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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model.

Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions.

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.

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.

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.

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.

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.

Dynamical origin of independent spiking and bursting activity in neural microcircuits.

The relationship between spiking and bursting dynamics is a key question in neuroscience, particularly in understanding the origins of different neural coding strategies and the mechanisms of motor command generation and neural circuit coordination. Experiments indicate that spiking and bursting dynamics can be independent. We hypothesize that different mechanisms for spike and burst generation, intrinsic neuron dynamics for spiking and a modulational network instability for bursting, are the origin of this independence.

Dynamics of sequential decision making.

We suggest a new paradigm for intelligent decision-making suitable for dynamical sequential activity of animals or artificial autonomous devices that depends on the characteristics of the internal and external world. To do it we introduce a new class of dynamical models that are described by ordinary differential equations with a finite number of possibilities at the decision points, and also include rules solving this uncertainty. Our approach is based on the competition between possible cognitive states using their stable transient dynamics.

Generation and reshaping of sequences in neural systems.

The generation of informational sequences and their reorganization or reshaping is one of the most intriguing subjects for both neuroscience and the theory of autonomous intelligent systems. In spite of the diversity of sequential activities of sensory, motor, and cognitive neural systems, they have many similarities from the dynamical point of view. In this review we discus the ideas, models, and mathematical image of sequence generation and reshaping on different levels of the neural hierarchy, i.

Heteroclinic synchronization: ultrasubharmonic locking.

According to the traditional view of synchronization, a weak periodic input is able to lock a nonlinear oscillator at a frequency close to that of the input (1:1 zone). If the forcing increases, it is possible to achieve synchronization at subharmonic bands also. Using a competitive dynamical system we show the inverse phenomenon: with a weak signal the 1:1 zone is narrow, but the synchronization of ultrasubharmonics is dominant.