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In practical radar systems, changes in the target aspect toward the radar will result in glint noise disturbances in the measurement data. The glint noise has heavy-tailed characteristics and cannot be perfectly modeled by the Gaussian distribution widely used in conventional tracking algorithms. In this article, we investigate the challenging problem of tracking a time-varying number of maneuvering targets in the context of glint noise with unknown statistics. By assuming a set of models for the possible motion modes of each single-target hypothesis and leveraging the multivariate Laplace distribution to model measurement noise, we propose a robust interacting multi-model multi-Bernoulli mixture filter based on the variational Bayesian method. Within this filter, the unknown noise statistics are adaptively learned while filtering and the predictive likelihood is approximately calculated by means of the variational lower bound. The effectiveness and superiority of our proposed filter is verified via computer simulations. [ABSTRACT FROM AUTHOR]

Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for FMLR models via an exponential power error distribution, which includes normal distributions and Laplace distributions as special cases. Under some regularity conditions, the consistency of order selection and the consistency of variable selection are established, and the asymptotic normality for the estimators of non-zero parameters is investigated. In addition, an efficient modified expectation-maximization (EM) algorithm and a majorization-maximization (MM) algorithm are proposed to implement the proposed optimization problem. Furthermore, we use the numerical simulations to demonstrate the finite sample performance of the proposed methodology. Finally, we apply the proposed approach to analyze a baseball salary data set. Results indicate that our proposed method obtains a smaller BIC value than the existing method. [ABSTRACT FROM AUTHOR]

Radiofrequency (RF) ablation represents an efficient strategy to reduce the volume of thyroid nodules. In this study, a finite element model was developed with the aim of optimizing RF parameters, e.g., input power and treatment duration, in order to achieve the target volume reduction rate (VRR) for a thyroid nodule. RF ablation is modelled as a coupled electro-thermal problem wherein the electric field is applied to induce tissue heating. The electric problem is solved with the Laplace equation, the temperature distribution is estimated with the Pennes bioheat equation, and the thermal damage is evaluated using the Arrhenius equation. The optimization model is applied to RF electrode with different active tip lengths in the interval from 5 mm to 40 mm at the 5 mm step. For each case, we also explored the influence of tumour blood perfusion rate on RF ablation outcomes. The model highlights that longer active tips are more efficient as they require lesser power and shorter treatment time to reach the target VRR. Moreover, this condition is characterized by a reduced transversal ablation zone. In addition, a higher blood perfusion increases the heat dispersion, requiring a different combination of RF power and time treatment to achieve the target VRR. The model may contribute to an improvement in patient-specific RF ablation treatment. [ABSTRACT FROM AUTHOR]

False data injection attack (FDIA) is a deliberate modification of measurement data collected by the power grid using vulnerabilities in power grid state estimation, resulting in erroneous judgments made by the power grid control center. As a symmetrical defense scheme, FDIA detection usually uses machine learning methods to detect attack samples. However, existing detection models for FDIA typically require large-scale training samples, which are difficult to obtain in practical scenarios, making it difficult for detection models to achieve effective detection performance. In light of this, this paper proposes a novel FDIA sample generation method to construct large-scale attack samples by introducing a hybrid Laplacian model capable of accurately fitting the distribution of data changes. First, we analyze the large-scale power system sensing measurement data and establish the data distribution model of symmetric Laplace distribution. Furthermore, a hybrid Laplace-domain symmetric distribution model with multi-dimensional component parameters is constructed, which can induce a deliberate deviation in the state estimation from its safe value by injecting into the power system measurement. Due to the influence of the multivariate parameters of the hybrid Laplace-domain distribution model, the sample deviation generated by this model can not only obtain an efficient attack effect, but also effectively avoid the recognition of the FDIA detection model. Extensive experiments are carried out over IEEE 14-bus and IEEE 118-bus test systems. The corresponding results unequivocally demonstrate that our proposed attack method can quickly construct large-scale FDIA attack samples and exhibit significantly higher resistance to detection by state-of-the-art detection models, while also offering superior concealment capabilities compared to traditional FDIA approaches. [ABSTRACT FROM AUTHOR]

This paper considers a retrial G-queue with collisions, transmission errors, and a finite number of sources, where service and repair time are both general distributions. The number of sources (terminals) is finite and a source cannot generate new requests until the channel (server) finishes its work, i.e., the rate at which new primary requests are generated varies inversely with the number of data frame (customer) in the system. A collision occurs when service requests arrive at a busy channel, and transmission errors prevent data frames from leaving the system after completing service. Two types of arrivals are considered. Negative customers will break down the system in the busy state and remove the customer under service. The application of our model is indicated, with a particular emphasis on communication networks such as the local-area networks (LAN) with CSMA/CD protocol. Recursive formulas have been derived to calculate the stationary joint distributions and the Laplace transform of reliability function by applying the discrete transformations method along with the supplementary variables technique (SVT). Furthermore, the comparative performance and reliability analysis have been conducted numerically. Numerical examples are provided to investigate the sensitivity of different parameters on performance measures and reliability indicators. [ABSTRACT FROM AUTHOR]

Traditional convolutional neural networks (CNNs) lack equivariance for transformations such as rotation and scaling. Consequently, they typically exhibit weak robustness when an input image undergoes generic transformations. Moreover, the complex model structure complicates the interpretation of learned low- and mid-level features. To address these issues, we introduce a Lie group equivariant convolutional neural network predicated on the Laplace distribution. This model's Lie group characteristics blend multiple mid- and low-level features in image representation, unveiling the Lie group geometry and spatial structure of the Laplace distribution function space. It efficiently computes and resists noise while capturing pertinent information between image regions and features. Additionally, it refines and formulates an equivariant convolutional network appropriate for the Lie group feature map, maximizing the utilization of the equivariant feature at each level and boosting data efficiency. Experimental validation of our methodology using three remote sensing datasets confirms its feasibility and superiority. By ensuring a high accuracy rate, it enhances data utility and interpretability, proving to be an innovative and effective approach. [ABSTRACT FROM AUTHOR]

Analytic and asymptotic properties of the generalized Student and generalized Lomax distributions are discussed, with the main focus on the representation of these distributions as scale mixtures of the laws that appear as limit distributions in classical limit theorems of probability theory, such as the normal, folded normal, exponential, Weibull, and Fréchet distributions. These representations result in the possibility of proving some limit theorems for statistics constructed from samples with random sizes in which the generalized Student and generalized Lomax distributions are limit laws. An overview of known properties of the generalized Student distribution is given, and some simple bounds for its tail probabilities are presented. An analog of the 'multiplication theorem' is proved, and the identifiability of scale mixtures of generalized Student distributions is considered. The normal scale mixture representation for the generalized Student distribution is discussed, and the properties of the mixing distribution in this representation are studied. Some simple general inequalities are proved that relate the tails of the scale mixture with that of the mixing distribution. It is proved that for some values of the parameters, the generalized Student distribution is infinitely divisible and admits a representation as a scale mixture of Laplace distributions. Necessary and sufficient conditions are presented that provide the convergence of the distributions of sums of a random number of independent random variables with finite variances and other statistics constructed from samples with random sizes to the generalized Student distribution. As an example, the convergence of the distributions of sample quantiles in samples with random sizes is considered. The generalized Lomax distribution is defined as the distribution of the absolute value of the random variable with the generalized Student distribution. It is shown that the generalized Lomax distribution can be represented as a scale mixture of folded normal distributions. The convergence of the distributions of maximum and minimum random sums to the generalized Lomax distribution is considered. It is demonstrated that the generalized Lomax distribution can be represented as a scale mixture of Weibull distributions or that of Fréchet distributions. As a consequence, it is demonstrated that the generalized Lomax distribution can be limiting for extreme statistics in samples with random size. The convergence of the distributions of mixed geometric random sums to the generalized Lomax distribution is considered, and the corresponding extension of the famous Rényi theorem is proved. The law of large numbers for mixed Poisson random sums is presented, in which the limit random variable has a generalized Lomax distribution. [ABSTRACT FROM AUTHOR]

This manuscript deals with a novel, nonlinear, and non-stationary stochastic model with symmetric, Laplacian distributed innovations. The obtained model, named Laplacian Split-BREAK (LSB) process, is intended for dynamic analysis of time series with pronounced and permanent fluctuations. By using the method of characteristic functions (CFs), the basic stochastic properties of the LSB process are proven, with a special emphasis on its asymptotic behaviour. The different procedures for estimating its parameters are also given, along with numerical simulations of the obtained estimators. Finally, it has been shown that the LSB process, as an adequate stochastic model, can be applied in the analysis of dynamics in the world market of crude oil and natural gas. [ABSTRACT FROM AUTHOR]

This article completes our studies on the formal construction of asymptotic approximations for statistics based on a random number of observations. Second order Chebyshev–Edgeworth expansions of asymptotically normally or chi-squared distributed statistics from samples with negative binomial or Pareto-like distributed random sample sizes are obtained. The results can have applications for a wide spectrum of asymptotically normally or chi-square distributed statistics. Random, non-random, and mixed scaling factors for each of the studied statistics produce three different limit distributions. In addition to the expected normal or chi-squared distributions, Student's t-, Laplace, Fisher, gamma, and weighted sums of generalized gamma distributions also occur. [ABSTRACT FROM AUTHOR]

Deep image prior (DIP) is a powerful technique for image restoration that leverages an untrained network as a handcrafted prior. DIP can also be used for hyperspectral image (HSI) denoising tasks and has achieved impressive performance. Recent works further incorporate different regularization terms to enhance the performance of DIP and successfully show notable improvements. However, most DIP-based methods for HSI denoising rarely consider the distribution of complicated HSI mixed noise. In this paper, we propose the asymmetric Laplace noise modeling deep image prior (ALDIP) for HSI mixed noise removal. Based on the observation that real-world HSI noise exhibits heavy-tailed and asymmetric properties, we model the HSI noise of each band using an asymmetric Laplace distribution. Furthermore, in order to fully exploit the spatial–spectral correlation, we propose ALDIP-SSTV, which combines ALDIP with a spatial–spectral total variation (SSTV) term to preserve more spatial–spectral information. Experiments on both synthetic data and real-world data demonstrate that ALDIP and ALDIP-SSTV outperform state-of-the-art HSI denoising methods. [ABSTRACT FROM AUTHOR]

A multi-sensor medical-image fusion technique, which integrates useful information from different single-modal images of the same tissue and provides a fused image that is more comprehensive and objective than a single-source image, is becoming an increasingly important technique in clinical diagnosis and treatment planning. The salient information in medical images often visually describes the tissue. To effectively embed salient information in the fused image, a multi-sensor medical image fusion method is proposed based on an embedding bilateral filter in least squares and salient detection via a deformed smoothness constraint. First, source images are decomposed into base and detail layers using a bilateral filter in least squares. Then, the detail layers are treated as superpositions of salient regions and background information; a fusion rule for this layer based on the deformed smoothness constraint and guided filtering was designed to successfully conserve the salient structure and detail information of the source images. A base-layer fusion rule based on modified Laplace energy and local energy is proposed to preserve the energy information of these source images. The experimental results demonstrate that the proposed method outperformed nine state-of-the-art methods in both subjective and objective quality assessments on the Harvard Medical School dataset. [ABSTRACT FROM AUTHOR]

In this paper, a Bayesian variable selection method for spatial autoregressive (SAR) quantile models is proposed on the basis of spike and slab prior for regression parameters. The SAR quantile models, which are more generalized than SAR models and quantile regression models, are specified by adopting the asymmetric Laplace distribution for the error term in the classical SAR models. The proposed approach could perform simultaneously robust parametric estimation and variable selection in the context of SAR quantile models. Bayesian statistical inferences are implemented by a detailed Markov chain Monte Carlo (MCMC) procedure that combines Gibbs samplers with a probability integral transformation (PIT) algorithm. In the end, empirical numerical examples including several simulation studies and a Boston housing price data analysis are employed to demonstrate the newly developed methodologies. [ABSTRACT FROM AUTHOR]

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. This paper proposes a mixture autoregressive model via an asymmetric exponential power distribution, which includes normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. Therefore, the proposed method can be seen as a generalization of some existing model, which can adapt to unknown error structures to improve prediction accuracy, even in the case of fat tail and asymmetry. In addition, an expectation-maximization algorithm is applied to implement the proposed optimization problem. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze the daily return series of the Hong Kong Hang Seng Index. The results indicate that the proposed method is more robust and adaptive to the error distributions than other existing methods. [ABSTRACT FROM AUTHOR]

The usual mean change-point detecting method based on normal linear regression is not robust to heavy-tailed data with potential outlying points. We propose a robust change-point estimation procedure based on a quantile regression model with asymmetric Laplace error distribution and develop a non-iterative sampling algorithm from a Bayesian perspective. The algorithm can generate independently and identically distributed samples approximately from the posterior distribution of the position of the change-point, which can be used for statistical inferences straightforwardly. The procedure combines the robustness of quantile regression and the computational efficiency of the non-iterative sampling algorithm. A simulation study is conducted to illustrate the performance of the procedure with satisfying findings, and finally, real data is analyzed to show the usefulness of the algorithm by comparison with the usual change-point detection method based on normal regression. [ABSTRACT FROM AUTHOR]

We consider the limit of the empirical spectral distribution of Laplace matrices of generalized random graphs. Applying the Stieltjes transform method, we prove under general conditions that the limit spectral distribution of Laplace matrices converges to the free convolution of the semicircular law and the normal law. [ABSTRACT FROM AUTHOR]

In this paper, we derive the Cramér–Rao lower bounds (CRLB) for direction of arrival (DoA) estimation by using sparse Bayesian learning (SBL) and the Laplace prior. CRLB is a lower bound on the variance of the estimator, the change of CRLB can indicate the effect of the specific factor to the DoA estimator, and in this paper a Laplace prior and the three-stage framework are used for the DoA estimation. We derive the CRLBs under different scenarios: (i) if the unknown parameters consist of deterministic and random variables, a hybrid CRLB is derived; (ii) if all the unknown parameters are random, a Bayesian CRLB is derived, and the marginalized Bayesian CRLB is obtained by marginalizing out the nuisance parameter. We also derive the CRLBs of the hyperparameters involved in the three-stage model and explore the effect of multiple snapshots to the CRLBs. We compare the derived CRLBs of SBL, finding that the marginalized Bayesian CRLB is tighter than other CRLBs when SNR is low and the differences between CRLBs become smaller when SNR is high. We also study the relationship between the mean squared error of the source magnitudes and the CRLBs, including numerical simulation results with a variety of antenna configurations such as different numbers of receivers and different noise conditions. [ABSTRACT FROM AUTHOR]

This paper presents a robust method for dealing with switching regression problems. Regression models with switch-points are broadly employed in diverse areas. Many traditional methods for switching regressions can falter in the presence of outliers or heavy-tailed distributions because of the modeling assumptions of Gaussian errors. The outlier corruption of datasets is often unavoidable. When misapplied, the Gaussian assumption can lead to incorrect inference making. The Laplace distribution is known as a longer-tailed alternative to the normal distributions and connected with the robust least absolute deviation regression criterion. We propose a robust switching regression model of Laplace distributed errors. To advance robustness, we extend the Laplace switching model to a fuzzy class model and create a robust algorithm named FCL through the fuzzy classification maximum likelihood procedure. The robustness properties and the advance of resistance against high-leverage outliers are discussed. Simulations and sensitivity analyses illustrate the effectiveness and superiority of the proposed algorithm. The experimental results indicate that FCL is much more robust than the EM-based algorithm. Furthermore, the Laplace-based algorithm is more time-saving than the t-based procedure. Diverse real-world applications demonstrate the practicality of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the maximum likelihood estimator for the parameter of first-order autoregressive models driven by the stationary Gaussian noises (Colored noise) together with an input. First, we will find the optimal input that maximizes the Fisher information, and then, with the method of the Laplace transform, both the asymptotic properties and the asymptotic design problem of the maximum likelihood estimator will be investigated. The results of the numerical simulation confirm the theoretical analysis and show that the proposed maximum likelihood estimator performs well in finite samples. [ABSTRACT FROM AUTHOR]

In this work, a new family of distributions based on the Laplace distribution is introduced. We define this new family by its stochastic representation as the sum of two independent random variables, one with a Laplace distribution and the other with an exponential distribution. Using a Monte Carlo simulation study, the statistical performance of the estimators obtained by the moments and maximum likelihood methods were empirically evaluated. We studied the coverage probabilities and mean length of the confidence intervals of the corresponding parameters based on the asymptotic normality of these estimators. This simulation study reported a good statistical performance of these estimators. Fits were made to three real data sets with the new distribution, two related to chemical concentrations and one to the environment, comparing it with three similar distributions given in the literature. We have used information criteria for the selection of models. These results showed that the exponentially modified Laplace model can be an alternative distribution to model skewed data with high kurtosis. The new approach is a contribution to the tools of statisticians and various professionals interested in modeling data with high kurtosis. [ABSTRACT FROM AUTHOR]

In this paper, the lognormal distribution is studied, and a new series representation is proposed. This series uses the powers of the bilinear function. From it, a simplified form is obtained and used to compute the Laplace transform of the distribution. [ABSTRACT FROM AUTHOR]

The ninth article, "Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications" by Mohammed et al. [[9]], seeks to investigate classical and Bayesian estimations of the Dagum distribution based on the adaptive progressive type II hybrid censoring scheme. In their article entitled "Robust Procedure for Change-Point Estimation Using Quantile Regression Model with Asymmetric Laplace Distribution", Yang [[10]] creates a non-iterative sampling process from a Bayesian perspective and offers a robust change-point estimation method based on a quantile regression model with an asymmetric Laplace error distribution. The second article, "Bayesian Reference Analysis for the Generalized Normal Linear Regression Model", by Tomazella et al. [[2]] suggests using the Bayesian reference analysis to estimate the generalized normal linear regression model's parameters. [Extracted from the article]

Space-time adaptive processing (STAP) is a well-known technique for slow-moving target detection in the clutter spreading environment. For an airborne conformal array radar, conventional STAP methods are unable to provide good performance in suppressing clutter because of the geometry-induced range-dependent clutter, non-uniform spatial steering vector, and polarization sensitivity. In this paper, a knowledge aided STAP method based on sparse learning via iterative minimization (SLIM) combined with Laplace distribution is proposed to improve the STAP performance for a conformal array. The proposed method can avoid selecting the user parameter. the proposed method constructs a dictionary matrix that is composed of the space-time steering vector by using the prior knowledge of the range cell under test (CUT) distributed in clutter ridge. Then, the estimated sparse parameters and noise power can be used to calculate a relatively accurate clutter plus noise covariance matrix (CNCM). This method could achieve superior performance of clutter suppression for a conformal array. Simulation results demonstrate the effectiveness of this method. [ABSTRACT FROM AUTHOR]

With the exponential growth in the amount of available data, traditional meteorological data processing algorithms have become overwhelmed. The application of artificial intelligence in simultaneous prediction of multi-parameter meteorological data has attracted much attention. However, existing single-task network models are generally limited by the data correlation dependence problem. In this paper, we use a priori knowledge for network design and propose a multitask model based on an asymmetric sharing mechanism, which effectively solves the correlation dependence problem in multi-parameter meteorological data prediction and achieves simultaneous prediction of multiple meteorological parameters with complex correlations for the first time. The performance of the multitask model depends largely on the relative weights among the task losses, and manually adjusting these weights is a difficult and expensive process, which makes it difficult for multitask learning to achieve the expected results in practice. In this paper, we propose an improved multitask loss processing method based on the assumptions of homoscedasticity uncertainty and the Laplace loss distribution and validate it using the German Jena dataset. The results show that the method can automatically balance the losses of each subtask and has better performance and robustness. [ABSTRACT FROM AUTHOR]

This paper deals with spatial data that can be modelled by partially linear varying coefficient spatial autoregressive models with Bayesian P-splines quantile regression. We evaluate the linear and nonlinear effects of covariates on the response and use quantile regression to present comprehensive information at different quantiles. We not only propose an empirical Bayesian approach of quantile regression using the asymmetric Laplace error distribution and employ P-splines to approximate nonparametric components but also develop an efficient Markov chain Monte Carlo technique to explore the joint posterior distributions of unknown parameters. Monte Carlo simulations show that our estimators not only have robustness for different spatial weight matrices but also perform better compared with quantile regression and instrumental variable quantile regression estimators in finite samples at different quantiles. Finally, a set of Sydney real estate data applications is analysed to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In the field of financial risk measurement, Asymmetric Laplace (AL) laws are used. The assumption of normalcy is used in traditional approaches for calculating financial risk. Asymmetric Laplace distribution, on the other hand, reveals the properties of empirical financial data sets much better than the normal model by leptokurtosis and skewness. According to recent financial data research, the regularity assumption is frequently broken. As a result, Asymmetric Laplace laws offer a simple, creative, and useful option to normal distributions when it comes to modeling financial data. We here engage AL distribution to explore specific formulas for the two commonly used risk measures, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). The currency exchange rates data are used to and worked out to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

We analyse the time evolution of the empirical cross-sectional distribution of firms' profit and growth rates. In particular, we analyse the conditional properties of the empirical distributions depending on the size of the firms and the business cycle phase. In order to do so, we employ the Laplace distribution as a benchmark, further considering the Subbotin and Asymmetric Exponential Power (AEP hereafter) distributions, to capture the potential asymmetry and leptokurtosis of the empirical distribution. Our results show that the profit rates of large firms are characterised by an asymmetric Laplace distribution with parameters largely independent of the business cycle phase. Small firms, instead, are characterised by the AEP distribution, which accounts for the conditional dependence of distribution on the phase of the business cycle. We observe that the largest firms are more robust to downturns compared to the small firms, given their invariant distributional characteristics during crisis periods. [ABSTRACT FROM AUTHOR]

Deconvolution provides an efficient technology to implement angular super-resolution for scanning radar forward-looking imaging. However, deconvolution is an ill-posed problem, of which the solution is not only sensitive to noise, but also would be easily deteriorate by the noise amplification when excessive iterations are conducted. In this paper, a penalized maximum likelihood angular super-resolution method is proposed to tackle these problems. Firstly, a new likelihood function is deduced by separately considering the noise in I and Q channels to enhance the accuracy of the noise modeling for radar imaging system. Afterwards, to conquer the noise amplification and maintain the resolving ability of the proposed method, a joint square-Laplace penalty is particularly formulated by making use of the outlier sensitivity property of square constraint as well as the sparse expression ability of Laplace distribution. Finally, in order to facilitate the engineering application of the proposed method, an accelerated iterative solution strategy is adopted to solve the obtained convex optimal problem. Experiments based on both synthetic data and real data demonstrate the effectiveness and superior performance of the proposed method. [ABSTRACT FROM AUTHOR]

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters that fit the shape of peakedness in bimodality on the real line. The special values of peakedness parameters of the distribution are a combination of half Laplace and half normal distributions on the real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and other distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data. A brief simulation study is presented. [ABSTRACT FROM AUTHOR]

For the mean curvature vector field H and the Laplace operator Δ of a submanifold in the Minkowski space, a submanifold satisfying the condition ΔH = fH + gC is known as a generalized null 2-type, where f and g are smooth functions, and C is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type submanifolds defined by B.-Y. Chen. In this paper, we study flat surfaces in the Minkowski 3-space L3 and classify generalized null 2-type flat surfaces. In addition, we show that the only generalized null 2-type null scroll in L3 is a B-scroll. [ABSTRACT FROM AUTHOR]

Multiresolution models such as the wavelet-domain hidden Markov tree (HMT) model provide a powerful approach for image modeling and processing because it captures the key features of the wavelet coefficients of real-world data. It is observed that the Laplace distribution is peakier in the center and has heavier tails compared with the Gaussian distribution. Thus we propose a new HMT model based on the two-state, zero-mean Laplace mixture model (LMM), the LMM-HMT, which provides significantly potential for characterizing real-world textures. By using the HMT segmentation framework, we develop LMM-HMT based segmentation methods for image textures and dynamic textures. The experimental results demonstrate the effectiveness of the introduced model and segmentation methods. [ABSTRACT FROM AUTHOR]

Three methods to estimate the presence of ground surface stones from publicly available Airborne Laser Scanning (ALS) point clouds are presented. The first method approximates the local curvature by local linear multi-scale fitting, and the second method uses Discrete-Differential Gaussian curvature based on the ground surface triangulation. The third baseline method applies Laplace filtering to Digital Elevation Model (DEM) in a 2 m regular grid data. All methods produce an approximate Gaussian curvature distribution which is then vectorized and classified by logistic regression. Two training data sets consisted of 88 and 674 polygons of mass-flow deposits, respectively. The locality of the polygon samples is a sparse canopy boreal forest, where the density of ALS ground returns is sufficiently high to reveal information about terrain micro-topography. The surface stoniness of each polygon sample was categorized for supervised learning by expert observation on the site. The leave-pair-out (L2O) cross-validation of the local linear fit method results in the area under curve AUC = 0.74 and AUC = 0.85 on two data sets, respectively. This performance can be expected to suit real world applications such as detecting coarse-grained sediments for infrastructure construction. A wall-to-wall predictor based on the study was demonstrated. [ABSTRACT FROM AUTHOR]

The Riemannian geometry of the space Pm, of m × m symmetric positive definite matrices, has provided effective tools to the fields of medical imaging, computer vision and radar signal processing. Still, an open challenge remains, which consists of extending these tools to correctly handle the presence of outliers (or abnormal data), arising from excessive noise or faulty measurements. The present paper tackles this challenge by introducing new probability distributions, called Riemannian Laplace distributions on the space Pm. First, it shows that these distributions provide a statistical foundation for the concept of the Riemannian median, which offers improved robustness in dealing with outliers (in comparison to the more popular concept of the Riemannian center of mass). Second, it describes an original expectation-maximization algorithm, for estimating mixtures of Riemannian Laplace distributions. This algorithm is applied to the problem of texture classification, in computer vision, which is considered in the presence of outliers. It is shown to give significantly better performance with respect to other recently-proposed approaches. [ABSTRACT FROM AUTHOR]

An investigation of a segmented annular coplanar capacitor is presented. We focus on its theoretical model, and a mathematical expression of the capacitance value is derived by solving a Laplace equation with Hankel transform. The finite element method is employed to verify the analytical result. Different control parameters are discussed, and each contribution to the capacitance value of the capacitor is obtained. On this basis, we analyze and optimize the structure parameters of a segmented coplanar capacitive tilt sensor, and three models with different positions of the electrode gap are fabricated and tested. The experimental result shows that the model (whose electrode-gap position is 10 mm from the electrode center) realizes a high sensitivity: 0.129 pF/° with a non-linearity of <0.4% FS (full scale of ±40°). This finding offers plenty of opportunities for various measurement requirements in addition to achieving an optimized structure in practical design. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain. This work is based on the method of fundamental solutions (MFS) by imposing the boundary Cauchy data in a least-square sense and minimisation of the objective function. This approach can also be considered with noisy boundary Cauchy data. The simplicity and efficiency of this method is illustrated in several numerical examples. [ABSTRACT FROM AUTHOR]

Pairs trading under the copula approach is revisited in this paper. It is well known that financial returns arising from indices in markets may not follow the features of normal distribution and may exhibit asymmetry or fatter tails, in particular. Due to this, the Laplace distribution is employed in this work to fit the marginal distribution function, which will then be employed in a copula function. In fact, a multivariate copula function is constructed on two indices (based on the Laplace marginal distribution), enabling us to obtain the associated probabilities required for the process of pairs trade and creating an efficient tool for trading. [ABSTRACT FROM AUTHOR]

We present the general results on the univariate tail conditional moments for a location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal, location-scale mixture of Student's t, location-scale mixture of logistic, and location-scale mixture of Laplace distributions. More specifically, we give the tail variance, the tail conditional skewness, and the tail conditional kurtosis of generalised hyperbolic distribution and Student–GIG mixture distribution. We give an illustrative example, which discusses the TCE, TV, TCS and TCK of three stocks, including Amazon, Google and Apple. [ABSTRACT FROM AUTHOR]

In this article, we study the hitting probability of a circumference C R for a correlated Brownian motion B ̲ (t) = B 1 (t) , B 2 (t) , ρ being the correlation coefficient. The analysis starts by first mapping the circle C R into an ellipse E with semiaxes depending on ρ and transforming the differential operator governing the hitting distribution into the classical Laplace operator. By means of two different approaches (one obtained by applying elliptic coordinates) we obtain the desired distribution as a series of Poisson kernels. [ABSTRACT FROM AUTHOR]

The Global Navigation Satellite System (GNSS) allows for the cost-effective estimation of the ionospheric total electron content (TEC). However, research on error characteristics of the derived TEC is scarce, which provides insights into the quality of the GNSS ionospheric observation. We investigate characteristics of errors in the derived TEC with data from ~260 GNSS dual-frequency receivers of the Crustal Movement Observation Network of China (CMONOC). The slant TEC is calculated from carrier phase measurements and the vertical TEC over China is fitted with a spatial resolution of 1° by 1° in latitude and longitude in four seasons of 2014. It is found that the errors of both the slant TEC and the derived TEC follow Laplace distribution rather than Gaussian distribution in all seasons. The errors of the slant TEC have sharper peaks than those of the derived TEC. The Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) of the slant TEC are typically 0.04 TECU and 0.2 TECU, while the MAE and RMSE of the fitting residuals for the derived TEC are typically 1 TECU and under 2 TECU, respectively. Both MAEs and RMSEs of the derived TEC have the largest value in spring and the smallest value in summer, while the seasonal dependence is only observed in RMSE of the slant TEC. [ABSTRACT FROM AUTHOR]

Some features of hydro- and thermo-dynamics, as applied to atmospheres and to stellar structures, are puzzling: (1) the suggestion, first made by Laplace, that our atmosphere has an adiabatic temperature distribution, is confirmed for the lower layers, but the explanation for this is very controversial; (2) the standard treatment of relativistic thermodynamics does not favor a systematic treatment of mixtures, such as the mixture of a perfect gas with radiation; (3) the concept of mass density in applications of general relativity to stellar structures is less than completely satisfactory; and (4) arguments in which a concept of energy and entropy play a role, in the context of hydro-thermodynamical systems and gravitation, are not always convincing. It is proposed that a formulation of thermodynamics as an action principle may be a suitable approach to adopt for a new investigation of these matters. This paper formulates the thermodynamics of ideal gases in a constant gravitational field in terms of the Gibbsean action principle. This approach, in the simplest cases, does not deviate from standard practice, but it lays the foundations for a more systematic approach to the various extensions, such as the incorporation of radiation, the consideration of mixtures and the integration with general relativity. We study the interaction between an ideal gas and the photon gas and the propagation of sound in a vertical, isothermal column. We determine the entropy that allows for the popular isothermal equilibrium and introduce the study of the associated adiabatic dynamics. This leads to the suggestion that the equilibrium of an ideal gas must be isentropic, in which case, the role of solar radiation would be merely to compensate for the loss of energy by radiation into the cosmos. An experiment with a centrifuge is proposed, to determine the influence of gravitation on the equilibrium distribution with a very high degree of precision. [ABSTRACT FROM AUTHOR]

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which is employed for the self-consistent description of the high-gain free-electron laser (FEL). It is shown that the Fox H-function is the Laplace image of the kernel of the integro-differential equation, which is also known as a fractional FEL equation with Caputo–Fabrizio type fractional derivative. Asymptotic solutions of the equation are analyzed as well. [ABSTRACT FROM AUTHOR]

In this paper, the quasi-projective synchronization of distributed-order recurrent neural networks is investigated. Firstly, based on the definition of the distributed-order derivative and metric space theory, two distributed-order differential inequalities are obtained. Then, by employing the Lyapunov method, Laplace transform, Laplace final value theorem, and some inequality techniques, the quasi-projective synchronization sufficient conditions for distributed-order recurrent neural networks are established in cases of feedback control and hybrid control schemes, respectively. Finally, two numerical examples are given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

A simple and direct procedure for implementing fractional-order filters with transfer functions that contain Laplace operators of different fractional orders is presented in this work. Based on a general fractional-order transfer function that describes fractional-order low-pass, high-pass, band-pass, band-stop and all-pass filters, the introduced concept deals with the consideration of this function as a whole, with its approximation being performed using a curve-fitting-based technique. Compared to the conventional procedure, where each fractional-order Laplace operator of the transfer function is individually approximated, the main offered benefit is the significant reduction in the order of the resulting rational function. Experimental results, obtained using a field-programmable analog array device, verify the validity of this concept. [ABSTRACT FROM AUTHOR]

The database of the HWind project sponsored by the National Oceanic and Atmospheric Administration (NOAA) for hurricanes between 1994 and 2013 is analysed. This is the first objective of the current research. Among these hurricanes, Hurricane Sandy was selected for a detailed study due to the number of files available and its social relevance, with this being the second objective of this study. Robust wind speed statistics showed a sharp increase in wind speed, around 6 m s−1 at the initial stage as Category 1, and a linear progression of its interquartile range, which increased at a rate of 0.54 m s−1 per day. Wind speed distributions were initially right-skewed. However, they evolved to nearly symmetrical or even left-skewed distributions. Robust kurtosis was similar to that of the Gaussian distribution. Due to the noticeable fraction of wind speed intermediate values, the Laplace distribution was used, its scale parameter increasing slightly during the hurricane's lifecycle. The key features of the current study were the surface and recirculation factor calculation. The surface area with a category equal to, or higher than, a tropical storm was calculated and assumed to be circular. Its radius increased linearly up to 600 km. Finally, parcel trajectories were spirals in the lower atmosphere but loops in the mid-troposphere due to wind translation and rotation. The recirculation factor varied, reaching values close to 0.9 and revealing atmospheric stratification. [ABSTRACT FROM AUTHOR]

A generalized multivariate problem due to V. M. Zolotarev is considered. Some related results on geometric random sums and (multivariate) geometric stable distributions are extended to a more general case of "anisotropic" random summation where sums of independent random vectors with multivariate random index having a special multivariate geometric distribution are considered. Anisotropic-geometric stable distributions are introduced. It is demonstrated that these distributions are coordinate-wise scale mixtures of elliptically contoured stable distributions with the Marshall–Olkin mixing distributions. The corresponding "anisotropic" analogs of multivariate Laplace, Linnik and Mittag–Leffler distributions are introduced. Some relations between these distributions are presented. [ABSTRACT FROM AUTHOR]

In this study we investigated, using a simple polymer model of bacterial chromosome, the subdiffusive behaviors of both cytoplasmic particles and various loci in different cell wall confinements. Non-Gaussian subdiffusion of cytoplasmic particles as well as loci were obtained in our Langevin dynamic simulations, which agrees with fluorescence microscope observations. The effects of cytoplasmic particle size, locus position, confinement geometry, and density on motions of particles and loci were examined systematically. It is demonstrated that the cytoplasmic subdiffusion can largely be attributed to the mechanical properties of bacterial chromosomes rather than the viscoelasticity of cytoplasm. Due to the randomly positioned bacterial chromosome segments, the surrounding environment for both particle and loci is heterogeneous. Therefore, the exponent characterizing the subdiffusion of cytoplasmic particle/loci as well as Laplace displacement distributions of particle/loci can be reproduced by this simple model. Nevertheless, this bacterial chromosome model cannot explain the different responses of cytoplasmic particles and loci to external compression exerted on the bacterial cell wall, which suggests that the nonequilibrium activity, e.g., metabolic reactions, play an important role in cytoplasmic subdiffusion. [ABSTRACT FROM AUTHOR]

We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the variance of the estimated likelihood. We review and compare particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation to estimate the posterior distribution of the parameters. Additionally, we conduct the review from the point of view of whether these methods are (1) easily adaptable to different model specifications; (2) adaptable to higher dimensions of the model in a straightforward way; (3) feasible in the multivariate case. We show that when using the stochastic volatility model for methods comparison, various data-generating processes have to be considered to make a fair assessment of the methods. Finally, we present a challenging specification of the multivariate stochastic volatility model, which is rarely used to illustrate the methods but constitutes an important practical application. [ABSTRACT FROM AUTHOR]

Second-order Chebyshev–Edgeworth expansions are derived for various statistics from samples with random sample sizes, where the asymptotic laws are scale mixtures of the standard normal or chi-square distributions with scale mixing gamma or inverse exponential distributions. A formal construction of asymptotic expansions is developed. Therefore, the results can be applied to a whole family of asymptotically normal or chi-square statistics. The random mean, the normalized Student t-distribution and the Student t-statistic under non-normality with the normal limit law are considered. With the chi-square limit distribution, Hotelling's generalized T 0 2 statistics and scale mixture of chi-square distributions are used. We present the first Chebyshev–Edgeworth expansions for asymptotically chi-square statistics based on samples with random sample sizes. The statistics allow non-random, random, and mixed normalization factors. Depending on the type of normalization, we can find three different limit distributions for each of the statistics considered. Limit laws are Student t-, standard normal, inverse Pareto, generalized gamma, Laplace and generalized Laplace as well as weighted sums of generalized gamma distributions. The paper continues the authors' studies on the approximation of statistics for randomly sized samples. [ABSTRACT FROM AUTHOR]

A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance. [ABSTRACT FROM AUTHOR]

Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for single hidden layer feed-forward neural networks, such as Randomized Radial Basis Function (RBF) Networks and Random Vector Functional-link (RVFL), the SCN randomly assigns the input weights and biases of the hidden nodes in a supervisory mechanism. Since the parameters in the hidden layers are randomly generated in uniform distribution, hypothetically, there is optimal randomness. Heavy-tailed distribution has shown optimal randomness in an unknown environment for finding some targets. Therefore, in this research, the authors used heavy-tailed distributions to randomly initialize weights and biases to see if the new SCN models can achieve better performance than the original SCN. Heavy-tailed distributions, such as Lévy distribution, Cauchy distribution, and Weibull distribution, have been used. Since some mixed distributions show heavy-tailed properties, the mixed Gaussian and Laplace distributions were also studied in this research work. Experimental results showed improved performance for SCN with heavy-tailed distributions. For the regression model, SCN-Lévy, SCN-Mixture, SCN-Cauchy, and SCN-Weibull used less hidden nodes to achieve similar performance with SCN. For the classification model, SCN-Mixture, SCN-Lévy, and SCN-Cauchy have higher test accuracy of 91.5%, 91.7% and 92.4%, respectively. Both are higher than the test accuracy of the original SCN. [ABSTRACT FROM AUTHOR]

This article is partially a review and partially a contribution. The classical two approaches to robustness, Huber's minimax and Hampel's based on influence functions, are reviewed with the accent on distribution classes of a non-neighborhood nature. Mainly, attention is paid to the minimax Huber's M-estimates of location designed for the classes with bounded quantiles and Meshalkin-Shurygin's stable M-estimates. The contribution is focused on the comparative performance evaluation study of these estimates, together with the classical robust M-estimates under the normal, double-exponential (Laplace), Cauchy, and contaminated normal (Tukey gross error) distributions. The obtained results are as follows: (i) under the normal, double-exponential, Cauchy, and heavily-contaminated normal distributions, the proposed robust minimax M-estimates outperform the classical Huber's and Hampel's M-estimates in asymptotic efficiency; (ii) in the case of heavy-tailed double-exponential and Cauchy distributions, the Meshalkin-Shurygin's radical stable M-estimate also outperforms the classical robust M-estimates; (iii) for moderately contaminated normal, the classical robust estimates slightly outperform the proposed minimax M-estimates. Several directions of future works are enlisted. [ABSTRACT FROM AUTHOR]