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In this paper we have for the first time proposed a novel transformed Gaussian process method for the estimation of rogue wave occurrence in a short crested mixed sea. The saddle point approximation of a specific joint density is utilised to further improve the computational efficiency of the proposed method. The proposed method has been applied to forecast the rogue wave occurrence in four short-crested mixed sea states, two with directional wave spectra based on measured surface elevation data at the coast of Yura, and another two with typical directional bimodal wave spectra. It is shown in these four cases that the proposed method can offer more accurate forecasting results than those obtained from the linear simulation method, from the transformation based on Hermite polynomials and from using the Rayleigh distribution model. It is also demonstrated that the proposed method is more efficient than the nonlinear simulation method. [ABSTRACT FROM AUTHOR]

Although partition temperature derived using the Darwin–Fowler method is exact for simple scenarios, the derivation for complex systems might reside in specific approximations whose viability is not ensured if the thermodynamic limit is not attained. This work elaborates on a related problem relevant to relativistic high-energy collisions. On the one hand, it is simple enough that closed-form expressions can be obtained precisely for the one-particle distribution function. On the other hand, the resulting expression is not an exponential form, and therefore, it is not straightforward that the notion of partition function could be implied. Specifically, we derive the one-particle distribution function for massless particles where the phase-space integration is performed exactly for the underlying canonical ensemble consisting of a given number of particles. We discuss the viability of the partition temperature in this case. Possible implications of the obtained results regarding the observed Tsallis distribution in transverse momentum spectra in high-energy collisions are also addressed. [ABSTRACT FROM AUTHOR]

Abstract The Gaussian approximation is commonly used to evaluate the performance of free space optical communication systems. However, other performance evaluation methods such as the saddle point approximation, Chernoff bound and the modified Chernoff bound have also been used. This paper investigates the performance of fixed and gain saturated optically preamplified communication systems limited by factors such as strong atmospheric turbulence and pointing errors using various evaluation methods. Average bit error rate results are obtained over a range of average transmitted powers for free space optical communication systems without pointing error and those with pointing error using different saturation regimes, normalised beam widths and pointing error standard deviations. Results obtained in this paper show over a propagation distance of 1500 m, a receiver diameter of 0.15 m performed better than a receiver diameter of 0.03 m when the pointing error standard deviation is 0.1. Also, a receiver diameter of 0.03 m performed better than a receiver diameter of 0.15 m when the pointing error standard deviation is 4. These results show that while larger receiving lenses performed better when pointing error effects are minimal or absent, smaller receiving lenses are better when pointing error effects are dominant. Additionally, it is shown in this paper that while fixed and gain saturated optical preamplifiers produced similar performances when the decision threshold at the receiver is adaptive, the saddle point approximation is not useful for gain saturated optically preamplified receivers. Also, results in this paper showed optimal and near-optimal adaptive decision thresholds for the modified Chernoff bound and Gaussian approximation, respectively.

Let q ⩾ 2 be a fixed prime power. We prove an asymptotic formula for counting the number of monic polynomials that are of degree n and have exactly k irreducible factors over the finite field F q . We also compare our results with the analogous existing ones in the integer case, where one studies all the natural numbers up to x with exactly k prime factors. In particular, we show that the number of monic polynomials grows at a surprisingly higher rate when k is a little larger than log n than what one would speculate from looking at the integer case. [ABSTRACT FROM AUTHOR]

Introduction/purpose: Saddle point approximation has been considered in the paper Methods: The saddle point method is used in several different fields of mathematics and physics. Several terms of the expansion for the factorial function have been explicitely computed. Results: The integrals estimated in this way have values close to the exact one. Conclusions: Higher order corrections are not negligible even when requiring moderate levels of precision.

Although partition temperature derived using the Darwin–Fowler method is exact for simple scenarios, the derivation for complex systems might reside in specific approximations whose viability is not ensured if the thermodynamic limit is not attained. This work elaborates on a related problem relevant to relativistic high-energy collisions. On the one hand, it is simple enough that closed-form expressions can be obtained precisely for the one-particle distribution function. On the other hand, the resulting expression is not an exponential form, and therefore, it is not straightforward that the notion of partition function could be implied. Specifically, we derive the one-particle distribution function for massless particles where the phase-space integration is performed exactly for the underlying canonical ensemble consisting of a given number of particles. We discuss the viability of the partition temperature in this case. Possible implications of the obtained results regarding the observed Tsallis distribution in transverse momentum spectra in high-energy collisions are also addressed.

The Gaussian approximation is commonly used to evaluate the performance of free space optical communication systems. However, other performance evaluation methods such as the saddle point approximation, Chernoff bound and the modified Chernoff bound have also been used. This paper investigates the performance of fixed and gain saturated optically preamplified communication systems limited by factors such as strong atmospheric turbulence and pointing errors using various evaluation methods. Average bit error rate results are obtained over a range of average transmitted powers for free space optical communication systems without pointing error and those with pointing error using different saturation regimes, normalised beam widths and pointing error standard deviations. Results obtained in this paper show over a propagation distance of 1500 m, a receiver diameter of 0.15 m performed better than a receiver diameter of 0.03 m when the pointing error standard deviation is 0.1. Also, a receiver diameter of 0.03 m performed better than a receiver diameter of 0.15 m when the pointing error standard deviation is 4. These results show that while larger receiving lenses performed better when pointing error effects are minimal or absent, smaller receiving lenses are better when pointing error effects are dominant. Additionally, it is shown in this paper that while fixed and gain saturated optical preamplifiers produced similar performances when the decision threshold at the receiver is adaptive, the saddle point approximation is not useful for gain saturated optically preamplified receivers. Also, results in this paper showed optimal and near-optimal adaptive decision thresholds for the modified Chernoff bound and Gaussian approximation, respectively. [ABSTRACT FROM AUTHOR]

Introduction/purpose: Saddle point approximation has been considered in the paper Methods: The saddle point method is used in several different fields of mathematics and physics. Several terms of the expansion for the factorial function have been explicitely computed. Results: The integrals estimated in this way have values close to the exact one. Conclusions: Higher order corrections are not negligible even when requiring moderate levels of precision. [ABSTRACT FROM AUTHOR]

Federated learning (FL) is a collaborative machine learning paradigm, which enables deep learning model training over a large volume of decentralized data residing in mobile devices without accessing clients’ private data. Driven by the ever increasing demand for model training of mobile applications or devices, a vast majority of FL tasks are implemented over wireless fading channels. Due to the time-varying nature of wireless channels, however, random delay occurs in both the uplink and downlink transmissions of FL. How to analyze the overall time consumption of a wireless FL task, or more specifically, a FL’s delay distribution, becomes a challenging but important open problem, especially for delay-sensitive model training. In this paper, we present a unified framework to calculate the approximate delay distributions of FL over arbitrary fading channels. Specifically, saddle point approximation, extreme value theory (EVT), and large deviation theory (LDT) are jointly exploited to find the approximate delay distribution along with its tail distribution, which characterizes the quality-of-service of a wireless FL system. Simulation results will demonstrate that our approximation method achieves a small approximation error, which vanishes with the increase of training accuracy. [ABSTRACT FROM AUTHOR]

The projected belief network (PBN) is a deep layered generative network with tractable likelihood function (LF) and can be used as a Bayesian classifier by training a separate model on each data class, and classifying based on maximum likelihood (ML). Unlike other generative models with tractable LF, the PBN can share an embodiment with a feed-forward classifier network. By training a PBN with a cost function that combines LF with classifier cross-entropy, its network weights can be “aligned” to the decision boundaries separating the data class from other classes. This results in a Bayesian classifier that rivals state of the art discriminative classifiers. These claims are backed up by classification experiments involving spectrograms of spoken keywords and handwritten characters. [ABSTRACT FROM AUTHOR]

Despite many advances in the field of computational system reliability analysis, estimating the joint probability distribution of correlated non‐normal state variables on the basis of incomplete statistical data brings great challenges for engineers. To avoid multidimensional integration, system reliability estimation usually requires the calculation of marginal failure probability and joint failure probability. The current article proposed an integrated approach for estimating system reliability on the basis of the high moment method, saddle point approximation, and copulas. First, the statistic moment estimation based on the stochastic perturbation theory is presented. Thereafter, by constructing CGF (concise cumulant generating function) for the state variable with its first four statistical moments, a fourth moment saddle point approximation method is established for the component reliability estimation. Second, the copula theory is briefly introduced and extensively utilized two‐dimensional copulas are presented. The best fit copula for estimating the probability of system failure is selected according to the AIC (Akaike Information Criterion). Finally, the derived method is applied to three numerical examples for the sake of a comprehensive validation. [ABSTRACT FROM AUTHOR]

Given the mutual information of finite-alphabet inputs cannot be calculated concisely and accurately over fading channels, this paper proposes a new method to calculate the mutual information. First, the applicability of the saddle point method is studied, and then the mutual information is estimated by the saddle point approximation method with known channel state information. Furthermore, we induce the expectation of mutual information over doubly correlated multiple-input multiple-output (MIMO) Rayleigh fading channels. The validity of the saddle point approximation method is verified by comparing the numerical results of the Monte Carlo method and the saddle point approximation method under different doubly correlated MIMO fading channel scenarios. [ABSTRACT FROM AUTHOR]

Given the mutual information of finite-alphabet inputs cannot be calculated concisely and accurately over fading channels, this paper proposes a new method to calculate the mutual information. First, the applicability of the saddle point method is studied, and then the mutual information is estimated by the saddle point approximation method with known channel state information. Furthermore, we induce the expectation of mutual information over doubly correlated multiple-input multiple-output (MIMO) Rayleigh fading channels. The validity of the saddle point approximation method is verified by comparing the numerical results of the Monte Carlo method and the saddle point approximation method under different doubly correlated MIMO fading channel scenarios.

Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory.

Nuclear Power Plants (NPPs) operate at very high temperature and high fluid mass flow rate which are favourable for Flow Accelerated Corrosion (FAC) resulting in wall thickness reduction in pipes, bends and other geometries. The prediction of progressive reduction in pipe wall thickness is required for safety of operating NPP. In this paper, Hougaard process stochastic model is proposed for prediction of wall thickness reduction in pipes between two consecutive in-service-inspections. The probability distribution function (PDF) for the Hougaard process is computationally unstable near the origin. Hence, its saddle point approximation was used along with method of maximum likelihood (MLE) to derive the mathematical expressions for the three parameters with generally given time interval between in-service-inspection and corresponding changes in wall thickness. The gamma process model fit and linear fit to data have also been carried out. The predictions of change in pipe wall thickness from probabilistic model are validated by using (a) Experimental data for FAC for 58° bend pipe and (b) NPP feeder pipe data on FAC. The results compare well with the experimental and field data used in analysis. [ABSTRACT FROM AUTHOR]

It is aimed to propose a copula based systematic quantitative method for system reliability analysis of engineering structures considering multiple dependent failure modes. The principles of the moment matching method, the copula theory and the bound theory are combined to achieve the purpose. As the very first step, the moment estimation of the limit state function of each component is calculated by anchored ANOVA (Analysis of Variance) expansion. The third moment saddle point approximation is then applied to derive the distribution of each performance function and evaluate the reliability index with obtained moments. By introducing copula functions into the narrow bounds theory, the traditional reliability method is improved. The best-fitting copula function is determined to ensure the accuracy of the joint probabilistic modeling between the dependent failure modes. A novel feature of the proposed method is the use of the copula concept, instead of traditional numerical integration commonly used in the joint failure probability estimation. Examples are presented to illustrate the accuracy and applicability of the presented method. [ABSTRACT FROM AUTHOR]

Depth perception in humans is obtained by comparing images generated by the two eyes to each other. Given the highly stochastic nature of neurons in the brain, this comparison requires maximizing the mutual information (MI) between the neuronal responses in the two eyes by distributing the coding information across a large number of neurons. Unfortunately, MI is not an extensive quantity, making it very difficult to predict how the accuracy of depth perception will vary with the number of neurons ( N ) in each eye. To address this question we present a two-arm, distributed decentralized sensors detection model. We demonstrate how the system can extract depth information from a pair of discrete valued stimuli represented here by a pair of random dot-matrix stereograms. Using the theory of large deviations we calculated the rate at which the global average error probability of our detector; and the MI between the two arms’ output, vary with N . We found that MI saturates exponentially with N at a rate which decays as 1 / N . The rate function approached the Chernoff distance between the two probability distributions asymptotically. Our results may have implications in computer stereo vision that uses Hebbian-based algorithms for terrestrial navigation. [ABSTRACT FROM AUTHOR]

Certain models for ocean wave spectra, including the Bretschneider and Pierson-Moskowitz spectra, have spectral densities in the form of the Fréchet probability density. The autocorrelation function (ACF) of the waves is the Fourier cosine transform of the spectral density. Mellin transforms are applied to obtain the ACF in the form of a Fox H -function. If the Fréchet shape parameter is rational, the ACF may also be expressed as a Meijer G -function. These generalised functions are difficult to compute, so power series and saddle point approximations are derived to compute the ACF. The speed and accuracy of these methods is assessed. [ABSTRACT FROM AUTHOR]

The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian process is obtained based on the equivalence of the level up-crossing rates of the two processes. A saddle point approximation procedure is applied for calculating the level up-crossing rates in this study. The accuracy and efficiency of the transformed Gaussian process method are validated by comparing the results predicted by using the method with those predicted by the Monte Carlo simulation method. [ABSTRACT FROM AUTHOR]

In the recent past there have been several attempts to obtain the equilibrium distribution of multiple populations and their moments in the context of some biological or ecological processes (e.g., Matis and Kiffe in Biometrics 52:155, 1996; Matis and Kiffe in Environ Ecol Stat 9:237, 2002; Renshaw in J Math Appl Med Biol, 15:1, 1998). In particular, the method of cumulant truncation (Matis and Kiffe in Biometrics 52:155, 1996) is a pioneering work in this field. However it requires solving a large number of cumulant functions even in the case of two simultaneous differential equations. Besides the solutions are approximate and depend on the precision of the software. Renshaw (Math Biosci 168:57, 2000) provided a nice extension of the univariate truncated saddle point procedure to multivariate scenarios. But this approach involves a multivariate Newton-Raphson type iterative algorithm whose performance and convergence are critically dependent on the choice of the initial values. In the present paper we propose a new and simple approach to obtain the equilibrium distribution of populations and their conditional moments in a system of differential equations of any dimension. Our proposed method, which is a natural extension of the classical variational matrix approach, has several advantages which are discussed in detail in the paper; among other things it includes the derivation of additional conditions which can be interpreted as environmental surrogates. [ABSTRACT FROM AUTHOR]

In this note upcrossing intensity of a level u by a non-Gaussian process-the Laplace Moving Average (LMA)-is estimated by means of a saddle point approximation of Rice's formula. A LMA-process is defined by power spectral density, skewness and kurtosis parameters. The method is illustrated by measurements of sea surface elevation and stresses in a vessel. [ABSTRACT FROM AUTHOR]

We consider an internally coded time-hopping coherent ultrashort light pulse code division multiple access scheme (TH-CULP CDMA) and analyze its performance in the fiber-optic communication systems. This system combines the TH and CULP CDMA techniques and exploits the advantages of both. In our method, each bit time interval is divided into Ns frames, and the spectral phase-coded pulse is transmitted in one of these frames. Two exclusive PN sequences are assigned to each user. One is added to a superorthogonal convolutional encoder output to select the transmission frame, and the other is used to encode the phase of the ultrashort pulse in the spectral domain. We evaluate the bit error rate (BER) of the system considering the effects of the multiple access interference (MAI) and thermal noise for both soft and hard decoders. The BER is evaluated using both the Chernoff bound and saddle point approximation. We compare the performance of our proposed system with that of the conventional CULP CDMA system. The numerical results indicate that for the same bit rate and processing gain, the performance of our proposed system (TH-CULP CDMA) is substantially better than that of the conventional CULP CDMA system. In addition, we observe that the hard decoder has a better performance at large number of users compared to the soft decoder [ABSTRACT FROM PUBLISHER]

In this paper, the authors derive the moment generating function (MGF) of the decision variable for a practical optical differential quadrature phase shift keying (DQPSK) receiver affected by phase noise and the amplifier spontaneous emission noise. The effect of the different optical filters, Gaussian, Fabry-Peacuterot (FP), and optical integrator, on the phase noise is examined. Using the saddle point approximation, the authors obtain numerically the bit error rate (BER) for the above system, as a function of the optical-signal-to-noise ratio (OSNR) and the source linewidth. The model is found to agree with previous published simulation results and the Monte Carlo simulations presented in this paper. The authors also calculate the BER floors for DQPSK inflicted by the phase noise and compare its performance with differential phase shift keying (DPSK). Finally, the authors examine the effect of interferometric demodulation on the relative intensity noise (RIN) spectra and the impact on the DQPSK system performance. In particular, the authors examine the influence of system dispersion on the receiver sensitivity [ABSTRACT FROM PUBLISHER]

In-band crosstalk can pose important limitations in an all-optical wavelength-division-multiplexed (WDM) network. Recent studies have demonstrated that differential phase shift keying (DPSK), can tolerate higher in-band crosstalk-noise levels compared to amplitude shift keying (ASK). In this paper, the performance of a DPSK receiver, limited by in-band crosstalk noise, is studied theoretically. The model takes into account both the in-band crosstalk noise as well as the amplified-spontaneous-emission (ASE) noise of the optical amplifiers. The model is based on the evaluation of the moment-generating function (MGF) of the decision variable through which, the error probability (EP) can be calculated by applying the saddle point approximation. This provides a rigorous model for the evaluation of the EP of a DPSK receiver in the presence of ASE and in-band crosstalk noises. In the absence of the ASE noise, a closed-form formula for the EP is also given that is useful for estimating the error floor set by the in-band crosstalk noise. [ABSTRACT FROM PUBLISHER]

Abstract: Intraband crosstalk (IXT) is one of the major factors limiting the performance of all-optical wavelength division multiplexing (WDM) networks. In this paper, the technology of forward error correction (FEC) is employed to improve the performance of a WDM network node impaired by IXT. Based on the moment generation function, a theoretical framework for the FEC coded optical receiver is presented, and the performance of the receiver in terms of IXT induced power penalty is evaluated by using saddle point approximation. The results show that due to FEC the power penalties can be significantly reduced by at least 3dB at the bit error rate of 10−10, so FEC technology can be used to increase scalabilities of wide area networks or decrease costs of local area networks. [Copyright &y& Elsevier]

This paper describes a study of the performance of various configurations for placing multiple optical amplifiers in a typical coherent ultrashort light pulse code-division multiple access (CULP-CDMA) communication system using the additive noise model. For this study, a comprehensive performance analysis was developed that takes into account multiple-access noise, noise due to optical amplifiers, and thermal noise using the saddle-point approximation technique. Prior to obtaining the overall system performance, the input/output statistical models for different elements of the system such as encoders/decoders, star coupler, and optical amplifiers were obtained. Performance comparisons between an ideal and lossless quantum-limited case and a typical CULP-CDMA with various losses exhibit more than 30 dB more power requirement to obtain the same bit-error rate (BER). Considering the saturation effect of optical amplifiers, this paper discusses an algorithm for amplifiers' gain setting in various stages of the network in order to overcome the nonlinear effects on signal modulation in optical amplifiers. Finally, using this algorithm, various configurations of multiple optical amplifiers in CULP-CDMA are discussed and the rules for the required optimum number of amplifiers are shown with their corresponding optimum locations to be implemented along the CULP-CDMA system. [ABSTRACT FROM PUBLISHER]

In many applications, ranging from target detection to safety monitoring systems, we are interested in determining whether or not to accept a hypothesis based on the information available. In this paper we model the reliability of threshold weighted voting systems (WVS) with multi-failure-modes, where a general recursive reliability function of the WVS is presented. We also develop approximation formulas for calculating the reliability of WVS based on a large number of units. We also develop reliability functions of time-dependent threshold weighted voting systems, where each unit is a function of time. Finally, the optimal stopping time that minimizes the total cost of the systems subject to a reliability constraint is discussed. [Copyright &y& Elsevier]

Non-linear waves have been a research topic for a long time, but have not yet entered common ocean engineering practice. In this article the problem of calculating the probability density function (pdf) for non-linear waves is investigated. The ‘saddle point approximation’ is applied to a second-order wave model to estimate the pdf. The performance of the approximation is compared with the performances of the more commonly used methods for different types of input spectra. In addition, a non-parametric transformation method, with extrapolation of the level crossing intensity, is proposed to estimate the pdf. One simulation and three different data sets are used to investigate the performance of the model. [Copyright &y& Elsevier]

In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to its strictly classical limit; unlike for Feynman type path integrals, the latter is well defined in the Marinov case. The topics covered include a random force representation of Marinov's integral based upon the concept of "Airy averaging", a related discussion of positivity-violating Wigner functions describing tunneling processes, and the role of the response field in maintaining quantum coherence and enabling interference phenomena. The double slit experiment for electrons and the Bohm–Aharonov effect are analyzed as illustrative examples. Furthermore, a surprising relationship between the instantons of the Marinov path integral over an analytically continued ("Wick rotated") response field, and the complex instantons of Feynman-type integrals is found. The latter play a prominent role in recent work towards a Picard–Lefschetz theory applicable to oscillatory path integrals and the resurgence program. • Moyal quantum mechanics and Marinov's path integral. • Classical and semiclassical limits of Marinov's path integral. • Oscillating functional integrals. • Instantons of the Marinov's path integral. [ABSTRACT FROM AUTHOR]

• This paper proposes two novel probabilistic load flow methods based on holomorphic embedding method. • Holomorphic method is used to solve the power flow in a faster and robust way. • Kernel Density Estimator (KDE) and Saddle Point Approximation (SPA) methods are used to efficiently estimate probabilistic characteristics of load flow outputs. • The correlations between random input variables with non-normal/normal probability distributions have been considered. • Several numerical tests are carried out to assess the robustness and performance. Probabilistic Load Flow (PLF) methods have been extensively regarded due to the growth of uncertainty and renewable energies penetration in power systems. Given that, the current study aims to propose two novel probabilistic load flow methods based on holomorphic embedding method. Holomorphic method, unlike other iterative methods, introduces a nonlinear equation solver in an independent class, recursively. To that end, Kernel Density Estimator (KDE) and Saddle Point Approximation (SPA) methods are used to efficiently estimate probabilistic characteristics of load flow outputs. The correlations between random input variables with non-normal/normal probability distributions have been considered. The proposed algorithms have been examined on the modified IEEE 14- and 118-bus systems. Finally, to consider the uncorrelated and correlated conditions, the researcher compared the simulation results of the two proposed methods with some well-known and published probabilistic iterative load flow methods such as Monte Carlo Simulation (MCS), Parzen Window (PW), Diffusion method, and 2n+1 Point Estimate Method (PEM). MCS is always a dependable solution but time-consuming that make it useless for large power systems. In the present study, the accurate results obtained from MCS are regarded as a reference. The comparison of results shows high efficiency and low computational burden of proposed methods, and also the accuracy of these methods in density function estimation of output random variables. [ABSTRACT FROM AUTHOR]

Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory. [ABSTRACT FROM AUTHOR]