Mikhail israel Rabinovich

University of California, San Diego | UCSD · BioCircuits Institute (BCI)

From the dynamical point of view, most cognitive phenomena are hierarchical, transient and sequential. Such cognitive spatio-temporal processes can be represented by a set of sequential metastable dynamical states together with their associated transitions: The state is quasi-stationary close to one metastable state before a rapid transition to ano...

Today, based on brain imaging analyses, we can consider the brilliant metaphor about event discreteness of the conscious process by William James (1890) to be an experimental fact. Such events compose sequences: linguistic, episodic memory, motor behavior, etc., whose dynamics are robust, reproducible, and sensitively react to incoming informationa...

Cognitive/behavioral brain functions are implemented through temporary correlated sequential activity of many brain elements that form universal anatomical and functional motifs, i.e., characteristic functional interactions among brain nodes, at different levels of the neural hierarchy. Such motif dynamics is determined by both the interconnections...

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 ensembl...

Retrieval of episodic memory is a dynamical process in the large scale brain networks. In social groups, the neural patterns, associated to specific events directly experienced by single members, are encoded, recalled and shared by all participants. Here we construct and study the dynamical model for the formation and maintaining of episodic memory...

Human behavior is a sequential process, and at least its mechanical side can be described by equations. A similar statement related to consciousness is not so evident. A common view is that consciousness is an intriguing but too complex phenomenon and thus a topic not ready for mathematical description. However, converging evidence from imaging and...

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....

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 -...

Combining the results of brain imaging and nonlinear dynamics provides a new hierarchical vision of brain network functionality that is helpful in understanding the relationship of the network to different mental tasks. Using these ideas it is possible to build adequate models for the description and prediction of different cognitive activities in...

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...

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 generates complex spatio-temporal patterns. The generation and modulation of coherent spiking activity in the IO is one key issue in cerebellar res...

Modulatory effect of the IL in autonomous IO networks. Activity movie showing the modulatory effect of the IL in an autonomous IO network model where each neuron is connected to its eight nearest neighbors with an electrical coupling gc = 0.05 mS/cm2 (cf. Figures 6 and Figures 12D, which shows the DWT analysis).

Synchronized activity in an autonomous strongly coupled IO network model. The network displayed in this video is equivalent to the network in Movie S1 but with a strong electrical coupling (gc < 0.8 mS/cm2). In this situation, there is almost total synchronization among neurons (see Figure 4F), only broken briefly when spiking behavior occurs, and...

Nearly constant spatial pattern topology in the absence of subthreshold oscillations. The video shows the activity of an autonomous IO network of tonically spiking neurons without subthreshold oscillations where each unit is connected to four neighbors with a weak electrical coupling (gc < 0.05 mS/cm2). The spiking behavior is induced in all neuron...

Coexistence and coordination of spatio-temporal patterns induced by stimuli. Activity of an IO network with two external stimuli. The number of connected neighbors is eight with gc = 0.05 mS/cm2. External stimuli are introduced as a constant current injected in clusters of closed neurons. In this case, we consider two clusters of 6 × 6 cells with I...

Nearly independent activity in an autonomous weakly coupled IO network model. Each neuron is connected to four neighbors with a weak electrical coupling (gc < 0.001 mS/cm2). See section 2.3 for a description of the graphical representation. Note that the time scale does not correspond with the simulation time. For low coupling conductances, the act...

Spatio-temporal patterns in an autonomous IO network model with weak coupling extended to further neighbors. Each neuron is connected to 12 neighbors with a weak electrical coupling (gc < 0.01 mS/cm2). The effect of increasing the number of connections between neighbors is equivalent to increasing the coupling strength to a moderate magnitude (cf....

Modulatory effect of the IL in the presence of stimuli. Activity movie showing the modulatory effect of the IL in the same network model as in Movie S10 but in the presence of two external stimuli (cf. Figures 8C and Figures 12D, which shows the DWT analysis).

Spatio-temporal patterns of coordinated activity in an autonomous moderately coupled IO network model. The network displayed in this video is analogous to the network in Movies S1, S2 but with a moderate electrical coupling among cells (gc < 0.08 mS/cm2). In this case, the individual neurons have quasi-synchronized subthreshold activity (see Figure...

Encoding of multiple simultaneous rhythms. The network in this video is equivalent to the network in Movie S6, but with 25 stimulated clusters of 6 × 6 cells with different current injections. Figure 8B shows the approximate position of each cluster. The effect observed here is the same observed in Movie S6, but with many more coexisting spiking rh...

Stimulus reverberation allows short memory mechanisms in the IO models. Activity movie showing the stimulus reverberation effect in an IO network model where each neuron is connected to four nearest neighbors with electrical coupling gc = 0.05 mS/cm2. Individual neuron parameters in this simulation are σ = 2 and Iinj = 0.35 μA/cm2. Note that parame...

The source-sink phenomena allows the IO models to attract the wave fronts to specific locations. Note that in this video the color scale changes with respect to the one used in the rest of IO activity movies. Here, blue color means that the corresponding neuron is under the firing threshold, and red indicates that neurons are firing. To better illu...

In this paper we formulate basic principles of cognitive human-robot team dynamics following lessons from experimental neuroscience: 1) the cognitive team dynamics in a changing complex environment is transient and can be considered as a temporal sequence of metastable states; 2) the human mental resources –attention and working memory capacity tha...

Experimental and theoretical approaches to global brain dynamics that draw on the latest research in the field. The consideration of time or dynamics is fundamental for all aspects of mental activity—perception, cognition, and emotion—because the main feature of brain activity is the continuous change of the underlying brain states even in a consta...

Experimental and theoretical approaches to global brain dynamics that draw on the latest research in the field. The consideration of time or dynamics is fundamental for all aspects of mental activity—perception, cognition, and emotion—because the main feature of brain activity is the continuous change of the underlying brain states even in a consta...

Experimental and theoretical approaches to global brain dynamics that draw on the latest research in the field. The consideration of time or dynamics is fundamental for all aspects of mental activity—perception, cognition, and emotion—because the main feature of brain activity is the continuous change of the underlying brain states even in a consta...

Understanding and predicting the behavior of complex multiagent systems like brain or ecological food net requires new approaches and paradigms. Traditional analyses based on just asymptotic results of behavior as time goes to infinity, or on straightforward mathematical images that can accommodate only fixed points or limit cycles do not tell much...

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 capac...

Experimental neuroscience is often based on the implicit premise that the neural mechanisms underlying perception, emotion and cognition are well approximated by steady-state measurements of neuron activity or snapshot of images. We will unfold a new paradigm in the study of brain mental dynamics departing from the stable transient activity neural...

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 te...

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...

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,...

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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 syst...

Here we consider a new mechanism of binding between different information modalities in the brain, i.e. heteroclinic binding. The basic model that we propose is able to explain the origin of the coordination of competitive dynamics of active brain modes representing the temporal processing of different sensory and/or intrinsic information (differen...

Experimental investigations of neural system functioning and brain activity are standardly based on the assumption that perceptions, emotions, and cognitive functions can be understood by analyzing steady-state neural processes and static tomographic snapshots. The new approaches discussed in this review are based on the analysis of transient proce...

This work formulates a sensor array optimization scheme for odor identification. It hinges on a performance index widely used in the signal theory, namely the Mahalanobis distance, which gives a solid quantification of the separability among odor classes. Optimizing this index over the controllable operating parameters of the sensor array minimizes...

The Lotka–Volterra (LV) equations can be used to model the behaviour of complex systems in nature. Trajectories in a stable heteroclinic channel (SHC) describe transient dynamics according to the winnerless competition principle in such a system. The existence of an SHC is guaranteed if the parameters of the LV equations satisfy a number of conditi...

The two central pattern generators (CPGs) in the 30-cell crustacean stomatogastric ganglion are the best-described neural circuits known in terms of cell identity and synaptic topology. Each CPG produces a distinct spatiotemporal rhythmic motor pattern that controls striated stomach muscles. Modeling is essential to help understand the basis for th...

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...

We present a new paradigm in the study of brain mental dynamics on the basis of the stable transient activity neural networks observed in experiments. This new approach is in contrast to traditional system analysis usually adopted in cognitive modeling. Transient dynamics offers a sound formalism of the observed qualities of brain activity, while p...

There is a growing body of evidence that slow brain rhythms are generated by simple inhibitory neural networks. Sequential switching of tonic spiking activity is a widespread phenomenon underlying such rhythms. A realistic generative model explaining such reproducible switching is a dynamical system that employs a closed stable heteroclinic channel...

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 mot...

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. When one is interested in just asymptotic results of evoluti...

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 s...

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 regul...

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...

DOI:https://doi.org/10.1103/PhysRevLett.101.079901

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 tran...

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 cru...

The odor transduction process has a large time constant and is susceptible to various types of noise. Therefore, the olfactory code at the sensor/receptor level is in general a slow and highly variable indicator of the input odor in both natural and artificial situations. Insects overcome this problem by using a neuronal device in their Antennal Lo...

Metastable domains, i.e. regions with perfect crystal patterns separated by domain walls–chains of dislocations–are found to exist in parametrically excited capillary ripples. Two typical mechanisms responsible for the transition of ensembles of domains to perfect crystals are revealed: collapse of individual domains when the domain wall is a close...

The spatio-temporal disorder on the background capillary ripples excited parametrically by a homogeneous field is investigated in fluids with various viscosities. Analysis of modulation wave characteristics in the spectra and spatio-temporal description has shown that the modulation wave dynamics is determined, to a significant degree, by nonlinear...

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 diff...

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 vie...

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 p...

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two deca...

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 signa...

We show in a model of spiking neurons that synaptic plasticity in the mushroom bodies in combination with the general fan-in, fan-out properties of the early processing layers of the olfactory system might be sufficient to account for its efficient recognition of odors. For a large variety of initial conditions the model system consistently finds a...

DOI:https://doi.org/10.1103/PhysRevE.72.069903

Sensory input plays a major role in controlling motor responses during most behavioral tasks. The vestibular organs in the marine mollusk Clione, the statocysts, react to the external environment and continuously adjust the tail and wing motor neurons to keep the animal oriented vertically. However, we suggested previously that during hunting behav...

Experimental observations on synaptic plasticity at individual glutamatergic synapses from the CA3 Shaffer collateral pathway onto CA1 pyramidal cells in the hippocampus suggest that the transitions in synaptic strength occur among discrete levels at individual synapses [C. C. H. Petersen, Proc. Natl. Acad. Sci. USA 85, 4732 (1998); O'Connor, Witte...

There are many types of neural networks involved in the sequential motor behavior of animals. For high species, the control and coordination of the network dynamics is a function of the higher levels of the central nervous system, in particular the cerebellum. However, in many cases, especially for invertebrates, such coordination is the result of...

Robustness and reproducibility of sequential spatio-temporal responses is an essential feature of many neural circuits in sensory and motor systems of animals. The most common mathematical images of dynamical regimes in neural systems are fixed points, limit cycles, chaotic attractors, and continuous attractors (attractive manifolds of neutrally st...

The neural circuits of birdsong appear to utilize specific time delays in their operation. In particular, the anterior forebrain pathway (AFP) is implicated in an approximately 40- to 50- ms time delay, DeltaT, playing a role in the relative timing of premotor signals from the nucleus HVc to the nucleus robust nucleus of the archistratium (RA) and...

We propose a theoretical framework for odor classification in the olfactory system of insects. The classification task is accomplished in two steps. The first is a transformation from the antennal lobe to the intrinsic Kenyon cells in the mushroom body. This transformation into a higher-dimensional space is an injective function and can be implemen...

Synchronous neural activity plays an important role in the functioning of the brain. In this paper we study the entrainment of a heterogeneous network of elec- trically coupled neurons by synapticaly mediated periodic stimulation. We demon- strate by computer simulations that input synapses with spike timing dependent plasticity (STDP) greatly enha...

The marine mollusk Clione limacina has a peculiar hunting behavior characterized by a complex sequence of loops and turns. We have developed a model of the receptor network of Clione's gravimetric organ to explain this behavior. In this paper we discuss the possible role of an activation phase lock among the statocyst receptor neurons to coordinate...

In mollusks, statocyst receptor cells (SRCs) interact with each other forming a neural network; their activity is determined by both the animal's orientation in the gravitational field and multimodal inputs. These two facts suggest that the function of the statocysts is not limited to sensing the animal's orientation. We studied the role of the sta...

Images of fluids in motion have served both scientific and artistic purposes at least since the time of Leonardo de Vinci over 500 years ago. The visualization of fluid flow has played a major role in the development of fluid dynamics and its technological and scientific applications, from the evolution of flight to the tracking of weather to under...

Two kinds of connections are known to exist in neural circuits: electrical (also called gap junctions) and chemical. Whereas chemical synapses are known to be plastic (i. e., modifiable), but slow, electrical transmission through gap junctions is not modifiable, but is very fast. We suggest the new artificial synapse that combines the best properti...

Invertebrate central pattern generators (CPGs) can serve as the basis for building biomimetic controllers based on real biological principles. Here we describe a CPG made of electronic neurons and synapses for robotic applications and for possible use in a clinical neuroprosthetic device

We discuss a VLSI electronic neuron circuit that implements the Hindmarsh and Rose neuron model. Magnitude and time scaling techniques are employed for a 2 V power supply operation. A subthreshold operation technique and a single MOS resistor are used to minimize area and power consumption. Output bursts of the electronic neuron can be modulated dy...

this paper we investigate the second issue preparatory to the large scale computations required for the first

Synchronization of neural activity is fundamental for many functions of the brain. We demonstrate that spike-timing dependent plasticity (STDP) enhances synchronization (entrainment) in a hybrid circuit composed of a spike generator, a dynamic clamp emulating an excitatory plastic synapse, and a chemically isolated neuron from the Aplysia abdominal...

We discuss a biophysical model of synaptic plasticity that provides a unified view of the outcomes of synaptic modification protocols, including: (1) prescribed time courses of postsynaptic intracellular Ca2+ release, (2) postsynaptic voltage clamping with presentation of presynaptic spike trains at various frequencies, (3) direct postsynaptic resp...

Sensory information is represented in a spatio-temporal code in the antennal lobe, the first processing stage of the olfactory system of insects. We propose a novel mechanism for decoding this information in the next processing stage, the mushroom body. The Kenyon cells in the mushroom body of insects exhibit lateral excitatory connections at their...

Periodic regimes are known to exist in different weakly coupled chaotic systems. In most cases these deterministic states exist in a very narrow region of parameter space of otherwise chaotic system. In this work we introduce a new type of coupling, namely activity-dependent coupling which strength depends on the time course of activity of connecte...

Information processing in neural networks by computation with attractors (steady states, limit cycles, strange attractors) has been extensively discussed in application to many neural systems: central pattern generators, sensory systems (e.g. visual, olfactory), hippocampus, etc. Computation with attractors in a traditional way faces а fundamental...

Central pattern generators (CPGs) controlling motor function are among the best-understood examples of oscillatory networks found in virtually every nervous system.

The ability of nonlinear dynamical systems to process incoming information is a key problem of many fundamental and applied sciences. Information processing by computation with attractors (steady states, limit cycles and strange attractors) has been a subject of many publications. In this paper we discuss a new direction in information dynamics bas...

Using a modified version of a phenomenological model for the dynamics of synaptic plasticity, we examine some recent experiments of Wu et al. [(2001) J Physiol 533:745-755]. We show that the model is quantitatively consistent with their experimental protocols producing long-term potentiation (LTP) and long-term depression (LTD) in slice preparation...

We study the synchronization of two model neurons coupled through a synapse having an activity-dependent strength. Our synapse follows the rules of spike-timing dependent plasticity. We show that this plasticity of the coupling between neurons produces enlarged frequency-locking zones and results in synchronization that is more rapid and much more...

Synchronization of oscillatory activity plays an important role in the functionality of many biological systems. In this talk we report the results of the study of synchronization of model Hodgkin-Huxley neurons coupled through a synapse having an activity-dependent strength. Dynamics of the synaptic strength that we use follows the rules of Spike-...

We introduce a biologically motivated dynamical principle of sequential memory which is based on winnerless competition (WLC) of event images. This mechanism is implemented in a two-layer neural model of sequential spatial memory. We present the learning dynamics which leads to the formation of a WLC network. After learning, the system is capable o...

Information processing in neural networks by computation with attractors (steady states, limit cycles, strange attractors) has been extensively discussed in application to many neural systems: central pattern generators, sensory systems (e.g. visual, olfactory), hippocampus, etc. Computation with attractors in a traditional way faces a fundamental...

In the presence of prey, the marine mollusk Clione limacina exhibits search behavior, i.e., circular motions whose plane and radius change in a chaotic-like manner. We have formulated a dynamical model of the chaotic hunting behavior of Clione based on physiological in vivo and in vitro experiments. The model includes a description of the action of...

Using the dynamic clamp technique, we investigated the effects of varying the time constant of mutual synaptic inhibition on the synchronization of bursting biological neurons. For this purpose, we constructed artificial half-center circuits by inserting simulated reciprocal inhibitory synapses between identified neurons of the pyloric circuit in t...

Using the dynamic clamp technique, we investigated the effects of varying the time constant of mutual synaptic inhibition on the synchronization of bursting biological neurons. For this purpose, we constructed artificial half-center circuits by inserting simulated reciprocal inhibitory synapses between identified neurons of the pyloric circuit in t...

Long-term synaptic plasticity leading to enhancement in synaptic efficacy (long-term potentiation, LTP) or decrease in synaptic efficacy (long-term depression, LTD) is widely regarded as underlying learning and memory in nervous systems. LTP and LTD at excitatory neuronal synapses are observed to be induced by precise timing of pre- and postsynapti...

We have built several networks of inferior olive (IO) model neurons to study the emerging spatio-temporal patterns of neuronal activity. The degree and extent of the electrical coupling, and the presence of stimuli were the main factors considered in the IO networks. The network activity was analyzed using a discrete wavelet transform which provide...

The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli...

The dynamic clamp protocol allows an experimenter to simulate the presence of membrane conductances in, and synaptic connections between, biological neurons. Existing protocols and commercial ADC/DAC boards provide ready control in and between < or =2 neurons. Control at >2 sites is desirable when studying neural circuits with serial or ring connec...

An essential question raised after the observation of highly variable bursting activity in individual neurons of Central Pattern Generators (CPGs) is how an assembly of such cells can cooperatively act to produce regular signals to motor systems. It is well known that some neurons in the lobster stomatogastric ganglion have a highly irregular spiki...

Central Pattern Generators (CPGs) are assemblies of neurons that act cooperatively to produce regular signals to motor systems. The individual behavior of some members of the CPGs has often been Observed as highly variable spiking-bursting activity. In spite of this fact, The collective behavior of the intact CPG produces always regular rhythmic ac...