Causes of extreme events revealed by Rényi information transfer.

Information-theoretic generalization of Granger causality principle, based on evaluation of conditional mutual information, also known as transfer entropy (CMI/TE), is redefined in the framework of Rényi entropy (RCMI/RTE). Using numerically generated data with a defined causal structure and examples of real data from the climate system, it is demonstrated that RCMI/RTE is able to identify the cause variable responsible for the occurrence of extreme values in an effect variable. In the presented example, the Siberian High was identified as the cause responsible for the increased probability of cold extremes in the winter and spring surface air temperature in Europe, while the North Atlantic Oscillation and blocking events can induce shifts of the whole temperature probability distribution.

Lead/Lag directionality is not generally equivalent to causality in nonlinear systems: Comparison of phase slope index and conditional mutual information.

Applications of causal techniques to neural time series have increased extensively over last decades, including a wide and diverse family of methods focusing on electroencephalogram (EEG) analysis. Besides connectivity inferred in defined frequency bands, there is a growing interest in the analysis of cross-frequency interactions, in particular phase and amplitude coupling and directionality. Some studies show contradicting results of coupling directionality from high frequency to low frequency signal components, in spite of generally considered modulation of a high-frequency amplitude by a low-frequency phase.

Compression complexity with ordinal patterns for robust causal inference in irregularly sampled time series.

Distinguishing cause from effect is a scientific challenge resisting solutions from mathematics, statistics, information theory and computer science. Compression-Complexity Causality (CCC) is a recently proposed interventional measure of causality, inspired by Wiener-Granger's idea. It estimates causality based on change in dynamical compression-complexity (or compressibility) of the effect variable, given the cause variable.

Phase-based causality analysis with partial mutual information from mixed embedding.

Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems.

Cross-Scale Causality and Information Transfer in Simulated Epileptic Seizures.

An information-theoretic approach for detecting causality and information transfer was applied to phases and amplitudes of oscillatory components related to different time scales and obtained using the wavelet transform from a time series generated by the Epileptor model. Three main time scales and their causal interactions were identified in the simulated epileptic seizures, in agreement with the interactions of the model variables. An approach consisting of wavelet transform, conditional mutual information estimation, and surrogate data testing applied to a single time series generated by the model was demonstrated to be successful in the identification of all directional (causal) interactions between the three different time scales described in the model.

Causality and Information Transfer Between the Solar Wind and the Magnetosphere-Ionosphere System.

An information-theoretic approach for detecting causality and information transfer is used to identify interactions of solar activity and interplanetary medium conditions with the Earth's magnetosphere-ionosphere systems. A causal information transfer from the solar wind parameters to geomagnetic indices is detected. The vertical component of the interplanetary magnetic field (Bz) influences the auroral electrojet (AE) index with an information transfer delay of 10 min and the geomagnetic disturbances at mid-latitudes measured by the symmetric field in the H component (SYM-H) index with a delay of about 30 min.

Coupling in complex systems as information transfer across time scales.

Complex systems such as the human brain or the Earth's climate consist of many subsystems interacting in intricate, nonlinear ways. Moreover, variability of such systems extends over broad ranges of spatial and temporal scales and dynamical phenomena on different scales also influence each other. In order to explain how to detect cross-scale causal interactions, we review information-theoretic formulation of the Granger causality in combination with computational statistics (surrogate data method) and demonstrate how this method can be used to infer driver-response relations from amplitudes and phases of coupled nonlinear dynamical systems.

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

The mechanism 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. We found that the transition to seizure is not a sudden phenomenon, but is instead a slow process that is 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 that is observable in systems characterized by transitions between dynamical regimes.

Causality, dynamical systems and the arrow of time.

Using several methods for detection of causality in time series, we show in a numerical study that coupled chaotic dynamical systems violate the first principle of Granger causality that the cause precedes the effect. While such a violation can be observed in formal applications of time series analysis methods, it cannot occur in nature, due to the relation between entropy production and temporal irreversibility. The obtained knowledge, however, can help to understand the type of causal relations observed in experimental data, namely, it can help to distinguish linear transfer of time-delayed signals from nonlinear interactions.

Comparison of six methods for the detection of causality in a bivariate time series.

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20000 points long clean time series but also noisy and short variants of the data.

Detection of coupling delay: A problem not yet solved.

Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed-the method based on conditional mutual information-the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping-the CCM method.

Smooth information flow in temperature climate network reflects mass transport.

A directed climate network is constructed by Granger causality analysis of air temperature time series from a regular grid covering the whole Earth. Using winner-takes-all network thresholding approach, a structure of a smooth information flow is revealed, hidden to previous studies. The relevance of this observation is confirmed by comparison with the air mass transfer defined by the wind field.

Small-world bias of correlation networks: From brain to climate.

Complex systems are commonly characterized by the properties of their graph representation. Dynamical complex systems are then typically represented by a graph of temporal dependencies between time series of state variables of their subunits. It has been shown recently that graphs constructed in this way tend to have relatively clustered structure, potentially leading to spurious detection of small-world properties even in the case of systems with no or randomly distributed true interactions.

Identifying causal gateways and mediators in complex spatio-temporal systems.

Identifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Earth's climate to volcanic eruptions, extreme events or geoengineering. Here a data-driven approach is introduced based on a dimension reduction, causal reconstruction, and novel network measures based on causal effect theory that go beyond standard complex network tools by distinguishing direct from indirect pathways. Applied to a data set of atmospheric dynamics, the method identifies several strongly uplifting regions acting as major gateways of perturbations spreading in the atmosphere.

Multiscale atmospheric dynamics: cross-frequency phase-amplitude coupling in the air temperature.

Interactions between dynamics on different temporal scales of about a century long record of data of the daily mean surface air temperature from various European locations have been detected using a form of the conditional mutual information, statistically tested using the Fourier-transform and multifractal surrogate data methods. An information transfer from larger to smaller time scales has been observed as the influence of the phase of slow oscillatory phenomena with the periods around 6-11 yr on the amplitudes of the variability characterized by the smaller temporal scales from a few months to 4-5 yr. The overall effect of the slow oscillations on the interannual temperature variability within the range 1-2 ° C has been observed in large areas of Europe.

Comparison of coherence and phase synchronization of the human sleep electroencephalogram.

Objective: Potential differences between coherence and phase synchronization analyses of human sleep electroencephalogram (EEG) are assessed and occurrences of phase vs. complete synchronization between EEG signals from different locations during different sleep stages are investigated.

Methods: Linear spectral coherence, mean phase coherence (MPC) z-score and Pearson's correlation coefficient of analytic amplitudes were evaluated for different spectral bands of whole-night EEG recordings from 25 healthy subjects.

Partitioning networks into clusters and residuals with average association.

We investigate the problem of detecting clusters exhibiting higher-than-average internal connectivity in networks of interacting systems. We show how the average association objective formulated in the context of spectral graph clustering leads naturally to a clustering strategy where each system is assigned to at most one cluster. A residual set is formed of the systems that are not members of any cluster.

Functional connectivity in resting-state fMRI: is linear correlation sufficient?

Functional connectivity (FC) analysis is a prominent approach to analyzing fMRI data, especially acquired under the resting state condition. The commonly used linear correlation FC measure bears an implicit assumption of Gaussianity of the dependence structure. If only the marginals, but not all the bivariate distributions are Gaussian, linear correlation consistently underestimates the strength of the dependence.

Identification of nonlinear oscillatory activity embedded in broadband neural signals.

Oscillatory phenomena in the brain activity and their synchronization are frequently studied using mathematical models and analytic tools derived from nonlinear dynamics. In many experimental situations, however, neural signals have a broadband character and if oscillatory activity is present, its dynamical origin is unknown. To cope with these problems, a framework for detecting nonlinear oscillatory activity in broadband time series is presented.

High-frequency network activity, global increase in neuronal activity, and synchrony expansion precede epileptic seizures in vitro.

How seizures start is a major question in epilepsy research. Preictal EEG changes occur in both human patients and animal models, but their underlying mechanisms and relationship with seizure initiation remain unknown. Here we demonstrate the existence, in the hippocampal CA1 region, of a preictal state characterized by the progressive and global increase in neuronal activity associated with a widespread buildup of low-amplitude high-frequency activity (HFA) (>100 Hz) and reduction in system complexity.

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.

Sensitization, epileptic-like symptoms and local synchronization in patients with paranoid schizophrenia.

Recent findings indicate that changes in synchronization of neural activities underlying sensitization and kindling could be more comprehensively understood using nonlinear methods. With this aim we have examined local synchronization using novel measure of coarse-grained information rate (CIR) in 8 EEG signals recorded at different cortical areas in 44 patients with paranoid schizophrenia. The values of local synchronization that could reflect sensitization related changes in EEG activities of cortical sites were then related to psychometric measures of epileptic-like symptoms and positive and negative schizophrenia symptoms (PANSS).

Phase synchronization analysis by assessment of the phase difference gradient.

Phase synchronization is an important phenomenon of nonlinear dynamics and has recently received much scientific attention. In this work a method for identifying phase synchronization epochs is described which focuses on estimating the gradient of segments of the generalized phase differences between phase slips in an experimental time series. In phase synchronized systems, there should be a zero gradient of the generalized phase differences even if the systems are contaminated by noise.

Detecting nonlinear oscillations in broadband signals.

A framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modeled as a linear stochastic process possibly passed through a static nonlinear transformation.

Chaos in schizophrenia associations, reality or metaphor?

There is evidence that schizophrenic associations display "chaotic", random-like behavior and decreased predictability. The evidence suggests a hypothesis that the "chaotic" mental disorganization could be explained within the concept of nonlinear dynamics and complexity in the brain that may cause chaotic neural organization. Testing of the hypothesis in the present study was performed using nonlinear analysis of bilateral electrodermal activity (EDA) during resting state and an association test in 56 schizophrenic patients and 44 healthy participants.