Roman Borisyuk

Bifurcation analysis of a neural network model

This paper describes the analysis of the well known neural network model by Wilson and Cowan. The neural network is modeled by a system of two ordinary differential equations that describe the evolution of average activities of excitatory and inhibitory populations of neurons. We analyze the dependence of the models behavior on two parameters. The parameter plane is partitioned into regions of equivalent behavior bounded by bifurcation curves, and the representative phase diagram is constructed for each region. This allows us to describe qualitatively the behavior of the model in each region and to predict changes in the model dynamics as parameters are varied. In particular, we show that for some parameter values the system can exhibit long-period oscillations. A new type of dynamical behavior is also found when the system settles down either to a stationary state or to a limit cycle depending on the initial point.

Dynamics and bifurcations of two coupled neural oscillators with different connection types

In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.

Oscillatory model of attention-guided object selection and novelty detection

We develop a new oscillatory model that combines consecutive selection of objects and discrimination between new and familiar objects. The model works with visual information and fulfils the following operations: (1) separation of different objects according to their spatial connectivity; (2) consecutive selection of objects located in the visual field into the attention focus; (3) extraction of features; (4) representation of objects in working memory; (5) novelty detection of objects. The functioning of the model is based on two main principles: the synchronization of oscillators through phase-locking and resonant increase of the amplitudes of oscillators if they work in-phase with other oscillators. The results of computer simulation of the model are described for visual stimuli representing printed words.

An oscillatory neural model of multiple object tracking

An oscillatory neural network model of multiple object tracking is described. The model works with a set of identical visual objects moving around the screen. At the initial stage, the model selects into the focus of attention a subset of objects initially marked as targets. Other objects are used as distractors. The model aims to preserve the initial separation between targets and distractors while objects are moving. This is achieved by a proper interplay of synchronizing and desynchronizing interactions in a multilayer network, where each layer is responsible for tracking a single target. The results of the model simulation are presented and compared with experimental data. In agreement with experimental evidence, simulations with a larger number of targets have shown higher error rates. Also, the functioning of the model in the case of temporarily overlapping objects is presented.

A model of theta rhythm production in the septal-hippocampal system and its modulation by ascending brain stem pathways.

Recent experimental observations have disclosed the existence of a septal‐hippocampal feedback circuit, composed of medial septum diagonal band of Broca (ms‐dbB) GABAergic projections to the inhibitory interneurons of the hippocampus, and hippocampal GABAergic projections to the ms‐dbB, the major targets of which are the GABAergic septo‐hippocampal projection cells. We propose that this feedback circuit provides the mechanism for the rhythmic suppression of interneuronal activity in the hippocampus, which is observed as low‐level GABAergic‐mediated theta activity. We also propose that this circuit may be the mechanism by which ascending brain stem pathways to the ms‐dbB, in particular from the reticular formation, can influence hippocampal information processing in response to particular behavioral states, by exercising control over the level and frequency of theta activity in the hippocampus. In support of these proposals, we describe a minimal computational model of the feedback circuit which uses a set of four coupled differential equations describing the average dynamic activity of the populations of excitatory and inhibitory cells involved in the circuit. We demonstrate through simulations the inherently robust 4–6‐Hz oscillatory dynamics of the circuit, and show that manipulation of internal connection strengths and external modulatory influences on this circuit changes the dynamics in a way which closely mimics corresponding manipulations in recent neurophysiological experiments investigating theta activity. Hippocampus 2000;10:698–716.

Axon and dendrite geography predict the specificity of synaptic connections in a functioning spinal cord network

BackgroundHow specific are the synaptic connections formed as neuronal networks develop and can simple rules account for the formation of functioning circuits? These questions are assessed in the spinal circuits controlling swimming in hatchling frog tadpoles. This is possible because detailed information is now available on the identity and synaptic connections of the main types of neuron.ResultsThe probabilities of synapses between 7 types of identified spinal neuron were measured directly by making electrical recordings from 500 pairs of neurons. For the same neuron types, the dorso-ventral distributions of axons and dendrites were measured and then used to calculate the probabilities that axons would encounter particular dendrites and so potentially form synaptic connections. Surprisingly, synapses were found between all types of neuron but contact probabilities could be predicted simply by the anatomical overlap of their axons and dendrites. These results suggested that synapse formation may not require axons to recognise specific, correct dendrites. To test the plausibility of simpler hypotheses, we first made computational models that were able to generate longitudinal axon growth paths and reproduce the axon distribution patterns and synaptic contact probabilities found in the spinal cord. To test if probabilistic rules could produce functioning spinal networks, we then made realistic computational models of spinal cord neurons, giving them established cell-specific properties and connecting them into networks using the contact probabilities we had determined. A majority of these networks produced robust swimming activity.ConclusionSimple factors such as morphogen gradients controlling dorso-ventral soma, dendrite and axon positions may sufficiently constrain the synaptic connections made between different types of neuron as the spinal cord first develops and allow functional networks to form. Our analysis implies that detailed cellular recognition between spinal neuron types may not be necessary for the reliable formation of functional networks to generate early behaviour like swimming.

Dynamics of neural networks with a central element

A neural network is considered which is designed as a system of phase oscillators and contains a central oscillator that interacts with a number of peripheral oscillators. Analytical and simulation methods are used to study the dynamics of the system that is conditioned by the interaction parameters and natural frequencies of the oscillators. The boundaries of parameter regions are found that correspond to the synchronization of the whole network or to partial synchronization between the central oscillator and a group of peripheral oscillators. For a system with two peripheral oscillators the bifurcation analysis is applied to describe the changes of synchronization modes. The implications of the results for attention modeling are discussed.

Object selection by an oscillatory neural network

We describe a new solution to the problem of consecutive selection of objects in a visual scene by an oscillatory neural network with the global interaction realised through a central executive element (central oscillator). The frequency coding is used to represent greyscale images in the network. The functioning of the network is based on three main principles: (1) the synchronisation of oscillators via phase-locking, (2) adaptation of the natural frequency of the central oscillator, and (3) resonant increase of the amplitudes of the oscillators which work in-phase with the central oscillator. Examples of network simulations are presented to show the reliability of the results of consecutive selection of objects under conditions of constant and varying brightness of the objects.

Oscillatory model of novelty detection

A model of novelty detection is developed which is based on an oscillatory mechanism of memory formation and information processing. The frequency encoding of the input information and adaptation of natural frequencies of network oscillators to the frequency of the input signal are used as the mechanism of information storage. The resonance amplification of network activity is used as a recognition principle for familiar stimuli. Application of the model to novelty detection in the hippocampus is discussed.

Can Simple Rules Control Development of a Pioneer Vertebrate Neuronal Network Generating Behavior

How do the pioneer networks in the axial core of the vertebrate nervous system first develop? Fundamental to understanding any full-scale neuronal network is knowledge of the constituent neurons, their properties, synaptic interconnections, and normal activity. Our novel strategy uses basic developmental rules to generate model networks that retain individual neuron and synapse resolution and are capable of reproducing correct, whole animal responses. We apply our developmental strategy to young Xenopus tadpoles, whose brainstem and spinal cord share a core vertebrate plan, but at a tractable complexity. Following detailed anatomical and physiological measurements to complete a descriptive library of each type of spinal neuron, we build models of their axon growth controlled by simple chemical gradients and physical barriers. By adding dendrites and allowing probabilistic formation of synaptic connections, we reconstruct network connectivity among up to 2000 neurons. When the resulting “network” is populated by model neurons and synapses, with properties based on physiology, it can respond to sensory stimulation by mimicking tadpole swimming behavior. This functioning model represents the most complete reconstruction of a vertebrate neuronal network that can reproduce the complex, rhythmic behavior of a whole animal. The findings validate our novel developmental strategy for generating realistic networks with individual neuron- and synapse-level resolution. We use it to demonstrate how early functional neuronal connectivity and behavior may in life result from simple developmental “rules,” which lay out a scaffold for the vertebrate CNS without specific neuron-to-neuron recognition.