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28
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.
Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity
 Neural Computation
, 2003
"... In model networks of Ecells and Icells (excitatory and inhibitory neurons) , synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the Ecells synchronize the Icells and vice versa. Under ideal conditions  homogeneity in relevant network parameters, ..."
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Cited by 42 (8 self)
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In model networks of Ecells and Icells (excitatory and inhibitory neurons) , synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the Ecells synchronize the Icells and vice versa. Under ideal conditions  homogeneity in relevant network parameters, and alltoall connectivity for instance  this mechanism can yield perfect synchronization.
Firing Rate of the Noisy Quadratic IntegrateandFire Neuron
, 2003
"... We calculate the firing rate of the quadratic integrateandfire neuron in response to a colored noise input current. Such an input current is a good approximation to the noise due to the random bombardment of spikes, with the correlation time of the noise corresponding to the decay time of the syna ..."
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Cited by 33 (3 self)
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We calculate the firing rate of the quadratic integrateandfire neuron in response to a colored noise input current. Such an input current is a good approximation to the noise due to the random bombardment of spikes, with the correlation time of the noise corresponding to the decay time of the synapses. The key parameter that determines the firing rate is the ratio of the correlation time of the colored noise, ¿s, to the neuronal time constant, ¿m. We calculate the firing rate exactly in two limits: when the ratio, ¿s=¿m, goes to zero (white noise) and when it goes to infinity. The correction to the short correlation time limit is O.¿s=¿m/, which is qualitatively different from that of the leaky integrateandfire neuron, where the correction is O. p ¿s=¿m/. The difference is due to the different boundary conditions of the probability density function of the membrane potential of the neuron at firing threshold. The correction to the long correlation time limit is O.¿m=¿s/. By combining the short and long correlation time limits, we derive an expression that provides a good approximation to the firing rate over the whole range of ¿s=¿m in the suprathreshold regime— that is, in a regime in which the average current is sufficient to make the cell fire. In the subthreshold regime, the expression breaks down somewhat when ¿s becomes large compared to ¿m.
IntegrateandFire Neurons Driven by Correlated Stochastic Input
, 2002
"... Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron’s response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times ..."
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Cited by 17 (4 self)
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Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron’s response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times of two simple integrateandfire model neurons driven by a correlated binary variable that represents the total input current. Analytic expressions were obtained for the average firing rate and coefficient of variation (a measure of spiketrain variability) as functions of the mean, variance, and correlation time of the stochastic input. The results of computer simulations were in excellent agreement with these expressions. In these models, an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains. However, the magnitude of the changes depends differentially on the relative values of the input mean and variance: the increase in firing rate is higher when the variance is large relative to the mean, whereas the increase in variability is higher when the variance is relatively small. In addition, the firing rate always tends to a finite limit value as the correlation time increases toward infinity, whereas the coefficient of variation typically diverges. These results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains.
Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons
 Neural Comp
, 2005
"... Abstract. Synchronous rhythmic spiking in neuronal networks can be brought about by the interaction between Ecells and Icells (excitatory and inhibitory cells): The Icells gate and synchronize the Ecells, and the Ecells drive and synchronize the Icells. We refer to rhythms generated in this wa ..."
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Cited by 14 (3 self)
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Abstract. Synchronous rhythmic spiking in neuronal networks can be brought about by the interaction between Ecells and Icells (excitatory and inhibitory cells): The Icells gate and synchronize the Ecells, and the Ecells drive and synchronize the Icells. We refer to rhythms generated in this way as “PING ” (PyramidalInterneuronal Gamma) rhythms. The PING mechanism requires that the drive II to the Icells be sufficiently low; the rhythm is lost when II gets too large. This can happen in (at least) two different ways. In the first mechanism, the Icells spike in synchrony, but get ahead of the Ecells, spiking without being prompted by the Ecells. We call this phase walkthrough of the Icells. In the second mechanism, the Icells fail to synchronize, and their activity leads to complete suppression of the Ecells. Noisy spiking in the Ecells, generated by noisy external drive, adds excitatory drive to the Icells and may lead to phase walkthrough. Noisy spiking in the Icells adds inhibition to the Ecells, and may lead to suppression of the Ecells. An analysis of the conditions under which noise leads to phase walkthrough of the Icells or suppression of the Ecells shows that PING rhythms at frequencies far below the gamma range are robust to noise only if network parameter values are tuned very carefully. Together with an argument explaining why the PING mechanism
Quantifying Statistical Interdependence by Message Passing on Graphs  PART II: MultiDimensional Point Processes
, 2009
"... Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, “events” are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are ..."
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Cited by 12 (10 self)
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Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, “events” are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. In Part I, onedimensional events are considered, this paper (Paper II) concerns multidimensional events. Although the basic idea is similar, the extension to multidimensional point processes involves a significantly harder combinatorial problem, and therefore, it is nontrivial. Also in the multidimensional, the problem of jointly computing the pairwise alignment and SES parameters is cast as a statistical inference problem. This problem is solved by coordinate descent, more specifically, by alternating the following two steps: (i) one estimates the SES parameters from a given pairwise alignment; (ii) with the resulting estimates, one refines the pairwise alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (Step 1), in
Eventdriven simulations of nonlinear integrateandfire neurons
"... Eventdriven strategies have been used to simulate exactly spiking neural networks. Previous works are limited to linear integrateandfire neurons. In this note we extend event driven schemes to a class of nonlinear integrateandfire models. Results are presented for the quadratic integrateandfir ..."
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Cited by 8 (1 self)
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Eventdriven strategies have been used to simulate exactly spiking neural networks. Previous works are limited to linear integrateandfire neurons. In this note we extend event driven schemes to a class of nonlinear integrateandfire models. Results are presented for the quadratic integrateandfire model with instantaneous or exponential synaptic currents. Extensions to conductancebased currents and exponential integrateandfire neurons are discussed. 1
Stochastic resonance in continuous and spiking neuron models with levy noise. Neural Networks
 IEEE Transactions on
, 2008
"... Abstract—Levy noise can help neurons detect faint or subthreshold signals. Levy noise extends standard Brownian noise to many types of impulsive jumpnoise processes found in real and model neurons as well as in models of finance and other random phenomena. Two new theorems and the Itô calculus show ..."
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Cited by 6 (6 self)
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Abstract—Levy noise can help neurons detect faint or subthreshold signals. Levy noise extends standard Brownian noise to many types of impulsive jumpnoise processes found in real and model neurons as well as in models of finance and other random phenomena. Two new theorems and the Itô calculus show that white Levy noise will benefit subthreshold neuronal signal detection if the noise process’s scaled drift velocity falls inside an interval that depends on the threshold values. These results generalize earlier “forbidden interval ” theorems of neuronal “stochastic resonance ” (SR) or noiseinjection benefits. Global and local Lipschitz conditions imply that additive white Levy noise can increase the mutual information or bit count of several feedback neuron models that obey a general stochastic differential equation (SDE). Simulation results show that the same noise benefits still occur for some infinitevariance stable Levy noise processes even though the theorems themselves apply only to finitevariance Levy noise. The Appendix proves the two Itôtheoretic lemmas that underlie the new Levy noisebenefit theorems. Index Terms—Levy noise, jump diffusion, mutual information, neuron models, signal detection, stochastic resonance (SR). I. STOCHASTIC RESONANCE IN NEURAL SIGNAL DETECTION STOCHASTIC RESONANCE (SR) occurs when noise benefits a system rather than harms it. Small amounts of noise can often enhance some forms of nonlinear signal processing
Gamma Oscillations and Stimulus Selection
, 2008
"... More coherent excitatory stimuli are known to have a competitive advantage over less coherent ones. We show here that this advantage is amplified greatly when the target includes inhibitory interneurons acting via GABAAreceptormediated synapses and the coherent input oscillates at gamma frequency. ..."
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Cited by 6 (1 self)
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More coherent excitatory stimuli are known to have a competitive advantage over less coherent ones. We show here that this advantage is amplified greatly when the target includes inhibitory interneurons acting via GABAAreceptormediated synapses and the coherent input oscillates at gamma frequency. We hypothesize that therein lies, at least in part, the functional significance of the experimentally observed link between attentional biasing of stimulus competition and gamma frequency rhythmicity.
Understanding neuronal dynamics by geometrical dissection of minimal models
 in Methods and Models in
"... 1.1. Nonlinear behaviors, time scales, our approach 5 1.2. Electrical activity of cells 6 2. Revisiting the HodgkinHuxley equations 10 ..."
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Cited by 6 (0 self)
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1.1. Nonlinear behaviors, time scales, our approach 5 1.2. Electrical activity of cells 6 2. Revisiting the HodgkinHuxley equations 10