Milan Palus

The Czech Academy of Sciences | AVCR · Institute of Computer Science

Principles and applications of statistical testing as a tool for inference of underlying mechanisms from experimental time series are discussed. The computational realizations of the test null hypoth- esis known as the surrogate data are introduced within the context of discerning nonlinear dynamics from noise, and discussed in examples of testing...

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 tr...

Air temperature variability on different time scales exhibits recurring patterns and quasi-oscillatory phenomena. Climate oscillations with the period about 7–8 years have been observed in many instrumental records in Europe. Although these oscillations are weak if considering their amplitude, they might have non-negligible influence on temperature...

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 demo...

The El Niño–Southern Oscillation (ENSO) is a dominant mode of climate variability influencing temperature and precipitation in distant parts of the world. Traditionally, the ENSO influence is assessed considering its amplitude. Focusing on its quasi-oscillatory dynamics comprising multiple timescales, we analyze the causal influence of phases of EN...

Currently, there is no clear understanding of the comprehensive set of variables that controls fluxes of relativistic electrons within the outer radiation belt. Herein, the methodology based on causal inference is applied for identification of factors that control fluxes of relativistic electrons in the outer belt. The patterns of interactions betw...

Many approaches to time series causality exist and have been inspired from fields such as statistics, information theory, physics and topology. We have proposed a method called compression-complexity causality (CCC) [1] inspired from the field of data compression in computer science. It is based on the idea that the compressibility of the 'effect'...

Time series often exhibit a combination of long-range drift and short-term stochastic fluctuations. Traditional methods for analyzing such series involve fitting regression models to capture the drift component and using the residuals to estimate the random component. We demonstrate, however, that estimating the drift in a real-time (time-resolved)...

The El Niño/Southern Oscillation (ENSO) is a dominant mode of climate variability influencing temperature and precipitation in distant parts of the world. Traditionally, the ENSO influence is assessed considering its amplitude. Focusing on its quasioscillatory dynamics comprising multiple time scales, we analyze causal influence of phases of ENSO o...

Consider two stationary time series with heavy-tailed marginal distributions. We aim to detect whether they have a causal relation, that is, if a change in one causes a change in the other. Usual methods for causal discovery are not well suited if the causal mechanisms only appear during extreme events. We propose a framework to detect a causal str...

Learning from successful applications of methods originating in statistical mechanics, complex systems science, or information theory in one scientific field (e.g., atmospheric physics or climatology) can provide important insights or conceptual ideas for other areas (e.g., space sciences) or even stimulate new research questions and approaches. Fo...

The ability to predict response to medication treatment of depressed patients, either early in the course of therapy or before treatment even begins can avoid trials of ineffective therapy and save patients from prolonged intervals of suffering. Symptom alleviation requires 4–6 weeks after starting current antidepressive medication. Based on the da...

This study analyzes causal connections between cross-hemispheric brain regions in individuals diagnosed with major depressive disorder (MDD) through Electroencephalography (EEG) data. A phase-based causality analysis technique is first validated on coupled Rössler systems and then employed on EEG recordings from MDD patients. Our results provide si...

In this paper, we infer the direction of information transfer between interacting subsystems using a cross-dependence index derived from the phase dynamics of coupled subsystems. First, we apply this method to unidirectionally coupled Rössler oscillators. This index always has a higher value along the direction of coupling than that opposite to the...

Understanding physical processes that drive dynamics of the radiation belts - the high-energy charged particle population trapped by the geomagnetic field in the inner magnetosphere, is of great importance for science and society. In fact, this population dynamically interacts with the solar wind and geomagnetic field over various temporal and spat...

Compression-Complexity Causality (CCC) is a recently proposed causality detection method for time series data. It employs complexity estimation techniques based on lossless data-compression algorithms. Along with being formulated as an ‘interventional’ scheme of causality estimation, it overcomes several limitations of traditional causality estimat...

To predict and determine the major drivers of climate has become even more important now as climate change poses a big challenge to humankind and our planet earth. Different studies employ either correlation, causality methods or modelling approaches to study the interaction between climate and climate forcing variables (anthropogenic or natural)....

Coding time series of continuous variables into a sequence of discrete symbols using the ordinal patterns (OP thereafter) of C. Bandt and B. Pompe opened new research avenues in many areas of mathematics, physics, statistics and computer science. OP coding strongly influenced the intersection of information theory and dynamical systems due to the r...

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-co...

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...

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-co...

Consider two stationary time series with heavy-tailed marginal distributions. We want to detect whether they have a causal relation, that is, if a change in one of them causes a change in the other. Usual methods for causality detection are not well suited if the causal mechanisms only manifest themselves in extremes. In this article, we propose ne...

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 s...

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 i...

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...

The identification of causality is the core issue in climate change studies. In this paper, driving force analysis and causal influence of NAO for Central European air temperature is presented using slow feature analysis and convergent cross-mapping. Results showed that the driving force of the dominate 7–8 year scale was reconstructed with central...

Statistical inference of causal interactions and synchronization between dynamical phenomena evolving on different temporal scales is of vital importance for better understanding and prediction of natural complex systems such as the Earth’s climate. This article introduces and applies information theory diagnostics to phase and amplitude time serie...

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 neuro...

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...

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...

Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These measures reflect dependence in static probability distributions, generated by systems’ evolution, rather than...

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 meth...

Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These measures reflect dependence in static probability distributions, generated by systems' evolution, rather than...

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,...

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...

Earth climate, in general, varies on many temporal and spatial scales. In particular, air temperature exhibits recurring patterns and quasi-oscillatory phenomena with different periods. Although these oscillations are usually weak in amplitude, they might have non-negligible influence on temperature variability on shorter timescales due to cross-sc...

Identifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Eartha € 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 networ...

An information-theoretic approach for detecting interactions and information transfer between two systems is extended to interactions between dynamical phenomena evolving on different time scales of a complex, multiscale process. The approach is demonstrated in the detection of an information transfer from larger to smaller time scales in a model m...

It is well established that the global climate is a complex phenomenon with dynamics driven by the interaction of a multitude of identifiable but intertwined subsystems. The identification, at some level, of these subsystems is an important step towards understanding climate dynamics. We present a method to determine the number of principal compone...

Complicated systems composed of many interacting subsystems are frequently studied as complex networks. In the simplest approach, a given real-world system is represented by an undirected graph composed of nodes standing for the subsystems and non-oriented unweighted edges for interactions present among the nodes; the characteristic properties of t...

Free download at: http://www.mdpi.com/1099-4300/15/6/2023 Across geosciences, many investigated phenomena relate to specific complex systems consisting of intricately intertwined interacting subsystems. Such dynamical complex systems can be represented by a directed graph, where each link denotes an existence of a causal relation, or information ex...

Climate data are increasingly analyzed by complex network analysis methods, including graph-theoretical approaches [1]. For such analysis, links between localized nodes of climate network are typically quantified by some statistical measures of dependence (connectivity) between measured variables of interest. To obtain information on the directiona...

Applications of the rotated principal component analysis (RPCA) have a long history in climatology usually due to efforts of finding specific circulation patterns (Barnston and Livezey 1987). Using this approach several well known patterns like the North Atlantic Oscillation (NAO) or the Pacific/North American Pattern (PNA) can be identified (Barns...

Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The term "connectivity" is used in the network context including the study of complex coupled dynamical systems. The choice of dependence measure is key for the results of the subsequent analysis and...

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths together with high clustering of the network, is one of the most discussed and studied. When dealing with coupled d...

Complex network theory allows for novel analyses of multivariate and spatio-temporal data [1]. Mutual dependencies between corresponding subsystems can be represented as a discrete structure - a weighted graph - where each subsystem is represented by a single vertex and each dependence by a connection (a weighted edge) between two such vertices. Th...

Using the enhanced Monte Carlo Singular System Analysis (MC SSA) [1], Palus & Novotna detected a number of oscillatory modes in monthly time series of sunspot numbers, geomagnetic activity aa index, North Atlantic Oscillation (NAO) index and near-surface air temperature from several mid-latitude European stations, some of them with common periods [...

Climate data are increasingly analyzed by complex network analysis methods, including graph-theoretical approaches [1]. For such analysis, links between localised nodes of climate network are typically quantified by some statistical measures of dependence (connectivity) between measured variables of interest. Nonlinear connectivity quantification m...

The theory of complex networks offers a rich set of tools aimed at understanding various aspects of high-dimensional spatiotemporal systems [1]. Recently, methods based on complex network theory have been applied to quantities characterizing climatic variability (e.g. [2]) with the aim of characterizing the behavior of the atmospheric system. Typic...

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. Linear spectral coherence, mean phase coherence (MPC) z-score and Pearson...

The K-means algorithm is very popular in the machine learning community due to its inherent simplicity. However, in its basic form, it is not suitable for use in problems which contain periodic attributes, such as oscillator phase, hour of day or directional heading. A commonly used technique of trigonometrically encoding periodic input attributes...

Free download at: http://www.nonlin-processes-geophys.net/18/751/2011/npg-18-751-2011.pdf The bias due to dynamical memory (serial correlations) in an association/dependence measure (absolute cross-correlation) is demonstrated in model data and identified in time series of meteorological variables used for construction of climate networks. Accounti...

Ever wider implementation of information technologies is flooding us by monitoring data. To an efficient risk management, those data have to be processed and assessed in the same rate as they are recorded and transported. Paper demonstrates some methods dealing with intrinsic, nonlinear dynamics of slope system for computerized safety assessment of...

Beginning from the 1950's, Palus and Novotná (2009) observed statistically significant phase coherence among oscillatory modes with the period of approximately 7-8 years detected in monthly time series of sunspot numbers, geomagnetic activity aa index, North Atlantic Oscillation (NAO) index and near-surface air temperature from several mid-latitude...

In recent years, there has been an increasing interest in the study of large-scale brain activity interaction structure from the perspective of complex networks, based on functional magnetic resonance imaging (fMRI) measurements. To assess the strength of interaction (functional connectivity, FC) between two brain regions, the linear (Pearson) corr...

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 corr...

Phase synchronization and directionality of human EEG data recorded under influence of audio-visual stimulation were investigated. EEG data came from 6 healthy volunteers repeatedly exposed to 20 min stimulation that comprised intervals with steady stimulation at 4 and 17 Hz. Entrainment of the brain waves and phase synchronization both significant...

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 i...

Technical issues related to construction of complex networks from multivariate time series are discussed, namely the definition of network edges using dependence measures estimated from pairs of time series. The estimated connectivity patterns may depend on choices of dependence measures, whether they are linear or nonlinear, global or scale/freque...

Daily mean near-surface air temperature series from seven European locations were processed in order to obtain reliable estimates of instantaneous phases of the annual cycle as an objective measure of timing of seasons. The recent changes of the latter do not depart from the range of natural phase fluctuations observed in the historical temperature...

Detection and extraction of quasi-oscillatory dynamical modes from instrumental records of meteorological variables, climatological proxies and proxies of solar activity, or other geophysical data became a useful tool in analysing variability of observed phenomena reflected in complex, multivariate geophysical signals. Recent development in nonline...

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 i...

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 pro...

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 bispectr...

Detection and extraction of quasi-oscillatory dynamical modes from instrumental records of meteorological variables, climatological proxies and proxies of solar activity, or other geophysical data became a useful tool in analysing variability of observed phenomena reflected in complex, multivariate geophysical signals. Recent development in nonline...

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...

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 p...

Oscillatory modes with the period of approximately 7–8 yr were detected in monthly time series of sunspot numbers, geomagnetic activity aa index, NAO (North Atlantic Oscillation) index and near-surface air temperature from several mid-latitude European locations. Instantaneous phases of the modes underwent synchronization analysis and their statist...