Errors elicit frontoparietal theta-gamma coupling that is modulated by endogenous estradiol levels.

Cognitive control-related error monitoring is intimately involved in behavioral adaptation, learning, and individual differences in a variety of psychological traits and disorders. Accumulating evidence suggests that a focus on women's health and ovarian hormones is critical to the study of such cognitive brain functions. Here we sought to identify a novel index of error monitoring using a time-frequency based phase amplitude coupling (t-f PAC) measure and examine its modulation by endogenous levels of estradiol in females. Forty-three healthy, naturally cycling young adult females completed a flanker task while continuous electroencephalogram was recorded on four occasions across the menstrual cycle. Results revealed significant error-related t-f PAC between theta phase generated in fronto-central areas and gamma amplitude generated in parietal-occipital areas. Moreover, this error-related theta-gamma coupling was enhanced by endogenous levels of estradiol both within females across the cycle as well as between females with higher levels of average circulating estradiol. While the role of frontal midline theta in error processing is well documented, this paper extends the extant literature by illustrating that error monitoring involves the coordination between multiple distributed systems with the slow midline theta activity modulating the power of gamma-band oscillatory activity in parietal regions. They further show enhancement of inter-regional coupling by endogenous estradiol levels, consistent with research indicating modulation of cognitive control neural functions by the endocrine system in females. Together, this work identifies a novel neurophysiological marker of cognitive control-related error monitoring in females that has implications for neuroscience and women's health.

Community detection in multi-frequency EEG networks.

Functional connectivity networks of the human brain are commonly studied using tools from complex network theory. Existing methods focus on functional connectivity within a single frequency band. However, it is well-known that higher order brain functions rely on the integration of information across oscillations at different frequencies. Therefore, there is a need to study these cross-frequency interactions. In this paper, we use multilayer networks to model functional connectivity across multiple frequencies, where each layer corresponds to a different frequency band. We then introduce the multilayer modularity metric to develop a multilayer community detection algorithm. The proposed approach is applied to electroencephalogram (EEG) data collected during a study of error monitoring in the human brain. The differences between the community structures within and across different frequency bands for two response types, i.e. error and correct, are studied. The results indicate that following an error response, the brain organizes itself to form communities across frequencies, in particular between theta and gamma bands while a similar cross-frequency community formation is not observed following the correct response.

Kernelized multiview signed graph learning for single-cell RNA sequencing data.

BACKGROUND: Characterizing the topology of gene regulatory networks (GRNs) is a fundamental problem in systems biology. The advent of single cell technologies has made it possible to construct GRNs at finer resolutions than bulk and microarray datasets. However, cellular heterogeneity and sparsity of the single cell datasets render void the application of regular Gaussian assumptions for constructing GRNs. Additionally, most GRN reconstruction approaches estimate a single network for the entire data. This could cause potential loss of information when single cell datasets are generated from multiple treatment conditions/disease states. RESULTS: To better characterize single cell GRNs under different but related conditions, we propose the joint estimation of multiple networks using multiple signed graph learning (scMSGL). The proposed method is based on recently developed graph signal processing (GSP) based graph learning, where GRNs and gene expressions are modeled as signed graphs and graph signals, respectively. scMSGL learns multiple GRNs by optimizing the total variation of gene expressions with respect to GRNs while ensuring that the learned GRNs are similar to each other through regularization with respect to a learned signed consensus graph. We further kernelize scMSGL with the kernel selected to suit the structure of single cell data. CONCLUSIONS: scMSGL is shown to have superior performance over existing state of the art methods in GRN recovery on simulated datasets. Furthermore, scMSGL successfully identifies well-established regulators in a mouse embryonic stem cell differentiation study and a cancer clinical study of medulloblastoma.

A practical introduction to EEG Time-Frequency Principal Components Analysis (TF-PCA).

This EEG methods tutorial provides both a conceptual and practical introduction to a promising data reduction approach for time-frequency representations of EEG data: Time-Frequency Principal Components Analysis (TF-PCA). Briefly, the unique value of TF-PCA is that it provides a data-reduction approach that does not rely on strong a priori constraints regarding the specific timing or frequency boundaries for an effect of interest. Given that the time-frequency characteristics of various neurocognitive process are known to change across development, the TF-PCA approach is thus particularly well suited for the analysis of developmental TF data. This tutorial provides the background knowledge, theory, and practical information needed to allow individuals with basic EEG experience to begin applying the TF-PCA approach to their own data. Crucially, this tutorial article is accompanied by a companion GitHub repository that contains example code, data, and a step-by-step guide of how to perform TF-PCA: https://github.com/NDCLab/tfpca-tutorial. Although this tutorial is framed in terms of the utility of TF-PCA for developmental data, the theory, protocols and code covered in this tutorial article and companion GitHub repository can be applied more broadly across populations of interest.

Assessment of dynamic phase amplitude coupling using matching pursuit.

BACKGROUND: Neuronal transmission and communication are enabled by the interactions across multiple oscillatory frequencies. Phase amplitude coupling (PAC) quantifies these interactions during cognitive brain functions. PAC is defined as the modulation of the amplitude of the high frequency rhythm by the phase of the low frequency rhythm. Existing PAC measures are limited to quantifying the average coupling within a time window of interest. However, as PAC is dynamic, it is necessary to quantify time-varying PAC. Existing time-varying PAC approaches are based on using a sliding window approach. These approaches do not adapt to the signal dynamics, and thus the arbitrary selection of the window length substantially hampers PAC estimation. NEW METHOD: To address the limitations of sliding window PAC estimation approaches, in this paper, we introduce a dynamic PAC measure that relies on matching pursuit (MP). This approach decomposes the signal into time and frequency localized atoms that best describe the signal. Dynamic PAC is quantified by computing the coupling between these time and frequency localized atoms. As such, the proposed approach is data-driven and tracks the change of PAC with time. We evaluate the proposed method on both synthesized and real electroencephalogram (EEG) data. RESULTS: The results from synthesized data show that the proposed method detects the coupled frequencies and the time variation of the coupling correctly with high time and frequency resolution. The analysis of EEG data revealed theta-gamma and alpha-gamma PAC during response and post-response time intervals. COMPARISON WITH EXISTING METHOD(S): Compared to the existing sliding window based approach, the proposed MP based dynamic PAC measure is more effective at capturing PAC within a short time window and is more robust to noise. This is because this method quantifies the low frequency phase and high frequency amplitude components from the time and frequency localized MP atoms and, as such, can capture the signal dynamics. CONCLUSIONS: We posit that the proposed MP based data-driven approach offers a more robust and possibly more sensitive method to effectively quantify and track dynamic PAC.

scSGL: kernelized signed graph learning for single-cell gene regulatory network inference.

MOTIVATION: Elucidating the topology of gene regulatory networks (GRNs) from large single-cell RNA sequencing datasets, while effectively capturing its inherent cell-cycle heterogeneity and dropouts, is currently one of the most pressing problems in computational systems biology. Recently, graph learning (GL) approaches based on graph signal processing have been developed to infer graph topology from signals defined on graphs. However, existing GL methods are not suitable for learning signed graphs, a characteristic feature of GRNs, which are capable of accounting for both activating and inhibitory relationships in the gene network. They are also incapable of handling high proportion of zero values present in the single cell datasets. RESULTS: To this end, we propose a novel signed GL approach, scSGL, that learns GRNs based on the assumption of smoothness and non-smoothness of gene expressions over activating and inhibitory edges, respectively. scSGL is then extended with kernels to account for non-linearity of co-expression and for effective handling of highly occurring zero values. The proposed approach is formulated as a non-convex optimization problem and solved using an efficient ADMM framework. Performance assessment using simulated datasets demonstrates the superior performance of kernelized scSGL over existing state of the art methods in GRN recovery. The performance of scSGL is further investigated using human and mouse embryonic datasets. AVAILABILITY AND IMPLEMENTATION: The scSGL code and analysis scripts are available on https://github.com/Single-Cell-Graph-Learning/scSGL. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Graph Theoretic Analysis of Multilayer EEG Connectivity Networks.

Over the past twenty years, functional connectivity of the human brain has been studied in detail using tools from complex network theory. These methods include graph theoretic metrics ranging from the micro-scale such as the degree of a node to the macro-scale such as the small worldness of the brain network. However, most of these network models focus on average activity within a time window of interest and given frequency band. Therefore, they cannot capture the changes in network connectivity across time and different frequency bands. Recently, multilayer brain networks have attracted a lot of attention as they can capture the full view of neuronal connectivity. In this paper, we introduce a multilayer view of the functional connectivity network of the brain, where each layer corresponds to a different frequency band. We construct multi-frequency connectivity networks from electroencephalogram data where the intra-layer edges are quantified by phase synchrony while the inter-layer edges are quantified by phase-amplitude coupling. We then introduce multilayer degree, participation coefficient and clustering coefficient to quantify the centrality of nodes across frequency layers and to identify the importance of different frequency bands. The proposed framework is applied to electroencephalogram data collected during a study of error monitoring in the human brain.

Multi-Branch Tensor Network Structure for Tensor-Train Discriminant Analysis.

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Two major challenges that confound current tensor based supervised learning algorithms are storage complexity and computational efficiency. In this paper, we address these problems by introducing a multi-branch tensor network structure. The multi-branch structure is a general tensor decomposition that includes Tucker and tensor-train (TT) as special cases and takes advantage of the flexibility of the tensor network to provide a better balance between storage and computational complexity. We then introduce a supervised discriminative tensor-train subspace learning approach referred to as tensor-train discriminant analysis (TTDA), and its implementations using the multi-branch tensor network structure. Multi-branch implementations of TTDA are shown to achieve lower storage and computational complexity while providing improved classification performance with respect to both Tucker and TT based supervised learning methods.

Multivariate Analysis of Bivariate Phase-Amplitude Coupling in EEG Data Using Tensor Robust PCA.

Cross-frequency coupling is emerging as a crucial mechanism that coordinates the integration of spectrally and spatially distributed neuronal oscillations. Recently, phase-amplitude coupling, a form of cross-frequency coupling, where the phase of a slow oscillation modulates the amplitude of a fast oscillation, has gained attention. Existing phase-amplitude coupling measures are mostly confined to either coupling within a region or between pairs of brain regions. Given the availability of multi-channel electroencephalography recordings, a multivariate analysis of phase amplitude coupling is needed to accurately quantify the coupling across multiple frequencies and brain regions. In the present work, we propose a tensor based approach, i.e., higher order robust principal component analysis, to identify response-evoked phase-amplitude coupling across multiple frequency bands and brain regions. Our experiments on both simulated and electroencephalography data demonstrate that the proposed multivariate phase-amplitude coupling method can capture the spatial and spectral dynamics of phase-amplitude coupling more accurately compared to existing methods. Accordingly, we posit that the proposed higher order robust principal component analysis based approach filters out the background phase-amplitude coupling activity and predominantly captures the event-related phase-amplitude coupling dynamics to provide insight into the spatially distributed brain networks across different frequency bands.

Time-Frequency Based Phase-Amplitude Coupling Measure For Neuronal Oscillations.

Oscillatory activity in the brain has been associated with a wide variety of cognitive processes including decision making, feedback processing, and working memory. The high temporal resolution provided by electroencephalography (EEG) enables the study of variation of oscillatory power and coupling across time. Various forms of neural synchrony across frequency bands have been suggested as the mechanism underlying neural binding. Recently, a considerable amount of work has focused on phase-amplitude coupling (PAC)- a form of cross-frequency coupling where the amplitude of a high frequency signal is modulated by the phase of low frequency oscillations. The existing methods for assessing PAC have some limitations including limited frequency resolution and sensitivity to noise, data length and sampling rate due to the inherent dependence on bandpass filtering. In this paper, we propose a new time-frequency based PAC (t-f PAC) measure that can address these issues. The proposed method relies on a complex time-frequency distribution, known as the Reduced Interference Distribution (RID)-Rihaczek distribution, to estimate both the phase and the envelope of low and high frequency oscillations, respectively. As such, it does not rely on bandpass filtering and possesses some of the desirable properties of time-frequency distributions such as high frequency resolution. The proposed technique is first evaluated for simulated data and then applied to an EEG speeded reaction task dataset. The results illustrate that the proposed time-frequency based PAC is more robust to varying signal parameters and provides a more accurate measure of coupling strength.

Graph-to-signal transformation based classification of functional connectivity brain networks.

Complex network theory has been successful at unveiling the topology of the brain and showing alterations to the network structure due to brain disease, cognitive function and behavior. Functional connectivity networks (FCNs) represent different brain regions as the nodes and the connectivity between them as the edges of a graph. Graph theoretic measures provide a way to extract features from these networks enabling subsequent characterization and discrimination of networks across conditions. However, these measures are constrained mostly to binary networks and highly dependent on the network size. In this paper, we propose a novel graph-to-signal transform that overcomes these shortcomings to extract features from functional connectivity networks. The proposed transformation is based on classical multidimensional scaling (CMDS) theory and transforms a graph into signals such that the Euclidean distance between the nodes of the network is preserved. In this paper, we propose to use the resistance distance matrix for transforming weighted functional connectivity networks into signals. Our results illustrate how well-known network structures transform into distinct signals using the proposed graph-to-signal transformation. We then compute well-known signal features on the extracted graph signals to discriminate between FCNs constructed across different experimental conditions. Based on our results, the signals obtained from the graph-to-signal transformation allow for the characterization of functional connectivity networks, and the corresponding features are more discriminative compared to graph theoretic measures.

Tensor Based Temporal and Multilayer Community Detection for Studying Brain Dynamics During Resting State fMRI.

OBJECTIVE: In recent years, resting state fMRI has been widely utilized to understand the functional organization of the brain for healthy and disease populations. Recent studies show that functional connectivity during resting state is a dynamic process. Studying this temporal dynamics provides a better understanding of the human brain compared to static network analysis. METHODS: In this paper, a new tensor based temporal and multi-layer community detection algorithm is introduced to identify and track the brain network community structure across time and subjects. The framework studies the temporal evolution of communities in fMRI connectivity networks constructed across different regions of interests. The proposed approach relies on determining the subspace that best describes the community structure using Tucker decomposition of the tensor. RESULTS: The brain dynamics are summarized into a set of functional connectivity states that are repeated over time and subjects. The dynamic behavior of the brain is evaluated in terms of consistency of different subnetworks during resting state. The results illustrate that some of the networks, such as the default mode, cognitive control and bilateral limbic networks, have low consistency over time indicating their dynamic behavior. CONCLUSION: The results indicate that the functional connectivity of the brain is dynamic and the detected community structure experiences smooth temporal evolution. SIGNIFICANCE: The work in this paper provides evidence for temporal brain dynamics during resting state through dynamic multi-layer community detection which enables us to better understand the behavior of different subnetworks.

Utilizing time-frequency amplitude and phase synchrony measure to assess feedback processing in a gambling task.

The neurophysiological mechanisms involved in the evaluation of performance feedback have been widely studied in the ERP literature over the past twenty years, but understanding has been limited by the use of traditional time-domain amplitude analytic approaches. Gambling outcome valence has been identified as an important factor modulating event-related potential (ERP) components, most notably the feedback negativity (FN). Recent work employing time-frequency analysis has shown that processes indexed by the FN are confounded in the time-domain and can be better represented as separable feedback-related processes in the theta (3-7 Hz) and delta (0-3 Hz) frequency bands. In addition to time-frequency amplitude analysis, phase synchrony measures have begun to further our understanding of performance evaluation by revealing how feedback information is processed within and between various brain regions. The current study aimed to provide an integrative assessment of time-frequency amplitude, inter-trial phase synchrony, and inter-channel phase synchrony changes following monetary feedback in a gambling task. Results revealed that time-frequency amplitude activity explained separable loss and gain processes confounded in the time-domain. Furthermore, phase synchrony measures explained unique variance above and beyond amplitude measures and demonstrated enhanced functional integration between medial prefrontal and bilateral frontal, motor, and occipital regions for loss relative to gain feedback. These findings demonstrate the utility of assessing time-frequency amplitude, inter-trial phase synchrony, and inter-channel phase synchrony together to better elucidate the neurophysiology of feedback processing.

A Tensor Decomposition-Based Approach for Detecting Dynamic Network States From EEG.

Functional connectivity (FC), defined as the statistical dependency between distinct brain regions, has been an important tool in understanding cognitive brain processes. Most of the current works in FC have focused on the assumption of temporally stationary networks. However, recent empirical work indicates that FC is dynamic due to cognitive functions. GOAL: The purpose of this paper is to understand the dynamics of FC for understanding the formation and dissolution of networks of the brain. METHOD: In this paper, we introduce a two-step approach to characterize the dynamics of functional connectivity networks (FCNs) by first identifying change points at which the network connectivity across subjects shows significant changes and then summarizing the FCNs between consecutive change points. The proposed approach is based on a tensor representation of FCNs across time and subjects yielding a four-mode tensor. The change points are identified using a subspace distance measure on low-rank approximations to the tensor at each time point. The network summarization is then obtained through tensor-matrix projections across the subject and time modes. RESULTS: The proposed framework is applied to electroencephalogram (EEG) data collected during a cognitive control task. The detected change-points are consistent with a priori known ERN interval. The results show significant connectivities in medial-frontal regions which are consistent with widely observed ERN amplitude measures. CONCLUSION: The tensor-based method outperforms conventional matrix-based methods such as singular value decomposition in terms of both change-point detection and state summarization. SIGNIFICANCE: The proposed tensor-based method captures the topological structure of FCNs which provides more accurate change-point-detection and state summarization.

Time-frequency phase-synchrony approaches with ERPs.

Time-frequency signal processing approaches are well-developed, and have been widely employed for the study of the energy distribution of event-related potential (ERP) data across time and frequency. Wavelet time-frequency transform (TFT) and Cohen's class of time-frequency distributions (TFD) are the most widely used in the field. While ERP TFT approaches have been most extensively developed for amplitude measures, reflecting the magnitude of regional neuronal activity, time-frequency phase-synchrony measures have gained increased utility in recent years for the assessment of functional connectivity. Phase synchrony measures can be used to index the functional integration between regions (interregional), in addition to the consistency of activity within region (intertrial). In this paper, we focus on a particular class of time-frequency distributions belonging to Cohen's class, known as the Reduced Interference Distribution (RID) for quantifying functional connectivity, which we recently introduced (Aviyente et al., 2011). The present report first summarizes common time-frequency approaches to computing phase-synchrony with ERP data in order to highlight the similarities and differences relative to the RID. In previous work, we demonstrated differences between the RID and wavelet approaches to indexing phase-synchrony, and have applied the RID to demonstrate that RID-based time-frequency phase-synchrony measures can index increased functional connectivity between medial and lateral prefrontal regions during control processing, observed in the theta band during the error-related negativity (ERN). Because ERN amplitude measures have been associated with two other widely studied medial-frontal theta components (no-go N2; feedback negativity, FN), the application of the RID phase synchrony measure in the present report extends our previous work with ERN to include theta activity during the no-go N2 (inhibitory processing) and the feedback negativity (FN; loss feedback processing). Findings support the idea that similar medial-lateral prefrontal functional connectivity underlies the ERN, no-go N2, and FN components, and provide initial validation that the proposed RID-based time-frequency phase-synchrony measure can index this activity.

Sending mixed signals: worry is associated with enhanced initial error processing but reduced call for subsequent cognitive control.

Worry is reliably associated with overactive action-monitoring processes as measured by the error-related negativity (ERN). However, worry is not associated with error-related behavioral adjustments which are typically used to infer increased cognitive control following errors. We hypothesized that this disconnect between overactive action monitoring and unimproved post-error adjustments in worriers is the result of reduced functional integration between medial and lateral prefrontal regions during generation of the ERN, understood to have an important role in mediating controlled processing. To test this, we examined ERN amplitude and interchannel phase synchrony extracted from scalp-recorded electroencephalographic data during error processing in 77 undergraduates who performed a Flankers task. Correlational and path analytic results demonstrated that worry was related to both an enlarged ERN and reduced phase synchrony. Although not directly related to post-error behavioral adjustments, results also revealed that worry was indirectly related to poor post-error adjustments through its association with reduced phase synchrony. Therefore, worry seems to affect multiple components of the action-monitoring system. It is related not just with the initial response to the error, but also with the transmission of information between networks involved in cognitive control processes.

Hierarchical Spectral Consensus Clustering for Group Analysis of Functional Brain Networks.

A central question in cognitive neuroscience is how cognitive functions depend on the integration of specialized widely distributed brain regions. In recent years, graph theoretical methods have been used to characterize the structure of the brain functional connectivity. In order to understand the organization of functional connectivity networks, it is important to determine the community structure underlying these complex networks. Moreover, the study of brain functional networks is confounded by the fact that most neurophysiological studies consists of data collected from multiple subjects; thus, it is important to identify communities representative of all subjects. Typically, this problem is addressed by averaging the data across subjects which omits the variability across subjects or using voting methods, which requires a priori knowledge of cluster labels. In this paper, we propose a hierarchical consensus spectral clustering approach to address these problems. Furthermore, new information-theoretic criteria are introduced for selecting the optimal community structure. The proposed framework is applied to electroencephalogram data collected during a study of error-related negativity to better understand the community structure of functional networks involved in the cognitive control.

Network community structure detection for directional neural networks inferred from multichannel multisubject EEG data.

In many neuroscience applications, one is interested in identifying the functional brain modules from multichannel, multiple subject neuroimaging data. However, most of the existing network community structure detection algorithms are limited to single undirected networks and cannot reveal the common community structure for a collection of directed networks. In this paper, we propose a community detection algorithm for weighted asymmetric (directed) networks representing the effective connectivity in the brain. Moreover, the issue of finding a common community structure across subjects is addressed by maximizing the total modularity of the group. Finally, the proposed community detection algorithm is applied to multichannel multisubject electroencephalogram data.

Computation of resting state networks from fMRI through a measure of phase synchrony.

Resting-state fMRI (rs-fMRI) studies of the human brain have demonstrated that low-frequency fluctuations can define functionally relevant resting state networks (RSNs). The majority of these methods rely on Pearson's correlation for quantifying the functional connectivity between the time series from different regions. However, it is well-known that correlation is limited to quantifying only linear relationships between the time series and assumes stationarity of the underlying processes. Many empirical studies indicate nonstationarity of the BOLD signals. In this paper, we adapt a measure of time-varying phase synchrony to quantify the functional connectivity and modify it to distinguish between synchronization and desynchronization. The proposed measure is compared to the conventional Pearson's correlation method for rs-fMRI analyses on two subjects (six scans per subject) in terms of their reproducibility.

Multiple subject analysis of functional brain network communities through co-regularized spectral clustering.

In recent years, the human brain has been characterized as a complex network composed of segregated modules linked by short path lengths. In order to understand the organization of the network, it is important to determine these modules underlying the functional brain networks. However, the study of these modules is confounded by the fact that most neurophysiological studies consist of data collected from multiple subjects. Typically, this problem is addressed by either averaging the data across subjects which omits the variability across subjects or using consensus clustering methods which treats all subjects equally irrespective of outliers in the data. In this paper, we adapt a recently introduced co-regularized multiview spectral clustering approach to address these problems. The proposed framework is applied to EEG data collected during a study of error-related negativity (ERN) to better understand the functional networks involved in cognitive control and to compare between the network structure between error and correct responses.