Applications of community detection techniques to brain graphs: Algorithmic considerations and implications for neural function

Coarse graining and criticality in the human connectome

In the face of the stupefying complexity of the human brain, network analysis is a most useful tool that allows one to greatly simplify the problem, typically by approximating the billions of neurons making up the brain by means of a coarse-grained picture with a practicable number of nodes. But even such relatively small and coarse networks, such as the human connectome with its 100-1000 nodes, may present challenges for some computationally demanding analyses that are incapable of handling networks with more than a handful of nodes. With such applications in mind, we set out to study the extent to which dynamical behavior and critical phenomena in the brain may be preserved following a severe coarse-graining procedure. Thus we proceeded to further coarse grain the human connectome by taking a modularity-based approach, the goal being to produce a network of a relatively small number of modules. After finding that the qualitative dynamical behavior of the coarse-grained networks reflected that of the original networks, albeit to a less pronounced extent, we then formulated a hypothesis based on the coarse-grained networks in the context of criticality in the Wilson-Cowan and Ising models, and we verified the hypothesis, which connected a transition value of the former with the critical temperature of the latter, using the original networks. This preservation of dynamical and critical behavior following a severe coarse-graining procedure, in principle, allows for the drawing of similar qualitative conclusions by analyzing much smaller networks, which opens the door for studying the human connectome in contexts typically regarded as computationally intractable, such as Integrated Information Theory and quantum models of the human brain.

Community detection in the human connectome: Method types, differences and their impact on inference

Community structure is a fundamental topological characteristic of optimally organized brain networks. Currently, there is no clear standard or systematic approach for selecting the most appropriate community detection method. Furthermore, the impact of method choice on the accuracy and robustness of estimated communities (and network modularity), as well as method-dependent relationships between network communities and cognitive and other individual measures, are not well understood. This study analyzed large datasets of real brain networks (estimated from resting-state fMRI fromn $$ n $$ = 5251 pre/early adolescents in the adolescent brain cognitive development [ABCD] study), andn $$ n $$ = 5338 synthetic networks with heterogeneous, data-inspired topologies, with the goal to investigate and compare three classes of community detection methods: (i) modularity maximization-based (Newman and Louvain), (ii) probabilistic (Bayesian inference within the framework of stochastic block modeling (SBM)), and (iii) geometric (based on graph Ricci flow). Extensive comparisons between methods and their individual accuracy (relative to the ground truth in synthetic networks), and reliability (when applied to multiple fMRI runs from the same brains) suggest that the underlying brain network topology plays a critical role in the accuracy, reliability and agreement of community detection methods. Consistent method (dis)similarities, and their correlations with topological properties, were estimated across fMRI runs. Based on synthetic graphs, most methods performed similarly and had comparable high accuracy only in some topological regimes, specifically those corresponding to developed connectomes with at least quasi-optimal community organization. In contrast, in densely and/or weakly connected networks with difficult to detect communities, the methods yielded highly dissimilar results, with Bayesian inference within SBM having significantly higher accuracy compared to all others. Associations between method-specific modularity and demographic, anthropometric, physiological and cognitive parameters showed mostly method invariance but some method dependence as well. Although method sensitivity to different levels of community structure may in part explain method-dependent associations between modularity estimates and parameters of interest, method dependence also highlights potential issues of reliability and reproducibility. These findings suggest that a probabilistic approach, such as Bayesian inference in the framework of SBM, may provide consistently reliable estimates of community structure across network topologies. In addition, to maximize robustness of biological inferences, identified network communities and their cognitive, behavioral and other correlates should be confirmed with multiple reliable detection methods.

A Comprehensive Survey on Community Detection With Deep Learning

Detecting a community in a network is a matter of discerning the distinct features and connections of a group of members that are different from those in other communities. The ability to do this is of great significance in network analysis. However, beyond the classic spectral clustering and statistical inference methods, there have been significant developments with deep learning techniques for community detection in recent years-particularly when it comes to handling high-dimensional network data. Hence, a comprehensive review of the latest progress in community detection through deep learning is timely. To frame the survey, we have devised a new taxonomy covering different state-of-the-art methods, including deep learning models based on deep neural networks (DNNs), deep nonnegative matrix factorization, and deep sparse filtering. The main category, i.e., DNNs, is further divided into convolutional networks, graph attention networks, generative adversarial networks, and autoencoders. The popular benchmark datasets, evaluation metrics, and open-source implementations to address experimentation settings are also summarized. This is followed by a discussion on the practical applications of community detection in various domains. The survey concludes with suggestions of challenging topics that would make for fruitful future research directions in this fast-growing deep learning field.

Regression and Alignment for Functional Data and Network Topology

In the brain, functional connections form a network whose topological organization can be described by graph-theoretic network diagnostics. These include characterizations of the community structure, such as modularity and participation coefficient, which have been shown to change over the course of childhood and adolescence. To investigate if such changes in the functional network are associated with changes in cognitive performance during development, network studies often rely on an arbitrary choice of pre-processing parameters, in particular the proportional threshold of network edges. Because the choice of parameter can impact the value of the network diagnostic, and therefore downstream conclusions, we propose to circumvent that choice by conceptualizing the network diagnostic as a function of the parameter. As opposed to a single value, a network diagnostic curve describes the connectome topology at multiple scales-from the sparsest group of the strongest edges to the entire edge set. To relate these curves to executive function and other covariates, we use scalar-on-function regression, which is more flexible than previous functional data-based models used in network neuroscience. We then consider how systematic differences between networks can manifest in misalignment of diagnostic curves, and consequently propose a supervised curve alignment method that incorporates auxiliary information from other variables. Our algorithm performs both functional regression and alignment via an iterative, penalized, and nonlinear likelihood optimization. The illustrated method has the potential to improve the interpretability and generalizability of neuroscience studies where the goal is to study heterogeneity among a mixture of function- and scalar-valued measures.

Optimizing parameter search for community detection in time-evolving networks of complex systems

Network representations have been effectively employed to analyze complex systems across various areas and applications, leading to the development of network science as a core tool to study systems with multiple components and complex interactions. There is a growing interest in understanding the temporal dynamics of complex networks to decode the underlying dynamic processes through the temporal changes in network structures. Community detection algorithms, which are specialized clustering algorithms, have been instrumental in studying these temporal changes. They work by grouping nodes into communities based on the structure and intensity of network connections over time, aiming to maximize the modularity of the network partition. However, the performance of these algorithms is highly influenced by the selection of resolution parameters of the modularity function used, which dictate the scale of the represented network, in both size of communities and the temporal resolution of the dynamic structure. The selection of these parameters has often been subjective and reliant on the characteristics of the data used to create the network. Here, we introduce a method to objectively determine the values of the resolution parameters based on the elements of self-organization and scale-invariance. We propose two key approaches: (1) minimization of biases in spatial scale network characterization and (2) maximization of scale-freeness in temporal network reconfigurations. We demonstrate the effectiveness of these approaches using benchmark network structures as well as real-world datasets. To implement our method, we also provide an automated parameter selection software package that can be applied to a wide range of complex systems.

Dynamic functional connectivity in schizophrenia and bipolar disorder: A review of the evidence and associations with psychopathological features

Alterations of functional network connectivity have been implicated in the pathophysiology of schizophrenia (SCZ) and bipolar disorder (BD). Recent studies also suggest that the temporal dynamics of functional connectivity (dFC) can be altered in these disorders. Here, we summarized the existing literature on dFC in SCZ and BD, and their association with psychopathological and cognitive features. We systematically searched PubMed, Web of Science, and Scopus for studies investigating dFC in SCZ and BD and identified 77 studies. Our findings support a general model of dysconnectivity of dFC in SCZ, whereas a heterogeneous picture arose in BD. Although dFC alterations are more severe and widespread in SCZ compared to BD, dysfunctions of a triple network system underlying goal-directed behavior and sensory-motor networks were present in both disorders. Furthermore, in SCZ, positive and negative symptoms were associated with abnormal dFC. Implications for understanding the pathophysiology of disorders, the role of neurotransmitters, and treatments on dFC are discussed. The lack of standards for dFC metrics, replication studies, and the use of small samples represent major limitations for the field.

Disordered network structure and function in dystonia: pathological connectivity vs. adaptive responses

Primary dystonia is thought to emerge through abnormal functional relationships between basal ganglia and cerebellar motor circuits. These interactions may differ across disease subtypes and provide a novel biomarker for diagnosis and treatment. Using a network mapping algorithm based on resting-state functional MRI (rs-fMRI), a method that is readily implemented on conventional MRI scanners, we identified similar disease topographies in hereditary dystonia associated with the DYT1 or DYT6 mutations and in sporadic patients lacking these mutations. Both networks were characterized by contributions from the basal ganglia, cerebellum, thalamus, sensorimotor areas, as well as cortical association regions. Expression levels for the two networks were elevated in hereditary and sporadic dystonia, and in non-manifesting carriers of dystonia mutations. Nonetheless, the distribution of abnormal functional connections differed across groups, as did metrics of network organization and efficiency in key modules. Despite these differences, network expression correlated with dystonia motor ratings, significantly improving the accuracy of predictions based on thalamocortical tract integrity obtained with diffusion tensor MRI (DTI). Thus, in addition to providing unique information regarding the anatomy of abnormal brain circuits, rs-fMRI functional networks may provide a widely accessible method to help in the objective evaluation of new treatments for this disorder.

Increased flexibility of brain dynamics in patients with multiple sclerosis

Patients with multiple sclerosis consistently show widespread changes in functional connectivity. Yet, alterations are heterogeneous across studies, underscoring the complexity of functional reorganization in multiple sclerosis. Here, we aim to provide new insights by applying a time-resolved graph-analytical framework to identify a clinically relevant pattern of dynamic functional connectivity reconfigurations in multiple sclerosis. Resting-state data from 75 patients with multiple sclerosis (N = 75, female:male ratio of 3:2, median age: 42.0 ± 11.0 years, median disease duration: 6 ± 11.4 years) and 75 age- and sex-matched controls (N = 75, female:male ratio of 3:2, median age: 40.2 ± 11.8 years) were analysed using multilayer community detection. Local, resting-state functional system and global levels of dynamic functional connectivity reconfiguration were characterized using graph-theoretical measures including flexibility, promiscuity, cohesion, disjointedness and entropy. Moreover, we quantified hypo- and hyper-flexibility of brain regions and derived the flexibility reorganization index as a summary measure of whole-brain reorganization. Lastly, we explored the relationship between clinical disability and altered functional dynamics. Significant increases in global flexibility (t = 2.38, P_FDR = 0.024), promiscuity (t = 1.94, P_FDR = 0.038), entropy (t = 2.17, P_FDR = 0.027) and cohesion (t = 2.45, P_FDR = 0.024) were observed in patients and were driven by pericentral, limbic and subcortical regions. Importantly, these graph metrics were correlated with clinical disability such that greater reconfiguration dynamics tracked greater disability. Moreover, patients demonstrate a systematic shift in flexibility from sensorimotor areas to transmodal areas, with the most pronounced increases located in regions with generally low dynamics in controls. Together, these findings reveal a hyperflexible reorganization of brain activity in multiple sclerosis that clusters in pericentral, subcortical and limbic areas. This functional reorganization was linked to clinical disability, providing new evidence that alterations of multilayer temporal dynamics play a role in the manifestation of multiple sclerosis.

Reconfigurations in brain networks upon awakening from slow wave sleep: Interventions and implications in neural communication

Sleep inertia is the brief period of impaired alertness and performance experienced immediately after waking. Little is known about the neural mechanisms underlying this phenomenon. A better understanding of the neural processes during sleep inertia may offer insight into the awakening process. We observed brain activity every 15 min for 1 hr following abrupt awakening from slow wave sleep during the biological night. Using 32-channel electroencephalography, a network science approach, and a within-subject design, we evaluated power, clustering coefficient, and path length across frequency bands under both a control and a polychromatic short-wavelength-enriched light intervention condition. We found that under control conditions, the awakening brain is typified by an immediate reduction in global theta, alpha, and beta power. Simultaneously, we observed a decrease in the clustering coefficient and an increase in path length within the delta band. Exposure to light immediately after awakening ameliorated changes in clustering. Our results suggest that long-range network communication within the brain is crucial to the awakening process and that the brain may prioritize these long-range connections during this transitional state. Our study highlights a novel neurophysiological signature of the awakening brain and provides a potential mechanism by which light improves performance after waking.

Dual communities in spatial networks

Both human-made and natural supply systems, such as power grids and leaf venation networks, are built to operate reliably under changing external conditions. Many of these spatial networks exhibit community structures. Here, we show that a relatively strong connectivity between the parts of a network can be used to define a different class of communities: dual communities. We demonstrate that traditional and dual communities emerge naturally as two different phases of optimized network structures that are shaped by fluctuations and that they both suppress failure spreading, which underlines their importance in understanding the shape of real-world supply networks.

Mapping the Nicotinic Acetylcholine Receptor Nanocluster Topography at the Cell Membrane with STED and STORM Nanoscopies

The cell-surface topography and density of nicotinic acetylcholine receptors (nAChRs) play a key functional role in the synapse. Here we employ in parallel two labeling and two super-resolution microscopy strategies to characterize the distribution of this receptor at the plasma membrane of the mammalian clonal cell line CHO-K1/A5. Cells were interrogated with two targeted techniques (confocal microscopy and stimulated emission depletion (STED) nanoscopy) and single-molecule nanoscopy (stochastic optical reconstruction microscopy, STORM) using the same fluorophore, Alexa Fluor 647, tagged onto either α-bungarotoxin (BTX) or the monoclonal antibody mAb35. Analysis of the topography of nanometer-sized aggregates (“nanoclusters”) was carried out using STORMGraph, a quantitative clustering analysis for single-molecule localization microscopy based on graph theory and community detection, and ASTRICS, an inter-cluster similarity algorithm based on computational geometry. Antibody-induced crosslinking of receptors resulted in nanoclusters with a larger number of receptor molecules and higher densities than those observed in BTX-labeled samples. STORM and STED provided complementary information, STED rendering a direct map of the mesoscale nAChR distribution at distances ~10-times larger than the nanocluster centroid distances measured in STORM samples. By applying photon threshold filtering analysis, we show that it is also possible to detect the mesoscale organization in STORM images.

Intermittent brain network reconfigurations and the resistance to social media influence

Since its development, social media has grown as a source of information and has a significant impact on opinion formation. Individuals interact with others and content via social media platforms in a variety of ways, but it remains unclear how decision-making and associated neural processes are impacted by the online sharing of informational content, from factual to fabricated. Here, we use EEG to estimate dynamic reconfigurations of brain networks and probe the neural changes underlying opinion change (or formation) within individuals interacting with a simulated social media platform. Our findings indicate that the individuals who changed their opinions are characterized by less frequent network reconfigurations while those who did not change their opinions tend to have more flexible brain networks with frequent reconfigurations. The nature of these frequent network configurations suggests a fundamentally different thought process between intervals in which individuals are easily influenced by social media and those in which they are not. We also show that these reconfigurations are distinct to the brain dynamics during an in-person discussion with strangers on the same content. Together, these findings suggest that brain network reconfigurations may not only be diagnostic to the informational context but also the underlying opinion formation.

A Functional Contextual Account of Background Knowledge in Categorization: Implications for Artificial General Intelligence and Cognitive Accounts of General Knowledge

Psychology has benefited from an enormous wealth of knowledge about processes of cognition in relation to how the brain organizes information. Within the categorization literature, this behavior is often explained through theories of memory construction called exemplar theory and prototype theory which are typically based on similarity or rule functions as explanations of how categories emerge. Although these theories work well at modeling highly controlled stimuli in laboratory settings, they often perform less well outside of these settings, such as explaining the emergence of background knowledge processes. In order to explain background knowledge, we present a non-similarity-based post-Skinnerian theory of human language called Relational Frame Theory (RFT) which is rooted in a philosophical world view called functional contextualism (FC). This theory offers a very different interpretation of how categories emerge through the functions of behavior and through contextual cues, which may be of some benefit to existing categorization theories. Specifically, RFT may be able to offer a novel explanation of how background knowledge arises, and we provide some mathematical considerations in order to identify a formal model. Finally, we discuss much of this work within the broader context of general semantic knowledge and artificial intelligence research.

Brain-wide visual habituation networks in wild type and fmr1 zebrafish

Habituation is a form of learning during which animals stop responding to repetitive stimuli, and deficits in habituation are characteristic of several psychiatric disorders. Due to technical challenges, the brain-wide networks mediating habituation are poorly understood. Here we report brain-wide calcium imaging during larval zebrafish habituation to repeated visual looming stimuli. We show that different functional categories of loom-sensitive neurons are located in characteristic locations throughout the brain, and that both the functional properties of their networks and the resulting behavior can be modulated by stimulus saliency and timing. Using graph theory, we identify a visual circuit that habituates minimally, a moderately habituating midbrain population proposed to mediate the sensorimotor transformation, and downstream circuit elements responsible for higher order representations and the delivery of behavior. Zebrafish larvae carrying a mutation in the fmr1 gene have a systematic shift toward sustained premotor activity in this network, and show slower behavioral habituation.

Multi-Attribute Decision Making Method for Node Importance Metric in Complex Network

Correctly measuring the importance of nodes in a complex network is critical for studying the robustness of the network, and designing a network security policy based on these highly important nodes can effectively improve security aspects of the network, such as the security of important data nodes on the Internet or the hardening of critical traffic hubs. Currently included are degree centrality, closeness centrality, clustering coefficient, and H-index. Although these indicators can identify important nodes to some extent, they are influenced by a single evaluation perspective and have limitations, so most of the existing evaluation methods cannot fully reflect the node importance information. In this paper, we propose a multi-attribute critic network decision indicator (MCNDI) based on the CRITIC method, considering the H-index, closeness centrality, k-shell indicator, and network constraint coefficient. This method integrates the information of network attributes from multiple perspectives and provides a more comprehensive measure of node importance. An experimental analysis of the Chesapeake Bay network and the contiguous USA network shows that MCNDI has better ranking monotonicity, more stable metric results, and is highly adaptable to network topology. Additionally, deliberate attack simulations on real networks showed that the method exhibits high convergence speed in attacks on USAir97 networks and technology routes networks.

Probing the association between resting-state brain network dynamics and psychological resilience

This study aimed at replicating a previously reported negative correlation between node flexibility and psychological resilience, that is, the ability to retain mental health in the face of stress and adversity. To this end, we used multiband resting-state BOLD fMRI (TR = .675 sec) from 52 participants who had filled out three psychological questionnaires assessing resilience. Time-resolved functional connectivity was calculated by performing a sliding window approach on averaged time series parcellated according to different established atlases. Multilayer modularity detection was performed to track network reconfigurations over time, and node flexibility was calculated as the number of times a node changes community assignment. In addition, node promiscuity (the fraction of communities a node participates in) and node degree (as proxy for time-varying connectivity) were calculated to extend previous work. We found no substantial correlations between resilience and node flexibility. We observed a small number of correlations between the two other brain measures and resilience scores that were, however, very inconsistently distributed across brain measures, differences in temporal sampling, and parcellation schemes. This heterogeneity calls into question the existence of previously postulated associations between resilience and brain network flexibility and highlights how results may be influenced by specific analysis choices.

Kuramoto Model-Based Analysis Reveals Oxytocin Effects on Brain Network Dynamics

The oxytocin effects on large-scale brain networks such as Default Mode Network (DMN) and Frontoparietal Network (FPN) have been largely studied using fMRI data. However, these studies are mainly based on the statistical correlation or Bayesian causality inference, lacking interpretability at the physical and neuroscience level. Here, we propose a physics-based framework of the Kuramoto model to investigate oxytocin effects on the phase dynamic neural coupling in DMN and FPN. Testing on fMRI data of 59 participants administrated with either oxytocin or placebo, we demonstrate that oxytocin changes the topology of brain communities in DMN and FPN, leading to higher synchronization in the FPN and lower synchronization in the DMN, as well as a higher variance of the coupling strength within the DMN and more flexible coupling patterns at group level. These results together indicate that oxytocin may increase the ability to overcome the corresponding internal oscillation dispersion and support the flexibility in neural synchrony in various social contexts, providing new evidence for explaining the oxytocin modulated social behaviors. Our proposed Kuramoto model-based framework can be a potential tool in network neuroscience and offers physical and neural insights into phase dynamics of the brain.

Distributed Subnetworks of Depression Defined by Direct Intracranial Neurophysiology

Major depressive disorder is a common and disabling disorder with high rates of treatment resistance. Evidence suggests it is characterized by distributed network dysfunction that may be variable across patients, challenging the identification of quantitative biological substrates. We carried out this study to determine whether application of a novel computational approach to a large sample of high spatiotemporal resolution direct neural recordings in humans could unlock the functional organization and coordinated activity patterns of depression networks. This group level analysis of depression networks from heterogenous intracranial recordings was possible due to application of a correlational model-based method for inferring whole-brain neural activity. We then applied a network framework to discover brain dynamics across this model that could classify depression. We found a highly distributed pattern of neural activity and connectivity across cortical and subcortical structures that was present in the majority of depressed subjects. Furthermore, we found that this depression signature consisted of two subnetworks across individuals. The first was characterized by left temporal lobe hypoconnectivity and pathological beta activity. The second was characterized by a hypoactive, but hyperconnected left frontal cortex. These findings have applications toward personalization of therapy.

Investigating the spectral features of the brain meso-scale structure at rest

Recent studies provide novel insights into the meso-scale organization of the brain, highlighting the co-occurrence of different structures: classic assortative (modular), disassortative, and core-periphery. However, the spectral properties of the brain meso-scale remain mostly unexplored. To fill this knowledge gap, we investigated how the meso-scale structure is organized across the frequency domain. We analyzed the resting state activity of healthy participants with source-localized high-density electroencephalography signals. Then, we inferred the community structure using weighted stochastic block-model (WSBM) to capture the landscape of meso-scale structures across the frequency domain. We found that different meso-scale modalities co-exist and are diversely organized over the frequency spectrum. Specifically, we found a core-periphery structure dominance, but we also highlighted a selective increase of disassortativity in the low frequency bands (<8 Hz), and of assortativity in the high frequency band (30-50 Hz). We further described other features of the meso-scale organization by identifying those brain regions which, at the same time, (a) exhibited the highest degree of assortativity, disassortativity, and core-peripheriness (i.e., participation) and (b) were consistently assigned to the same community, irrespective from the granularity imposed by WSBM (i.e., granularity-invariance). In conclusion, we observed that the brain spontaneous activity shows frequency-specific meso-scale organization, which may support spatially distributed and local information processing.

A practical two-sample test for weighted random graphs

Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph populations. Several statistical tests have been devised for this purpose in the context of binary graphs. However, many of the practical networks are weighted and existing procedures cannot be directly applied to weighted graphs. In this paper, we study the weighted graph two-sample hypothesis testing problem and propose a practical test statistic. We prove that the proposed test statistic converges in distribution to the standard normal distribution under the null hypothesis and analyze its power theoretically. The simulation study shows that the proposed test has satisfactory performance and it substantially outperforms the existing counterpart in the binary graph case. A real data application is provided to illustrate the method.

Static and dynamic functional connectivity supports the configuration of brain networks associated with creative cognition

Creative cognition is recognized to involve the integration of multiple spontaneous cognitive processes and is manifested as complex networks within and between the distributed brain regions. We propose that the processing of creative cognition involves the static and dynamic re-configuration of brain networks associated with complex cognitive processes. We applied the sliding-window approach followed by a community detection algorithm and novel measures of network flexibility on the blood-oxygen level dependent (BOLD) signal of 8 major functional brain networks to reveal static and dynamic alterations in the network reconfiguration during creative cognition using functional magnetic resonance imaging (fMRI). Our results demonstrate the temporal connectivity of the dynamic large-scale creative networks between default mode network (DMN), salience network, and cerebellar network during creative cognition, and advance our understanding of the network neuroscience of creative cognition.

Detecting brain network communities: Considering the role of information flow and its different temporal scales

The identification of community structure in graphs continues to attract great interest in several fields. Network neuroscience is particularly concerned with this problem considering the key roles communities play in brain processes and functionality. Most methods used for community detection in brain graphs are based on the maximization of a parameter-dependent modularity function that often obscures the physical meaning and hierarchical organization of the partitions of network nodes. In this work, we present a new method able to detect communities at different scales in a natural, unrestricted way. First, to obtain an estimation of the information flow in the network we release random walkers to freely move over it. The activity of the walkers is separated into oscillatory modes by using empirical mode decomposition. After grouping nodes by their co-occurrence at each time scale, k-modes clustering returns the desired partitions. Our algorithm was first tested on benchmark graphs with favorable performance. Next, it was applied to real and simulated anatomical and/or functional connectomes in the macaque and human brains. We found a clear hierarchical repertoire of community structures in both the anatomical and the functional networks. The observed partitions range from the evident division in two hemispheres -in which all processes are managed globally- to specialized communities seemingly shaped by physical proximity and shared function. Additionally, the spatial scales of a network's community structure (characterized by a measure we term within-communities path length) appear inversely proportional to the oscillatory modes' average frequencies. The proportionality constant may constitute a network-specific propagation velocity for the information flow. Our results stimulate the research of hierarchical community organization in terms of temporal scales of information flow in the brain network.

Reconfigurations within resonating communities of brain regions following TMS reveal different scales of processing

An overarching goal of neuroscience research is to understand how heterogeneous neuronal ensembles cohere into networks of coordinated activity to support cognition. To investigate how local activity harmonizes with global signals, we measured electroencephalography (EEG) while single pulses of transcranial magnetic stimulation (TMS) perturbed occipital and parietal cortices. We estimate the rapid network reconfigurations in dynamic network communities within specific frequency bands of the EEG, and characterize two distinct features of network reconfiguration, flexibility and allegiance, among spatially distributed neural sources following TMS. Using distance from the stimulation site to infer local and global effects, we find that alpha activity (8–12 Hz) reflects concurrent local and global effects on network dynamics. Pairwise allegiance of brain regions to communities on average increased near the stimulation site, whereas TMS-induced changes to flexibility were generally invariant to distance and stimulation site. In contrast, communities within the beta (13–20 Hz) band demonstrated a high level of spatial specificity, particularly within a cluster comprising paracentral areas. Together, these results suggest that focal magnetic neurostimulation to distinct cortical sites can help identify both local and global effects on brain network dynamics, and highlight fundamental differences in the manifestation of network reconfigurations within alpha and beta frequency bands.

TMS may be used to probe the causal link between local regional activity and global brain dynamics. Using simultaneous TMS-EEG and dynamic community detection, we introduce what we call “resonating communities” or frequency band-specific clusters in the brain, as a way to index local and global processing. These resonating communities within the alpha and beta bands display both global (or integrating) behavior and local specificity, highlighting fundamental differences in the manifestation of network reconfigurations.

Network topology of symbolic and nonsymbolic number comparison

Studies of brain activity during number processing suggest symbolic and nonsymbolic numerical stimuli (e.g., Arabic digits and dot arrays) engage both shared and distinct neural mechanisms. However, the extent to which number format influences large-scale functional network organization is unknown. In this study, using 7 Tesla MRI, we adopted a network neuroscience approach to characterize the whole-brain functional architecture supporting symbolic and nonsymbolic number comparison in 33 adults. Results showed the degree of global modularity was similar for both formats. The symbolic format, however, elicited stronger community membership among auditory regions, whereas for nonsymbolic, stronger membership was observed within and between cingulo-opercular/salience network and basal ganglia communities. The right posterior inferior temporal gyrus, left intraparietal sulcus, and two regions in the right ventromedial occipital cortex demonstrated robust differences between formats in terms of their community membership, supporting prior findings that these areas are differentially engaged based on number format. Furthermore, a unified fronto-parietal/dorsal attention community in the nonsymbolic condition was fractionated into two components in the symbolic condition. Taken together, these results reveal a pattern of overlapping and distinct network architectures for symbolic and nonsymbolic number processing.

Finding Community of Brain Networks Based on Neighbor Index and DPSO with Dynamic Crossover

Background: :

The brain networks can provide us an effective way to analyze brain function and brain disease detection. In brain networks, there exist some import neural unit modules, which contain meaningful biological insights.

Objective::

Therefore, we need to find the optimal neural unit modules effectively and efficiently.

Method::

In this study, we propose a novel algorithm to find community modules of brain networks by combining Neighbor Index and Discrete Particle Swarm Optimization (DPSO) with dynamic crossover, abbreviated as NIDPSO. The differences between this study and the existing ones lie in that NIDPSO is proposed first to find community modules of brain networks, and dose not need to predefine and preestimate the number of communities in advance.

Results: :

We generate a neighbor index table to alleviate and eliminate ineffective searches and design a novel coding by which we can determine the community without computing the distances amongst vertices in brain networks. Furthermore, dynamic crossover and mutation operators are designed to modify NIDPSO so as to alleviate the drawback of premature convergence in DPSO.

Conclusion:

The numerical results performing on several resting-state functional MRI brain networks demonstrate that NIDPSO outperforms or is comparable with other competing methods in terms of modularity, coverage and conductance metrics.

Neural computing in four spatial dimensions

Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to neural networks computations performed in higher dimensions. We illustrate the operational procedure to build a real or artificial neural network able to detect, assess and quantify a fourth spatial dimension. We show how, starting from two-dimensional shapes embedded in a 2D topological charge pump, it is feasible to achieve the corresponding four-dimensional shapes, which encompass a larger amount of information. Synthesis of surface shape components, viewed topologically as shape descriptions in the form of feature vectors that vary over time, leads to a 4D view of cerebral activity. This novel, relatively straightforward architecture permits to increase the amount of available qbits in a fixed volume.

Characterization of network switching in disorder of consciousness at multiple time scales

OBJECTIVE

Recent works have shown that flexible information processing is closely related to the reconfiguration of human brain networks underlying brain functions. However, the role of network switching for consciousness is poorly explored and whether such transition can indicate the behavioral performance of patients with disorders of consciousness (DOC) remains unknown. Here, we investigate the relationship between the switching of brain networks (states) over time and the consciousness levels.

APPROACH

By applying multilayer network methods, we calculated time-resolved functional connectivity from source-level EEG data in different frequency bands. At various time scales, we explored how the human brain changes its community structure and traverses across defined network states (integrated and segregated states) in subjects with different consciousness levels.

MAIN RESULTS

Network switching in the human brain is decreased with increasing time scale opposite to that in random systems. Transitions of community assignment (denoted by flexibility) are negatively correlated with the consciousness levels (particularly in the alpha band) at short time scales. At long time scales, the opposite trend is found. Compared to healthy controls, patients show a new balance between dynamic segregation and integration, with decreased proportion and mean duration of segregated state (contrary to those of integrated state) at small scales.

SIGNIFICANCE

These findings may contribute to the development of EEG-based network analysis and shed new light on the pathological mechanisms of neurological disorders like DOC.

Finding Community Modules of Brain Networks Based on PSO with Uniform Design

The brain has the most complex structures and functions in living organisms, and brain networks can provide us an effective way for brain function analysis and brain disease detection. In brain networks, there exist some important neural unit modules, which contain many meaningful biological insights. It is appealing to find the neural unit modules and obtain their affiliations. In this study, we present a novel method by integrating the uniform design into the particle swarm optimization to find community modules of brain networks, abbreviated as UPSO. The difference between UPSO and the existing ones lies in that UPSO is presented first for detecting community modules. Several brain networks generated from functional MRI for studying autism are used to verify the proposed algorithm. Experimental results obtained on these brain networks demonstrate that UPSO can find community modules efficiently and outperforms the other competing methods in terms of modularity and conductance. Additionally, the comparison of UPSO and PSO also shows that the uniform design plays an important role in improving the performance of UPSO.

Spectral partitioning identifies individual heterogeneity in the functional network topography of ventral and anterior medial prefrontal cortex

Regions of human medial prefrontal cortex (mPFC) and posterior cingulate cortex (PCC) are part of the default network (DN), and additionally are implicated in diverse cognitive functions ranging from autobiographical memory to subjective valuation. Our ability to interpret the apparent co-localization of task-related effects with DN-regions is constrained by a limited understanding of the individual-level heterogeneity in mPFC/PCC functional organization. Here we used cortical surface-based meta-analysis to identify a parcel in human PCC that was more strongly associated with the DN than with valuation effects. We then used resting-state fMRI data and a data-driven network analysis algorithm, spectral partitioning, to partition mPFC and PCC into "DN" and "non-DN" subdivisions in individual participants (n = 100 from the Human Connectome Project). The spectral partitioning algorithm identified individual-level cortical subdivisions that varied markedly across individuals, especially in mPFC, and were reliable across test/retest datasets. Our results point toward new strategies for assessing whether distinct cognitive functions engage common or distinct mPFC subregions at the individual level.

Multiscale Functional Clustering Reveals Frequency Dependent Brain Organization in Type II Focal Cortical Dysplasia With Sleep Hypermotor Epilepsy

OBJECTIVE

A multiscale functional clustering approach is proposed to investigate the organization of the epileptic networks during different sleep stages and in relation with the occurrence of seizures.

METHOD

Stereo-electroencephalographic signals from seven pharmaco-resistant epileptic patients (focal cortical dysplasia type II) were analyzed. The discrete wavelet transform provided a multiscale framework on which a data-driven functional clustering procedure was applied, based on multivariate measures of integration and mutual information. The most interacting functional clusters (FCs) within the sampled brain areas were extracted.

RESULTS

FCs characterized by strongly integrated activity were observed mostly in the beta and alpha frequency bands, immediately before seizure onset and in deep sleep stages. These FCs generally included the electrodes from the epileptogenic zone. Furthermore, repeatable patterns were found across ictal events in the same patient.

CONCLUSION

In line with previous studies, our findings provide evidence of the important role of beta and alpha activity in seizures generation and support the relation between epileptic activity and sleep stages.

SIGNIFICANCE

Despite the small number of subjects included in the study, the present results suggest that the proposed multiscale functional clustering approach is a useful tool for the identification of the frequency-dependent mechanisms underlying seizure generation.

Heuristics for Spreading Alarm throughout a Network

This paper provides heuristic methods for obtaining a burning number, which is a graph parameter measuring the speed of the spread of alarm, information, or contagion. For discrete time steps, the heuristics determine which nodes (centers, hubs, vertices, users) should be alarmed (in other words, burned) and in which order, when afterwards each alarmed node alarms its neighbors in the network at the next time step. The goal is to minimize the number of discrete time steps (i.e., time) it takes for the alarm to reach the entire network, so that all the nodes in the networks are alarmed. The burning number is the minimum number of time steps (i.e., number of centers in a time sequence alarmed “from outside”) the process must take. Since the problem is NP complete, its solution for larger networks or graphs has to use heuristics. The heuristics proposed here were tested on a wide range of networks. The complexity of the heuristics ranges in correspondence to the quality of their solution, but all the proposed methods provided a significantly better solution than the competing heuristic.

Relational flexibility of network elements based on inconsistent community detection

Community identification of network components enables us to understand the mesoscale clustering structure of networks. A number of algorithms have been developed to determine the most likely community structures in networks. Such a probabilistic or stochastic nature of this problem can naturally involve the ambiguity in resultant community structures. More specifically, stochastic algorithms can result in different community structures for each realization in principle. In this study, instead of trying to "solve" this community degeneracy problem, we turn the tables by taking the degeneracy as a chance to quantify how strong companionship each node has with other nodes. For that purpose, we define the concept of companionship inconsistency that indicates how inconsistently a node is identified as a member of a community regarding the other nodes. Analyzing model and real networks, we show that companionship inconsistency discloses unique characteristics of nodes, thus we suggest it as a new type of node centrality. In social networks, for example, companionship inconsistency can classify outsider nodes without firm community membership and promiscuous nodes with multiple connections to several communities. In infrastructure networks such as power grids, it can diagnose how the connection structure is evenly balanced in terms of power transmission. Companionship inconsistency, therefore, abstracts individual nodes' intrinsic property on its relationship to a higher-order organization of the network.

Atypical Flexibility in Dynamic Functional Connectivity Quantifies the Severity in Autism Spectrum Disorder

Resting-state functional connectivity (FC) analyses have shown atypical connectivity in autism spectrum disorder (ASD) as compared to typically developing (TD). However, this view emerges from investigating static FC overlooking the whole brain transient connectivity patterns. In our study, we investigated how age and disease influence the dynamic changes in functional connectivity of TD and ASD. We used resting-state functional magnetic resonance imaging (rs-fMRI) data stratified into three cohorts: children (7-11 years), adolescents (12-17 years), and adults (18+ years) for the analysis. The dynamic variability in the connection strength and the modular organization in terms of measures such as flexiblity, cohesion strength, and disjointness were explored for each subject to characterize the differences between ASD and TD. In ASD, we observed significantly higher inter-subject dynamic variability in connection strength as compared to TD. This hyper-variability relates to the symptom severity in ASD. We also found that whole-brain flexibility correlates with static modularity only in TD. Further, we observed a core-periphery organization in the resting-state, with Sensorimotor and Visual regions in the rigid core; and DMN and attention areas in the flexible periphery. TD also develops a more cohesive organization of sensorimotor areas. However, in ASD we found a strong positive correlation of symptom severity with flexibility of rigid areas and with disjointness of sensorimotor areas. The regions of the brain showing high predictive power of symptom severity were distributed across the cortex, with stronger bearings in the frontal, motor, and occipital cortices. Our study demonstrates that the dynamic framework best characterizes the variability in ASD.

The multidimensional brain

Brain activity takes place in three spatial-plus time dimensions. This rather obvious claim has been recently questioned by papers that, taking into account the big data outburst and novel available computational tools, are starting to unveil a more intricate state of affairs. Indeed, various brain activities and their correlated mental functions can be assessed in terms of trajectories embedded in phase spaces of dimensions higher than the canonical ones. In this review, I show how further dimensions may not just represent a convenient methodological tool that allows a better mathematical treatment of otherwise elusive cortical activities, but may also reflect genuine functional or anatomical relationships among real nervous functions. I then describe how to extract hidden multidimensional information from real or artificial neurodata series, and make clear how our mind dilutes, rather than concentrates as currently believed, inputs coming from the environment. Finally, I argue that the principle "the higher the dimension, the greater the information" may explain the occurrence of mental activities and elucidate the mechanisms of human diseases associated with dimensionality reduction.

Memory systems 2018 - Towards a new paradigm

The multiple memory systems theory (MMS) postulates that the brain stores information based on the independent and parallel activity of a number of modules, each with distinct properties, dynamics, and neural basis. Much of the evidence for this theory comes from dissociation studies indicating that damage to restricted brain areas cause selective types of memory deficits. MMS has been the prevalent paradigm in memory research for more than thirty years, even as it has been adjusted several times to accommodate new data. However, recent empirical results indicating that the memory systems are not always dissociable constitute a challenge to fundamental tenets of the current theory because they suggest that representations formed by individual memory systems can contribute to more than one type of memory-driven behavioral strategy. This problem can be addressed by applying a dynamic network perspective to memory architecture. According to this view, memory networks can reconfigure or transiently couple in response to environmental demands. Within this context, the neural network underlying a specific memory system can act as an independent unit or as an integrated component of a higher order meta-network. This dynamic network model proposes a way in which empirical evidence that challenges the idea of distinct memory systems can be incorporated within a modular memory architecture. The model also provides a framework to account for the complex interactions among memory systems demonstrated at the behavioral level. Advances in the study of dynamic networks can generate new ideas to experimentally manipulate and control memory in basic or clinical research.

Spatial Embedding Imposes Constraints on Neuronal Network Architectures

Recent progress towards understanding circuit function has capitalized on tools from network science to parsimoniously describe the spatiotemporal architecture of neural systems. Such tools often address systems topology divorced from its physical instantiation. Nevertheless, for embedded systems such as the brain, physical laws directly constrain the processes of network growth, development, and function. We review here the rules imposed by the space and volume of the brain on the development of neuronal networks, and show that these rules give rise to a specific set of complex topologies. These rules also affect the repertoire of neural dynamics that can emerge from the system, and thereby inform our understanding of network dysfunction in disease. We close by discussing new tools and models to delineate the effects of spatial embedding.

Network Approaches to Understand Individual Differences in Brain Connectivity: Opportunities for Personality Neuroscience

Over the past decade, advances in the interdisciplinary field of network science have provided a framework for understanding the intrinsic structure and function of human brain networks. A particularly fruitful area of this work has focused on patterns of functional connectivity derived from noninvasive neuroimaging techniques such as functional magnetic resonance imaging. An important subset of these efforts has bridged the computational approaches of network science with the rich empirical data and biological hypotheses of neuroscience, and this research has begun to identify features of brain networks that explain individual differences in social, emotional, and cognitive functioning. The most common approach estimates connections assuming a single configuration of edges that is stable across the experimental session. In the literature, this is referred to as a static network approach, and researchers measure static brain networks while a subject is either at rest or performing a cognitively demanding task. Research on social and emotional functioning has primarily focused on linking static brain networks with individual differences, but recent advances have extended this work to examine temporal fluctuations in dynamic brain networks. Mounting evidence suggests that both the strength and flexibility of time-evolving brain networks influence individual differences in executive function, attention, working memory, and learning. In this review, we first examine the current evidence for brain networks involved in cognitive functioning. Then we review some preliminary evidence linking static network properties to individual differences in social and emotional functioning. We then discuss the applicability of emerging dynamic network methods for examining individual differences in social and emotional functioning. We close with an outline of important frontiers at the intersection between network science and neuroscience that will enhance our understanding of the neurobiological underpinnings of social behavior.