This article provides a new, more comprehensive view of event-related brain dynamics founded on an information-based approach to modeling electroencephalographic (EEG) dynamics. Most EEG research focuses either on peaks 'evoked' in average eventrelated potentials (ERPs) or on changes 'induced' in the EEG power spectrum by experimental events. Although these measures are nearly complementary, they do not fully model the event-related dynamics in the data, and cannot isolate the signals of the contributing cortical areas. We propose that many ERPs and other EEG features are better viewed as time/frequency perturbations of underlying field potential processes. The new approach combines independent component analysis (ICA), time/frequency analysis, and trial-by-trial visualization that measures EEG source dynamics without requiring an explicit head model. Scalp EEG signals are produced by partial synchronization of neuronal-scale field potentials across areas of cortex of centimetre-squared scale. Although once viewed by some as a form of brain 'noise', it appears increasingly probable that this synchronization optimizes relations between spike-mediated 'top-down' and 'bottom-up' communication, both within and between brain areas. This optimization might have particular importance during motivated anticipation of, and attention to, meaningful events and associations -and in response to their anticipated consequences [1 -3]. This new view of cortical and scalp-recorded field dynamics requires a new data analysis approach. Here, we suggest how a combination of signal processing and visualization methods can give a more adequate model of the spatially distributed eventrelated EEG dynamics that support cognitive events. Traditional analysis of event-related EEG data proceeds in one of two directions. In the time-domain approach, researchers average a set of data trials or epochs time-locked to some class of events, yielding an ERP waveform at each data channel. The frequency-domain approach averages changes in the frequency power spectrum of the whole EEG data time locked to the same events, producing a two-dimensional image that we call the eventrelated spectral perturbation (ERSP; see Box 1). Neither ERP nor ERSP measures of event-related data fully model their dynamics. Imagine, by analogy, a snapshot of a seashore view created by averaging together a large number of snapshots taken at different times. This average snapshot would not show the waves! Similarly, ERP averaging filters out most of the EEG data, leaving only a small portion phase-locked to the time-locking events (see Box 1). The ERP and ERSP are nearly complementary. Oscillatory (ERSP) changes 'induced' by experimental events can be poorly represented in, or completely absent from the time-domain features of the ERP 'evoked' by the same events

We show that during visual working memory, the electroencephalographic (EEG) process producing 5 – 7 Hz frontal midline theta (fmQ) activity exhibits multiple spectral modes involving at least three frequency bands and a wide range of amplitudes. The process accounting for the fmQ increase during working memory was separated from 71-channel data by clustering on time/frequency transforms of components returned by independent component analysis (ICA). Dipole models of fmQ component scalp maps were consistent with their generation in or near dorsal anterior cingulate cortex. From trial to trial, theta power of fmQ components varied widely but correlated moderately with theta power in other frontal and left temporal processes. The weak mean increase in frontal midline theta power with increasing memory load, produced entirely by the fmQ components, largely reflected progressively stronger theta activity in a relatively small proportion of trials. During presentations of letter series to be memorized or ignored, fmQ components also exhibited 12– 15 Hz low-beta activity that was stronger during memorized than during ignored letter trials, independent of letter duration. The same components produced a brief 3-Hz burst 500 ms after onset of the probe letter following each letter sequence. A new decomposition method, log spectral ICA, applied to normalized log time/frequency transforms of fmQ component Memorize-letter trials, showed that their low-beta activity reflected harmonic energy in continuous, sharppeaked theta wave trains as well as independent low-beta bursts. Possibly, the observed fmQ process variability may index dynamic adjustments in medial frontal cortex to trial-specific behavioral context and task demands.

The ability to evaluate outcomes of previous decisions is critical to adaptive decision-making. The feedback-related negativity (FRN) is an eventrelated potential (ERP) modulation that distinguishes losses from wins, but little is known about the effects of outcome probability on these ERP responses. Further, little is known about the frequency characteristics of feedback processing, for example, event-related oscillations and phase synchronizations. Here, we report an EEG experiment designed to address these issues. Subjects engaged in a probabilistic reinforcement learning task in which we manipulated, across blocks, the probability of winning and losing to each of two possible decision options. Behaviorally, all subjects quickly adapted their decision-making to maximize rewards. ERP analyses revealed that the probability of reward modulated neural responses to wins, but not to losses. This was seen both acrossblocksaswellaswithinblocks,as learning progressed. Frequency decomposition via complex wavelets revealed that EEG responses to losses, compared to wins, were associated with enhanced power and phase coherence in the theta frequency band. As in the ERP analyses, power and phase coherence values following wins but not losses were modulated by reward probability. Some findings between ERP and frequency analyses diverged, suggesting that these analytic approaches provide complementary insights into neural processing. These findings suggest that the neural mechanisms of feedback processing may differ between wins and losses.

Factor analysis and discriminant analysis are often used as complementary approaches to identify linear components in two dimensional data arrays. For three dimensional arrays, which may organize data in dimensions such as space, time, and trials, the opportunity arises to combine these two approaches. A new method, Bilinear Discriminant Component Analysis (BDCA), is derived and demonstrated in the context of functional brain imaging data for which it seems ideally suited. The work suggests to identify a subspace projection which optimally separates classes while ensuring that each dimension in this space captures an independent contribution to the discrimination.

A major challenge for neuroscience is to map accurately the spatiotemporal patterns of activity of the large neuronal populations that are believed to underlie computing in the human brain. To study a specific example, we selected the mismatch negativity (MMN) brain wave (an event-related potential, ERP) because it gives an electrophysiological index of a bprimitive intelligenceQ capable of detecting changes, even abstract ones, in a regular auditory pattern. ERPs have a temporal resolution of milliseconds but appear to result from mixed neuronal contributions whose spatial location is not fully understood. Thus, it is important to separate these sources in space and time. To tackle this problem, a two-step approach was designed combining the independent component analysis (ICA) and low-resolution tomography (LORETA) algorithms. Here we implement this approach to analyze the subsecond spatiotemporal dynamics of MMN cerebral sources using trial-by-trial experimental data. We show evidence that a cerebral computation mechanism underlies MMN. This mechanism is mediated by the orchestrated activity of several spatially distributed brain sources located in the temporal, frontal, and parietal areas, which activate at distinct time intervals and are grouped in six main statistically independent components.

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As human neuroimaging techniques have matured, the experimental questions about human brain dynamics that can be posed and answered have become more refined. Recent research in hemodynamic imaging has produced software that allows straightforward comparison of metabolic and in particular blood-oxygen dependent activities in equivalent brain areas of subjects whose

The problem of missing data is ubiquitous in domains such as biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, and communication networks---all domains in which data collection is subject to occasional errors. Moreover, these data sets can be quite large and have more than two axes of variation, e.g., sender, receiver, time. Many applications in those domains aim to capture the underlying latent structure of the data; in other words, they need to factorize data sets with missing entries. If we cannot address the problem of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP), and formulate the CP model as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) using a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes.

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 rule-based 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 low-probability notes, as compared to high-probability notes, elicited a larger (i) negative ERP component at a late time period (400-450 ms), (ii) beta band (14-30 Hz) oscillation over the parietal lobe, and (iii) long-range phase synchronization between multiple brain regions. Altogether, the study demonstrated that statistical learning produces information-theoretic 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 event-related 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 rule-based 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 best-known rule-based 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. High-probability notes are expected, while low-probability 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 i-th 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 n-gram models commonly used in statistical language modeling The most elementary n-gram 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 zeroth-order 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 first-order 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. Fixed-order models such as these suffer from a number of problems. Low-order 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 n-gram 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 n-grams 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 higher-order predictions (which are more specific to the context) receive greater weighting than lower-order 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, low-order statistical regularities captured by these models, the predictions of the model can also reflect higher-order 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 long-and short-term 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 long-term 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 19-72 years, mean age 27.58 years) consisting of 20 musicians (10 females and 10 males, age range 19-72 years, mean age 30.5 years, 18 right-handed, 2 left-handed) and 20 non-musicians (7 females and 13 males, age range 19-40 years, mean age 29.6 years, 17 right-handed, 3 left-handed) 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 non-musicians 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 self-identified as being left-handed. 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 19-26 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 10-20 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 high-pass filter at 0.5 Hz was applied to remove linear trends and a notch filter at 50 Hz (49-51 Hz) was applied to eliminate line noise. The EEG data were further cleaned of remaining artefacts by means of wavelet-enhanced independent component analysis Data analyses We performed the following types of data analysis. (i) The standard time-averaging technique to analyze the ERPs associated with high-and low-probability notes. The ERPs for each subject and condition were baseline-corrected with the mean activity from 200 to 0 ms before the note onset. Next, we computed the wavelet based time-frequency 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 time-frequency 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 1-Hz interval between each frequency. To study changes in the spectral power, we used the TFR of the wavelet energy (Tallon-Baudry 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 (4-7 Hz), alpha (8-13 Hz), beta (14-30 Hz), and gamma (31-60 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 baseline-corrected (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 (4-7 Hz), alpha (8-13 Hz), beta (14-30 Hz), and gamma (31-60 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 time-frequency 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: high-and lowprobability. The size of the pitch interval preceding the high-probability notes (mean = 2.4 semitones) was found to be smaller than that preceding the low-probability 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 rule-based model, the two-factor model of

Explaining the emergence of a coherent conscious percept and an intentional agent from the activity of distributed neurons is key to understanding how the brain produces higher cognitive processes. Gamma-band synchronization has been proposed to be a mechanism for the functional integration of neural populations that together form a transitory, large-scale, task- and/or percept-specific net-work. The operation of this mechanism in the context of attention orienting entails that cortical regions representing attended loca-tions should show more gamma-band synchronization with other cortical areas than would those representing unattended locations. This increased synchronization should be apparent in the same time frame as that of the deployment of attention to a particular location. In order to observe this effect, we made electroencephalogram recordings while subjects attended to one side or the other of the visual field (which we confirmed by event-related potential analysis) and calculated phase-locking statistics between the signals recorded at relevant electrode pairs. We observed in-creased gamma-band phase synchronization between visual cortex contralateral to the attended location and other, widespread, cortical areas approximately 240--380 ms after the directional cue was presented, confirming the prediction of a large-scale gamma synchronous network oriented to the cued location.