Cognitive chimera states in human brain networks

Bifurcations and collective states of Kuramoto oscillators with higher-order interactions and rotational symmetry breaking

We study a network of identical Kuramoto oscillators with higher-order interactions that also break the rotational symmetry of the system. To gain analytical insights into this model, we use the Watanabe-Strogatz Ansatz, which allows us to reduce the dimensionality of the original system of equations. The study of stability and bifurcations of the reduced system reveals a codimension two Bogdanov-Takens bifurcation and several other associated bifurcations. Such analysis is corroborated by numerical simulations of the associated Kuramoto system, which, in turn, unveils a variety of collective behaviors such as synchronized motion, oscillation death, chimeras, incoherent states, and traveling waves. Importantly, this system displays a case where alternating chimeras emerge in an indistinguishable single population of oscillators, which may offer insights into the unihemispheric slow-wave sleep phenomenon observed in mammals and birds.

Recovery of activation propagation and self-sustained oscillation abilities in stroke brain networks

Healthy brain networks usually show highly efficient information communication and self-sustained oscillation abilities. However, how the brain network structure affects these dynamics after an injury (stroke) is not very clear. The recovery of structure and dynamics of stroke brain networks over time is still not known precisely. Based on the analysis of a large number of strokes' brain network data, we show that stroke changes the network properties in connection weights, average degree, clustering, community, etc. Yet, they will recover gradually over time to some extent. We then adopt a simplified reaction-diffusion model to investigate stroke patients' activation propagation and self-sustained oscillation abilities. Our results reveal that the stroke slows the adoption time across different brain scales, indicating a weakened brain's activation propagation ability. In addition, we show that the lifetime of self-sustained oscillatory patterns at 3 months post-stroke, patients' brains significantly depart from the healthy ones. Finally, we examine the properties of core networks of self-sustained oscillatory patterns, in which the directed edges denote the main pathways of activation propagation. Our results demonstrate that the lifetime and recovery of self-sustaining patterns are related to the properties of core networks, and the properties in the post-stroke greatly vary from those in the healthy group. Most importantly, the strokes' activation propagation and self-sustained oscillation abilities significantly improve at 1 year post-stroke, driven by structural connection repair. This work may help us to understand the relationship between structure and function in brain disorders.

Information Entropy in Chimera States of Human Dynamics

In human dynamics, functioning relies on intricate coordination patterns. Networks of synchronized oscillators in various biological and semiotic fields shape these dynamics. We have observed stability, instability, and transitions at multiple levels, indicating that coordination happens on all scales. We have examined coordination models for simplified and complex dynamics. In empirical research, we can frequently observe chimera states as the coexistence of coherence and incoherence, even in homogeneous networks. They are more evident in the heterogenous networks' standard in human dynamics, where oscillators and nodes are mixed as different types. This paper proposes a simplified and overarching model for mixed chimeras. We discuss the information dynamics in these types of networks and their pattern transitions.

Multiscale effective connectivity analysis of brain activity using neural ordinary differential equations

Neural mechanisms and underlying directionality of signaling among brain regions depend on neural dynamics spanning multiple spatiotemporal scales of population activity. Despite recent advances in multimodal measurements of brain activity, there is no broadly accepted multiscale dynamical models for the collective activity represented in neural signals. Here we introduce a neurobiological-driven deep learning model, termed multiscale neural dynamics neural ordinary differential equation (msDyNODE), to describe multiscale brain communications governing cognition and behavior. We demonstrate that msDyNODE successfully captures multiscale activity using both simulations and electrophysiological experiments. The msDyNODE-derived causal interactions between recording locations and scales not only aligned well with the abstraction of the hierarchical neuroanatomy of the mammalian central nervous system but also exhibited behavioral dependences. This work offers a new approach for mechanistic multiscale studies of neural processes.

Synaptic effects on the intermittent synchronization of gamma rhythms

Synchronization of neural activity in the gamma frequency band is associated with various cognitive phenomena. Abnormalities of gamma synchronization may underlie symptoms of several neurological and psychiatric disorders such as schizophrenia and autism spectrum disorder. Properties of neural oscillations in the gamma band depend critically on the synaptic properties of the underlying circuits. This study explores how synaptic properties in pyramidal-interneuronal circuits affect not only the average synchronization strength but also the fine temporal patterning of neural synchrony. If two signals show only moderate synchrony strength, it may be possible to consider these dynamics as alternating between synchronized and desynchronized states. We use a model of connected circuits that produces pyramidal-interneuronal gamma oscillations to explore the temporal patterning of synchronized and desynchronized intervals. Changes in synaptic strength may alter the temporal patterning of synchronized dynamics (even if the average synchrony strength is not changed). Larger values of local synaptic connections promote longer desynchronization durations, while larger values of long-range synaptic connections promote shorter desynchronization durations. Furthermore, we show that circuits with different temporal patterning of synchronization may have different sensitivity to synaptic input. Thus, the alterations of synaptic strength may mediate physiological properties of neural circuits not only through change in the average synchrony level of gamma oscillations, but also through change in how synchrony is patterned in time over very short time scales.

Introduction to Focus Issue: Chimera states: From theory and experiments to technology and living systems

One of the pillars of modern science is the concept of symmetries. Spontaneously breaking such symmetries gives rise to non-trivial states, which can explain a variety of phenomena around us. Chimera states, characterized by the coexistence of localized synchronized and unsynchronized dynamics, are a novel example. This Focus Issue covers recent developments in the study of chimera states, from both theoretical and experimental points of view, including an emphasis on prospective practical realization for application in technology and living systems.

Synaptic plasticity: from chimera states to synchronicity oscillations in multilayer neural networks

This research scrutinizes the simultaneous evolution of each layer within a multilayered complex neural network and elucidates the effect of synaptic plasticity on inter-layer dynamics. In the absence of synaptic plasticity, a predominant feedforward effect is observed, resulting in the manifestation of complete synchrony in deep networks, with each layer assuming a chimera state. A significant increase in the number of synchronized neurons is observed as the layers augment, culminating in complete synchronization in the deeper sections. The study categorizes the layers into three distinct parts: the initial layers (1-4) demonstrate the emergence of non-uniformity in the random firing of neurons; the middle layers (5-7) exhibit an amplification of this non-uniformity, forming a higher degree of synchronization; and the final layers (8-10) display a completely synchronized process. The introduction of synaptic plasticity disrupts this synchrony, inducing periodic oscillation characteristics across layers. The specificity of these oscillations is notably accentuated with increasing network depth. These insights shed light on the interplay between neural network complexity and synaptic plasticity in influencing synchronization dynamics, presenting avenues for enhanced neural network architectures and refined neuroscientific models. The findings underscore the imperative to delve deeper into the implications of synaptic plasticity on the structure and function of intricate multi-layer neural networks.

High-Mode Coupling Yields Multicoherent-Phase Phenomena in Nonlocally Coupled Oscillators

Capturing the intricate dynamics of partially coherent patterns in coupled oscillator systems is vibrant and one of the crucial areas of nonlinear sciences. Considering higher-order Fourier modes in the coupling, we discover a novel type of clustered coherent state in phase models, where inside the coherent region oscillators are further split into q dynamically equivalent subgroups with a 2π/q phase difference between two neighboring subgroups, forming a multicoherent-phase (MUP) chimera state. Both a self-consistency analysis and the Ott-Antonsen dimension reduction techniques are used to theoretically derive these solutions, whose stability are further demonstrated by spectral analysis. The universality of MUP effects is demonstrated by generalized twisted states and higher-order spatial swarm chimera states of swarmalators which are beyond pure phase models since oscillators can move in space.

Self-consistent autocorrelation of a disordered Kuramoto model in the asynchronous state

The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has received limited attention. Here, we adapt and enhance the mean-field approach originally proposed by Stiller and Radons [Phys. Rev. E 58, 1789 (1998)1063-651X10.1103/PhysRevE.58.1789] to study the asynchronous state in the Kuramoto model with a finite number of oscillators and with disordered connectivity. By employing an iterative stochastic mean field approximation, the complex N-oscillator system can effectively be reduced to a one-dimensional dynamics, both for homogeneous and heterogeneous networks. This method allows us to investigate the power spectra of individual oscillators as well as of the multiplicative "network noise" in the Kuramoto model in the asynchronous regime. By taking into account the finite system size and disorder in the connectivity, our findings become relevant for the dynamics of coupled oscillators that appear in the context of biological or technical systems.

Task-specific topology of brain networks supporting working memory and inhibition

Network neuroscience explores the brain's connectome, demonstrating that dynamic neural networks support cognitive functions. This study investigates how distinct cognitive abilities-working memory and cognitive inhibitory control-are supported by unique brain network configurations constructed by estimating whole-brain networks using mutual information. The study involved 195 participants who completed the Sternberg Item Recognition task and Flanker tasks while undergoing electroencephalography recording. A mixed-effects linear model analyzed the influence of network metrics on cognitive performance, considering individual differences and task-specific dynamics. The findings indicate that working memory and cognitive inhibitory control are associated with different network attributes, with working memory relying on distributed networks and cognitive inhibitory control on more segregated ones. Our analysis suggests that both strong and weak connections contribute to cognitive processes, with weak connections potentially leading to a more stable and support networks of memory and cognitive inhibitory control. The findings indirectly support the network neuroscience theory of intelligence, suggesting different functional topology of networks inherent to various cognitive functions. Nevertheless, we propose that understanding individual variations in cognitive abilities requires recognizing both shared and unique processes within the brain's network dynamics.

Impact of pulse exposure on chimera state in ensemble of FitzHugh-Nagumo systems

In this article, we consider the influence of a periodic sequence of Gaussian pulses on a chimera state in a ring of coupled FitzHugh-Nagumo systems. We found that on the way to complete spatial synchronization, one can observe a number of variations of chimera states that are not typical for the parameter range under consideration. For example, the following modes were found: breathing chimera, chimera with intermittency in the incoherent part, traveling chimera with strong intermittency, and others. For comparison, here we also consider the impact of a harmonic influence on the same chimera, and to preserve the generality of the conclusions, we compare the regimes caused by both a purely positive harmonic influence and a positive-negative one.

Spatial-Temporal Analysis of Neural Desynchronization in Sleeplike States Reveals Critical Dynamics

Sleep is characterized by nonrapid eye movement sleep, originating from widespread neuronal synchrony, and rapid eye movement sleep, with neuronal desynchronization akin to waking behavior. While these were thought to be global brain states, recent research suggests otherwise. Using time-frequency analysis of mesoscopic voltage-sensitive dye recordings of mice in a urethane-anesthetized model of sleep, we find transient neural desynchronization occurring heterogeneously across the cortex within a background of synchronized neural activity, in a manner reminiscent of a critical spreading process and indicative of an "edge-of-synchronization" phase transition.

Changes in Community Structure of Brain Dynamic Functional Connectivity States in Mild Cognitive Impairment

Recent researches have noted many changes of short-term dynamic modalities in mild cognitive impairment (MCI) patients' brain functional networks. In this study, the dynamic functional brain networks of 82 MCI patients and 85 individuals in the normal control (NC) group were constructed using the sliding window method and Pearson correlation. The window size was determined using single-scale time-dependent (SSTD) method. Subsequently, k-means was applied to cluster all window samples, identifying three dynamic functional connectivity (DFC) states. Collective sparse symmetric non-negative matrix factorization (cssNMF) was then used to perform community detection on these states and quantify differences in brain regions. Finally, metrics such as within-community connectivity strength, community strength, and node diversity were calculated for further analysis. The results indicated high similarity between the two groups in state 2, with no significant differences in optimal community quantity and functional segregation (p < 0.05). However, for state 1 and state 3, the optimal community quantity was smaller in MCI patients compared to the NC group. In state 1, MCI patients had lower within-community connectivity strength and overall strength than the NC group, whereas state 3 showed results opposite to state 1. Brain regions with statistical difference included MFG.L, ORBinf.R, STG.R, IFGtriang.L, CUN.L, CUN.R, LING.R, SOG.L, and PCUN.R. This study on DFC states explores changes in the brain functional networks of patients with MCI from the perspective of alterations in the community structures of DFC states. The findings could provide new insights into the pathological changes in the brains of MCI patients.

Enhanced simulations of whole-brain dynamics using hybrid resting-state structural connectomes

The human brain, composed of billions of neurons and synaptic connections, is an intricate network coordinating a sophisticated balance of excitatory and inhibitory activities between brain regions. The dynamical balance between excitation and inhibition is vital for adjusting neural input/output relationships in cortical networks and regulating the dynamic range of their responses to stimuli. To infer this balance using connectomics, we recently introduced a computational framework based on the Ising model, which was first developed to explain phase transitions in ferromagnets, and proposed a novel hybrid resting-state structural connectome (rsSC). Here, we show that a generative model based on the Kuramoto phase oscillator can be used to simulate static and dynamic functional connectomes (FC) with rsSC as the coupling weight coefficients, such that the simulated FC aligns well with the observed FC when compared with that simulated traditional structural connectome.

Fractal basins as a mechanism for the nimble brain

An interesting feature of the brain is its ability to respond to disparate sensory signals from the environment in unique ways depending on the environmental context or current brain state. In dynamical systems, this is an example of multi-stability, the ability to switch between multiple stable states corresponding to specific patterns of brain activity/connectivity. In this article, we describe chimera states, which are patterns consisting of mixed synchrony and incoherence, in a brain-inspired dynamical systems model composed of a network with weak individual interactions and chaotic/periodic local dynamics. We illustrate the mechanism using synthetic time series interacting on a realistic anatomical brain network derived from human diffusion tensor imaging. We introduce the so-called vector pattern state (VPS) as an efficient way of identifying chimera states and mapping basin structures. Clustering similar VPSs for different initial conditions, we show that coexisting attractors of such states reveal intricately "mingled" fractal basin boundaries that are immediately reachable. This could explain the nimble brain's ability to rapidly switch patterns between coexisting attractors.

Nonequilibrium thermodynamic signatures of collective dynamical states around chimera in a chemical reaction network

Different dynamical states ranging from coherent, incoherent to chimera, multichimera, and related transitions are addressed in a globally coupled nonlinear continuum chemical oscillator system by implementing a modified complex Ginzburg-Landau equation. Besides dynamical identifications of observed states using standard qualitative metrics, we systematically acquire nonequilibrium thermodynamic characterizations of these states obtained via coupling parameters. The nonconservative work profiles in collective dynamics qualitatively reflect the time-integrated concentration of the activator, and the majority of the nonconservative work contributes to the entropy production over the spatial dimension. It is illustrated that the evolution of spatial entropy production and semigrand Gibbs free-energy profiles associated with each state are connected yet completely out of phase, and these thermodynamic signatures are extensively elaborated to shed light on the exclusiveness and similarities of these states. Moreover, a relationship between the proper nonequilibrium thermodynamic potential and the variance of activator concentration is established by exhibiting both quantitative and qualitative similarities between a Fano factor like entity, derived from the activator concentration, and the Kullback-Leibler divergence associated with the transition from a nonequilibrium homogeneous state to an inhomogeneous state. Quantifying the thermodynamic costs for collective dynamical states would aid in efficiently controlling, manipulating, and sustaining such states to explore the real-world relevance and applications of these states.

Task-relevant brain dynamics among cognitive subsystems induced by regional stimulation in a whole-brain computational model

Cognition involves the global integration of distributed brain regions that are known to work cohesively as cognitive subsystems during brain functioning. Empirical evidence has suggested that spatiotemporal phase relationships between brain regions, measured as synchronization and metastability, may encode important task-relevant information. However, it remains largely unknown how phase relationships aggregate at the level of cognitive subsystems under different cognitive processing. Here, we probe this question by simulating task-relevant brain dynamics through regional stimulation of a whole-brain dynamical network model operating in the resting-state dynamical regime. The model is constructed with structurally embedded Stuart-Laudon oscillators and then fitted with human resting-state functional magnetic resonance imaging data. Based on this framework, we first demonstrate the plausibility of introducing the cognitive system partition into the modeling analysis framework by showing that the clustering of regions across functional networks is better circumscribed by the predefined partition. At the cognitive subsystem level, we focus on how task-relevant phase dynamics are organized in terms of synchronization and metastability. We found that patterns of cognitive synchronization are more task specific, whereas patterns of cognitive metastability are more consistent across different states, suggesting it may encode a more task-general property during cognitive processing, an inherent property conferred by brain organization. This consistent network architecture in cognitive metastability may be related to the distinct functional responses of realistic cognitive systems. We also provide empirical evidence to partially support our computational results. Our paper may provide insights for the mechanisms underlying task-relevant brain dynamics, and establish a model-based link between brain structure, dynamics, and cognition, a fundamental step for computationally aided brain interventions.

Chimera resonance in networks of chaotic maps

We explore numerically the impact of additive Gaussian noise on the spatiotemporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters. It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance.

The synchronizing role of multiplexing noise: Exploring Kuramoto oscillators and breathing chimeras

The synchronization of spatiotemporal patterns in a two-layer multiplex network of identical Kuramoto phase oscillators is studied, where each layer is a non-locally coupled ring. Particular focus is on the role played by a noisy inter-layer communication. It is shown that modulating the inter-layer coupling strength by uncommon noise has a significant impact on the dynamics of the network, in particular, that modulating the interlayer coupling by noise can counter-intuitively induce synchronization in networks. It is further shown that increasing the noise intensity has many other analogous effects to that of increasing the interlayer coupling strength. For example, the noise intensity can also induce state transitions in a similar way, in some cases causing the layers to completely synchronize within themselves. It is discussed how such disturbances may in many cases be beneficial to multilayer systems. These effects are demonstrated both for white noise and for other kinds of colored noise. A "floating" breathing chimera state is also discovered in this system.

Sensitive dynamics of brain cognitive networks and its resource constraints

It is well known that brain functions are closely related to the synchronization of brain networks, but the underlying mechanisms are still not completely understood. To study this problem, we here focus on the synchronization of cognitive networks, in contrast to that of a global brain network, as individual brain functions are in fact performed by different cognitive networks but not the global network. In detail, we consider four different levels of brain networks and two approaches, i.e., either with or without resource constraints. For the case of without resource constraints, we find that global brain networks have fundamentally different behaviors from that of the cognitive networks; i.e., the former has a continuous synchronization transition, while the latter shows a novel transition of oscillatory synchronization. This feature of oscillation comes from the sparse links among the communities of cognitive networks, resulting in coupling sensitive dynamics of brain cognitive networks. While for the case of resource constraints, we find that at the global level, the synchronization transition becomes explosive, in contrast to the continuous synchronization for the case of without resource constraints. At the level of cognitive networks, the transition also becomes explosive and the coupling sensitivity is significantly reduced, thus guaranteeing the robustness and fast switch of brain functions. Moreover, a brief theoretical analysis is provided.

Study on characteristic of epileptic multi-electroencephalograph base on Hilbert-Huang transform and brain network dynamics

Lots of studies have been carried out on characteristic of epileptic Electroencephalograph (EEG). However, traditional EEG characteristic research methods lack exploration of spatial information. To study the characteristics of epileptic EEG signals from the perspective of the whole brain，this paper proposed combination methods of multi-channel characteristics from time-frequency and spatial domains. This paper was from two aspects: Firstly, signals were converted into 2D Hilbert Spectrum (HS) images which reflected the time-frequency characteristics by Hilbert-Huang Transform (HHT). These images were identified by Convolutional Neural Network (CNN) model whose sensitivity was 99.8%, accuracy was 98.7%, specificity was 97.4%, F1-score was 98.7%, and AUC-ROC was 99.9%. Secondly, the multi-channel signals were converted into brain networks which reflected the spatial characteristics by Symbolic Transfer Entropy (STE) among different channels EEG. And the results show that there are different network properties between ictal and interictal phase and the signals during the ictal enter the synchronization state more quickly, which was verified by Kuramoto model. To summarize, our results show that there was different characteristics among channels for the ictal and interictal phase, which can provide effective physical non-invasive indicators for the identification and prediction of epileptic seizures.

Chimera states in multiplex networks: Chameleon-like across-layer synchronization

Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.

Noise improves the association between effects of local stimulation and structural degree of brain networks

Stimulation to local areas remarkably affects brain activity patterns, which can be exploited to investigate neural bases of cognitive function and modify pathological brain statuses. There has been growing interest in exploring the fundamental action mechanisms of local stimulation. Nevertheless, how noise amplitude, an essential element in neural dynamics, influences stimulation-induced brain states remains unknown. Here, we systematically examine the effects of local stimulation by using a large-scale biophysical model under different combinations of noise amplitudes and stimulation sites. We demonstrate that noise amplitude nonlinearly and heterogeneously tunes the stimulation effects from both regional and network perspectives. Furthermore, by incorporating the role of the anatomical network, we show that the peak frequencies of unstimulated areas at different stimulation sites averaged across noise amplitudes are highly positively related to structural connectivity. Crucially, the association between the overall changes in functional connectivity as well as the alterations in the constraints imposed by structural connectivity with the structural degree of stimulation sites is nonmonotonically influenced by the noise amplitude, with the association increasing in specific noise amplitude ranges. Moreover, the impacts of local stimulation of cognitive systems depend on the complex interplay between the noise amplitude and average structural degree. Overall, this work provides theoretical insights into how noise amplitude and network structure jointly modulate brain dynamics during stimulation and introduces possibilities for better predicting and controlling stimulation outcomes.

Within-subject reproducibility varies in multi-modal, longitudinal brain networks

Network neuroscience provides important insights into brain function by analyzing complex networks constructed from diffusion Magnetic Resonance Imaging (dMRI), functional MRI (fMRI) and Electro/Magnetoencephalography (E/MEG) data. However, in order to ensure that results are reproducible, we need a better understanding of within- and between-subject variability over long periods of time. Here, we analyze a longitudinal, 8 session, multi-modal (dMRI, and simultaneous EEG-fMRI), and multiple task imaging data set. We first confirm that across all modalities, within-subject reproducibility is higher than between-subject reproducibility. We see high variability in the reproducibility of individual connections, but observe that in EEG-derived networks, during both rest and task, alpha-band connectivity is consistently more reproducible than connectivity in other frequency bands. Structural networks show a higher reliability than functional networks across network statistics, but synchronizability and eigenvector centrality are consistently less reliable than other network measures across all modalities. Finally, we find that structural dMRI networks outperform functional networks in their ability to identify individuals using a fingerprinting analysis. Our results highlight that functional networks likely reflect state-dependent variability not present in structural networks, and that the type of analysis should depend on whether or not one wants to take into account state-dependent fluctuations in connectivity.

Moving from phenomenological to predictive modelling: Progress and pitfalls of modelling brain stimulation in-silico

Brain stimulation is an increasingly popular neuromodulatory tool used in both clinical and research settings; however, the effects of brain stimulation, particularly those of non-invasive stimulation, are variable. This variability can be partially explained by an incomplete mechanistic understanding, coupled with a combinatorial explosion of possible stimulation parameters. Computational models constitute a useful tool to explore the vast sea of stimulation parameters and characterise their effects on brain activity. Yet the utility of modelling stimulation in-silico relies on its biophysical relevance, which needs to account for the dynamics of large and diverse neural populations and how underlying networks shape those collective dynamics. The large number of parameters to consider when constructing a model is no less than those needed to consider when planning empirical studies. This piece is centred on the application of phenomenological and biophysical models in non-invasive brain stimulation. We first introduce common forms of brain stimulation and computational models, and provide typical construction choices made when building phenomenological and biophysical models. Through the lens of four case studies, we provide an account of the questions these models can address, commonalities, and limitations across studies. We conclude by proposing future directions to fully realise the potential of computational models of brain stimulation for the design of personalized, efficient, and effective stimulation strategies.

Alternating chimera states in complex networks with modular structures

Chimera, the coexistence state of synchronization and non-synchronization, widely exists in complex networks. It has a great potentially explanatory power for the unihemispheric sleep of birds and some mammals, in which the synchronizations of the hemispheres of the cerebral cortex are evolving alternately. In this study, a coupled nonlinear oscillator system with a topology of the modular complex network was constructed to simulate the left and right hemispheres of the brain. The results showed that a stable chimera, an alternating chimera, and a breathing chimera were produced when the coupling strength and connection probability of the left and right hemispheres were changed. Further, we studied the effect of noise on rich synchronous patterns and found that the alternating chimera was robust to Gaussian white noise when the strength was not very large. Finally, our study was extended to a complex network with three sub-networks, and an alternating chimera could exist in two or three sub-networks. Our research provides a deeper insight into the mechanism of brain function like unihemispheric sleep.

From Turing patterns to chimera states in the 2D Brusselator model

The Brusselator has been used as a prototype model for autocatalytic reactions and, in particular, for the Belousov-Zhabotinsky reaction. When coupled at the diffusive limit, the Brusselator undergoes a Turing bifurcation resulting in the formation of classical Turing patterns, such as spots, stripes, and spirals in two spatial dimensions. In the present study, we use generic nonlocally coupled Brusselators and show that in the limit of the coupling range R→1 (diffusive limit), the classical Turing patterns are recovered, while for intermediate coupling ranges and appropriate parameter values, chimera states are produced. This study demonstrates how the parameters of a typical nonlinear oscillator can be tuned so that the coupled system passes from spatially stable Turing structures to dynamical spatiotemporal chimera states.

Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations

Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to "deeper" stable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.

Effect of mobility on collective phase dynamics of nonlocally coupled oscillators with a phase lag

Nonlocally coupled oscillators with a phase lag self-organize into various patterns, such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, whereas it destroys coherence for a repulsive coupling. The transition behaviors are discussed in terms of the timescales of synchronization and diffusion of the oscillators. We also find a novel spatiotemporal pattern at the border between coherent and incoherent states.

Basins of attraction of chimera states on networks

Networks of identical coupled oscillators display a remarkable spatiotemporal pattern, the chimera state, where coherent oscillations coexist with incoherent ones. In this paper we show quantitatively in terms of basin stability that stable and breathing chimera states in the original two coupled networks typically have very small basins of attraction. In fact, the original system is dominated by periodic and quasi-periodic chimera states, in strong contrast to the model after reduction, which can not be uncovered by the Ott-Antonsen ansatz. Moreover, we demonstrate that the curve of the basin stability behaves bimodally after the system being subjected to even large perturbations. Finally, we investigate the emergence of chimera states in brain network, through inducing perturbations by stimulating brain regions. The emerged chimera states are quantified by Kuramoto order parameter and chimera index, and results show a weak and negative correlation between these two metrics.

Functional control of oscillator networks

Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators’ parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators’ phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids.

In network systems governed by oscillatory activity, such as brain networks or power grids, configurations of synchrony may define network functions. The authors introduce a control approach for the formation of desired synchrony patterns through optimal interventions on the network parameters.

What Models and Tools can Contribute to a Better Understanding of Brain Activity?

Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.

Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses

The union of the Kuramoto–Sakaguchi model and the Hebb dynamics reproduces the Lisman switch through a bistability in synchronized states. Here, we show that, within certain ranges of the frustration parameter, the chimera pattern can emerge, causing a different, time-evolving, distribution in the Hebbian synaptic strengths. We study the stability range of the chimera as a function of the frustration (phase-lag) parameter. Depending on the range of the frustration, two different types of chimeras can appear spontaneously, i.e., from randomized initial conditions. In the first type, the oscillators in the coherent region rotate, on average, slower than those in the incoherent region; while in the second type, the average rotational frequencies of the two regions are reversed, i.e., the coherent region runs, on average, faster than the incoherent region. We also show that non-stationary behavior at finite N can be controlled by adjusting the natural frequency of a single pacemaker oscillator. By slowly cycling the frequency of the pacemaker, we observe hysteresis in the system. Finally, we discuss how we can have a model for learning and memory.

Dynamic Alterations in Functional Connectivity Density in Amyotrophic Lateral Sclerosis: A Resting-State Functional Magnetic Resonance Imaging Study

Background and Aims

Current knowledge on the temporal dynamics of the brain functional organization in amyotrophic lateral sclerosis (ALS) is limited. This is the first study on alterations in the patterns of dynamic functional connection density (dFCD) involving ALS.

Methods

We obtained resting-state functional magnetic resonance imaging (fMRI) data from 50 individuals diagnosed with ALS and 55 healthy controls (HCs). We calculated the functional connectivity (FC) between a given voxel and all other voxels within the entire brain and yield the functional connection density (FCD) value per voxel. dFCD was assessed by sliding window correlation method. In addition, the standard deviation (SD) of dFCD across the windows was computed voxel-wisely to measure dFCD variability. The difference in dFCD variability between the two groups was compared using a two-sample t-test following a voxel-wise manner. The receiver operating characteristic (ROC) curve was used to assess the between-group recognition performance of the dFCD variability index.

Results

The dFCD variability was significantly reduced in the bilateral precentral and postcentral gyrus compared with the HC group, whereas a marked increase was observed in the left middle frontal gyrus of ALS patients. dFCD variability exhibited moderate potential (areas under ROC curve = 0.753-0.837, all P < 0.001) in distinguishing two groups.

Conclusion

ALS patients exhibit aberrant dynamic property in brain functional architecture. The dFCD evaluation improves our understanding of the pathological mechanisms underlying ALS and may assist in its diagnosis.

Nonequilibrium thermodynamic characterization of chimeras in a continuum chemical oscillator system

The emergence of the chimera state as the counterintuitive spatial coexistence of synchronous and asynchronous regimes is addressed here in a continuum chemical oscillator system by implementing a relevant complex Ginzburg-Landau equation with global coupling. This study systematically acquires and characterizes the evolution of nonequilibrium thermodynamic entities corresponding to the chimera state. The temporal evolution of the entropy production rate exhibits a beat pattern with a series of equidistant spectral lines in the frequency domain. Symmetric profiles associated with the incoherent regime appear in descriptions of the dynamics and thermodynamics of the chimera. It is shown that identifying the semigrand Gibbs free energy of the state as the Gabor elementary function can reveal the guiding role of the information uncertainty principle in shaping the chimera energetics.

Test–Retest Reliability of Synchrony and Metastability in Resting State fMRI

In recent years, interest has been growing in dynamic characteristic of brain signals from resting-state functional magnetic resonance imaging (rs-fMRI). Synchrony and metastability, as neurodynamic indexes, are considered as one of methods for analyzing dynamic characteristics. Although much research has studied the analysis of neurodynamic indices, few have investigated its reliability. In this paper, the datasets from the Human Connectome Project have been used to explore the test–retest reliabilities of synchrony and metastability from multiple angles through intra-class correlation (ICC). The results showed that both of these indexes had fair test–retest reliability, but they are strongly affected by the field strength, the spatial resolution, and scanning interval, less affected by the temporal resolution. Denoising processing can help improve their ICC values. In addition, the reliability of neurodynamic indexes was affected by the node definition strategy, but these effects were not apparent. In particular, by comparing the test–retest reliability of different resting-state networks, we found that synchrony of different networks was basically stable, but the metastability varied considerably. Among these, DMN and LIM had a relatively higher test–retest reliability of metastability than other networks. This paper provides a methodological reference for exploring the brain dynamic neural activity by using synchrony and metastability in fMRI signals.

Frequency chimera state induced by differing dynamical timescales

We report the occurrence of a self-emerging frequency chimera state in spatially extended systems of coupled oscillators, where the coherence and incoherence are defined with respect to the emergent frequency of the oscillations. This is generated by the local coupling among nonlinear oscillators evolving under differing dynamical timescales starting from random initial conditions. We show how they self-organize to structured patterns with spatial domains of coherence that are in frequency synchronization, coexisting with domains that are incoherent in frequencies. Our study has relevance in understanding such patterns observed in real-world systems like neuronal systems, power grids, social and ecological networks, where differing dynamical timescales is natural and realistic among the interacting systems.

Human Synchronization Maps-The Hybrid Consciousness of the Embodied Mind

We examine the theoretical implications of empirical studies developed over recent years. These experiments have explored the biosemiotic nature of communication streams from emotional neuroscience and embodied mind perspectives. Information combinatorics analysis enabled a deeper understanding of the coupling and decoupling dynamics of biosemiotics streams. We investigated intraindividual and interpersonal relations as coevolution dynamics of hybrid couplings, synchronizations, and desynchronizations. Cluster analysis and Markov chains produced evidence of chimaera states and phase transitions. A probabilistic and nondeterministic approach clarified the properties of these hybrid dynamics. Thus, multidimensional theoretical models can represent the hybrid nature of human interactions.

Network Controllability in Transmodal Cortex Predicts Positive Psychosis Spectrum Symptoms

BACKGROUND

The psychosis spectrum (PS) is associated with structural dysconnectivity concentrated in transmodal cortex. However, understanding of this pathophysiology has been limited by an overreliance on examining direct interregional connectivity. Using network control theory, we measured variation in both direct and indirect connectivity to a region to gain new insights into the pathophysiology of the PS.

METHODS

We used psychosis symptom data and structural connectivity in 1068 individuals from the Philadelphia Neurodevelopmental Cohort. Applying a network control theory metric called average controllability, we estimated each brain region's capacity to leverage its direct and indirect structural connections to control linear brain dynamics. Using nonlinear regression, we determined the accuracy with which average controllability could predict PS symptoms in out-of-sample testing. We also examined the predictive performance of regional strength, which indexes only direct connections to a region, as well as several graph-theoretic measures of centrality that index indirect connectivity. Finally, we assessed how the prediction performance for PS symptoms varied over the functional hierarchy spanning unimodal to transmodal cortex.

RESULTS

Average controllability outperformed all other connectivity features at predicting positive PS symptoms and was the only feature to yield above-chance predictive performance. Improved prediction for average controllability was concentrated in transmodal cortex, whereas prediction performance for strength was uniform across the cortex, suggesting that indexing indirect connections through average controllability is crucial in association cortex.

CONCLUSIONS

Examining interindividual variation in direct and indirect structural connections to transmodal cortex is crucial for accurate prediction of positive PS symptoms.

Widespread plasticity of cognition-related brain networks in single-sided deafness revealed by randomized window-based dynamic functional connectivity

As an extreme type of partial auditory deprivation, single-sided deafness (SSD) has been demonstrated to lead to extensive neural plasticity according to multimodal neuroimaging studies. Among them, resting-state functional magnetic resonance imaging (rs-fMRI) offers valuable information on functional connectivities (FCs). However, most previous SSD rs-fMRI studies assumed that the extracted FC remains stationary during the entire fMRI scan and neglected dynamic functional activities. Existing fixed window-based dynamic FC analysis also ignores dynamic functional activities under different temporal terms. Additionally, due to the cost constraints of using MRI machines, using data-driven methods for unbiased hypothesis investigations may require more effective sample data augmentation techniques. To tackle these challenges and problems together, in this study, we proposed a dynamic window with a random length and position to extract participants' dynamic characteristics under different temporal terms and to extract more information from the dataset. Then, we proposed a nodal efficiency-based correlation matrix to describe the relationships of synergism between regions as features and applied a linear support vector machine (SVM) model to learn the importance of the features, which helped to identify SSD patients and healthy controls. A total of 68 participants (including 23 with left SSD, 20 with right SSD and 25 healthy controls) were enrolled. Our proposed approach with a random window showed clear improvement compared with traditional static and fixed window-based dynamic FC by using the linear SVM model. FCs related to the frontoparietal, somatomotor, dorsal attention, limbic and default mode networks played significant roles in differentiating SSD patients from healthy controls. Additionally, FCs between the somatomotor and frontoparietal networks made the greatest contribution to the classification model. Regarding brain regions, FCs related to the superior frontal gyrus, superior parietal lobule, superior temporal gyrus, amygdala, and orbital gyrus played significant roles. These findings suggest that networks and regions related to higher-order cognitive functions showed the most significant FC alterations in SSD, which may represent a compensatory collaboration of cognitive resources in SSD.

Remote firing propagation in the neural network of C. elegans

Understanding the mechanisms of firing propagation in brain networks has been a long-standing problem in the fields of nonlinear dynamics and network science. In general, it is believed that a specific firing in a brain network may be gradually propagated from a source node to its neighbors and then to the neighbors' neighbors and so on. Here, we explore firing propagation in the neural network of Caenorhabditis elegans and surprisingly find an abnormal phenomenon, i.e., remote firing propagation between two distant and indirectly connected nodes with the intermediate nodes being inactivated. This finding is robust to source nodes but depends on the topology of network such as the unidirectional couplings and heterogeneity of network. Further, a brief theoretical analysis is provided to explain its mechanism and a principle for remote firing propagation is figured out. This finding provides insights for us to understand how those cognitive subnetworks emerge in a brain network.

Effect of remote signal propagation in an empirical brain network

Increasing evidence has shown that brain functions are seriously influenced by the heterogeneous structure of a brain network, but little attention has been paid to the aspect of signal propagation. We here study how a signal is propagated from a source node to other nodes on an empirical brain network by a model of bistable oscillators. We find that the unique structure of the brain network favors signal propagation in contrast to other heterogeneous networks and homogeneous random networks. Surprisingly, we find an effect of remote propagation where a signal is not successfully propagated to the neighbors of the source node but to its neighbors' neighbors. To reveal its underlying mechanism, we simplify the heterogeneous brain network into a heterogeneous chain model and find that the accumulation of weak signals from multiple channels makes a strong input signal to the next node, resulting in remote propagation. Furthermore, a theoretical analysis is presented to explain these findings.

Brain Connectivity Studies on Structure-Function Relationships: A Short Survey with an Emphasis on Machine Learning

This short survey reviews the recent literature on the relationship between the brain structure and its functional dynamics. Imaging techniques such as diffusion tensor imaging (DTI) make it possible to reconstruct axonal fiber tracks and describe the structural connectivity (SC) between brain regions. By measuring fluctuations in neuronal activity, functional magnetic resonance imaging (fMRI) provides insights into the dynamics within this structural network. One key for a better understanding of brain mechanisms is to investigate how these fast dynamics emerge on a relatively stable structural backbone. So far, computational simulations and methods from graph theory have been mainly used for modeling this relationship. Machine learning techniques have already been established in neuroimaging for identifying functionally independent brain networks and classifying pathological brain states. This survey focuses on methods from machine learning, which contribute to our understanding of functional interactions between brain regions and their relation to the underlying anatomical substrate.

Understanding neural flexibility from a multifaceted definition

Flexibility is a hallmark of human intelligence. Emerging studies have proposed several flexibility measurements at the level of individual regions, to produce a brain map of neural flexibility. However, flexibility is usually inferred from separate components of brain activity (i.e., intrinsic/task-evoked), and different definitions are used. Moreover, recent studies have argued that neural processing may be more than a task-driven and intrinsic dichotomy. Therefore, the understanding to neural flexibility is still incomplete. To address this issue, we propose a multifaceted definition of neural flexibility according to three key features: broad cognitive engagement, distributed connectivity, and adaptive connectome dynamics. For these three features, we first review the advances in computational approaches, their functional relevance, and their potential pitfalls. We then suggest a set of metrics that can help us assign a flexibility rating to each region. Subsequently, we present an emergent probabilistic view for further understanding the functional operation of individual regions in the unified framework of intrinsic and task-driven states. Finally, we highlight several areas related to the multifaceted definition of neural flexibility for future research. This review not only strengthens our understanding of flexible human brain, but also suggests that the measure of neural flexibility could bridge the gap between understanding intrinsic and task-driven brain function dynamics.

Regulating heat conduction of complex networks by distributed nodes masses

Developing efficient strategy to regulate heat conduction is a challenging problem, with potential implication in the field of thermal materials. We here focus on a potential thermal material, i.e. complex networks of nanowires and nanotubes, and propose a model where the mass of each node is assigned proportional to its degree with [Formula: see text], to investigate how distributed nodes masses can impact the heat flow in a network. We find that the heat conduction of complex network can be either increased or decreased, depending on the controlling parameter [Formula: see text]. Especially, there is an optimal heat conduction at [Formula: see text] and it is independent of network topologies. Moreover, we find that the temperature distribution within a complex network is also strongly influenced by the controlling parameter [Formula: see text]. A brief theoretical analysis is provided to explain these results. These findings may open up appealing applications in the cases of demanding either increasing or decreasing heat conduction, and our approach of regulating heat conduction by distributed nodes masses may be also valuable to the challenge of controlling waste heat dissipation in highly integrated and miniaturized modern devices.

Mechanism for Strong Chimeras

Chimera states have attracted significant attention as symmetry-broken states exhibiting the unexpected coexistence of coherence and incoherence. Despite the valuable insights gained from analyzing specific systems, an understanding of the general physical mechanism underlying the emergence of chimeras is still lacking. Here, we show that many stable chimeras arise because coherence in part of the system is sustained by incoherence in the rest of the system. This mechanism may be regarded as a deterministic analog of noise-induced synchronization and is shown to underlie the emergence of strong chimeras. These are chimera states whose coherent domain is formed by identically synchronized oscillators. Recognizing this mechanism offers a new meaning to the interpretation that chimeras are a natural link between coherence and incoherence.

Evaluating the phase dynamics of coupled oscillators via time-variant topological features

By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient for identifying more specific behaviors. To improve this situation, we propose a topological approach that constructs the quantitative features describing the phase evolution of oscillators. Here, the phase data are mapped into a high-dimensional space at each time, and the topological features describing the shape of the data are subsequently extracted from the mapped points. These features are extended to time-variant topological features by adding the evolution time as an extra dimension in the topological feature space. The time-variant features provide crucial insights into the evolution of phase dynamics. Combining these features with the kernel method, we characterize the multiclustered synchronized dynamics during the early evolution stages. Finally, we demonstrate that our method can qualitatively explain chimera states. The experimental results confirmed the superiority of our method over those based on order parameters, especially when the available data are limited to the early-stage dynamics.

Estimating integrated information in bidirectional neuron-astrocyte communication

There is growing evidence that suggests the importance of astrocytes as elements for neural information processing through the modulation of synaptic transmission. A key aspect of this problem is understanding the impact of astrocytes in the information carried by compound events in neurons across time. In this paper, we investigate how the astrocytes participate in the information integrated by individual neurons in an ensemble through the measurement of "integrated information." We propose a computational model that considers bidirectional communication between astrocytes and neurons through glutamate-induced calcium signaling. Our model highlights the role of astrocytes in information processing through dynamical coordination. Our findings suggest that the astrocytic feedback promotes synergetic influences in the neural communication, which is maximized when there is a balance between excess correlation and spontaneous spiking activity. The results were further linked with additional measures such as net synergy and mutual information. This result reinforces the idea that astrocytes have integrative properties in communication among neurons.

Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure-dynamics relationship in human brain

Human cerebral cortex displays various dynamics patterns under different states, however the mechanism how such diverse patterns can be supported by the underlying brain network is still not well understood. Human brain has a unique network structure with different regions of interesting to perform cognitive tasks. Using coupled neural mass oscillators on human cortical network and paying attention to both global and local regions, we observe a new feature of chimera states with multiple spatial scales and a positive correlation between the synchronization preference of local region and the degree of symmetry of the connectivity of the region in the network. Further, we use the concept of effective symmetry in the network to build structural and dynamical hierarchical trees and find close matching between them. These results help to explain the multiple brain rhythms observed in experiments and suggest a generic principle for complex brain network as a structure substrate to support diverse functional patterns.