To be published in Behavioral and Brain Sciences (in press)

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.

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 self-organization 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 no-task 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 Cre1utzfeldt-Jakob’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 no-task, 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

Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequency-specific 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 lumped-parameter 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 phase-locked activity, with a phase shift of 0 or π 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 event-related transients to derive physiologically informed basis functions for statistical modelling of average evoked responses.

What is the enactive approach to cognition? Over the last 15 years this banner has grown to become a respectable alternative to traditional frameworks in cognitive science. It is at the same time a label with different interpretations and upon which different doubts have been cast. This paper elaborates on the core ideas that define the enactive approach and their implications: autonomy, sensemaking, emergence, embodiment, and experience. These are coherent, radical and very powerful concepts that establish clear methodological guidelines for research. The paper also looks at the problems that arise from taking these ideas seriously. The enactive approach has plenty of room for elaboration in many different areas and many challenges to respond to. In particular, we concentrate on the problems surrounding several theories of value-appraisal and valuegeneration. The enactive view takes the task of understanding meaning and value very seriously and elaborates a proper scientific alternative to reductionist attempts to tackle these issues by functional localization. Another area where the enactive framework can make a significant contribution is social interaction and

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In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation. 1

The overall goal of this chapter is to explore the initial findings of neuroscientific research

The aim of this work was to investigate the mechanisms that shape evoked electroencephalographic (EEG) and magneto-encephalographic (MEG) responses. We used a neuronally plausible model to characterise the dependency of response components on the models parameters. This generative model was a neural mass model of hierarchically arranged areas using three kinds of inter-area connections (forward, backward and lateral). We investigated how responses, at each level of a cortical hierarchy, depended on the strength of connections or coupling. Our strategy was to systematically add connections and examine the responses of each successive architecture. We did this in the context of deterministic responses and then with stochastic spontaneous activity. Our aim was to show, in a simple way, how event-related dynamics depend on extrinsic connectivity. To emphasise the importance of nonlinear interactions, we tried to disambiguate the components of event-related potentials (ERPs) or event-related fields

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