Dynamic small-world behavior in functional brain networks unveiled by an event-related networks approach

Inverse stochastic resonance in adaptive small-world neural networks

Inverse stochastic resonance (ISR) is a counterintuitive phenomenon where noise reduces the oscillation frequency of an oscillator to a minimum occurring at an intermediate noise intensity, and sometimes even to the complete absence of oscillations. In neuroscience, ISR was first experimentally verified with cerebellar Purkinje neurons [Buchin et al., PLOS Comput. Biol. 12, e1005000 (2016)]. These experiments showed that ISR enables a locally optimal information transfer between the input and output spike train of neurons. Subsequent studies have further demonstrated the efficiency of information processing and transfer in neural networks with small-world network topology. We have conducted a numerical investigation into the impact of adaptivity on ISR in a small-world network of noisy FitzHugh-Nagumo (FHN) neurons, operating in a bi-metastable regime consisting of a metastable fixed point and a metastable limit cycle. Our results show that the degree of ISR is highly dependent on the value of the FHN model's timescale separation parameter ε. The network structure undergoes dynamic adaptation via mechanisms of either spike-time-dependent plasticity (STDP) with potentiation-/depression-domination parameter P or homeostatic structural plasticity (HSP) with rewiring frequency F. We demonstrate that both STDP and HSP amplify the effect of ISR when ε lies within the bi-stability region of FHN neurons. Specifically, at larger values of ε within the bi-stability regime, higher rewiring frequencies F are observed to enhance ISR at intermediate (weak) synaptic noise intensities, while values of P consistent with depression-domination (potentiation-domination) consistently enhance (deteriorate) ISR. Moreover, although STDP and HSP control parameters may jointly enhance ISR, P has a greater impact on improving ISR compared to F. Our findings inform future ISR enhancement strategies in noisy artificial neural circuits, aiming to optimize local information transfer between input and output spike trains in neuromorphic systems and prompt venues for experiments in neural networks.

Synchronization in STDP-driven memristive neural networks with time-varying topology

Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons driven by spike-timing-dependent plasticity (STDP) and temporal networks subject to homeostatic structural plasticity (HSP) rules remain unclear. Here, we bridge this gap by determining the configurations required to achieve high and stable degrees of complete synchronization (CS) and phase synchronization (PS) in time-varying small-world and random neural networks driven by STDP and HSP. In particular, we found that decreasing P (which enhances the strengthening effect of STDP on the average synaptic weight) and increasing F (which speeds up the swapping rate of synapses between neurons) always lead to higher and more stable degrees of CS and PS in small-world and random networks, provided that the network parameters such as the synaptic time delay [Formula: see text], the average degree [Formula: see text], and the rewiring probability [Formula: see text] have some appropriate values. When [Formula: see text], [Formula: see text], and [Formula: see text] are not fixed at these appropriate values, the degree and stability of CS and PS may increase or decrease when F increases, depending on the network topology. It is also found that the time delay [Formula: see text] can induce intermittent CS and PS whose occurrence is independent F. Our results could have applications in designing neuromorphic circuits for optimal information processing and transmission via synchronization phenomena.

Statistical models of complex brain networks: a maximum entropy approach

The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying network structure is crucial to understand the brain functioning under both healthy and pathological conditions. Yet, analyzing brain networks is challenging, in part because their structure represents only one possible realization of a generative stochastic process which is in general unknown. Having a formal way to cope with such intrinsic variability is therefore central for the characterization of brain network properties. Addressing this issue entails the development of appropriate tools mostly adapted from network science and statistics. Here, we focus on a particular class of maximum entropy models for networks, i.e. exponential random graph models, as a parsimonious approach to identify the local connection mechanisms behind observed global network structure. Efforts are reviewed on the quest for basic organizational properties of human brain networks, as well as on the identification of predictive biomarkers of neurological diseases such as stroke. We conclude with a discussion on how emerging results and tools from statistical graph modeling, associated with forthcoming improvements in experimental data acquisition, could lead to a finer probabilistic description of complex systems in network neuroscience.

Topologically convergent and divergent large scale complex networks among Alzheimer's disease spectrum patients: A systematic review

Alzheimer's disease (AD) is associated with disruption at the level of a large-scale complex network. To explore the underlying mechanisms in the progression of AD, graph theory was used to quantitatively analyze the topological properties of structural and functional connections. Although an increasing number of studies have shown altered global and nodal network properties, little is known about the topologically convergent and divergent patterns between structural and functional networks among AD-spectrum patients. In this review, we summarized the topological patterns of the large-scale complex networks using multimodal neuroimaging graph theory analysis in AD spectrum patients. Convergent deficits in the connectivity characteristics were primarily in the default mode network (DMN) itself both in the structural and functional networks, while a divergent changes in the neighboring regions of the DMN were also observed between the patient groups. Together, the application of graph theory to large-scale complex brain networks provides quantitative insights into topological principles of brain network organization, which may lead to increasing attention in identifying the underlying neuroimaging pathological changes and predicting the progression of AD.

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

Non-Markovian temporal networks with auto- and cross-correlated link dynamics

Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often observed to be non-Markovian, and the dynamics of their links are often correlated. Hence, to accurately model these networks, predict their evolution, and understand how information and other relevant quantities propagate over them, the inclusion of both memory and dynamical dependencies between links is key. In this article we introduce a general class of models of temporal networks based on discrete autoregressive processes for link dynamics. As a concrete and useful case study, we then concentrate on a specific model within this class, which allows to generate temporal networks with a specified underlying structural backbone, and with precise control over the dynamical dependencies between links and the strength and length of their memories. In this network model the presence of each link is influenced not only by its past activity, but also by the past activities of other links, as specified by a coupling matrix, which directly controls the causal relations, and hence the correlations, among links. We propose a maximum likelihood method for estimating the model's parameters from data, showing how the model allows a more realistic description of real-world temporal networks and also to predict their evolution. Due to the flexibility of maximum likelihood inference, we illustrate how to deal with heterogeneity and time-varying patterns, possibly including also nonstationary network dynamics. We then use our network model to investigate the role that, both the features of memory and the type of correlations in the dynamics of links have on the properties of processes occurring over a temporal network. Namely, we study the speed of a spreading process, as measured by the time it takes for diffusion to reach equilibrium. Through both numerical simulations and analytical results, we are able to separate the roles of autocorrelations and neighborhood correlations in link dynamics, showing that not only is the speed of diffusion nonmonotonically dependent on the memory length, but also that correlations among neighboring links help to speed up the spreading process, while autocorrelations slow it back down. Our results have implications in the study of opinion formation, the modeling of social networks, and the spreading of epidemics through mobile populations.

The shape of memory in temporal networks

How to best define, detect and characterize network memory, i.e. the dependence of a network’s structure on its past, is currently a matter of debate. Here we show that the memory of a temporal network is inherently multidimensional, and we introduce a mathematical framework for defining and efficiently estimating the microscopic shape of memory, which characterises how the activity of each link intertwines with the activities of all other links. We validate our methodology on a range of synthetic models, and we then study the memory shape of real-world temporal networks spanning social, technological and biological systems, finding that these networks display heterogeneous memory shapes. In particular, online and offline social networks are markedly different, with the latter showing richer memory and memory scales. Our theory also elucidates the phenomenon of emergent virtual loops and provides a novel methodology for exploring the dynamically rich structure of complex systems.

The evolution of networks with structure changing in time is dependent on their past states and relevant to diffusion and spreading processes. The authors show that temporal network’s memory is described by multidimensional patterns at a microscopic scale, and cannot be reduced to a scalar quantity.

Neuronal synchronization in long-range time-varying networks

We study synchronization in neuronal ensembles subject to long-range electrical gap junctions which are time-varying. As a representative example, we consider Hindmarsh-Rose neurons interacting based upon temporal long-range connections through electrical couplings. In particular, we adopt the connections associated with the direct 1-path network to form a small-world network and follow-up with the corresponding long-range network. Further, the underlying direct small-world network is allowed to temporally change; hence, all long-range connections are also temporal, which makes the model much more realistic from the neurological perspective. This time-varying long-range network is formed by rewiring each link of the underlying 1-path network stochastically with a characteristic rewiring probability p_r, and accordingly all indirect k(>1)-path networks become temporal. The critical interaction strength to reach complete neuronal synchrony is much lower when we take up rapidly switching long-range interactions. We employ the master stability function formalism in order to characterize the local stability of the state of synchronization. The analytically derived stability condition for the complete synchrony state agrees well with the numerical results. Our work strengthens the understanding of time-varying long-range interactions in neuronal ensembles.

Event-related network changes unfold the dynamics of cortical integration during face processing

Face perception arises from a collective activation of brain regions in the occipital, parietal and temporal cortices. Despite the wide acknowledgment that these regions act in an intertwined network, the network behavior itself is poorly understood. Here we present a study in which time-varying connectivity estimated from EEG activity elicited by facial expressions presentation was characterized using graph-theoretical measures of node centrality and global network topology. Results revealed that face perception results from a dynamic reshaping of the network architecture, characterized by the emergence of hubs located in the occipital and temporal regions of the scalp. The importance of these nodes can be observed from the early stages of visual processing and reaches a climax in the same time-window in which the face-sensitive N170 is observed. Furthermore, using Granger causality, we found that the time-evolving centrality of these nodes is associated with ERP amplitude, providing a direct link between the network state and local neural response. Additionally, investigating global network topology by means of small-worldness and modularity, we found that face processing requires a functional network with a strong small-world organization that maximizes integration, at the cost of segregated subdivisions. Interestingly, we found that this architecture is not static, but instead, it is implemented by the network from stimulus onset to ~200 ms. Altogether, this study reveals the event-related changes underlying face processing at the network level, suggesting that a distributed processing mechanism operates through dynamically weighting the contribution of the cortical regions involved.

Network-based brain computer interfaces: principles and applications

Brain-computer interfaces (BCIs) make possible to interact with the external environment by decoding the mental intention of individuals. BCIs can therefore be used to address basic neuroscience questions but also to unlock a variety of applications from exoskeleton control to neurofeedback (NFB) rehabilitation. In general, BCI usability critically depends on the ability to comprehensively characterize brain functioning and correctly identify the user's mental state. To this end, much of the efforts have focused on improving the classification algorithms taking into account localized brain activities as input features. Despite considerable improvement BCI performance is still unstable and, as a matter of fact, current features represent oversimplified descriptors of brain functioning. In the last decade, growing evidence has shown that the brain works as a networked system composed of multiple specialized and spatially distributed areas that dynamically integrate information. While more complex, looking at how remote brain regions functionally interact represents a grounded alternative to better describe brain functioning. Thanks to recent advances in network science, i.e. a modern field that draws on graph theory, statistical mechanics, data mining and inferential modelling, scientists have now powerful means to characterize complex brain networks derived from neuroimaging data. Notably, summary features can be extracted from these networks to quantitatively measure specific organizational properties across a variety of topological scales. In this topical review, we aim to provide the state-of-the-art supporting the development of a network theoretic approach as a promising tool for understanding BCIs and improve usability.

Chimera-like states induced by additional dynamic nonlocal wirings

We investigate the existence of chimera-like states in a small-world network of chaotically oscillating identical Rössler systems with an addition of randomly switching nonlocal links. By varying the small-world coupling strength, we observe no chimera-like state either in the absence of nonlocal wirings or with static nonlocal wirings. When we give an additional nonlocal wiring to randomly selected nodes and if we allow the random selection of nodes to change with time, we observe the onset of chimera-like states. Upon increasing the number of randomly selected nodes gradually, we find that the incoherent window keeps on shrinking, whereas the chimera-like window widens up. Moreover, the system attains a completely synchronized state comparatively sooner for a lower coupling strength. Also, we show that one can induce chimera-like states by a suitable choice of switching times, coupling strengths, and a number of nonlocal links. We extend the above-mentioned randomized injection of nonlocal wirings for the cases of globally coupled Rössler oscillators and a small-world network of coupled FitzHugh-Nagumo oscillators and obtain similar results.

Predictability of real temporal networks

Links in most real networks often change over time. Such temporality of links encodes the ordering and causality of interactions between nodes and has a profound effect on network dynamics and function. Empirical evidence has shown that the temporal nature of links in many real-world networks is not random. Nonetheless, it is challenging to predict temporal link patterns while considering the entanglement between topological and temporal link patterns. Here, we propose an entropy-rate-based framework, based on combined topological–temporal regularities, for quantifying the predictability of any temporal network. We apply our framework on various model networks, demonstrating that it indeed captures the intrinsic topological–temporal regularities whereas previous methods considered only temporal aspects. We also apply our framework on 18 real networks of different types and determine their predictability. Interestingly, we find that, for most real temporal networks, despite the greater complexity of predictability brought by the increase in dimension, the combined topological–temporal predictability is higher than the temporal predictability. Our results demonstrate the necessity for incorporating both temporal and topological aspects of networks in order to improve predictions of dynamical processes.

Static and dynamic attractive-repulsive interactions in two coupled nonlinear oscillators

Many systems exhibit both attractive and repulsive types of interactions, which may be dynamic or static. A detailed understanding of the dynamical properties of a system under the influence of dynamically switching attractive or repulsive interactions is of practical significance. However, it can also be effectively modeled with two coexisting competing interactions. In this work, we investigate the effect of time-varying attractive-repulsive interactions as well as the hybrid model of coexisting attractive-repulsive interactions in two coupled nonlinear oscillators. The dynamics of two coupled nonlinear oscillators, specifically limit cycles as well as chaotic oscillators, are studied in detail for various dynamical transitions for both cases. Here, we show that dynamic or static attractive-repulsive interactions can induce an important transition from the oscillatory to steady state in identical nonlinear oscillators due to competitive effects. The analytical condition for the stable steady state in dynamic interactions at the low switching time period and static coexisting interactions are calculated using linear stability analysis, which is found to be in good agreement with the numerical results. In the case of a high switching time period, oscillations are revived for higher interaction strength.

Invariance and stability conditions of interlayer synchronization manifold

We investigate interlayer synchronization in a stochastic multiplex hypernetwork which is defined by the two types of connections, one is the intralayer connection in each layer with hypernetwork structure and the other is the interlayer connection between the layers. Here all types of interactions within and between the layers are allowed to vary with a certain rewiring probability. We address the question about the invariance and stability of the interlayer synchronization state in this stochastic multiplex hypernetwork. For the invariance of interlayer synchronization manifold, the adjacency matrices corresponding to each tier in each layer should be equal and the interlayer connection should be either bidirectional or the interlayer coupling function should vanish after achieving the interlayer synchronization state. We analytically derive a necessary-sufficient condition for local stability of the interlayer synchronization state using master stability function approach and a sufficient condition for global stability by constructing a suitable Lyapunov function. Moreover, we analytically derive that intralayer synchronization is unattainable for this network architecture due to stochastic interlayer connections. Remarkably, our derived invariance and stability conditions (both local and global) are valid for any rewiring probabilities, whereas most of the previous stability conditions are only based on a fast switching approximation.

Electrophysiological Correlates of Response Time Variability During a Sustained Attention Task

Individuals with Attention Deficit Hyperactivity Disorder (ADHD) tend to perform cognitive tasks with greater Response Time Variability (RTV). Greater RTV in ADHD may be due to inefficient functional connectivity of the brain during information processing. This study aimed to investigate the relationship between brain connectivity, RTV, and levels of ADHD symptoms. Twenty-eight children aged 9–12 years and 49 adolescents aged 15–18 years performed the Sustained Attention to Response Task (SART) while EEG was recorded. The participants’ levels of ADHD symptoms were measured using self- and parent-rated questionnaires. The ex-Gaussian analysis and The Fast Fourier Transform were used to measure multiple aspects of RTV. Functional connectivity between 64 electrodes was computed during task performance, and global efficiency and modularity were calculated, reflecting integration and segregation of the brain, respectively. There was a positive association between multiple RTV measures and the level of ADHD symptoms, where participants with higher levels of ADHD symptoms showed greater RTV, except for sigma from the ex-Gaussian analysis. More efficient brain network activity, measured by global efficiency, was associated with reduced RTV. Children showed greater RTV and less efficient brain network activity compared with the adolescents. These findings support the view that stable responses are achieved with more integrated (and efficient) brain connectivity.

Emergence of synchronization in multiplex networks of mobile Rössler oscillators

Different aspects of synchronization emerging in networks of coupled oscillators have been examined prominently in the last decades. Nevertheless, little attention has been paid on the emergence of this imperative collective phenomenon in networks displaying temporal changes in the connectivity patterns. However, there are numerous practical examples where interactions are present only at certain points of time owing to physical proximity. In this work, we concentrate on exploring the emergence of interlayer and intralayer synchronization states in a multiplex dynamical network comprising of layers having mobile nodes performing two-dimensional lattice random walk. We thoroughly illustrate the impacts of the network parameters, in particular, the vision range ϕ and the step size u together with the inter- and intralayer coupling strengths ε and k on these synchronous states arising in coupled Rössler systems. The presented numerical results are very well validated by analytically derived necessary conditions for the emergence and stability of the synchronous states. Furthermore, the robustness of the states of synchrony is studied under both structural and dynamical perturbations. We find interesting results on interlayer synchronization for a continuous removal of the interlayer links as well as for progressively created static nodes. We demonstrate that the mobility parameters responsible for intralayer movement of the nodes can retrieve interlayer synchrony under such structural perturbations. For further analysis of survivability of interlayer synchrony against dynamical perturbations, we proceed through the investigation of single-node basin stability, where again the intralayer mobility properties have noticeable impacts. We also discuss the scenarios related mainly to effects of the mobility parameters in cases of varying lattice size and percolation of the whole network.

Network neuroscience for optimizing brain-computer interfaces

Human-machine interactions are being increasingly explored to create alternative ways of communication and to improve our daily life. Based on a classification of the user's intention from the user's underlying neural activity, brain-computer interfaces (BCIs) allow direct interactions with the external environment while bypassing the traditional effector of the musculoskeletal system. Despite the enormous potential of BCIs, there are still a number of challenges that limit their societal impact, ranging from the correct decoding of a human's thoughts, to the application of effective learning strategies. Despite several important engineering advances, the basic neuroscience behind these challenges remains poorly explored. Indeed, BCIs involve complex dynamic changes related to neural plasticity at a diverse range of spatiotemporal scales. One promising antidote to this complexity lies in network science, which provides a natural language in which to model the organizational principles of brain architecture and function as manifest in its interconnectivity. Here, we briefly review the main limitations currently affecting BCIs, and we offer our perspective on how they can be addressed by means of network theoretic approaches. We posit that the emerging field of network neuroscience will prove to be an effective tool to unlock human-machine interactions.

Markov Model-Based Method to Analyse Time-Varying Networks in EEG Task-Related Data

The dynamic nature of functional brain networks is being increasingly recognized in cognitive neuroscience, and methods to analyse such time-varying networks in EEG/MEG data are required. In this work, we propose a pipeline to characterize time-varying networks in single-subject EEG task-related data and further, evaluate its validity on both simulated and experimental datasets. Pre-processing is done to remove channel-wise and trial-wise differences in activity. Functional networks are estimated from short non-overlapping time windows within each “trial,” using a sparse-MVAR (Multi-Variate Auto-Regressive) model. Functional “states” are then identified by partitioning the entire space of functional networks into a small number of groups/symbols via k-means clustering.The multi-trial sequence of symbols is then described by a Markov Model (MM). We show validity of this pipeline on realistic electrode-level simulated EEG data, by demonstrating its ability to discriminate “trials” from two experimental conditions in a range of scenarios. We then apply it to experimental data from two individuals using a Brain-Computer Interface (BCI) via a P300 oddball task. Using just the Markov Model parameters, we obtain statistically significant discrimination between target and non-target trials. The functional networks characterizing each ‘state’ were also highly similar between the two individuals. This work marks the first application of the Markov Model framework to infer time-varying networks from EEG/MEG data. Due to the pre-processing, results from the pipeline are orthogonal to those from conventional ERP averaging or a typical EEG microstate analysis. The results provide powerful proof-of-concept for a Markov model-based approach to analyzing the data, paving the way for its use to track rapid changes in interaction patterns as a task is being performed. MATLAB code for the entire pipeline has been made available.

Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks

We study synchronization of dynamical systems coupled in time-varying network architectures, composed of two or more network topologies, corresponding to different interaction schemes. As a representative example of this class of time-varying hypernetworks, we consider coupled Hindmarsh-Rose neurons, involving two distinct types of networks, mimicking interactions that occur through the electrical gap junctions and the chemical synapses. Specifically, we consider the connections corresponding to the electrical gap junctions to form a small-world network, while the chemical synaptic interactions form a unidirectional random network. Further, all the connections in the hypernetwork are allowed to change in time, modeling a more realistic neurobiological scenario. We model this time variation by rewiring the links stochastically with a characteristic rewiring frequency f. We find that the coupling strength necessary to achieve complete neuronal synchrony is lower when the links are switched rapidly. Further, the average time required to reach the synchronized state decreases as synaptic coupling strength and/or rewiring frequency increases. To quantify the local stability of complete synchronous state we use the Master Stability Function approach, and for global stability we employ the concept of basin stability. The analytically derived necessary condition for synchrony is in excellent agreement with numerical results. Further we investigate the resilience of the synchronous states with respect to increasing network size, and we find that synchrony can be maintained up to larger network sizes by increasing either synaptic strength or rewiring frequency. Last, we find that time-varying links not only promote complete synchronization, but also have the capacity to change the local dynamics of each single neuron. Specifically, in a window of rewiring frequency and synaptic coupling strength, we observe that the spiking behavior becomes more regular.

The dynamics of human cognition: Increasing global integration coupled with decreasing segregation found using iEEG

Cognitive processing requires the ability to flexibly integrate and process information across large brain networks. How do brain networks dynamically reorganize to allow broad communication between many different brain regions in order to integrate information? We record neural activity from 12 epileptic patients using intracranial EEG while performing three cognitive tasks. We assess how the functional connectivity between different brain areas changes to facilitate communication across them. At the topological level, this facilitation is characterized by measures of integration and segregation. Across all patients, we found significant increases in integration and decreases in segregation during cognitive processing, especially in the gamma band (50-90 Hz). We also found higher levels of global synchronization and functional connectivity during task execution, again particularly in the gamma band. More importantly, functional connectivity modulations were not caused by changes in the level of the underlying oscillations. Instead, these modulations were caused by a rearrangement of the mutual synchronization between the different nodes as proposed by the "Communication Through Coherence" Theory.

Time-varying multiplex network: Intralayer and interlayer synchronization

A large class of engineered and natural systems, ranging from transportation networks to neuronal networks, are best represented by multiplex network architectures, namely a network composed of two or more different layers where the mutual interaction in each layer may differ from other layers. Here we consider a multiplex network where the intralayer coupling interactions are switched stochastically with a characteristic frequency. We explore the intralayer and interlayer synchronization of such a time-varying multiplex network. We find that the analytically derived necessary condition for intralayer and interlayer synchronization, obtained by the master stability function approach, is in excellent agreement with our numerical results. Interestingly, we clearly find that the higher frequency of switching links in the layers enhances both intralayer and interlayer synchrony, yielding larger windows of synchronization. Further, we quantify the resilience of synchronous states against random perturbations, using a global stability measure based on the concept of basin stability, and this reveals that intralayer coupling strength is most crucial for determining both intralayer and interlayer synchrony. Lastly, we investigate the robustness of interlayer synchronization against a progressive demultiplexing of the multiplex structure, and we find that for rapid switching of intralayer links, the interlayer synchronization persists even when a large number of interlayer nodes are disconnected.

Oscillations during observations: Dynamic oscillatory networks serving visuospatial attention

The dynamic allocation of neural resources to discrete features within a visual scene enables us to react quickly and accurately to salient environmental circumstances. A network of bilateral cortical regions is known to subserve such visuospatial attention functions; however the oscillatory and functional connectivity dynamics of information coding within this network are not fully understood. Particularly, the coding of information within prototypical attention-network hubs and the subsecond functional connections formed between these hubs have not been adequately characterized. Herein, we use the precise temporal resolution of magnetoencephalography (MEG) to define spectrally specific functional nodes and connections that underlie the deployment of attention in visual space. Twenty-three healthy young adults completed a visuospatial discrimination task designed to elicit multispectral activity in visual cortex during MEG, and the resulting data were preprocessed and reconstructed in the time-frequency domain. Oscillatory responses were projected to the cortical surface using a beamformer, and time series were extracted from peak voxels to examine their temporal evolution. Dynamic functional connectivity was then computed between nodes within each frequency band of interest. We find that visual attention network nodes are defined functionally by oscillatory frequency, that the allocation of attention to the visual space dynamically modulates functional connectivity between these regions on a millisecond timescale, and that these modulations significantly correlate with performance on a spatial discrimination task. We conclude that functional hubs underlying visuospatial attention are segregated not only anatomically but also by oscillatory frequency, and importantly that these oscillatory signatures promote dynamic communication between these hubs. Hum Brain Mapp 38:5128-5140, 2017. © 2017 Wiley Periodicals, Inc.

Functional Synchronization: The Emergence of Coordinated Activity in Human Systems

The topical landscape of psychology is highly compartmentalized, with distinct phenomena explained and investigated with recourse to theories and methods that have little in common. Our aim in this article is to identify a basic set of principles that underlie otherwise diverse aspects of human experience at all levels of psychological reality, from neural processes to group dynamics. The core idea is that neural, behavioral, mental, and social structures emerge through the synchronization of lower-level elements (e.g., neurons, muscle movements, thoughts and feelings, individuals) into a functional unit—a coherent structure that functions to accomplish tasks. The coherence provided by the formation of functional units may be transient, persisting only as long as necessary to perform the task at hand. This creates the potential for the repeated assembly and disassembly of functional units in accordance with changing task demands. This perspective is rooted in principles of complexity science and non-linear dynamical systems and is supported by recent discoveries in neuroscience and recent models in cognitive and social psychology. We offer guidelines for investigating the emergence of functional units in different domains, thereby honoring the topical differentiation of psychology while providing an integrative foundation for the field.

Synchronization of moving oscillators in three dimensional space

We investigate the macroscopic behavior of a dynamical network consisting of a time-evolving wiring of interactions among a group of random walkers. We assume that each walker (agent) has an oscillator and show that depending upon the nature of interaction, synchronization arises where each of the individual oscillators are allowed to move in such a random walk manner in a finite region of three dimensional space. Here, the vision range of each oscillator decides the number of oscillators with which it interacts. The live interaction between the oscillators is of intermediate type (i.e., not local as well as not global) and may or may not be bidirectional. We analytically derive the density dependent threshold of coupling strength for synchronization using linear stability analysis and numerically verify the obtained analytical results. Additionally, we explore the concept of basin stability, a nonlinear measure based on volumes of basin of attractions, to investigate how stable the synchronous state is under large perturbations. The synchronization phenomenon is analyzed taking limit cycle and chaotic oscillators for wide ranges of parameters like interaction strength k between the walkers, speed of movement v, and vision range r.

Small-world human brain networks: Perspectives and challenges

Modelling the human brain as a complex network has provided a powerful mathematical framework to characterize the structural and functional architectures of the brain. In the past decade, the combination of non-invasive neuroimaging techniques and graph theoretical approaches enable us to map human structural and functional connectivity patterns (i.e., connectome) at the macroscopic level. One of the most influential findings is that human brain networks exhibit prominent small-world organization. Such a network architecture in the human brain facilitates efficient information segregation and integration at low wiring and energy costs, which presumably results from natural selection under the pressure of a cost-efficiency balance. Moreover, the small-world organization undergoes continuous changes during normal development and ageing and exhibits dramatic alterations in neurological and psychiatric disorders. In this review, we survey recent advances regarding the small-world architecture in human brain networks and highlight the potential implications and applications in multidisciplinary fields, including cognitive neuroscience, medicine and engineering. Finally, we highlight several challenging issues and areas for future research in this rapidly growing field.

Interaction between synchronization and motion in a system of mobile agents

In this paper, we study synchronization in time-varying networks inherited by the Vicsek's model of self-propelled particles. In our model, each particle/agent moves in a two dimensional space according to the Vicsek's rules and is associated to a chaotic system. The dynamics of two oscillators are coupled with each other only when agents are at a distance less than an interaction radius. We investigate the system behavior with respect to some fundamental parameters, and, in particular, to the noise level, which for increasing intensity drives the system from an ordered motion to a disordered one. We show that the global dynamics is ruled by the interplay between motion characteristics and dynamical coupling with synchronization either favored or inhibited by a coordinated motion of the self-propelled particles. Finally, we provide semi-analytical estimation for the synchronization thresholds for interconnections occurring at a time-scale shorter than that of the associated dynamical systems.

The relationship between ERP components and EEG spatial complexity in a visual Go/Nogo task

The ERP components and variations of spatial complexity or functional connectivity are two distinct dimensions of neurophysiological events in the visual Go/Nogo task. Extensive studies have been conducted on these two distinct dimensions; however, no study has investigated whether these two neurophysiological events are linked to each other in the visual Go/Nogo task. The relationship between spatial complexity of electroencephalographic (EEG) data, quantified by the measure omega complexity, and event-related potential (ERP) components in a visual Go/Nogo task was studied. We found that with the increase of spatial complexity level, the latencies of N1 and N2 component were shortened and the amplitudes of N1, N2, and P3 components were decreased. The anterior Go/Nogo N2 effect and the Go/Nogo P3 effect were also found to be decreased with the increase of EEG spatial complexity. In addition, the reaction times in high spatial complexity trials were significantly shorter than those of medium and low spatial complexity trials when the time interval used to estimate the EEG spatial complexity was extended to 0∼1,000 ms after stimulus onset. These results suggest that high spatial complexity may be associated with faster cognitive processing and smaller postsynaptic potentials that occur simultaneously in large numbers of cortical pyramidal cells of certain brain regions. The EEG spatial complexity is closely related with demands of certain cognitive processes and the neural processing efficiency of human brain.

NEW & NOTEWORTHY

The reaction times, the latencies/amplitudes of event-related potential (ERP) components, the Go/Nogo N2 effect, and the Go/Nogo P3 effect are linked to the electroencephalographic (EEG) spatial complexity level. The EEG spatial complexity is closely related to demands of certain cognitive processes and could reflect the neural processing efficiency of human brain. Obtaining the single-trial ERP features through single-trial spatial complexity may be a more efficient approach than traditional methods.

Topological persistence vineyard for dynamic functional brain connectivity during resting and gaming stages

BACKGROUND

Recent studies have shown the dynamic functional connectivity (FC) of the brain. Accordingly, new challenges have arisen for analyzing and interpreting this rich information.

NEW METHOD

We identified the patterns of coherent FC using a novel method in computational topology called the persistence vineyard. It has been developed to track the characteristic change of the network topology under data perturbations in a threshold-free manner.

RESULTS

We showed the relevance of this new approach by examining the dynamic FC in the resting and gaming stages of 26 healthy subjects. Our proposed method revealed stage and band-specific FC states that were topologically robust.

COMPARISON WITH EXISTING METHODS

While principal component analysis (PCA) estimated similar patterns to our FC states, it produced spurious connectivity due to its orthogonality assumption. Temporal variations of local and global network properties were examined with graph measures. However, unlike the persistence vineyard approach, their results were affected by the network density and its unknown topology.

CONCLUSIONS

Unlike the existing methods, the persistence vineyard provided a more reliable and robust way to estimate FC states. Their extracted network topology changes showed patterns consistent with those of previous studies. Therefore, it may be a potentially powerful tool for studying the dynamic brain network.

Exploring the structure and function of temporal networks with dynamic graphlets

MOTIVATION

With increasing availability of temporal real-world networks, how to efficiently study these data? One can model a temporal network as a single aggregate static network, or as a series of time-specific snapshots, each being an aggregate static network over the corresponding time window. Then, one can use established methods for static analysis on the resulting aggregate network(s), but losing in the process valuable temporal information either completely, or at the interface between different snapshots, respectively. Here, we develop a novel approach for studying a temporal network more explicitly, by capturing inter-snapshot relationships.

RESULTS

We base our methodology on well-established graphlets (subgraphs), which have been proven in numerous contexts in static network research. We develop new theory to allow for graphlet-based analyses of temporal networks. Our new notion of dynamic graphlets is different from existing dynamic network approaches that are based on temporal motifs (statistically significant subgraphs). The latter have limitations: their results depend on the choice of a null network model that is required to evaluate the significance of a subgraph, and choosing a good null model is non-trivial. Our dynamic graphlets overcome the limitations of the temporal motifs. Also, when we aim to characterize the structure and function of an entire temporal network or of individual nodes, our dynamic graphlets outperform the static graphlets. Clearly, accounting for temporal information helps. We apply dynamic graphlets to temporal age-specific molecular network data to deepen our limited knowledge about human aging.

AVAILABILITY AND IMPLEMENTATION

http://www.nd.edu/∼cone/DG.

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network properties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.

Evaluating the effect of aging on interference resolution with time-varying complex networks analysis

In this study we used graph theory analysis to investigate age-related reorganization of functional networks during the active maintenance of information that is interrupted by external interference. Additionally, we sought to investigate network differences before and after averaging network parameters between both maintenance and interference windows. We compared young and older adults by measuring their magnetoencephalographic recordings during an interference-based working memory task restricted to successful recognitions. Data analysis focused on the topology/temporal evolution of functional networks during both the maintenance and interference windows. We observed that: (a) Older adults require higher synchronization between cortical brain sites in order to achieve a successful recognition, (b) The main differences between age groups arise during the interference window,

Complex brain network properties in late L2 learners and native speakers

Whether the neural mechanisms that underlie the processing of a second language in highly proficient late bilinguals (L2 late learners) are similar or not to those that underlie the processing of the first language (L1) is still an issue under debate. In this study, a group of late learners of Spanish whose native language is English and a group of Spanish monolinguals were compared while they read sentences, some of which contained syntactic violations. A brain complex network analysis approach was used to assess the time-varying topological properties of the functional networks extracted from the electroencephalography (EEG) recording. Late L2 learners showed a lower degree of parallel information transfer and a slower propagation between regions of the brain functional networks while processing sentences containing a gender mismatch condition as compared with a standard sentence configuration. In contrast, no such differences between these conditions were detected in the Spanish monolinguals. This indicates that when a morphosyntactic language incongruence that does not exist in the native language is presented in the second language, the neural activation pattern is configured differently in highly proficient late bilinguals than in monolinguals.

Synchronization in time-varying networks

We study the stability of the synchronized state in time-varying complex networks using the concept of basin stability, which is a nonlocal and nonlinear measure of stability that can be easily applied to high-dimensional systems [P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Phys. 9, 89 (2013)]. The time-varying character is included by stochastically rewiring each link with the average frequency f. We find that the time taken to reach synchronization is lowered and the stability range of the synchronized state increases considerably in dynamic networks. Further we uncover that small-world networks are much more sensitive to link changes than random ones, with the time-varying character of the network having a significant effect at much lower rewiring frequencies. At very high rewiring frequencies, random networks perform better than small-world networks and the synchronized state is stable over a much wider window of coupling strengths. Lastly we show that the stability range of the synchronized state may be quite different for small and large perturbations, and so the linear stability analysis and the basin stability criterion provide complementary indicators of stability.

The effects of pharmacological treatment on functional brain connectome in obsessive-compulsive disorder

BACKGROUND

Previous neuroimaging studies of obsessive-compulsive disorder (OCD) have reported both baseline functional alterations and pharmacological changes in localized brain regions and connections; however, the effects of selective serotonin reuptake inhibitor (SSRI) treatment on the whole-brain functional network have not yet been elucidated.

METHODS

Twenty-five drug-free OCD patients underwent resting-state functional magnetic resonance imaging. After 16-weeks, seventeen patients who received SSRI treatment were rescanned. Twenty-three matched healthy control subjects were examined at baseline for comparison, and 21 of them were rescanned after 16 weeks. Topological properties of brain networks (including small-world, efficiency, modularity, and connectivity degree) were analyzed cross-sectionally and longitudinally with graph-theory approach.

RESULTS

At baseline, OCD patients relative to healthy control subjects showed decreased small-world efficiency (including local clustering coefficient, local efficiency, and small-worldness) and functional association between default-mode and frontoparietal modules as well as widespread altered connectivity degrees in many brain areas. We observed clinical improvement in OCD patients after 16 weeks of SSRI treatment, which was accompanied by significantly elevated small-world efficiency, modular organization, and connectivity degree. Improvement of obsessive-compulsive symptoms was significantly correlated with changes in connectivity degree in right ventral frontal cortex in OCD patients after treatment.

CONCLUSIONS

This is first study to use graph-theory approach for investigating valuable biomarkers for the effects of SSRI on neuronal circuitries of OCD patients. Our findings suggest that OCD phenomenology might be the outcome of disrupted optimal balance in the brain networks and that reinstating this balance after SSRI treatment accompanies significant symptom improvement.

A graph theoretic approach to dynamic functional connectivity tracking and network state identification

With the advances in neuroimaging technology, it is now possible to measure human brain activity with increasing temporal and spatial resolution. This vast amount of spatio-temporal data requires the development of computational methods capable of building an integrated picture of the functional networks for a better understanding of the healthy and diseased brain [1]. Although the construction of these networks from neuroimaging data is well-established [2], current approaches are limited to the characterization of the global topology of static networks where the links between different brain regions represent average connectivity over a long time period [3], [2]. Recent studies suggest that human cognition arises from the rapid formation and dissociation of synchronized neural activity on short time scales in the order of milliseconds [4]. There is a strong need for new electroencephalogram (EEG)-based analytic frameworks for monitoring dynamic functional network activity. In this paper, we propose a graph theoretic approach for tracking the changing topology of functional connectivity networks across time. First, we introduce an event detection algorithm based on node level feature extraction and principal components analysis of time-dependent node correlation matrices. Then, we propose a k-means based clustering approach to characterize each time interval with the most common connectivity states. Finally, the proposed methodology is applied to the study of the dynamics of functional connectivity networks during error-related negativity (ERN).

Incidental and intentional learning of verbal episodic material differentially modifies functional brain networks

Learning- and memory-related processes are thought to result from dynamic interactions in large-scale brain networks that include lateral and mesial structures of the temporal lobes. We investigate the impact of incidental and intentional learning of verbal episodic material on functional brain networks that we derive from scalp-EEG recorded continuously from 33 subjects during a neuropsychological test schedule. Analyzing the networks' global statistical properties we observe that intentional but not incidental learning leads to a significantly increased clustering coefficient, and the average shortest path length remains unaffected. Moreover, network modifications correlate with subsequent recall performance: the more pronounced the modifications of the clustering coefficient, the higher the recall performance. Our findings provide novel insights into the relationship between topological aspects of functional brain networks and higher cognitive functions.

On the discovery of group-consistent graph substructure patterns from brain networks

Complex networks constitute a recurring issue in the analysis of neuroimaging data. Recently, network motifs have been identified as patterns of interconnections since they appear in a significantly higher number than in randomized networks, in a given ensemble of anatomical or functional connectivity graphs. The current approach for detecting and enumerating motifs in brain networks requires a predetermined motif repertoire and can operate only with motifs of small size (consisting of few nodes). There is a growing interest in methodologies for frequent graph-based pattern mining in large graph datasets that can facilitate adaptive design of motifs. The results presented in this paper are based on the graph-based Substructure pattern mining (gSpan) algorithm and introduce a manifold of ways to exploit it for data-driven motif extraction in connectomics research. Functional connectivity graphs from electroencephalographic (EEG) recordings during resting state and mental calculations are used to demonstrate our approach. Relying on either time-invariant or time-evolving graphs, characteristic motifs associated with various frequency bands were derived and compared. With a suitable manipulation, the gSpan discovers motifs which are specific to performing mental arithmetics. Finally, the subject-dependent temporal signatures of motifs' appearance revealed the transient nature of the evolving functional connectivity (math-related motifs "come and go").

Source space analysis of event-related dynamic reorganization of brain networks

How the brain works is nowadays synonymous with how different parts of the brain work together and the derivation of mathematical descriptions for the functional connectivity patterns that can be objectively derived from data of different neuroimaging techniques. In most cases static networks are studied, often relying on resting state recordings. Here, we present a quantitative study of dynamic reconfiguration of connectivity for event-related experiments. Our motivation is the development of a methodology that can be used for personalized monitoring of brain activity. In line with this motivation, we use data with visual stimuli from a typical subject that participated in different experiments that were previously analyzed with traditional methods. The earlier studies identified well-defined changes in specific brain areas at specific latencies related to attention, properties of stimuli, and tasks demands. Using a recently introduced methodology, we track the event-related changes in network organization, at source space level, thus providing a more global and complete view of the stages of processing associated with the regional changes in activity. The results suggest the time evolving modularity as an additional brain code that is accessible with noninvasive means and hence available for personalized monitoring and clinical applications.

Synchronization dynamics and evidence for a repertoire of network states in resting EEG

Intrinsically driven neural activity generated at rest exhibits complex spatiotemporal dynamics characterized by patterns of synchronization across distant brain regions. Mounting evidence suggests that these patterns exhibit fluctuations and nonstationarity at multiple time scales. Resting-state electroencephalographic (EEG) recordings were examined in 12 young adults for changes in synchronization patterns on a fast time scale in the range of tens to hundreds of milliseconds. Results revealed that EEG dynamics continuously underwent rapid transitions between intermittently stable states. Numerous approximate recurrences of states were observed within single recording epochs, across different epochs separated by longer times, and between participants. For broadband (4-30 Hz) data, a majority of states could be grouped into three families, suggesting the existence of a limited repertoire of core states that is continually revisited and shared across participants. Our results document the existence of fast synchronization dynamics iterating amongst a small set of core networks in the resting brain, complementing earlier findings of nonstationary dynamics in electromagnetic recordings and transient EEG microstates.