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Broadband criticality of human brain network synchronization, PLoS
 Comput. Biol
, 2009
"... Selforganized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in largescale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, longrange correlations in space and ..."
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Selforganized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in largescale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, longrange correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phaselock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phaselocking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal ‘‘avalanches’ ’ previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human
Unsupervised statistical learning underpins computational, behavioural, and neural manifestations of musical expectation.
 NeuroImage,
, 2010
"... The ability to anticipate forthcoming events has clear evolutionary advantages, and predictive successes or failures often entail significant psychological and physiological consequences. In music perception, the confirmation and violation of expectations are critical to the communication of emotio ..."
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The ability to anticipate forthcoming events has clear evolutionary advantages, and predictive successes or failures often entail significant psychological and physiological consequences. In music perception, the confirmation and violation of expectations are critical to the communication of emotion and aesthetic effects of a composition. Neuroscientific research on musical expectations has focused on harmony. Although harmony is important in Western tonal styles, other musical traditions, emphasizing pitch and melody, have been rather neglected. In this study, we investigated melodic pitch expectations elicited by ecologically valid musical stimuli by drawing together computational, behavioural, and electrophysiological evidence. Unlike rulebased models, our computational model acquires knowledge through unsupervised statistical learning of sequential structure in music and uses this knowledge to estimate the conditional probability (and information content) of musical notes. Unlike previous behavioural paradigms that interrupt a stimulus, we devised a new paradigm for studying auditory expectation without compromising ecological validity. A strong negative correlation was found between the probability of notes predicted by our model and the subjectively perceived degree of expectedness. Our electrophysiological results showed that lowprobability notes, as compared to highprobability notes, elicited a larger (i) negative ERP component at a late time period (400450 ms), (ii) beta band (1430 Hz) oscillation over the parietal lobe, and (iii) longrange phase synchronization between multiple brain regions. Altogether, the study demonstrated that statistical learning produces informationtheoretic descriptions of musical notes that are proportional to their perceived expectedness and are associated with characteristic patterns of neural activity. © 2009 Elsevier Inc. All rights reserved. Introduction The brain's ability to anticipate forthcoming events accurately and efficiently has a clear adaptive value and predictive successes and failures often entail significant psychological and physiological consequences, modulating arousal and affecting reward circuits in the brain Previous research has investigated eventrelated potential (ERP) responses to violations of expectation in harmony While harmony is important in Western tonal music, it plays a less significant role in other musical traditions, which emphasize pitch, timbre, and rhythm. To date, little is known about the neural correlates of expectation in these musical dimensions. However, there is a sparse literature reporting ERP responses to violations of melodic expectation, and the picture appears to be somewhat more complex than for violations of harmonic expectation. Early studies To address these issues, we systematically investigated melodic expectation using a tripartite approach involving distinct computational, behavioural, and electrophysiological (electroencephalogram, EEG) components. Instead of designing stimuli to match experimental hypotheses, our work started with an operational definition of musical expectation embodied in a computational model Materials and methods Computational models of musical expectation Existing computational models of musical expectation fall into two groups: (i) supervised or rulebased models which generate expectations according to some static rules that predict what will happen next in a given context and (ii) unsupervised models which generate expectation based on learned associations between events that cooccur and uses these acquired associations to predict future events on the basis of the current context. Probably the bestknown rulebased account of melodic expectation is that of In this study, we adopted a model of musical expectation based on statistical learning, probability estimation and information theory. We hypothesised that, while listening to music (or, indeed, perceiving other phenomena which are sequential in time), the brain anticipates or predicts possible continuations of the current (musical) context. These predictions were based on a model of the perceived domain (music, in the current case) formed by an inductive process of unsupervised statistical learning of perceived sequential structure. The learned model encodes past experience, and can be used to anticipate future events on that basis, using its acquired statistical knowledge of sequential structure to generate estimates of the probabilities of known events occurring, conditional upon the current sequential context. In music, such expectations depend on many aspects of musical structure, including harmony, but here we focused on pitch expectations for single note continuations to melodic contexts. Specifically, we predicted that a listener estimates the probability of different anticipated pitched continuations to a melody using the frequency with which each one has followed the context in his/her previous musical experience. Highprobability notes are expected, while lowprobability notes are unexpected. We have developed a computational model that embodies this account of expectation. The model's goal is to estimate in any context a conditional probability distribution governing the probability of the pitch of the next note in a melody given the preceding notes. Thus, if we represent a melody X of n notes as a sequence of pitches, x 1 , x 2 , ..., x n , the goal of the model is to estimate the conditional probability of the ith note in the melody, p(x i x 1 , .., x i − 1 ). Given these estimates of conditional probability, the model's expectations may be quantified by information content The model has been designed to produce probability estimates that are as accurate as possible and we now summarise how this is achieved. Probabilities were estimated using ngram models commonly used in statistical language modeling The most elementary ngram model of melodic pitch structure (a monogram model where n = 1) simply tabulates the frequency of occurrence for each chromatic pitch encountered in a traversal of each melody in the training set. During prediction, the expectations of the model are governed by a zerothorder pitch distribution derived from the frequency counts and do not depend on the preceding context of the melody. In a digram model (where n = 2), however, frequency counts are maintained for sequences of two pitch symbols and predictions are governed by a firstorder pitch distribution derived from the frequency counts associated with only those digrams whose initial pitch symbol matches the final pitch symbol in the melodic context. Fixedorder models such as these suffer from a number of problems. Loworder models (such as the monogram model discussed above) clearly fail to provide an adequate account of the structural influence of the context on expectations. However, increasing the order can prevent the model from capturing much of the statistical regularity present in the training set. An extreme case occurs when the model encounters an ngram that does not appear in the training set in which case it returns an estimated probability of zero. To address these problems, the models used in the present research maintain frequency counts during training for ngrams of all possible values of n in any given context. During prediction, distributions are estimated using a weighted linear combination of all models below a variable order bound, which is determined in each predictive context using simple heuristics designed to minimize model uncertainty. The combination is designed such that higherorder predictions (which are more specific to the context) receive greater weighting than lowerorder predictions (which are more general). In a given melodic context, therefore, the predictions of the model may reflect the influence of both the digram model and (to a lesser extent) the monogram model discussed above. Furthermore, in addition to the general, loworder statistical regularities captured by these models, the predictions of the model can also reflect higherorder regularities which are more specific to the current melodic context (to the extent that these exist in the training set). For the purposes of this study, the model derives its pitch predictions from a representation of pitch interval and scale degree reflecting the fundamental influence of melodic and tonal structure respectively (though in other work we use richer representations). Each note in a melody is represented by a pair of values: first, the pitch interval preceding the note; and second, the scale degree of the note relative to the notated key of the melody. The longand shortterm models produce probability distributions generated over an alphabet of such pairs and these are converted into probabilities for concrete chromatic pitches before being combined. The longterm component was trained on the corpus of melodies shown in Ethics statement Both behavioural and electrophysiological experiments were approved by the local ethics committee of the Department of Psychology at Goldsmiths College, University of London. Informed written consent was obtained from all participants. Behavioural experiment Participants and experimental design Forty participants (17 females and 23 males, age range 1972 years, mean age 27.58 years) consisting of 20 musicians (10 females and 10 males, age range 1972 years, mean age 30.5 years, 18 righthanded, 2 lefthanded) and 20 nonmusicians (7 females and 13 males, age range 1940 years, mean age 29.6 years, 17 righthanded, 3 lefthanded) took part in the experiment. Musicians had an average of 12.5 years of training and had played a musical instrument for an average of 22.5 years, whereas nonmusicians had an average of 0.48 years of formal training and had played an instrument for an average of 1.6 years. All participants were either students or staff at Goldsmiths, University of London, and were in good health, with normal hearing and no past history of neurological illness. In total, five participants selfidentified as being lefthanded. The stimuli consisted of 28 hymn melodies (see In each melodic excerpt, two notes were selected as locations to probe the expectations of listeners. The probe locations were selected according to the predictions of the computational model of perceived pitch expectations in melody (Pearce and Wiggins, 2006) described earlier. According to the model, in the melodic context in which they appear, one of these notes has a high conditional probability of occurrence while the other has a low probability of occurrence. Participants were instructed to listen carefully to the musical stimuli presented binaurally by headphones. For each stimulus, the probe locations were indicated by the rotating hand of a clock, which counted down, stepwise, in quarters, in time with the music, informing the participant in advance when they were required to respond. The participant was required to give a rating on a Likert scale of 1 to 7 (1 being highly unexpected and 7 being highly expected) on how expected or unexpected the probe note was in the context of the preceding melodic passage. After listening to each melody, the participants were asked to indicate if it was familiar to them. Practice trials were provided for familiarisation with the experimental procedure. The order of presentation of the stimuli was randomised across participants. Electrophysiological experiment Participants and experimental design Twenty healthy adult humans (13 males and 7 females, age range 1926 years, mean age 20.7 years) participated in the EEG study. None of the participants had taken part in the behavioural study. All participants were in good health, had no past history of neurological disorders, and had no reported hearing difficulties. None of the participants reported having any formal musical training. The same set of 28 melodic excerpts selected for the behavioural experiment was used here. To avoid artefacts caused by eye/head movements, the participants were asked to listen attentively to each melodic excerpt with eyes closed. No explicit expectedness ratings were requested, and the participants were not made overtly aware of the location of the probe notes, thereby emphasizing the implicit aspect of melodic processing. Data acquisition and preprocessing EEG signals were recorded from 28 Ag/AgCl electrodes according to the extended 1020 system (Fp1, Fp2, F7, F3, Fz, F4, F8, FC3, FCz, FC4, C5, C3, Cz, C4, C6, CP5, CP3, CPz, CP4, CP6, P7, P3, Pz, P4, P8, O1, Oz, O2) We used the EEGLAB Matlab® Toolbox (Delorme and Makeig, 2004) for visualization and filtering purposes. A highpass filter at 0.5 Hz was applied to remove linear trends and a notch filter at 50 Hz (4951 Hz) was applied to eliminate line noise. The EEG data were further cleaned of remaining artefacts by means of waveletenhanced independent component analysis Data analyses We performed the following types of data analysis. (i) The standard timeaveraging technique to analyze the ERPs associated with highand lowprobability notes. The ERPs for each subject and condition were baselinecorrected with the mean activity from 200 to 0 ms before the note onset. Next, we computed the wavelet based timefrequency representations (TFR) to analyze (ii) the spectral power of the oscillatory contents and (iii) the spatiotemporal dynamics of the phase coupling as measured by bivariate synchronization analysis A complex Morlet wavelet was used to extract timefrequency complex phases, at an electrode i and epoch k, and amplitudes of the EEG signal x(t). The frequency domain was sampled from 2 to 60 Hz with a 1Hz interval between each frequency. To study changes in the spectral power, we used the TFR of the wavelet energy (TallonBaudry et al., 1997). After removing the baseline level (200 prestimulus), we normalized the wavelet energy with the standard deviation of the baseline period and expressed it as percentage of power change. Oscillatory activity was analyzed in the theta (47 Hz), alpha (813 Hz), beta (1430 Hz), and gamma (3160 Hz) frequency bands. Bivariate phase synchronization is a useful approach to assess phase synchronization between neurophysiological signals where n is the number of epochs. This index approaches 0 (1) for no (strict) phase relationship between the considered electrode pair across the epochs. The average of this index across pairs of electrodes represents a measure of global synchronization strength (R). For the bivariate synchronization analysis, a modified version of the nearestneighbour Hjorth Laplacian algorithm computed by Taylor's series expansion The PLI ranges between 0 for no coupling or coupling around 0 mod π, and 1 for nonzero phase coupling. We used an average reference before computing the PLI. At each frequency from 2 to 60 Hz with a step size of 1 Hz, the indexes R ij and PLI ij were computed and baselinecorrected (baseline being 200 ms prestimulus). They were subsequently averaged across electrodes to obtain a measure of the global synchronization strength, R and PLI. We focused our analysis on the theta (47 Hz), alpha (813 Hz), beta (1430 Hz), and gamma (3160 Hz) frequency bands. Statistics To assess the statistical differences in the spectral power and phase synchronization and phase lag indices, we first averaged these measures for each participant and condition across all electrodes. Next, for each timefrequency point in the bands under study, the averaged measures were analyzed by means of a nonparametric pairwise permutation test Results Behavioural experiment There were two categories of probe notes: highand lowprobability. The size of the pitch interval preceding the highprobability notes (mean = 2.4 semitones) was found to be smaller than that preceding the lowprobability notes (mean = 5.3, t = 6.6, p b 0.01). Furthermore, using the empirical key profiles of The mean expectedness ratings and response times are summarised in For the perceived expectedness ratings, the analysis revealed significant main effects of probe type, F Finally, to assess the significance of these results, we compared the performance of our proposed computational model with a competing rulebased model, the twofactor model of
Diagnosis of alzheimers disease from EEG signals: Where are we standing
 Current Alzheimer Research
"... This paper reviews recent progress in the diagnosis of Alzheimer’s disease (AD) from electroencephalograms (EEG). Three major effects of AD on EEG have been observed: slowing of the EEG, reduced complexity of the EEG signals, and perturbations in EEG synchrony. In recent years, a variety of sophisti ..."
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This paper reviews recent progress in the diagnosis of Alzheimer’s disease (AD) from electroencephalograms (EEG). Three major effects of AD on EEG have been observed: slowing of the EEG, reduced complexity of the EEG signals, and perturbations in EEG synchrony. In recent years, a variety of sophisticated computational approaches has been proposed to detect those subtle perturbations in the EEG of AD patients. The paper first describes methods that try to detect slowing of the EEG. Next the paper deals with several measures for EEG complexity, and explains how those measures have been used to study fluctuations in EEG complexity in AD patients. Then various measures of EEG synchrony are considered in the context of AD diagnosis. Also the issue of EEG preprocessing is briefly addressed. Before one can analyze EEG, it is necessary to remove artifacts due to for example head and eye movement or interference from electronic equipment. Preprocessing of EEG has in recent years received much attention. In this paper, several stateoftheart preprocessing techniques are outlined, for example, based on blind source separation and other nonlinear filtering paradigms. In addition, the paper outlines opportunities and limitations of computational approaches for diagnosing AD based on EEG. At last, future challenges and open problems are discussed.
Quantifying Statistical Interdependence by Message Passing on Graphs  PART II: MultiDimensional Point Processes
, 2009
"... Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, “events” are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are ..."
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Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, “events” are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. In Part I, onedimensional events are considered, this paper (Paper II) concerns multidimensional events. Although the basic idea is similar, the extension to multidimensional point processes involves a significantly harder combinatorial problem, and therefore, it is nontrivial. Also in the multidimensional, the problem of jointly computing the pairwise alignment and SES parameters is cast as a statistical inference problem. This problem is solved by coordinate descent, more specifically, by alternating the following two steps: (i) one estimates the SES parameters from a given pairwise alignment; (ii) with the resulting estimates, one refines the pairwise alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (Step 1), in
A Granger causality measure for point process models of ensembled neural spiking activity
 PLOS Comput. Biol
"... The ability to identify directional interactions that occur among multiple neurons in the brain is crucial to an understanding of how groups of neurons cooperate in order to generate specific brain functions. However, an optimal method of assessing these interactions has not been established. Grange ..."
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The ability to identify directional interactions that occur among multiple neurons in the brain is crucial to an understanding of how groups of neurons cooperate in order to generate specific brain functions. However, an optimal method of assessing these interactions has not been established. Granger causality has proven to be an effective method for the analysis of the directional interactions between multiple sets of continuousvalued data, but cannot be applied to neural spike train recordings due to their discrete nature. This paper proposes a point process framework that enables Granger causality to be applied to point process data such as neural spike trains. The proposed framework uses the point process likelihood function to relate a neuron’s spiking probability to possible covariates, such as its own spiking history and the concurrent activity of simultaneously recorded neurons. Granger causality is assessed based on the relative reduction of the point process likelihood of one neuron obtained excluding one of its covariates compared to the likelihood obtained using all of its covariates. The method was tested on simulated data, and then applied to neural activity recorded from the primary motor cortex (MI) of a Felis catus subject. The interactions present in the simulated data were predicted with a high degree of accuracy, and when applied to the real neural data, the proposed method identified causal relationships between many of the recorded neurons. This paper proposes a novel method that successfully applies Granger causality to point process
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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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.
Causal Network Inference via Group Sparse Regularization
"... This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a “false connection score ” ..."
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This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a “false connection score ” ψ. In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that ψ < 1. The false connection score is also demonstrated to be a useful metric of recovery in nonasymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach.
Evolving Signal Processing for Brain–Computer Interfaces
, 2012
"... This paper discusses the challenges associated with building robust and useful BCI models from accumulated biological knowledge and data, and the technical problems associated with incorporating multimodal physiological, behavioral, and contextual data that may become ubiquitous in the future. ..."
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This paper discusses the challenges associated with building robust and useful BCI models from accumulated biological knowledge and data, and the technical problems associated with incorporating multimodal physiological, behavioral, and contextual data that may become ubiquitous in the future.
Heritability of ‘‘smallworld’’ networks in the brain: A graph theoretical analysis of restingstate EEG functional connectivity
, 2008
"... Abstract: Recent studies have shown that restingstate functional networks as studied with fMRI, EEG, and MEG may be socalled smallworld networks. We investigated to what extent the characteristic features of smallworld networks are genetically determined. To represent functional connectivity bet ..."
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Abstract: Recent studies have shown that restingstate functional networks as studied with fMRI, EEG, and MEG may be socalled smallworld networks. We investigated to what extent the characteristic features of smallworld networks are genetically determined. To represent functional connectivity between brain areas, we measured resting EEG in 574 twins and their siblings and calculated the synchronization likelihood between each pair of electrodes. We applied a threshold to obtain a binary graph from which we calculated the clustering coefficient C (describing local interconnectedness) and average path length L (describing global interconnectedness) for each individual. Modeling of MZ and DZ twin and sibling resemblance indicated that across various frequency bands 46–89 % of the individual differences in C and 37–62 % of the individual differences in L are heritable. It is asserted that C, L, and a smallworld organization are viable markers of genetic differences in brain organization. Hum Brain Mapp
Synchronization measures of the scalp electroencephalogram can discriminate healthy from Alzheimer's subjects
 Int. J. Neural Syst
, 2007
"... Three synchronization measures are applied to scalp electroencephalogram (EEG) data collected from 20 patients diagnosed to have either: (1) no dementia, (2) mild cognitive impairment (MCI), or (3) Alzheimer’s disease (AD). We apply the three synchronization measures — the phase synchronization, and ..."
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Three synchronization measures are applied to scalp electroencephalogram (EEG) data collected from 20 patients diagnosed to have either: (1) no dementia, (2) mild cognitive impairment (MCI), or (3) Alzheimer’s disease (AD). We apply the three synchronization measures — the phase synchronization, and two measures of nonlinear interdependency — to the data collected from awake patients resting with eyes closed. We show that the synchronization in potential between electrodes near the left and right occipital lobes provides a statistically significant discriminant between the healthy and AD subjects, and the MCI and AD subjects. None of the three measures appears able to distinguish between the healthy and MCI subjects, although MCI subjects show synchronization values intermediate between healthy subjects (with high synchronization values) and AD subjects (with low synchronization values) on average. Keywords: 1.