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54
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 107 (5 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.
A neural mass model for MEG/EEG: coupling and neuronal dynamics
 NeuroImage
, 2003
"... Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequencyspecific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their func ..."
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Cited by 81 (21 self)
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Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequencyspecific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their functional significance remains a matter of debate. Some of the mechanisms that generate these signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. The kinetics of the ensuing population dynamics determine the frequency of oscillations. In this work we extended the classical nonlinear lumpedparameter model of alpha rhythms, initially developed by Lopes da Silva and colleagues [Kybernetik 15 (1974) 27], to generate more complex dynamics. We show that the whole spectrum of MEG/EEG signals can be reproduced within the oscillatory regime of this model by simply changing the population kinetics. We used the model to examine the influence of coupling strength and propagation delay on the rhythms generated by coupled cortical areas. The main findings were that (1) coupling induces phaselocked activity, with a phase shift of 0 or &pi; when the coupling is bidirectional, and (2) both coupling and propagation delay are critical determinants of the MEG/EEG spectrum. In forthcoming articles, we will use this model to (1) estimate how neuronal interactions are expressed in MEG/EEG oscillations and establish the construct validity of various indices of nonlinear coupling, and (2) generate eventrelated transients to derive physiologically informed basis functions for statistical modelling of average evoked responses.
Information selfstructuring: key principle for learning and development
 Proc. of the 4 th Int. Conf. on Development and Learning
, 2005
"... Abstract Intelligence and intelligencelike processes are characterized by a complex yet balanced interplay across multiple time scales between an agent’s brain, body, and environment. Through sensor and motor activity natural organisms and robots are continuously and dynamically coupled to their e ..."
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Cited by 37 (2 self)
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Abstract Intelligence and intelligencelike processes are characterized by a complex yet balanced interplay across multiple time scales between an agent’s brain, body, and environment. Through sensor and motor activity natural organisms and robots are continuously and dynamically coupled to their environments. We argue that such coupling represents a major functional rationale for the ability of embodied agents to actively structure their sensory input and to generate statistical regularities. Such regularities in the multimodal sensory data relayed to the brain are critical for enabling appropriate developmental processes, perceptual categorization, adaptation, and learning. We show how information theoretical measures can be used to quantify statistical structure in sensory and motor channels of a robot capable of saliencydriven, attentionguided behavior. We also discuss the potential importance of such measures for understanding sensorimotor coordination in organisms (in particular, visual attention) and for robot design. Index Terms – embodied interaction, information theory, information structure I.
Dynamic causal modelling of induced responses
 NeuroImage
, 2008
"... This paper describes a dynamic causal model (DCM) for induced or spectral responses as measured with the electroencephalogram (EEG) or the magnetoencephalogram (MEG). We model the timevarying power, over a range of frequencies, as the response of a distributed system of coupled electromagnetic sour ..."
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Cited by 18 (4 self)
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This paper describes a dynamic causal model (DCM) for induced or spectral responses as measured with the electroencephalogram (EEG) or the magnetoencephalogram (MEG). We model the timevarying power, over a range of frequencies, as the response of a distributed system of coupled electromagnetic sources to a spectral perturbation. The model parameters encode the frequency response to exogenous input and coupling among sources and different frequencies. The Bayesian inversion of this model, given data enables inferences about the parameters of a particular model and allows us to compare different models, or hypotheses. One key aspect of the model is that it differentiates between linear and nonlinear coupling; which correspond to within and betweenfrequency coupling respectively. To establish the face validity of our approach, we generate synthetic data and test the identifiability of various parameters to ensure they can be estimated accurately, under different levels of noise. We then apply our model to EEG data from a faceperception experiment, to ask whether there is evidence for nonlinear coupling between early visual cortex and fusiform areas.
Methods for quantifying the causal structure of bivariate time series
 Int. J. of Bifurcation and Chaos
, 2006
"... In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear m ..."
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Cited by 14 (1 self)
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In the study of complex systems one of the major concerns is the detection and characterization of causal interdependencies and couplings between different subsystems. The nature of such dependencies is typically not only nonlinear but also asymmetric and thus makes the use of symmetric and linear methods ineffective. Moreover, signals sampled from real world systems are noisy and short, posing additional constraints on the estimation of the underlying couplings. In this article, we compare a set of six recently introduced methods for quantifying the causal structure of bivariate time series extracted from systems with complex dynamical behavior. We discuss the usefulness of the methods for detecting asymmetric couplings and directional flow of information in the context of uni and bidirectionally coupled deterministic chaotic systems. Key words: causal structure, nonlinear time series analysis, coupled systems, information flow
Information dynamics and emergent computation in recurrent circuits of spiking neurons
 Proc. of NIPS 2003, Advances in Neural Information Processing Systems. Volume 16
, 2004
"... We employ an efficient method using Bayesian and linear classifiers for analyzing the dynamics of information in highdimensional states of generic cortical microcircuit models. It is shown that such recurrent circuits of spiking neurons have an inherent capability to carry out rapid computations o ..."
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Cited by 12 (2 self)
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We employ an efficient method using Bayesian and linear classifiers for analyzing the dynamics of information in highdimensional states of generic cortical microcircuit models. It is shown that such recurrent circuits of spiking neurons have an inherent capability to carry out rapid computations on complex spike patterns, merging information contained in the order of spike arrival with previously acquired context information. 1
Quantifying patterns of agentenvironment interaction. Robotics and Autonomous Systems (in press
, 2005
"... This article explores the assumption that a deeper (quantitative) understanding of the informationtheoretic implications of sensorymotor coordination can help endow robots not only with better sensory morphologies, but also with better exploration strategies. Specifically, we investigate by means ..."
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Cited by 11 (4 self)
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This article explores the assumption that a deeper (quantitative) understanding of the informationtheoretic implications of sensorymotor coordination can help endow robots not only with better sensory morphologies, but also with better exploration strategies. Specifically, we investigate by means of statistical and informationtheoretic measures, to what extent sensorymotor coordinated activity can generate and structure information in the sensory channels of a simulated agent interacting with its surrounding environment. The results show how the usage of correlation, entropy, and mutual information can be employed (a) to segment an observed behavior into distinct behavioral states, (b) to analyze the informational relationship between the different components of the sensorymotor apparatus, and (c) to identify patterns (or fingerprints) in the sensorymotor interaction between the agent and its local environment. Key words: Selfstructuring of information, sensorymotor coordination, agentenvironment interaction 1
Biomechanically Informed Nonlinear Speech Signal Processing, DPhil Thesis
, 2007
"... Linear digital signal processing based around linear, timeinvariant systems theory nds substantial application in speech processing. The linear acoustic sourcelter theory of speech production provides ready biomechanical justication for using linear techniques. Nonetheless, biomechanical studies s ..."
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Cited by 8 (2 self)
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Linear digital signal processing based around linear, timeinvariant systems theory nds substantial application in speech processing. The linear acoustic sourcelter theory of speech production provides ready biomechanical justication for using linear techniques. Nonetheless, biomechanical studies surveyed in this thesis display signicant nonlinearity and nonGaussianity, casting doubt on the linear model of speech production. In order therefore to test the appropriateness of linear systems assumptions for speech production, surrogate data techniques can be used. This study uncovers systematic
aws in the design and use of existing surrogate data techniques, and, by making novel improvements, develops a more reliable technique. Collating the largest set of speech signals todate compatible with this new technique, this study next demonstrates that the linear assumptions are not appropriate for all speech signals. Detailed analysis shows that while vowel production from healthy subjects cannot be explained within the linear assumptions, consonants can. Linear assumptions also fail for most vowel production by pathological subjects with voice disorders. Combining this new empirical evidence with information from biomechanical studies concludes that the
Variable selection in classification trees based on imprecise probabilities
 ISIPTA’05: Proceedings of the Fourth International Symposium on Imprecise Probabilities and their Applications, Fabio G. Cozman, Robert Nau and Teddy Seidenfeld (Editors). (Published by SIPTA
, 2005
"... Classification trees are a popular statistical tool with multiple applications. Recent advancements of traditional classification trees, such as the approach of classification trees based on imprecise probabilities by Abellán and Moral (2005), effectively address their tendency to overfitting. How ..."
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Cited by 8 (3 self)
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Classification trees are a popular statistical tool with multiple applications. Recent advancements of traditional classification trees, such as the approach of classification trees based on imprecise probabilities by Abellán and Moral (2005), effectively address their tendency to overfitting. However, another flaw inherent in traditional classification trees is not eliminated by the imprecise probability approach: Due to a systematic finite samplebias in the estimator of the entropy criterion employed in variable selection, categorical predictor variables with low information content are preferred if they have a high number of categories. Mechanisms involved in variable selection in classification trees based on imprecise probabilities are outlined theoretically as well as by means of simulation studies. Corrected estimators are proposed, which prove to be capable of reducing estimation bias as a source of variable selection bias.