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In this paper, we investigate the optimal design of phase modulation waveforms using the theoretical model of Tm3+-doped fiber amplifiers. The proposed design suppresses the SBS effect in the 2 μm-band Tm3+-doped fiber amplifiers with the help of a reference point-based multi-device non-dominated sequential genetic algorithm (NSGA-III). At the same time, synthesis efficiency is ensured. Different from the previous use of conventional multi-objective genetic algorithms to suppress the SBS effect in narrow linewidth amplifiers in the 1 μm band, the maximum SBS threshold is 121 W at a signal linewidth of 496 MHz with a more uniform distribution of Pareto solutions under this scheme. The signal linewidth of 680.61 MHz increases the SBS threshold by almost 20 W and the operating speed by several times compared to a conventional multi-objective genetic algorithm at different modulation depths, modulation frequencies and modulation periods. The threshold enhancement factor of the SBS signal with optimal modulation is 2.12 times that of the sinusoidal signal with an extended bandwidth of 700 MHz. The 2 μm laser obtained by this scheme enables more accurate and longer distance ranges in coherent detection. [ABSTRACT FROM AUTHOR]

We provide a model in which an intermediary can choose between wholesale or agency. The possibility that buyers and sellers transact directly limits his market power and, thus, creates incentives for him to deter the emergence of bilateral exchanges. In equilibrium, the intermediary chooses agency and thereby pre-empts the emergence of a competing bilateral exchange if the matching technology of the competing exchange is sufficiently efficient. For symmetric Pareto distributions, whenever agency is chosen in equilibrium, consumer and social surplus decrease while listing and transaction prices tend to increase. The predictions of our model are broadly consistent with empirical evidence. [ABSTRACT FROM AUTHOR]

Many copula families, including the classes of Archimedean, elliptical and Liouville copulas, may be written as the survival copula of a random vector R × (Y 1 , Y 2) , where R is a strictly positive random variable independent of the random vector (Y 1 , Y 2). A unified framework is presented for studying the dependence structure underlying this stochastic representation, which is called the background risk model. Formulas for the copula, Kendall's tau and tail dependence coefficients are obtained and special cases are detailed. The usefulness of the construction for model building is illustrated with an extension of Archimedean copulas with completely monotone generators, based on the Farlie–Gumbel–Morgenstern copula. In particular, explicit expressions for the distribution and the Tail-Value-at-Risk of the aggregated risk R Y 1 + R Y 2 are available in a generalization of the widely used multivariate Pareto-II model. [ABSTRACT FROM AUTHOR]

Abstract This paper establishes the possibility of utilizing energy harvesting from mechanical vibrations to estimate extreme value responses of the host structure and demonstrates the calibration of these estimates for excitation spectra typical to natural systems. For illustrative purposes, a cantilever type energy harvester is considered for wind excitation. The extreme value estimates are established through a Generalized Pareto Distribution (GPD). Classically well-known Kaimal and Davenport spectra for wind have been considered in this paper for comparison purposes. The applicability of GPD for processes with short-range dependence is explored in both linear and nonlinear systems. The work also demonstrates how return levels can be mapped using energy harvesting levels and indicates that vibration energy harvesting, in its own right, has the potential to be used for extreme value analysis and estimates. The work has impact on health monitoring and assessment of built infrastructure in various stages of repair or disrepair and exposed to nature throughout their lifetime. [ABSTRACT FROM AUTHOR]

Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized and represented in a number of different ways. Moreover, generalized Pareto distributions enjoy a number of interesting stability properties. An overview of the main features of such distributions is given, expressed compactly in several parametrizations, giving the potential user of these distributions a convenient catalogue of ways to handle and work with generalized Pareto distributions. [ABSTRACT FROM AUTHOR]

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process : a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. [ABSTRACT FROM AUTHOR]

In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak assumptions on their marginal distributions and their copula. The extremal behaviour of the marginal variables is characterised by the generalised Pareto distribution and their extremal dependence through subclasses of the limiting representations of Ledford and Tawn (1997) and Heffernan and Tawn (2004). We find that the upper-tail behaviour of the aggregate is driven by different factors dependent on the signs of the marginal shape parameters; if they are both negative, the extremal behaviour of the aggregate is determined by both marginal shape parameters and the coefficient of asymptotic independence (Ledford and Tawn, 1996); if they are both positive or have different signs, the upper-tail behaviour of the aggregate is given solely by the largest marginal shape. We also derive the aggregate upper-tail behaviour for some well known copulae which reveals further insight into the tail structure when the copula falls outside the conditions for the subclasses of the limiting dependence representations. [ABSTRACT FROM AUTHOR]

• A transformed extreme value distribution method is proposed based on the Box-Cox transformation. • An absolute skewness minimization criterion is proposed to find the optimal Box-Cox transformation parameter. • The uniform design method and random function-spectral representation method are combined to estimate the statistical moments of the transformed extreme value. • The transformed extreme value distribution is covered by the generalized Gaussian distribution. This paper proposes a novel approach for dynamic reliability analysis of uncertain structures subjected to non-stationary stochastic excitations. This approach calculates the first-passage probabilities by evaluating the transformed extreme value distribution (TEVD) instead of the original extreme value distribution (EVD). The Box-Cox transformation is first used to symmetrize the extreme value, and then the generalized Gaussian distribution (GGD) is suggested to approximate the main body and tails of the TEVD. An absolute skewness minimization criterion is proposed to find the optimal Box-Cox transformation parameter. Furthermore, the random-function spectral representation method (RFSRM) and uniform design method (UDM) are successfully combined to estimate the first four central moments of the transformed extreme value with a small sample size. Two numerical examples involving linear and nonlinear shear-frame structures under nonstationary ground motions are investigated. The results indicate that the proposed method can be used for dynamic reliability analysis with high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Abstract: It is well-known that if a random vector is in the generalized domain of attraction of the multivariate normal law (GDAN), then all its components are in the domain of attraction of the normal law (DAN) and, moreover, the Euclidean inner products of with all the nonrandom vectors of unit Euclidean norm are also in DAN. However, these two implications are known to be nonreversible in general. In this paper, a condition is given under which these implications are proved to become reversible, and thus characterizations of GDAN. Large enough classes and an example of random vectors satisfying this condition are provided. Also, the multivariate Student -statistic that is based on independent copies of a random vector satisfying this condition is proved to be asymptotically standard normal only if is in GDAN. A corollary to the thus established result parallels a previous resolution of this problem for a spherically symmetric in the literature. [Copyright &y& Elsevier]

Abstract: Imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains. Although imaging genetics has attracted growing attention and interest, most brain-wide genome-wide association studies focus on voxel-wise single-locus approaches, without taking advantage of the spatial information in images or combining the effect of multiple genetic variants. In this paper we present a fast implementation of voxel- and cluster-wise inferences based on the random field theory to fully use the spatial information in images. The approach is combined with a multi-locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms (SNP) with imaging traits. A fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p-value estimates based on parametric tail approximation. We explored the relation between 448,294 single nucleotide polymorphisms and 18,043 genes in 31,662 voxels of the entire brain across 740 elderly subjects from the Alzheimer''s Disease Neuroimaging Initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. We find method to be more sensitive compared with voxel-wise single-locus approaches. A number of genes were identified as having significant associations with volumetric changes. The most associated gene was GRIN2B, which encodes the N-methyl-d-aspartate (NMDA) glutamate receptor NR2B subunit and affects both the parietal and temporal lobes in human brains. Its role in Alzheimer''s disease has been widely acknowledged and studied, suggesting the validity of the approach. The various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains. [Copyright &y& Elsevier]

Abstract: Let be an almost sure continuous stochastic process ( compact subset of ) in the domain of attraction of some max-stable process, with index function constant over . We study the tail distribution of , which turns out to be of Generalized Pareto type with an extra ‘spatial’ parameter (the areal coefficient from Coles and Tawn (1996) ). Moreover, we discuss how to estimate the tail probability for some high value , based on independent and identically distributed copies of . In the course we also give an estimator for the areal coefficient. We prove consistency of the proposed estimators. Our methods are applied to the total rainfall in the North Holland area; i.e. represents in this case the rainfall over the region for which we have observations, and its integral amounts to total rainfall. The paper has two main purposes: first to formalize and justify the results of Coles and Tawn (1996) ; further we treat the problem in a non-parametric way as opposed to their fully parametric methods. [Copyright &y& Elsevier]

• Proposed a fatigue life assessment method with time-domain extrapolation for dynamic stress based on extreme value theory. • Proposed the determination methods of the optimal parameters for the POT Pareto distribution model based on minimum fitting error. • Indicated that using the fatigue analysis results under short-term load to replace the fatigue analysis results under long-term load will cause the apparent error. • Clarified the relation between extrapolation multiples and relative errors, and proposed the appropriate extrapolation multiple for fatigue life assessment method based on time-domain extrapolation. Structural fatigue reliability assessment is one of the research directions for railway vehicles' mechanical problems. Obtaining the representative stress spectrum is the basis of fatigue life assessment, and its adequacy and integrity will directly affect the accuracy of the assessment results. However, because of the limited conditions, many dynamic stress tests are completed in the short-term, which makes the fatigue evaluation results based on short-term test data challenging to reflect the structure's anti-fatigue status under the long-term service. Therefore, it is necessary to extrapolate the stress spectrum from small samples to large samples while retaining real data probability distribution characteristics. In this paper, a fatigue life assessment method with time-domain extrapolation for dynamic stress based on extreme value theory is proposed for the first time. Take a test point near the weld of the rotary arm positioning seat of a railway vehicle's bogie frame as a case study. Firstly, three time-series signals of dynamic stress of the test point in the initial, middle, and final stages of a whole wheel reprofile period are selected. The pre-processing and equal-weight linear superposition are carried out to them. Secondly, the tail probability distribution of the time-series signal after linear superposition is estimated by applying the POT Pareto distribution model, and its confidence level is 99%. Finally, the dynamic stress spectrum under the long-term service is obtained by several-multiple extrapolation of the superimposed time-series signals with the fitting probability distribution function, and the fatigue life of the test point based on the extrapolated dynamic stress spectrum is assessed. Compared with the commonly-used linear extrapolation method, the cumulative fatigue damage with the time-domain extrapolation method based on extreme value theory increased by 0.168%, and the safe operation mileage decreased by 2670 km. Therefore, indicate that using the fatigue analysis results under short-term load (i.e., linear extrapolation) to replace the fatigue analysis results under long-term load will cause the apparent error, which is indeed worthy of attention. And the fatigue life assessment method based on time-domain extrapolation is safer. Provide the method reference and theoretical support for fatigue life assessment under the long-term service. [ABSTRACT FROM AUTHOR]

Abstract: As cluster-based Web servers are increasingly adopted to host a variety of network-based services, improving the performance of such servers has become critical to satisfy the customers’ demands. Especially, the user response time is an important factor so that clients feel satisfied with the Web services. In this paper, we investigate the feasibility of minimizing the response time of a server by exploiting the advantages of both user-level communication and coscheduling. We, thus, propose a coscheduled server model based on the recently proposed distributed PRESS Web server, where the remote cache accesses can be coscheduled on different nodes to reduce the response time. We experiment this concept using two known coscheduling techniques, called dynamic coscheduling (DCS) and DCS with immediate blocking. We have developed a comprehensive simulation testbed that captures the underlying communication layer in a cluster, the characteristics of various coscheduling algorithms, and the characteristics of the distributed server model to estimate the average delay and throughput with different system configurations. The accuracy of the VIA communication layer and the DCS mechanism is verified using measurements on a 16-node Linux cluster. Extensive simulation of four server models (PRESS over VIA, coscheduled PRESS model with DCS, with DCS and blocking, and Adaptive) using 32-node cluster configurations indicates that the average response time of a distributed server can be minimized significantly by coscheduling the communicating processes. The use of the DCS scheme reduced the average latency up to four times to the PRESS over VIA model that uses only user-level communication. [Copyright &y& Elsevier]

We study random polytopes of the form [ X 1 , ... , X n ] defined as convex hulls of independent and identically distributed random points X 1 , ... , X n in R d with one of the following densities: f d , β (x) = c d , β (1 − ‖ x ‖ 2) β , ‖ x ‖ < 1 , (beta distribution, β > − 1) or f ˜ d , β (x) = c ˜ d , β (1 + ‖ x ‖ 2) − β , x ∈ R d , (beta' distribution, β > d / 2). Here, c d , β and c ˜ d , β are normalizing constants. This setting also includes the uniform distribution on the unit sphere and the standard normal distribution as limiting cases. We derive exact and asymptotic formulae for the expected number of k -faces of [ X 1 , ... , X n ] for arbitrary k ∈ { 0 , 1 , ... , d − 1 }. We prove that for any such k this expected number is strictly monotonically increasing with n. Also, we compute the expected internal and external angles of these polytopes at faces of every dimension and, more generally, the expected conic intrinsic volumes of their tangent cones. By passing to the large n limit in the beta' case, we compute the expected f -vector of the convex hull of Poisson point processes with power-law intensity function. Using convex duality, we derive exact formulae for the expected number of k -faces of the zero cell for a class of isotropic Poisson hyperplane tessellations in R d. This family includes the zero cell of a classical stationary and isotropic Poisson hyperplane tessellation and the typical cell of a stationary Poisson–Voronoi tessellation as special cases. In addition, we prove precise limit theorems for this f -vector in the high-dimensional regime, as d → ∞. Finally, we relate the d -dimensional beta and beta' distributions to the generalized Pareto distributions known in extreme-value theory. [ABSTRACT FROM AUTHOR]

• A general multi-objective optimized wavelet filter (MOWF) is proposed for extracting the repetitive transients. • A simple rule in designing the multi-objective fitness functions for wavelet parameters optimization is given. • The distribution of Pareto solutions is utilized to select the knee point to identify the informative frequency band (IFB). • Experiments verify its superior than the single-objective method in extracting repetitive transients. Optimal wavelet filter is a commonly used and effective tool for bearing fault diagnosis. To locate the informative frequency band for extracting fault-induced repetitive transients, the wavelet parameters are traditionally optimized with a single criterion such as kurtosis, smoothness index, etc. calculated from the narrow-band filtered signal or its envelope. However, in some cases it is difficult for them to fully depict the fault characters and to be robust to different background noises. In this work, a general multi-objective optimized wavelet filter is proposed to adaptively extract the bearing fault features. To take impulsiveness and cyclostationarity into consideration simultaneously, a general rule as maximum sparsity of the squared envelope and squared envelope spectrum is given to design the multi-objective fitness functions. The Pareto solutions which score better under all objectives in the sense of non-domination are utilized to estimate the informative frequency band with the help of differential evolution and a robust knee point selection strategy using kernel density estimation. A simulated and two cases of real wheelset bearing signals are applied to evaluate its performance, some comparisons with peer single-objective and multi-objective methods are also conducted to illustrate its consistency and robustness in extracting the fault-induced repetitive transients under complex interferences. [ABSTRACT FROM AUTHOR]

We consider robust and nonparametric estimation of the coefficient of tail dependence in presence of random covariates. The estimator is obtained by fitting the extended Pareto distribution locally to properly transformed bivariate observations using the minimum density power divergence criterion. We establish convergence in probability and asymptotic normality of the proposed estimator under some regularity conditions. The finite sample performance is evaluated with a small simulation experiment, and the practical applicability of the method is illustrated on a real dataset of air pollution measurements. [ABSTRACT FROM AUTHOR]

This paper reviews generalized Pareto copulas (GPC), which are a key to multivariate extreme value theory. Any generalized Pareto copula can be represented in an easy analytical way using a particular type of norm on R d , called D -norm. The characteristic property of a generalized Pareto copula is its exceedance stability. They might help to end the following debate: What is a multivariate generalized Pareto distribution? We present an easy way to simulate data from an arbitrary generalized Pareto copula and, thus, form an arbitrary generalized Pareto distribution. As an application we derive nonparametric estimates of the probability that a random vector, which follows a generalized Pareto copula, exceeds a high threshold, together with confidence intervals. A case study on joint exceedance probabilities for air pollutants completes the paper. [ABSTRACT FROM AUTHOR]