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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
Extracting Oscillations: Neuronal Coincidence Detection with Noisy Periodic Spike Input
, 1998
"... How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integra ..."
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Cited by 19 (6 self)
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How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integrateandfire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code.
Spiking phineas gage: A neurocomputational theory of cognitive affective integration in decision making
 Psychological Review
, 2004
"... The authors present a neurological theory of how cognitive information and emotional information are integrated in the nucleus accumbens during effective decision making. They describe how the nucleus accumbens acts as a gateway to integrate cognitive information from the ventromedial prefrontal cor ..."
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Cited by 19 (8 self)
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The authors present a neurological theory of how cognitive information and emotional information are integrated in the nucleus accumbens during effective decision making. They describe how the nucleus accumbens acts as a gateway to integrate cognitive information from the ventromedial prefrontal cortex and the hippocampus with emotional information from the amygdala. The authors have modeled this integration by a network of spiking artificial neurons organized into separate areas and used this computational model to simulate 2 kinds of cognitive–affective integration. The model simulates successful performance by people with normal cognitive–affective integration. The model also simulates the historical case of Phineas Gage as well as subsequent patients whose ability to make decisions became impeded by damage to the ventromedial prefrontal cortex. Some people like to make decisions by flipping a coin, after assigning one choice to heads and another to tails. The point is not to make the decision indicated by the flip but rather to see how they feel about the choice that the coin flip tells them to do. Flipping the coin is an effective way to find out their emotional reactions to various alternatives, indicating the emotional weight they attach to them. From the perspective of mathematical theories of decision making such as those that say that people do or should maximize expected utility, the coinflip exercise is bizarre. But, there is increasing appreciation in cognitive science that emotions
Dynamics of Strongly Coupled Spiking Neurons
 Neural Computation
, 2000
"... We present a dynamical theory of integrateandfire neurons with strong synaptic coupling. We show how phaselocked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike interval ..."
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Cited by 14 (2 self)
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We present a dynamical theory of integrateandfire neurons with strong synaptic coupling. We show how phaselocked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates. A fundamental result is that for slow interactions, there is good agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are presented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Second, an asymmetric network with a mixture of excitation and inhibition is shown to exhibit periodic bursting patterns. Finally, a onedimensional network of neurons with longrange interactions is shown to desynchronize to a state with a spatially periodic pattern of mean firing rates across the network. This is modulated by deterministic fluctuations of the instantaneous firing rate whose size is an increasing function of the speed of synaptic response. 1
Coding Properties of Spiking Neurons: Reverse and CrossCorrelations
, 2001
"... What is the 'meaning' of a single spike? Spiketriggered averaging ('reverse correlations') yields the typical input just before a spike. Similarly, crosscorrelations describe the probability of firing an output spike given (one additional) presynaptic input spike. In this paper, we analytically ca ..."
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Cited by 8 (3 self)
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What is the 'meaning' of a single spike? Spiketriggered averaging ('reverse correlations') yields the typical input just before a spike. Similarly, crosscorrelations describe the probability of firing an output spike given (one additional) presynaptic input spike. In this paper, we analytically calculate reverse and crosscorrelations for a spiking neuron model with escape noise. The influence of neuronal parameters (such as the membrane time constant, the noise level, and the mean firing rate) on the form of the correlation function is illustrated. The calculation is done in the framework of a population theory that is reviewed. The relation of the population activity equations to population density methods is discussed. Finally, we indicate the role of crosscorrelations in spiketime dependent Hebbian plasticity. 2001 Elsevier Science Ltd. All rights reserved.
A Computational Framework for Cortical Learning
 Biological Cybernetics
, 2004
"... this paper is available at www.cnl.salk.edu/~suri/hebb.) Note that this simulation serves only as an illustration due to two limitations. First, the synaptic strengths would only be guaranteed to converge to the desired values w i * if the adaptive synapses did not themselves influence the output of ..."
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Cited by 4 (0 self)
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this paper is available at www.cnl.salk.edu/~suri/hebb.) Note that this simulation serves only as an illustration due to two limitations. First, the synaptic strengths would only be guaranteed to converge to the desired values w i * if the adaptive synapses did not themselves influence the output of the neuron. Second, the learning rule ensures that the synaptic strengths remain positive although strictly positive correlations are not guaranteed
What's Different With Spiking Neurons?
"... In standard neural network models neurons are described in terms of mean firing rates, viz., an analog signal. Most real neurons, however, communicate by pulses, called action potentials or simply `spikes'. In this chapter the main di#erences between spike coding and rate coding are described. The i ..."
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Cited by 3 (0 self)
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In standard neural network models neurons are described in terms of mean firing rates, viz., an analog signal. Most real neurons, however, communicate by pulses, called action potentials or simply `spikes'. In this chapter the main di#erences between spike coding and rate coding are described. The integrateandfire model is studied as a simple model of a spiking neuron. Fast transients, synchrony, and coincidence detection are discussed as examples where spike coding is relevant. A description by spikes rather than rates has implications for learning rules. We show the relation of a spiketime dependent learning rule to standard Hebbian learning. Finally, learning rule and temporal coding are illustrated using the example of a coincidence detecting neuron in the barn owl auditory system. Keywords: temporal coding, coincidence detection, spikes, spiking neurons, integrateand fire neurons, auditory system, Hebbian learning, spiketime dependent plasticity 1. SPIKES AND RATES In mos...
Associative Memory Using Action Potential Timing
, 1996
"... The dynamics and collective properties of feedback networks with spiking neurons are investigated. Special emphasis is given to the potential computational role of subthreshold oscillations. It is shown that model systems with integrateandfire neurons can function as associative memories on two di ..."
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Cited by 1 (0 self)
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The dynamics and collective properties of feedback networks with spiking neurons are investigated. Special emphasis is given to the potential computational role of subthreshold oscillations. It is shown that model systems with integrateandfire neurons can function as associative memories on two distinct levels. On the first level, binary patterns are represented by the spike activity  "to fire or not to fire." On the second level, analog patterns are encoded in the relative firing times between individual spikes or between spikes and an underlying subthreshold oscillation. Both coding schemes may coexist within the same network. The results suggest that cortical neurons may perform a broad spectrum of associative computations far beyond the scope of the traditional firingrate picture. Introduction A significant fraction of the communication between single neurons is based on action potentials, short pulses of electrochemical activity. The biological relevance of the exact tempor...
doi:10.1155/2009/704075 Research Article Comparison and Regulation of Neuronal Synchronization for
"... We discuss effects of various experimentally supported STDP learning rules on frequency synchronization of two unidirectional coupled neurons systematically. First, we show that synchronization windows for all STDP rules cannot be enhanced compared to constant connection under the same model. Then, ..."
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We discuss effects of various experimentally supported STDP learning rules on frequency synchronization of two unidirectional coupled neurons systematically. First, we show that synchronization windows for all STDP rules cannot be enhanced compared to constant connection under the same model. Then, we explore the influence of learning parameters on synchronization window and find optimal parameters that lead to the widest window. Our findings indicate that synchronization strongly depends on the specific shape and the parameters of the STDP update rules. Thus, we give some explanations by analyzing the synchronization mechanisms for various STDP rules finally. Copyright © 2009 Y. Ruan and G. Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.