Moments of the First Passage Time Under External Driving

Lindner, Benjamin

doi:10.1007/s10955-004-2269-5

Cited by 27 publications

(38 citation statements)

References 46 publications

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“…At low firing frequencies, within each ISI the exponential evolution of the adaptation process has decayed, meaning that each ε n = α and correlations disappear. Correspondingly, the spike-count variance reduction is given exclusively by the FPT statistics (this case corresponds to τ d → 0 in [43,45]), and we denote this regime as an intrinsic reduction in Fig. 6.…”

Section: Spike-count Variance Reductionmentioning

confidence: 99%

Onset of negative interspike interval correlations in adapting neurons

Urdapilleta

2011

Phys. Rev. E

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Negative serial correlations in single spike trains are an effective method to reduce the variability of spike counts. One of the factors contributing to the development of negative correlations between successive interspike intervals is the presence of adaptation currents. In this work, based on a hidden Markov model and a proper statistical description of conditional responses, we obtain analytically these correlations in an adequate dynamical neuron model resembling adaptation. We derive the serial correlation coefficients for arbitrary lags, under a small adaptation scenario. In this case, the behavior of correlations is universal and depends on the first-order statistical description of an exponentially driven time-inhomogeneous stochastic process.

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Section: Spike-count Variance Reductionmentioning

confidence: 99%

Onset of negative interspike interval correlations in adapting neurons

Urdapilleta

2011

Phys. Rev. E

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“…See, for instance, [32] and [33]. Lindner [11] calculated moments of the FPT for both exponentially decaying and periodic driving terms similar to the situation described in (4.1) below. However, knowing the moments of the FPT distribution does not provide a strictly positive lower bound for the tail of the density.…”

Section: Relation To Other Asymptotic Fpt Density Resultsmentioning

confidence: 92%

A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process

Thomas

2011

J. Appl. Probab.

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We prove that the first passage time density ρ(t) for an Ornstein-Uhlenbeck process X(t) obeying dX = −βX dt + σ dW to reach a fixed threshold θ from a suprathreshold initial condition x 0 > θ > 0 has a lower bound of the form ρ(t) > k exp[−pe 6βt ] for positive constants k and p for times t exceeding some positive value u. We obtain explicit expressions for k, p, and u in terms of β, σ , x 0 , and θ, and discuss the application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.

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“…A general theory for deriving the moments of the first passage time for the Ornstein-Uhlenbeck process in the presence of a weak time-dependent drift using a FokkerPlanck approach has been developed (Lindner 2004). While most studies involve the use of either a weak stimulus, thus enabling the use of linear response theory, or weak noise, a recently proposed method that is based upon discrete state Markovian modeling provides results that show good agreement over a wide parameter range that extends beyond the weak driving limit (Schindler et al 2004(Schindler et al , 2005.…”

Section: Fokker-planck Formalismmentioning

confidence: 99%

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

2006

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The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker-Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).

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Moments of the First Passage Time Under External Driving

Cited by 27 publications

References 46 publications

Onset of negative interspike interval correlations in adapting neurons

Onset of negative interspike interval correlations in adapting neurons

A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

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