are either stochastic or affected by numerous external influences, which cannot be described in any other way than a stochastic component in system dynamics. In a series of numerical experiments, Gaussian random deviates were added to a set of chaotic time series with different Lyapunov exponents. It is demonstrated, that the estimated Lyapunov exponents fail to distinguish different noisy chaotic time series, when relatively small scales are used. The distinction can be reestablished by using larger scales. Using larger scales, however, the estimated Lyapunov exponent is determined by macroscopic statistical properties of the series, that is, it provides ..

Nonlinearity in Normal Human EEG: Cycles, temporal asymmetry, nonstationarity and randomness, not chaos

Two-hour vigilance and sleep EEG recordings from five healthy volunteers were analyzed using a method for identifying nonlinearity and chaos, which combines the redundancy -- linear redundancy approach with the surrogate data technique. A nonlinear component in the EEG was detected, however, inconsistent with the hypothesis of low-dimensional chaos. A possibility, that a temporally asymmetric process may underlie or influence the EEG dynamics, was indicated. A process, that merges nonstationary nonlinear deterministic oscillations with randomness, is proposed for an explanation of observed properties of the analyzed EEG signals. Taking these results into consideration, the use of dimensional and related chaos-based algorithms in quantitative EEG analysis is critically discussed. 1 Introduction During the last decade there has been a sustained interest in describing neural processes and brainsignals, especially the electroencephalogram (EEG), within the context of nonlinear dynamics an..

On entropy rates of dynamical systems and Gaussian processes

A possibility of a relation between the Kolmogorov-Sinai entropy of a dynamical system and the entropy rate of a Gaussian process isospectral to time series generated by the dynamical system is numerically investigated using discrete and continuous chaotic dynamical systems. The results suggest that such a relation as a nonlinear one-to-one function may exist when the Kolmogorov-Sinai entropy varies smoothly with variations of system's parameters, but is broken in critical states near bifurcation points. 1 Entropy rates Entropy rates will be considered as a tool for quantitative characterization of dynamic processes evolving in time. Let fx i g be a time series, i.e., a series of measurements done on a system in consecutive instants of time i = 1; 2; : : :. The time series fx i g can be considered as a realization of a stochastic process fX i g, characterized by the joint probability distribution function p(x 1 ; : : : ; xn ), p(x 1 ; : : : ; xn ) = Prf(X 1 ; : : : ; Xn ) = (x 1 ; : ..

Detection of Nonlinearity and Chaos in Time Series

A method for identification of nonlinearity and chaos in time series is presented. Nonlinearity is tested using a procedure which combines redundancy and surrogate data techniques. After positive identification of the nonlinear character of the data under study, the possible presence of underlying chaotic dynamics can be assessed by a marginal redundancy approach, because of the direct relationship of the marginal redundancy to the Kolmogorov-Sinai entropy of the dynamical system that generates the data. 1 Introduction Ideas and concepts from nonlinear dynamics and deterministic chaos theory have led to a number of algorithms which are able, in principle, to identify and quantify underlying nonlinear deterministic/chaotic dynamics in time series (Abraham et al. 1989, Grassberger & Procaccia 1983, Mayer-Kress 1986). After extensive use, however, many of these algorithms were found to be chronically unreliable, often This article (further referred to as article [I]) was written as a ..

Coarse-Grained Entropy Rates for Characterization of Complex Time Series

A method for classification of complex time series using coarse-grained entropy rates (CER's) is presented. The CER's, which are computed from information-theoretic functionals -- redundancies, are relative measures of regularity and predictability, and for data generated by dynamical systems they are related to Kolmogorov-Sinai entropy. A deterministic dynamical origin of the data under study, however, is not a necessary condition for the use of the CER's, since the entropy rates can be defined for stochastic processes as well. Sensitivity of the CER's to changes in data dynamics and their robustness with respect to noise are tested by using numerically generated time series resulted from both deterministic -- chaotic and stochastic processes. Potential application of the CER's in analysis of physiological signals or other complex time series is demonstrated by using examples from pharmaco-EEG and tremor classification. 1 Introduction A number of descriptive measures, like dimensions..