Robust transient dynamics and brain functions

Pathological cell assembly dynamics in a striatal MSN network model

Under normal conditions the principal cells of the striatum, medium spiny neurons (MSNs), show structured cell assembly activity patterns which alternate sequentially over exceedingly long timescales of many minutes. It is important to understand this activity since it is characteristically disrupted in multiple pathologies, such as Parkinson's disease and dyskinesia, and thought to be caused by alterations in the MSN to MSN lateral inhibitory connections and in the strength and distribution of cortical excitation to MSNs. To understand how these long timescales arise we extended a previous network model of MSN cells to include synapses with short-term plasticity, with parameters taken from a recent detailed striatal connectome study. We first confirmed the presence of sequentially switching cell clusters using the non-linear dimensionality reduction technique, Uniform Manifold Approximation and Projection (UMAP). We found that the network could generate non-stationary activity patterns varying extremely slowly on the order of minutes under biologically realistic conditions. Next we used Simulation Based Inference (SBI) to train a deep net to map features of the MSN network generated cell assembly activity to MSN network parameters. We used the trained SBI model to estimate MSN network parameters from ex-vivo brain slice calcium imaging data. We found that best fit network parameters were very close to their physiologically observed values. On the other hand network parameters estimated from Parkinsonian, decorticated and dyskinetic ex-vivo slice preparations were different. Our work may provide a pipeline for diagnosis of basal ganglia pathology from spiking data as well as for the design pharmacological treatments.

An investigation into the abnormal dynamic connection mechanism of generalized anxiety disorders based on non-homogeneous Markov models

BACKGROUND

The dynamic and hierarchical nature of the functional brain network. The neural dynamical systems tend to converge to multiple attractors (stable fixed points or dynamical states) in long run. Little is known about how the changes in this brain dynamic "long-term" behavior of the connectivity flow of brain network in generalized anxiety disorder (GAD).

METHODS

This study recruited 92 patients with GAD and 77 healthy controls (HC). We applied a reachable probability approach combining a Non-homogeneous Markov model with transition probability to quantify all possible connectivity flows and the hierarchical structure of brain functional systems at the dynamic level and the stationary probability vector (10-step transition probabilities) to describe the steady state of the system in the long run. A random forest algorithm was conducted to predict the severity of anxiety.

RESULTS

The dynamic functional patterns in distributed brain networks had larger possibility to converge in bilateral thalamus, posterior cingulate cortex (PCC), right superior occipital gyrus (SOG) and smaller possibility to converge in bilateral superior temporal gyrus (STG) and right parahippocampal gyrus (PHG) in patients with GAD compared to HC. The abnormal transition probability pattern could predict anxiety severity in patients with GAD.

LIMITATIONS

Small samples and subjects taking medications may have influenced our results. Future studies are expected to rule out the potential confounding effects.

CONCLUSION

Our results have revealed abnormal dynamic neural communication and integration in emotion regulation in patients with GAD, which give new insights to understand the dynamics of brain function of patients with GAD.

Heteroclinic networks for brain dynamics

Heteroclinic networks are a mathematical concept in dynamic systems theory that is suited to describe metastable states and switching events in brain dynamics. The framework is sensitive to external input and, at the same time, reproducible and robust against perturbations. Solutions of the corresponding differential equations are spatiotemporal patterns that are supposed to encode information both in space and time coordinates. We focus on the concept of winnerless competition as realized in generalized Lotka-Volterra equations and report on results for binding and chunking dynamics, synchronization on spatial grids, and entrainment to heteroclinic motion. We summarize proposals of how to design heteroclinic networks as desired in view of reproducing experimental observations from neuronal networks and discuss the subtle role of noise. The review is on a phenomenological level with possible applications to brain dynamics, while we refer to the literature for a rigorous mathematical treatment. We conclude with promising perspectives for future research.

On relaxation times of heteroclinic dynamics

Heteroclinic dynamics provide a suitable framework for describing transient dynamics such as cognitive processes in the brain. It is appreciated for being well reproducible and at the same time highly sensitive to external input. It is supposed to capture features of switching statistics between metastable states in the brain. Beyond the high sensitivity, a further desirable feature of these dynamics is to enable a fast adaptation to new external input. In view of this, we analyze relaxation times of heteroclinic motion toward a new resting state, when oscillations in heteroclinic networks are arrested by a quench of a bifurcation parameter from a parameter regime of oscillations to a regime of equilibrium states. As it turns out, the relaxation is underdamped and depends on the nesting of the attractor space, the size of the attractor's basin of attraction, the depth of the quench, and the level of noise. In the case of coupled heteroclinic units, it depends on the coupling strength, the coupling type, and synchronization between different units. Depending on how these factors are combined, finite relaxation times may support or impede a fast switching to new external input. Our results also shed some light on the discussion of how the stability of a system changes with its complexity.

Quasipotentials for coupled escape problems and the gate-height bifurcation

The escape statistics of a gradient dynamical system perturbed by noise can be estimated using properties of the associated potential landscape. More generally, the Freidlin and Wentzell quasipotential (QP) can be used for similar purposes, but computing this is nontrivial and it is only defined relative to some starting point. In this paper we focus on computing quasipotentials for coupled bistable units, numerically solving a Hamilton- Jacobi-Bellman type problem. We analyze noise induced transitions using the QP in cases where there is no potential for the coupled system. Gates (points on the boundary of basin of attraction that have minimal QP relative to that attractor) are used to understand the escape rates from the basin, but these gates can undergo a global change as coupling strength is changed. Such a global gate-height bifurcation is a generic qualitative transition in the escape properties of parametrized nongradient dynamical systems for small noise.

Extreme transient dynamics

We study the extreme transient dynamics of four self-excited pendula coupled via the movable beam. A slight difference in the pendula lengths induces the appearance of traveling phase behavior, within which the oscillators synchronize, but the phases between the nodes change in time. We discuss various scenarios of traveling states (involving different pendula) and their properties, comparing them with classical synchronization patterns of phase-locking. The research investigates the problem of transient dynamics preceding the stabilization of the network on a final synchronous attractor, showing that the width of transient windows can become extremely long. The relation between the behavior of the system within the transient regime and its initial conditions is examined and described. Our results include both identical and non-identical pendula masses, showing that the distribution of the latter ones is related to the transients. The research performed in this paper underlines possible transient problems occurring during the analysis of the systems when the slow evolution of the dynamics can be misinterpreted as the final behavior.

It's about time: Linking dynamical systems with human neuroimaging to understand the brain

Most human neuroscience research to date has focused on statistical approaches that describe stationary patterns of localized neural activity or blood flow. While these patterns are often interpreted in light of dynamic, information-processing concepts, the static, local, and inferential nature of the statistical approach makes it challenging to directly link neuroimaging results to plausible underlying neural mechanisms. Here, we argue that dynamical systems theory provides the crucial mechanistic framework for characterizing both the brain's time-varying quality and its partial stability in the face of perturbations, and hence, that this perspective can have a profound impact on the interpretation of human neuroimaging results and their relationship with behavior. After briefly reviewing some key terminology, we identify three key ways in which neuroimaging analyses can embrace a dynamical systems perspective: by shifting from a local to a more global perspective, by focusing on dynamics instead of static snapshots of neural activity, and by embracing modeling approaches that map neural dynamics using "forward" models. Through this approach, we envisage ample opportunities for neuroimaging researchers to enrich their understanding of the dynamic neural mechanisms that support a wide array of brain functions, both in health and in the setting of psychopathology.

Multistability and evolution of chimera states in a network of type II Morris-Lecar neurons with asymmetrical nonlocal inhibitory connections

Formation of synchronous activity patterns is an essential property of neuronal networks that has been of central interest to synchronization theory. Chimera states, where both synchronous and asynchronous activities of neurons co-exist in a single network, are particularly poignant examples of such patterns, whose dynamics and multistability may underlie brain function, such as cognitive tasks. However, dynamical mechanisms of coherent state formation in spiking neuronal networks as well as ways to control these states remain unclear. In this paper, we take a step in this direction by considering the evolution of chimera states in a network of class II excitable Morris-Lecar neurons with asymmetrical nonlocal inhibitory connections. Using the adaptive coherence measure, we are able to partition the network parameter space into regions of various collective behaviors (antiphase synchronous clusters, traveling waves, different types of chimera states as well as a spiking death regime) and have shown multistability between the various regimes. We track the evolution of the chimera states as a function of changed key network parameters and found transitions between various types of chimera states. We further find that the network can demonstrate long transients leading to quasi-persistence of activity patterns in the border regions hinting at near-criticality behaviors.

Oscillations and variability in neuronal systems: interplay of autonomous transient dynamics and fast deterministic fluctuations

Neuronal systems are subject to rapid fluctuations both intrinsically and externally. These fluctuations can be disruptive or constructive. We investigate the dynamic mechanisms underlying the interactions between rapidly fluctuating signals and the intrinsic properties of the target cells to produce variable and/or coherent responses. We use linearized and non-linear conductance-based models and piecewise constant (PWC) inputs with short duration pieces. The amplitude distributions of the constant pieces consist of arbitrary permutations of a baseline PWC function. In each trial within a given protocol we use one of these permutations and each protocol consists of a subset of all possible permutations, which is the only source of uncertainty in the protocol. We show that sustained oscillatory behavior can be generated in response to various forms of PWC inputs independently of whether the stable equilibria of the corresponding unperturbed systems are foci or nodes. The oscillatory voltage responses are amplified by the model nonlinearities and attenuated for conductance-based PWC inputs as compared to current-based PWC inputs, consistent with previous theoretical and experimental work. In addition, the voltage responses to PWC inputs exhibited variability across trials, which is reminiscent of the variability generated by stochastic noise (e.g., Gaussian white noise). Our analysis demonstrates that both oscillations and variability are the result of the interaction between the PWC input and the target cell's autonomous transient dynamics with little to no contribution from the dynamics in vicinities of the steady-state, and do not require input stochasticity.

Empirical Bayes estimation of pairwise maximum entropy model for nonlinear brain state dynamics

The pairwise maximum entropy model (pMEM) has recently gained widespread attention to exploring the nonlinear characteristics of brain state dynamics observed in resting-state functional magnetic resonance imaging (rsfMRI). Despite its unique advantageous features, the practical application of pMEM for individuals is limited as it requires a much larger sample than conventional rsfMRI scans. Thus, this study proposes an empirical Bayes estimation of individual pMEM using the variational expectation-maximization algorithm (VEM-MEM). The performance of the VEM-MEM is evaluated for several simulation setups with various sample sizes and network sizes. Unlike conventional maximum likelihood estimation procedures, the VEM-MEM can reliably estimate the individual model parameters, even with small samples, by effectively incorporating the group information as the prior. As a test case, the individual rsfMRI of children with attention deficit hyperactivity disorder (ADHD) is analyzed compared to that of typically developed children using the default mode network, executive control network, and salient network, obtained from the Healthy Brain Network database. We found that the nonlinear dynamic properties uniquely established on the pMEM differ for each group. Furthermore, pMEM parameters are more sensitive to group differences and are better associated with the behavior scores of ADHD compared to the Pearson correlation-based functional connectivity. The simulation and experimental results suggest that the proposed method can reliably estimate the individual pMEM and characterize the dynamic properties of individuals by utilizing empirical information of the group brain state dynamics.

State-Dependent Effective Connectivity in Resting-State fMRI

The human brain at rest exhibits intrinsic dynamics transitioning among the multiple metastable states of the inter-regional functional connectivity. Accordingly, the demand for exploring the state-specific functional connectivity increases for a deeper understanding of mental diseases. Functional connectivity, however, lacks information about the directed causal influences among the brain regions, called effective connectivity. This study presents the dynamic causal modeling (DCM) framework to explore the state-dependent effective connectivity using spectral DCM for the resting-state functional MRI (rsfMRI). We established the sequence of brain states using the hidden Markov model with the multivariate autoregressive coefficients of rsfMRI, summarizing the functional connectivity. We decomposed the state-dependent effective connectivity using a parametric empirical Bayes scheme that models the effective connectivity of consecutive windows with the time course of the discrete states as regressors. We showed the plausibility of the state-dependent effective connectivity analysis in a simulation setting. To test the clinical applicability, we applied the proposed method to characterize the state- and subtype-dependent effective connectivity of the default mode network in children with combined-type attention deficit hyperactivity disorder (ADHD-C) compared with age-matched, typically developed children (TDC). All 88 children were subtyped according to the occupation times (i.e., dwell times) of the three dominant functional connectivity states, independently of clinical diagnosis. The state-dependent effective connectivity differences between ADHD-C and TDC according to the subtypes and those between the subtypes of ADHD-C were expressed mainly in self-inhibition, magnifying the importance of excitation inhibition balance in the subtyping. These findings provide a clear motivation for decomposing the state-dependent dynamic effective connectivity and state-dependent analysis of the directed coupling in exploring mental diseases.

Intermittent evolution routes to the periodic or the chaotic orbits in Rulkov map

This paper concerns the intermittent evolution routes to the asymptotic regimes in the Rulkov map. That is, the windows with transient approximate periodic and transient chaotic behaviors occur alternatively before the system reaches the periodic or the chaotic orbits. Meanwhile, the evolution routes to chaotic orbits can be classified into different types according to the windows before reaching asymptotic chaotic states. In addition, the initial values can be regarded as a key factor affecting the asymptotic behaviors and the evolution routes. The effects of the initial values are given by parameter planes, bifurcation diagrams, and waveforms. In order to investigate whether the intermittent evolution routes can be learned by machine learning, some experiments are given to understanding the differences between the trajectories of the Rulkov map generated by the numerical simulations and predicted by the neural networks. These results show that there is about 60% accuracy rate of successfully predicting both the evolution routes and the asymptotic period-3 orbits using a three-layer feedforward neural network, while the bifurcation diagrams can be reconstructed using reservoir computing except a few parameter conditions.

A reachable probability approach for the analysis of spatio-temporal dynamics in the human functional network

The dynamic architecture of the human brain has been consistently observed. However, there is still limited modeling work to elucidate how neuronal circuits are hierarchically and flexibly organized in functional systems. Here we proposed a reachable probability approach based on non-homogeneous Markov chains, to characterize all possible connectivity flows and the hierarchical structure of brain functional systems at the dynamic level. We proved at the theoretical level the convergence of the functional brain network system, and demonstrated that this approach is able to detect network steady states across connectivity structure, particularly in areas of the default mode network. We further explored the dynamically hierarchical functional organization centered at the primary sensory cortices. We observed smaller optimal reachable steps to their local functional regions, and differentiated patterns in larger optimal reachable steps for primary perceptual modalities. The reachable paths with the largest and second largest transition probabilities between primary sensory seeds via multisensory integration regions were also tracked to explore the flexibility and plasticity of the multisensory integration. The present work provides a novel approach to depict both the stable and flexible hierarchical connectivity organization of the human brain.

Perception-driven dynamics of mimicry based on attractor field model

We provide a formal account of an interface that bridges two different levels of dynamic processes manifested by mimicry: prey-prey interactions and predators' perception. Mimicry is a coevolutionary process between an animate selective agent and at least two similar organisms selected by agent's perception-driven actions. Attractor field model explains perceived similarity of forms by noting that in both human and animal cognition, morphologically intermediate forms are more likely to be perceived as belonging to rare rather than abundant forms. We formalize this model in terms of predators' perception space deformation using numerical simulations and argue that the probability of confusion between similar species creates pressure on the perception space, which in turn leads to inflation of regions of perception space with high density of species representations. Such inflation causes increased discrimination between species by a predator, which implies that adaptive mimicry could initially emerge more easily among atypical species because they do not need the same level of similarity to the model. We provide a theoretical instrument to conceptualize interdependence between objective measurable matrices and perceived matrices of the same external reality. We believe that our framework leads to a more precise understanding of the evolution of mimicry.

Bayesian estimation of maximum entropy model for individualized energy landscape analysis of brain state dynamics

The pairwise maximum entropy model (MEM) for resting state functional MRI (rsfMRI) has been used to generate energy landscape of brain states and to explore nonlinear brain state dynamics. Researches using MEM, however, has mostly been restricted to fixed‐effect group‐level analyses, using concatenated time series across individuals, due to the need for large samples in the parameter estimation of MEM. To mitigate the small sample problem in analyzing energy landscapes for individuals, we propose a Bayesian estimation of individual MEM using variational Bayes approximation (BMEM). We evaluated the performances of BMEM with respect to sample sizes and prior information using simulation. BMEM showed advantages over conventional maximum likelihood estimation in reliably estimating model parameters for individuals with small sample data, particularly utilizing the empirical priors derived from group data. We then analyzed individual rsfMRI of the Human Connectome Project to show the usefulness of MEM in differentiating individuals and in exploring neural correlates for human behavior. MEM and its energy landscape properties showed high subject specificity comparable to that of functional connectivity. Canonical correlation analysis identified canonical variables for MEM highly associated with cognitive scores. Inter‐individual variations of cognitive scores were also reflected in energy landscape properties such as energies, occupation times, and basin sizes at local minima. We conclude that BMEM provides an efficient method to characterize dynamic properties of individuals using energy landscape analysis of individual brain states.

A Computational Framework for Controlling the Self-Restorative Brain Based on the Free Energy and Degeneracy Principles

The brain is a non-linear dynamical system with a self-restoration process, which protects itself from external damage but is often a bottleneck for clinical treatment. To treat the brain to induce the desired functionality, formulation of a self-restoration process is necessary for optimal brain control. This study proposes a computational model for the brain's self-restoration process following the free-energy and degeneracy principles. Based on this model, a computational framework for brain control is established. We posited that the pre-treatment brain circuit has long been configured in response to the environmental (the other neural populations') demands on the circuit. Since the demands persist even after treatment, the treated circuit's response to the demand may gradually approximate the pre-treatment functionality. In this framework, an energy landscape of regional activities, estimated from resting-state endogenous activities by a pairwise maximum entropy model, is used to represent the pre-treatment functionality. The approximation of the pre-treatment functionality occurs via reconfiguration of interactions among neural populations within the treated circuit. To establish the current framework's construct validity, we conducted various simulations. The simulations suggested that brain control should include the self-restoration process, without which the treatment was not optimal. We also presented simulations for optimizing repetitive treatments and optimal timing of the treatment. These results suggest a plausibility of the current framework in controlling the non-linear dynamical brain with a self-restoration process.

Deep Temporal Organization of fMRI Phase Synchrony Modes Promotes Large-Scale Disconnection in Schizophrenia

Itinerant dynamics of the brain generates transient and recurrent spatiotemporal patterns in neuroimaging data. Characterizing metastable functional connectivity (FC) - particularly at rest and using functional magnetic resonance imaging (fMRI) - has shaped the field of dynamic functional connectivity (DFC). Mainstream DFC research relies on (sliding window) correlations to identify recurrent FC patterns. Recently, functional relevance of the instantaneous phase synchrony (IPS) of fMRI signals has been revealed using imaging studies and computational models. In the present paper, we identify the repertoire of whole-brain inter-network IPS states at rest. Moreover, we uncover a hierarchy in the temporal organization of IPS modes. We hypothesize that connectivity disorder in schizophrenia (SZ) is related to the (deep) temporal arrangement of large-scale IPS modes. Hence, we analyze resting-state fMRI data from 68 healthy controls (HC) and 51 SZ patients. Seven resting-state networks (and their sub-components) are identified using spatial independent component analysis. IPS is computed between subject-specific network time courses, using analytic signals. The resultant phase coupling patterns, across time and subjects, are clustered into eight IPS states. Statistical tests show that the relative expression and mean lifetime of certain IPS states have been altered in SZ. Namely, patients spend (45%) less time in a globally coherent state and a subcortical-centered state, and (40%) more time in states reflecting anticoupling within the cognitive control network, compared to the HC. Moreover, the transition profile (between states) reveals a deep temporal structure, shaping two metastates with distinct phase synchrony profiles. A metastate is a collection of states such that within-metastate transitions are more probable than across. Remarkably, metastate occupation balance is altered in SZ, in favor of the less synchronous metastate that promotes disconnection across networks. Furthermore, the trajectory of IPS patterns is less efficient, less smooth, and more restricted in SZ subjects, compared to the HC. Finally, a regression analysis confirms the diagnostic value of the defined IPS measures for SZ identification, highlighting the distinctive role of metastate proportion. Our results suggest that the proposed IPS features may be used for classification studies and for characterizing phase synchrony modes in other (clinical) populations.

Dynamic effective connectivity

Metastability is a key source of itinerant dynamics in the brain; namely, spontaneous spatiotemporal reorganization of neuronal activity. This itinerancy has been the focus of numerous dynamic functional connectivity (DFC) analyses - developed to characterize the formation and dissolution of distributed functional patterns over time, using resting state fMRI. However, aside from technical and practical controversies, these approaches cannot recover the neuronal mechanisms that underwrite itinerant (e.g., metastable) dynamics-due to their descriptive, model-free nature. We argue that effective connectivity (EC) analyses are more apt for investigating the neuronal basis of metastability. To this end, we appeal to biologically-grounded models (i.e., dynamic causal modelling, DCM) and dynamical systems theory (i.e., heteroclinic sequential dynamics) to create a probabilistic, generative model of haemodynamic fluctuations. This model generates trajectories in the parametric space of EC modes (i.e., states of connectivity) that characterize functional brain architectures. In brief, it extends an established spectral DCM, to generate functional connectivity data features that change over time. This foundational paper tries to establish the model's face validity by simulating non-stationary fMRI time series and recovering key model parameters (i.e., transition probabilities among connectivity states and the parametric nature of these states) using variational Bayes. These data are further characterized using Bayesian model comparison (within and between subjects). Finally, we consider practical issues that attend applications and extensions of this scheme. Importantly, the scheme operates within a generic Bayesian framework - that can be adapted to study metastability and itinerant dynamics in any non-stationary time series.

Graph-theoretical analysis for energy landscape reveals the organization of state transitions in the resting-state human cerebral cortex

The resting-state brain is often considered a nonlinear dynamic system transitioning among multiple coexisting stable states. Despite the increasing number of studies on the multistability of the brain system, the processes of state transitions have rarely been systematically explored. Thus, we investigated the state transition processes of the human cerebral cortex system at rest by introducing a graph-theoretical analysis of the state transition network. The energy landscape analysis of brain state occurrences, estimated using the pairwise maximum entropy model for resting-state fMRI data, identified multiple local minima, some of which mediate multi-step transitions toward the global minimum. The state transition among local minima is clustered into two groups according to state transition rates and most inter-group state transitions were mediated by a hub transition state. The distance to the hub transition state determined the path length of the inter-group transition. The cortical system appeared to have redundancy in inter-group transitions when the hub transition state was removed. Such a hub-like organization of transition processes disappeared when the connectivity of the cortical system was altered from the resting-state configuration. In the state transition, the default mode network acts as a transition hub, while coactivation of the prefrontal cortex and default mode network is captured as the global minimum. In summary, the resting-state cerebral cortex has a well-organized architecture of state transitions among stable states, when evaluated by a graph-theoretical analysis of the nonlinear state transition network of the brain.

Dynamic functional connectivity states characterize NREM sleep and wakefulness

According to recent neuroimaging studies, temporal fluctuations in functional connectivity patterns can be clustered into dynamic functional connectivity (DFC) states and correspond to fluctuations in vigilance. However, whether there consistently exist DFC states associated with wakefulness and sleep stages and what are the characteristics and electrophysiological origin of these states remain unclear. The aims of the current study were to investigate the properties of DFC in different sleep stages and to explore the relationship between the characteristics of DFC and slow‐wave activity. We collected both eyes‐closed wakefulness and sleep data from 48 healthy young volunteers with simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) recordings. EEG data were employed as the gold standard of sleep stage scoring, and DFC states were estimated based on fMRI data. The results demonstrated that DFC states of the fMRI signals consistently corresponded to wakefulness and nonrapid eye movement sleep stages independent of the number of clusters. Furthermore, the mean dwell time of these states significantly correlated with slow‐wave activity. The inclusion or omission of regression of the global signal and the selection of parcellation schemes exerted minimal effects on the current findings. These results provide strong evidence that DFC states underlying fMRI signals match the fluctuations of vigilance and suggest a possible electrophysiological source of DFC states corresponding to vigilance states.

Reliable Sequential Activation of Neural Assemblies by Single Pyramidal Cells in a Three-Layered Cortex

Recent studies reveal the occasional impact of single neurons on surround firing statistics and even simple behaviors. Exploiting the advantages of a simple cortex, we examined the influence of single pyramidal neurons on surrounding cortical circuits. Brief activation of single neurons triggered reliable sequences of firing in tens of other excitatory and inhibitory cortical neurons, reflecting cascading activity through local networks, as indicated by delayed yet precisely timed polysynaptic subthreshold potentials. The evoked patterns were specific to the pyramidal cell of origin, extended over hundreds of micrometers from their source, and unfolded over up to 200 ms. Simultaneous activation of pyramidal cell pairs indicated balanced control of population activity, preventing paroxysmal amplification. Single cortical pyramidal neurons can thus trigger reliable postsynaptic activity that can propagate in a reliable fashion through cortex, generating rapidly evolving and non-random firing sequences reminiscent of those observed in mammalian hippocampus during "replay" and in avian song circuits.

Bifurcation analysis of the dynamics of interacting subnetworks of a spiking network

We analyze the collective dynamics of hierarchically structured networks of densely connected spiking neurons. These networks of sub-networks may represent interactions between cell assemblies or different nuclei in the brain. The dynamical activity pattern that results from these interactions depends on the strength of synaptic coupling between them. Importantly, the overall dynamics of a brain region in the absence of external input, so called ongoing brain activity, has been attributed to the dynamics of such interactions. In our study, two different network scenarios are considered: a system with one inhibitory and two excitatory subnetworks, and a network representation with three inhibitory subnetworks. To study the effect of synaptic strength on the global dynamics of the network, two parameters for relative couplings between these subnetworks are considered. For each case, a bifurcation analysis is performed and the results have been compared to large-scale network simulations. Our analysis shows that Generalized Lotka-Volterra (GLV) equations, well-known in predator-prey studies, yield a meaningful population-level description for the collective behavior of spiking neuronal interaction, which have a hierarchical structure. In particular, we observed a striking equivalence between the bifurcation diagrams of spiking neuronal networks and their corresponding GLV equations. This study gives new insight on the behavior of neuronal assemblies, and can potentially suggest new mechanisms for altering the dynamical patterns of spiking networks based on changing the synaptic strength between some groups of neurons.

Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI

A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. Here we advance a state space model (SSM) based on generative piecewise-linear recurrent neural networks (PLRNN) to assess dynamics from neuroimaging data. In contrast to many other nonlinear time series models which have been proposed for reconstructing latent dynamics, our model is easily interpretable in neural terms, amenable to systematic dynamical systems analysis of the resulting set of equations, and can straightforwardly be transformed into an equivalent continuous-time dynamical system. The major contributions of this paper are the introduction of a new observation model suitable for functional magnetic resonance imaging (fMRI) coupled to the latent PLRNN, an efficient stepwise training procedure that forces the latent model to capture the 'true' underlying dynamics rather than just fitting (or predicting) the observations, and of an empirical measure based on the Kullback-Leibler divergence to evaluate from empirical time series how well this goal of approximating the underlying dynamics has been achieved. We validate and illustrate the power of our approach on simulated 'ground-truth' dynamical systems as well as on experimental fMRI time series, and demonstrate that the learnt dynamics harbors task-related nonlinear structure that a linear dynamical model fails to capture. Given that fMRI is one of the most common techniques for measuring brain activity non-invasively in human subjects, this approach may provide a novel step toward analyzing aberrant (nonlinear) dynamics for clinical assessment or neuroscientific research.

Complex temporal patterns processing by a neural mass model of a cortical column

It is well known that neuronal networks are capable of transmitting complex spatiotemporal information in the form of precise sequences of neuronal discharges characterized by recurrent patterns. At the same time, the synchronized activity of large ensembles produces local field potentials that propagate through highly dynamic oscillatory waves, such that, at the whole brain scale, complex spatiotemporal dynamics of electroencephalographic (EEG) signals may be associated to sensorimotor decision making processes. Despite these experimental evidences, the link between highly temporally organized input patterns and EEG waves has not been studied in detail. Here, we use a neural mass model to investigate to what extent precise temporal information, carried by deterministic nonlinear attractor mappings, is filtered and transformed into fluctuations in phase, frequency and amplitude of oscillatory brain activity. The phase shift that we observe, when we drive the neural mass model with specific chaotic inputs, shows that the local field potential amplitude peak appears in less than one full cycle, thus allowing traveling waves to encode temporal information. After converting phase and amplitude changes obtained into point processes, we quantify input-output similarity following a threshold-filtering algorithm onto the amplitude wave peaks. Our analysis shows that the neural mass model has the capacity for gating the input signal and propagate selected temporal features of that signal. Finally, we discuss the effect of local excitatory/inhibitory balance on these results and how excitability in cortical columns, controlled by neuromodulatory innervation of the cerebral cortex, may contribute to set a fine tuning and gating of the information fed to the cortex.

Dynamic Computation in Visual Thalamocortical Networks

Contemporary neurodynamical frameworks, such as coordination dynamics and winnerless competition, posit that the brain approximates symbolic computation by transitioning between metastable attractive states. This article integrates these accounts with electrophysiological data suggesting that coherent, nested oscillations facilitate information representation and transmission in thalamocortical networks. We review the relationship between criticality, metastability, and representational capacity, outline existing methods for detecting metastable oscillatory patterns in neural time series data, and evaluate plausible spatiotemporal coding schemes based on phase alignment. We then survey the circuitry and the mechanisms underlying the generation of coordinated alpha and gamma rhythms in the primate visual system, with particular emphasis on the pulvinar and its role in biasing visual attention and awareness. To conclude the review, we begin to integrate this perspective with longstanding theories of consciousness and cognition.

Alternating activity patterns and a chimeralike state in a network of globally coupled excitable Morris-Lecar neurons

Spatiotemporal chaos collapses to either a rest state or a propagating pulse in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Adding global varying synaptic coupling to the ring network reveals complex transient behavior. Spatiotemporal chaos collapses into a transient pulse that reinitiates spatiotemporal chaos to allow sequential pattern switching until a collapse to the rest state. A domain of irregular neuron activity coexists with a domain of inactive neurons forming a transient chimeralike state. Transient spatial localization of the chimeralike state is observed for stronger synapses.

The Understanding Capacity and Information Dynamics in the Human Brain

This article proposes a theory of neuronal processes underlying cognition, focusing on the mechanisms of understanding in the human brain. Understanding is a product of mental modeling. The paper argues that mental modeling is a form of information production inside the neuronal system extending the reach of human cognition "beyond the information given" (Bruner, J.S., Beyond the Information Given, 1973). Mental modeling enables forms of learning and prediction (learning with understanding and prediction via explanation) that are unique to humans, allowing robust performance under unfamiliar conditions having no precedents in the past history. The proposed theory centers on the notions of self-organization and emergent properties of collective behavior in the neuronal substrate. The theory motivates new approaches in the design of intelligent artifacts (machine understanding) that are complementary to those underlying the technology of machine learning.

Neurogenetic profiles delineate large-scale connectivity dynamics of the human brain

Experimental and modeling work of neural activity has described recurrent and attractor dynamic patterns in cerebral microcircuits. However, it is still poorly understood whether similar dynamic principles exist or can be generalizable to the large-scale level. Here, we applied dynamic graph theory-based analyses to evaluate the dynamic streams of whole-brain functional connectivity over time across cognitive states. Dynamic connectivity in local networks is located in attentional areas during tasks and primary sensory areas during rest states, and dynamic connectivity in distributed networks converges in the default mode network (DMN) in both task and rest states. Importantly, we find that distinctive dynamic connectivity patterns are spatially associated with Allen Human Brain Atlas genetic transcription levels of synaptic long-term potentiation and long-term depression-related genes. Our findings support the neurobiological basis of large-scale attractor-like dynamics in the heteromodal cortex within the DMN, irrespective of cognitive state.

Discrete Sequential Information Coding: Heteroclinic Cognitive Dynamics

Discrete sequential information coding is a key mechanism that transforms complex cognitive brain activity into a low-dimensional dynamical process based on the sequential switching among finite numbers of patterns. The storage size of the corresponding process is large because of the permutation capacity as a function of control signals in ensembles of these patterns. Extracting low-dimensional functional dynamics from multiple large-scale neural populations is a central problem both in neuro- and cognitive- sciences. Experimental results in the last decade represent a solid base for the creation of low-dimensional models of different cognitive functions and allow moving toward a dynamical theory of consciousness. We discuss here a methodology to build simple kinetic equations that can be the mathematical skeleton of this theory. Models of the corresponding discrete information processing can be designed using the following dynamical principles: (i) clusterization of the neural activity in space and time and formation of information patterns; (ii) robustness of the sequential dynamics based on heteroclinic chains of metastable clusters; and (iii) sensitivity of such sequential dynamics to intrinsic and external informational signals. We analyze sequential discrete coding based on winnerless competition low-frequency dynamics. Under such dynamics, entrainment, and heteroclinic coordination leads to a large variety of coding regimes that are invariant in time.

Fundamental computational constraints on the time course of perception and action

A cognitive system faced with contingent events that cause rapid changes in sensory data may (i) incrementally incorporate new data into the ongoing perceptual and motor processing; or (ii) restart processing on each new event; or (iii) sample the data and hold onto the sample until its processing is complete, while disregarding any contingent changes. We offer a set of computational first-principles arguments for a hypothesis, according to which any system that contends with certain classes of perception and behavioral control tasks must include the sample-and-hold option (possibly alongside the other two, which may be useful in other tasks). This hypothesis has implications for understanding the dynamics of perception and action. In particular, a sample-and-hold channel necessarily processes sensory data on some kind of cycle (which does not imply precise periodicity). Further, being prepared to face the world at all times requires that the sampling that initiates each cycle be triggered by every significant action on part of the agent itself, such as saccades. We survey a range of evidence for the sample-and-hold functionality, touching upon diverse phenomena such as attentional blink and backward masking, the yoking of olfaction to respiration, thalamocortical interactions, and metastable brain dynamics in perception and consciousness.

Terminal Transient Phase of Chaotic Transients

Transient chaos in spatially extended systems can be characterized by the length of the transient phase, which typically grows quickly with the system size (supertransients). For a large class of these systems, the chaotic phase terminates abruptly, without any obvious precursors in commonly used observables. Here we investigate transient spatiotemporal chaos in two different models of this class. By probing the state space using perturbed trajectories we show the existence of a "terminal transient phase," which occurs prior to the abrupt collapse of chaotic dynamics. During this phase the impact of perturbations is significantly different from the earlier transient and particular patterns of (non)susceptible regions in state space occur close to the chaotic trajectories. We therefore hypothesize that even without perturbations proper precursors for the collapse of chaotic transients exist, which might be highly relevant for coping with spatiotemporal chaos in cardiac arrhythmias or brain functionality, for example.

Transient chaos and associated system-intrinsic switching of spacetime patterns in two synaptically coupled layers of Morris-Lecar neurons

Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a single layer of diffusively coupled, excitable Morris-Lecar neurons. Weak synaptic coupling of two such layers reveals system intrinsic switching of spatiotemporal activity patterns within and between the layers at irregular times. Within a layer, switching sequences include spatiotemporal chaos, erratic and regular pulse propagation, spontaneous network wide neuron activity, and rest state. A momentary substantial reduction in neuron activity in one layer can reinitiate transient spatiotemporal chaos in the other layer, which can induce a swap of spatiotemporal chaos with a pulse state between the layers. Presynaptic input maximizes the distance between propagating pulses, in contrast to pulse merging in the absence of synapses.

Hierarchical dynamics of informational patterns and decision-making

Traditional studies on the interaction of cognitive functions in healthy and disordered brains have used the analyses of the connectivity of several specialized brain networks-the functional connectome. However, emerging evidence suggests that both brain networks and functional spontaneous brain-wide network communication are intrinsically dynamic. In the light of studies investigating the cooperation between different cognitive functions, we consider here the dynamics of hierarchical networks in cognitive space. We show, using an example of behavioural decision-making based on sequential episodic memory, how the description of metastable pattern dynamics underlying basic cognitive processes helps to understand and predict complex processes like sequential episodic memory recall and competition among decision strategies. The mathematical images of the discussed phenomena in the phase space of the corresponding cognitive model are hierarchical heteroclinic networks. One of the most important features of such networks is the robustness of their dynamics. Different kinds of instabilities of these dynamics can be related to 'dynamical signatures' of creativity and different psychiatric disorders. The suggested approach can also be useful for the understanding of the dynamical processes that are the basis of consciousness.

Dynamical system with plastic self-organized velocity field as an alternative conceptual model of a cognitive system

It is well known that architecturally the brain is a neural network, i.e. a collection of many relatively simple units coupled flexibly. However, it has been unclear how the possession of this architecture enables higher-level cognitive functions, which are unique to the brain. Here, we consider the brain from the viewpoint of dynamical systems theory and hypothesize that the unique feature of the brain, the self-organized plasticity of its architecture, could represent the means of enabling the self-organized plasticity of its velocity vector field. We propose that, conceptually, the principle of cognition could amount to the existence of appropriate rules governing self-organization of the velocity field of a dynamical system with an appropriate account of stimuli. To support this hypothesis, we propose a simple non-neuromorphic mathematical model with a plastic self-organized velocity field, which has no prototype in physical world. This system is shown to be capable of basic cognition, which is illustrated numerically and with musical data. Our conceptual model could provide an additional insight into the working principles of the brain. Moreover, hardware implementations of plastic velocity fields self-organizing according to various rules could pave the way to creating artificial intelligence of a novel type.

Initial-state-dependent, robust, transient neural dynamics encode conscious visual perception

Recent research has identified late-latency, long-lasting neural activity as a robust correlate of conscious perception. Yet, the dynamical nature of this activity is poorly understood, and the mechanisms governing its presence or absence and the associated conscious perception remain elusive. We applied dynamic-pattern analysis to whole-brain slow (< 5 Hz) cortical dynamics recorded by magnetoencephalography (MEG) in human subjects performing a threshold-level visual perception task. Up to 1 second before stimulus onset, brain activity pattern across widespread cortices significantly predicted whether a threshold-level visual stimulus was later consciously perceived. This initial state of brain activity interacts nonlinearly with stimulus input to shape the evolving cortical activity trajectory, with seen and unseen trials following well separated trajectories. We observed that cortical activity trajectories during conscious perception are fast evolving and robust to small variations in the initial state. In addition, spontaneous brain activity pattern prior to stimulus onset also influences unconscious perceptual making in unseen trials. Together, these results suggest that brain dynamics underlying conscious visual perception belongs to the class of initial-state-dependent, robust, transient neural dynamics.

What brain mechanisms underlie conscious perception? A commonly adopted paradigm for studying this question is to present human subjects with threshold-level stimuli. When shown repeatedly, the same stimulus is sometimes consciously perceived, sometimes not. Using magnetoencephalography, we shed light on the neural mechanisms governing whether the stimulus is consciously perceived in a given trial. We observed that depending on the initial brain state defined by widespread activity pattern in the slow cortical potential (<5 Hz) range, a physically identical, brief (30–60 ms) stimulus input triggers distinct sequences of activity pattern evolution over time that correspond to either consciously perceiving the stimulus or not. Such activity pattern evolution forms a “trajectory” in the state space and affords significant single-trial decoding of perceptual outcome from 1 sec before to 3 sec after stimulus onset. While previous theories on conscious perception have emphasized sustained, high-level activity, we found that brain dynamics underlying conscious perception exhibit fast-changing activity patterns. These results significantly further our understanding on the neural mechanisms governing conscious access of a stimulus and the dynamical nature of distributed neural activity underlying conscious perception.

Computing by Robust Transience: How the Fronto-Parietal Network Performs Sequential, Category-Based Decisions

Decision making involves dynamic interplay between internal judgements and external perception, which has been investigated in delayed match-to-category (DMC) experiments. Our analysis of neural recordings shows that, during DMC tasks, LIP and PFC neurons demonstrate mixed, time-varying, and heterogeneous selectivity, but previous theoretical work has not established the link between these neural characteristics and population-level computations. We trained a recurrent network model to perform DMC tasks and found that the model can remarkably reproduce key features of neuronal selectivity at the single-neuron and population levels. Analysis of the trained networks elucidates that robust transient trajectories of the neural population are the key driver of sequential categorical decisions. The directions of trajectories are governed by network self-organized connectivity, defining a "neural landscape" consisting of a task-tailored arrangement of slow states and dynamical tunnels. With this model, we can identify functionally relevant circuit motifs and generalize the framework to solve other categorization tasks.

On wakefulness fluctuations as a source of BOLD functional connectivity dynamics

Human brain dynamics and functional connectivity fluctuate over a range of temporal scales in coordination with internal states and environmental demands. However, the neurobiological significance and consequences of functional connectivity dynamics during rest have not yet been established. We show that the coarse-grained clustering of whole-brain dynamic connectivity measured with magnetic resonance imaging reveals discrete patterns (dynamic connectivity states) associated with wakefulness and sleep. We validate this using EEG in healthy subjects and patients with narcolepsy and by matching our results with previous findings in a large collaborative database. We also show that drowsiness may account for previous reports of metastable connectivity states associated with different levels of functional integration. This implies that future studies of transient functional connectivity must independently monitor wakefulness. We conclude that a possible neurobiological significance of dynamic connectivity states, computed at a sufficiently coarse temporal scale, is that of fluctuations in wakefulness.

Brain network dynamics in high-functioning individuals with autism

Theoretically, autism should be underpinned by aberrant brain dynamics. However, how brain activity changes over time in individuals with autism spectrum disorder (ASD) remains unknown. Here we characterize brain dynamics in autism using an energy-landscape analysis applied to resting-state fMRI data. Whereas neurotypical brain activity frequently transits between two major brain states via an intermediate state, high-functioning adults with ASD show fewer neural transitions due to an unstable intermediate state, and these infrequent transitions predict the severity of autism. Moreover, in contrast to the controls whose IQ is correlated with the neural transition frequency, IQ scores of individuals with ASD are instead predicted by the stability of their brain dynamics. Finally, such brain–behaviour associations are related to functional segregation between brain networks. These findings suggest that atypical functional coordination in the brains of adults with ASD underpins overly stable neural dynamics, which supports both their ASD symptoms and cognitive abilities.

Though individuals with autism spectrum disorder (ASD) show a number of neural abnormalities, the relationship between global dynamic neural patterns and ASD symptoms remains unclear. Here, authors describe such global brain dynamics, relate these to cognitive abilities, ASD symptoms, and predict ASD diagnosis.

Multistability and Long-Timescale Transients Encoded by Network Structure in a Model of C. elegans Connectome Dynamics

The neural dynamics of the nematode Caenorhabditis elegans are experimentally low-dimensional and may be understood as long-timescale transitions between multiple low-dimensional attractors. Previous modeling work has found that dynamic models of the worm's full neuronal network are capable of generating reasonable dynamic responses to certain inputs, even when all neurons are treated as identical save for their connectivity. This study investigates such a model of C. elegans neuronal dynamics, finding that a wide variety of multistable responses are generated in response to varied inputs. Specifically, we generate bifurcation diagrams for all possible single-neuron inputs, showing the existence of fixed points and limit cycles for different input regimes. The nature of the dynamical response is seen to vary according to the type of neuron receiving input; for example, input into sensory neurons is more likely to drive a bifurcation in the system than input into motor neurons. As a specific example we consider compound input into the neuron pairs PLM and ASK, discovering bistability of a limit cycle and a fixed point. The transient timescales in approaching each of these states are much longer than any intrinsic timescales of the system. This suggests consistency of our model with the characterization of dynamics in neural systems as long-timescale transitions between discrete, low-dimensional attractors corresponding to behavioral states.

Iterative free-energy optimization for recurrent neural networks (INFERNO)

The intra-parietal lobe coupled with the Basal Ganglia forms a working memory that demonstrates strong planning capabilities for generating robust yet flexible neuronal sequences. Neurocomputational models however, often fails to control long range neural synchrony in recurrent spiking networks due to spontaneous activity. As a novel framework based on the free-energy principle, we propose to see the problem of spikes' synchrony as an optimization problem of the neurons sub-threshold activity for the generation of long neuronal chains. Using a stochastic gradient descent, a reinforcement signal (presumably dopaminergic) evaluates the quality of one input vector to move the recurrent neural network to a desired activity; depending on the error made, this input vector is strengthened to hill-climb the gradient or elicited to search for another solution. This vector can be learned then by one associative memory as a model of the basal-ganglia to control the recurrent neural network. Experiments on habit learning and on sequence retrieving demonstrate the capabilities of the dual system to generate very long and precise spatio-temporal sequences, above two hundred iterations. Its features are applied then to the sequential planning of arm movements. In line with neurobiological theories, we discuss its relevance for modeling the cortico-basal working memory to initiate flexible goal-directed neuronal chains of causation and its relation to novel architectures such as Deep Networks, Neural Turing Machines and the Free-Energy Principle.

Metastable Pain-Attention Dynamics during Incremental Exhaustive Exercise

Background: Pain attracts attention on the bodily regions. Attentional allocation toward pain results from the neural communication across the brain-wide network "connectome" which consists of pain-attention related circuits. Connectome is intrinsically dynamic and spontaneously fluctuating on multiple time-scales. The present study delineates the pain-attention dynamics during incremental cycling performed until volitional exhaustion and investigates the potential presence of nested metastable dynamics. Method: Fifteen young and physically active adults completed a progressive incremental cycling test and reported their discomfort and pain on a body map every 15 s. Results: The analyses revealed that the number of body locations with perceived pain and discomfort increased throughout five temporal windows reaching an average of 4.26 ± 0.59 locations per participant. A total of 37 different locations were reported and marked as painful for all participants throughout the cycling task. Significant differences in entropy were observed between all temporal windows except the fourth and fifth windows. Transient dynamics of bodily locations with perceived discomfort and pain were spanned by three principal components. The metastable dynamics of the body pain locations groupings over time were discerned by three time scales: (1) the time scale of shifts (15 s); (2) the time scale of metastable configurations (100 s), and (3) the observational time scale (1000 s). Conclusion: The results of this study indicate that body locations perceived as painful increase throughout the incremental cycling task following a switching metastable and nested dynamics. These findings support the view that human brain is intrinsically organized into active, mutually interacting complex and nested functional networks, and that subjective experiences inherent in pain perception depict identical dynamical principles to the neural tissue in the brain.

Comparison of Functional Connectivity Estimated from Concatenated Task-State Data from Block-Design Paradigm with That of Continuous Task

Functional connectivity (FC) analysis with data collected as continuous tasks and activation analysis using data from block-design paradigms are two main methods to investigate the task-induced brain activation. If the concatenated data of task blocks extracted from the block-design paradigm could provide equivalent FC information to that derived from continuous task data, it would shorten the data collection time and simplify experimental procedures, and the already collected data of block-design paradigms could be reanalyzed from the perspective of FC. Despite being used in many studies, such a hypothesis of equivalence has not yet been tested from multiple perspectives. In this study, we collected fMRI blood-oxygen-level-dependent signals from 24 healthy subjects during a continuous task session as well as in block-design task sessions. We compared concatenated task blocks and continuous task data in terms of region of interest- (ROI-) based FC, seed-based FC, and brain network topology during a short motor task. According to our results, the concatenated data was not significantly different from the continuous data in multiple aspects, indicating the potential of using concatenated data to estimate task-state FC in short motor tasks. However, even under appropriate experimental conditions, the interpretation of FC results based on concatenated data should be cautious and take the influence due to inherent information loss during concatenation into account.

Cell Assembly Dynamics of Sparsely-Connected Inhibitory Networks: A Simple Model for the Collective Activity of Striatal Projection Neurons

Striatal projection neurons form a sparsely-connected inhibitory network, and this arrangement may be essential for the appropriate temporal organization of behavior. Here we show that a simplified, sparse inhibitory network of Leaky-Integrate-and-Fire neurons can reproduce some key features of striatal population activity, as observed in brain slices. In particular we develop a new metric to determine the conditions under which sparse inhibitory networks form anti-correlated cell assemblies with time-varying activity of individual cells. We find that under these conditions the network displays an input-specific sequence of cell assembly switching, that effectively discriminates similar inputs. Our results support the proposal that GABAergic connections between striatal projection neurons allow stimulus-selective, temporally-extended sequential activation of cell assemblies. Furthermore, we help to show how altered intrastriatal GABAergic signaling may produce aberrant network-level information processing in disorders such as Parkinson's and Huntington's diseases.

Literary narrative as a cognitive structure in the brain

This paper proposes that literary narrative is the result of an unconscious computation in the brain, a computation that arises from the dynamical interaction of specific innate and representational lower-order neuronal circuits and mappings. It is also proposed that these specific circuits constitute the fundamental building blocks of literary narrative. The analysis further suggests that as literary narrative evolves in the brain, its development is influenced by an evolutionarily-biased broad class of attractors known as archetypes. In this context, a description of literary narrative is devised, and six phases leading to the production of literary narrative are then identified. The description presented here may have applications in the production of literary narrative by artificial systems.

Learning of Chunking Sequences in Cognition and Behavior

We often learn and recall long sequences in smaller segments, such as a phone number 858 534 22 30 memorized as four segments. Behavioral experiments suggest that humans and some animals employ this strategy of breaking down cognitive or behavioral sequences into chunks in a wide variety of tasks, but the dynamical principles of how this is achieved remains unknown. Here, we study the temporal dynamics of chunking for learning cognitive sequences in a chunking representation using a dynamical model of competing modes arranged to evoke hierarchical Winnerless Competition (WLC) dynamics. Sequential memory is represented as trajectories along a chain of metastable fixed points at each level of the hierarchy, and bistable Hebbian dynamics enables the learning of such trajectories in an unsupervised fashion. Using computer simulations, we demonstrate the learning of a chunking representation of sequences and their robust recall. During learning, the dynamics associates a set of modes to each information-carrying item in the sequence and encodes their relative order. During recall, hierarchical WLC guarantees the robustness of the sequence order when the sequence is not too long. The resulting patterns of activities share several features observed in behavioral experiments, such as the pauses between boundaries of chunks, their size and their duration. Failures in learning chunking sequences provide new insights into the dynamical causes of neurological disorders such as Parkinson’s disease and Schizophrenia.

Because chunking is a hallmark of the brain’s organization, efforts to understand its dynamics can provide valuable insights into the brain and its disorders. For identifying the dynamical principles of chunking learning, we hypothesize that perceptual sequences can be learned and stored as a chain of metastable fixed points in a low-dimensional dynamical system, similar to the trajectory of a ball rolling down a pinball machine. During a learning phase, the interactions in the network evolve such that the network learns a chunking representation of the sequence, as when memorizing a phone number in segments. In the example of the pinball machine, learning can be identified with the gradual placement of the pins. After learning, the pins are placed in a way that, at each run, the ball follows the same trajectory (recall of the same sequence) that encodes the perceptual sequence. Simulations show that the dynamics are endowed with the hallmarks of chunking observed in behavioral experiments, such as increased delays observed before loading new chunks.

Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the “within” versus “between” connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed “winnerless competition”, which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a general approach to study the dynamics of interacting populations of spiking networks.