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A general method for the creation of strange nonchaotic attractor is proposed. As an example, the strange nonchaotic attractor in a high-dimensional globally coupled neural system is studied numerically. For such an attractor, the time interval of continuously positive finite-time Lyapunov exponent must be smaller than the period of the driving stimulus, although it has a long-time positive tail. The intermittency between laminar and burst behavior is a characteristic dynamic of the strange nonchaotic attractors. Simulation results show that the chaotic phase occurs only within a small region around the origin in the parameter space. More than half of the large nonchaotic region is the strange nonchaotic phase. The chaotic phase is typically surrounded by strange nonchaotic attractors. This result also suggests that some biological signals that have a strange structure may be nonchaotic rather than chaotic.

The present report describes the dynamic foundations of long-standing experimental work in the field of oscillatory dynamics in the human and animal brain. It aims to show the role of multiple oscillations in the integrative brain function, memory, and complex perception by a recently introduced conceptional framework: the super-synergy in the whole brain. Results of recent experiments related to the percept of the grandmother-face support our concept of super-synergy in the whole brain in order to explain manifestation of Gestalts and Memory-Stages. This report may also provide new research avenues in macrodynamics of the brain.

In many signal processing applications, especially in the analysis of complex physiological systems, an important problem is to detect and quantify the interdependencies between signals (or time series). In this paper, we focus on asymmetrical relations between two time series with the aim of quantification of the directional influences between them in the sense of "who drives whom and how strongly". To meet this aim, we modify the mixed state analysis, which was proposed by Wiesenfeldt et al. [2001] to detect primarily the nature of the coupling (unidirectional or bidirectional), for the quantification of the strength of coupling in each direction. We introduce the predictability improvement of one time series by additional consideration of another time series. The newly developed measure is an analogue of the information theoretic concept of transfer entropy and is applicable to short time series. We demonstrate the application of this approach to coupled deterministic systems and to EEG data.

We discuss a notion of information processing in brain and behavioral dynamics, in particular the processing of meaningful information, which is testable by means of an experimental coordination and transition paradigm. Two hypotheses on the existence and persistence of mappings between the dynamics of behavioral and brain signals are formulated. A mathematical foundation for the first hypothesis is suggested by means of Volterra integral expansions and by means of excitable systems. Brain signals are captured as cortical currents, as well as the resulting scalp topographies, such as electroencephalograms (EEG) and magnetoencephalograms (MEG). Experimental evidence is provided to support the hypothesis on the existence of such spatiotemporal mappings between behavioral and brain signals.

Binocular rivalry is a useful experimental paradigm to investigate aspects of neocortical dynamics related to conscious perception. Frequency-tagged EEG responses to a sine-flickered visual stimulus were contrasted between episodes of perceptual dominance, i.e. conscious perception of that stimulus and perceptual nondominance, i.e. conscious perception of a rival stimulus presented at a different frequency to the other eye. The amplitude and phase distribution of the stimulus-evoked steady-state responses depended on the stimulus modulation frequency, consistent with the presence of global resonance phenomena. At the apparent global resonance frequency, conscious perception of the stimulus modulated the steady-state response over the entire array of electrodes. These effects were significant at electrodes far from the primary visual cortex, including temporal, central, and frontal electrodes. The phase structure of the steady-state response was also investigated using coherence measures. Coherence between electrodes mostly increased during conscious perception of the stimulus. Analysis of partial coherence, removing stimulus-locked responses, indicated that synchronization of each signal to the stimulus flicker at each electrode and synchronization between signals that vary with respect to the stimulus flicker at each electrode both contribute to observed increases in coherence during conscious perception. These distinct modes of synchronization may reflect two different physiological mechanisms by which sensory signals are integrated across the cerebral cortex during conscious experience.

We present an entropy and complexity analysis of intracranially recorded EEG from patients suffering from a left frontal lobe epilepsy. Our approach is based on symbolic dynamics and Shannon entropy. In particular, we will discuss the possibility to monitor long-term dynamical changes in brain electrical activity. This might offer an alternative approach for the analysis and more fundamental understanding of human epilepsies.

A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.

The interaction of large populations of neurons gives rise to electrical events in the brain, which can be observed at several spatial scales. We show that mutually consistent explanations and simulation of experimental data can be achieved for cortical gamma activity, synchronous oscillation, and the main features of the EEG power spectrum including the cerebral rhythms, and evoked potentials. These simulations include consideration of dendritic and synaptic dynamics, AMPA, NMDA and GABA receptors, and intracortical and cortical/subcortical interactions.

The dynamic properties exhibited in the simulations, Hebbian synaptic modification regulated by a limited set of innate "reward" mechanisms, and infomax principles, can be combined to yield an explanation of elementary adaptive learning.

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed.

In this contribution, eleven different measures of the complexity of multichannel EEGs are described, and their effectiveness in discriminating between two behavioral conditions (eyes open resting versus eyes closed resting) is compared. Ten of the methods were variants of the algorithmic complexity and the covariance complexity. The eleventh measure was a multivariate complexity measure proposed by Tononi and Edelman. The most significant between-condition change was observed with Tononi–Edelman complexity which decreased in the eyes open condition. Of the algorithmic complexity measures tested, the binary Lempel–Ziv complexity and the binary Lempel–Ziv redundancy of the first principal component following mean normalization and normalization against the standard deviation gave the most significant between-group discrimination. A time-dependent generalization of the covariance complexity that can be applied to nonstationary multichannel signals is also described.

We investigate the applicability of the permutation entropy H and a synchronization index γ that is based on the changing tendency of temporal permutation entropies to analyze noisy time series from nonstationary dynamical systems with poorly understood properties. Using model systems, we first study the interdependencies of parameters involved in the calculation of both measures. Having identified appropriate parameter settings we then analyze long-lasting EEG time series recorded from an epilepsy patient. Our findings indicate that γ could be of interest for studies on the predictability of epileptic seizures.

The evaluation of the topological properties of brain networks is an emerging research topic, since the estimated cerebral connectivity patterns often have relatively large size and complex structure. Since a graph is a mathematical representation of a network, the use of a theoretical graph approach would describe concisely the topological features of the functional network estimated from neuroimaging techniques. In particular, by applying the process of coherence analysis to high-density EEG recordings, rich visualizations can be developed that provide a means for spatiotemporal analysis of changes in synchronous brain activity. In the present work, we studied the changes in brain synchronization networks during performance of a complex visuomotor task with strategic components in normal subjects. In particular, we evaluated the differences in the functional network topology associated with human learning by calculating global and local efficiency indexes. Our results suggest that during an initial period of learning, which is probably related to the most significant cognitive processes, the particular organization of functional links in the alpha frequency band (8–12 Hz) tends to increase the efficiency of communication within the cerebral network. Such evidence could be interpreted as due to the need for a new strategy formulation. Overall, this approach enabled us to capture a shift in topology made during the process of learning and thus helped us to shed more light on the neural correlates of strategy formulation. Our findings provide strong support for the efficacy of theoretical graph analysis to study complex brain networks.

Today, the human brain can be studied as a whole. Electroencephalography, magnetoencephalography, or functional magnetic resonance imaging (fMRI) techniques provide functional connectivity patterns between different brain areas, and during different pathological and cognitive neuro-dynamical states. In this tutorial, we review novel complex networks approaches to unveil how brain networks can efficiently manage local processing and global integration for the transfer of information, while being at the same time capable of adapting to satisfy changing neural demands.

Three methods of nonlinear time series analysis, Lempel–Ziv complexity, prediction error and covariance complexity were employed to distinguish between the electroencephalograms (EEGs) of normal children, children with mild autism, and children with severe autism. Five EEG tracings per cluster of children aged three to seven medically diagnosed with mild, severe and no autism were used in the analysis. A general trend seen was that the EEGs of children with mild autism were significantly different from those with severe or no autism. No significant difference was observed between normal children and children with severe autism. Among the three methods used, the method that was best able to distinguish between EEG tracings of children with mild and severe autism was found to be the prediction error, with a t-Test confidence level of above 98%.

The concept of redundancy is a critical resource of the brain enhancing the resilience to neural damages and dysfunctions. In the present work, we propose a graph-based methodology to investigate the connectivity redundancy in brain networks. By taking into account all the possible paths between pairs of nodes, we considered three complementary indexes, characterizing the network redundancy (i) at the global level, i.e. the scalar redundancy (ii) across different path lengths, i.e. the vectorial redundancy (iii) between node pairs, i.e. the matricial redundancy. We used this procedure to investigate the functional connectivity estimated from a dataset of high-density EEG signals in a group of healthy subjects during a no-task resting state. The statistical comparison with a benchmark dataset of random networks, having the same number of nodes and links of the EEG nets, revealed a significant (p < 0.05) difference for all the three indexes. In particular, the redundancy in the EEG networks, for each frequency band, appears radically higher than random graphs, thus revealing a natural tendency of the brain to present multiple parallel interactions between different specialized areas. Notably, the matricial redundancy showed a high (p < 0.05) redundancy between the scalp sensors over the parieto-occipital areas in the Alpha range of EEG oscillations (7.5–12.5 Hz), which is known to be the most responsive channel during resting state conditions.

Manual acupuncture (MA) is widely used in Traditional Chinese Medicine clinic for pain treatment and controlling stress. To investigate how MA modulates brain activities, electroencephalograph (EEG) signals are recorded with 20 channels by MA at ST36 of right leg in 11 healthy subjects during rest. Two novel nonlinear measures based on ordinal patterns of EEG series, i.e. permutation entropy (PE) and order index (OI), are adopted to investigate the nonlinear complexity characteristic in EEG data at different acupuncture states. It is observed that the recorded EEG series during and after MA have higher PE values and lower OI values compared to before MA. The results show that MA at ST36 can increase EEG complexity, which is especially obvious during MA. Our findings suggest that the PE and OI measures are promising methods to reveal EEG dynamical changes associated with MA stimulus, which could provide a potential for further exploring the interactions between acupuncture and brain activity. Moreover, these preliminary conclusions highlight the beneficial modulations of brain activity by MA, which could contribute to understanding the acupuncture effects on brain, as well as the neurophysiological mechanisms underlying MA.

The primary goal of this study was to investigate the impact of monochord (MC) sounds, a type of archaic sounds used in music therapy, on the neural complexity of EEG signals obtained from patients undergoing chemotherapy. The secondary goal was to compare the EEG signal complexity values for monochords with those for progressive muscle relaxation (PMR), an alternative therapy for relaxation. Forty cancer patients were randomly allocated to one of the two relaxation groups, MC and PMR, over a period of six months; continuous EEG signals were recorded during the first and last sessions. EEG signals were analyzed by applying signal mode complexity, a measure of complexity of neuronal oscillations. Across sessions, both groups showed a modulation of complexity of beta-2 band (20–29Hz) at midfrontal regions, but only MC group showed a modulation of complexity of theta band (3.5–7.5Hz) at posterior regions. Therefore, the neuronal complexity patterns showed different changes in EEG frequency band specific complexity resulting in two different types of interventions. Moreover, the different neural responses to listening to monochords and PMR were observed after regular relaxation interventions over a short time span.

Epileptic seizures are generated by abnormal activity of neurons. The prediction of epileptic seizures is an important issue in the field of neurology, since it may improve the quality of life of patients suffering from drug resistant epilepsy. In this study a new similarity index based on symbolic dynamic techniques which can be used for extracting behavior of chaotic time series is presented. Using Freiburg EEG dataset, it is found that the method is able to detect the behavioral changes of the neural activity prior to epileptic seizures, so it can be used for prediction of epileptic seizure. A sensitivity of 63.75% with 0.33 false positive rate (FPR) in all 21 patients and sensitivity of 96.66% with 0.33 FPR in eight patients were achieved using the proposed method. Moreover, the method was evaluated by applying on Logistic and Tent map with different parameters to demonstrate its robustness and ability in determining similarity between two time series with the same chaotic characterization.

Multiscale sample entropy (MSE) of human electroencephalogram (EEG) data from patients under different pathological conditions of Alzheimer's disease (AD) was evaluated to measure the complexity of the signal. Quantifying the complexity level with respect to various temporal scales, MSE analysis provides a dynamical description of AD development. When compared to EEG data from normal subjects, EEG data from subjects with mild cognitive impairment (MCI) showed nearly the same complexity profile, but a scale discrepancy which may occur from a spectral abnormality. EEG data from severe AD patients showed a loss of complexity over the wide range of time scales, indicating a destruction of nonlinear structures in brain dynamics. We compare the MSE method and spectral analysis to propose that nonlinear dynamical approach combining a multiscale method is crucial for revealing AD mechanisms.

The advent of multiple electrode recording, dense arrays and mathematical techniques such as non-linear dynamics has invigorated brain electrical recording techniques. Taking advantage of the excellent temporal resolution of the EEG, this summary review details several innovations, concentrating on (1) the rapid changes in electrical activity and a consequent stable complex pattern; and (2) the utilization of engineering techniques that have been applied across scales ranging upward from quantum physics. The implications for brain localization and for communication science are developed.