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.

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 bridge between brain and mind.

The bridge between brain structures as computational devices and the content of mental processes hinges on the solution of several problems: (i) inference of the cognitive brain networks from neurophysiological and imaging data; (ii) inference of cognitive mind networks - interactions between mental processes such as attention and working memory - based on cognitive and behavioral experiments; and (iii) the discovery of general dynamical principles for cognition based on dynamical models. In this opinion article, we focus on the third problem and discuss how it provides the bridge between the solutions to the first two problems. We consider the possibility of creating low-dimensional dynamical models from multidimensional spatiotemporal data and its application to robust sequential cognitive processes in the context of finite processing capacity of the mind.

Hierarchical nonlinear dynamics of human attention.

Attention is the process of focusing mental resources on a specific cognitive/behavioral task. Such brain dynamics involves different partially overlapping brain functional networks whose interconnections change in time according to the performance stage, and can be stimulus-driven or induced by an intrinsically generated goal. The corresponding activity can be described by different families of spatiotemporal discrete patterns or sequential dynamic modes. Since mental resources are finite, attention modalities compete with each other at all levels of the hierarchy, from perception to decision making and behavior. Cognitive activity is a dynamical process and attention possesses some universal dynamical characteristics. Thus, it is time to apply nonlinear dynamical theory for the description and prediction of hierarchical attentional tasks. Such theory has to include the analyses of attentional control stability, the time cost of attention switching, the finite capacity of informational resources in the brain, and the normal and pathological bifurcations of attention sequential dynamics. In this paper we have integrated today's knowledge, models and results in these directions.

Robust sequential working memory recall in heterogeneous cognitive networks.

Psychiatric disorders are often caused by partial heterogeneous disinhibition in cognitive networks, controlling sequential and spatial working memory (SWM). Such dynamic connectivity changes suggest that the normal relationship between the neuronal components within the network deteriorates. As a result, competitive network dynamics is qualitatively altered. This dynamics defines the robust recall of the sequential information from memory and, thus, the SWM capacity. To understand pathological and non-pathological bifurcations of the sequential memory dynamics, here we investigate the model of recurrent inhibitory-excitatory networks with heterogeneous inhibition. We consider the ensemble of units with all-to-all inhibitory connections, in which the connection strengths are monotonically distributed at some interval. Based on computer experiments and studying the Lyapunov exponents, we observed and analyzed the new phenomenon-clustered sequential dynamics. The results are interpreted in the context of the winnerless competition principle. Accordingly, clustered sequential dynamics is represented in the phase space of the model by two weakly interacting quasi-attractors. One of them is similar to the sequential heteroclinic chain-the regular image of SWM, while the other is a quasi-chaotic attractor. Coexistence of these quasi-attractors means that the recall of the normal information sequence is intermittently interrupted by episodes with chaotic dynamics. We indicate potential dynamic ways for augmenting damaged working memory and other cognitive functions.

Chunking dynamics: heteroclinics in mind.

Recent results of imaging technologies and non-linear dynamics make possible to relate the structure and dynamics of functional brain networks to different mental tasks and to build theoretical models for the description and prediction of cognitive activity. Such models are non-linear dynamical descriptions of the interaction of the core components-brain modes-participating in a specific mental function. The dynamical images of different mental processes depend on their temporal features. The dynamics of many cognitive functions are transient. They are often observed as a chain of sequentially changing metastable states. A stable heteroclinic channel (SHC) consisting of a chain of saddles-metastable states-connected by unstable separatrices is a mathematical image for robust transients. In this paper we focus on hierarchical chunking dynamics that can represent several forms of transient cognitive activity. Chunking is a dynamical phenomenon that nature uses to perform information processing of long sequences by dividing them in shorter information items. Chunking, for example, makes more efficient the use of short-term memory by breaking up long strings of information (like in language where one can see the separation of a novel on chapters, paragraphs, sentences, and finally words). Chunking is important in many processes of perception, learning, and cognition in humans and animals. Based on anatomical information about the hierarchical organization of functional brain networks, we propose a cognitive network architecture that hierarchically chunks and super-chunks switching sequences of metastable states produced by winnerless competitive heteroclinic dynamics.

Transient dynamics and rhythm coordination of inferior olive spatio-temporal patterns.

The inferior olive (IO) is a neural network belonging to the olivo-cerebellar system whose neurons are coupled with electrical synapses and display subthreshold oscillations and spiking activity. The IO is frequently proposed as the generator of timing signals to the cerebellum. Electrophysiological and imaging recordings show that the IO network generates complex spatio-temporal patterns. The generation and modulation of coherent spiking activity in the IO is one key issue in cerebellar research. In this work, we build a large scale IO network model of electrically coupled conductance-based neurons to study the emerging spatio-temporal patterns of its transient neuronal activity. Our modeling reproduces and helps to understand important phenomena observed in IO in vitro and in vivo experiments, and draws new predictions regarding the computational properties of this network and the associated cerebellar circuits. The main factors studied governing the collective dynamics of the IO network were: the degree of electrical coupling, the extent of the electrotonic connections, the presence of stimuli or regions with different excitability levels and the modulatory effect of an inhibitory loop (IL). The spatio-temporal patterns were analyzed using a discrete wavelet transform to provide a quantitative characterization. Our results show that the electrotonic coupling produces quasi-synchronized subthreshold oscillations over a wide dynamical range. The synchronized oscillatory activity plays the role of a timer for a coordinated representation of spiking rhythms with different frequencies. The encoding and coexistence of several coordinated rhythms is related to the different clusterization and coherence of transient spatio-temporal patterns in the network, where the spiking activity is commensurate with the quasi-synchronized subthreshold oscillations. In the presence of stimuli, different rhythms are encoded in the spiking activity of the IO neurons that nevertheless remains constrained to a commensurate value of the subthreshold frequency. The stimuli induced spatio-temporal patterns can reverberate for long periods, which contributes to the computational properties of the IO. We also show that the presence of regions with different excitability levels creates sinks and sources of coordinated activity which shape the propagation of spike wave fronts. These results can be generalized beyond IO studies, as the control of wave pattern propagation is a highly relevant problem in the context of normal and pathological states in neural systems (e.g., related to tremor, migraine, epilepsy) where the study of the modulation of activity sinks and sources can have a potential large impact.

Information flow dynamics in the brain.

Timing and dynamics of information in the brain is a hot field in modern neuroscience. The analysis of the temporal evolution of brain information is crucially important for the understanding of higher cognitive mechanisms in normal and pathological states. From the perspective of information dynamics, in this review we discuss working memory capacity, language dynamics, goal-dependent behavior programming and other functions of brain activity. In contrast with the classical description of information theory, which is mostly algebraic, brain flow information dynamics deals with problems such as the stability/instability of information flows, their quality, the timing of sequential processing, the top-down cognitive control of perceptual information, and information creation. In this framework, different types of information flow instabilities correspond to different cognitive disorders. On the other hand, the robustness of cognitive activity is related to the control of the information flow stability. We discuss these problems using both experimental and theoretical approaches, and we argue that brain activity is better understood considering information flows in the phase space of the corresponding dynamical model. In particular, we show how theory helps to understand intriguing experimental results in this matter, and how recent knowledge inspires new theoretical formalisms that can be tested with modern experimental techniques.

Robust transient dynamics and brain functions.

In the last few decades several concepts of dynamical systems theory (DST) have guided psychologists, cognitive scientists, and neuroscientists to rethink about sensory motor behavior and embodied cognition. A critical step in the progress of DST application to the brain (supported by modern methods of brain imaging and multi-electrode recording techniques) has been the transfer of its initial success in motor behavior to mental function, i.e., perception, emotion, and cognition. Open questions from research in genetics, ecology, brain sciences, etc., have changed DST itself and lead to the discovery of a new dynamical phenomenon, i.e., reproducible and robust transients that are at the same time sensitive to informational signals. The goal of this review is to describe a new mathematical framework - heteroclinic sequential dynamics - to understand self-organized activity in the brain that can explain certain aspects of robust itinerant behavior. Specifically, we discuss a hierarchy of coarse-grain models of mental dynamics in the form of kinetic equations of modes. These modes compete for resources at three levels: (i) within the same modality, (ii) among different modalities from the same family (like perception), and (iii) among modalities from different families (like emotion and cognition). The analysis of the conditions for robustness, i.e., the structural stability of transient (sequential) dynamics, give us the possibility to explain phenomena like the finite capacity of our sequential working memory - a vital cognitive function -, and to find specific dynamical signatures - different kinds of instabilities - of several brain functions and mental diseases.

Nonlinear dynamics of emotion-cognition interaction: when emotion does not destroy cognition?

Emotion (i.e., spontaneous motivation and subsequent implementation of a behavior) and cognition (i.e., problem solving by information processing) are essential to how we, as humans, respond to changes in our environment. Recent studies in cognitive science suggest that emotion and cognition are subserved by different, although heavily integrated, neural systems. Understanding the time-varying relationship of emotion and cognition is a challenging goal with important implications for neuroscience. We formulate here the dynamical model of emotion-cognition interaction that is based on the following principles: (1) the temporal evolution of cognitive and emotion modes are captured by the incoming stimuli and competition within and among themselves (competition principle); (2) metastable states exist in the unified emotion-cognition phase space; and (3) the brain processes information with robust and reproducible transients through the sequence of metastable states. Such a model can take advantage of the often ignored temporal structure of the emotion-cognition interaction to provide a robust and generalizable method for understanding the relationship between brain activation and complex human behavior. The mathematical image of the robust and reproducible transient dynamics is a Stable Heteroclinic Sequence (SHS), and the Stable Heteroclinic Channels (SHCs). These have been hypothesized to be possible mechanisms that lead to the sequential transient behavior observed in networks. We investigate the modularity of SHCs, i.e., given a SHS and a SHC that is supported in one part of a network, we study conditions under which the SHC pertaining to the cognition will continue to function in the presence of interfering activity with other parts of the network, i.e., emotion.

Dynamical principles of emotion-cognition interaction: mathematical images of mental disorders.

The key contribution of this work is to introduce a mathematical framework to understand self-organized dynamics in the brain that can explain certain aspects of itinerant behavior. Specifically, we introduce a model based upon the coupling of generalized Lotka-Volterra systems. This coupling is based upon competition for common resources. The system can be regarded as a normal or canonical form for any distributed system that shows self-organized dynamics that entail winnerless competition. Crucially, we will show that some of the fundamental instabilities that arise in these coupled systems are remarkably similar to endogenous activity seen in the brain (using EEG and fMRI). Furthermore, by changing a small subset of the system's parameters we can produce bifurcations and metastable sequential dynamics changing, which bear a remarkable similarity to pathological brain states seen in psychiatry. In what follows, we will consider the coupling of two macroscopic modes of brain activity, which, in a purely descriptive fashion, we will label as cognitive and emotional modes. Our aim is to examine the dynamical structures that emerge when coupling these two modes and relate them tentatively to brain activity in normal and non-normal states.

Robust microcircuit synchronization by inhibitory connections.

Microcircuits in different brain areas share similar architectural and biophysical properties with compact motor networks known as central pattern generators (CPGs). Consequently, CPGs have been suggested as valuable biological models for understanding of microcircuit dynamics and particularly, their synchronization. We use a well known compact motor network, the lobster pyloric CPG to study principles of intercircuit synchronization. We couple separate pyloric circuits obtained from two animals via artificial synapses and observe how their synchronization depends on the topology and kinetic parameters of the computer-generated synapses. Stable in-phase synchronization appears when electrically coupling the pacemaker groups of the two networks, but reciprocal inhibitory connections produce more robust and regular cooperative activity. Contralateral inhibitory connections offer effective synchronization and flexible setting of the burst phases of the interacting networks. We also show that a conductance-based mathematical model of the coupled circuits correctly reproduces the observed dynamics illustrating the generality of the phenomena.

Chemosensor-driven artificial antennal lobe transient dynamics enable fast recognition and working memory.

The speed and accuracy of odor recognition in insects can hardly be resolved by the raw descriptors provided by olfactory receptors alone due to their slow time constant and high variability. The animal overcomes these barriers by means of the antennal lobe (AL) dynamics, which consolidates the classificatory information in receptor signal with a spatiotemporal code that is enriched in odor sensitivity, particularly in its transient. Inspired by this fact, we propose an easily implementable AL-like network and show that it significantly expedites and enhances the identification of odors from slow and noisy artificial polymer sensor responses. The device owes its efficiency to two intrinsic mechanisms: inhibition (which triggers a competition) and integration (due to the dynamical nature of the network). The former functions as a sharpening filter extracting the features of receptor signal that favor odor separation, whereas the latter implements a working memory by accumulating the extracted features in trajectories. This cooperation boosts the odor specificity during the receptor transient, which is essential for fast odor recognition.

Dynamical origin of the effective storage capacity in the brain's working memory.

The capacity of working memory (WM), a short-term buffer for information in the brain, is limited. We suggest a model for sequential WM that is based upon winnerless competition amongst representations of available informational items. Analytical results for the underlying mathematical model relate WM capacity and relative lateral inhibition in the corresponding neural network. This implies an upper bound for WM capacity, which is, under reasonable neurobiological assumptions, close to the "magical number seven."

Neuronal synchrony: peculiarity and generality.

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their "dynamical repertoire" includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale).

Pacemaker and network mechanisms of rhythm generation: cooperation and competition.

The origin of rhythmic activity in brain circuits and CPG-like motor networks is still not fully understood. The main unsolved questions are (i) What are the respective roles of intrinsic bursting and network based dynamics in systems of coupled heterogeneous, intrinsically complex, even chaotic, neurons? (ii) What are the mechanisms underlying the coexistence of robustness and flexibility in the observed rhythmic spatio-temporal patterns? One common view is that particular bursting neurons provide the rhythmogenic component while the connections between different neurons are responsible for the regularisation and synchronisation of groups of neurons and for specific phase relationships in multi-phasic patterns. We have examined the spatio-temporal rhythmic patterns in computer-simulated motif networks of H-H neurons connected by slow inhibitory synapses with a non-symmetric pattern of coupling strengths. We demonstrate that the interplay between intrinsic and network dynamics features either cooperation or competition, depending on three basic control parameters identified in our model: the shape of intrinsic bursts, the strength of the coupling and its degree of asymmetry. The cooperation of intrinsic dynamics and network mechanisms is shown to correlate with bistability, i.e., the coexistence of two different attractors in the phase space of the system corresponding to different rhythmic spatio-temporal patterns. Conversely, if the network mechanism of rhythmogenesis dominates, monostability is observed with a typical pattern of winnerless competition between neurons. We analyse bifurcations between the two regimes and demonstrate how they provide robustness and flexibility to the network performance.

Transient cognitive dynamics, metastability, and decision making.

The idea that cognitive activity can be understood using nonlinear dynamics has been intensively discussed at length for the last 15 years. One of the popular points of view is that metastable states play a key role in the execution of cognitive functions. Experimental and modeling studies suggest that most of these functions are the result of transient activity of large-scale brain networks in the presence of noise. Such transients may consist of a sequential switching between different metastable cognitive states. The main problem faced when using dynamical theory to describe transient cognitive processes is the fundamental contradiction between reproducibility and flexibility of transient behavior. In this paper, we propose a theoretical description of transient cognitive dynamics based on the interaction of functionally dependent metastable cognitive states. The mathematical image of such transient activity is a stable heteroclinic channel, i.e., a set of trajectories in the vicinity of a heteroclinic skeleton that consists of saddles and unstable separatrices that connect their surroundings. We suggest a basic mathematical model, a strongly dissipative dynamical system, and formulate the conditions for the robustness and reproducibility of cognitive transients that satisfy the competing requirements for stability and flexibility. Based on this approach, we describe here an effective solution for the problem of sequential decision making, represented as a fixed time game: a player takes sequential actions in a changing noisy environment so as to maximize a cumulative reward. As we predict and verify in computer simulations, noise plays an important role in optimizing the gain.

Artificial synaptic modification reveals a dynamical invariant in the pyloric CPG.

The sequential firing of neurons in central pattern generators (CPGs) is generally thought to be a result of an interaction between intrinsic cellular and synaptic properties of the component neurons. Due to experimental limitations, it is usually difficult to address the role of each of these properties separately. We have done so by using the crustacean stomatogastric CPG and the dynamic clamp technique to measure how the network responds to the selective modification of an individual important synapse. Our results show that the burst periods and the phase lags between the constrictor (LP) and dilator (PD) neurons across preparations showed significant variability during equivalent experimental manipulations. Despite this variability, the ratio between the change in the burst period and the change in the phase lag between the same neurons was tightly preserved in all preparations, revealing a dynamical invariant in the system. This dynamical invariant was preserved despite the individual variability in the period and phase lag measurements, suggesting a tightly regulated constraint between the parameters of the network.