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Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking
 NEURAL COMPUTATION
, 2000
"... An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrateandfire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analy ..."
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Cited by 134 (25 self)
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An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrateandfire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived. The response of a population of noisy integrateandfire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized `locked' solutions is analyzed.
Populations of Spiking Neurons
 PULSED NEURAL NETWORKS, CHAPTER 10
, 1998
"... Introduction In standard neural network theory, neurons are described in terms of mean firing rates. The analog input variable I is mapped via a nonlinear gain function g to an analog output variable = g(I) which may be interpreted as the mean firing rate. If the input consists of output rates j ..."
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Cited by 83 (3 self)
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Introduction In standard neural network theory, neurons are described in terms of mean firing rates. The analog input variable I is mapped via a nonlinear gain function g to an analog output variable = g(I) which may be interpreted as the mean firing rate. If the input consists of output rates j of other neurons weighted by a factor w ij , we arrive at the standard formula i = g( X j w ij j ) (10.1) which is the starting point of most neural network theories. As we have seen in Chapter 1, the firing rate defined by a temporal average over many spikes of a single neuron is a concept which works well if the input is constant or changes on a time scale which is slow with respect to the size of the temporal averaging window. Sensory inpu
Evolution of spiking neural controllers for autonomous visionbased robots
 in: T. Gomi (Ed.), Evolutionary Robotics IV
, 2001
"... Abstract. We describe a set of preliminary experiments to evolve spiking neural controllers for a visionbased mobile robot. All the evolutionary experiments are carried out on physical robots without human intervention. After discussing how to implement and interface these neurons with a physical r ..."
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Cited by 46 (12 self)
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Abstract. We describe a set of preliminary experiments to evolve spiking neural controllers for a visionbased mobile robot. All the evolutionary experiments are carried out on physical robots without human intervention. After discussing how to implement and interface these neurons with a physical robot, we show that evolution finds relatively quickly functional spiking controllers capable of navigating in irregularly textured environments without hitting obstacles using a very simple genetic encoding and fitness function. Neuroethological analysis of the network activity let us understand the functioning of evolved controllers and tell the relative importance of single neurons independently of their observed firing rate. Finally, a number of systematic lesion experiments indicate that evolved spiking controllers are very robust to synaptic strength decay that typically occurs in hardware implementations of spiking circuits. 1 Spiking Neural Circuits The great majority of biological neurons communicate by sending pulses along
Stationary Bumps in Networks of Spiking Neurons
"... Introduction Neuronal activity due to recurrent excitations in the form of a spatially localized pulse or bump has been proposed as a mechanism for feature selectivity in models of the visual system (Somers, Nelson, & Sur, 1995; Hansel & Sompolinsky, 1998), the head direction system (Skaggs, Kniera ..."
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Cited by 46 (15 self)
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Introduction Neuronal activity due to recurrent excitations in the form of a spatially localized pulse or bump has been proposed as a mechanism for feature selectivity in models of the visual system (Somers, Nelson, & Sur, 1995; Hansel & Sompolinsky, 1998), the head direction system (Skaggs, Knieram, Kudrimoti, & McNaughton, 1995; Zhang, 1996; Redish, Elga, & Touretzky, 1996), and working memory (Wilson & Cowan, 1973; Amit & Brunel, 1997; Camperi & Wang, 1998). Many of the previous mathematical formulations of such structures have employedpopulation rate models (Wilson &Cowan, 1972, 1973; Amari, 1977; Kishimoto & Amari, 1979; Hansel & Sompolinsky, 1998). (See Ermentrout, 1998, for a recent review.) Here, we consider a network of spiking neurons that shows such structures and investigate their properties. In our network we #nd localized timestationary states
Intrinsic Stabilization of Output Rates by SpikeBased Hebbian Learning
 Neural Computation
, 2001
"... We study analytically a model of longterm synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time dierences between presynaptic and postsynaptic spikes. The changes due to correlated input and output spikes are quanti ed by means of a learn ..."
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Cited by 38 (12 self)
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We study analytically a model of longterm synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time dierences between presynaptic and postsynaptic spikes. The changes due to correlated input and output spikes are quanti ed by means of a learning window. We show that plasticity can lead to an intrinsic stabilization of the mean ring rate of the postsynaptic neuron. Subtractive normalization of the synaptic weights (summed over all presynaptic inputs converging on a postsynaptic neuron) follows if, in addition, the mean input rates and the mean input correlations are identical at all synapses. If the integral over the learning window is positive, ringrate stabilization requires a nonHebbian component, whereas such a component is not needed, if the integral of the learning window is negative. A negative integral corresponds to `antiHebbian' learning in a model with slowly varying ring rates. For spikebased learning, a strict distinction between Hebbian and `antiHebbian' rules is questionable since learning is driven by correlations on the time scale of the learning window. The correlations between presynaptic and postsynaptic ring are evaluated for a piecewiselinear Poisson model and for a noisy spiking neuron model with refractoriness. While a negative integral over the learning window leads to intrinsic rate stabilization, the positive part of the learning window picks up spatial and temporal correlations in the input.
The Number of Synaptic Inputs and the Synchrony of Large Sparse Neuronal Networks
, 1999
"... The prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons. We study synchronization in models of large networks of spiking neurons with random sparse connectivity. Synchrony oc ..."
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Cited by 35 (1 self)
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The prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons. We study synchronization in models of large networks of spiking neurons with random sparse connectivity. Synchrony occurs only when the average number of synapses, M , that a cell receives is larger than a critical value, M c . Below M c , the system is in an asynchronous state. In the limit of weak coupling, assuming identical neurons, we reduce the model to a system of phase oscillators which are coupled via an effective interaction, \Gamma. In this framework, we develop an approximate theory for sparse networks of identical neurons to estimate M c analytically from the Fourier coefficients of \Gamma. Our approach relies on the assumption that the dynamics of a neuron depend mainly on the number of cells that are presynaptic to it. We apply this theory to compute M c for a model of inhibitory networks of integrateandfire (I&F) neurons as a function of the intrinsic neuronal properties (e.g., the refractory period T r ), the synaptic time constants and the strength of the external stimulus, I ext . The number M c is found to be nonmonotonous with the strength of I ext . For T r = 0, we estimate the minimum value of M c over all the parameters of the model to be 363:8. Above M c , the neurons tend to fire in: 1) smeared one cluster states at high firing rates and 2) smeared two or more cluster states at low firing rates. Refractoriness decreases M c at intermediate and high firing rates. These results are compared against numerical simulations. We show numerically that systems with different sizes, N , behave in the same way provided the connectivity, M , is such a way that 1=M eff = 1=...
Synchrony and Desynchrony in IntegrateandFire Oscillators
 NEURAL COMPUTATION
, 1999
"... Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coup ..."
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Cited by 24 (1 self)
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Due to many experimental reports of synchronous neural activity in the brain, there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization. Contrary to Hopfield and Herz (1995), we find that networks of locally coupled integrateandfire oscillators can quickly synchronize. Furthermore, we examine the time needed to synchronize such networks. We observe that these networks synchronize at times proportional to the logarithm of their size, and we give the parameters used to control the rate of synchronization. Inspired by locally excitatory globally inhibitory oscillator network (LEGION) dynamics with relaxation oscillators (Terman & Wang, 1995), we find that global inhibition can play a similar role of desynchronization in a network of integrateandfire oscillators. We illustrate that a LEGION architecture with integrateandfire oscillators can be similarly used to address image analysis.
Mechanisms of PhaseLocking and Frequency Control in Pairs of coupled Neural Oscillators
, 2000
"... INTRODUCTION Oscillations occur in many networks of neurons, and are associated with motor behavior, sensory processing, learning, arousal, attention and pathology (Parkinson's tremor, epilepsy). Such oscillations can be generated in many ways. This chapter discusses some mathematical issues associ ..."
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Cited by 21 (5 self)
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INTRODUCTION Oscillations occur in many networks of neurons, and are associated with motor behavior, sensory processing, learning, arousal, attention and pathology (Parkinson's tremor, epilepsy). Such oscillations can be generated in many ways. This chapter discusses some mathematical issues associated with creation of coherent rhythmic activity in networks of neurons. We focus on pairs of cells, since many of the issues for larger networks are most clearly displayed in that context. As we will show, there are many mechanisms for interactions among the network components, and these can have different mathematical properties. A description of behavior of larger networks using some of the mechanisms described in this chapter can be found in the related chapter by Rubin and Terman. For reviews of papers about oscillatory behavior in specific networks in the nervous system, see Gray (1994), Marder and Calabrese (1996), Singer (1993), and Traub et al (1999). The chapter is organiz