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Nonlinear Multivariate Analysis of Neurophysiological Signals
 Progress in Neurobiology
, 2005
"... Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have allowed the study of various types of synchronization from ..."
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Cited by 103 (4 self)
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Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have allowed the study of various types of synchronization from time series. In this work, we first describe the multivariate linear methods most commonly used in neurophysiology and show that they can be extended to assess the existence of nonlinear interdependences between signals. We then review the concepts of entropy and mutual information followed by a detailed description of nonlinear methods based on the concepts of phase synchronization, generalized synchronization and event synchronization. In all cases, we show how to apply these methods to study different kinds of neurophysiological data. Finally, we illustrate the use of multivariate surrogate data test for the assessment of the strength (strong or weak) and the type (linear or nonlinear) of interdependence between neurophysiological signals.
Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field
, 2005
"... Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called ‘chaos theory’, has now progressed to a stage, where it becomes possible to study selforganization and pattern formation in the complex neuronal networks of the br ..."
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Cited by 79 (0 self)
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Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called ‘chaos theory’, has now progressed to a stage, where it becomes possible to study selforganization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of EEG or MEG, an attractor of the underlying dynamical system, and characterizing it in terms of its dimension (an estimate of the degrees of freedom of the system), or its Lyapunov exponents and entropy (reflecting unpredictability of the dynamics due to the sensitive dependence on initial conditions). More recently developed nonlinear measures characterize other features of local brain dynamics (forecasting, time asymmetry, determinism) or the nonlinear synchronization between recordings from different brain regions. Nonlinear time series has been applied to EEG and MEG of healthy subjects during notask resting states, perceptual processing, performance of cognitive tasks and different sleep stages. Many pathologic states have been examined as well, ranging from toxic states, seizures, and psychiatric disorders to Alzheimer’s, Parkinson’s and Cre1utzfeldtJakob’s disease. Interpretation of these results in terms of ‘functional sources ’ and ‘functional networks ’ allows the identification of three basic patterns of brain dynamics: (i) normal, ongoing dynamics during a notask, resting state in healthy subjects; this state is characterized by a high dimensional complexity and a relatively low and fluctuating level of synchronization of the neuronal networks; (ii) hypersynchronous, highly nonlinear dynamics of epileptic seizures; (iii) dynamics of degenerative encephalopathies with an abnormally low level of between area synchronization. Only intermediate levels of rapidly fluctuating synchronization, possibly due to critical dynamics near a phase transition, are associated with normal information
Is there chaos in the brain? II. Experimental evidence and related models
 C. R. Biol
, 2003
"... The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The meth ..."
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Cited by 53 (0 self)
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The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The methods used in each of these studies have almost invariably combined the analysis of experimental data with simulations using formal models, often based on modified Huxley and Hodgkin equations and/or of the Hindmarsh and Rose models of bursting neurons. Due to technical limitations, the results of these simulations have prevailed over experimental ones in studies on the nonlinear properties of large cortical networks and higher brain functions. Yet, and although a convincing proof of chaos (as defined mathematically) has only been obtained at the level of axons, of single and coupled cells, convergent results can be interpreted as compatible with the notion that signals in the brain are distributed according to chaotic patterns at all levels of its various forms of hierarchy. This chronological account of the main landmarks of nonlinear neurosciences follows an earlier publication [Faure, Korn, C. R. Acad. Sci. Paris, Ser. III 324 (2001) 773–793] that was focused on the basic concepts of nonlinear dynamics and methods of investigations which allow chaotic processes to be distinguished from stochastic ones and on the rationale for envisioning their control using external perturbations. Here we present the data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system.
Identifying neural drivers with functional MRI: an electrophysiological validation
 PLoS Biol
, 2008
"... Whether functional magnetic resonance imaging (fMRI) allows the identification of neural drivers remains an open question of particular importance to refine physiological and neuropsychological models of the brain, and/or to understand neurophysiopathology. Here, in a rat model of absence epilepsy s ..."
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Cited by 34 (1 self)
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Whether functional magnetic resonance imaging (fMRI) allows the identification of neural drivers remains an open question of particular importance to refine physiological and neuropsychological models of the brain, and/or to understand neurophysiopathology. Here, in a rat model of absence epilepsy showing spontaneous spikeandwave discharges originating from the first somatosensory cortex (S1BF), we performed simultaneous electroencephalographic (EEG) and fMRI measurements, and subsequent intracerebral EEG (iEEG) recordings in regions strongly activated in fMRI (S1BF, thalamus, and striatum). fMRI connectivity was determined from fMRI time series directly and from hidden state variables using a measure of Granger causality and Dynamic Causal Modelling that relates synaptic activity to fMRI. fMRI connectivity was compared to directed functional coupling estimated from iEEG using asymmetry in generalised synchronisation metrics. The neural driver of spikeandwave discharges was estimated in S1BF from iEEG, and from fMRI only when hemodynamic effects were explicitly removed. Functional connectivity analysis applied directly on fMRI signals failed because hemodynamics varied between regions, rendering temporal precedence irrelevant. This paper provides the first experimental substantiation of the theoretical possibility to improve interregional coupling estimation from hidden neural states of fMRI. As such, it has important implications for future studies on brain connectivity using functional neuroimaging.
The Delay Vector Variance Method for Detecting Determinism and Nonlinearity in Time Series
 Physica D
, 2004
"... A novel `Delay Vector Variance' (DVV) method for detecting the presence of determinism and nonlinearity in a time series is introduced. The method is based upon the examination of local predictability of a signal. Additionally, it spans the complete range of local linear models due to the stand ..."
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Cited by 24 (7 self)
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A novel `Delay Vector Variance' (DVV) method for detecting the presence of determinism and nonlinearity in a time series is introduced. The method is based upon the examination of local predictability of a signal. Additionally, it spans the complete range of local linear models due to the standardisation to the distribution of pairwise distances between delay vectors. This provides consistent and easytointerpret diagrams, which convey information about the nature of a time series. In Preprint submitted to Elsevier Science 3 April 2002 order to gain further insight into the technique, a DVV scatter diagram is introduced, which plots the DVV curve against that for a globally linear model (surrogate data). This way, the deviation from the bisector line represents a qualitative measure of nonlinearity, which can be used additionally for constructing a quantitative measure for statistical testing. The proposed method is compared to existing methods on synthetic, as well as standard realworld signals, and is shown to provide more consistent results overall, compared to other, established nonlinearity analysis methods.
Glacial variability over the last two million years: an extended depthderived agemodel, continuous obliquity pacing, and the Pleistocene progression
 Quat. Sci. Rev
, 2007
"... An agemodel not relying upon orbital assumptions is estimated over the last 2Ma using depth in marine sediment cores as a proxy for time. Agemodel uncertainty averages!10Ka in the early Pleistocene ("2–1Ma) and!7Ka in the late Pleistocene ("1Ma to the present). Twelve benthic and five plan ..."
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Cited by 24 (3 self)
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An agemodel not relying upon orbital assumptions is estimated over the last 2Ma using depth in marine sediment cores as a proxy for time. Agemodel uncertainty averages!10Ka in the early Pleistocene ("2–1Ma) and!7Ka in the late Pleistocene ("1Ma to the present). Twelve benthic and five planktic d18 O records are pinned to the agemodel and averaged together to provide a record of glacial variability. Major deglaciation features are identified over the last 2Ma and a remarkable 33 out of 36 occur when Earth’s obliquity is anomalously large. During the early Pleistocene deglaciations occur nearly every obliquity cycle giving a 40Ka timescale, while late Pleistocene deglaciations more often skip one or two obliquity beats, corresponding to 80 or 120Ka glacial cycles which, on average, give the "100Ka variability. This continuous obliquity pacing indicates that the glacial theory can be simplified. An explanation for the "100Ka glacial cycles only requires a change in the likelihood of skipping an obliquity cycle, rather than new sources of longperiod variability. Furthermore, changes in glacial variability are not marked by any single transition so much as they exhibit a steady progression over the entire Pleistocene. The mean, variance, skewness, and timescale associated with the glacial cycles all exhibit an approximately linear trend over the last 2Ma. A simple model having an obliquity modulated threshold and only three adjustable parameters is shown to reproduce the trends, timing, and spectral evolution associated with the Pleistocene glacial variability.
A Novel Method for Determining the Nature of Time Series
, 2003
"... The Delay Vector Variance (DVV) method, which analyses the nature of a time series with respect to the prevalence of deterministic or stochastic components, is introduced. Due to the standardisation within the DVV method, it is possible both to statistically test for the presence of nonlinearities ..."
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Cited by 18 (2 self)
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The Delay Vector Variance (DVV) method, which analyses the nature of a time series with respect to the prevalence of deterministic or stochastic components, is introduced. Due to the standardisation within the DVV method, it is possible both to statistically test for the presence of nonlinearities in a time series, and to visually inspect the results in a DVV scatter diagram. This approach is convenient for interpretation as it conveys information about the linear or nonlinear nature, as well as about the prevalence of deterministic or stochastic components in the time series, thus unifying the existing approaches which deal either with only deterministic versus stochastic, or the linear versus nonlinear aspect. The results on biomedical time series, namely heart rate variability (HRV) and functional Magnetic Resonance Imaging (fMRI) time series, illustrate the applicability of the proposed DVVmethod.
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"... Establish a collaborative productionprocurement system with contract portfolio approach ..."
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Establish a collaborative productionprocurement system with contract portfolio approach
Estimation and interpretation of 1/f a noise in Human Cognition
, 2004
"... Recent analyses of serial correlations in cognitive tasks have provided preliminary evidence of the presence of a particular form of longrange serial dependence known as 1/f noise. It has been argued that longrange dependence has been largely ignored in mainstream cognitive psychology even though ..."
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Cited by 17 (2 self)
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Recent analyses of serial correlations in cognitive tasks have provided preliminary evidence of the presence of a particular form of longrange serial dependence known as 1/f noise. It has been argued that longrange dependence has been largely ignored in mainstream cognitive psychology even though it accounts for a substantial proportion of variability in behavior (see, e.g., Gilden, 1997, 2001). In this article, we discuss the defining characteristics of longrange dependence and argue that claims about its presence need to be evaluated by testing against the alternative hypothesis of shortrange dependence. For the data from three experiments, we accomplish such tests with autoregressive fractionally integrated movingaverage time series modeling. We find that longrange serial dependence in these experiments can be explained by any of several mechanisms, including mixtures of a small number of shortrange processes.
Correntropy as a novel measure for nonlinearity tests. Signal Processing 89(1
, 2009
"... Abstract—Statistical tests have become an essential step in nonlinear system modeling due to the complexities involved in their analysis. Correntropy is a kernelbased similarity measure which includes the information of both distribution and time structure of a stochastic process. The correntropy f ..."
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Abstract—Statistical tests have become an essential step in nonlinear system modeling due to the complexities involved in their analysis. Correntropy is a kernelbased similarity measure which includes the information of both distribution and time structure of a stochastic process. The correntropy function’s capability of preserving nonlinear characteristics and high order moments makes it a suitable candidate as a statistic for determining whether a nonlinear structure exists within the system that created the observed time series. Experiments based on surrogate data methods have confirmed that correntropy can be employed as a discriminant measure for detecting nonlinear characteristics in time series. I.