Functional Brain Networks: Does the Choice of Dependency Estimator and Binarization Method Matter?

Detection of Low Resilience Using Data-Driven Effective Connectivity Measures

Conventional thresholding techniques for graph theory analysis, such as absolute, proportional and mean degree, have often been used in characterizing human brain networks under different mental disorders, such as mental stress. However, these approaches may not always be reliable as conventional thresholding approaches are subjected to human biases. Using a mental resilience study, we investigate if data-driven thresholding techniques such as Global Cost Efficiency (GCE-abs) and Orthogonal Minimum Spanning Trees (OMSTs) could provide equivalent results, whilst eliminating human biases. We implemented Phase Slope Index (PSI) to compute effective brain connectivity, and applied data-driven thresholding approaches to filter the brain networks in order to identify key features of low resilience within a cohort of healthy individuals. Our dataset encompassed resting-state EEG recordings gathered from a total of 36 participants (31 females and 5 males). Relevant features were extracted to train and validate a classifier model (Support Vector Machine, SVM). The detection of low stress resilience among healthy individuals using the SVM model scores an accuracy of 80.6% with GCE-abs, and 75% with OMSTs, respectively.

Persistent homology reveals robustness loss in inhaled substance abuse rs-fMRI networks

Analyzing functional brain activity through functional magnetic resonance imaging (fMRI) is commonly done using tools from graph theory for the analysis of the correlation matrices. A drawback of these methods is that the networks must be restricted to values of the weights of the edges within certain thresholds and there is no consensus about the best choice of such thresholds. Topological data analysis (TDA) is a recently-developed tool in algebraic topology which allows us to analyze networks through combinatorial spaces obtained from them, with the advantage that all the possible thresholds can be considered at once. In this paper we applied TDA, in particular persistent homology, to study correlation matrices from rs-fMRI, and through statistical analysis, we detected significant differences between the topological structures of adolescents with inhaled substance abuse disorder (ISAD) and healthy controls. We interpreted the topological differences as indicative of a loss of robustness in the functional brain networks of the ISAD population.

MDD brain network analysis based on EEG functional connectivity and graph theory

Background

Existing studies have shown that the brain network of major depression disorder (MDD) has abnormal topologies. However, constructing reliable MDD brain networks is still an open problem.

New method

This paper proposed a reliable MDD brain network construction method. First, seven connectivity methods are used to calculate the correlation between channels and obtain the functional connectivity matrix. Then, the matrix is binarized using four binarization methods to obtain the EEG brain network. Besides, we proposed an improved binarization method based on the criterion of maximizing differences between groups: the adaptive threshold (AT) method. The AT can automatically set the optimal binarization threshold and overcome the artificial influence of traditional methods. After that, several network metrics are extracted from the brain network to analyze inter-group differences. Finally, we used statistical analysis and Fscore values to compare the performance of different methods and establish the most reliable method for brain network construction.

Results

In theta, alpha, and total frequency bands, the clustering coefficient, global efficiency, local efficiency, and degree of the MDD brain network decrease, and the path length of the MDD brain network increases.

Comparison with existing methods

The results show that AT outperforms the existing binarization methods. Compared with other methods, the brain network construction method based on phase-locked value (PLV) and AT has better reliability.

Conclusions

MDD has brain dysfunction, particularly in the frontal and temporal lobes.

Reconstructing brain functional networks through identifiability and deep learning

We propose a novel approach for the reconstruction of functional networks representing brain dynamics based on the idea that the coparticipation of two brain regions in a common cognitive task should result in a drop in their identifiability, or in the uniqueness of their dynamics. This identifiability is estimated through the score obtained by deep learning models in supervised classification tasks and therefore requires no a priori assumptions about the nature of such coparticipation. The method is tested on EEG recordings obtained from Alzheimer's and Parkinson's disease patients, and matched healthy volunteers, for eyes-open and eyes-closed resting-state conditions, and the resulting functional networks are analysed through standard topological metrics. Both groups of patients are characterised by a reduction in the identifiability of the corresponding EEG signals, and by differences in the patterns that support such identifiability. Resulting functional networks are similar, but not identical to those reconstructed by using a correlation metric. Differences between control subjects and patients can be observed in network metrics like the clustering coefficient and the assortativity in different frequency bands. Differences are also observed between eyes open and closed conditions, especially for Parkinson's disease patients.

Disrupted properties of functional brain networks in major depressive disorder during emotional face recognition: an EEG study via graph theory analysis

Previous neuroimaging studies have revealed abnormal brain networks in patients with major depressive disorder (MDD) in emotional processing. While any cognitive task consists of a series of stages, little is yet known about the topology of functional brain networks in MDD for these stages during emotional face recognition. To address this problem, electroencephalography (EEG)-based functional brain networks of MDD patients at different stages of facial information processing were investigated in this study. First, EEG signals were collected from 16 patients with MDD and 18 age-, gender-, and education-matched normal subjects when performing an emotional face recognition task. Second, the global field power (GFP) method was employed to divide group-averaged event-related potentials into different stages. Third, using the phase transfer entropy (PTE) approach, the brain networks of MDD patients and normal individuals were constructed for each stage in negative and positive face processing, respectively. Finally, we compared the topological properties of brain networks of each stage between the two groups using graph theory approaches. The results showed that the analyzed three stages of emotional face processing corresponded to specific neurophysiological phases, namely, visual perception, face recognition, and emotional decision-making. It was also demonstrated that depressed patients showed abnormally decreased characteristic path length at the visual perception stage of negative face recognition and normalized characteristic path length in the stage of emotional decision-making during positive face processing compared to healthy subjects. Furthermore, while both the MDD and normal groups' brain networks were found to exhibit small-world network characteristics, the brain network of patients with depression tended to be randomized. Moreover, for patients with MDD, the centro-parietal region may lose its status as a hub in the process of facial expression identification. Together, our findings suggested that altered emotional function in MDD patients might be associated with disruptions in the topological organization of functional brain networks during emotional face recognition, which further deepened our understanding of the emotion processing dysfunction underlying MDD.

Fingerprints of decreased cognitive performance on fractal connectivity dynamics in healthy aging

Analysis of brain functional connectivity (FC) could provide insight in how and why cognitive functions decline even in healthy aging (HA). Despite FC being established as fluctuating over time even in the resting state (RS), dynamic functional connectivity (DFC) studies involving healthy elderly individuals and assessing how these patterns relate to cognitive performance are yet scarce. In our recent study we showed that fractal temporal scaling of functional connections in RS is not only reduced in HA, but also predicts increased response latency and reduced task solving accuracy. However, in that work we did not address changes in the dynamics of fractal connectivity (FrC) strength itself and its plausible relationship with mental capabilities. Therefore, here we analyzed RS electroencephalography recordings of the same subject cohort as previously, consisting of 24 young and 19 healthy elderly individuals, who also completed 7 different cognitive tasks after data collection. Dynamic fractal connectivity (dFrC) analysis was carried out via sliding-window detrended cross-correlation analysis (DCCA). A machine learning method based on recursive feature elimination was employed to select the subset of connections most discriminative between the two age groups, identifying 56 connections that allowed for classifying participants with an accuracy surpassing 92%. Mean of DCCA was found generally increased, while temporal variability of FrC decreased in the elderly when compared to the young group. Finally, dFrC indices expressed an elaborate pattern of associations-assessed via Spearman correlation-with cognitive performance scores in both groups, linking fractal connectivity strength and variance to increased response latency and reduced accuracy in the elderly population. Our results provide further support for the relevance of FrC dynamics in understanding age-related cognitive decline and might help to identify potential targets for future intervention strategies.

The scalp time-varying network of auditory spatial attention in "cocktail-party" situations

Sound source localization in "cocktail-party" situations is a remarkable ability of the human auditory system. However, the neural mechanisms underlying auditory spatial attention are still largely unknown. In this study, the "cocktail-party" situations are simulated through multiple sound sources and presented through head-related transfer functions and headphones. Furthermore, the scalp time-varying network of auditory spatial attention is constructed using the high-temporal resolution electroencephalogram, and its network properties are measured quantitatively using graph theory analysis. The results show that the time-varying network of auditory spatial attention in "cocktail-party" situations is more complex and partially different than in simple acoustic situations, especially in the early- and middle-latency periods. The network coupling strength increases continuously over time, and the network hub shifts from the posterior temporal lobe to the parietal lobe and then to the frontal lobe region. In addition, the right hemisphere has a stronger network strength for processing auditory spatial information in "cocktail-party" situations, i.e., the right hemisphere has higher clustering levels, higher transmission efficiency, and more node degrees during the early- and middle-latency periods, while this phenomenon disappears and appears symmetrically during the late-latency period. These findings reveal different network patterns and properties of auditory spatial attention in "cocktail-party" situations during different periods and demonstrate the dominance of the right hemisphere in the dynamic processing of auditory spatial information.

Graph-based analysis of EEG for schizotypy classification applying flicker Ganzfeld stimulation

Ganzfeld conditions induce alterations in brain function and pseudo-hallucinatory experiences, particularly in people with high positive schizotypy. The current study uses graph-based parameters to investigate and classify brain networks under Ganzfeld conditions as a function of positive schizotypy. Participants from the general population (14 high schizotypy (HS), 29 low schizotypy (LS)) had an electroencephalography assessment during Ganzfeld conditions, with varying visual activation (8 frequencies of random light flicker) and soundscape-induced mood (neutral, serenity, and anxiety). Weighted functional networks were computed in six frequency sub-bands (delta, theta, alpha-low, alpha-high, beta, and gamma) as a function of light-flicker frequency and mood. The brain network was analyzed using graph theory parameters, including clustering coefficient (CC), strength, and global efficiency (GE). It was found that the LS groups had higher CC and strength than the HS groups, especially in bilateral temporal and frontotemporal brain regions. Moreover, some decreases in CC and strength measures were found in LS groups among occipital and parieto-occipital brain regions. LS groups also had significantly higher GE in all Ganzfeld conditions compared to the HS groups. The random under-sampling boosting (RUSBoost) algorithm achieved the best classification performance with an accuracy of 95.34%, specificity of 96.55%, and sensitivity of 92.85% during an anxiety-induction Ganzfeld condition. This is the first exploration of the relationship between brain functional state changes under Ganzfeld conditions in individuals who vary in positive schizotypy. The accuracy of graph-based parameters in classifying brain states as a function of schizotypy is shown, particularly for brain activity during anxiety induction, and should be investigated in psychosis.

Accumulation of network redundancy marks the early stage of Alzheimer's disease

Brain wiring redundancy counteracts aging-related cognitive decline by reserving additional communication channels as a neuroprotective mechanism. Such a mechanism plays a potentially important role in maintaining cognitive function during the early stages of neurodegenerative disorders such as Alzheimer's disease (AD). AD is characterized by severe cognitive decline and involves a long prodromal stage of mild cognitive impairment (MCI). Since MCI subjects are at high risk of converting to AD, identifying MCI individuals is essential for early intervention. To delineate the redundancy profile during AD progression and enable better MCI diagnosis, we define a metric that reflects redundant disjoint connections between brain regions and extract redundancy features in three high-order brain networks-medial frontal, frontoparietal, and default mode networks-based on dynamic functional connectivity (dFC) captured by resting-state functional magnetic resonance imaging (rs-fMRI). We show that redundancy increases significantly from normal control (NC) to MCI individuals and decreases slightly from MCI to AD individuals. We further demonstrate that statistical features of redundancy are highly discriminative and yield state-of-the-art accuracy of up to 96.8 ± 1.0% in support vector machine (SVM) classification between NC and MCI individuals. This study provides evidence supporting the notion that redundancy serves as a crucial neuroprotective mechanism in MCI.

Evaluating test-retest reliability and sex-/age-related effects on temporal clustering coefficient of dynamic functional brain networks

The multilayer dynamic network model has been proposed as an effective method to understand the brain function. In particular, derived from the definition of clustering coefficient in static networks, the temporal clustering coefficient provides a direct measure of the topological stability of dynamic brain networks and shows potential in predicting altered brain functions. However, test-retest reliability and demographic-related effects on this measure remain to be evaluated. Using a data set from the Human Connectome Project (157 male and 180 female healthy adults; 22-37 years old), the present study investigated: (1) the test-retest reliability of temporal clustering coefficient across four repeated resting-state functional magnetic resonance imaging scans as measured by intraclass correlation coefficient (ICC); and (2) sex- and age-related effects on temporal clustering coefficient. The results showed that (1) the temporal clustering coefficient had overall moderate test-retest reliability (ICC > 0.40 over a wide range of densities) at both global and subnetwork levels, (2) female subjects showed significantly higher temporal clustering coefficient than males at both global and subnetwork levels, particularly within the default-mode and subcortical regions, and (3) temporal clustering coefficient of the subcortical subnetwork was positively correlated with age in young adults. The results of sex effects were robustly replicated in an independent REST-meta-MDD data set, while the results of age effects were not. Our findings suggest that the temporal clustering coefficient is a relatively reliable and reproducible approach for identifying individual differences in brain function, and provide evidence for demographically related effects on the human brain dynamic connectomes.

Brain-wide network analysis of resting-state neuromagnetic data

The present study performed a brain-wide network analysis of resting-state magnetoencephalograms recorded from 53 healthy participants to visualize elaborate brain maps of phase- and amplitude-derived graph-theory metrics at different frequencies. To achieve this, we conducted a vertex-wise computation of threshold-independent graph metrics by combining proportional thresholding and a conjunction analysis and applied them to a correlation analysis of age and brain networks. Source power showed a frequency-dependent cortical distribution. Threshold-independent graph metrics derived from phase- and amplitude-based connectivity showed similar or different distributions depending on frequency. Vertex-wise age-brain correlation maps revealed that source power at the beta band and the amplitude-based degree at the alpha band changed with age in local regions. The present results indicate that a brain-wide analysis of neuromagnetic data has the potential to reveal neurophysiological network features in the human brain in a resting state.

Brain network analysis for the discrimination of dementia disorders using electrophysiology signals: A systematic review

Background

Dementia-related disorders have been an age-long challenge to the research and healthcare communities as their various forms are expressed with similar clinical symptoms. These disorders are usually irreversible at their late onset, hence their lack of validated and approved cure. Since their prodromal stages usually lurk for a long period of time before the expression of noticeable clinical symptoms, a secondary prevention which has to do with treating the early onsets has been suggested as the possible solution. Connectivity analysis of electrophysiology signals has played significant roles in the diagnosis of various dementia disorders through early onset identification.

Objective

With the various applications of electrophysiology signals, the purpose of this study is to systematically review the step-by-step procedures of connectivity analysis frameworks for dementia disorders. This study aims at identifying the methodological issues involved in such frameworks and also suggests approaches to solve such issues.

Methods

In this study, ProQuest, PubMed, IEEE Xplore, Springer Link, and Science Direct databases are employed for exploring the evolution and advancement of connectivity analysis of electrophysiology signals of dementia-related disorders between January 2016 to December 2022. The quality of assessment of the studied articles was done using Cochrane guidelines for the systematic review of diagnostic test accuracy.

Results

Out of a total of 4,638 articles found to have been published on the review scope between January 2016 to December 2022, a total of 51 peer-review articles were identified to completely satisfy the review criteria. An increasing trend of research in this domain is identified within the considered time frame. The ratio of MEG and EEG utilization found within the reviewed articles is 1:8. Most of the reviewed articles employed graph theory metrics for their analysis with clustering coefficient (CC), global efficiency (GE), and characteristic path length (CPL) appearing more frequently compared to other metrics.

Significance

This study provides general insight into how to employ connectivity measures for the analysis of electrophysiology signals of dementia-related disorders in order to better understand their underlying mechanism and their differential diagnosis.

Application of machine learning and complex network measures to an EEG dataset from ayahuasca experiments

Ayahuasca is a blend of Amazonian plants that has been used for traditional medicine by the inhabitants of this region for hundreds of years. Furthermore, this plant has been demonstrated to be a viable therapy for a variety of neurological and mental diseases. EEG experiments have found specific brain regions that changed significantly due to ayahuasca. Here, we used an EEG dataset to investigate the ability to automatically detect changes in brain activity using machine learning and complex networks. Machine learning was applied at three different levels of data abstraction: (A) the raw EEG time series, (B) the correlation of the EEG time series, and (C) the complex network measures calculated from (B). Further, at the abstraction level of (C), we developed new measures of complex networks relating to community detection. As a result, the machine learning method was able to automatically detect changes in brain activity, with case (B) showing the highest accuracy (92%), followed by (A) (88%) and (C) (83%), indicating that connectivity changes between brain regions are more important for the detection of ayahuasca. The most activated areas were the frontal and temporal lobe, which is consistent with the literature. F3 and PO4 were the most important brain connections, a significant new discovery for psychedelic literature. This connection may point to a cognitive process akin to face recognition in individuals during ayahuasca-mediated visual hallucinations. Furthermore, closeness centrality and assortativity were the most important complex network measures. These two measures are also associated with diseases such as Alzheimer's disease, indicating a possible therapeutic mechanism. Moreover, the new measures were crucial to the predictive model and suggested larger brain communities associated with the use of ayahuasca. This suggests that the dissemination of information in functional brain networks is slower when this drug is present. Overall, our methodology was able to automatically detect changes in brain activity during ayahuasca consumption and interpret how these psychedelics alter brain networks, as well as provide insights into their mechanisms of action.

Abnormal Properties of Cortical Functional Brain Network in Major Depressive Disorder: Graph Theory Analysis Based on Electroencephalography-Source Estimates

Studies of scalp electroencephalography (EEG) had shown altered topological organization of functional brain networks in patients with major depressive disorder (MDD). However, most previous EEG-based network analyses were performed at sensor level, while the interpretation of obtained results was not straightforward due to volume conduction effect. To reduce the impact of this defect, the whole cortical functional brain networks of MDD patients were studied during resting state based on EEG-source estimates in this paper. First, scalp EEG signals were recorded from 19 patients with MDD and 20 normal controls under resting eyes-closed state, and cortical neural signals were estimated by using sLORETA method. Then, the correntropy coefficient of wavelet packet coefficients was performed to calculate functional connectivity (FC) matrices in four different frequency bands: δ, θ, α, β, respectively. Afterwards, topological properties of brain networks were analyzed by graph theory approaches. The results showed that the global FC strength of MDD patients was significantly higher than that of healthy subjects in α band. Also, it was found that MDD patients have abnormally increased clustering coefficient and local efficiency in both α and β bands compared to normal people. Furthermore, patients with MDD exhibited increased nodal clustering coefficients in the left lingual gryus and left precuneus in α band. In addition, β band global clustering coefficient was positively correlated with the scores of depression severity. Therefore, the findings indicated the cortical functional brain networks in MDD patients were disruptions, which suggested it would be one of potential causes of depression.

Analysis of EEG brain connectivity of children with ADHD using graph theory and directional information transfer

Research shows that Attention Deficit Hyperactivity Disorder (ADHD) is related to a disorder in brain networks. The purpose of this study is to use an effective connectivity measure and graph theory to examine the impairments of brain connectivity in ADHD. Weighted directed graphs based on electroencephalography (EEG) signals of 61 children with ADHD and 60 healthy children were constructed. The edges between two nodes (electrodes) were calculated by Phase Transfer Entropy (PTE). PTE is calculated for five frequency bands: delta, theta, alpha, beta, and gamma. The graph theory measures were divided into two categories: global and local. Statistical analysis with global measures indicates that in children with ADHD, the segregation of brain connectivity increases while the integration of the brain connectivity decreases compared to healthy children. These brain network differences were identified in the delta and theta frequency bands. The classification accuracy of 89.4% is obtained for both in-degree and strength measures in the theta band. Our result indicated local graph measures classified ADHD and healthy subjects with accuracy of 91.2 and 90% in theta and delta bands, respectively. Our analysis may provide a new understanding of the differences in the EEG brain network of children with ADHD and healthy children.

Monitoring the Impact of Spaceflight on the Human Brain

Extended exposure to radiation, microgravity, and isolation during space exploration has significant physiological, structural, and psychosocial effects on astronauts, and particularly their central nervous system. To date, the use of brain monitoring techniques adopted on Earth in pre/post-spaceflight experimental protocols has proven to be valuable for investigating the effects of space travel on the brain. However, future (longer) deep space travel would require some brain function monitoring equipment to be also available for evaluating and monitoring brain health during spaceflight. Here, we describe the impact of spaceflight on the brain, the basic principles behind six brain function analysis technologies, their current use associated with spaceflight, and their potential for utilization during deep space exploration. We suggest that, while the use of magnetic resonance imaging (MRI), positron emission tomography (PET), and computerized tomography (CT) is limited to analog and pre/post-spaceflight studies on Earth, electroencephalography (EEG), functional near-infrared spectroscopy (fNIRS), and ultrasound are good candidates to be adapted for utilization in the context of deep space exploration.

Network structure from a characterization of interactions in complex systems

Many natural and man-made complex dynamical systems can be represented by networks with vertices representing system units and edges the coupling between vertices. If edges of such a structural network are inaccessible, a widely used approach is to identify them with interactions between vertices, thereby setting up a functional network. However, it is an unsolved issue if and to what extent important properties of a functional network on the global and the local scale match those of the corresponding structural network. We address this issue by deriving functional networks from characterizing interactions in paradigmatic oscillator networks with widely-used time-series-analysis techniques for various factors that alter the collective network dynamics. Surprisingly, we find that particularly key constituents of functional networks—as identified with betweenness and eigenvector centrality—coincide with ground truth to a high degree, while global topological and spectral properties—clustering coefficient, average shortest path length, assortativity, and synchronizability—clearly deviate. We obtain similar concurrences for an empirical network. Our findings are of relevance for various scientific fields and call for conceptual and methodological refinements to further our understanding of the relationship between structure and function of complex dynamical systems.

Exploring Network Properties Across Preclinical Stages of Alzheimer’s Disease Using a Visual Short-Term Memory and Attention Task with High-Density Electroencephalography: A Brain-Connectome Neurophysiological Study

Background: Visual short-term memory (VSTMT) and visual attention (VAT) exhibit decline in the Alzheimer’s disease (AD) continuum; however, network disruption in preclinical stages is scarcely explored. Objective: To advance our knowledge about brain networks in AD and discover connectivity alterations during VSTMT and VAT. Methods: Twelve participants with AD, 23 with mild cognitive impairment (MCI), 17 with subjective cognitive decline (SCD), and 21 healthy controls (HC) were examined using a neuropsychological battery at baseline and follow-up (three years). At baseline, the subjects were examined using high density electroencephalography while performing a VSTMT and VAT. For exploring network organization, we constructed weighted undirected networks and examined clustering coefficient, strength, and betweenness centrality from occipito-parietal regions. Results: One-way ANOVA and pair-wise t-test comparisons showed statistically significant differences in HC compared to SCD (t (36) = 2.43, p = 0.026), MCI (t (42) = 2.34, p = 0.024), and AD group (t (31) = 3.58, p = 0.001) in Clustering Coefficient. Also with regards to Strength, higher values for HC compared to SCD (t (36) = 2.45, p = 0.019), MCI (t (42) = 2.41, p = 0.020), and AD group (t (31) = 3.58, p = 0.001) were found. Follow-up neuropsychological assessment revealed converge of 65% of the SCD group to MCI. Moreover, SCD who were converted to MCI showed significant lower values in all network metrics compared to the SCD that remained stable. Conclusion: The present findings reveal that SCD exhibits network disorganization during visual encoding and retrieval with intermediate values between MCI and HC.

A hands-on tutorial on network and topological neuroscience

The brain is an extraordinarily complex system that facilitates the optimal integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging at different scales and from numerous modalities. With that comes the need for sophisticated tools for analysis. The field of network neuroscience has been trying to tackle these challenges, and graph theory has been one of its essential branches through the investigation of brain networks. Recently, topological data analysis has gained more attention as an alternative framework by providing a set of metrics that go beyond pairwise connections and offer improved robustness against noise. In this hands-on tutorial, our goal is to provide the computational tools to explore neuroimaging data using these frameworks and to facilitate their accessibility, data visualisation, and comprehension for newcomers to the field. We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses the 1000 Functional Connectomes Project dataset. Moreover, we would like to highlight one part of our notebook dedicated to the realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pairwise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.

Ranking of communities in multiplex spatiotemporal models of brain dynamics

As a relatively new field, network neuroscience has tended to focus on aggregate behaviours of the brain averaged over many successive experiments or over long recordings in order to construct robust brain models. These models are limited in their ability to explain dynamic state changes in the brain which occurs spontaneously as a result of normal brain function. Hidden Markov Models (HMMs) trained on neuroimaging time series data have since arisen as a method to produce dynamical models that are easy to train but can be difficult to fully parametrise or analyse. We propose an interpretation of these neural HMMs as multiplex brain state graph models we term Hidden Markov Graph Models. This interpretation allows for dynamic brain activity to be analysed using the full repertoire of network analysis techniques. Furthermore, we propose a general method for selecting HMM hyperparameters in the absence of external data, based on the principle of maximum entropy, and use this to select the number of layers in the multiplex model. We produce a new tool for determining important communities of brain regions using a spatiotemporal random walk-based procedure that takes advantage of the underlying Markov structure of the model. Our analysis of real multi-subject fMRI data provides new results that corroborate the modular processing hypothesis of the brain at rest as well as contributing new evidence of functional overlap between and within dynamic brain state communities. Our analysis pipeline provides a way to characterise dynamic network activity of the brain under novel behaviours or conditions.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-022-00454-2.

Age-Related Alterations in EEG Network Connectivity in Healthy Aging

Emerging studies have reported that functional brain networks change with increasing age. Graph theory is applied to understand the age-related differences in brain behavior and function, and functional connectivity between the regions is examined using electroencephalography (EEG). The effect of normal aging on functional networks and inter-regional synchronization during the working memory (WM) state is not well known. In this study, we applied graph theory to investigate the effect of aging on network topology in a resting state and during performing a visual WM task to classify aging EEG signals. We recorded EEGs from 20 healthy middle-aged and 20 healthy elderly subjects with their eyes open, eyes closed, and during a visual WM task. EEG signals were used to construct the functional network; nodes are represented by EEG electrodes; and edges denote the functional connectivity. Graph theory matrices including global efficiency, local efficiency, clustering coefficient, characteristic path length, node strength, node betweenness centrality, and assortativity were calculated to analyze the networks. We applied the three classifiers of K-nearest neighbor (KNN), a support vector machine (SVM), and random forest (RF) to classify both groups. The analyses showed the significantly reduced network topology features in the elderly group. Local efficiency, global efficiency, and clustering coefficient were significantly lower in the elderly group with the eyes-open, eyes-closed, and visual WM task states. KNN achieved its highest accuracy of 98.89% during the visual WM task and depicted better classification performance than other classifiers. Our analysis of functional network connectivity and topological characteristics can be used as an appropriate technique to explore normal age-related changes in the human brain.

A survey of brain network analysis by electroencephalographic signals

Brain network analysis is one efficient tool in exploring human brain diseases and can differentiate the alterations from comparative networks. The alterations account for time, mental states, tasks, individuals, and so forth. Furthermore, the changes determine the segregation and integration of functional networks that lead to network reorganization (or reconfiguration) to extend the neuroplasticity of the brain. Exploring related brain networks should be of interest that may provide roadmaps for brain research and clinical diagnosis. Recent electroencephalogram (EEG) studies have revealed the secrets of the brain networks and diseases (or disorders) within and between subjects and have provided instructive and promising suggestions and methods. This review summarized the corresponding algorithms that had been used to construct functional or effective networks on the scalp and cerebral cortex. We reviewed EEG network analysis that unveils more cognitive functions and neural disorders of the human and then explored the relationship between brain science and artificial intelligence which may fuel each other to accelerate their advances, and also discussed some innovations and future challenges in the end.

The functional brain favours segregated modular connectivity at old age unless affected by neurodegeneration

Brain's modular connectivity gives this organ resilience and adaptability. The ageing process alters the organised modularity of the brain and these changes are further accentuated by neurodegeneration, leading to disorganisation. To understand this further, we analysed modular variability-heterogeneity of modules-and modular dissociation-detachment from segregated connectivity-in two ageing cohorts and a mixed cohort of neurodegenerative diseases. Our results revealed that the brain follows a universal pattern of high modular variability in metacognitive brain regions: the association cortices. The brain in ageing moves towards a segregated modular structure despite presenting with increased modular heterogeneity-modules in older adults are not only segregated, but their shape and size are more variable than in young adults. In the presence of neurodegeneration, the brain maintains its segregated connectivity globally but not locally, and this is particularly visible in dementia with Lewy bodies and Parkinson's disease dementia; overall, the modular brain shows patterns of differentiated pathology.

Principles and open questions in functional brain network reconstruction

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

Transcranial photobiomodulation changes topology, synchronizability, and complexity of resting state brain networks

Objective. Transcranial photobiomodulation (tPBM) is a recently proposed non-invasive brain stimulation approach with various effects on the nervous system from the cells to the whole brain networks. Specially in the neural network level, tPBM can alter the topology and synchronizability of functional brain networks. However, the functional properties of the neural networks after tPBM are still poorly clarified.Approach. Here, we employed electroencephalography and different methods (conventional and spectral) in the graph theory analysis to track the significant effects of tPBM on the resting state brain networks. The non-parametric statistical analysis showed that just one short-term tPBM session over right medial frontal pole can significantly change both topological (i.e. clustering coefficient, global efficiency, local efficiency, eigenvector centrality) and dynamical (i.e. energy, largest eigenvalue, and entropy) features of resting state brain networks.Main results. The topological results revealed that tPBM can reduce local processing, centrality, and laterality. Furthermore, the increased centrality of central electrode was observed.Significance. These results suggested that tPBM can alter topology of resting state brain network to facilitate the neural information processing. On the other hand, the dynamical results showed that tPBM reduced stability of synchronizability and increased complexity in the resting state brain networks. These effects can be considered in association with the increased complexity of connectivity patterns among brain regions and the enhanced information propagation in the resting state brain networks. Overall, both topological and dynamical features of brain networks suggest that although tPBM decreases local processing (especially in the right hemisphere) and disrupts synchronizability of network, but it can increase the level of information transferring and processing in the brain network.

Scale-Free Coupled Dynamics in Brain Networks Captured by Bivariate Focus-Based Multifractal Analysis

While most connectivity studies investigate functional connectivity (FC) in a scale-dependent manner, coupled neural processes may also exhibit broadband dynamics, manifesting as power-law scaling of their measures of interdependence. Here we introduce the bivariate focus-based multifractal (BFMF) analysis as a robust tool for capturing such scale-free relations and use resting-state electroencephalography (EEG) recordings of 12 subjects to demonstrate its performance in reconstructing physiological networks. BFMF was employed to characterize broadband FC between 62 cortical regions in a pairwise manner, with all investigated connections being tested for true bivariate multifractality. EEG channels were also grouped to represent the activity of six resting-state networks (RSNs) in the brain, thus allowing for the analysis of within- and between- RSNs connectivity, separately. Most connections featured true bivariate multifractality, which could be attributed to the genuine scale-free coupling of neural dynamics. Bivariate multifractality showed a characteristic topology over the cortex that was highly concordant among subjects. Long-term autocorrelation was higher in within-RSNs, while the degree of multifractality was generally found stronger in between-RSNs connections. These results offer statistical evidence of the bivariate multifractal nature of functional coupling in the brain and validate BFMF as a robust method to capture such scale-independent coupled dynamics.

Decreased connection density and modularity of functional brain networks during n-back working memory paradigm

INTRODUCTION

Investigating how the brain adapts to increased mental workload through large-scale functional reorganization appears as an important research question. Functional connectivity (FC) aims at capturing how disparate regions of the brain dynamically interact, while graph theory provides tools for the topological characterization of the reconstructed functional networks. Although numerous studies investigated how FC is altered in response to increased working memory (WM) demand, current results are still contradictory as few studies confirmed the robustness of these findings in a low-density setting.

METHODS

In this study, we utilized the n-back WM paradigm, in which subjects were presented stimuli (single digits) sequentially, and their task was to decide for each given stimulus if it matched the one presented n-times earlier. Electroencephalography recordings were performed under a control (0-back) and two task conditions of varying difficulty (2- and 3-back). We captured the characteristic connectivity patterns for each difficulty level by performing FC analysis and described the reconstructed functional networks with various graph theoretical measures.

RESULTS

We found a substantial decrease in FC when transitioning from the 0- to the 2- or 3-back conditions, however, no differences relating to task difficulty were identified. The observed changes in brain network topology could be attributed to the dissociation of two (frontal and occipitotemporal) functional modules that were only present during the control condition. Furthermore, behavioral and performance measures showed both positive and negative correlations to connectivity indices, although only in the higher frequency bands.

CONCLUSION

The marked decrease in FC may be due to temporarily abandoned connections that are redundant or irrelevant in solving the specific task. Our results indicate that FC analysis is a robust tool for investigating the response of the brain to increased cognitive workload.

Synchrony and Complexity in State-Related EEG Networks: An Application of Spectral Graph Theory

The brain may be considered as a synchronized dynamic network with several coherent dynamical units. However, concerns remain whether synchronizability is a stable state in the brain networks. If so, which index can best reveal the synchronizability in brain networks? To answer these questions, we tested the application of the spectral graph theory and the Shannon entropy as alternative approaches in neuroimaging. We specifically tested the alpha rhythm in the resting-state eye closed (rsEC) and the resting-state eye open (rsEO) conditions, a well-studied classical example of synchrony in neuroimaging EEG. Since the synchronizability of alpha rhythm is more stable during the rsEC than the rsEO, we hypothesized that our suggested spectral graph theory indices (as reliable measures to interpret the synchronizability of brain signals) should exhibit higher values in the rsEC than the rsEO condition. We performed two separate analyses of two different datasets (as elementary and confirmatory studies). Based on the results of both studies and in agreement with our hypothesis, the spectral graph indices revealed higher stability of synchronizability in the rsEC condition. The k-mean analysis indicated that the spectral graph indices can distinguish the rsEC and rsEO conditions by considering the synchronizability of brain networks. We also computed correlations among the spectral indices, the Shannon entropy, and the topological indices of brain networks, as well as random networks. Correlation analysis indicated that although the spectral and the topological properties of random networks are completely independent, these features are significantly correlated with each other in brain networks. Furthermore, we found that complexity in the investigated brain networks is inversely related to the stability of synchronizability. In conclusion, we revealed that the spectral graph theory approach can be reliably applied to study the stability of synchronizability of state-related brain networks.

Investigation on the Alteration of Brain Functional Network and Its Role in the Identification of Mild Cognitive Impairment

Mild cognitive impairment (MCI) is generally regarded as a prodromal stage of Alzheimer’s disease (AD). In coping with the challenges caused by AD, we analyzed resting-state functional magnetic resonance imaging data of 82 MCI subjects and 93 normal controls (NCs). The alteration of brain functional network in MCI was investigated on three scales, including global metrics, nodal characteristics, and modular properties. The results supported the existence of small worldness, hubs, and community structure in the brain functional networks of both groups. Compared with NCs, the network altered in MCI over all the three scales. In scale I, we found significantly decreased characteristic path length and increased global efficiency in MCI. Moreover, altered global network metrics were associated with cognitive level evaluated by neuropsychological assessments. In scale II, the nodal betweenness centrality of some global hubs, such as the right Crus II of cerebellar hemisphere (CERCRU2.R) and fusiform gyrus (FFG.R), changed significantly and associated with the severity and cognitive impairment in MCI. In scale III, although anatomically adjacent regions tended to be clustered into the same module regardless of group, discrepancies existed in the composition of modules in both groups, with a prominent separation of the cerebellum and a less localized organization of community structure in MCI compared with NC. Taking advantages of random forest approach, we achieved an accuracy of 91.4% to discriminate MCI patients from NCs by integrating cognitive assessments and network analysis. The importance of the used features fed into the classifier further validated the nodal characteristics of CERCRU2.R and FFG.R could be potential biomarkers in the identification of MCI. In conclusion, the present study demonstrated that the brain functional connectome data altered at the stage of MCI and could assist the automatic diagnosis of MCI patients.

Correlation Guided Graph Learning to Estimate Functional Connectivity Patterns From fMRI Data

OBJECTIVE

Recently, functional magnetic resonance imaging (fMRI)-derived brain functional connectivity (FC) patterns have been used as fingerprints to predict individual differences in phenotypic measures, and cognitive dysfunction associated with brain diseases. In these applications, how to accurately estimate FC patterns is crucial yet technically challenging.

METHODS

In this article, we propose a correlation guided graph learning (CGGL) method to estimate FC patterns for establishing brain-behavior relationships. Different from the existing graph learning methods which only consider the graph structure across brain regions-of-interest (ROIs), our proposed CGGL takes into account both the temporal correlation of ROIs across time points, and the graph structure across ROIs. The resulting FC patterns reflect substantial inter-individual variations related to the behavioral measure of interest.

RESULTS

We validate the effectiveness of our proposed CGGL on the Philadelphia Neurodevelopmental Cohort data for separately predicting three behavioral measures based on resting-state fMRI. Experimental results demonstrate that the proposed CGGL outperforms other competing FC pattern estimation methods.

CONCLUSION

Our method increases the predictive power of the constructed FC patterns when establishing brain-behavior relationships, and gains meaningful insights into relevant biological mechanisms.

SIGNIFICANCE

The proposed CGGL offers a more powerful, and reliable method to estimate FC patterns, which can be used as fingerprints in many brain network studies.

Topological Network Analysis of Early Alzheimer's Disease Based on Resting-State EEG

Previous studies made progress in the early diagnosis of Alzheimer's disease (AD) using electroencephalography (EEG) without considering EEG connectivity. To fill this gap, we explored significant differences between early AD patients and controls based on frequency domain and spatial properties using functional connectivity in mild cognitive impairment (MCI) and mild AD datasets. Four global metrics, network resilience, connection-level metrics and node versatility were used to distinguish between controls and patients. The results show that the main frequency bands that are different between MCI patients and controls are the θ and low α bands, and the differently affected brain areas are the frontal, left temporal and parietal areas. Compared to MCI patients, in patients with mild AD, the main frequency bands that are different are the low and high α bands, and the main differently affected brain region is a larger right temporal area. Four LOFC bands were used as input to train the ResNet-18 model. For the MCI dataset, the average accuracy of 20 runs was 93.42% and the best accuracy was 98.33%, while for the mild AD dataset, the average accuracy was 98.54% and the best accuracy was 100%. To determine the timing of early treatment and discovering the susceptible patients, and to slow the progression of the disease, we assume that the occurrence of MCI and mild AD and their progression to more serious AD and dementia could be inferred by analyzing the topological structure of the brain network generated by EEG. Our findings provide a novel solution for connectome-based biomarker analysis to improve personalized medicine.

Multifractal and Entropy-Based Analysis of Delta Band Neural Activity Reveals Altered Functional Connectivity Dynamics in Schizophrenia

Dynamic functional connectivity (DFC) was established in the past decade as a potent approach to reveal non-trivial, time-varying properties of neural interactions – such as their multifractality or information content –, that otherwise remain hidden from conventional static methods. Several neuropsychiatric disorders were shown to be associated with altered DFC, with schizophrenia (SZ) being one of the most intensely studied among such conditions. Here we analyzed resting-state electroencephalography recordings of 14 SZ patients and 14 age- and gender-matched healthy controls (HC). We reconstructed dynamic functional networks from delta band (0.5–4 Hz) neural activity and captured their spatiotemporal dynamics in various global network topological measures. The acquired network measure time series were made subject to dynamic analyses including multifractal analysis and entropy estimation. Besides group-level comparisons, we built a classifier to explore the potential of DFC features in classifying individual cases. We found stronger delta-band connectivity, as well as increased variance of DFC in SZ patients. Surrogate data testing verified the true multifractal nature of DFC in SZ, with patients expressing stronger long-range autocorrelation and degree of multifractality when compared to controls. Entropy analysis indicated reduced temporal complexity of DFC in SZ. When using these indices as features, an overall cross-validation accuracy surpassing 89% could be achieved in classifying individual cases. Our results imply that dynamic features of DFC such as its multifractal properties and entropy are potent markers of altered neural dynamics in SZ and carry significant potential not only in better understanding its pathophysiology but also in improving its diagnosis. The proposed framework is readily applicable for neuropsychiatric disorders other than schizophrenia.

Metabolomics and Multi-Omics Integration: A Survey of Computational Methods and Resources

As researchers are increasingly able to collect data on a large scale from multiple clinical and omics modalities, multi-omics integration is becoming a critical component of metabolomics research. This introduces a need for increased understanding by the metabolomics researcher of computational and statistical analysis methods relevant to multi-omics studies. In this review, we discuss common types of analyses performed in multi-omics studies and the computational and statistical methods that can be used for each type of analysis. We pinpoint the caveats and considerations for analysis methods, including required parameters, sample size and data distribution requirements, sources of a priori knowledge, and techniques for the evaluation of model accuracy. Finally, for the types of analyses discussed, we provide examples of the applications of corresponding methods to clinical and basic research. We intend that our review may be used as a guide for metabolomics researchers to choose effective techniques for multi-omics analyses relevant to their field of study.

Time evolution of the behaviour of Brazilian legislative Representatives using a complex network approach

The follow up of Representative behavior after elections is imperative for a democratic Representative system, at the very least to punish betrayal with no re-election. Our goal was to show how to follow Representatives’ and how to show behavior in real situations and observe trends in political crises including the onset of game changing political instabilities. We used correlation and correlation distance matrices of Brazilian Representative votes during four presidential terms. Re-ordering these matrices with Minimal Spanning Trees displays the dynamical formation of clusters for the sixteen year period, which includes one Presidential impeachment. The reordered matrices, colored by correlation strength and by the parties clearly show the origin of observed clusters and their evolution over time. When large clusters provide government support cluster breaks, political instability arises, which could lead to an impeachment, a trend we observed three years before the Brazilian President was impeached. We believe this method could be applied to foresee other political storms.

Determining the Hierarchical Architecture of the Human Brain Using Subject-Level Clustering of Functional Networks

Optimal integration and segregation of neuronal connections are necessary for efficient large-scale network communication between distributed cortical regions while allowing for modular specialization. This dynamic in the cortex is enabled at the network mesoscale by the organization of nodes into communities. Previous in vivo efforts to map the mesoscale architecture in humans had several limitations. Here we characterize a consensus multiscale community organization of the functional cortical network. We derive this consensus from the clustering of subject-level networks. We applied this analysis to magnetic resonance imaging data from 1003 healthy individuals part of the Human Connectome Project. The hierarchical atlas and code will be made publicly available for future investigators.

Weighted network measures reveal differences between dementia types: An EEG study

The diagnosis of dementia with Lewy bodies (DLB) versus Alzheimer's disease (AD) can be difficult especially early in the disease process. However, one inexpensive and non‐invasive biomarker which could help is electroencephalography (EEG). Previous studies have shown that the brain network architecture assessed by EEG is altered in AD patients compared with age‐matched healthy control people (HC). However, similar studies in Lewy body diseases, that is, DLB and Parkinson's disease dementia (PDD) are still lacking. In this work, we (a) compared brain network connectivity patterns across conditions, AD, DLB and PDD, in order to infer EEG network biomarkers that differentiate between these conditions, and (b) tested whether opting for weighted matrices led to more reliable results by better preserving the topology of the network. Our results indicate that dementia groups present with reduced connectivity in the EEG α band, whereas DLB shows weaker posterior–anterior patterns within the β‐band and greater network segregation within the θ‐band compared with AD. Weighted network measures were more consistent across global thresholding levels, and the network properties reflected reduction in connectivity strength in the dementia groups. In conclusion, β‐ and θ‐band network measures may be suitable as biomarkers for discriminating DLB from AD, whereas the α‐band network is similarly affected in DLB and PDD compared with HC. These variations may reflect the impairment of attentional networks in Parkinsonian diseases such as DLB and PDD.

Space-time recurrences for functional connectivity evaluation and feature extraction in motor imagery brain-computer interfaces

This work presents a classification performance comparison between different frameworks for functional connectivity evaluation and complex network feature extraction aiming to distinguish motor imagery classes in electroencephalography (EEG)-based brain-computer interfaces (BCIs). The analysis was performed in two online datasets: (1) a classical benchmark-the BCI competition IV dataset 2a-allowing a comparison with a representative set of strategies previously employed in this BCI paradigm and (2) a statistically representative dataset for signal processing technique comparisons over 52 subjects. Besides exploring three classical similarity measures-Pearson correlation, Spearman correlation, and mean phase coherence-this work also proposes a recurrence-based alternative for estimating EEG brain functional connectivity, which takes into account the recurrence density between pairwise electrodes over a time window. These strategies were followed by graph feature evaluation considering clustering coefficient, degree, betweenness centrality, and eigenvector centrality. The features were selected by Fisher's discriminating ratio and classification was performed by a least squares classifier in agreement with classical and online BCI processing strategies. The results revealed that the recurrence-based approach for functional connectivity evaluation was significantly better than the other frameworks, which is probably associated with the use of higher order statistics underlying the electrode joint probability estimation and a higher capability of capturing nonlinear inter-relations. There were no significant differences in performance among the evaluated graph features, but the eigenvector centrality was the best feature regarding processing time. Finally, the best ranked graph-based attributes were found in classical EEG motor cortex positions for the subjects with best performances, relating functional organization and motor activity. Graphical Abstract Evaluating functional connectivity based on Space-Time Recurrence Counting for motor imagery classification in brain-computer interfaces. Recurrences are evaluated between electrodes over a time window, and, after a density threshold, the electrodes adjacency matrix is stablish, leading to a graph. Graph-based topological measures are used for motor imagery classification.

Discordant attributes of structural and functional brain connectivity in a two-layer multiplex network

Several studies have suggested that functional connectivity (FC) is constrained by the underlying structural connectivity (SC) and mutually correlated. However, not many studies have focused on differences in the network organization of SC and FC, and on how these differences may inform us about their mutual interaction. To explore this issue, we adopt a multi-layer framework, with SC and FC, constructed using Magnetic Resonance Imaging (MRI) data from the Human Connectome Project, forming a two-layer multiplex network. In particular, we examine node strength assortativity within and between the SC and FC layer. We find that, in general, SC is organized assortatively, indicating brain regions are on average connected to other brain regions with similar node strengths. On the other hand, FC shows disassortative mixing. This discrepancy is apparent also among individual resting-state networks within SC and FC. In addition, these patterns show lateralization, with disassortative mixing within FC subnetworks mainly driven from the left hemisphere. We discuss our findings in the context of robustness to structural failure, and we suggest that discordant and lateralized patterns of associativity in SC and FC may provide clues to understand laterality of some neurological dysfunctions and recovery.

Configuration model for correlation matrices preserving the node strength

Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices, such as those derived from random matrix theory, that partially preserve properties of the original matrix. We propose a model to generate such reference correlation and covariance matrices for the given matrix. Correlation matrices are often analyzed as networks, which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node. Given this background, the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes, akin to configuration models for conventional networks. Our algorithm is derived from the maximum entropy principle. We will apply the proposed algorithm to measurement of clustering coefficients and community detection, both of which require a null model to assess the statistical significance of the obtained results.

Topological structures are consistently overestimated in functional complex networks

Functional complex networks have meant a pivotal change in the way we understand complex systems, being the most outstanding one the human brain. These networks have classically been reconstructed using a frequentist approach that, while simple, completely disregards the uncertainty that derives from data finiteness. We provide here an alternative solution based on Bayesian inference, with link weights treated as random variables described by probability distributions, from which ensembles of networks are sampled. By using both statistical and topological considerations, we prove that the role played by links’ uncertainty is equivalent to the introduction of a random rewiring, whose omission leads to a consistent overestimation of topological structures. We further show that this bias is enhanced in short time series, suggesting the existence of a theoretical time resolution limit for obtaining reliable structures. We also propose a simple sampling process for correcting topological values obtained in frequentist networks. We finally validate these concepts through synthetic and real network examples, the latter representing the brain electrical activity of a group of people during a cognitive task.

An efficient algorithm for estimating brain covariance networks

Often derived from partial correlations or many pairwise analyses, covariance networks represent the inter-relationships among regions and can reveal important topological structures in brain measures from healthy and pathological subjects. However both approaches are not consistent network estimators and are sensitive to the value of the tuning parameters. Here, we propose a consistent covariance network estimator by maximising the network likelihood (MNL) which is robust to the tuning parameter. We validate the consistency of our algorithm theoretically and via a simulation study, and contrast these results against two well-known approaches: the graphical LASSO (gLASSO) and Pearson pairwise correlations (PPC) over a range of tuning parameters. The MNL algorithm had a specificity equal to and greater than 0.94 for all sample sizes in the simulation study, and the sensitivity was shown to increase as the sample size increased. The gLASSO and PPC demonstrated a specificity-sensitivity trade-off over a range of values of tuning parameters highlighting the discrepancy in the results for misspecified values. Application of the MNL algorithm to the case study data showed a loss of connections between healthy and impaired groups, and improved ability to identify between lobe connectivity in contrast to gLASSO networks. In this work, we propose the MNL algorithm as an effective approach to find covariance brain networks, which can inform the organisational features in brain-wide analyses, particularly for large sample sizes.

Clustering Coefficients for Correlation Networks

Graph theory is a useful tool for deciphering structural and functional networks of the brain on various spatial and temporal scales. The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighboring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other) measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients (i.e., abundance of triangles around a focal node) are useful in characterizing individual nodes. In contrast, the conventional local clustering coefficients were strongly correlated with and therefore may be confounded by the node's connectivity. The proposed methods are expected to help us to understand clustering and lack thereof in correlational brain networks, such as those derived from functional time series and across-participant correlation in neuroanatomical properties.

Accounting for the complex hierarchical topology of EEG phase-based functional connectivity in network binarisation

Research into binary network analysis of brain function faces a methodological challenge in selecting an appropriate threshold to binarise edge weights. For EEG phase-based functional connectivity, we test the hypothesis that such binarisation should take into account the complex hierarchical structure found in functional connectivity. We explore the density range suitable for such structure and provide a comparison of state-of-the-art binarisation techniques, the recently proposed Cluster-Span Threshold (CST), minimum spanning trees, efficiency-cost optimisation and union of shortest path graphs, with arbitrary proportional thresholds and weighted networks. We test these techniques on weighted complex hierarchy models by contrasting model realisations with small parametric differences. We also test the robustness of these techniques to random and targeted topological attacks. We find that the CST performs consistenty well in state-of-the-art modelling of EEG network topology, robustness to topological network attacks, and in three real datasets, agreeing with our hypothesis of hierarchical complexity. This provides interesting new evidence into the relevance of considering a large number of edges in EEG functional connectivity research to provide informational density in the topology.

Macroscopic and microscopic spectral properties of brain networks during local and global synchronization

We introduce a practical and computationally not demanding technique for inferring interactions at various microscopic levels between the units of a network from the measurements and the processing of macroscopic signals. Starting from a network model of Kuramoto phase oscillators, which evolve adaptively according to homophilic and homeostatic adaptive principles, we give evidence that the increase of synchronization within groups of nodes (and the corresponding formation of synchronous clusters) causes also the defragmentation of the wavelet energy spectrum of the macroscopic signal. Our methodology is then applied to getting a glance into the microscopic interactions occurring in a neurophysiological system, namely, in the thalamocortical neural network of an epileptic brain of a rat, where the group electrical activity is registered by means of multichannel EEG. We demonstrate that it is possible to infer the degree of interaction between the interconnected regions of the brain during different types of brain activities and to estimate the regions' participation in the generation of the different levels of consciousness.