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In this paper, we consider diffusion-based molecular communication with and without drift between two static nano-machines. We employ type-based information encoding, releasing a single molecule per information bit. At the receiver, we consider an asynchronous detection algorithm which exploits the arrival order of the molecules. In such systems, transposition errors fundamentally undermine reliability and capacity. Thus, in this paper, we study the impact of transpositions on the system performance. Toward this, we present an analytical expression for the exact bit error probability (BEP) caused by transpositions and derive computationally tractable approximations of the BEP for diffusion-based channels with and without drift. Based on these results, we analyze the BEP when background is not negligible and derive the optimal bit interval that minimizes the BEP. Simulation results confirm the theoretical results and show the error and goodput performance for different parameters such as block size or noise generation rate. [ABSTRACT FROM AUTHOR]

The approximations for the Q-function reported in the literature so far have mainly been developed to overcome not only the difficulties, but also the limitations, caused in different research areas, by the nonexistence of the closed form expression for the Q-function. Unlike the previous papers, we propose the novel approximation for the Q-function not for solving some particular problem. Instead, we analyze this problem in one general manner and we provide one general solution, which has wide applicability. Specifically, in this paper, we set two goals, which are somewhat contrary to each other. The one is the simplicity of the analytical form of Q-function approximation and the other is the relatively high accuracy of the approximation for a wide range of arguments. Since we propose a two-parametric approximation for the Q-function, by examining the effect of the parameters choice on the accuracy of the approximation, we manage to determine the most suitable parameters of approximation and to achieve these goals simultaneously. The simplicity of the analytical form of our approximation along with its relatively high accuracy, which is comparable to or even better than that of the previously proposed approximations of similar analytical form complexity, indicates its wide applicability. [ABSTRACT FROM AUTHOR]

In this paper we have calculated escape rate from a meta stable state in the presence of both colored internal thermal and external nonthermal noises. For the internal noise we have considered usual Gaussian distribution but the external noise may be Gaussian or non-Gaussian in characteristic. The calculated rate is valid for low noise strength of non-Gaussian noise such that an effective Gaussian approximation of non-Gaussian noise wherein the higher order even cumulants of order '4' and higher are neglected. The rate expression we derived here reduces to the known results of the literature, as well as for purely external noise driven activated rate process. The latter exhibits how the rate changes if one switches from non-Gaussian to Gaussian character of the external noise. [ABSTRACT FROM AUTHOR]

Inter-discharge interval distribution modeling of the motor unit firing pattern plays an important role in electromyographic decomposition and the statistical analysis of firing patterns. When modeling firing patterns obtained from automatic procedures, false positives and false negatives can be taken into account to enhance performance in estimating firing pattern statistics. Available models of this type, however, are only approximate and use Gaussian distributions, which are not strictly suitable for modeling renewal point processes. In this paper, the theory of point processes is used to derive an exact solution to the distribution when a gamma distribution is used to model the physiological firing pattern. Besides being exact, the solution provides a way to model the skewness of the inter-discharge distribution, and this may make it possible to obtain a better fit with available experimental data. In order to demonstrate potential applications of the model, we use it to obtain a maximum likelihood estimator of firing pattern statistics. Our tests found this estimator to be reliable over a wide range of firing conditions, whether dealing with real or simulated firing patterns, the proposed solution had better agreement than other models. Graphical Abstract Model of the MU firing pattern generation and detection: fT,1(τ), IDI PDF of the physiological firing pattern; fT(τ), IDI PDF after modeling undetected firings (false negatives); fS(τ), IDI PDF after modeling classification errors (false positives). [ABSTRACT FROM AUTHOR]

The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modelling tool for seismic tomography with high-frequency data. FGA has been previously developed and verified as an efficient solver for high-frequency acoustic wave propagation (P wave). The main contribution of this paper consists of three aspects: (1) We derive the FGA formulation for the 3-D elastic wave equation. Rather than standard ray-based methods (e.g. geometric optics and Gaussian beam method), the derivation requires to do asymptotic expansion in the week sense (integral form) so that one is able to perform integration by parts. Compared to the FGA theory for acoustic wave equation, the calculations in the derivation are much more technically involved due to the existence of both P and S waves, and the coupling of the polarized directions for SH and SV waves. In particular, we obtain the diabatic coupling terms for SH and SV waves, with the form closely connecting to the concept of Berry phase that is intensively studied in quantum mechanics and topology (Chern number). The accuracy and parallelizability of the FGA algorithm is illustrated by comparing to the spectral element method for 3-D elastic wave equation in homogeneous media. (2) We derive the interface conditions of FGA for 3-D elastic wave equation based on an Eulerian formulation and the Snell's law. We verify these conditions by simulating high-frequency elastic wave propagation in a 1-D layered Earth model. In this example, we also show that it is natural to apply the FGA algorithm to geometries with non-Cartesian coordinates. (3) We apply the developed FGA algorithm for 3-D seismic wave-equation-based traveltime tomography and full waveform inversion, respectively. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a novel echo signal calculation model for the underwater laser detection of short-range targets. An underwater laser ranging process simulation model is established combined with the echo time identification method. The distance distribution of the underwater target laser range was simulated through time delay and peak detection methods. Simulation results show that the distance dispersion forms an approximately Gaussian distribution. The precision of the system as-assessed by time delay method is higher than the peak detection method. The system ranging accuracy decreases as target distance increases. Seawater simulation results are consistent with experimental underwater short-range goals determined in a target range experiment at sea. The small angle scattering approximation error increases when the target distance is far away — at a certain target distance, the simulation results do slightly deviate from the experimental results. The results presented here may provide a workable reference for the parameter design and ranging error correction of underwater near-range target laser detection systems. [ABSTRACT FROM AUTHOR]

This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic two-point correlation function measurements. Our comparison includes seven approximate methods, which can be divided into three categories: predictive methods that follow the evolution of the linear density field deterministically (ice-cola, peak patch, and pinocchio), methods that require a calibration with N -body simulations (patchy and halogen), and simpler recipes based on assumptions regarding the shape of the probability distribution function (PDF) of density fluctuations (lognormal and Gaussian density fields). We analyse the impact of using covariance estimates obtained from these approximate methods on cosmological analyses of galaxy clustering measurements, using as a reference the covariances inferred from a set of full N -body simulations. We find that all approximate methods can accurately recover the mean parameter values inferred using the N -body covariances. The obtained parameter uncertainties typically agree with the corresponding N -body results within 5 per cent for our lower mass threshold and 10 per cent for our higher mass threshold. Furthermore, we find that the constraints for some methods can differ by up to 20 per cent depending on whether the halo samples used to define the covariance matrices are defined by matching the mass, number density, or clustering amplitude of the parent N -body samples. The results of our configuration-space analysis indicate that most approximate methods provide similar results, with no single method clearly outperforming the others. [ABSTRACT FROM AUTHOR]

Voice conversion (VC) is a technique that aims to transform the individuality of a source speech so as to mimic that of a target speech while keeping the message unaltered. In our previous work, Gaussian process (GP) was introduced into the literature of VC for the first time, for the sake of overcoming the "over-fitting" problem inherent in the state-of-the-art VC methods, which gives very promising results. However, standard GP usually acts as somewhat a smoothing device more than a universal approximator. In this paper, we further attempt to improve the flexibility of GP-based VC by resorting to the expressive kernels that are derived to model the spectral density with Gaussian mixture model (GMM). Our new method benefits from the expressiveness of the new kernel while the inference of GP remains simple and analytic as usual. Experiments demonstrate both objectively and subjectively that the individualities of the converted speech are much more closer to those of the target while speech quality obtained is comparable to the standard GP-based method. [ABSTRACT FROM AUTHOR]

This paper proposes a reflectance distribution model that is able to express complex reflections from materials such as Japanese lacquerware and Maki-e to produce highly realistic computer graphics. Our method improves the Ward model for materials with anisotropic reflection, and uses the approximate coefficients calculated from measured reflectance distribution data to reconstruct the actual reflectance. Our research derives a Gaussian distribution summation method and a modified Fresnel reflectance approximation function from measured reflectance data. Our Fresnel reflectance approximation function adds parameters to Schlick's approximation function to control the whole curve and extinction component, and is thus closer to the actual Fresnel reflectance. Based on these functions, a decision process is developed for the approximation coefficients, and this makes it possible to easily reconstruct the actual reflectance. The reconstructed reflectance distributions obtained using these coefficients are compared with measured reflectance data using the L2 norm of the difference. In addition, reconstructed Fresnel reflection effects are compared with those from actual sample materials. Using these coefficient values, this paper shows a sample of simulated Maki-e images under two different lighting environments. [ABSTRACT FROM AUTHOR]

We present an innovative approach to quickly estimate collateral damage based on the given weapon-target assignment (WTA). That is, having the predetermined WTA, we estimate the collateral damage of friendly or neutral entities based on the lethality of engaging weapons and the geo-locations of all the entities in the theater. Specifically, we calculate the probability of killing/destroying k friendly (or neutral) assets for given k. The main motivation of this paper is twofold. First, quick collateral damage estimation (QCDE) can support commanders in the battlefields with a new quick decision-making capability. Second, our QCDE could support WTA capabilities with collateral damage consideration. Our computational results indicate that the error in estimating collateral damage is significantly less than 1% and that the execution times are of the order of milliseconds for \boldsymbol k(\boldsymbol k\,<\, \mathbf 9) assets. Hence, the natural research challenge related to this paper would be the extension of our quick collateral damage estimation to \boldsymbol \textitk \,\mathbf \ge \, \mathbf 9 that would execute in reasonable time and give a reasonable quality solution. [ABSTRACT FROM PUBLISHER]

High penetration of renewable energy sources and the increasing share of stochastic loads require the explicit representation of uncertainty in tools such as the optimal power flow (OPF). Current approaches follow either a linearized approach or an iterative approximation of nonlinearities. This paper proposes a semidefinite relaxation of a chance-constrained AC-OPF, which is able to provide guarantees for global optimality. Using a piecewise affine policy, we can ensure tractability, accurately model large power deviations, and determine suitable corrective control policies for active power, reactive power, and voltage. We state a tractable formulation for two types of uncertainty sets. Using a scenario-based approach and making no prior assumptions about the probability distribution of the forecast errors, we obtain a robust formulation for a rectangular uncertainty set. Alternatively, assuming a Gaussian distribution of the forecast errors, we propose an analytical reformulation of the chance constraints suitable for semidefinite programming. We demonstrate the performance of our approach on the IEEE 24 and 118 bus system using realistic day-ahead forecast data and obtain tight near-global optimality guarantees. [ABSTRACT FROM PUBLISHER]

Multi-hop relaying is well known to extend the range of wireless communications. However, the end-to-end performance of the multi-hop relaying channel degrades compared to that observed at the first hop. This performance degradation mainly arises due to: 1) half-duplex loss and 2) hopping or relaying loss. In this paper, we analyze the degradation in outage probability and ergodic capacity due to hopping loss in a multiple-input multiple-output (MIMO) dual-hop decode-and-forward relaying network over Rayleigh fading channels. In particular, we characterize analytically the performance degradation by deriving closed-form approximations of ergodic capacity and outage probability in the single-source single-relay single-user, single-source multiple-relay single-user, and single-source single-relay multiple-user topologies. These approximations also provide insights on how to overcome performance degradations due to hopping loss. Moreover, we show that cooperative relaying schemes can recover a significant portion of the hopping loss. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time-delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In literature the references to EM estimation of product mixtures are not very frequent. The simplifying assumption of product components, e.g. diagonal covariance matrices in case of Gaussian mixtures, is usually considered only as a compromise because of some computational constraints or limited dataset. We have found that the product mixtures are rarely used intentionally as a preferable approximating tool. Probably, most practitioners do not 'trust' the product components because of their formal similarity to 'naive Bayes models.' Another reason could be an unrecognized numerical instability of EM algorithm in multidimensional spaces. In this paper we recall that the product mixture model does not imply the assumption of independence of variables. It is even not restrictive if the number of components is large enough. In addition, the product components increase numerical stability of the standard EM algorithm, simplify the EM iterations and have some other important advantages. We discuss and explain the implementation details of EM algorithm and summarize our experience in estimating product mixtures. Finally we illustrate the wide applicability of product mixtures in pattern recognition and in other fields. [ABSTRACT FROM AUTHOR]

In this paper, two very high accurate models to approximate the lower truncated normal cumulative distribution have been developed. Mill's ratio with an order of 1 and 2 is used to develop two models to approximate the density of normal cumulative distribution, and then these two models are modified to approximate the density of the lower truncated normal cumulative distribution. The first model (i.e., order of 1) was very simple and very accurate with maximum absolute error of about 0.0015 over the domain [ZL : ∞]. ZL is the truncation point and it takes any value from negative infinity to zero (i.e., ZL ∊[-∞:0]). The second model (i.e., order of 2) is more advanced and can provide a superior accuracy of a maximum absolute error of less than 0.00004. Particularly, the first model can be used whenever an industrial engineer/practitioner needs to estimate probabilities and statistics associated with the lower truncated normal distribution due to its simplicity and accuracy. Further, we strongly recommend using the first model in the case of manual solutions. Although the second model provides superior accurate results, it is complicated and hard to be used manually. [ABSTRACT FROM AUTHOR]

In an earlier paper Kume & Wood (2005) showed how the normalizing constant of the Fisher–Bingham distribution on a sphere can be approximated with high accuracy using a univariate saddlepoint density approximation. In this sequel, we extend the approach to a more general setting and derive saddlepoint approximations for the normalizing constants of multicomponent Fisher–Bingham distributions on Cartesian products of spheres, and Fisher–Bingham distributions on Stiefel manifolds. In each case, the approximation for the normalizing constant is essentially a multivariate saddlepoint density approximation for the joint distribution of a set of quadratic forms in normal variables. Both first-order and second-order saddlepoint approximations are considered. Computational algorithms, numerical results and theoretical properties of the approximations are presented. In the challenging high-dimensional settings considered in this paper the saddlepoint approximations perform very well in all examples considered. [ABSTRACT FROM AUTHOR]

Online tracking time-varying number of targets is a challenging issue due to measurement noise, target birth or death, and association uncertainty, especially when target number is large. In this paper, we propose an efficient approximation of the Labeled Multi-Bernoulli (LMB) filter to perform online multitarget state estimation and track maintenance efficiently. On the basis of the original LMB filer, we propose a target posterior approximation technique to use a weighted single Gaussian component representing each individual target. Moreover, we present the Gaussian mixture implementation of the proposed efficient approximation of the LMB filter under linear, Gaussian assumptions on the target dynamic model and measurement model. Numerical results verify that our proposed efficient approximation of the LMB filer achieves accurate tracking performance and runs several times faster than the original LMB filer. [ABSTRACT FROM AUTHOR]

This paper presents the Gaussian subordination framework to generate optimal one-sided approximations to multidimensional real-valued functions by functions of prescribed exponential type. Such extremal problems date back to the works of Beurling and Selberg and provide a variety of applications in analysis and analytic number theory. Here we majorize and minorize (on RN) the Gaussian x ↦ e-πλ. . . where λ > 0 is a free parameter, by functions with distributional Fourier transforms supported on Euclidean balls, optimizing weighted L1-errors. By integrating the parameter λ against suitable measures, we solve the analogous problem for a wide class of radial functions. Applications to inequalities and periodic analogues are discussed. The constructions presented here rely on the theory of de Branges spaces of entire functions and on new interpolation tools derived from the theory of Laplace transforms of Laguerre-P'olya where λ > 0 is a free parameter, by functions with distributional Fourier transforms supported on Euclidean balls, optimizing weighted L1-errors. By integrating the parameter λ against suitable measures, we solve the analogous problem for a wide class of radial functions. Applications to inequalities and periodic analogues are discussed. The constructions presented here rely on the theory of de Branges spaces of entire functions and on new interpolation tools derived from the theory of Laplace transforms of Laguerre-P'olya functions.functions. [ABSTRACT FROM AUTHOR]

Asymptotic approximations such as the first- and second-order reliability method (FORM, SORM) are sometimes preferred in reliability analysis due to their efficiency. Bayesian updating for practical engineering problems can produce unnormalized and multimodal distributions, which cannot be directly used in FORM. The Laplace method can approximate such distributions using a weighted multivariate normal distribution. The weighting scheme for different modes must be carefully made in order to achieve accurate results. In this paper, a new weighting scheme and an optimal weighting scheme are proposed to improve the accuracy of Laplace approximation for multimodal distributions. The proposed weighting schemes are compared with existing weighting schemes in detail, and it is shown that the proposed weighting schemes can produce more accurate results in some cases. Based on that, an asymptotic approximation method for reliability estimation and system response predictions involving unnormalized multimodal distributions is proposed. The method integrates the Laplace method, FORM, and inverse FORM to formulate a completely asymptotic analysis cycle. The overall method is applied to two engineering cases: A simplified bridge model and a steam turbine rotor Bayesian analysis with real ultrasonic inspection data. Results are compared with existing simulation-based methods to investigate the efficiency and accuracy of the method. [ABSTRACT FROM PUBLISHER]

We estimate d-dimensional least squares approximations of an arbitrary d-regular measure μ via discrete curvatures of d+2 variables. The main result bounds the least squares error of approximating μ (or its restrictions to balls) with a d-plane by an average of the discrete Menger-type curvature over a restricted set of simplices. Its proof is constructive and even suggests an algorithm for an approximate least squares d-plane. A consequent result bounds a multiscale error term (used for quantifying the approximation of μ with a sufficiently regular surface) by an integral of the discrete Menger-type curvature over all simplices. The preceding paper (part I) provided the opposite inequalities of these two results. This paper also demonstrates the use of a few other discrete curvatures which are different from the Menger-type curvature. Furthermore, it shows that a curvature suggested by Léger (Ann. Math. 149(3), pp. 831–869, ) does not fit within our framework. [ABSTRACT FROM AUTHOR]

Abstract: When missing data are either missing completely at random (MCAR) or missing at random (MAR), the maximum likelihood (ML) estimation procedure preserves many of its properties. However, in any statistical modeling, the distribution specification for the likelihood function is at best only an approximation to the real world. In particular, since the normal-distribution-based ML is typically applied to data with heterogeneous marginal skewness and kurtosis, it is necessary to know whether such a practice still generates consistent parameter estimates. When the manifest variables are linear combinations of independent random components and missing data are MAR, this paper shows that the normal-distribution-based MLE is consistent regardless of the distribution of the sample. Examples also show that the consistency of the MLE is not guaranteed for all nonnormally distributed samples. When the population follows a confirmatory factor model, and data are missing due to the magnitude of the factors, the MLE may not be consistent even when data are normally distributed. When data are missing due to the magnitude of measurement errors/uniqueness, MLEs for many of the covariance parameters related to the missing variables are still consistent. This paper also identifies and discusses the factors that affect the asymptotic biases of the MLE when data are not missing at random. In addition, the paper also shows that, under certain data models and MAR mechanism, the MLE is asymptotically normally distributed and the asymptotic covariance matrix is consistently estimated by the commonly used sandwich-type covariance matrix. The results indicate that certain formulas and/or conclusions in the existing literature may not be entirely correct. [Copyright &y& Elsevier]

Abstract  This paper proposes a non-parametric method for the classification of thin-layer chromatographic (TLC) images from patterns represented in a dissimilarity space. Each pattern corresponds to a mixture of Gaussian approximation of the intensity profile. The methodology comprises various phases, including image processing and analysis steps to extract the chromatographic profiles and a classification phase to discriminate among two groups, one corresponding to normal cases and the other to three pathological classes. We present an extensive study of several dissimilarity-based approaches analysing the influence of the dissimilarity measure and the prototype selection method on the classification performance. The main conclusions of this paper are that, Match and Profile-difference dissimilarity measures present better results, and a new prototype selection methodology achieves a performance similar or even better than conventional methods. Furthermore, we also concluded that simplest classifiers, such as k-NN and linear discriminant classifiers (LDCs), present good performance being the overall classification error less than 10% for the four-class problem. [ABSTRACT FROM AUTHOR]

This paper presents a novel similarity measure in a texture retrieval framework based on statistical modeling in wavelet domain. In this context, we use the recently proposed finite mixture of generalized Gaussian distribution (MoGG) thanks to its ability to model accurately a wide range of wavelet sub-bands histograms. This model has already been relied on the approximation of Kullback–Leibler divergence (KLD) which hinders significantly the retrieval process. To overcome this drawback, we introduce the Cauchy–Schwarz divergence (CSD) between two MoGG distributions as a similarity measure. Hence, an analytic closed-form expression of this measure is developed in the case of fixed shape parameter. Otherwise, when the shape parameter is variable, two approximations are derived using the well-known stochastic integration with Monte-Carlo simulations and numerical integration with Simpson׳s rule. Experiments conducted on a well known dataset show good performance of the CSD in terms of retrieval rates and the computational time improvement compared to the KLD. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish a global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Lévy process and a Gaussian white noise experiment observed up to a time T , with T tending to ∞ . These approximations are given in the sense of the Le Cam distance, under some smoothness conditions on the unknown Lévy density. All the asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other. [ABSTRACT FROM AUTHOR]

This paper presents a new data assimilation approach based on the particle filter (PF) that has potential for nonlinear/non-Gaussian applications in geoscience. Particle filters provide a Monte Carlo approximation of a system's probability density, while making no assumptions regarding the underlying error distribution. The proposed method is similar to the PF in that particles-also referred to as ensemble members-are weighted based on the likelihood of observations in order to approximate posterior probabilities of the system state. The new approach, denoted the local PF, extends the particle weights into vector quantities to reduce the influence of distant observations on the weight calculations via a localization function. While the number of particles required for standard PFs scales exponentially with the dimension of the system, the local PF provides accurate results using relatively few particles. In sensitivity experiments performed with a 40-variable dynamical system, the local PF requires only five particles to prevent filter divergence for both dense and sparse observation networks. Comparisons of the local PF and ensemble Kalman filters (EnKFs) reveal advantages of the new method in situations resembling geophysical data assimilation applications. In particular, the new filter demonstrates substantial benefits over EnKFs when observation networks consist of densely spaced measurements that relate nonlinearly to the model state-analogous to remotely sensed data used frequently in weather analyses. [ABSTRACT FROM AUTHOR]

This paper studies link travel time estimation using entry/exit time stamps of trips on a steady-state transportation network. We propose two inference methods based on the likelihood principle, assuming each link associates with a random travel time. The first method considers independent and Gaussian distributed link travel times, using the additive property that trip time has a closed-form distribution as the summation of link travel times. We particularly analyze the mean estimates when the variances of trip time estimates are known with a high degree of precision and examine the uniqueness of solutions. Two cases are discussed in detail: one with known paths of all trips and the other with unknown paths of some trips. We apply the Gaussian mixture model and the Expectation–Maximization (EM) algorithm to deal with the latter. The second method splits trip time proportionally among links traversed to deal with more general link travel time distributions such as log-normal. This approach builds upon an expected log-likelihood function which naturally leads to an iterative procedure analogous to the EM algorithm for solutions. Simulation tests on a simple nine-link network and on the Sioux Falls network respectively indicate that the two methods both perform well. The second method (i.e., trip splitting approximation) generally runs faster but with larger errors of estimated standard deviations of link travel times. [ABSTRACT FROM AUTHOR]

The principal part of this paper is devoted to the study of the distribution and density functions of the ratio of two normal random variables. It gives several representations of the distribution function in terms of the vivariate normal distribution and Nicholson's V function, both of which have been extensively studied, and for which tables and computational procedures are readily available. One of these representations leads to an easy derivation of the density function in terms of the Cauchy density and the normal density and integral. A number of graphs of the possible shapes of the density are given, together with an indication of when the density is unimodal or bimodal. The last part of the paper discusses the distribution of the ratio (u[sub 1] + ... + u[sub n])/(v[sub I] + ... + v[sub m]) where the u's and v's are independent, uniform variables. The exact distribution for all n and m is given, and some approximations discussed. [ABSTRACT FROM AUTHOR]

Dictionary in Local Coordinate Coding (LCC) is important to approximate a non-linear function with linear ones. Optimizing dictionary from predefined coding schemes is a challenge task. This paper focuses on learning dictionary from two Locality Coding Adaptors (LCAs), i.e., locality Gaussian Adaptor (GA) and locality Euclidean Adaptor (EA), for large-scale and high-dimension datasets. Online dictionary learning is formulated as two cycling steps, local coding and dictionary updating. Both stages scale up gracefully to large-scale datasets with millions of data. The experiments on different applications demonstrate that our method leads to a faster dictionary learning than the classical ones or the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

SUMMARY Several approaches have been proposed for evaluating the capacity value of intermittent generation. In this paper, we assume that the uncertainty included in demand, existing generation, and intermittent generation, can be treated by means of a normal distribution model. Using a newly developed approximation method similar to the Garver approximation, and the Z-stochastic approach, the effective load carrying capability method is comprehensively surveyed. The percentile method adopted in the higher demand level is also discussed in connection with the probabilistic properties of intermittent generation. Numerical examples and a simulation illustrating the probabilistic approach are included. [ABSTRACT FROM AUTHOR]

Subclass discriminant analysis (SDA) is a recently developed dimensionality reduction technique which takes into consideration the intrinsic structure information lurking in data by approximating unknown distribution of each class with multiple Gaussian distributions, namely, subclasses. However, in SDA, the separability between heterogeneous subclasses, i.e. those from different classes, is measured by the between-subclass scatter calculated as average distance between the means of these subclasses. In this paper, in the view of maximum margin principle, we propose a novel feature extraction method coined structural max-margin discriminant analysis (SMDA), in order to enhance the performance of SDA. Specifically, SMDA targets at finding an orthogonal linear embedded subspace in which the margin, defined as the minimum pairwise between-subclasses distance, is maximized and simultaneously the within-subclasses scatter is minimized. The concrete formulation of the resulting model boils down to a nonconvex optimization problem that can be solved by combining the constrained concave–convex procedure with the column generation technique. We evaluate the proposed SMDA on several benchmark datasets and the experimental results confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper attempts to develop a repetitive group sampling (RGS) plan by variables inspection for controlling the process fraction defective or the number of nonconformities when the quality characteristic follows a normal distribution and has only the lower or upper specification limit. The proposed sampling plan is derived by the exact sampling distribution rather than the approximation approach. The plan parameters are solved by a nonlinear optimization model which minimizes the average sample number required for inspection and fulfills the classical two-point conditions on the operating characteristic (OC) curve. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. The results indicate that the proposed variables RGS plan could significantly reduce samples required for inspection compared to the traditional variables single sampling plan. [ABSTRACT FROM AUTHOR]

In this paper, we present a Bayesian-based super-resolution algorithm that uses approximations of symmetric alpha-stable ( \(S\alpha S\) ) Markov random fields as prior. The approximated \(S\alpha S\) prior is used to perform maximum a posteriori (MAP) estimation for the high-resolution (HR) image reconstruction process. Compared with other state-of-the-art prior models, the proposed prior can better capture the heavy tails of the distribution of the HR image. Thus, the edges of the reconstructed HR image are preserved better in our method. As the corresponding energy function is nonconvex, the graduated nonconvexity method is used to solve the MAP estimation. Experiments confirm the better fit achieved by the proposed model to the actual data distribution and the consequent improvement in terms of visual quality over previously proposed super-resolution algorithms. [ABSTRACT FROM PUBLISHER]

This paper derives a saddlepoint based approximation for the cumulative distribution function of the Bartlett-Box M-statistic that tests the equality of covariance matrices for several samples from graphical Gaussian models Markov with respect to a decomposable graph [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the distribution of the product of a Wishart random matrix and a Gaussian random vector. We derive a stochastic representation for the elements of the product. Using this result, the exact joint density for an arbitrary linear combination of the elements of the product is obtained. Furthermore, the derived stochastic representation allows us to simulate samples of arbitrary size by generating independently distributed chi-squared random variables and standard multivariate normal random vectors for each element of the sample. Additionally to the Monte Carlo approach, we suggest another approximation of the density function, which is based on the Gaussian integral and the third order Taylor expansion. We investigate, with a numerical study, the properties of the suggested approximations. A good performance is documented for both methods. [Copyright &y& Elsevier]

Abstract: In existing soft decode-and-forward (SDF) cooperative communication systems, the source node is idling in the second time phase while the relay transmits the soft information. In fact, the source can transmit the hard information that cooperates with the relay's soft information using distributed space-time block codes (DSTBC). In this paper, we theoretically derive the detection performance in the second time phase by either using or not using the DSTBC based on the assumption that the soft information can be approximated by Gaussian distribution. This result also enables the optimal power allocation between the source and the relay in the second time phase. Finally, we show via simulation that the advantage of using DSTBC in the second time phase leads to the overall performance improvement of the coded cooperative system. [Copyright &y& Elsevier]

We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one step further and we show that the fluctuations around the Hartree evolution satisfy a central limit theorem. Interestingly, the variance of the limiting Gaussian distribution is determined by a time-dependent Bogoliubov transformation describing the dynamics of initial coherent states in a Fock space representation of the system. [ABSTRACT FROM AUTHOR]

In this work, we discuss the approximation of elliptic problems with log-normal random coefficients using the Wick product and the Mikulevicius-Rozovskii formula. The main idea is that the multiplication between the log-normal coefficient and the gradient of the solution can be regarded as a Taylor-like expansion in terms of the Wick product and the Malliavin derivative. For the classical model, the coefficients of Wiener chaos expansion are fully coupled together in the uncertainty propagator, while the Wick-Malliavin model yields an uncertain propagator with weak coupling in the upper-triangular part for a relatively small truncation order in the Mikulevicius-Rozovskii formula. In this paper we focus on the difference between the classical model and the Wick-Malliavin model with respect to the standard deviation of the underlying Gaussian random process. Both theoretical and numerical discussions are presented. [ABSTRACT FROM AUTHOR]

Abstract: Nowadays most of the current kernel learning approaches are showing good results in small datasets and fail to scale to large ones. As such, it is necessary to develop faster kernel optimization algorithms that perform better with larger datasets, especially, for the “Big Data” applications. This paper presents a novel fast method to optimize the Gaussian kernel function for two-class pattern classification tasks, where it is desirable for the kernel machines to use an optimized kernel that adapts well to the input data and the learning tasks. We propose to optimize the Gaussian kernel function by using the formulated kernel target alignment criterion. By adopting the Euler–Maclaurin formula and the local and global extremal properties of the approximate kernel separability criterion, the approximate criterion function can be proved to have a determined global minimum point. Thus, when the approximate criterion function is a sufficient approximation of the criterion function, through using a Newton-based algorithm, the proposed optimization is simply solved without being repeated the searching procedure with different starting points to locate the best local minimum. The proposed method is evaluated on thirteen data sets with three Gaussian-kernel-based learning algorithms. The experimental results show that the criterion function has the determined global minimum point for the all thirteen data sets, the proposed method achieves the best high time efficiency performance and the best overall classification performance. [Copyright &y& Elsevier]

Abstract: Oscillating gradients provide an optimal probe of small pore sizes in diffusion MRI. While sinusoidal oscillations have been popular for some time, recent work suggests additional benefits of square or trapezoidal oscillating waveforms. This paper presents analytical expressions of the free and restricted diffusion signal for trapezoidal and square oscillating gradient spin echo (OGSE) sequences using the Gaussian phase distribution (GPD) approximation and generalises existing similar expressions for sinusoidal OGSE. Accurate analytical models are necessary for exploitation of these pulse sequences in imaging studies, as they allow model fitting and parameter estimation in reasonable computation times. We evaluate the accuracy of the approximation against synthesised data from the Monte Carlo (MC) diffusion simulator in Camino and Callaghan’s matrix method and we show that the accuracy of the approximation is within a few percent of the signal, while providing several orders of magnitude faster computation. Moreover, since the expressions for trapezoidal wave are complex, we test sine and square wave approximations to the trapezoidal OGSE signal. The best approximations depend on the gradient amplitude and the oscillation frequency and are accurate to within a few percent. Finally, we explore broader applications of trapezoidal OGSE, in particular for non-model based applications, such as apparent diffusion coefficient estimation, where only sinusoidal waveforms have been considered previously. We show that with the right apodisation, trapezoidal waves also have benefits by virtue of the higher diffusion weighting they provide compared to sinusoidal gradients. [Copyright &y& Elsevier]

Inventory control systems used in practice are quite often modeling the lead-time demand by a normal distribution. This may result in considerable errors when the real demand is low and discrete. For such demand, it is usually better to use a discrete demand distribution. However, this will increase the computational effort. A natural question is under what circumstances a normal approximation is feasible. This paper analyzes this question in a numerical study. Our study indicates that a normal approximation works reasonably well when the average lead-time demand is something like 10 or higher and the coefficient of variation is bounded by something like 2. The normal approximation works better for a high backorder cost or, equivalently, a high service level. [ABSTRACT FROM AUTHOR]

In many communication channels the impulsive noise is usually assumed to be of a symmetric alpha stable (S αS) distribution. Unfortunately, except for the Gaussian, Cauchy, and Lévy laws, the analytical expressions for the probability density functions (PDF) of alpha stable distributions are unknown, resulting in very limited application of this distribution. In a practical system, the bi-parameter Cauchy-Gaussian mixture (BCGM) distribution is used to approximate the PDF of the S αS distribution to tackle this difficulty. In this paper, we derive the optimal mixture ratio of the BCGM model based on the minimum square error criterion and furthermore propose a simplified and robust version of BCGM for the S αS distribution. Numerical simulations show that our proposed model achieves better performance and is more robust than the conventional models, without incurring additional complexity. [ABSTRACT FROM AUTHOR]

Abstract: The notions of invariant sets and ultimate bounds are important concepts in the analysis of dynamical systems and very useful tools for the design of control systems. Several approaches have been reported for the characterisation of these sets, including constructive methods for their computation and procedures to obtain different approximations. However, there are shortcomings in those concepts, in the sense that no general probability distributions can be considered for the disturbances affecting the system (which, for example, precludes the assumption of Gaussian distributions insofar as they are not bounded). Motivated by those shortcomings, we propose in this paper the novel concepts of probabilistic ultimate bounds and probabilistic invariant sets, which extend the notions of invariant sets and ultimate bounds to consider ‘containment in probability’, and have the important feature of allowing stochastic noises with more general distributions, including the ubiquitous Gaussian distribution, to be considered. We introduce some key definitions for these sets, establish their main properties and develop methods for their computation. A numerical example illustrates the main ideas. [Copyright &y& Elsevier]

Abstract: In this paper the limits of elliptical copulas under univariate conditioning are characterized, allowing for the conditioning random variable to have a rapidly varying tail. Further, we investigate the quality of approximation by imposing some weak asymptotic restrictions. [Copyright &y& Elsevier]