Output Dead-Time in Point Processes

Picinbono, B.

doi:10.1080/03610910903268833

Cited by 9 publications

(16 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the following we describe an extension of renewal theory for ensembles of point processes with time varying input. For stationary input rate, many previous publications have investigated the statistics of the PPD [8][9][10][11]. In case of slowly varying input rates, expressions for mean and variance of detector counts have been derived arXiv:1002.3798v3 [math.PR] 24 Jun 2010 Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium dynamics of stochastic point processes with refractoriness

et al. 2010

View full text Add to dashboard Cite

Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze nonstationary renewal processes.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonequilibrium dynamics of stochastic point processes with refractoriness

et al. 2010

View full text Add to dashboard Cite

show abstract

“…As previously stated, however, a recursive algorithm for this purpose has been introduced in [11]. We shall use this algorithm for the estimation of the coincidence function after an output dead-time effect when the input is a Poisson process.…”

Section: A Poisson Process With Output Dead Timementioning

confidence: 99%

“…Indeed, the algorithm yielding the life time after dead time presented in [11] introduces much more complexity and calculation time. This limits the possible values of M and, thus, the statistical precision of the procedure.…”

Section: A Poisson Process With Output Dead Timementioning

confidence: 99%

“…An algorithm for generating this kind of life time has been presented in [11], and its principle is outlined in the Appendix. The normalized correlation function of the first-order life time is exponential or p |n| .…”

Section: Pp With Uniform Distribution and Correlated Life Timesmentioning

confidence: 99%

“…The explicit expression of the result is almost impossible to obtain in closed form. A recursive algorithm, however, has been introduced and analyzed in [11]. This algorithm is used for the estimation of the coincidence function when the initial PP is a Poisson process.…”

Section: ])mentioning

confidence: 99%

See 2 more Smart Citations

Measurements of Second-Order Properties of Point Processes

Picinbono

2008

IEEE Trans. Instrum. Meas.

Self Cite

View full text Add to dashboard Cite

Abstract-The second-order statistical properties of point processes (PPs) are described by the coincidence function which can be measured by a coincidence device, but such measurements are long and complicated. We propose another method of measurement, and we analyze its performances. The starting point is that the coincidence function can be deduced from the probability density functions of the life times (the distances between points) of the process. The idea is to transform the PP into a positive signal whose values are these distances. From an appropriate processing of this signal, we deduce the coincidence function. For the validation of the method, we use PPs for which the coincidence function is known. The agreement between theory and experiment is, in general, excellent. Finally, the method is applied to measure the coincidence functions of some PPs for which no theoretical result is available.

show abstract

A numerical method for computing interval distributions for an inhomogeneous Poisson point process modified by random dead times

Peterson

2021

Biol Cybern

View full text Add to dashboard Cite

The inhomogeneous Poisson point process is a common model for time series of discrete, stochastic events. When an event from a point process is detected, it may trigger a random dead time in the detector, during which subsequent events will fail to be detected. It can be difficult or impossible to obtain a closed-form expression for the distribution of intervals between detections, even when the rate function (often referred to as the intensity function) and the dead-time distribution are given. Here, a method is presented to numerically compute the interval distribution expected for any arbitrary inhomogeneous Poisson point process modified by dead times drawn from any arbitrary distribution. In neuroscience, such a point process is used to model trains of neuronal spikes triggered by the detection of excitatory events while the neuron is not refractory. The assumptions of the method are that the process is observed over a finite observation window and that the detector is not in a dead state at the start of the observation window. Simulations are used to verify the method for several example point processes. The method should be useful for modeling and understanding the relationships between the rate functions and interval distributions of the event and detection processes, and how these relationships depend on the dead-time distribution.

show abstract

Output Dead-Time in Point Processes

Cited by 9 publications

References 18 publications

Nonequilibrium dynamics of stochastic point processes with refractoriness

Nonequilibrium dynamics of stochastic point processes with refractoriness

Measurements of Second-Order Properties of Point Processes

A numerical method for computing interval distributions for an inhomogeneous Poisson point process modified by random dead times

Contact Info

Product

Resources

About