Théorie Exacte de la Distribution de la Somme des Photoélectrons Emis en L Points

1972 ◽  
Vol 50 (12) ◽  
pp. 1307-1314 ◽  
Author(s):  
Jacques Bures ◽  
Claude Delisle ◽  
Andrzej Zardecki
Keyword(s):  
Physical Meaning ◽  
Factorial Moment ◽  
Moment Generating Function ◽  
Exact Formula ◽  
Coherence Time ◽  
Exact Expression ◽  
Detection Time ◽  
Factorial Moments ◽  
Statistical Behavior ◽  
The Difference

The statistical behavior of photoelectrons emitted at L points of a photocathode in partially coherent Gaussian light is considered. The exact formula for the cumulants and the factorial moment generating function is derived. An exact expression for the photocount distribution and for the factorial moments is obtained in the case when the detection time is much smaller than the coherence time. Two cases of interest which were treated earlier by the same authors are also considered. In particular, the case of two points of detection is of special interest because a physical meaning can be given to the difference of the normalized eigenvalues. Finally, both the exact and approximate theories are compared with the experimental photocount distribution for four different geometrical arrangements.

Détermination de la Surface de Cohérence à Partir d'une Expérience de Photocomptage

1972 ◽  
Vol 50 (8) ◽  
pp. 760-768 ◽  
Author(s):  
Jacques Bures ◽  
Claude Delisle ◽  
Andrzej Zardecki
Keyword(s):  
Degrees Of Freedom ◽  
Coherence Time ◽  
Theoretical Distribution ◽  
Detection Time ◽  
Coherent Light ◽  
Second Moment ◽  
Partially Coherent Light ◽  
Elementary Surface ◽  
The Mean ◽  
Circular Source

The theoretical distribution, with exact second moment, of the number of photoelectrons emitted by an extended photodetector illuminated with partially coherent light is first derived. Then the parameter N, the number of degrees of freedom, is obtained from the second moment of the distribution, for [Formula: see text] (T is the detection time and Tc the coherence time). N is then plotted as a function of the surface of the detector expressed in three different ways for both circular source and detector and square source and detector. In both cases the source is considered to be of uniform brightness. An elementary surface called the surface of coherence is determined by extrapolating towards small values the asymptotical behavior of N for large values of the detection surface. For both sources, this surface of coherence is equal to [Formula: see text]. λ0 is the mean wavelength, D the distance between the source and the detector, and Ss the surface of the source.

scholarly journals Simple derivations of properties of counting processes associated with Markov renewal processes

2005 ◽  
Vol 42 (04) ◽  
pp. 1031-1043 ◽  
Author(s):  
Frank Ball ◽  
Robin K. Milne
Keyword(s):  
Renewal Process ◽  
Factorial Moment ◽  
Probability Generating Function ◽  
Stochastic Modelling ◽  
Markov Renewal Process ◽  
Counting Processes ◽  
Continuous Time Markov Chain ◽  
Factorial Moments ◽  
Asymptotic Expressions ◽  
Markov Renewal Processes

A simple, widely applicable method is described for determining factorial moments of N̂ t , the number of occurrences in (0,t] of some event defined in terms of an underlying Markov renewal process, and asymptotic expressions for these moments as t → ∞. The factorial moment formulae combine to yield an expression for the probability generating function of N̂ t , and thereby further properties of such counts. The method is developed by considering counting processes associated with events that are determined by the states at two successive renewals of a Markov renewal process, for which it both simplifies and generalises existing results. More explicit results are given in the case of an underlying continuous-time Markov chain. The method is used to provide novel, probabilistically illuminating solutions to some problems arising in the stochastic modelling of ion channels.

scholarly journals Simple derivations of properties of counting processes associated with Markov renewal processes

2005 ◽  
Vol 42 (4) ◽  
pp. 1031-1043 ◽  
Author(s):  
Frank Ball ◽  
Robin K. Milne
Keyword(s):  
Renewal Process ◽  
Factorial Moment ◽  
Probability Generating Function ◽  
Stochastic Modelling ◽  
Markov Renewal Process ◽  
Counting Processes ◽  
Continuous Time Markov Chain ◽  
Factorial Moments ◽  
Asymptotic Expressions ◽  
Markov Renewal Processes

A simple, widely applicable method is described for determining factorial moments of N̂t, the number of occurrences in (0,t] of some event defined in terms of an underlying Markov renewal process, and asymptotic expressions for these moments as t → ∞. The factorial moment formulae combine to yield an expression for the probability generating function of N̂t, and thereby further properties of such counts. The method is developed by considering counting processes associated with events that are determined by the states at two successive renewals of a Markov renewal process, for which it both simplifies and generalises existing results. More explicit results are given in the case of an underlying continuous-time Markov chain. The method is used to provide novel, probabilistically illuminating solutions to some problems arising in the stochastic modelling of ion channels.

scholarly journals New perspectives on the Erlang-A queue

2019 ◽  
Vol 51 (01) ◽  
pp. 268-299 ◽  
Author(s):  
Andrew Daw ◽  
Jamol Pender
Keyword(s):  
Generating Function ◽  
Large Scale ◽  
Moment Generating Function ◽  
Urban Mobility ◽  
Cumulant Generating Function ◽  
True Model ◽  
The Difference ◽  
The Moment ◽  
Stochastic Representations ◽  
Transient And Steady State

AbstractThe nonstationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large-scale multiserver service systems that may experience customer abandonments, such as call centers, hospitals, and urban mobility systems. In this paper we develop novel approximations to all of its transient and steady state moments, the moment generating function, and the cumulant generating function. We also provide precise bounds for the difference of our approximations and the true model. More importantly, we show that our approximations have explicit stochastic representations as shifted Poisson random variables. Moreover, we are also able to show that our approximations and bounds also hold for nonstationary Erlang-B and Erlang-C queueing models under certain stability conditions.

Generalized Hypergeometric Factorial Moment Distribution of Order k

2000 ◽  
Vol 50 (1-2) ◽  
pp. 71-78 ◽  
Author(s):  
C. Satheesh Kumar ◽  
T. S. K. Moothathu
Keyword(s):  
Negative Binomial ◽  
Factorial Moment ◽  
Mass Function ◽  
Discrete Distributions ◽  
Probability Mass Function ◽  
Factorial Moments ◽  
Point Distribution ◽  
Moment Distribution ◽  
Special Cases ◽  
Probability Mass

Here we introduce the generalized hypergeometric functional moment distribution of order k (GHFMD (k)) in the distribution of the random sum [Formula: see text] having Hira no's k-point distribution, where N, independent of X j's, has the generalized hypergeomet ric factorial moment distribution. Well-known discrete distributions of order k such as cluster binomial, cluster negative binomial and extended Poisson are shown to be special cases of GHFMD(k). The probability mass function, recurrence relations for probabilities and factorial moments of GHFMD (k) are found out. The beta or the gamma mixture of GHFMD (k) is shown to be a GHFMD (k). Finally GHFMD (k) is obtained as a limit of another GHFMD (k). AMS (2000) Subject Classification: Primary 60E05, 60E10; Secondary 33C20.

Distribution de la Somme des Photoélectrons Détectés en L Points sous Eclairement Gaussien Partiellement Cohérent

1971 ◽  
Vol 49 (24) ◽  
pp. 3064-3074 ◽  
Author(s):  
Jacques Bures ◽  
Claude Delisle ◽  
Andrzej Zardecki
Keyword(s):  
Experimental Verification ◽  
Spatial Coherence ◽  
Coherence Time ◽  
Thermal Source ◽  
General Function ◽  
Detection Time ◽  
Coherent Light ◽  
Second Moment ◽  
Partially Coherent Light ◽  
Spatial And Temporal Characteristics

The analysis of the photocount distribution in incoherent Gaussian light detected in L space points of a photodetector is extended to the case of partially coherent light. The second moment of the derived distribution is exact. A function η is introduced which accounts for the spatial coherence aspect of light as does the function ξ, (Mandel) for the temporal coherence aspect. A more general function ζ, which for cross-spectrally pure light reduces to the product ζ = ηξ, depends on both spatial and temporal characteristics of coherence. It is shown both theoretically and experimentally that many different geometrical configurations yield the same normalized second moment. A pseudo-thermal source [Formula: see text] where T is the detection time and Tc the coherence time) is used for the experimental verification.

scholarly journals Asymptotic Analysis of the kth Subword Complexity

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 207 ◽  
Author(s):  
Lida Ahmadi ◽  
Mark Daniel Ward
Keyword(s):  
Mellin Transform ◽  
Complex Analysis ◽  
Factorial Moment ◽  
Probability Generating Function ◽  
Exact Expression ◽  
A Value ◽  
Auto Correlation ◽  
Point Analysis ◽  
Subword Complexity ◽  
Binary Strings

Patterns within strings enable us to extract vital information regarding a string’s randomness. Understanding whether a string is random (Showing no to little repetition in patterns) or periodic (showing repetitions in patterns) are described by a value that is called the kth Subword Complexity of the character string. By definition, the kth Subword Complexity is the number of distinct substrings of length k that appear in a given string. In this paper, we evaluate the expected value and the second factorial moment (followed by a corollary on the second moment) of the kth Subword Complexity for the binary strings over memory-less sources. We first take a combinatorial approach to derive a probability generating function for the number of occurrences of patterns in strings of finite length. This enables us to have an exact expression for the two moments in terms of patterns’ auto-correlation and correlation polynomials. We then investigate the asymptotic behavior for values of k = Θ ( log n ) . In the proof, we compare the distribution of the kth Subword Complexity of binary strings to the distribution of distinct prefixes of independent strings stored in a trie. The methodology that we use involves complex analysis, analytical poissonization and depoissonization, the Mellin transform, and saddle point analysis.

Comptage des Photoélectrons Provenant de Points Statistiquement Indépendants et d'une Surface Etendue de la Photocathode

1971 ◽  
Vol 49 (10) ◽  
pp. 1255-1262 ◽  
Author(s):  
Jacques Bures ◽  
Claude Delisle
Keyword(s):  
Relative Size ◽  
Coherence Time ◽  
The Other ◽  
Detection Time ◽  
Circular Area ◽  
Physical Point ◽  
Other Hand ◽  
The One ◽  
Coherence Area

The experimental photocount distribution from a photocathode illuminated by a pseudothermal source is compared with theory. The detection time is much smaller than the coherence time [Formula: see text]. The agreement is excellent for an illuminated area composed of holes small enough to be considered as points and far enough to guarantee incoherence among them. But, for an extended circular area, the agreement is good only in the limits when that area is very small or very large with respect to the coherence area. Finally, we consider on the one hand, the evaluation of an extended detection area as a function of the number of statistically independent points, L, and on the other hand, the relative size of a physical point.

INTERMITTENCY IN 4.5A AND 14.5A GeV/c28Si-NUCLEUS INTERACTIONS

2002 ◽  
Vol 11 (02) ◽  
pp. 131-141 ◽  
Author(s):  
W. BARI ◽  
N. AHMAD ◽  
M. M. KHAN ◽  
SHAKEEL AHMAD ◽  
M. ZAFAR ◽  
...  
Keyword(s):  
Factorial Moment ◽  
Fractal Dimensions ◽  
Fractal Nature ◽  
Factorial Moments ◽  
Linear Behavior ◽  
Rapidity Interval ◽  
Thermal Phase Transition ◽  
Thermal Phase ◽  
The Moment ◽  
Scaled Factorial Moments

The occurrence of intermittent patterns in 14.5 A GeV/c 28 Si -nucleus interactions is examined in terms of Scaled Factorial Moments (SFMs), introduced by Bialas and Peschanski. Further, to examine the dependence of various interesting characteristics of SFMs on incident energy, the data on 4.5 A GeV/c 28 Si -nucleus collisions available in our laboratory are analyzed. Interestingly, log-log plots between rapidity interval δη and the qth order factorial moment Fq for both the energies exhibit linear behavior indicating thereby the presence of intermittency in the interactions investigated. Moreover, to look at the fractal nature of the particle emitting sources, variation of the fractal dimensions, dq with the order of the moment is investigated. Finally, study of the variation of λq [=(ϕq+1)/q)] with the order of the moment, q indicates a possibility of non-thermal phase transition in certain types of events

scholarly journals BOLD Noise Assumptions in fMRI

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Alle Meije Wink ◽  
Jos B. T. M. Roerdink
Keyword(s):  
Time Series ◽  
High Precision ◽  
Gaussian Noise ◽  
Resting State ◽  
Statistical Tests ◽  
Exact Expression ◽  
Blood Oxygenation ◽  
Temporal Noise ◽  
First Results ◽  
The Difference

This paper discusses the assumption of Gaussian noise in the blood-oxygenation-dependent (BOLD) contrast for functional MRI (fMRI). In principle, magnitudes in MRI images follow a Rice distribution. We start by reviewing differences between Rician and Gaussian noise. An analytic expression is derived for the null (resting-state) distribution of the difference between two Rician distributed images. This distribution is shown to be symmetric, and an exact expression for its standard deviation is derived. This distribution can be well approximated by a Gaussian, with very high precision for high SNR, and high precision for lower SNR. Tests on simulated and real MR images show that subtracting the time-series mean in fMRI yields asymmetrically distributed temporal noise. Subtracting a resting-state time series from the first results in symmetric and nearly Gaussian noise. This has important consequences for fMRI analyses using standard statistical tests.

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