Cooperative behavior in the periodically modulated Wiener process: Noise-induced complexity in a model neutron

Bulsara, Adi R.; Lowen, Steven B.; Cd, Rees

doi:10.1103/physreve.49.4989

Cited by 106 publications

(86 citation statements)

References 67 publications

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“…In this case, resonance generally arises as some stochastic rate coincides with the given oscillating frequency. A simple IF model, with passive membrane properties, displays stochastic resonance (Bulsara et al 1994) but not the subthreshold and firing-rate resonance studied here.…”

Section: Firing-rate Dynamicsmentioning

confidence: 65%

From Subthreshold to Firing-Rate Resonance

Richardson

Brunel

Hakim³

2003

Journal of Neurophysiology

271

367

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. Many types of neurons exhibit subthreshold resonance. However, little is known about whether this frequency preference influences spike emission. Here, the link between subthreshold resonance and firing rate is examined in the framework of conductance-based models. A classification of the subthreshold properties of a general class of neurons is first provided. In particular, a class of neurons is identified in which the input impedance exhibits a suppression at a nonzero low frequency as well as a peak at higher frequency. The analysis is then extended to the effect of subthreshold resonance on the dynamics of the firing rate. The considered input current comprises a background noise term, mimicking the massive synaptic bombardment in vivo. Of interest is the modulatory effect an additional weak oscillating current has on the instantaneous firing rate. When the noise is weak and firing regular, the frequency most preferentially modulated is the firing rate itself. Conversely, when the noise is strong and firing irregular, the modulation is strongest at the subthreshold resonance frequency. These results are demonstrated for two specific conductance-based models and for a generalization of the integrate-and-fire model that captures subthreshold resonance. They suggest that resonant neurons are able to communicate their frequency preference to postsynaptic targets when the level of noise is comparable to that prevailing in vivo.

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Section: Firing-rate Dynamicsmentioning

confidence: 65%

From Subthreshold to Firing-Rate Resonance

Richardson

Brunel

Hakim³

2003

Journal of Neurophysiology

271

367

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“…The spike train power spectrum is given by (Stratonovich 1967) S IG (f ; ν, C V ) = 1 − |P (f ; ν, C V )| 2 |1 −P (f ; ν, C V )| 2 , whereP (f ; ν, C V ) is the Fourier transform of the inverse Gaussian, Eq. (140), given bỹ P (f ; ν, C V ) = exp 1 − 1 − 4πiC 2 V f /ν C 2 V (Holden 1976;Bulsara et al 1994;Chacron et al 2005). The power spectrum of the synaptic current is then, according to Eq.…”

Section: A5 Inverse Gaussian Inputmentioning

confidence: 99%

Statistical structure of neural spiking under non-Poissonian or other non-white stimulation

2015

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Nerve cells in the brain generate sequences of action potentials with a complex statistics. Theoretical attempts to understand this statistics were largely limited to the case of a temporally uncorrelated input (Poissonian shot noise) from the neurons in the surrounding network. However, the stimulation from thousands of other neurons has various sorts of temporal structure. Firstly, input spike trains are temporally correlated because their firing rates can carry complex signals and because of cell-intrinsic properties like neural refractoriness, bursting, or adaptation. Secondly, at the connections between neurons, the synapses, usagedependent changes in the synaptic weight (short-term plasticity) further shape the correlation structure of the effective input to the cell. From the theoretical side, it is poorly understood how these correlated stimuli, socalled colored noise, affect the spike train statistics. In particular, no standard method exists to solve the associated first-passage-time problem for the interspikeinterval statistics with an arbitrarily colored noise. Assuming that input fluctuations are weaker than the mean neuronal drive, we derive simple formulas for the essential interspike-interval statistics for a canon- ical model of a tonically firing neuron subjected to arbitrarily correlated input from the network. We verify our theory by numerical simulations for three paradigmatic situations that lead to input correlations: (i) ratecoded naturalistic stimuli in presynaptic spike trains; (ii) presynaptic refractoriness or bursting; (iii) synaptic short-term plasticity. In all cases, we find severe effects on interval statistics. Our results provide a framework for the interpretation of firing statistics measured in vivo in the brain.

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“…First, keeping the potential shape, the driving force as well as the boundary and initial conditions as simple as possible allows in some cases for an exact, in others for an approximate solution. This kind of approach was pursued in the late 1980's [8,21,22] and during the 1990's [3,4,9,11,16] (see also Ref. [23], ch.…”

Section: Introductionmentioning

confidence: 99%

Moments of the First Passage Time Under External Driving

Lindner

2004

Journal of Statistical Physics

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A general theory is derived for the moments of the first passage time of a one-dimensional Markov process in presence of a weak time-dependent forcing. The linear corrections to the moments can be expressed by quadratures of the potential and of the time-dependent probability density of the unperturbed system or equivalently by its Laplace transform. If none of the latter functions is known, the derived formulas may still be useful for specific cases including a slow driving or a driving with power at only small or large times. In the second part of the paper, explicite expressions for mean and variance of the first passage time are derived for the cases of a linear or a parabolic potential and an exponentially decaying driving force. The analytical results are found to be in excellent agreement with computer simulations of the respective first-passage processes.The particular examples furthermore demonstrate that already the effect of a simple exponential driving can be fairly involved implying a nontrivial nonmonotonous behavior of mean and variance as functions of the driving's time scale.

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Cooperative behavior in the periodically modulated Wiener process: Noise-induced complexity in a model neutron

Cited by 106 publications

References 67 publications

From Subthreshold to Firing-Rate Resonance

From Subthreshold to Firing-Rate Resonance

Statistical structure of neural spiking under non-Poissonian or other non-white stimulation

Moments of the First Passage Time Under External Driving

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