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PowerLaw Shot Noise
, 1990
"... We explore the behavior of powerlaw shot noise, for which the associated impulse response functions assume a decaying powerlaw form. We obtain expressions for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities ..."
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Cited by 64 (6 self)
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We explore the behavior of powerlaw shot noise, for which the associated impulse response functions assume a decaying powerlaw form. We obtain expressions for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exhibits 1=ftype behavior over a substantial range of frequencies, so that the process serves as a source of 1=f ff shot noise for ff in the range 0 ! ff ! 2. For other parameters the amplitude probability density function is a L'evystable random variable with dimension less than unity. This process then behaves as a fractal shot noise that does not converge to a Gaussian amplitude distribution as the driving rate increases without limit. Fractal shot noise is a stationary continuoustime process that is fundamentally different from fractional Brownian motion. We consider several physical processes that are well described by powerlaw shot noise in certain domains: 1=f shot noise, Cherenkov radiation from a random stream of charged particles, diffusion of randomly injected concentration packets, the electric field at the growing edge of a quantum wire, and the mass distribution of solidparticle aggregates. I.
Fractal Character of the Neural Spike Train in the Visual System of the Cat
, 1997
"... d from one cell to the other or has a common origin. The gammar renewal process model, often used in the analysis of visualneuron interevent intervals, describes certain shortterm features of the RGC and LGN data reasonably well but fails to account for the longduration correlation. We present ..."
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Cited by 36 (4 self)
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d from one cell to the other or has a common origin. The gammar renewal process model, often used in the analysis of visualneuron interevent intervals, describes certain shortterm features of the RGC and LGN data reasonably well but fails to account for the longduration correlation. We present a new model for visualsystem nervespike firings: a gammar renewal process whose mean is modulated by fractal binomial noise. This fractal, doubly stochastic point process characterizes the statistical behavior of both RGC and LGN data sets remarkably well. 1997 Optical Society of America [S07403232(97)002020] 1. INTRODUCTION The sequence of action potentials recorded from cat retinal ganglion cells 116 (RGC's) and lateralgeniculatenucleus (LGN) cells 1721 remains irregular even when the retina is thoroughly adapted to a steady stimulus of fixed luminance. The statis
Point process models for selfsimilar network trac, with applications
 Comm. Statist. Stochastic Models
, 1998
"... Abstract Selfsimilar processes based on fractal point processes (FPPs) provide natural and attractive network traffic models. We show that the point process formulation yields a wide range of FPPs which in turn yield a diversity of parsimonious, computationally efficient, and highly practical asym ..."
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Cited by 23 (4 self)
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Abstract Selfsimilar processes based on fractal point processes (FPPs) provide natural and attractive network traffic models. We show that the point process formulation yields a wide range of FPPs which in turn yield a diversity of parsimonious, computationally efficient, and highly practical asymptotic secondorder selfsimilar processes. Using this framework, we show that the relevant secondorder fractal characteristics such as longrange dependence (LRD), slowlydecaying variance, and 1/f noise are completely characterized by three fundamental quantities: mean arrival rate, Hurst parameter, and fractal onset time. Four models are proposed, and the relationship between their model parameters and the three fundamental quantities are analyzed. By successfully applying the proposed models to Bellcore's Ethernet traces, we show that the FPP models prove useful in evaluating and predicting the queueing performance of various types of fractal traffic sources. Keywords: point process, fractal, selfsimilarity, longrange dependence, traffic modeling 1 Throughout this paper, selfsimilarity refers to asymptotic secondorder selfsimilarity [4], [13] unless otherwise defined.
Effects of random deletion and additive noise on bunched and antibunched photon counting statistics
 Opt. Lett
, 1982
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Cascaded Stochastic Processes in Optics
 Traitement du Signal
, 1999
"... Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor their timing more judicious. In a paper entitled "Photoe ..."
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Cited by 1 (1 self)
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Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor their timing more judicious. In a paper entitled "Photoelectron Shot Noise", published in the Journal of Mathematical Physics in 1970, when quantum optics was in its infancy, they obtained results that were to serve as an important building block in analyzing and generating many di#erent forms of light. We present some variations on the theme of cascaded stochastic processes in optics. Processus stochastiques en cascade d'importance en optique ResumeIl y a trente ans, Bernard Picinbono et ses collegues ont traite rigoureusement un probleme important : comment un champ optique est converti en une suite de photoelectrons apres detection. Leur choix de ce probleme ne pouvait pas etre meilleur et a revele un caractere pionnier. Dans un article intitule "Photoelectron Shot Noise", publie dans le Journal of Mathematical Physics en 1970, alors que l'optique quantique n'etait encore qu'a ses debuts, ils obtinrent des resultats qui constituerent un important point de depart pour analyser et generer de nombreuses et diverses formes de lumieres. Nous presentons des variations sur le theme des processus stochastiques en cascade, en optique. 1
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"... Cascaded stochastic processes in optics Processus stochastiques en cascade d'importance en optique abstract and key words Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon det ..."
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Cascaded stochastic processes in optics Processus stochastiques en cascade d'importance en optique abstract and key words Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor thei r timing more judicious. In a paper entitled &quot;Photoelectron Shot Noise&quot;, published in the Journal of Mathematical Physics in 1970, when quantum optics was in its infancy, they obtained results that were to serve as an important building block i n analyzing and generating many different forms of Tight. We present some variations on the theme of cascaded stochasti c processes in optics. Poisson process, shot noise, selfexciting process, doublystochastic process, compound Poisson process, doublyPoisson, triggered optical emissions, multiplyPoisson, cascadedPoisson, correlatedPoisson, nonclassical light, subPoisson light. résumé et mots clés Il y a trente ans, Bernard Picinbono et ses collègues ont traité rigoureusement un problème important: comment un champ optiqu e est converti en une suite de photoélectrons après détection. Leur choix de ce problème ne pouvait pas être meilleur et a révélé u n
unknown title
, 1995
"... Teich et al. Vol. 14, No. 3/March 1997/J. Opt. Soc. Am. A 529 Fractal character of the neural spike train in the visual system of the cat ..."
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Teich et al. Vol. 14, No. 3/March 1997/J. Opt. Soc. Am. A 529 Fractal character of the neural spike train in the visual system of the cat
BE (Melb)
, 1997
"... Spatiotemporal coding of sound in the auditory nerve for cochlear implants ..."
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Spatiotemporal coding of sound in the auditory nerve for cochlear implants