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Global competition and local cooperation in a network of neural oscillators
Abstract
An architecture of locally excitatory, globally inhibitory oscillator networks is proposed and investigated both analytically and by computer simulation. The model for each oscillator corresponds to a standard relaxation oscillator with two time scales. Oscillators are locally coupled by a scheme that resembles excitatory synaptic coupling, and each oscillator also inhibits other oscillators through a common inhibitor. Oscillators are driven to be oscillatory by external stimulation. The network exhibits a mechanism of selective gating, whereby an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern, while preventing the other oscillators from jumping up. We show analytically that with the selective gating mechanism, the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks. Computer simulations demonstrate the model's promising ability for segmenting multiple input patterns in real time. This model lays a physical foundation for the oscillatory correlation theory of feature binding and may provide an effective computational framework for scene segmentation and figure/ ground segregation.
... In addition, the y-nullcline is assumed to be a monotone increasing function of x that intersects with x-nullcline at the unique equilibrium point, and G > 0 (G < 0) below (above) the y-nullcline curve. This model framework includes several in the literature [54][55][56], and often higher dimensional models can be reduced to two dimensional models in this form [3]. ...
... F(x, y) = µ(3x − x 3 ) − y + I app , G(x, y) = (γ(1 + tanh(β(x − δ))) − y). This model is inspired by that of [56]. It has a cubic nonlinearity as for the FitzHugh-Nagumo model [59,60], but with a nonlinearity in the equation for the "recovery" variable which is similar to that for a gating variable in a conductance-based model. ...
... We apply our analytical results to an example model inspired by that of Terman and Wang [56]. We solve for the equilibria of the model and show that the resting point always persists, while for sufficiently large excitatory coupling a saddle node bifurcation occurs giving rise to two other equilibria. ...
We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via delayed synaptic coupling between the excitatory neurons, while each inhibitory neuron is connected only to the corresponding excitatory neuron in the same population. We show that multiple equilibria can exist depending on the strength of the excitatory coupling between the populations. We conduct linear stability analysis of the equilibria and derive necessary conditions for delay-induced Hopf bifurcation. We show that these can induce two qualitatively different phase-locked behaviors, with the type of behavior determined by the sizes of the coupling delays. Numerical bifurcation analysis and simulations supplement and confirm our analytical results. Our work shows that the resting equilibrium point is unaffected by the coupling, thus the network exhibits bistability between a rest state and an oscillatory state. This may help understand how rhythms spontaneously arise in neuronal networks.
... This model is inspired by that of [56]. It has a cubic nonlinearity as in for the FitzHugh-Nagumo model [24,42], but with a nonlinearity in the equation for the "recovery" variable which is similar to that for a gating variable in a conductance-based model. ...
... We apply our analytical results to an example model inspired by that of Terman and Wang [56]. We solve for the equilibria of the model and show that the resting point always persists, while for sufficiently large excitatory 475 coupling a saddle node bifurcation occurs giving rise to two other equilibria. ...
... In this paper we consider a single cell model inspired by that of Terman and Wang [56]. The model is based on the FitzHugh-Nagumo [24,42] model but with a nonlinearity in equation for the "recovery" variable which is 575 similar to that for a gating variable in a conductance-based model. ...
We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via delayed synaptic coupling between the excitatory neurons, while each inhibitory neuron is connected only to the corresponding excitatory neuron in the same population. We show that multiple equilibria can exist depending on the strength of the excitatory coupling between the populations. We conduct linear stability analysis of the equilibria and derive necessary conditions for delay-induced Hopf bifurcation. We show that these can induce two qualitatively different phase-locked behaviors, with the type of behavior determined by the sizes of the coupling delays. Numerical bifurcation analysis and simulations supplement and confirm our analytical results. Our work shows that the resting equilibrium point is unaffected by the coupling, thus the network exhibits bistability between a rest state and an oscillatory state. This may help understand how rhythms spontaneously arise neuronal networks.
... Consequently, there must exist a mechanism responsible for stable desynchronisation of oscillations of the groups of neurons corresponding to different objects. Global competition of the oscillations between groups of locally synchronised neurons may follow such a mechanism [107,108]. A model for a neural network in the frames of which this mechanism is carried on was proposed in Ref. [107]: ...
... Global competition of the oscillations between groups of locally synchronised neurons may follow such a mechanism [107,108]. A model for a neural network in the frames of which this mechanism is carried on was proposed in Ref. [107]: ...
... Oscillations of all neurons belonging to the same segment is almost synchronous. However, there exists constant phase shift between different segments[107]. ...
Construction of a dynamical theory of neural assemblies has been a goal of physicists, mathematicians and biologists for many years now. Experimental achievements in modern neurobiology have allowed researchers to approach this goal. Significant advances have been made for small neural networks, which are generators of the rhytmic activities of living organisms. The subject of the present review is the problem of synchronisation, one of the major aspects of the dynamical theory. It is shown that synchronisation plays a key role in the activity of both minimal neural networks (neural pair) and neural ensembles with a large number of elements (cortex).
... Evidence of relationships between oscillations and the maintenance of working memory in humans has been obtained in numerous neurophysiological, imaging, and computational studies [6, 23-25, 27, 36, 48-54]. Oscillatory models have been developed both in the context of working memory [35,[55][56][57] and of binding [37,[58][59][60], and models -often with an eye towards image processing -have employed the distinction between bound and distinct objects as synchronous or asynchronous oscillations [37,[60][61][62][63][64]. These models tend to be spiking 27 . ...
... We also note that, while we have explored these networks within the context of the persistent activity observed in working memory dynamics, the presented behaviors would persist if we did not include NMDA dynamics, instead providing sustained drive to the excitatory and inhibitory populations (e.g., we show the same qualitative dynamics for such a reduced system with one population in Appendix A). Object differentiation and feature binding, as required in image segmentation, for example, may thus be modeled in our network using the same mechanisms described in the present results without consideration for persistent activity, so that simply removing the stimulus immediately quenches the activity of the selected populations, as in other work dealing with image analysis [61][62][63][64]. ...
Neural oscillations have been implicated in many different basic brain and cognitive processes. Oscillatory activity has been suggested to play a role in neural binding, and more recently in the maintenance of information in working memory. This latter work has focused primarily on oscillations in terms of providing a “code” in working memory. However, oscillations may additionally play a fundamental role in essential properties and behaviors that neuronal networks must exhibit in order to produce functional working memory. In the present work, we present a biologically plausible working memory model and demonstrate that specific types of stable oscillatory dynamics may play a critical role in facilitating properties of working memory, including transitions between different memory states and a multi-item working memory capacity. We also show these oscillatory dynamics may facilitate and provide an underlying mechanism to enable a range of different types of binding in the context of working memory.
Author summary
Working memory is a form of short-term memory that is limited in capacity to perhaps 3 – 5 items. Various studies have shown that ensembles of neurons oscillate during working memory retention, and cross-frequency coupling (between, e.g., theta and gamma frequencies) has been conjectured as underlying the observed limited capacity. Binding occurs when different objects or concepts are associated with each other and can persist as working memory representations; neuronal synchrony has been hypothesized as the neural correlate. We propose a novel computational model of a network of oscillatory neuronal populations that capture salient attributes of working memory and binding by allowing for both stable synchronous and asynchronous activity. The oscillatory dynamics we describe may provide a mechanism that can facilitate aspects of working memory, such as maintaining multiple items active at once, creating rich neural representations of memories via binding, and rapidly transitioning activtation patterns based on selective inputs.
... The effects of global coupling in shaping the network oscillatory patterns has been studied in a variety of systems both experimentally and theoretically. These include oscillatory chemical reactions [32][33][34][35][36][37], electrochemical oscillators [38][39][40][41][42][43][44][45][46][47][48], laser arrays [49], catalytic reactions [50], salt-water oscillators [51], metabolic oscillators and cellular dynamics [20,52,53], cardiac oscillators [54,55], coupling through quorum sensing [56][57][58][59][60], circadian oscillators [61][62][63], neuronal networks [5,[64][65][66][67][68][69] and image processing [65,70]. ...
... The effects of global coupling in shaping the network oscillatory patterns has been studied in a variety of systems both experimentally and theoretically. These include oscillatory chemical reactions [32][33][34][35][36][37], electrochemical oscillators [38][39][40][41][42][43][44][45][46][47][48], laser arrays [49], catalytic reactions [50], salt-water oscillators [51], metabolic oscillators and cellular dynamics [20,52,53], cardiac oscillators [54,55], coupling through quorum sensing [56][57][58][59][60], circadian oscillators [61][62][63], neuronal networks [5,[64][65][66][67][68][69] and image processing [65,70]. ...
Relaxation oscillators may exhibit small amplitude oscillations (SAOs) in addition to the typical large amplitude oscillations (LAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. We investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear (PWL) relaxation oscillators where global feedback acting on the rate of change of the activator (fast variable) involves the inhibitor (slow variable). We also investigate of these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry breaking global feedback effects.
... The NMDA synapses allow for bistability in our model, so that only transient stimuli, applied to the excitatory components, are required to trigger the active oscillatory states, consistent with experimental findings and other modeling efforts that have employed NMDA. While others have examined oscillatory models in working memory and binding [36,38,39,[54][55][56][57][58][59][60][61][62][63][64][65][66], to our knowledge none have employed NMDA as a mechanism for bistability, used numerical continuation to define regions of parameter space that allow for the oscillations of interest, or explored in detail the combinatorially rich oscillatory states and transitions between them. ...
... Oscillatory models have been developed both in the context of working memory [36,[54][55][56] and of binding [38,[57][58][59], and models-often with an eye towards image processinghave employed the distinction between bound and distinct objects as synchronous or asynchronous oscillations [38,[59][60][61][62]66]. These models tend to be spiking networks, appeal to cross-frequency coupling (e.g., theta-gamma codings), provide unrealistic connections (e.g., delayed self-inhibition for excitatory elements), use delays or constant inputs to produce persistent oscillatory activity, or employ structured architectures (e.g., using Hopfield networks, Hebbian rules, or pre-wired assemblies). ...
Neural oscillations have been recorded and implicated in many different basic brain and cognitive processes. For example, oscillatory neural activity has been suggested to play a role in binding and in the maintenance of information in working memory. With respect to the latter, the majority of work has focused primarily on oscillations in terms of providing a “code” in working memory. However, oscillations may additionally play a fundamental role by enabling or facilitating essential properties and behaviors that neuronal networks must exhibit in order to produce functional working memory and the processes it supports, such as combining items in memory into bound objects or separating bound objects into distinct items. In the present work, we present a biologically plausible working memory model and demonstrate that specific types of stable oscillatory dynamics that arise may play critical roles in providing mechanisms for working memory and the cognitive functions that it supports. Specifically, these roles include (1) enabling a range of different types of binding, (2) both enabling and limiting capacities of bound and distinct items held active in working memory, and (3) facilitating transitions between active working memory states as required in cognitive function. Several key results arise within the examinations, such as the occurrence of different network capacities for working memory and binding, differences in processing times for transitions in working memory states, and the emergence of a combinatorially rich and complex range of oscillatory states that are sufficient to map onto a wide range of cognitive operations supported by working memory, such as variable binding, reasoning, and language. In particular, we show that these oscillatory states and their transitions can provide a specific instantiation of current established connectionist models in representing these functions. Finally, we further characterize the dependence of the relevant oscillatory solutions on certain critical parameters, including mutual inhibition and synaptic timescales.
... The effects of global coupling in shaping the network oscillatory patterns has been studied in a variety of systems both experimentally and theoretically. These include oscillatory chemical reactions [32][33][34][35][36][37], electrochemical oscillators [38][39][40][41][42][43][44][45][46][47][48], laser arrays [49], catalytic reactions [50], salt-water oscillators [51], metabolic oscillators and cellular dynamics [20,52,53], cardiac oscillators [54,55], coupling through quorum sensing [56][57][58][59][60], circadian oscillators [61][62][63], neuronal networks [5,[64][65][66][67][68][69] and image processing [65,70]. ...
... The effects of global coupling in shaping the network oscillatory patterns has been studied in a variety of systems both experimentally and theoretically. These include oscillatory chemical reactions [32][33][34][35][36][37], electrochemical oscillators [38][39][40][41][42][43][44][45][46][47][48], laser arrays [49], catalytic reactions [50], salt-water oscillators [51], metabolic oscillators and cellular dynamics [20,52,53], cardiac oscillators [54,55], coupling through quorum sensing [56][57][58][59][60], circadian oscillators [61][62][63], neuronal networks [5,[64][65][66][67][68][69] and image processing [65,70]. ...
Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.
... Attentive states typically involve oscillatory regimes trying to anticipate some magnitude of the expected stimulus. Extensive reviews of the oscillations occurring in the cerebral cortex during cognition were offered by Buzsáki (2006), Wang (2010) and, from the viewpoint of synchrony, many computational issues connected to the binding problem were discussed in Wang (2005) (see also Quiles, Wang, Zhao, Romero, &Huang, 2011 andTerman &Wang, 1995). Reviews about other aspects of attention were given by Carrasco (2011), Desimone and Duncan (1995) and Itti and Koch (2001). ...
... Attentive states typically involve oscillatory regimes trying to anticipate some magnitude of the expected stimulus. Extensive reviews of the oscillations occurring in the cerebral cortex during cognition were offered by Buzsáki (2006), Wang (2010) and, from the viewpoint of synchrony, many computational issues connected to the binding problem were discussed in Wang (2005) (see also Quiles, Wang, Zhao, Romero, &Huang, 2011 andTerman &Wang, 1995). Reviews about other aspects of attention were given by Carrasco (2011), Desimone and Duncan (1995) and Itti and Koch (2001). ...
The role of sensory inputs in the modelling of synchrony regimes is exhibited by means of networks of spiking cells where the relative strength of the inhibitory interaction is controlled by the activation of a linear unit working as a gating variable. Adaptation to stimulus size is determined by the value of a changing length scale, modelled by the time-varying radius of a circular receptive field. In this set-up, ‘consolidation’ time intervals relevant to attentional effects are shown to depend on the dynamics governing the evolution of the introduced length scale.
... The de-noising approach is capable of eliminating noise while preserving the original EEG singularity. 3) Wavelet packet transform is one of the most recent and highly promising approaches to appear in the field of WT-based picture compression algorithms (38,39). The ideal design parameters for a data compression strategy applied to medical images of various imaging modalities are found by A. S. Tolba (40). ...
The term "digital health technology" describes the application of technology, including telemedicine, m-health, and ehealth, to diagnose and enhance healthcare. Plenty of research and advancements in technology have been conducted to enhance and advance the field. Digital health technologies are frequently used in the pharmaceutical industry at different stages of medication design, data analysis for clinical trials, etc. Research and inquiries in the disciplines of biotechnology and bioengineering are increasingly concentrating on technology and healthcare. The study analyzes aspects of the digital ecosystem, digital health, and innovation pertinent to the healthcare industry. By fusing information technology and health services, digital health technology has completely transformed the healthcare sector.
... Certain deficiencies, injuries, and genetic defects are detectable by the CNS and mechanisms of compensation are available (Terman & Wang, 1995). Besides, the CNS processes are a combination of electrical and chemical processes. ...
This paper is a discussion of computational tools and circuits that deal with the internal and external worlds of the human body. The information processing avenues in the central nervous system (CNS) are an important part of the development. All sensory channels and the vision system are involved. It clarifies the role of the sensory system in internal coordinate systems and for all activities of the CNS. It includes the inherent redundancy aspects of the motor system as well. The visual system is involved in sports such as soccer and basketball and for being aware of and paying attention to both the internal world and the external reality surrounding the athlete.
... Previous works (Terman and Wang 1995;Campbell and Wang 1996;Ursino et al. 2009) demonstrated that, in order to produce a robust synchronized activity, reciprocal inhibition between units is more appropriate than a reciprocal excitation. Hence, we assumed that, during training, synapses of the type K (thus producing inhibition), are reinforced in layer L2 via a Hebbian mechanism, linking cortical columns in the same object (see section below). ...
Recent experimental evidence suggests that oscillatory activity plays a pivotal role in the maintenance of information in working memory, both in rodents and humans. In particular, cross-frequency coupling between theta and gamma oscillations has been suggested as a core mechanism for multi-item memory. The aim of this work is to present an original neural network model, based on oscillating neural masses, to investigate mechanisms at the basis of working memory in different conditions. We show that this model, with different synapse values, can be used to address different problems, such as the reconstruction of an item from partial information, the maintenance of multiple items simultaneously in memory, without any sequential order, and the reconstruction of an ordered sequence starting from an initial cue. The model consists of four interconnected layers; synapses are trained using Hebbian and anti-Hebbian mechanisms, in order to synchronize features in the same items, and desynchronize features in different items. Simulations show that the trained network is able to desynchronize up to nine items without a fixed order using the gamma rhythm. Moreover, the network can replicate a sequence of items using a gamma rhythm nested inside a theta rhythm. The reduction in some parameters, mainly concerning the strength of GABAergic synapses, induce memory alterations which mimic neurological deficits. Finally, the network, isolated from the external environment (“imagination phase”) and stimulated with high uniform noise, can randomly recover sequences previously learned, and link them together by exploiting the similarity among items.
... Computational models of coupled oscillators have been studied extensively in the past [1][2][3][4] , and have been used to develop faithful models of Central Pattern Generators (CPGs) 5,6 . Using both theoretical studies and software simulations, many relevant properties of such systems have been investigated to model mechanisms of locomotion [6][7][8][9] , respiratory and cardiac rhythms 10,11 , and to drive or control rhythmic movements in robotics [12][13][14][15][16] . ...
Neural coupled oscillators are a useful building block in numerous models and applications. They were analyzed extensively in theoretical studies and more recently, in biologically realistic simulations of spiking neural networks. The advent of mixed-signal analog/digital neuromorphic electronic circuits provides new means for implementing neural coupled oscillators on compact low-power spiking neural network hardware platforms. However, their implementation on this noisy, low-precision and inhomogeneous computing substrate raises new challenges with regards to stability and controllability. In this work, we present a robust, spiking neural network model of neural coupled oscillators and validate it with an implementation on a mixed-signal neuromorphic processor. We demonstrate its robustness showing how to reliably control and modulate the oscillator's frequency and phase shift, despite the variability of the silicon synapse and neuron properties. We show how this ultra-low power neural processing system can be used to build an adaptive cardiac pacemaker modulating the heart rate with respect to the respiration phases and compare it with surface ECG and respiratory signal recordings of dogs at rest. The implementation of our model in neuromorphic electronic hardware shows its robustness on a highly variable substrate and extends the toolbox for applications requiring rhythmic outputs such as pacemakers.
... Dynamical system approaches has been used to analyze synchronized and clustered activity of excitatory-inhibitory networks of neurons [10], [16], [18], [19], [20], [21], [22]. However, previous analysis either considered small networks or networks with special architectures. ...
Coherent activity of two or many interconnected neurons is thought to play
important role in processing information in the central nervous system. Synchronous neural activity is believed to be part of many cognitive and sensory processing tasks such as feature binding, attention and memory construction. High levels of synchronization has been implicated in brain disorders like epilepsy, schizophrenia, Alzheimer's disease and Parkinson. Therefore, studying mechanisms underlying synchrony in the brain is of fundamental importance in understanding brain processes.
There has been little mathematical analysis of neural networks because the equations used to model these systems typically exhibit highly non-linear and stiff patterns. It is often difficult to make sense of the main events of neuronal dynamics from these models. In particular, in a network setting the question arises whether all the details described in the network models are required to comprehend the computation in large population of neurons. To gain intuitive insight into the dynamical properties of networks, by taking advantage of existence of different time scales in "spike generating" and modulatory current variables, we reduced the model to a biologically realistic discrete map involving most of the original system parameters to investigate the behavior of two layer excitatory-inhibitory oscillatory-synchronous neural networks for many different parameters as well as for many different network architectures including the ones that lead to lurching waves and irregular behaviors.
... The processing through synchronous oscillations is related to the temporal coding: an object is represented by temporal correlation of firing activities of spatially distributed neurons (von der Malsburg, 1981). In practice, a special form of temporal correlation, called oscillatory correlation, has been successfully applied to several computational problems (Terman and Wang, 1995;von der Malsburg and Schneider, 1986;Wang and Terman, 1997;Wang, 2005). The oscillatory correlation role can be described as follows: oscillators which represent different features of the same object are synchronized, while oscillators coding different objects are desynchronized (Wang, 2005). ...
Object selection refers to the mechanism of extracting objects of interest while ignoring other objects and background in a given visual scene. It is a fundamental issue for many computer vision and image analysis techniques and it is still a challenging task to artificial visual systems. Chaotic phase synchronization takes place in cases involving almost identical dynamical systems and it means that the phase difference between the systems is kept bounded over the time, while their amplitudes remain chaotic and may be uncorrelated. Instead of complete synchronization, phase synchronization is believed to be a mechanism for neural integration in brain. In this paper, an object selection model is proposed. Oscillators in the network representing the salient object in a given scene are phase synchronized, while no phase synchronization occurs for background objects. In this way, the salient object can be extracted. In this model, a shift mechanism is also introduced to change attention from one object to another. Computer simulations show that the model produces some results similar to those observed in natural vision systems.
... Exactly how this is accomplished is still uncertain, but apparently there are cortical mechanisms that promote sparseness (Barth & Poulet, 2012). Moreover, global inhibition tends to destroy synchronization (Terman & Wang, 1995) and decrease amplitude, so that, in the presence of certain input, development of a spatial pattern would be quenched for some time period. Intermittent application of global inhibition could encourage transient development of varied spatial patterns controlled by parameter values that change with stimulus or other input conditions. ...
A family of stochastic processes has quasi-cycle oscillations if its otherwise-damped oscillations are sustained by noise. Such a family forms the reaction part of a stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice. We find spatial patterns of oscillating quasi-cycles that resemble Turing patterns, called quasi-patterns. Specific properties of these patterns, such as local phase synchronization, can be predicted from the parameters of the reaction and of the Mexican Hat coupling. When the damping parameters of the reaction and diffusion parts are small and balanced, phase synchronization vanishes but amplitude patterns persist. These results extend our knowledge of the behaviour of coupled neural field equations and its dependence on stochastic fluctuations.
... Using different functions would not alter the results significantly. These functions are modified from those used in [30,50] so that the properties of f and g are as illustrated in figure 1. The function f is the same nonlinearity as in the FitzHugh-Nagumo [63,64] model, which is the simplest nonlinearity exhibiting a cubic xnullcline. ...
We study synaptically coupled neuronal networks to identify the role of coupling delays in network synchronized behaviour. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled with time-delayed synapses. The excitatory population is uncoupled, while the inhibitory population is tightly coupled without time delay. A geometric singular perturbation analysis yields existence and stability conditions for periodic solutions where the excitatory cells are synchronized and different phase relationships between the excitatory and inhibitory populations can occur, along with formulae for the periods of such solutions. In particular, we show that if there are no delays in the coupling, oscillations where the excitatory population is synchronized cannot occur. Numerical simulations are conducted to supplement and validate the analytical results. The analysis helps to explain how coupling delays in either excitatory or inhibitory synapses contribute to producing synchronized rhythms.
This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.
... As has increasingly been recognized in the past decades, the network paradigm is a useful one within which to understand and study a very large variety of natural systems [1][2][3][4][5][6]. These ideas have been applied in diverse contexts, with nodes representing entities ranging from neurons [7], genes [8,9], and humans [10], to animals [11], power grids [12], railway stations [13] etc. Depending upon how these nodes interact with each other, the connecting links can be unidirectional or bidirectional, and further, can have interesting topological structure. It has thus been found necessary and useful to study different types of networks, ranging from purely random networks such as that described by Erdős and Rényi (ER) [14], to highly structured networks with a power-law degree distribution [15], ordered networks in which some links are disordered [16], modular networks, and so on. ...
We examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata. Each automaton has b active states, a single silent state and r−b−1 refractory states, and can show ‘spiking’ or ‘bursting’ behavior, depending on the values of b. We show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of Erdõs–Rényi graphs as a function of edge probability. Different forms of heterogeneity allow distinct structural phase transitions to become relevant. We also show that the dynamics on the network can be described by a semi-annealed process and, as a result, can be related to the Boolean Lyapunov exponent.
... In her simulations, different groups of neurons are activated during separate epochs of gamma (with or without beta); if these groups later on are stimulated simultaneously, they become active at different phases of an oscillation or oscillate at somewhat different frequencies, creating a separation. D. L. Wang and colleagues (Liu and Wang, 1999;Terman and Wang, 1995;Wang and Terman, 1997) investigated the ability of a collection of cells to segment a visual scene. As in the current work, oscillators that fire produce inhibition that suppresses other cells. ...
... Neurons which represent the same object could be 'labeled' by the fact that they fire synchronously [Malsburg, 1981;Malsburg and Buhmann, 1992;Eckhorn et al., 1988;. Coding by synchrony has been studied extensively both experimentally [Eckhorn et al., 1988;Singer, 1994;Engel et al., 1991ab;Kreiter and Singer, 1992] and in models [Wang et al., 1990;Malsburg and Buhmann, 1992;Eckhorn, 1990;Aertsen and Arndt, 1993;Koenig and Schillen, 1991;Schillen and Koenig, 1991;Gerstner et al., 1993;Ritz et al. 1993;Terman and Wang, 1995;. For a review of potential mechanism, see [Ritz and Sejnowski, 1997]. ...
... This approach has been successfully applied to image segmentation. In the locally excitatory globally inhibitory oscillator network model proposed by [4] [5], coupled oscillators are represented by ordinary differential equations. This method effectively segments input images into image regions [6] [7]. ...
In this
study, we propose a novel discrete-time coupled model to generate oscillatory
responses via periodic points with a high periodic order. Our coupled system
comprises one-dimensional oscillators based on the Rulkov map and a single
globally coupled oscillator. Because the waveform of a one-dimensional
oscillator has sharply defined peaks, the coupled system can be applied to dynamic
image segmentation. Our proposed system iteratively transforms the coupling of
each oscillator based on an input value that corresponds to the pixel value of
an input image. This approach enables our system to segment image regions in
which pixel values gradually change with respect to a connected region. We conducted
a bifurcation analysis of a single oscillator and a three-coupled model.
Through simulations, we demonstrated that our system works well for gray-level
images with three isolated image regions.
... The dynamics of networks of spiking neurones have received in the last decade a large amount of interest from theorists. Early studies focused on fully connected and noiseless systems [1, 28, 33, 34, 39, 48, 65, 69], or locally coupled systems [43, 64]. In these systems, the dynamics generally converges to states in which neurones behave like oscillators. ...
Recent advances in the understanding of the dynamics of populations of spiking neurones are reviewed. These studies shed light on how a population of neurones can follow arbitrary variations in input stimuli, how the dynamics of the population depends on the type of noise, and how recurrent connections influence the dynamics. The importance of inhibitory feedback for the generation of irregularity in single cell behaviour is emphasized. Examples of computation that recurrent networks with excitatory and inhibitory cells can perform are then discussed. Maintenance of a network state as an attractor of the system is discussed as a model for working memory function, in both object and spatial modalities. These models can be used to interpret and make predictions about electrophysiological data in the awake monkey.
... The authors then extract waterbodies by applying a threshold value to these indices, extracting both wide and narrow waterbodies and finally combining all the extracted waterbodies. An automatic object-based waterbody extraction method was developed by [5] based on NDWI using the Locally Excitatory Globally Inhibitory Oscillator Networks (LEGION) as promulgated by [6]. Using a Perceptron Model, [7] developed an automated waterbody extraction routine for Landsat-7 ETM+ by feeding the low reflectance of water in the SWIR band, the relatively lower reflectance in the NIR band to the green band and in the red to the NIR band, and a binary of the summation of NDWI and MNDWI as feature vectors to the model. ...
Water is a very important natural resource and it supports all life forms on earth. It is used by humans in various ways including drinking, agriculture and for scientific research. The aim of this research was to develop a routine to automatically extract water masks from RapidEye images, which could be used for further investigation such as water quality monitoring and change detection. A Python-based algorithm was therefore developed for this particular purpose. The developed routine combines three spectral indices namely Simple Ratios (SRs), Normalized Green Index (NGI) and Normalized Difference Water Index (NDWI). The two SRs are calculated between the NIR and green band, and between the NIR and red band. The NGI is calculated by rationing the green band to the sum of all bands in each image. The NDWI is calculated by differencing the green to the NIR and dividing by the sum of the green and NIR bands. The routine generates five intermediate water masks, which are spatially intersected to create a single intermediate water mask. In order to remove very small waterbodies and any remaining gaps in the intermediate water mask, morphological opening and closing were performed to generate the final water mask. This proposed algorithm was used to extract water masks from some RapidEye images. It yielded an Overall Accuracy of 95% and a mean Kappa Statistic of 0.889 using the confusion matrix approach.
... 利用 TW 神经元模型 [27] , 我们构造具有电突 触耦合及 WS 小世界拓扑结构的神经元网络系统, ...
In this paper, by using the Terman-Wang small-world neuronal network with electrical synapse coupling, we investigate the synchronous dynamics of neuronal network system subjected to spatially correlated white noise. First, the dynamical mean-field approximation theory is extended to the small-world network system under spatially correlated white noise, through which the original 2N-dimensional stochastic differential equations of the network system are transformed to 11-dimensional deterministic moment differential equations. Then, based on this set of moment differential equations, the key effects of spatially correlated noise and network structure on the synchronous firing property are discussed in the Terman-Wang neuronal network system. The results show that the synchronization ratio of this considered neuronal network system becomes higher not only as the noise correlation coefficient is increased but also as the coupling strength and the average vertex degree are added. Those results imply that the noise spatial correlation coefficient, the coupling strength, and the average vertex degree can play a positive role in inducing synchronous neuronal behaviors. Furthermore, the synchronous dynamics of the original neuronal network system, obtained by direct numerical simulations, is compared with those obtained by the dynamical mean-field approximation theory, and good consistence between them is revealed.
Complex systems are based on interacting local computational units may show non-trivial emerging behaviors. Examples are the time evolution of an infectious disease in a certain city that is mutually influenced by an ongoing outbreak of the same disease in another city, or the case of a neuron firing spontaneously while processing the effects of afferent axon potentials.
A fundamental question is whether the time evolutions of interacting local units remain dynamically independent of each other, or whether they will change their states simultaneously, following identical rhythms. This is the notion of synchronization, which we will study throughout this chapter. Starting with the paradigmatic Kuramoto model we will learn that synchronization processes may be driven either by averaging dynamical variables, or through causal mutual influences. On the way, we will visit piecewise linear dynamical systems and the reference model for infectious diseases, the SIRS model.
The diverse roles of inhibition in neural circuits and other dynamical networks are receiving renewed interest.
Here, it is shown that increasing global inhibitory feedback leads to gradual rounding of first-order transition
between dynamical phases, turning it into second-order transition. The effect is initially observed in an
electronic model consisting of a bi-dimensional array of neon glow lamps, where global inhibition can be
simply introduced through a resistor in series with the supply voltage. The experimental findings are confirmed
using both an extended numerical model and a mean-field approximation, then replicated across different
models of neural dynamics, namely, the Wilson–Cowan model and a network of leaky integrate-and-fire
neurons. Across all these systems, a critical point is always found as a function of a pair of parameters
controlling local excitability and global inhibition strength, and a general explanation revealing the roles of
the shape of the activation function and voltage fluctuations versus the extinction time-scale is provided.
It is speculated that the brain could use global inhibition as a versatile means of shifting between first- and
second-order dynamics, addressing the conundrum regarding the coexistence in neural dynamics of phenomena
stemming from both. Some reflections regarding the comparison with other physical systems and the possible
physiological significance are offered, and a hypothetical setup for an optogenetics experiment on cultured
neurons is put forward.
Neural coupled oscillators are a useful building block in numerous models and applications. They were analyzed extensively in theoretical studies and more recently in biologically realistic simulations of spiking neural networks. The advent of mixed-signal analog/digital neuromorphic electronic circuits provides new means for implementing neural coupled oscillators on compact, low-power, spiking neural network hardware platforms. However, their implementation on this noisy, low-precision and inhomogeneous computing substrate raises new challenges with regards to stability and controllability. In this work, we present a robust, spiking neural network model of neural coupled oscillators and validate it with an implementation on a mixed-signal neuromorphic processor. We demonstrate its robustness showing how to reliably control and modulate the oscillator’s frequency and phase shift, despite the variability of the silicon synapse and neuron properties. We show how this ultra-low power neural processing system can be used to build an adaptive cardiac pacemaker modulating the heart rate with respect to the respiration phases and compare it with surface ECG and respiratory signal recordings from dogs at rest. The implementation of our model in neuromorphic electronic hardware shows its robustness on a highly variable substrate and extends the toolbox for applications requiring rhythmic outputs such as pacemakers.
Costly punishment and reward have been regarded as potential means to handle the conundrum of cooperation. However, providing incentives is costly, thus the emergence of costly punishment and reward is a major puzzle in the evolution of cooperation. Recently, it is found that pure punishers, who do not help others but punish free-riders, have an evolutionary advantage. In this work, based on the pure punishment strategy, we further propose tax-based pure punishment and reward strategies in the public goods game respectively by considering that in realistic world the dedicated sanctioning or rewarding agencies can receive a certain amount of revenue tax to penalize evildoers or reward good men. By means of theoretical analysis and numerical calculations, we find that tax-based pure punishment (reward) has an evolutionary advantage over pure punishment (reward) in sustaining cooperation, and tax-based pure reward can lead to higher level of cooperation than tax-based pure punishment.
The present work deals with the analysis of the synchronization possibility in chaotic oscillators, either completely or per phase, using a coupling force among them, so they can be used in attention systems. The neural models used were Hodgkin-Huxley, Hindmarsh-Rose, Integrate-and-Fire, and Spike-Response-Model. Discrete models such as Aihara, Rulkov, Izhikevic, and Courbage-Nekorkin-Vdovin were also evaluated. The dynamical systems’ parameters were varied in the search for chaos, by analyzing trajectories and bifurcation diagrams. Then, a coupling term was added to the models to analyze synchronization in a couple, a vector, and a lattice of oscillators. Later, a lattice with variable parameters is used to simulate different biological neurons. Discrete models did not synchronize in vectors and lattices, but the continuous models were successful in all stages, including the Spike Response Model, which synchronized without the use of a coupling force, only by the synchronous time arrival of presynaptic stimuli. However, this model did not show chaotic characteristics. Finally, in the models in which the previous results were satisfactory, lattices were studied where the coupling force between neurons varied in a non-random way, forming clusters of oscillators with strong coupling to each other, and low coupling with others. The possibility of identifying the clusters was observed in the trajectories and phase differences among all neurons in the reticulum detecting where it occurred and where there was no synchronization. Also, the average execution time of the last stage showed that the fastest model is the Integrate-and-Fire.
LEGION (Locally Excitatory, Globally Inhibitory Oscillator Network)topology has demonstrated good capabilities in scene segmentation applications. However, the implementation of LEGION algorithm requires machines with high performance to process a set of complex differential equations limiting its use in practical real-time applications. Recently, several authors have proposed alternative methods based on spiking neural networks (SNN)to create oscillatory neural networks with low computational complexity and highly feasible to be implemented on digital hardware to perform adaptive segmentation of images. Nevertheless, existing SNN with LEGION configuration focus on the membrane model leaving aside the behavior of the synapses although they play an important role in the synchronization of several segments by self-adapting their weights. In this work, we propose a SNN-LEGION configuration along with normalized weight of the synapses to self-adapt the SNN network to synchronize several segments of any size and shape at the same time. The proposed SNN-LEGION method involves a global inhibitor, which is in charge of performing the segmentation process between different objects with different sizes and shapes on time. To validate the proposal, the SNN-LEGION method is implemented on an optimized scalable neuromorphic architecture. Our preliminary results demonstrate that the proposed normalization process of the synaptic weights along with the SNN-LEGION configuration keep the capacity of the LEGION network to separate the segments on time, which can be useful in video processing applications such as vision processing systems for mobile robots, offering lower computational complexity and area consumption compared with previously reported solutions.
In this numerical work, we have systematically studied the dynamical phase transitions in the Kuramoto–Sakaguchi model of synchronizing phase oscillators controlled by disorder in the Sakaguchi phases. We derive the numerical steady state phase diagrams for quenched and annealed kinds of disorder in the Sakaguchi parameters, using the conventional order parameter and other such statistical quantities as strength of incoherence and discontinuity measures. We have also considered the correlation profile of the local order parameter fluctuations in the various phases identified. The phase diagrams for quenched disorder are qualitatively much different from those in the global coupling regime. The order of various transitions is confirmed by a study of the distribution of the order parameter and its fourth order Binder's cumulant across the transition for an ensemble of initial distribution of phases. For the annealed type of disorder, in contrast to the case with quenched disorder, the system is almost insensitive to the amount of disorder. We also elucidate the role of chimeralike states in the synchronizing transition of the system, and study the effect of disorder on these states. Finally, we seek justification of our results from simulations guided by the Ott–Antonsen ansatz.
Pulsed neural network models can account for the cognitive processes in which internal states change rapidly and abruptly. This study constructed a pulsed neural network model for selective visual attention based on the temporal tagging hypothesis. According to the temporal tagging hypothesis, the effect of visual attention reflects the modulation of spatiotemporal correlation of neural activities, not the modulation of firing rates. The proposed model produced the temporal synchrony of spikes purely within the simple spike response model framework. The model could simulate the data from Moran & Desimone (1985), and showed that simple pulsed neural networks without excessive neurophysiological details were at the appropriate level for the models of visual cognition. Compared with traditional connectionist models, pulsed neural network models appear to be the better framework to deal with real-time temporal dynamics of cognitive process including feature binding.
Integrated circuit of a new neuron chain with a synapse function for Hodgkin-Huxley model which is a good electrical model about a real biological neuron is implemented in a 0.5?m 1 poly 2 metal CMOS technology. Pulse type neuron chain consist of series connected current controlled single neurons through synapses. For the realization of the single neuron, a pair of voltage mode oscillators using operational transconductance amplifiers and capacitors is used. The synapse block which is a connection element between neurons consist of a voltage-current conversion circuit using current mirror. SPICE simulation results of the proposed circuit show 160 mV amplitude pulse output and propagation of the signal through synapses. Measurements of the fabricated pulse type neuron chip in condition of ?2.5\;V power supply are shown and compared with the simulated results.
In this chapter we touch on several application areas in which time scale separation arises naturally. As you can guess from the rather diverse set of section headings, it is quite reasonable to conjecture that most quantitative sciences that employ mathematical modeling may eventually encounter various multiscale problems. Each section centers on one or two key examples in which one can clearly identify the time scale separation parameter as well as apply many of the methods discussed in this book.
Here we consider the dynamics of complex systems constituted of interacting local computational units that have their own non-trivial dynamics. An example for a local dynamical system is the time evolution of an infectious disease in a certain city that is weakly influenced by an ongoing outbreak of the same disease in another city; or the case of a neuron in a state where it fires spontaneously under the influence of the afferent axon potentials. A fundamental question is then whether the time evolutions of these local computational unit will remain dynamically independent of each other or whether, at some point, they will start to change their states all in the same rhythm. This is the notion of “synchronization”, which we will study throughout this chapter. Starting with the paradigmal Kuramoto model we will learn that synchronization processes may be driven either by averaging dynamical variables or through causal mutual influences.
We investigate the spatial and temporal aspects of firing patterns in a network of integrate-and-fire neurons arranged in a one-dimensional ring topology. The coupling is stochastic and shaped like a Mexican hat with local excitation and lateral inhibition. With perfect precision in the couplings, the attractors of activity in the network occur at every position in the ring. Inhomogeneities in the coupling break the translational invariance of localized attractors and lead to synchronization within highly active as well as weakly active clusters. The interspike interval variability is high, consistent with recent observations of spike time distributions in visual cortex. The robustness of our results is demonstrated with more realistic simulations on a network of McGregor neurons which model conductance changes and after-hyperpolarization potassium currents.
The present study analyses the problem of binding and segmentation of a visual scene by means of a network of neural oscillators, laying emphasis on the problems of fragmentation, perception of details at different scales and spatial attention. The work is based on a two-layer model: a second layer of Wilson–Cowan oscillators is inhibited by information from the first layer. Moreover, the model uses a global inhibitor (GI) to segment objects. Spatial attention consists of an excitatory input, surrounded by an inhibitory annulus. A single object is identified by synchronous oscillatory activity of neural groups. The main idea of this work is that segmentation of objects at different detail levels can be achieved by linking parameters of the GI (i.e. the threshold and the inhibition strength) with the dimension of the zone selected by attention and with the dimension of the smaller objects to be detected. Simulations show that three possible kinds of behavior can be attained with the model, through proper choice of the GI parameters and attention input: (i) large objects in the visual scene are perceived, while small details are suppressed; (ii) large objects are perceived, while details are assembled together to constitute a single ‘noise term’; (iii) if attention is focused on a smaller area and the GI parameters modulated accordingly (i.e. the threshold and attention strength are reduced) details are individually perceived as separate objects. These results suggest that the GI and attention may represent two concurrent aspects of the same attentive mechanism, i.e. they should work together to provide flexible management of a visual scene at different levels of detail.
Synchronisation and coordination are omnipresent and essential in humans interactions. Because of their unavoidable and unintentional aspect, those phenomena could be the consequences of a low level mechanism: a driving force originating from external stimuli called the entrainment effect. In the light of its importance in interaction and wishing to define new HRI, we suggest to model this entrainment to highlight its efficiency for gesture learning during imitative games and for reducing the computational complexity. We will put forward the capacity of adaptation offered by the entrainment effect. Hence, we present in this paper a neural model for gesture learning by imitation using entrainment effect applied to a NAO robot interacting with a human partner.
Spin-torque induced magnetization dynamics in a magnetoresistive nanopillar with a conically magnetized free layer and an in-plane magnetized reference layer is theoretically studied. Two modes are observed for zero-bias-field self-oscillation, the occurrence of which depends on applied current density: one is the in-plane oscillation mode at small current density and the other is the out-of-plane oscillation mode at large current density. The mechanism for the appearance of these oscillation modes are explained, and the critical current densities of the modes are presented.
We study the role of network architecture and synaptic inputs in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. Through analysis and numerics, we show that the stability of the completely synchronous state, representing the largest cluster, only depends on the number of synaptic inputs each neuron receives, independent from all other details of the network topology. We also give a simple combinatorial algorithm that finds synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We address the asymptotic stability of cluster synchronization in excitatory networks of bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.
In this paper proposed a GPU-based parallel processing method for real-time image segmentation with neural oscillator network. Range image segmentation methods can be divided into two categories: edge-based and region-based. Edge-base method is sensitive to noise and region-based method is hard to extracting the boundary detail between the object. However, by using LEGION (Locally Excitatory Globally Inhibitory oscillator networks) to do range image segmentation can overcome above disadvantages. The reason why LEGION is suitable for parallel processing that each oscillator calculate with its 8-neiborhood oscillators in real time when we process image segmentation by LEGION. Thus, using GPU-based parallel processing with LEGION can improve the speed to realize real-time image segmentation.
A new model based on the structure of V1 area in the biological visual system was presented for image searching. The model only uses the known V1 elements, such as orientation selective cells and horizontal intra-cortical connections. The knowledge, which will control the dynamic of the neurons, is represented by the chain code of the object's contour. The chain code is presented to the neural network in timing pulse form. By cooperating with the dynamic weights, only the neurons of the contour according with the object contour will reach the active state and stay there. Finally the contour that conforms to the knowledge contour emerges in the visual area, and the object is located.
An image segmentation scheme was presented on the basis of locally excitatory, globally inhibitory oscillator network (LEGION). Based on the concept of the lateral potential, a solution to remove noisy regions in an image was proposed for LEGION. The temporal evolution of every stimulated oscilltor and network properties were illustrated by computer simulation. The dynamic connection weight addressing the grouping principles of proximity, similarity and connectedness was setup. Using HSI space, the dynamic connection weight emphasizing the Hue information was established, and better experimental results than that based on RGB space were obtained.
In this paper propose a GPU-based parallel processing method for real-time image segmentation with neural oscillator network. Range image segmentation methods can be divided into two categories: edge-based and region-based. Edge-base method is sensitive to noise and region-based method is hard to extracting the boundary detail between the object. However, by using LEGION (Locally Excitatory Globally Inhibitory oscillator networks) to do range image segmentation can overcome above disadvantages. The reason why LEGION is suitable for parallel processing that each oscillator calculate with its 8-neiborhood oscillators in real time when we process image segmentation by LEGION. Thus, using GPU-based parallel processing with LEGION can improve the speed to realize real-time image segmentation.
The goal of this paper is to show how to modify associative memory such that it can discriminate several stored patterns in a composite input and represent them simultaneously. Segmention of patterns takes place in the temporal domain, components of one pattern becoming temporally correlated with each other and anticorrelated with the components of all other patterns. Correlations are created naturally by the usual associative connections. In our simulations, temporal patterns take the form of oscillatory bursts of activity. Model oscillators consist of pairs of local cell populations connected appropriately. Transition of activity from one pattern to another is induced by delayed self-inhibition or simply by noise.
Current concepts in neurobiology of vision assume that local object features are represented by distributed neuronal populations in the brain. Such representations can lead to ambiguities if several distinct objects are simultaneously present in the visual field. Temporal characteristics of the neuronal activity have been proposed as a possible solution to this problem and have been found in various cortical areas.
In this paper we introduce a delayed nonlinear oscillator to investigate temporal coding in neuronal networks. We show synchronization within two-dimensional layers consisting of oscillatory elements coupled by excitatory delay connections. The observed correlation length is large compared to coupling length. Following the experimental situation, we then demonstrate the response of such layers to two short stimulus bars of varying gap distance. Coherency of stimuli is reflected by the temporal correlation of the responses, which closely resembles the experimental observations.
A nerve net model for the visual cortex of higher vertebrates is presented. A simple learning procedure is shown to be sufficient for the organization of some essential functional properties of single units. The rather special assumptions usually made in the literature regarding preorganization of the visual cortex are thereby avoided. The model consists of 338 neurones forming a sheet analogous to the cortex. The neurones are connected randomly to a retina of 19 cells. Nine different stimuli in the form of light bars were applied. The afferent connections were modified according to a mechanism of synaptic training. After twenty presentations of all the stimuli individual cortical neurones became sensitive to only one orientation. Neurones with the same or similar orientation sensitivity tended to appear in clusters, which are analogous to cortical columns. The system was shown to be insensitive to a background of disturbing input excitations during learning. After learning it was able to repair small defects introduced into the wiring and was relatively insensitive to stimuli not used during training.
There are now a wide variety of image segmentation techniques, some considered general purpose and some designed for specific classes of images. These techniques can be classified as: measurement space guided spatial clustering, single linkage region growing schemes, hybrid linkage region growing schemes, centroid linkage region growing schemes, spatial clustering schemes, and split-and-merge schemes. In this paper, each of the major classes of image segmentation techniques is defined and several specific examples of each class of algorithm are described. The techniques are illustrated with examples of segmentations performed on real images.
Recent experimental findings (Gray et al. 1989; Eckhorn et al. 1988) seem to indicate that rapid oscillations and phase-lockings of different populations of cortical neurons play an important role in neural computations. In particular, global stimulus properties could be reflected in the correlated firing of spatially distant cells. Here we describe how simple coupled oscillator networks can be used to model the data and to investigate whether useful tasks can be performed by oscillator architectures. A specific demonstration is given for the problem of preattentive texture discrimination. Texture images are convolved with different sets of Gabor filters feeding into several corresponding arrays of coupled oscillators. After a brief transient, the dynamic evolution in the arrays leads to a separation of the textures by a phase labeling mechanism. The importance of noise and of long range connections is briefly discussed.
A summary of brain theory is given so far as it is contained within the framework of Localization Theory. Diffculties of this "conventional theory" are traced back to a specific deficiency: there is no way to express relations between active cells (as for instance their representing parts of the same object). A new theory is proposed to cure this deficiency. It introduces a new kind of dynamical control, termed synaptic modulation, according to which synapses switch between a conducting and a non- conducting state. The dynamics of this variable is controlled on a fast time scale by correlations in the temporal fine structure of cellular signals. Furthermore, conventional synaptic plasticity is replaced by a refined version. Synaptic modulation and plasticity form the basis for short-term and long-term memory, respectively. Signal correlations, shaped by the variable network, express structure and relationships within objects. In particular, the figure-ground problem may be solved in this way. Synaptic modulation introduces flexibility into cerebral networks which is necessary to solve the invariance problem. Since momentarily useless connections are deactivated, interference between different memory traces can be reduced, and memory capacity increased, in comparison with conventional associative memory.
We present a model of sensory segmentation that is based on the generation and processing of temporal tags in the form of oscillations, as suggested by the Dynamic Link Architecture. The model forms the basis for a natural solution to the sensory segmentation problem. It can deal with multiple segments, can integrate different cues and has the potential for processing hierarchical structures. Temporally tagged segments can easily be utilized in neural systems and form a natural basis for object recognition and learning. The model consists of a "cortical" circuit, an array of units that act as local feature detectors. Units are formulated as neural oscillators. Knowledge relevant to segmentation is encoded by connections. In accord with simple Gestalt laws, our concrete model has intracolumnar connections, between all units with overlapping receptive fields, and intercolumnar connections, between units responding to the same quality in different positions. An inhibitory connection system prevents total correlation and controls the grain of the segmentation. In simulations with synthetic input data we show the performance of the circuit, which produces signal correlation within segments and anticorrelation between segments.
The segmentation of visual scenes is a fundamental process of early vision, but the underlying neural mechanisms are still largely unknown. Theoretical considerations as well as neurophysiological findings point to the importance in such processes of temporal correlations in neuronal activity. In a previous model, we showed that reentrant signaling among rhythmically active neuronal groups can correlate responses along spatially extended contours. We now have modified and extended this model to address the problems of perceptual grouping and figure-ground segregation in vision. A novel feature is that the efficacy of the connections is allowed to change on a fast time scale. This results in active reentrant connections that amplify the correlations among neuronal groups. The responses of the model are able to link the elements corresponding to a coherent figure and to segregate them from the background or from another figure in a way that is consistent with the so-called Gestalt laws.
Neurons in area 17 of cat visual cortex display oscillatory responses that can synchronize across spatially separate columns in a stimulus-specific way. Response synchronization has now been shown to occur also between neurons in area 17 of the right and left cerebral hemispheres. This synchronization was abolished by section of the corpus callosum. Thus, the response synchronization is mediated by corticocortical connections. These data are compatible with the hypothesis that temporal synchrony of neuronal discharges serves to bind features within and between the visual hemifields.
Recent studies have shown that neurons in area 17 of cat visual cortex display oscillatory responses which can synchronize across spatially separate orientation columns. Here, we demonstrate that unit responses recorded from the posteromedial lateral suprasylvian area, a visual association area specialized for the analysis of motion, also exhibit an oscillatory temporal structure. Cross-correlation analysis of unit responses reveals that cells in area 17 and the posteromedial lateral suprasylvian area can oscillate synchronously. Moreover, we find that the interareal synchronization is sensitive to features of the visual stimuli, such as spatial continuity and coherence of motion. These results support the hypothesis that synchronous neuronal oscillations may serve to establish relationships between features processed in different areas of visual cortex.
Recent experiments have revealed tightly synchronized oscillatory discharges in local assemblies of cortical neurons as well as phase coherency of oscillations at distant cortical sites. These findings are consistent with the theory of neuronal group selection, a population theory of brain function that is based on the properties of local groups of neurons. A set of computer simulations shows that cooperative interactions within and among neuronal groups can generate the observed phenomena. In the simulations, oscillations within neuronal groups are generated through local excitatory and inhibitory interactions. Different groups in general oscillate in an uncorrelated fashion. Coherency of the oscillatory activity of different neuronal groups depends crucially on reciprocal reentrant signaling and can reflect the spatial continuity of a stimulus. Separated or discontinuous features of a given stimulus can be transiently associated in a temporally coherent pattern through reentrant signaling between groups in networks responding to different aspects of that stimulus. A simulation of reentrant activity between arrays of neuronal groups selective for oriented lines and pattern motion displays cross-correlations between groups that are responsive to different parts of a stimulus contour if these parts move together. Such coherency among neuronal groups might be used in the discrimination of a stimulus from other stationary or differentially moving elements in a visual scene.
A fundamental step in visual pattern recognition is the establishment of relations between spatially separate features. Recently, we have shown that neurons in the cat visual cortex have oscillatory responses in the range 40-60 Hz (refs 1, 2) which occur in synchrony for cells in a functional column and are tightly correlated with a local oscillatory field potential. This led us to hypothesize that the synchronization of oscillatory responses of spatially distributed, feature selective cells might be a way to establish relations between features in different parts of the visual field. In support of this hypothesis, we demonstrate here that neurons in spatially separate columns can synchronize their oscillatory responses. The synchronization has, on average, no phase difference, depends on the spatial separation and the orientation preference of the cells and is influenced by global stimulus properties.
Primary visual coding can be characterized by the receptive field (RF) properties of single neurons. Subject of this paper is our search for a global, second coding step beyond the RF-concept that links related features in a visual scene. In recent models of visual coding, oscillatory activities have been proposed to constitute such linking signals. We tested the neurophysiological relevance of this hypothesis for the visual system. Single and multiple spikes as well as local field potentials were recorded simultaneously from several locations in the primary visual cortex (A17 and A18) using 7 or 19 individually advanceable fiber-microelectrodes (250 or 330 microns apart). Stimulus-evoked (SE)-resonances of 35-85 Hz were found in these three types of signals throughout the visual cortex when the primary coding channels were activated by their specific stimuli. Stimulus position, orientation, movement direction and velocity, ocularity and stationary flicker caused specific SE-resonances. Coherent SE-resonances were found at distant cortical positions when at least one of the primary coding properties was similar. Coherence was found 1) within a vertical cortex column, 2) between neighbouring hypercolumns, and 3) between two different cortical areas. We assume that the coherence of SE-resonances is mediated by recurrent excitatory intra- and inter-areal connections via phase locking between assemblies that represent the linking features of the actual visual scene. Visually related activities are, thus, transiently labelled by a temporal code that signalizes their momentary association.
Sensory segmentation is an outstanding unsolved problem of theoretical, practical and technical importance. The basic idea of a solution is described in the form of a model. The response of "neurons" within the sensory field is temporally unstable. Segmentation is expressed by synchronization within segments and desynchronization between segments. Correlations are generated by an autonomous pattern formation process. Neuronal coupling is the result both of peripheral evidence (similarity of local quality) and of central evidence (common membership in a stored pattern). The model is consistent with known anatomy and physiology. However, a new physiological function, synaptic modulation, has to be postulated. The present paper restricts explicit treatment to the peripheral evidence represented by amplitude modulations globally present in all components of a sound spectrum. Generalization to arbitrary sensory qualities will be the subject of a later paper. The model is an application and illustration of the Correlation Theory of brain function.
Computer techniques readily extract from the brainwaves an orderly sequence of brain potentials locked in time to sound stimuli. The potentials that appear 8 to 80 msec after the stimulus resemble 3 or 4 cycles of a 40-Hz sine wave; we show here that these waves combined to form a single, stable, composite wave when the sounds are repeated at rates around 40 per sec. This phenomenon, the 40-Hz event-related potential (ERP), displays several properties of theoretical and practical interest. First, it reportedly disappears with surgical anesthesia, and it resembles similar phenomena in the visual and olfactory system, facts which suggest that adequate processing of sensory information may require cyclical brain events in the 30- to 50-Hz range. Second, latency and amplitude measurements on the 40-Hz ERP indicate it may contain useful information on the number and basilar membrane location of the auditory nerve fibers a given tone excites. Third, the response is present at sound intensities very close to normal adult thresholds for the audiometric frequencies, a fact that could have application in clinical hearing testing.
We present a theoretical model which is used to explain the intersegmental coordination of the neural networks responsible for generating locomotion in the isolated spinal cord of lamprey. A simplified mathematical model of a limit cycle oscillator is presented which consists of only a single dependent variable, the phase theta(t). By coupling N such oscillators together we are able to generate stable phase locked motions which correspond to traveling waves in the spinal cord, thus simulating "fictive swimming". We are also able to generate irregular "drifting" motions which are compared to the experimental data obtained from cords with selective surgical lesions.
Synchronization properties of locally coupled neural oscillators were investigated analytically and by computer simulation. When coupled in a manner that mimics excitatory chemical synapses, oscillators having more than one time scale (relaxation oscillators) are shown to approach synchrony using mechanisms very different from that of oscillators with a more sinusoidal waveform. The relaxation oscillators make critical use of fast modulations of their thresholds, leading to a rate of synchronization relatively independent of coupling strength within some basin of attraction; this rate is faster for oscillators that have conductance-based features than for neural caricatures such as the FitzHugh-Nagumo equations that lack such features. Computer simulations of one-dimensional arrays show that oscillators in the relaxation regime synchronize much more rapidly than oscillators with the same equations whose parameters have been modulated to yield a more sinusoidal waveform. We present a heuristic explanation of this effect based on properties of the coupling mechanisms that can affect the way the synchronization scales with array length. These results suggest that the emergent synchronization behavior of oscillating neural networks can be dramatically influenced by the intrinsic properties of the network components. Possible implications for perceptual feature binding and attention are discussed.
An oscillator neural network model that is capable of processing local and global attributes of sensory input is proposed and analyzed. Local features in the input are encoded in the average firing rate of the neurons while the relationships between these features can modulate the temporal structure of the neuronal output. Neurons that share the same receptive field interact via relatively strong feedback connections, while neurons with different fields interact via specific, relatively weak connections. The model is studied in the context of processing visual stimuli that are coded for orientation. The effect of axonal propagation delays on synchronization of oscillatory activity is analyzed. We compare our theoretical results with recent experimental evidence on coherent oscillatory activity in the cat visual cortex. The computational capabilities of the model for performing discrimination and segmentation tasks are demonstrated. Coding and linking of visual features other than orientation are discussed.
A variety of researches are examined from the standpoint of information theory. It is shown that the unaided observer is severely limited in terms of the amount of information he can receive, process, and remember. However, it is shown that by the use of various techniques, e.g., use of several stimulus dimensions, recoding, and various mnemonic devices, this informational bottleneck can be broken. 20 references. (PsycINFO Database Record (c) 2006 APA, all rights reserved).
Neurons in area 17 of cat visual cortex display oscillatory responses
that can synchronize across spatially separate columns in a
stimulus-specific way. Response synchronization has now been shown to
occur also between neurons in area 17 of the right and left cerebral
hemispheres. This synchronization was abolished by section of the corpus
callosum. Thus, the response synchronization is mediated by
corticocortical connections. These data are compatible with the
hypothesis that temporal synchrony of neuronal discharges serves to bind
features within and between the visual hemifields.
Visual awareness is a favorable form of consciousness to study neurobiologically. We propose that it takes two forms: a very fast form, linked to iconic memory, that may be difficult to study; and a somewhat slower one involving visual attention and short-term memory. In the slower form an attentional
mechanism transiently binds together all those neurons whose activity relates to the relevant features of a single visual object. We suggest this is done by generating coherent semi-synchronous oscillations, probably in the 40-70 Hz range. These oscillations then activate a transient short-term
(working) memory. We outfit several lines of experimental work that might advance the understanding of the neural mechanisms involved. The neural basis of very short-term memory especially needs more experimental study.
Acoustic energy from many different sources is present in the environment at all times. In order for a listener to recognize and understand the auditory environment, it is necessary to disentangle the acoustic wave form and analyze each separate event. This process is referred to as temporal pattern segmentation, or auditory scene analysis (Bregman, 1990). Its task is to break down an auditory scene, or total acoustic input, into a number of coherent segments, each of which has a high probability of coming from the same source. Temporal pattern segmentation (temporal segmentation for short) is a remarkable achievement of the auditory system, playing a fundamental role in auditory perception. It has much in common with visual segmentation of a scene into different objects. Segmentation can be based on either current input or prior knowledge. Segmentation based on current input relies on the similarities of local qualities within the input pattern itself, such as frequency, timing, or amplitude. On the other hand, segmentation based on prior knowledge relies on patterns stored in memory to segregate the auditory input. These two processes occur simultaneously in auditory scene analysis.
It has been demonstrated that the nervous system exhibits stimulus-dependent oscillations, and synchronization exists in spatially remote sites which reflects global stimulus properties. This paper addresses the neural mechanisms that underlie this phenomenon. We find that locally coupled neural oscillators can yield global phase synchrony. The model assumes that the efficacy of the connections can be modified on a fast time scale. Based on the known connectivity of the visual cortex, the model outputs closely resemble the experimental findings of neural oscillations. This model lays a computational foundation for Gestalt perceptual grouping.
Recent studies have shown that neurons in area 17 of cat visual cortex display oscillatory responses which can synchronize across spatially separate orientation columns. Here, we demonstrate that unit responses recorded from the posteromedial lateral suprasylvian area, a visual association area specialized for the analysis of motion, also exhibit an oscillatory temporal structure. Cross-correlation analysis of unit responses reveals that cells in area 17 and the posteromedial lateral suprasylvian area can oscillate synchronously. Moreover, we find that the interareal synchronization is sensitive to features of the visual stimuli, such as spatial continuity and coherence of motion. These results support the hypothesis that synchronous neuronal oscillations may serve to establish relationships between features processed in different areas of visual cortex.
The segmentation algorithm proposed in this paper is a complex form of thresholdingwhich utilizes multiple thresholds. The algorithm consists of two major components: a threshold selection component and a relaxation component. The threshold selection component is the primary focus of this paper. It automatically selects a threshold so as to maximize the global average contrast of edges detected by the threshold across the image. This algorithm for threshold selection compares favorably with other methods for automatic threshold selection. The threshold selection algorithm can be applied recursively to select additional thresholds by ignoring any edges which have already been detected by previously selected thresholds. The relaxation component utilizes the immediate spatial context of each pixel to update both the label at the pixel and the feature measurement at the pixel. The update function proposes a new feature value at the pixel defined by a weighted average of the central pixel and all of its neighbors. When the local evidence for shifting the feature value is consistent then the value adopted will be close to the proposed value; however, when the local evidence is inconsistent the value adopted will be close to the original value. The relaxation is independently performed for each threshold selected. The resulting binary images are intersected to produce the final segmentation. This algorithm not only works well for simple images but also produces reasonable segmentations for complex images.
A mathematical model of the process of pattern recognition in the first olfactory sensory cortex of the rabbit is presented. It explains the formation and alteration of spatial patterns in neural activity observed experimentally during classical Pavlovian conditioning. On each inspiration of the animal, a surge of receptor input enters the olfactory bulb. EEG activity recorded at the surface of the bulb undergoes a transition from a low amplitude background state of temporal disorder to coherent oscillation. There is a distinctive spatial pattern of rms amplitude in this oscillation which changes reliably to a second pattern during each successful recognition by the animal of a conditioned stimulus odor. When a new odor is paired as conditioned stimulus, these patterns are replaced by new patterns that stabilize as the animal adapts to the new environment.I will argue that a unification of the theories of pattern formation and associative memory is required to account for these observations. This is achieved in a model of the bulb as a discrete excitable medium with spatially inhomogeneous coupling expressed by a connection matrix. The theory of multiple Hopf bifurcations is employed to find coupled equations for the amplitudes of competing unstable oscillatory modes. These may be created in the system by proper coupling and selectively evoked by specific classes of inputs. This allows a view of limit cycle attractors as “stored” fixed points of a gradient vector field and thereby recovers the more familiar dynamical systems picture of associative memory.
A neural network model of synchronized oscillator activity in visual cortex is presented in order to account for recent neurophysiological findings that such synchronization may reflect global properties of the stimulus. In these recent experiments, it was reported that synchronization of oscillatory firing responses to moving bar stimuli occurred not only for nearby neurons, but also occurred between neurons separated by several cortical columns (several mm of cortex) when these neurons shared some receptive field preferences specific to the stimuli. These results were obtained not only for single bar stimuli but also across two disconnected, but colinear, bars moving in the same direction. Our model and computer simulations obtain these synchrony results across both single and double bar stimuli. For the double bar case, synchronous oscillations are induced in the region between the bars, but no oscillations are induced in the regions beyond the stimuli. These results were achieved with cellular units that exhibit limit cycle oscillations for a robust range of input values, but which approach an equilibrium state when undriven. Single and double bar synchronization of these oscillators was achieved by different, but formally related, models of preattentive visual boundary segmentation and attentive visual object recognition, as well as nearest-neighbor and randomly coupled models. In preattentive visual segmentation, synchronous oscillations may reflect the binding of local feature detectors into a globally coherent grouping. In object recognition, synchronous oscillations may occur during an attentive resonant state that triggers new learning. These modelling results support earlier theoretical predictions of synchronous visual cortical oscillations and demonstrate the robustness of the mechanisms capable of generating synchrony.
We study pacemaker rhythms generated by two nonoscillatory model cells that are coupled by inhibitory synapses. A minimal ionic model that exhibits postinhibitory rebound (PIR) is presented. When the post-synaptic conductance depends instantaneously on presynaptic potential the classical alternating rhythm is obtained. Using phase-plane analysis we identify two underlying mechanisms, release and escape, for the out-of-phase oscillation. When the postsynaptic conductance is not instantaneous but decays slowly, the two cells can oscillate synchronously with no phase difference. In each case, different stable activity patterns can coexist over a substantial parameter range.
We study theoretically how an interaction between assemblies of neuronal oscillators can be modulated by the pattern of external stimuli. It is shown that spatial variations in the stimuli can control the magnitude and phase of the synchronization between the output of neurons with different receptive fields. This modulation emerges from cooperative dynamics in the network, without the need for specialized, activity-dependent synapses. Our results further suggest that the modulation of neuronal interactions by extended features of a stimulus may give rise to complex spatiotemporal fluctuations in the phases of neuronal oscillations.
A neural network model for explaining experimentally observed neuronal responses in cat primary visual cortex is proposed. In our model, the basic functional unit is an orientation column which is represented by a large homogeneous population of neurons modeled as integrate-and-fire type excitable elements. The orientation column exhibits spontaneous collective oscillations in activity in response to suitable visual stimuli. Such oscillations are caused by mutual synchronization among the neurons within the column. Numerical simulation for various stimulus patterns shows that as a result of activity correlations between different columns, the amplitude and the phase of the oscillation in each column depend strongly on the global feature of the stimulus pattern. These results satisfactorily account for experimental observations.
In the past, picture segmentation has been performed by merging small primitive regions or by recursively splitting the whole picture. This paper combines the two approaches with significant increase in processing speed while maintaining small memory requirements. The data structure is described in detail and examples of implementations are given.
It is rigorously proved that at any nonzero temperature, a one- or
two-dimensional isotropic spin-S Heisenberg model with finite-range
exchange interaction can be neither ferromagnetic nor antiferromagnetic.
The method of proof is capable of excluding a variety of types of
ordering in one and two dimensions.
A computational model is presented for the visual recognition of three-dimensional objects based upon their spatial correspondence with two-dimensional features in an image. A number of components of this model are developed in further detail and implemented as computer algorithms. At the highest level, a verification process has been developed which can determine exact values of viewpoint and object parameters from hypothesized matches between three-dimensional object features and two-dimensional image features. This provides a reliable quantitative procedure for evaluating the correctness of an interpretation, even in the presence of noise or occlusion. Given a reliable method for final evaluation of correspondence, the remaining components of the system are aimed at reducing rthe size of the search space which must be covered. Unlike many previous approaches, this recognition process does not assume that is is possible to directly derive depth information from the image. Instead, the primary descriptive component is a process of perceptual organization, which spatial relations are detected directly among two-dimensional image features. A basic requirement of the recognition process is that perceptual organization should accurately distinguish meaningful groupings from those which arise by accident of viewpoint or position.
Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model" has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a "physiological state diagram," with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.
Simultaneous records of the EEG were made from rectangular arrays of 60–64 electrodes successfully implanted over the surfaces of the olfactory bulb and cortex of 9 cats and 34 rabbits. Analysis was focused on bursts of sinusoidal activity at frequencies of 38–80 Hz that accompanied respiration in waking motivated animals and resemble the induced wave of Adrian. The bursts occured in focal areas of the bulb and cortex at peak rms amplitudes averaging about 80 μV and rising by a factor of about 3 times above the relatively inactive areas. The foci sometimes appeared as randomly scattered small active zones but often were confluent into irregular shapes or occasionally a smoothly elliptical shape. From 20–40% of the bulbar surface is enclosed within the half-(peak)amplitude contours of bulbar foci.The foci differed greatly in size, shape, location and amplitude between animals, but for each animal the shape was relatively constant over days and weeks. Maximum variation occured at scattered sites on the slopes of foci and there was also low rms amplitude, low (spatial) frequency variation from burst to burst and from day to day. The phase differences between sites within bursts were a small fraction of a cycle (5–8%). The foci were not significantly altered in shape or location by presenting odors to the animals but were abolished or changed under barbiturate anesthesia. Preliminary results from bulbar evoked potentials suggest that foci may result from specialized conditions created by centrifugal input or from interactions between the bulb and more central structures.The results fail to support the hypothesis that different odors are represented by activity in grossly different parts of the bulb. If the spatial distributions of the bursts reflect specific information, that information cannot depend on the odor being received but may depend on internal states including motivation and perhaps expectancy. The EEG amplitude patterns are more likely to contain this information than the frequency or phase distributions of bursts, for which the ranges of variation appear too small. The main problem for analysis is the reduction of the vast amount of data from multichannel recording. Some solutions used here include calculation of rms amplitudes and normalization of amplitude patterns for single bursts.RésuméDes enregistrements simultanés de l'EEG ont été effectués au moyen de faisceaux rectangulaires de 60–64 électrodes implantées avec succés sur les surfaces du bulbe olfactif et du cortex chez 9 chats et 34 lapins. L'analyse est centrée sur les bouffées d'activité sinusoïdale aux fréquences de 38–80 Hz, qui accompagnent la respiration chez des animaux éveillés et actifs et qui ressemblent aux ondes induites d'Adrian. Ces bouffées surviennent dans des aires focalisées du bulbe et du cortex avec des amplitudes de pics rms d'environ, en moyenne, 80 μV, et environ 3 fois plus amples que dans les aires relativement inactives. Ces foyers apparaissent parfois comme un ensemble aléatoire de petites zones actives mais souvent confluent en formes irrégulières ou occasionnellement en une forme légérement elliptique. 20–40% de la surface du bulbe est contenu à l'intérieur des contours du foyer bulbaire d'amplitude correspondant à la moitié de l'amplitude de pics.Ces foyers diffèrent grandement en dimension, forme, localisation et amplitude d'un animal à l'autre, mais pour chaque animal la forme est relativement constante d'un jour à l'autre ou d'une semaine à l'autre. La variation maximale survient à des points répartis sur les pentes du foyer, où on note également des amplitudes rms basses, une variation faible (spatiale) de fréquence d'une bouffée à l'autre et d'un jour à l'autre. Les différences de phase entre les localisations à l'intériur des bouffées sont d'une petite fraction d'un cycle (5–8%). Les foyers ne sont pas significativement modifiés dans leur forme ou leur localisation lorsqu'on présente des odeurs aux animaux, mais sont abolis ou changent sous anesthésie barbiturique. Des résultats préliminaires concernant les potentiels évoqués bulbaires suggèrent que ces foyers peuvent résulter de conditions spécialisées créées par les afférences centrifuges ou venant des interactions entre le bulbe et des structures plus centrales.Ces résultats ne confirment pas l'hypothése suivant laquelle différentes odeurs sont représentées par la mise en jeu de parties trés différentes du bulbe. Si les distributions spatiales des bouffées reflètent l'information spécifique, cette information ne peut pas dépendre de l'odeur qui est reçue mais peut dépendre d'états internes comprenant la motivation et peut être l'attente. Les patterns d'amplitude EEG sont plus susceptibles de contenir cette information que la fréquence ou la distribution de phase des bouffées, pour lesquelles les marges de variations apparaissent trop faibles. Le problème essentiel pour l'analyse est la réduction de la vaste quantité de données venant d'enregistrement à plusieurs canaux. Certaines solutions utilisées dans ce travail comportent le calcul des amplitudes rms et la normalisation des patterns d'amplitude pour des bouffées isolées.
Synchronous 25- to 35-Hz oscillations were observed in local field potentials and unit activity in sensorimotor cortex of awake rhesus monkeys. The oscillatory episodes occurred often when the monkeys retrieved raisins from a Klüver board or from unseen locations using somatosensory feedback; they occurred less often during performance of repetitive wrist flexion and extension movements. The amplitude, duration, and frequency of oscillations were not directly related to movement parameters in behaviors studied so far. The occurrence of the oscillations was not consistently related to bursts of activity in forearm muscles, but cycle-triggered averages of electromyograms revealed synchronous modulation in flexor and extensor muscles. The phase of the oscillations changed continuously from the surface to the deeper layers of the cortex, reversing their polarity completely at depths exceeding 800 microns. The oscillations could become synchronized over a distance of 14 mm mediolaterally in precentral cortex. Coherent oscillations could also occur at pre- and postcentral sites separated by an estimated tangential intracortical distance of 20 mm. Activity of single units was commonly seen to burst in synchrony with field potential oscillations. These findings suggest that such oscillations may facilitate interactions between cells during exploratory and manipulative movements, requiring attention to sensorimotor integration.
It is suggested that in the brain the internal attentional searchlight, proposed by Treisman and others, is controlled by the reticular complex of the thalamus (including the closely related perigeniculate nucleus) and that the expression of the searchlight is the production of rapid bursts of firing in a subset of thalamic neurons. It is also suggested that the conjunctions produced by the attentional searchlight are mediated by rapidly modifiable synapses--here called Malsburg synapses--and especially by rapid bursts acting on them. The activation of Malsburg synapses is envisaged as producing transient cell assemblies, including "vertical" ones that temporarily unite neurons at different levels in the neural hierarchy.
Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.
Relaxation oscillators interacting via models of excitatory chemical synapses with sharp thresholds can have stable anti-phase as well as in-phase solutions. The mechanism for anti-phase demonstrated in this paper relies on the fact that, in a large class of neural models, excitatory input slows down the receiving oscillator over a portion of its trajectory. We analyze the effect of this "virtual delay" in an abstract model, and then show that the hypotheses of that model hold for widely used descriptions of bursting neurons.
A dynamical neural network model of binocular stereopsis is proposed to solve the problem of segmentation which remains ambiguous even when the problem of binocular correspondence is solved. Being compatible with the recent neurophysiological findings (Engel et al. 1991), the model assumes that neural cells show oscillatory activities and that segmentation into a coherent depth surface is coded by synchronization of activities. Employing appropriate constraints for segmentation, the present model shows proper segmentation of depth surfaces and also solves segmentational ambiguity caused by a gap. It is newly shown that binocularly-unmatched monocular cells are discriminated in temporal segmentation of monocular cells caused by recurrent interactions between monocular and binocular cells. Integrative interactions with the other visual components through temporal segmentation are also discussed.
A neural network with excitatory neurons for associative storage and inhibitory neurons for control of firing rates is proposed. In distinction to attractor neural networks which are endowed with fixed-point dynamics, the basic recall mode of the network consists of a relaxation to a limit cycle originating from an inhibitory feedback loop. Nonlocal synaptic connections between excitatory neurons store all the information and yield robust associative abilities of the network. Inhibitory neutrons with short-range connections and nonlinear interaction (shunting) are introduced to stabilize low levels of neural activity. The mean firing rate per neuron ranges between 0.1 and 0.5 impulses per Monte Carlo step (MCS). The average activity of excitatory and inhibitory neurons oscillates with frequency of 0.5/MCS. The model generalizes the attractor concept for associative memory and brings logical neural networks closer to biological reality.