Measurements of Second-Order Properties of Point Processes

Picinbono, B.

doi:10.1109/tim.2007.911690

Cited by 5 publications

(10 citation statements)

References 9 publications

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“…The use of multiple histograms allows us to measure the PDFs f n (x) for a finite number M of lifetimes and we estimate c(x) by using a finite sum of M terms instead of a series. The precision and the performance of the method is analyzed inPicinbono (2008). In the cases in which c(x) can be calculated analytically the results of measurements are in excellent agreement with those of the calculations.…”

mentioning

confidence: 81%

“…where dN (θ) is the number of points of the PP appearing in the interval [θ, θ + dθ[. Some of its properties and the principle of its measurement are discussed in Picinbono (2008) and here we limit the presentation to the most fundamental properties. The basic result concerning the coincidence function…”

Section: Statement Of the Problem And (Notations) Notationmentioning

confidence: 99%

“…where λ is the (density) intensity of the PP and f n (x) the PDF of the lifetime of order n of the PP. This expression is used for the measurement of the coincidence function as indicated in Picinbono (2008). and it is (almost the only) a rare example where theory and experiment can easily be compared.…”

Section: Statement Of the Problem And (Notations) Notationmentioning

confidence: 99%

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Output Dead-Time in Point Processes

Picinbono

2009

Communications in Statistics - Simulation and Computation

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Dead-time effects modify the statistical properties of point processes. For their analysis we define a point process by the intervals between successive points and we calculate their transformation by dead-time. It cannot be expressed in closed form but we show that it can be written in a recursive form. Using this recursion, various statistical properties of point processes with dead-time are analyzed. We focus on the probability distribution of the intervals between points and the coincidence function describing the second-order properties. For the rare processes where calculations are possible there is an excellent agreement between computer experiments and theory.

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mentioning

confidence: 81%

Section: Statement Of the Problem And (Notations) Notationmentioning

confidence: 99%

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Output Dead-Time in Point Processes

Picinbono

2009

Communications in Statistics - Simulation and Computation

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“…is the Heaviside step function. In particular, to the best of our knowledge, the first relevant paper dates back to 1947 [5] and has been followed by both in-depth studies [1, [6][7][8][9][12][13][14] and applied studies for neuroscience [2, 10,11,[15][16][17][18][19][20] (see also [21] and [22]).…”

Section: Comparison With the Renewal Theorymentioning

confidence: 99%

Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results

Paraskevov

Minkin

2019

Preprint

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Many events are followed by an absolute refractory state, when for some time after the event a repetition of a similar event is impossible. If uniform events, each of which is followed by the same period of absolute refractoriness, occur randomly, as in the Bernoulli scheme, then the event probability as a function of time can exhibit damped transient oscillations caused by a specific initial condition. Here we give an exact analytical description of the oscillations, with a focus on application within neuroscience. The resulting formulas stand out for their relative simplicity, enabling analytical calculation of the damping coefficients for the second and third peaks of the event probability.

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“…This relation is used for the measurements of c(x) [15] with the series replaced by a sum of a finite number of terms. We shall present various results of such measurements in what follows.…”

Section: Short Review On Point Processes and Their Use In Statistmentioning

confidence: 99%

Some properties of point processes in statistical optics

Picinbono

Bendjaballah

2010

Phys. Rev. A

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International audienceThe analysis of the statistical properties of the point process (PP) of photon detection times can be used to determine whether or not an optical field is classical, in the sense that its statistical description does not require the methods of quantum optics. This determination is, however, more difficult than ordinarily admitted and the first aim of this paper is to illustrate this point by using some results of the PP theory. For example, it is well known that the analysis of the photodetection of classical fields exhibits the so-called bunching effect. But this property alone cannot be used to decide the nature of a given optical field. Indeed, we have presented examples of point processes for which a bunching effect appears and yet they cannot be obtained from a classical field. These examples are illustrated by computer simulations. Similarly, it is often admitted that for fields with very low light intensity the bunching or antibunching can be described by using the statistical properties of the distance between successive events of the point process, which simplifies the experimental procedure. We have shown that, while this property is valid for classical PPs, it has no reason to be true for nonclassical PPs, and we have presented some examples of this situation also illustrated by computer simulations

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Measurements of Second-Order Properties of Point Processes

Cited by 5 publications

References 9 publications

Output Dead-Time in Point Processes

Output Dead-Time in Point Processes

Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results

Some properties of point processes in statistical optics

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