Neuroscience. Transient dynamics for neural processing

Transient dynamics and their control in time-delay autonomous Boolean ring networks

Biochemical systems with switch-like interactions, such as gene regulatory networks, are well modeled by autonomous Boolean networks. Specifically, the topology and logic of gene interactions can be described by systems of continuous piecewise-linear differential equations, enabling analytical predictions of the dynamics of specific networks. However, most models do not account for time delays along links associated with spatial transport, mRNA transcription, and translation. To address this issue, we have developed an experimental test bed to realize a time-delay autonomous Boolean network with three inhibitory nodes, known as a repressilator, and use it to study the dynamics that arise as time delays along the links vary. We observe various nearly periodic oscillatory transient patterns with extremely long lifetime, which emerge in small network motifs due to the delay, and which are distinct from the eventual asymptotically stable periodic attractors. For repeated experiments with a given network, we find that stochastic processes give rise to a broad distribution of transient times with an exponential tail. In some cases, the transients are so long that it is doubtful the attractors will ever be approached in a biological system that has a finite lifetime. To counteract the long transients, we show experimentally that small, occasional perturbations applied to the time delays can force the trajectories to rapidly approach the attractors.

Dynamical regimes of four oscillators with excitatory pulse coupling

Dynamics of four almost identical chemical oscillators pulse coupled via excitatory coupling with time delays are systematically studied.

Hierarchical Chunking of Sequential Memory on Neuromorphic Architecture with Reduced Synaptic Plasticity

Chunking refers to a phenomenon whereby individuals group items together when performing a memory task to improve the performance of sequential memory. In this work, we build a bio-plausible hierarchical chunking of sequential memory (HCSM) model to explain why such improvement happens. We address this issue by linking hierarchical chunking with synaptic plasticity and neuromorphic engineering. We uncover that a chunking mechanism reduces the requirements of synaptic plasticity since it allows applying synapses with narrow dynamic range and low precision to perform a memory task. We validate a hardware version of the model through simulation, based on measured memristor behavior with narrow dynamic range in neuromorphic circuits, which reveals how chunking works and what role it plays in encoding sequential memory. Our work deepens the understanding of sequential memory and enables incorporating it for the investigation of the brain-inspired computing on neuromorphic architecture.

Spintronic Nanodevices for Bioinspired Computing

Bioinspired hardware holds the promise of low-energy, intelligent, and highly adaptable computing systems. Applications span from automatic classification for big data management, through unmanned vehicle control, to control for biomedical prosthesis. However, one of the major challenges of fabricating bioinspired hardware is building ultra-high-density networks out of complex processing units interlinked by tunable connections. Nanometer-scale devices exploiting spin electronics (or spintronics) can be a key technology in this context. In particular, magnetic tunnel junctions (MTJs) are well suited for this purpose because of their multiple tunable functionalities. One such functionality, non-volatile memory, can provide massive embedded memory in unconventional circuits, thus escaping the von-Neumann bottleneck arising when memory and processors are located separately. Other features of spintronic devices that could be beneficial for bioinspired computing include tunable fast nonlinear dynamics, controlled stochasticity, and the ability of single devices to change functions in different operating conditions. Large networks of interacting spintronic nanodevices can have their interactions tuned to induce complex dynamics such as synchronization, chaos, soliton diffusion, phase transitions, criticality, and convergence to multiple metastable states. A number of groups have recently proposed bioinspired architectures that include one or several types of spintronic nanodevices. In this paper, we show how spintronics can be used for bioinspired computing. We review the different approaches that have been proposed, the recent advances in this direction, and the challenges toward fully integrated spintronics complementary metal-oxide-semiconductor (CMOS) bioinspired hardware.

Basin entropy: a new tool to analyze uncertainty in dynamical systems

In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied. Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log2, the basin is fractal.

Non-reward neural mechanisms in the orbitofrontal cortex

Single neurons in the primate orbitofrontal cortex respond when an expected reward is not obtained, and behaviour must change. The human lateral orbitofrontal cortex is activated when non-reward, or loss occurs. The neuronal computation of this negative reward prediction error is fundamental for the emotional changes associated with non-reward, and with changing behaviour. Little is known about the neuronal mechanism. Here we propose a mechanism, which we formalize into a neuronal network model, which is simulated to enable the operation of the mechanism to be investigated. A single attractor network has a reward population (or pool) of neurons that is activated by expected reward, and maintain their firing until, after a time, synaptic depression reduces the firing rate in this neuronal population. If a reward outcome is not received, the decreasing firing in the reward neurons releases the inhibition implemented by inhibitory neurons, and this results in a second population of non-reward neurons to start and continue firing encouraged by the spiking-related noise in the network. If a reward outcome is received, this keeps the reward attractor active, and this through the inhibitory neurons prevents the non-reward attractor neurons from being activated. If an expected reward has been signalled, and the reward attractor neurons are active, their firing can be directly inhibited by a non-reward outcome, and the non-reward neurons become activated because the inhibition on them is released. The neuronal mechanisms in the orbitofrontal cortex for computing negative reward prediction error are important, for this system may be over-reactive in depression, under-reactive in impulsive behaviour, and may influence the dopaminergic 'prediction error' neurons.

Charting moment-to-moment brain signal variability from early to late childhood

Large-scale brain signals exhibit rich intermittent patterning, reflecting the fact that the cortex actively eschews fixed points in favor of itinerant wandering with frequent state transitions. Fluctuations in endogenous cortical activity occur at multiple time scales and index a dynamic repertoire of network states that are continuously explored, even in the absence of external sensory inputs. Here, we quantified such moment-to-moment brain signal variability at rest in a large, cross-sectional sample of children ranging in age from seven to eleven years. Our findings revealed a monotonic rise in the complexity of electroencephalogram (EEG) signals as measured by sample entropy, from the youngest to the oldest age cohort, across a range of time scales and spatial regions. From year to year, the greatest changes in intraindividual brain signal variability were recorded at electrodes covering the anterior cortical zones. These results provide converging evidence concerning the age-dependent expansion of functional cortical network states during a critical developmental period ranging from early to late childhood.

Neural activity of orbitofrontal cortex contributes to control of waiting

The willingness to wait for delayed reward and information is of fundamental importance for deliberative behaviors. The orbitofrontal cortex (OFC) is thought to be a core component of the neural circuitry underlying the capacity to control waiting. However, the neural correlates of active waiting and the causal role of the OFC in the control of waiting still remain largely unknown. Here, we trained rats to perform a waiting task (waiting for a pseudorandom time to obtain the water reward), and recorded neuronal ensembles in the OFC throughout the task. We observed that subset OFC neurons exhibited ramping activities throughout the waiting process. Receiver operating characteristic analysis showed that neural activities during the waiting period even predicted the trial outcomes (patient vs. impatient) on a trial-by-trial basis. Furthermore, optogenetic activation of the OFC during the waiting period improved the waiting performance, but did not influence rats' movement to obtain the reward. Taken together, these findings reveal that the neural activity in the OFC contributes to the control of waiting.

Suppressing epileptic activity in a neural mass model using a closed-loop proportional-integral controller

Closed-loop control is a promising deep brain stimulation (DBS) strategy that could be used to suppress high-amplitude epileptic activity. However, there are currently no analytical approaches to determine the stimulation parameters for effective and safe treatment protocols. Proportional-integral (PI) control is the most extensively used closed-loop control scheme in the field of control engineering because of its simple implementation and perfect performance. In this study, we took Jansen's neural mass model (NMM) as a test bed to develop a PI-type closed-loop controller for suppressing epileptic activity. A graphical stability analysis method was employed to determine the stabilizing region of the PI controller in the control parameter space, which provided a theoretical guideline for the choice of the PI control parameters. Furthermore, we established the relationship between the parameters of the PI controller and the parameters of the NMM in the form of a stabilizing region, which provided insights into the mechanisms that may suppress epileptic activity in the NMM. The simulation results demonstrated the validity and effectiveness of the proposed closed-loop PI control scheme.

Spike-Based Bayesian-Hebbian Learning of Temporal Sequences

Many cognitive and motor functions are enabled by the temporal representation and processing of stimuli, but it remains an open issue how neocortical microcircuits can reliably encode and replay such sequences of information. To better understand this, a modular attractor memory network is proposed in which meta-stable sequential attractor transitions are learned through changes to synaptic weights and intrinsic excitabilities via the spike-based Bayesian Confidence Propagation Neural Network (BCPNN) learning rule. We find that the formation of distributed memories, embodied by increased periods of firing in pools of excitatory neurons, together with asymmetrical associations between these distinct network states, can be acquired through plasticity. The model’s feasibility is demonstrated using simulations of adaptive exponential integrate-and-fire model neurons (AdEx). We show that the learning and speed of sequence replay depends on a confluence of biophysically relevant parameters including stimulus duration, level of background noise, ratio of synaptic currents, and strengths of short-term depression and adaptation. Moreover, sequence elements are shown to flexibly participate multiple times in the sequence, suggesting that spiking attractor networks of this type can support an efficient combinatorial code. The model provides a principled approach towards understanding how multiple interacting plasticity mechanisms can coordinate hetero-associative learning in unison.

From one moment to the next, in an ever-changing world, and awash in a deluge of sensory data, the brain fluidly guides our actions throughout an astonishing variety of tasks. Processing this ongoing bombardment of information is a fundamental problem faced by its underlying neural circuits. Given that the structure of our actions along with the organization of the environment in which they are performed can be intuitively decomposed into sequences of simpler patterns, an encoding strategy reflecting the temporal nature of these patterns should offer an efficient approach for assembling more complex memories and behaviors. We present a model that demonstrates how activity could propagate through recurrent cortical microcircuits as a result of a learning rule based on neurobiologically plausible time courses and dynamics. The model predicts that the interaction between several learning and dynamical processes constitute a compound mnemonic engram that can flexibly generate sequential step-wise increases of activity within neural populations.

Building a minimum frustration framework for brain functions over long time scales

The minimum frustration principle (MFP) is a computational approach stating that, over the long time scales of evolution, proteins' free energy decreases more than expected by thermodynamical constraints as their amino acids assume conformations progressively closer to the lowest energetic state. This Review shows that this general principle, borrowed from protein folding dynamics, can also be fruitfully applied to nervous function. Highlighting the foremost role of energetic requirements, macromolecular dynamics, and above all intertwined time scales in brain activity, the MFP elucidates a wide range of mental processes from sensations to memory retrieval. Brain functions are compared with trajectories that, over long nervous time scales, are attracted toward the low-energy bottom of funnel-like structures characterized by both robustness and plasticity. We discuss how the principle, derived explicitly from evolution and selection of a funneling structure from microdynamics of contacts, is unlike other brain models equipped with energy landscapes, such as the Bayesian and free energy principles and the Hopfield networks. In summary, we make available a novel approach to brain function cast in a biologically informed fashion, with the potential to be operationalized and assessed empirically. © 2016 Wiley Periodicals, Inc.

State-Dependent Propagation of Neuronal Sub-Population in Spontaneous Synchronized Bursts

Repeating stable spatiotemporal patterns emerge in synchronized spontaneous activity in neuronal networks. The repertoire of such patterns can serve as memory, or a reservoir of information, in a neuronal network; moreover, the variety of patterns may represent the network memory capacity. However, a neuronal substrate for producing a repertoire of patterns in synchronization remains elusive. We herein hypothesize that state-dependent propagation of a neuronal sub-population is the key mechanism. By combining high-resolution measurement with a 4096-channel complementary metal-oxide semiconductor (CMOS) microelectrode array (MEA) and dimensionality reduction with non-negative matrix factorization (NMF), we investigated synchronized bursts of dissociated rat cortical neurons at approximately 3 weeks in vitro. We found that bursts had a repertoire of repeating spatiotemporal patterns, and different patterns shared a partially similar sequence of sub-population, supporting the idea of sequential structure of neuronal sub-populations during synchronized activity. We additionally found that similar spatiotemporal patterns tended to appear successively and periodically, suggesting a state-dependent fluctuation of propagation, which has been overlooked in existing literature. Thus, such a state-dependent property within the sequential sub-population structure is a plausible neural substrate for performing a repertoire of stable patterns during synchronized activity.

FPGA-Based Stochastic Echo State Networks for Time-Series Forecasting

Hardware implementation of artificial neural networks (ANNs) allows exploiting the inherent parallelism of these systems. Nevertheless, they require a large amount of resources in terms of area and power dissipation. Recently, Reservoir Computing (RC) has arisen as a strategic technique to design recurrent neural networks (RNNs) with simple learning capabilities. In this work, we show a new approach to implement RC systems with digital gates. The proposed method is based on the use of probabilistic computing concepts to reduce the hardware required to implement different arithmetic operations. The result is the development of a highly functional system with low hardware resources. The presented methodology is applied to chaotic time-series forecasting.

Recurrent Spiking Networks Solve Planning Tasks

A recurrent spiking neural network is proposed that implements planning as probabilistic inference for finite and infinite horizon tasks. The architecture splits this problem into two parts: The stochastic transient firing of the network embodies the dynamics of the planning task. With appropriate injected input this dynamics is shaped to generate high-reward state trajectories. A general class of reward-modulated plasticity rules for these afferent synapses is presented. The updates optimize the likelihood of getting a reward through a variant of an Expectation Maximization algorithm and learning is guaranteed to convergence to a local maximum. We find that the network dynamics are qualitatively similar to transient firing patterns during planning and foraging in the hippocampus of awake behaving rats. The model extends classical attractor models and provides a testable prediction on identifying modulating contextual information. In a real robot arm reaching and obstacle avoidance task the ability to represent multiple task solutions is investigated. The neural planning method with its local update rules provides the basis for future neuromorphic hardware implementations with promising potentials like large data processing abilities and early initiation of strategies to avoid dangerous situations in robot co-worker scenarios.

Effects of self-coupling and asymmetric output on metastable dynamical transient firing patterns in arrays of neurons with bidirectional inhibitory coupling

Metastable dynamical transient patterns in arrays of bidirectionally coupled neurons with self-coupling and asymmetric output were studied. First, an array of asymmetric sigmoidal neurons with symmetric inhibitory bidirectional coupling and self-coupling was considered and the bifurcations of its steady solutions were shown. Metastable dynamical transient spatially nonuniform states existed in the presence of a pair of spatially symmetric stable solutions as well as unstable spatially nonuniform solutions in a restricted range of the output gain of a neuron. The duration of the transients increased exponentially with the number of neurons up to the maximum number at which the spatially nonuniform steady solutions were stabilized. The range of the output gain for which they existed reduced as asymmetry in a sigmoidal output function of a neuron increased, while the existence range expanded as the strength of inhibitory self-coupling increased. Next, arrays of spiking neuron models with slow synaptic inhibitory bidirectional coupling and self-coupling were considered with computer simulation. In an array of Class 1 Hindmarsh-Rose type models, in which each neuron showed a graded firing rate, metastable dynamical transient firing patterns were observed in the presence of inhibitory self-coupling. This agreed with the condition for the existence of metastable dynamical transients in an array of sigmoidal neurons. In an array of Class 2 Bonhoeffer-van der Pol models, in which each neuron had a clear threshold between firing and resting, long-lasting transient firing patterns with bursting and irregular motion were observed.

Statistical Frequency-Dependent Analysis of Trial-to-Trial Variability in Single Time Series by Recurrence Plots

For decades, research in neuroscience has supported the hypothesis that brain dynamics exhibits recurrent metastable states connected by transients, which together encode fundamental neural information processing. To understand the system's dynamics it is important to detect such recurrence domains, but it is challenging to extract them from experimental neuroscience datasets due to the large trial-to-trial variability. The proposed methodology extracts recurrent metastable states in univariate time series by transforming datasets into their time-frequency representations and computing recurrence plots based on instantaneous spectral power values in various frequency bands. Additionally, a new statistical inference analysis compares different trial recurrence plots with corresponding surrogates to obtain statistically significant recurrent structures. This combination of methods is validated by applying it to two artificial datasets. In a final study of visually-evoked Local Field Potentials in partially anesthetized ferrets, the methodology is able to reveal recurrence structures of neural responses with trial-to-trial variability. Focusing on different frequency bands, the δ-band activity is much less recurrent than α-band activity. Moreover, α-activity is susceptible to pre-stimuli, while δ-activity is much less sensitive to pre-stimuli. This difference in recurrence structures in different frequency bands indicates diverse underlying information processing steps in the brain.

Cortical Correlates of Low-Level Perception: From Neural Circuits to Percepts

Low-level perception results from neural-based computations, which build a multimodal skeleton of unconscious or self-generated inferences on our environment. This review identifies bottleneck issues concerning the role of early primary sensory cortical areas, mostly in rodent and higher mammals (cats and non-human primates), where perception substrates can be searched at multiple scales of neural integration. We discuss the limitation of purely bottom-up approaches for providing realistic models of early sensory processing and the need for identification of fast adaptive processes, operating within the time of a percept. Future progresses will depend on the careful use of comparative neuroscience (guiding the choices of experimental models and species adapted to the questions under study), on the definition of agreed-upon benchmarks for sensory stimulation, on the simultaneous acquisition of neural data at multiple spatio-temporal scales, and on the in vivo identification of key generic integration and plasticity algorithms validated experimentally and in simulations.

Visually Evoked Spiking Evolves While Spontaneous Ongoing Dynamics Persist

Neurons in the primary visual cortex spontaneously spike even when there are no visual stimuli. It is unknown whether the spiking evoked by visual stimuli is just a modification of the spontaneous ongoing cortical spiking dynamics or whether the spontaneous spiking state disappears and is replaced by evoked spiking. This study of laminar recordings of spontaneous spiking and visually evoked spiking of neurons in the ferret primary visual cortex shows that the spiking dynamics does not change: the spontaneous spiking as well as evoked spiking is controlled by a stable and persisting fixed point attractor. Its existence guarantees that evoked spiking return to the spontaneous state. However, the spontaneous ongoing spiking state and the visual evoked spiking states are qualitatively different and are separated by a threshold (separatrix). The functional advantage of this organization is that it avoids the need for a system reorganization following visual stimulation, and impedes the transition of spontaneous spiking to evoked spiking and the propagation of spontaneous spiking from layer 4 to layers 2-3.

Reservoir computing and the Sooner-is-Better bottleneck

Prior language input is not lost but integrated with the current input. This principle is demonstrated by “reservoir computing”: Untrained recurrent neural networks project input sequences onto a random point in high-dimensional state space. Earlier inputs can be retrieved from this projection, albeit less reliably so as more input is received. The bottleneck is therefore not “Now-or-Never” but “Sooner-is-Better.”

Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay

The dynamics of four almost identical pulse coupled chemical oscillators with time delay are systematically studied.

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.

Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding

Brain-wide interactions generating complex neural dynamics are considered crucial for emergent cognitive functions. However, the irreducible nature of nonlinear and high-dimensional dynamical interactions challenges conventional reductionist approaches. We introduce a model-free method, based on embedding theorems in nonlinear state-space reconstruction, that permits a simultaneous characterization of complexity in local dynamics, directed interactions between brain areas, and how the complexity is produced by the interactions. We demonstrate this method in large-scale electrophysiological recordings from awake and anesthetized monkeys. The cross-embedding method captures structured interaction underlying cortex-wide dynamics that may be missed by conventional correlation-based analysis, demonstrating a critical role of time-series analysis in characterizing brain state. The method reveals a consciousness-related hierarchy of cortical areas, where dynamical complexity increases along with cross-area information flow. These findings demonstrate the advantages of the cross-embedding method in deciphering large-scale and heterogeneous neuronal systems, suggesting a crucial contribution by sensory-frontoparietal interactions to the emergence of complex brain dynamics during consciousness.

A Duet for one

This paper considers communication in terms of inference about the behaviour of others (and our own behaviour). It is based on the premise that our sensations are largely generated by other agents like ourselves. This means, we are trying to infer how our sensations are caused by others, while they are trying to infer our behaviour: for example, in the dialogue between two speakers. We suggest that the infinite regress induced by modelling another agent - who is modelling you - can be finessed if you both possess the same model. In other words, the sensations caused by others and oneself are generated by the same process. This leads to a view of communication based upon a narrative that is shared by agents who are exchanging sensory signals. Crucially, this narrative transcends agency - and simply involves intermittently attending to and attenuating sensory input. Attending to sensations enables the shared narrative to predict the sensations generated by another (i.e. to listen), while attenuating sensory input enables one to articulate the narrative (i.e. to speak). This produces a reciprocal exchange of sensory signals that, formally, induces a generalised synchrony between internal (neuronal) brain states generating predictions in both agents. We develop the arguments behind this perspective, using an active (Bayesian) inference framework and offer some simulations (of birdsong) as proof of principle.

Controlled generation of switching dynamics among metastable states in pulse-coupled oscillator networks

Switching dynamics among saddles in a network of nonlinear oscillators can be exploited for information encoding and processing (hence computing), but stable attractors in the system can terminate the switching behavior. An effective control strategy is presented to sustain switching dynamics in networks of pulse-coupled oscillators. The support for the switching behavior is a set of saddles, or unstable invariant sets in the phase space. We thus identify saddles with a common property, localize the system in the vicinity of them, and then guide the system from one metastable state to another to generate desired switching dynamics. We demonstrate that the control method successfully generates persistent switching trajectories and prevents the system from entering stable attractors. In addition, there exists correspondence between the network structure and the switching dynamics, providing fundamental insights on the development of a computing paradigm based on the switching dynamics.

Dynamic trajectory of multiple single-unit activity during working memory task in rats

Working memory plays an important role in complex cognitive tasks. A popular theoretical view is that transient properties of neuronal dynamics underlie cognitive processing. The question raised here as to how the transient dynamics evolve in working memory. To address this issue, we investigated the multiple single-unit activity dynamics in rat medial prefrontal cortex (mPFC) during a Y-maze working memory task. The approach worked by reconstructing state space from delays of the original single-unit firing rate variables, which were further analyzed using kernel principal component analysis (KPCA). Then the neural trajectories were obtained to visualize the multiple single-unit activity. Furthermore, the maximal Lyapunov exponent (MLE) was calculated to quantitatively evaluate the neural trajectories during the working memory task. The results showed that the neuronal activity produced stable and reproducible neural trajectories in the correct trials while showed irregular trajectories in the incorrect trials, which may establish a link between the neurocognitive process and behavioral performance in working memory. The MLEs significantly increased during working memory in the correctly performed trials, indicating an increased divergence of the neural trajectories. In the incorrect trials, the MLEs were nearly zero and remained unchanged during the task. Taken together, the trial-specific neural trajectory provides an effective way to track the instantaneous state of the neuronal population during the working memory task and offers valuable insights into working memory function. The MLE describes the changes of neural dynamics in working memory and may reflect different neuronal population states in working memory.

Amphetamine Exerts Dose-Dependent Changes in Prefrontal Cortex Attractor Dynamics during Working Memory

Modulation of neural activity by monoamine neurotransmitters is thought to play an essential role in shaping computational neurodynamics in the neocortex, especially in prefrontal regions. Computational theories propose that monoamines may exert bidirectional (concentration-dependent) effects on cognition by altering prefrontal cortical attractor dynamics according to an inverted U-shaped function. To date, this hypothesis has not been addressed directly, in part because of the absence of appropriate statistical methods required to assess attractor-like behavior in vivo. The present study used a combination of advanced multivariate statistical, time series analysis, and machine learning methods to assess dynamic changes in network activity from multiple single-unit recordings from the medial prefrontal cortex (mPFC) of rats while the animals performed a foraging task guided by working memory after pretreatment with different doses of d-amphetamine (AMPH), which increases monoamine efflux in the mPFC. A dose-dependent, bidirectional effect of AMPH on neural dynamics in the mPFC was observed. Specifically, a 1.0 mg/kg dose of AMPH accentuated separation between task-epoch-specific population states and convergence toward these states. In contrast, a 3.3 mg/kg dose diminished separation and convergence toward task-epoch-specific population states, which was paralleled by deficits in cognitive performance. These results support the computationally derived hypothesis that moderate increases in monoamine efflux would enhance attractor stability, whereas high frontal monoamine levels would severely diminish it. Furthermore, they are consistent with the proposed inverted U-shaped and concentration-dependent modulation of cortical efficiency by monoamines.

Wavelet-based regularity analysis reveals recurrent spatiotemporal behavior in resting-state fMRI

One of the major findings from multimodal neuroimaging studies in the past decade is that the human brain is anatomically and functionally organized into large-scale networks. In resting state fMRI (rs-fMRI), spatial patterns emerge when temporal correlations between various brain regions are tallied, evidencing networks of ongoing intercortical cooperation. However, the dynamic structure governing the brain's spontaneous activity is far less understood due to the short and noisy nature of the rs-fMRI signal. Here, we develop a wavelet-based regularity analysis based on noise estimation capabilities of the wavelet transform to measure recurrent temporal pattern stability within the rs-fMRI signal across multiple temporal scales. The method consists of performing a stationary wavelet transform to preserve signal structure, followed by construction of "lagged" subsequences to adjust for correlated features, and finally the calculation of sample entropy across wavelet scales based on an "objective" estimate of noise level at each scale. We found that the brain's default mode network (DMN) areas manifest a higher level of irregularity in rs-fMRI time series than rest of the brain. In 25 aged subjects with mild cognitive impairment and 25 matched healthy controls, wavelet-based regularity analysis showed improved sensitivity in detecting changes in the regularity of rs-fMRI signals between the two groups within the DMN and executive control networks, compared with standard multiscale entropy analysis. Wavelet-based regularity analysis based on noise estimation capabilities of the wavelet transform is a promising technique to characterize the dynamic structure of rs-fMRI as well as other biological signals.

Dynamics of multistable states during ongoing and evoked cortical activity

Single-trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory, and decision-making. Yet, very little is known about the network mechanisms responsible for its genesis. It is often assumed that the onset of state sequences is triggered by an external stimulus. Here we show that state sequences can be observed also in the absence of overt sensory stimulation. Analysis of multielectrode recordings from the gustatory cortex of alert rats revealed ongoing sequences of states, where single neurons spontaneously attain several firing rates across different states. This single-neuron multistability represents a challenge to existing spiking network models, where typically each neuron is at most bistable. We present a recurrent spiking network model that accounts for both the spontaneous generation of state sequences and the multistability in single-neuron firing rates. Each state results from the activation of neural clusters with potentiated intracluster connections, with the firing rate in each cluster depending on the number of active clusters. Simulations show that the model's ensemble activity hops among the different states, reproducing the ongoing dynamics observed in the data. When probed with external stimuli, the model predicts the quenching of single-neuron multistability into bistability and the reduction of trial-by-trial variability. Both predictions were confirmed in the data. Together, these results provide a theoretical framework that captures both ongoing and evoked network dynamics in a single mechanistic model.

Single-trial dynamics of motor cortex and their applications to brain-machine interfaces

Increasing evidence suggests that neural population responses have their own internal drive, or dynamics, that describe how the neural population evolves through time. An important prediction of neural dynamical models is that previously observed neural activity is informative of noisy yet-to-be-observed activity on single-trials, and may thus have a denoising effect. To investigate this prediction, we built and characterized dynamical models of single-trial motor cortical activity. We find these models capture salient dynamical features of the neural population and are informative of future neural activity on single trials. To assess how neural dynamics may beneficially denoise single-trial neural activity, we incorporate neural dynamics into a brain–machine interface (BMI). In online experiments, we find that a neural dynamical BMI achieves substantially higher performance than its non-dynamical counterpart. These results provide evidence that neural dynamics beneficially inform the temporal evolution of neural activity on single trials and may directly impact the performance of BMIs.

In online experiments with monkeys the authors demonstrate, for the first time, that incorporating neural dynamics substantially improves brain–machine interface performance. This result is consistent with a framework hypothesizing that motor cortex is a dynamical machine that generates movement.

Modulating conscious movement intention by noninvasive brain stimulation and the underlying neural mechanisms

Conscious intention is a fundamental aspect of the human experience. Despite long-standing interest in the basis and implications of intention, its underlying neurobiological mechanisms remain poorly understood. Using high-definition transcranial DC stimulation (tDCS), we observed that enhancing spontaneous neuronal excitability in both the angular gyrus and the primary motor cortex caused the reported time of conscious movement intention to be ∼60-70 ms earlier. Slow brain waves recorded ∼2-3 s before movement onset, as well as hundreds of milliseconds after movement onset, independently correlated with the modulation of conscious intention by brain stimulation. These brain activities together accounted for 81% of interindividual variability in the modulation of movement intention by brain stimulation. A computational model using coupled leaky integrator units with biophysically plausible assumptions about the effect of tDCS captured the effects of stimulation on both neural activity and behavior. These results reveal a temporally extended brain process underlying conscious movement intention that spans seconds around movement commencement.

Metastable dynamics in heterogeneous neural fields

We present numerical simulations of metastable states in heterogeneous neural fields that are connected along heteroclinic orbits. Such trajectories are possible representations of transient neural activity as observed, for example, in the electroencephalogram. Based on previous theoretical findings on learning algorithms for neural fields, we directly construct synaptic weight kernels from Lotka-Volterra neural population dynamics without supervised training approaches. We deliver a MATLAB neural field toolbox validated by two examples of one- and two-dimensional neural fields. We demonstrate trial-to-trial variability and distributed representations in our simulations which might therefore be regarded as a proof-of-concept for more advanced neural field models of metastable dynamics in neurophysiological data.

Active inference, communication and hermeneutics

Hermeneutics refers to interpretation and translation of text (typically ancient scriptures) but also applies to verbal and non-verbal communication. In a psychological setting it nicely frames the problem of inferring the intended content of a communication. In this paper, we offer a solution to the problem of neural hermeneutics based upon active inference. In active inference, action fulfils predictions about how we will behave (e.g., predicting we will speak). Crucially, these predictions can be used to predict both self and others--during speaking and listening respectively. Active inference mandates the suppression of prediction errors by updating an internal model that generates predictions--both at fast timescales (through perceptual inference) and slower timescales (through perceptual learning). If two agents adopt the same model, then--in principle--they can predict each other and minimise their mutual prediction errors. Heuristically, this ensures they are singing from the same hymn sheet. This paper builds upon recent work on active inference and communication to illustrate perceptual learning using simulated birdsongs. Our focus here is the neural hermeneutics implicit in learning, where communication facilitates long-term changes in generative models that are trying to predict each other. In other words, communication induces perceptual learning and enables others to (literally) change our minds and vice versa.

Stochastic Dynamics Underlying Cognitive Stability and Flexibility

Cognitive stability and flexibility are core functions in the successful pursuit of behavioral goals. While there is evidence for a common frontoparietal network underlying both functions and for a key role of dopamine in the modulation of flexible versus stable behavior, the exact neurocomputational mechanisms underlying those executive functions and their adaptation to environmental demands are still unclear. In this work we study the neurocomputational mechanisms underlying cue based task switching (flexibility) and distractor inhibition (stability) in a paradigm specifically designed to probe both functions. We develop a physiologically plausible, explicit model of neural networks that maintain the currently active task rule in working memory and implement the decision process. We simplify the four-choice decision network to a nonlinear drift-diffusion process that we canonically derive from a generic winner-take-all network model. By fitting our model to the behavioral data of individual subjects, we can reproduce their full behavior in terms of decisions and reaction time distributions in baseline as well as distractor inhibition and switch conditions. Furthermore, we predict the individual hemodynamic response timecourse of the rule-representing network and localize it to a frontoparietal network including the inferior frontal junction area and the intraparietal sulcus, using functional magnetic resonance imaging. This refines the understanding of task-switch-related frontoparietal brain activity as reflecting attractor-like working memory representations of task rules. Finally, we estimate the subject-specific stability of the rule-representing attractor states in terms of the minimal action associated with a transition between different rule states in the phase-space of the fitted models. This stability measure correlates with switching-specific thalamocorticostriatal activation, i.e., with a system associated with flexible working memory updating and dopaminergic modulation of cognitive flexibility. These results show that stochastic dynamical systems can implement the basic computations underlying cognitive stability and flexibility and explain neurobiological bases of individual differences.

In this work we develop a neurophysiologically inspired dynamical model that is capable of solving a complex behavioral task testing cognitive stability and flexibility. We can individually fit the behavior of each of 20 human subjects that conducted this stability-flexibility task during functional magnetic resonance imaging (fMRI). The physiological nature of our model allows us to estimate the energy consumption of the rule-representing module, which we use to predict the hemodynamic fMRI response. Through this model-based prediction, we localize the rule module to a frontoparietal network known to be required for cognitive stability and flexibility. In this way we both validate our model, which is based on noisy attractor dynamics, and specify the computational role of a cortical network that is well-established in human neuroimaging research. Additionally, we quantify the individual stability of the rule-representing states and relate this stability to individual differences in energy consumption during task switching versus distractor inhibition. Hereby we show that the activation of a thalamocorticostriatal network involved in the dopaminergic modulation of cognitive stability is modulated by the model-derived stability of the frontoparietal rule-representing network. Altogether, we show that noisy dynamic systems are likely to implement the basic computations underlying cognitive stability and flexibility.

Minimal approach to neuro-inspired information processing

To learn and mimic how the brain processes information has been a major research challenge for decades. Despite the efforts, little is known on how we encode, maintain and retrieve information. One of the hypothesis assumes that transient states are generated in our intricate network of neurons when the brain is stimulated by a sensory input. Based on this idea, powerful computational schemes have been developed. These schemes, known as machine-learning techniques, include artificial neural networks, support vector machine and reservoir computing, among others. In this paper, we concentrate on the reservoir computing (RC) technique using delay-coupled systems. Unlike traditional RC, where the information is processed in large recurrent networks of interconnected artificial neurons, we choose a minimal design, implemented via a simple nonlinear dynamical system subject to a self-feedback loop with delay. This design is not intended to represent an actual brain circuit, but aims at finding the minimum ingredients that allow developing an efficient information processor. This simple scheme not only allows us to address fundamental questions but also permits simple hardware implementations. By reducing the neuro-inspired reservoir computing approach to its bare essentials, we find that nonlinear transient responses of the simple dynamical system enable the processing of information with excellent performance and at unprecedented speed. We specifically explore different hardware implementations and, by that, we learn about the role of nonlinearity, noise, system responses, connectivity structure, and the quality of projection onto the required high-dimensional state space. Besides the relevance for the understanding of basic mechanisms, this scheme opens direct technological opportunities that could not be addressed with previous approaches.

Hierarchical process memory: memory as an integral component of information processing

Models of working memory (WM) commonly focus on how information is encoded into and retrieved from storage at specific moments. However, in the majority of real-life processes, past information is used continuously to process incoming information across multiple timescales. Considering single-unit, electrocorticography, and functional imaging data, we argue that (i) virtually all cortical circuits can accumulate information over time, and (ii) the timescales of accumulation vary hierarchically, from early sensory areas with short processing timescales (10s to 100s of milliseconds) to higher-order areas with long processing timescales (many seconds to minutes). In this hierarchical systems perspective, memory is not restricted to a few localized stores, but is intrinsic to information processing that unfolds throughout the brain on multiple timescales.

Information processing via physical soft body

Soft machines have recently gained prominence due to their inherent softness and the resulting safety and resilience in applications. However, these machines also have disadvantages, as they respond with complex body dynamics when stimulated. These dynamics exhibit a variety of properties, including nonlinearity, memory, and potentially infinitely many degrees of freedom, which are often difficult to control. Here, we demonstrate that these seemingly undesirable properties can in fact be assets that can be exploited for real-time computation. Using body dynamics generated from a soft silicone arm, we show that they can be employed to emulate desired nonlinear dynamical systems. First, by using benchmark tasks, we demonstrate that the nonlinearity and memory within the body dynamics can increase the computational performance. Second, we characterize our system’s computational capability by comparing its task performance with a standard machine learning technique and identify its range of validity and limitation. Our results suggest that soft bodies are not only impressive in their deformability and flexibility but can also be potentially used as computational resources on top and for free.

Is cognition enough to explain cognitive development?

Traditional views separate cognitive processes from sensory-motor processes, seeing cognition as amodal, propositional, and compositional, and thus fundamentally different from the processes that underlie perceiving and acting. These were the ideas on which cognitive science was founded 30 years ago. However, advancing discoveries in neuroscience, cognitive neuroscience, and psychology suggests that cognition may be inseparable from processes of perceiving and acting. From this perspective, this study considers the future of cognitive science with respect to the study of cognitive development.

Extending Gurwitsch's field theory of consciousness

Aron Gurwitsch's theory of the structure and dynamics of consciousness has much to offer contemporary theorizing about consciousness and its basis in the embodied brain. On Gurwitsch's account, as we develop it, the field of consciousness has a variable sized focus or "theme" of attention surrounded by a structured periphery of inattentional contents. As the field evolves, its contents change their status, sometimes smoothly, sometimes abruptly. Inner thoughts, a sense of one's body, and the physical environment are dominant field contents. These ideas can be linked with (and help unify) contemporary theories about the neural correlates of consciousness, inattention, the small world structure of the brain, meta-stable dynamics, embodied cognition, and predictive coding in the brain.

How can we study reasoning in the brain?

The brain did not develop a dedicated device for reasoning. This fact bears dramatic consequences. While for perceptuo-motor functions neural activity is shaped by the input's statistical properties, and processing is carried out at high speed in hardwired spatially segregated modules, in reasoning, neural activity is driven by internal dynamics and processing times, stages, and functional brain geometry are largely unconstrained a priori. Here, it is shown that the complex properties of spontaneous activity, which can be ignored in a short-lived event-related world, become prominent at the long time scales of certain forms of reasoning. It is argued that the neural correlates of reasoning should in fact be defined in terms of non-trivial generic properties of spontaneous brain activity, and that this implies resorting to concepts, analytical tools, and ways of designing experiments that are as yet non-standard in cognitive neuroscience. The implications in terms of models of brain activity, shape of the neural correlates, methods of data analysis, observability of the phenomenon, and experimental designs are discussed.

Detecting event-related recurrences by symbolic analysis: applications to human language processing

Quasi-stationarity is ubiquitous in complex dynamical systems. In brain dynamics, there is ample evidence that event-related potentials (ERPs) reflect such quasi-stationary states. In order to detect them from time series, several segmentation techniques have been proposed. In this study, we elaborate a recent approach for detecting quasi-stationary states as recurrence domains by means of recurrence analysis and subsequent symbolization methods. We address two pertinent problems of contemporary recurrence analysis: optimizing the size of recurrence neighbourhoods and identifying symbols from different realizations for sequence alignment. As possible solutions for these problems, we suggest a maximum entropy criterion and a Hausdorff clustering algorithm. The resulting recurrence domains for single-subject ERPs are obtained as partition cells reflecting quasi-stationary brain states.

Arrhythmogenic transient dynamics in cardiac myocytes

Cardiac action potential alternans and early afterdepolarizations (EADs) are linked to cardiac arrhythmias. Periodic action potentials (period 1) in healthy conditions bifurcate to other states such as period 2 or chaos when alternans or EADs occur in pathological conditions. The mechanisms of alternans and EADs have been extensively studied under steady-state conditions, but lethal arrhythmias often occur during the transition between steady states. Why arrhythmias tend to develop during the transition is unclear. We used low-dimensional mathematical models to analyze dynamical mechanisms of transient alternans and EADs. We show that depending on the route from one state to another, action potential alternans and EADs may occur during the transition between two periodic steady states. The route taken depends on the time course of external perturbations or intrinsic signaling, such as β-adrenergic stimulation, which regulate cardiac calcium and potassium currents with differential kinetics.

Exploiting short-term memory in soft body dynamics as a computational resource

Soft materials are not only highly deformable, but they also possess rich and diverse body dynamics. Soft body dynamics exhibit a variety of properties, including nonlinearity, elasticity and potentially infinitely many degrees of freedom. Here, we demonstrate that such soft body dynamics can be employed to conduct certain types of computation. Using body dynamics generated from a soft silicone arm, we show that they can be exploited to emulate functions that require memory and to embed robust closed-loop control into the arm. Our results suggest that soft body dynamics have a short-term memory and can serve as a computational resource. This finding paves the way towards exploiting passive body dynamics for control of a large class of underactuated systems.

Medial prefrontal activity during delay period contributes to learning of a working memory task

Cognitive processes require working memory (WM) that involves a brief period of memory retention known as the delay period. Elevated delay-period activity in the medial prefrontal cortex (mPFC) has been observed, but its functional role in WM tasks remains unclear. We optogenetically suppressed or enhanced activity of pyramidal neurons in mouse mPFC during the delay period. Behavioral performance was impaired during the learning phase but not after the mice were well trained. Delay-period mPFC activity appeared to be more important in memory retention than in inhibitory control, decision-making, or motor selection. Furthermore, endogenous delay-period mPFC activity showed more prominent modulation that correlated with memory retention and behavioral performance. Thus, properly regulated mPFC delay-period activity is critical for information retention during learning of a WM task.

Dynamic stability of sequential stimulus representations in adapting neuronal networks

The ability to acquire and maintain appropriate representations of time-varying, sequential stimulus events is a fundamental feature of neocortical circuits and a necessary first step toward more specialized information processing. The dynamical properties of such representations depend on the current state of the circuit, which is determined primarily by the ongoing, internally generated activity, setting the ground state from which input-specific transformations emerge. Here, we begin by demonstrating that timing-dependent synaptic plasticity mechanisms have an important role to play in the active maintenance of an ongoing dynamics characterized by asynchronous and irregular firing, closely resembling cortical activity in vivo. Incoming stimuli, acting as perturbations of the local balance of excitation and inhibition, require fast adaptive responses to prevent the development of unstable activity regimes, such as those characterized by a high degree of population-wide synchrony. We establish a link between such pathological network activity, which is circumvented by the action of plasticity, and a reduced computational capacity. Additionally, we demonstrate that the action of plasticity shapes and stabilizes the transient network states exhibited in the presence of sequentially presented stimulus events, allowing the development of adequate and discernible stimulus representations. The main feature responsible for the increased discriminability of stimulus-driven population responses in plastic networks is shown to be the decorrelating action of inhibitory plasticity and the consequent maintenance of the asynchronous irregular dynamic regime both for ongoing activity and stimulus-driven responses, whereas excitatory plasticity is shown to play only a marginal role.