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Data irregularity in cancer genomics studies has been widely observed in the form of outliers and heavy‐tailed distributions in the complex traits. In the past decade, robust variable selection methods have emerged as powerful alternatives to the nonrobust ones to identify important genes associated with heterogeneous disease traits and build superior predictive models. In this study, to keep the remarkable features of the quantile LASSO and fully Bayesian regularized quantile regression while overcoming their disadvantage in the analysis of high‐dimensional genomics data, we propose the spike‐and‐slab quantile LASSO through a fully Bayesian spike‐and‐slab formulation under the robust likelihood by adopting the asymmetric Laplace distribution (ALD). The proposed robust method has inherited the prominent properties of selective shrinkage and self‐adaptivity to the sparsity pattern from the spike‐and‐slab LASSO (Roc̆ková and George, J Am Stat Associat, 2018, 113(521): 431–444). Furthermore, the spike‐and‐slab quantile LASSO has a computational advantage to locate the posterior modes via soft‐thresholding rule guided Expectation‐Maximization (EM) steps in the coordinate descent framework, a phenomenon rarely observed for robust regularization with nondifferentiable loss functions. We have conducted comprehensive simulation studies with a variety of heavy‐tailed errors in both homogeneous and heterogeneous model settings to demonstrate the superiority of the spike‐and‐slab quantile LASSO over its competing methods. The advantage of the proposed method has been further demonstrated in case studies of the lung adenocarcinomas (LUAD) and skin cutaneous melanoma (SKCM) data from The Cancer Genome Atlas (TCGA). [ABSTRACT FROM AUTHOR]

This research incorporates realized volatility and overnight information into risk models, wherein the overnight return often contributes significantly to the total return volatility. Extending a semiparametric regression model based on asymmetric Laplace distribution, we propose a family of RES‐CAViaR‐oc models by adding overnight return and realized measures as a nowcasting technique for simultaneously forecasting Value‐at‐Risk (VaR) and expected shortfall (ES). We utilize Bayesian methods to estimate unknown parameters and forecast VaR and ES jointly for the proposed model family. We also conduct extensive backtests based on joint elicitability of the pair of VaR and ES during the out‐of‐sample period. Our empirical study on four international stock indices confirms that overnight return and realized volatility are vital in tail risk forecasting. [ABSTRACT FROM AUTHOR]

Riverbed elevations play a crucial role in sediment transport and flow resistance, making it essential to understand and quantify their effects. This knowledge is vital for various fields, including river engineering and stream ecology. Previous observations have revealed that fluctuations in the bed surface can exhibit both multifractal and monofractal behaviors. Specifically, the probability distribution function (PDF) of elevation increments may transition from Laplace (two‐sided exponential) to Gaussian with increasing scales or consistently remain Gaussian, respectively. These differences at the finest timescale lead to distinct patterns of bedload particle exchange with the bed surface, thereby influencing particle resting times and streamwise transport. In this paper, we utilize the fractional Laplace motion (FLM) model to analyze riverbed elevation series, demonstrating its capability to capture both mono‐ and multi‐fractal behaviors. Our focus is on studying the resting time distribution of bedload particles during downstream transport, with the FLM model primarily parameterized based on the Laplace distribution of increments PDF at the finest timescale. Resting times are extracted from the bed elevation series by identifying pairs of adjacent deposition and entrainment events at the same elevation. We demonstrate that in cases of insufficient data series length, the FLM model robustly estimates the tail exponent of the resting time distribution. Notably, the tail of the exceedance probability distribution of resting times is much heavier for experimental measurements displaying Laplace increments PDF at the finest scale, compared to previous studies observing Gaussian PDF for bed elevation. Plain Language Summary: The evolution of riverbed elevations is difficult to describe due to its highly variable and strongly non‐linear nature. Understanding and quantifying the dynamics of riverbed elevations are important for river engineering and stream ecology, and serve as the basis for numerical models of predicting sediment transport as well as interpreting stratigraphy from the past records. Through laboratory experiments, we have observed that the form of elevation increment PDF can change from Laplace to Gaussian as the timescale increases. This phenomenon is successfully modeled in this paper for the first time by the fractional Laplace motion, which essentially generates bed elevation series for the evolution of bed surface height at a certain spatial location of the bed. This series contains information on how long a bedload particle can rest (resting time) in the riverbed before it can be re‐entrained to move downstream, the determination of which by other means (e.g., particle‐tracking measurements) is challenging. By extracting resting times embedded in this bed elevation series, we obtain statistics (i.e., the tail behavior of the resting time distribution) that are key for correctly modeling the transport of bedload particles, and more specifically, that can help us to understand the anomalous bedload diffusion process. Key Points: The Fractional Laplace motion (FLM) can be used to describe the evolution of the distribution of bed elevation increments over different timescalesCorrectly predicting bed elevation fluctuations at the finest timescale is critical for estimating resting times for bedload tracer transportFLM model provides a means of robustly estimating the tail exponent of the resting time distribution in case of insufficient data series length [ABSTRACT FROM AUTHOR]

A key aspect where extreme values methods differ from standard statistical models is through having asymptotic theory to provide a theoretical justification for the nature of the models used for extrapolation. In multivariate extremes, many different asymptotic theories have been proposed, partly as a consequence of the lack of ordering property with vector random variables. One class of multivariate models, based on conditional limit theory as one variable becomes extreme has received wide practical usage. The underpinning value of this approach has been supported by further theoretical characterisations of the limiting relationships. However, the paper "Conditional extreme value models: fallacies and pitfalls" by Holger Drees and Anja Janßen provides a number of counterexamples to these results. This paper studies these counterexamples in a conditional extremes framework which involves marginal standardisation to a common exponentially decaying tailed marginal distribution. Our calculations show that some of the issues identified can be addressed in this way. [ABSTRACT FROM AUTHOR]

Despite the increasing importance of high‐dimensional varying coefficient models, the study of their Bayesian versions is still in its infancy. This paper contributes to the literature by developing a sparse empirical Bayes formulation that addresses the problem of high‐dimensional model selection in the framework of Bayesian varying coefficient modelling under Gaussian process (GP) priors. To break the computational bottleneck of GP‐based varying coefficient modelling, we introduce the low‐cost computation strategy that incorporates linear algebra techniques and the Laplace approximation into the evaluation of the high‐dimensional posterior model distribution. A simulation study is conducted to demonstrate the superiority of the proposed Bayesian method compared to an existing high‐dimensional varying coefficient modelling approach. In addition, its applicability to real data analysis is illustrated using yeast cell cycle data. [ABSTRACT FROM AUTHOR]

High‐breakdown‐point estimators of multivariate location and shape matrices, such as the MM‐estimator with smoothed hard rejection and the Rocke S‐estimator, are generally designed to have high efficiency for Gaussian data. However, many phenomena are non‐Gaussian, and these estimators can therefore have poor efficiency. This article proposes a new tunable S‐estimator, termed the Sq‐estimator, for the general class of symmetric elliptical distributions, a class containing many common families such as the multivariate Gaussian, t‐, Cauchy, Laplace, hyperbolic, and normal inverse Gaussian distributions. Across this class, the Sq‐estimator is shown to generally provide higher maximum efficiency than other leading high‐breakdown estimators while maintaining the maximum breakdown point. Furthermore, the Sq‐estimator is demonstrated to be distributionally robust, and its robustness to outliers is demonstrated to be on par with these leading estimators while also being more stable with respect to initial conditions. From a practical viewpoint, these properties make the Sq‐estimator broadly applicable for practitioners. These advantages are demonstrated with an example application—the minimum‐variance optimal allocation of financial portfolio investments. [ABSTRACT FROM AUTHOR]

This paper is devoted to a new two‐parameter distribution on ℤ having an original additive stochastic structure. It is defined by the sum of two independent discrete random variables, where one is defined based on the Laplace distribution and the other on a transformed version of a distribution that can be viewed as a relative binomial distribution. It can thus also be viewed as a perturbed version of the Laplace distribution. We present some interesting properties of the proposed distribution, such as its moments (ordinary, non‐central, incomplete moments, etc.), characteristic function, skewness, and kurtosis, among others. The distribution is also applied to practical datasets from finance and health studies, where it is seen to perform better than some of the existing models defined on ℤ. [ABSTRACT FROM AUTHOR]

In this study, Laplace transformation, which is very important for solutions to initial value problems, is examined. To solve the initial value problem of a discrete‐time equation, Laplace implements the conversion method. Here, Laplace transformation is used to obtain an approach to the solutions of random difference equations formed by randomizing components of deterministic difference equations. For random behavior of linear difference equations under random effects, uniform, geometric, binomial, Poisson, and Bernouilli distributions are used, and approximate expected value, variance, standard deviation, and confidence interval of equations obtained by Laplace transformation are calculated. The results were obtained through the Maple package program. [ABSTRACT FROM AUTHOR]

We consider the process capability index (PCI), a widely used quality‐related statistic used to assess the quality of products and performance of monitored processes in various industries. It is widely known that the conventional PCIs perform well when the quality process being monitored has a normal distribution. Unfortunately, using the indices to evaluate a non‐normally distributed process often leads to inaccurate results. In this article, we consider a new PCI, Cpc$C_{pc}$, that can be used in both normal and non‐normal scenarios. The objective of this article is threefold: (i) We provide a corrected form of the confidence interval for Cpc$C_{pc}$. (ii) We compare the performance of three nonparametric bootstrap confidence intervals (BCIs) for Cpc$C_{pc}$. Specifically, the standard bootstrap, percentile bootstrap, and bias‐corrected percentile bootstrap. Under various distributional assumptions such as the normal, chi‐square, Student t, Laplace, and two‐parameter exponential distributions, the estimated coverage probabilities and average width of the confidence intervals and BCIs for Cpc$C_{pc}$ are compared. (iii) The power of the respective bootstrap approaches is evaluated by using the equivalence relation between confidence interval construction and two‐sided hypothesis testing. We also provide the receiver operating characteristic curves to evaluate their performance. Finally, as an illustrative example, an actual data set related to groove dimensions (in inches) measured from a manufacturing process of ignition keys is re‐analyzed to illustrate the utility of the proposed methods. [ABSTRACT FROM AUTHOR]

Purpose: For quantitative susceptibility mapping (QSM), the lack of ground‐truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with built‐in parameter estimation, and incorporate the nonlinear formulation of the dipole inversion to achieve a robust recovery of the susceptibility maps. Theory: From a Bayesian perspective, the image wavelet coefficients are approximately sparse and modeled by the Laplace distribution. The measurement noise is modeled by a Gaussian‐mixture distribution with two components, where the second component is used to model the noise outliers. Through probabilistic inference, the susceptibility map and distribution parameters can be jointly recovered using approximate message passing (AMP). Methods: We compare our proposed AMP with built‐in parameter estimation (AMP‐PE) to the state‐of‐the‐art L1‐QSM, FANSI, and MEDI approaches on the simulated and in vivo datasets, and perform experiments to explore the optimal settings of AMP‐PE. Reproducible code is available at: https://github.com/EmoryCN2L/QSM%5fAMP%5fPE. Results: On the simulated Sim2Snr1 dataset, AMP‐PE achieved the lowest NRMSE, deviation from calcification moment and the highest SSIM, while MEDI achieved the lowest high‐frequency error norm. On the in vivo datasets, AMP‐PE is robust and successfully recovers the susceptibility maps using the estimated parameters, whereas L1‐QSM, FANSI and MEDI typically require additional visual fine‐tuning to select or double‐check working parameters. Conclusion: AMP‐PE provides automatic and adaptive parameter estimation for QSM and avoids the subjectivity from the visual fine‐tuning step, making it an excellent choice for the clinical setting. [ABSTRACT FROM AUTHOR]

This article derives some large sample properties of weighted l1‐penalized corrected quantile estimators of the regression parameter vector in a high‐dimensional errors in variables (EIVs) linear regression model. In this model, the number of predictors p depends on the sample size n and tends to infinity, generally at a faster rate than n, as n tends to infinity. Moreover, the measurement errors in the covariates are assumed to have linear stationary temporal dependence and known Laplace marginal distribution while the regression errors are assumed to be independent non‐identically distributed random variables having possibly heavy tails. The article discusses some rates of consistency of these estimators, a model consistency result and an appropriate data adaptive algorithm for obtaining a suitable choice of weights. A simulation study assesses the finite sample performance of some of the proposed estimators. This article also contains analogs of Massart's inequality for independent and short memory moving average predictors, which is instrumental in establishing the said consistency rates of the above mentioned estimators in the current setup of high dimensional EIVs regression models. [ABSTRACT FROM AUTHOR]

In three‐dimensional (3D) equilibrium, reconstruction defining parameters of an ideal magneto‐hydrodynamic equilibrium are inferred from a set of plasma diagnostic measurements. For the reconstructed parameters, various forms of uncertainty estimates exist within common 3D reconstruction frameworks. These estimates often assume a Gaussian posterior distribution. The validity of this assumption is not obvious in such highly nonlinear inverse problems, and therefore the accuracy of the estimates cannot be guaranteed. In this work, we formulate the problem of 3D equilibrium reconstruction in a Bayesian sense and explore the posterior distribution of reconstruction parameters via Markov chain Monte Carlo (MCMC) sampling. The target reconstruction parameters, that is, shape and scaling factors of the pressure and toroidal current‐density profiles as well as the total toroidal flux, are taken from a reduced subspace of Wendelstein 7‐X equilibrium configurations. Since the corresponding forward model evaluations are computationally demanding, we replace the forward model via a polynomial chaos expansion surrogate. We compare the posterior distribution obtained via MCMC sampling to Laplace's approximation, which assumes a Gaussian posterior. We find that the two approaches provide similar results in regimes where the uncertainty on the plasma diagnostic signals is low. However, discrepancies between the posteriors are observed in cases of higher diagnostic signal uncertainty. Therefore, we provide further validation of the commonly used Laplace's approximation as a method of uncertainty quantification in 3D equilibrium reconstruction and showcase some of its limitations. [ABSTRACT FROM AUTHOR]

Collecting microscale water droplets suspended in the wind, that is, fog, using permeable surfaces is a promising solution to the worldwide problem of water scarcity and is of great interest to industries, such as mist elimination and recapturing water in cooling towers. In the past few decades, this topic has attracted a drastically increasing number of researchers across a wide range of subjects. However, many aspects remain unclear, such as the definition and process of fog collection, fog collection determined from the perspectives of both the fog capture process and the liquid transport process, and how surface characteristics affect fog collection performance. In this review, we introduce and discuss fog collection from the perspectives of aerodynamics-governed fog-capturing processes and interfacialphenomena-determined liquid transport processes. Then, an emphasis is given to the design and engineering of permeable surfaces at different length scales to optimize the fog collection performance, including the dimension, morphology, and arrangement of wires at the millimetric scale, unidirectional spreading, and Laplace pressure gradient induced by asymmetric surface geometry and nano-/microstructures. At last, a brief outlook of future research directions is provided. [ABSTRACT FROM AUTHOR]

The high-throughput production of monodisperse droplets is paramount in most of the applications in droplet microfluidics. In a flow-focusing junction, a straightforward way to increase droplet production rate is to increase the flow rates. However, at a critical flow velocity, the droplet monodispersity breaks down due to a transition from the dripping to the jetting regime. As a result, a much more polydisperse droplet population is generated. The change from monodisperse to polydisperse droplet production emerges from the intrinsic properties of the instabilities of jets. In the jetting regime, droplet pinch-off is governed by a convective instability which amplifies random noise when traveling down the jet leading to an irregular breakup. We show that with the use of an amplitude-modulated electric signal, we select the breakup frequency of the jet. Matching the perturbation frequency close to the natural breakup frequency of the jet, we increase the monodispersity of the droplet population. This method is applicable to droplet production at a high throughput, that is, beyond the dripping to jetting threshold, including an active control since the frequency, and hence droplet sizes, are determined by the forcing frequency. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM), which is often referred to as three-dimensional printing, revolutionizes manufacturing by providing a high degree of design freedom and customization. Several AM methods entail precise control of droplet interfacial properties to ensure the high quality of the printed products. At the same time, the rapid growth of AM technology has made it possible to prepare novel surfaces with complex structures, further expanding the range of potential applications of droplet interface. To provide a unified framework to guide the continuous development of AM that involves droplet interface, this manuscript reviews related work in this field from two aspects--the droplet interface phenomenon in AM processes and the applications of droplet interface prepared by AM. Limitations of existing works are discussed, and potential future directions are suggested. [ABSTRACT FROM AUTHOR]

Liquid marbles (LMs) are nonsticky droplets stabilized by hydrophobic solid particles that are adsorbed at the liquid-air interface. LMs are emerging as a potential platform in digital microfluidics, sensing applications, storage unit, biological incubation, and cosmetic applications. Incorporating multifunctional particles to form Janus liquid marble (JLM) could enhance the capabilities of the pristine LM. JLMs are multifunctional next-generation LMs comprising two hemispherical domains of distinct physicochemical properties such as size, hydrophobicity, electrical conductivity, surface functionalization, stimuli-responsivity, and so on. The JLMs offer precise control on the manipulability and enhanced performance over pristine LMs. Though the properties, applications, and progress of LMs are detailed in the recent literature, a focused review encompassing the fabrication, recent developments, potential applications of JLMs, and the challenges regarding its reliable fabrication remains a gap in the literature. The review provides insights into the importance of JLMs, systematically discussing the fabrication strategies, applications, challenges, and future directions. [ABSTRACT FROM AUTHOR]

For general parametric statistical models with some variables being contaminated with the Laplace measurement error, we propose an extrapolation algorithm to estimate the unknown parameters. By applying the conditional expectation directly to the target function, either the function to be optimized or an estimation equation, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation procedure and thus provides a viable alternative to the classical simulation extrapolation algorithm. Large sample properties of the resulting estimator are discussed. Finite sample performance of the proposed extrapolation estimation procedure is demonstrated by examples and numerical simulation studies. [ABSTRACT FROM AUTHOR]

Longitudinal data on patient-reported outcomes (PROs), such as quality of life of patients, are frequently collected in clinical trials and other medical studies. Joint analysis of these data with survival times may improve the accuracy of statistical inferences, especially when PRO measurements may be missing after the death of patients. Classical linear mixed models are often used as the models for the longitudinal measurements in a joint analysis, but it may not be suitable for longitudinal PRO measurements with potential ceiling and floor effects caused by a large portion of patients who report either a maximum or minimum score. In this paper, we introduce a new joint model that uses a longitudinal Tobit model for the longitudinal outcomes with potential ceiling and floor effects and a Cox proportional hazard model for survival time with a random effect connecting these two models. An estimation procedure based on the partial likelihood and Laplace approximation is developed to estimate the parameters in both models, and a random weighting method is proposed to calculate the variances of these parameter estimators. Performances of the proposed procedures are evaluated through simulation studies and an application to the analysis of quality of life data from a clinical trial. [ABSTRACT FROM AUTHOR]

In this paper, we develop a Bayesian hierarchical model and associated computation strategy for simultaneously conducting parameter estimation and variable selection in binary quantile regression. We specify customary asymmetric Laplace distribution on the error term and assign quantile‐dependent priors on the regression coefficients and a binary vector to identify the model configuration. Thanks to the normal‐exponential mixture representation of the asymmetric Laplace distribution, we proceed to develop a novel three‐stage computational scheme starting with an expectation–maximization algorithm and then the Gibbs sampler followed by an importance re‐weighting step to draw nearly independent Markov chain Monte Carlo samples from the full posterior distributions of the unknown parameters. Simulation studies are conducted to compare the performance of the proposed Bayesian method with that of several existing ones in the literature. Finally, two real‐data applications are provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

Clustering has received much attention in statistics and machine learning with the aim of developing statistical models and autonomous algorithms which are capable of acquiring information from raw data in order to perform exploratory analysis. Several techniques have been developed to cluster sampled univariate vectors only considering the average value over the whole period and as such they have not been able to explore fully the underlying distribution as well as other features of the data, especially in presence of structured time series. We propose a model‐based clustering technique that is based on quantile regression permitting us to cluster bivariate time series at different quantile levels. We model the within cluster density using asymmetric Laplace distribution allowing us to take into account asymmetry in the distribution of the data. We evaluate the performance of the proposed technique through a simulation study. The method is then applied to cluster time series observed from Glob‐color satellite data related to trophic status indices with aim of evaluating their temporal dynamics in order to identify homogeneous areas, in terms of trophic status, in the Gulf of Gabes. [ABSTRACT FROM AUTHOR]

Laplace approximations are commonly used to approximate high‐dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we provide a new result on the size of the error in first‐ and higher‐order Laplace approximations, in terms of the rate of growth of information about each of the integrated variables. By contrast with many existing results, we allow for variation in the rate of information growth among the different integrated variables. We apply our results to investigate the quality of Laplace approximations to the likelihood in some generalized linear mixed models. [ABSTRACT FROM AUTHOR]

In double emulsions, the inner and outer droplet size distribution (DSD) determines the quality of the double emulsion and is therefore essential to be measured. Low‐field high‐resolution pulsed‐field gradient nuclear magnetic resonance is used to measure the inner DSD in water‐in‐oil‐in‐water double emulsions. The Gaussian phase distribution approach is employed with a mixture of two normal distributions to predict bimodal inner droplets. This approach allows the prediction of the swelling of inner droplet during storage of double emulsions, and thus to validate a phenomenological population balance model estimating inner droplet swelling. Only a fraction of the inner droplets are found to swell during storage, due to differences in the Laplace pressure, thus leading to the formation of a bimodal size distribution of the inner droplets. Practical Applications: This methodology is useful to predict the evolution of double emulsions during storage, in a wide range of applications, such as food and pharmaceutical products. [ABSTRACT FROM AUTHOR]

The existing privacy protection schemes for Location‐Based Service (LBS) only protect users' location privacy or query privacy, which can not adopt both of the privacy protections simultaneously in the LBS system. Moreover, these schemes cannot take into account the spatial‐temporal correlation and background knowledge. In response to the above mentioned questions, the LBS Privacy Protection Scheme Based on Differential Privacy (DPLQ) is proposed. The method contains two kinds of privacy protection algorithms: users' location privacy protection algorithm and users' query privacy protection algorithm. The users' location privacy protection algorithm divides the map using the Voronoi diagram, choosing l fake location points based on the improved k‐means algorithm and l‐diversity idea, and protects users' location privacy with the Laplace mechanism. Based on the k‐anonymous algorithm, the users' query privacy protection algorithm builds a query k‐anonymous set according to the neighbour users' query requests at the same time t in the cluster and the historical query probability of the region's POI and protects users' query privacy with the exponential mechanism. Through setting the privacy protection intensity of the algorithm by the users, the generated location dataset and query k‐anonymous set can resist a variety of attacks from malicious attackers. Theoretical analysis and experimental results show that the scheme can effectively protect the location privacy and query privacy of users. [ABSTRACT FROM AUTHOR]

We propose a flexible Bayesian semiparametric quantile regression model based on Dirichlet process mixtures of generalized asymmetric Laplace distributions for fitting curves with shape restrictions. The generalized asymmetric Laplace distribution exhibits more flexible tail behaviour than the frequently used asymmetric Laplace distribution in Bayesian quantile regression. In addition, nonparametric mixing over the shape and scale parameters with the Dirichlet process mixture extends its flexibility and improves the goodness of fit. By assuming the derivatives of the regression functions to be the squares of the Gaussian processes, our approach ensures that the resulting functions have shape restrictions such as monotonicity, convexity and concavity. The introduction of shape restrictions prevents overfitting and helps obtain smoother and more stable estimates of the quantile curves, especially in the tail quantiles for small and moderate sample sizes. Furthermore, the proposed shape‐restricted quantile semiparametric regression model deals with sparse estimation for regression coefficients using the horseshoe+ prior distribution, and it is extended to cases with group‐specific curve estimation and censored data. The usefulness of the proposed models is demonstrated using simulated datasets and real applications. [ABSTRACT FROM AUTHOR]

Recently, with the increased intermittent renewable energy penetration, many power grids have been incorporated into a large‐scale long‐distance UHV AC–DC hybrid system. In the actual grid, power disturbances, such as DC blocking faults and trip‐off of wind turbines, often occur, resulting in power shortages and large frequency fluctuations. However, the existing approaches to assess the system frequency security are not reliable. This paper proposes an analytic formula for the system frequency response based on a generic system frequency‐response (SFR) model, which can be applied to modern large‐scale power systems. First, a generic SFR model with a reasonable structure is designed according to the parameter determination strategy. Second, according to the transfer function in the model, the time‐domain analytic formula of the frequency response is obtained by realizing the inverse Laplace transform. Moreover, four main indexes are established to represent the characteristics of the frequency dynamic process in different periods, and these indexes are qualitatively and quantitatively analysed. Finally, the New England 10‐unit 39‐bus power system and East China Power Grid are considered to demonstrate the key features of the proposed method. The results show that the proposed analytic assessment method can be effectively adopted in several applications. [ABSTRACT FROM AUTHOR]

In skywave radar, the slow‐time samples received in a certain range‐azimuth cell are usually processed for signal analysis and target detection. Particularly, to extract the principal components, such as sea clutter and target signal, in slow‐time samples, the Hankel matrix structure and subspace‐based methods are often applied, which can also reduce the additive Gaussian noise. In the real environment, the slow‐time samples sometimes are seriously contaminated by the transient interference, affecting the performance of useful signal reconstruction. The robust low‐rank matrix recovery methods have been applied to solve this problem, where the transient interference is assumed to be sparse, following the Laplace distribution. However, the Hankel structures of useful signal and transient interference have not been fully utilized in the conventional methods, which can enhance the reconstruction performance. Here, the robust low‐rank Hankel matrix recovery problems is reformulated for skywave radar slow‐time samples and solve them with the inexact augmented Lagrange multiplier method. Additionally, the low‐rank Hankel matrix completion problem is discussed, where the location of the transient interference is determined. The experimental results have demonstrated the good performance of our proposed methods and also some interesting conclusions are obtained. [ABSTRACT FROM AUTHOR]

Growth curve models have been widely used to analyse longitudinal data in social and behavioural sciences. Although growth curve models with normality assumptions are relatively easy to estimate, practical data are rarely normal. Failing to account for non‐normal data may lead to unreliable model estimation and misleading statistical inference. In this work, we propose a robust approach for growth curve modelling using conditional medians that are less sensitive to outlying observations. Bayesian methods are applied for model estimation and inference. Based on the existing work on Bayesian quantile regression using asymmetric Laplace distributions, we use asymmetric Laplace distributions to convert the problem of estimating a median growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model. Monte Carlo simulation studies have been conducted to evaluate the numerical performance of the proposed approach with data containing outliers or leverage observations. The results show that the proposed approach yields more accurate and efficient parameter estimates than traditional growth curve modelling. We illustrate the application of our robust approach using conditional medians based on a real data set from the Virginia Cognitive Aging Project. [ABSTRACT FROM AUTHOR]

Lee and Jo examine a first-order bivariate random coefficient integer-valued autoregressive model and investigate some of the corresponding inferential procedures: parameter estimation (conditional least squares, modified quasi-likelihood, and exponential family quasi-likelihood methods) and parameter change testing. Peña and Tsay consider the problem of clustering stationary scalar time series using their marginal properties and a hierarchical method. Taniguchi Sensei - our colleague and friend Masanobu Taniguchi - retired from Waseda University in Tokyo at the end of March 2022 after a long and productive career that put Waseda on the international map of time series analysis and mathematical statistics. [Extracted from the article]

The exponentially weighted moving average (EWMA) control chart is a memory chart that is widely used in process monitoring to spot small and persistent disturbances in the process parameter(s). This chart requires normality of the quality characteristic(s) of interest and a smaller choice of smoothing parameter. Any deviations from these conditions affect its performance in terms of efficiency and robustness. For the said two concerns, this study develops a new mixed EWMA chart under progressive setup (mixed EWMA–progressive mean [MEP] chart). The proposed MEP chart combines the advantages of robustness (under nonnormal scenarios) and high sensitivity to small and persistent shifts in the process mean. The performance of the proposed MEP control chart is evaluated in terms of average run length and some other characteristics of run length distribution. The assessment of the proposed chart is made under standard normal, student's t, gamma, Laplace, logistic, exponential, contaminated normal and lognormal distributions. The performance of the proposed MEP chart is also compared with some existing competitors including the classical EWMA, the classical cumulative sum (CUSUM), the homogenously weighted moving average, the mixed EWMA–CUSUM, the mixed CUSUM–EWMA and the double EWMA charts. The analysis reveals that the proposal of this study offers a superior design structure relative to its competing counterparts. An application from substrates manufacturing process (in which flow width of the resist is the key quality characteristic) is also provided in the study. [ABSTRACT FROM AUTHOR]

In this paper, the multivariate Laplace distribution (also called L1 distribution) is adopted to construct a robust probabilistic principal component regression model (MRPPCR‐L1) under multiple operating modes. In the practical industrial chemistry process, outliers exist due to incorrect recording, disturbances, and process noises and might result in modelling distortion. To address this problem, Laplace distribution, instead of the Gaussian distribution in traditional methods, is introduced to reduce the negative influence of outliers. Moreover, probabilistic principal component regression is employed for dealing with the mixture modelling problem owing to its probabilistic property to determine the operating modes. The formulation of this approach is derived with the expectation maximum algorithm and the soft sensing model is also developed for prediction. Compared to the conventional method, a numerical example and the Tennessee Eastman process are used to demonstrate the robust modelling performance of the proposed method. [ABSTRACT FROM AUTHOR]

We study the dependence of the first eigenvalue of the Finsler p‐Laplacian and the corresponding eigenfunctions on perturbation of the domain and we generalize a few results known for the standard p‐Laplacian. In particular, we prove a Frechét differentiability result for the eigenvalues, compute the corresponding Hadamard formulas and prove a continuity result for the eigenfunctions. Finally, we briefly discuss a well‐known overdetermined problem and we show how to deduce the Rellich–Pohozaev identity for the Finsler p‐Laplacian from the Hadamard formula. [ABSTRACT FROM AUTHOR]

We study the 1‐ or 2‐level density of families of L‐functions for Hecke–Maass forms over an imaginary quadratic field F. For test functions whose Fourier transform is supported in (−32,32), we prove that the 1‐level density for Hecke–Maass forms over F of square‐free level q, as N(q) tends to infinity, agrees with that of the orthogonal random matrix ensembles. For Hecke–Maass forms over F of full level, we prove similar statements for the 1‐ and 2‐level densities, as the Laplace eigenvalues tend to infinity. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error. Starting with the modal regression procedure developed for the measurement error‐free case, a non‐trivial modification is made so that the modified version can effectively correct the potential bias caused by measurement error. Large sample properties of the proposed estimate, such as the convergence rate and the asymptotic normality, are thoroughly investigated. A simulation study and real data application are conducted to illustrate the satisfying finite sample performance of the proposed estimation procedure. A modal estimation procedure is proposed for nonlinear regression models when the covariates are measured with Laplace error. It enjoys the merits of both robustness and bias reduction. [ABSTRACT FROM AUTHOR]

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Not only in low‐field nuclear magnetic resonance, Laplace inversion is a relevant and challenging topic. Considerable conceptual and technical progress has been made, especially for the inversion of data encoding two decay dimensions. Distortion of spectra by overfitting of even moderate noise is counteracted requiring a priori smooth spectra. In this contribution, we treat the case of simple and fast one‐dimensional decay experiments that are repeated many times in a series in order to study the evolution of a sample or process. Incorporating the a priori knowledge that also in the series dimension evolution should be smooth, peak position can be stabilized and resolution improved in the decay dimension. It is explained how the standard one‐dimensional regularized Laplace inversion can be extended quite simply in order to include regularization in the series dimension. Obvious improvements compared with series of one‐dimensional inversions are presented for simulated as well as experimental data. For the latter, comparison with multiexponential fitting is performed. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of estimating the Laplace transform of volatility within a fixed time interval [0,T] using high‐frequency sampling, where we assume that the discretized observations of the latent process are contaminated by microstructure noise. We use the pre‐averaging approach to deal with the effect of microstructure noise. Under the high‐frequency scenario, we obtain a consistent estimator whose convergence rate is Δn−1/4, which is known as the optimal convergence rate of the estimation of integrated volatility functionals under the presence of microstructure noise. The related central limit theorem is established. The simulation studies justify the finite‐sample performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

This paper presents an analytical method towards Laplace transform inversion of composite functions with the aid of Bell polynomial series. The presented results are used to derive the exact solution of fractional distributed order relaxation processes as well as time‐domain impulse response of fractional distributed order operators in new series forms. Evaluation of the obtained series expansions through computer simulations is also given. The results are then used to present novel series expansions for some special functions, including the one‐parameter Mittag‐Leffler function. It is shown that truncating these series expansions when combined with using potential partition polynomials provides efficient approximations for these functions. At the end, the results are shown to be also useful in studying asymptotical behavior of partial Bell polynomials. Numerical simulations as well as analytical examples are provided to verify the results of this paper. [ABSTRACT FROM AUTHOR]

We develop an efficient computational model for simulating fluid invasion patterns emerging in variable aperture fractures. This two‐dimensional model takes into account the effect of capillary force on the fluid‐fluid interfaces and viscous pressure drop in both fluid phases. The pressure distribution is solved at each time step based on mass balance and local cubic law, considering an imposed pressure jump condition at the fluid‐fluid interface. This pressure jump corresponds to the Laplace pressure which includes both terms related to the out‐of‐plane (aperture‐spanning) curvature and to the in‐plane curvature. Simulating a configuration that emulates viscous fingering in two‐dimensional random porous media confirms that the model accounts properly for the role of viscous forces. Furthermore, direct comparison with previously obtained experimental results shows that the model reproduces the observed drainage patterns in a rough fracture reasonably well. The evolutions of tip location, the inlet pressures, and the invading phase fractal dimensions are analyzed to characterize the transition from capillary fingering to viscous fingering regimes. A radial injection scenario of immiscible invasion is also studied with varying modified capillary number and viscosity ratio, showing displacement patterns ranging from capillary fingering to viscous fingering to stable displacement. Such simulations using two contact angles show that the invading phase becomes more compact when the wetting condition changes from strong to weak drainage, as already observed in 2‐D porous media. The model can be used to bridge the gap in spatial scales of two‐phase flow between pore‐scale modeling approaches and the continuum Darcy‐scale models. Plain Language Summary: The flow of two or more fluids in fractured media is an important process involved in many industrial and environmental applications in the subsurface with examples spanning from contaminant transport to petroleum recovery to geological storage of carbon dioxide. Understanding and controlling two‐phase flow in fractures is critical from both the scientific and technological points of view. In this study, we focus on the displacement of one fluid by another immiscible one in a rough fracture, a fundamental process underlying two‐phase flow in fractured media. We develop an efficient computational model for simulating fluid invasion patterns emerging in rough fractures. This model takes into account the effect of capillary force on the fluid‐fluid interfaces and viscous pressure drop in both fluid phases. Direct comparison with experimental results shows that the model output matches the observed patterns reasonably well. In addition, generic simulations demonstrate the ability of the model to produce flow patterns that fall into regimes whose dependence on the viscosity ratio and capillary number is similar to that of the classical phase diagram. The model can be used to bridge the gap in spatial scales of two‐phase flow between pore‐scale modeling approaches and the continuum Darcy‐scale models. Key Points: An efficient, intermediate‐scale model is developed for dynamic, immiscible displacement in rough geological fracturesThe model reproduces essential features of experimentally observed drainage patterns from capillary to viscous fingeringThe model is advantageous over CFD approaches in computational efficiency and accuracy, especially in low to medium capillary number flows [ABSTRACT FROM AUTHOR]

Summary: The partial element equivalent circuit (PEEC) electromagnetic method has attracted a lot of attention for its capability to give a circuit interpretation to Maxwell's equations. The PEEC equivalent circuits are usually connected with terminations such as drivers and receivers in a time‐domain circuit simulator. Passivity is a fundamental property for the time‐domain simulations of circuit models connected to terminations at their electrical ports. Stable, but nonpassive, models can produce unstable systems when connected to other stable, even passive, loads. The so‐called quasi‐static PEEC formulations leads to a descriptor state‐space circuital representation of the electromagnetic phenomena. Multiple state‐space representations are possible. In this paper, we study the passivity property of different quasi‐static PEEC representations in detail. A novel analytical additive decomposition is proposed concerning the admittance formulation, which allows extracting the polynomial part of the transfer function that represents the behavior at infinity in the Laplace domain. This decomposition is discussed from a mathematical and a physical point of view. Such a detailed study for the passivity of quasi‐static PEEC models and the novel analytical decomposition is not available in the literature. Numerical results support the theoretical analysis. The partial element equivalent circuit (PEEC) method is able to give a circuit interpretation to Maxwell's equations. Passivity is a fundamental property for the time‐domain simulations of circuit models connected to terminations at their electrical ports. In this paper, we study the passivity property of different quasi‐static PEEC representations and a novel analytical additive decomposition is proposed which allows extracting the polynomial part of the admittance transfer function that represents the behavior at infinity in the Laplace domain. [ABSTRACT FROM AUTHOR]

An analysis of unsteady MHD natural convective flow, transfer of mass, and radiation past linearly accelerated slanted plate inserted in an immersed permeable medium with uniform permeability, variable temperature, and concentration within the sight of a slanted magnetic field has been done. The novelty of the current examination is to analyze the effect of a slanted magnetic field on the flow phenomena with heat source/sink and destructive reaction for linearly accelerated slanted plate. The governing equations have been solved by using Laplace transform strategy. The estimations of flow velocity, concentration, and temperature are exhibited graphically, while local skin friction, mass, and heat transfer rates are put on view in tabular form for different values of relevant stream parameters. It is fascinating to observe that the raise of inclination angle of an applied magnetic field diminishes both velocity profiles and local skin friction. [ABSTRACT FROM AUTHOR]

We consider a singularly perturbed elliptic Dirichlet problem in the case of a degenerate equation's multiple root. The existence of problem solution is proved. A complete asymptotic expansion of the solution is constructed and justified. It has distinctive features. The boundary layer becomes a three‐zone layer with different solution behavior in each of three zones. The solution of elliptic problem considered is a stationary solution of the corresponding parabolic problem. Asymptotic stability of this solution is proved and its attraction domain is found. We have considered the extended version of concept of stationary solution attraction domain. [ABSTRACT FROM AUTHOR]

A correct quantification of mass and energy exchange processes among Earth's land surface, groundwater, and atmosphere requires an accurate parameterization of soil hydraulic properties. Pedotransfer functions (PTFs) are useful in this regard because they estimate these otherwise difficult to obtain characteristics using texture and other ubiquitous soil data. Most PTFs estimate parameters of empirical hydraulic functions with modest accuracy. In a continued pursuit of improving global‐scale PTF estimates, we evaluated whether improvements can be obtained when estimating parameters of hydraulic functions that make physically based assumptions. To this end, we developed a PTF that estimates the parameters of the Kosugi retention and hydraulic conductivity functions (Kosugi, 1994, https://doi.org/10.1029/93WR02931, 1996, https://doi.org/10.1029/96WR01776), which explicitly assume a lognormal pore size distribution and apply the Young‐Laplace equation to derive a corresponding pressure head distribution. Using a previously developed combination of machine learning and bootstrapping, the developed five hierarchical PTFs allow for estimates under practical data‐poor to data‐rich conditions. Using an independent global data set containing nearly 50,000 samples (118,000 retention points), we demonstrated that the new Kosugi‐based PTFs outperformed two van Genuchten‐based PTFs calibrated on the same data. The new PTFs were applied to a 1 × 1 km2 global map of texture and bulk density, thus producing maps of the parameters, field capacity, wilting point, plant available water, and associated uncertainties. Soil hydraulic parameters exhibit a much larger variability in the Northern Hemisphere than in the Southern Hemisphere, which is likely due to the geographical distribution of climate zones that affect weathering and sedimentation processes. Key Points: We developed a set of hierarchical pedotransfer functions for the semiphysical Kosugi water retention modelAn evaluation using globally representative data demonstrated that the PTFs outperformed PTFs based on the van Genuchten retention modelGlobal maps of hydraulic parameters, derived quantities, and associated uncertainties were produced at 1‐km resolution [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of the time‐domain elastic wave scattering problem in an unbounded structure. The transparent boundary condition is developed to reformulate the scattering problem into an initial‐boundary value problem in an infinite slab. The well posedness and stability are established for the reduced problem in both the frequency and time domains. Our proofs are based on the energy method, the Lax‐Milgram theorem, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the elastic displacement by taking special test functions for the time‐domain variational problems of the Navier equation. [ABSTRACT FROM AUTHOR]

In this paper, we establish the consistency of the model selection criterion based on the quasi‐marginal likelihood (QML) obtained from Laplace‐type estimators. We consider cases in which parameters are strongly identified, weakly identified and partially identified. Our Monte Carlo results confirm our consistency results. Our proposed procedure is applied to select among New Keynesian macroeconomic models using US data. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new procedure to design optimal electrodes for cochlear implants. The main objective of this study is to find a set of electrode designs that maximize the focalization and minimize the power consumption simultaneously. To achieve that, a criterion to measure the ability of focalization of an electrode is proposed. It is presented a procedure to determine (1) the electrical potential induced by an electrode by solving the Laplace equation through the finite element method; (2) the response of a neuron to an applied field using NEURON, a compartmentalized cell model; (3) the optimization to find the best electrode designs according to power consumption and focalization by 2 evolutionary multiobjective methods based on the non‐dominated sorting genetic algorithm II: a straight multiobjective approach and a seeded multiobjective approach. An electrode design formed by 2 conductive rings with a possible difference of potential between them is proposed. It is analyzed that the response of the neuron is determined by the shape and the difference of the potential between the electrode rings. Our procedure successfully achieves a nondominated set of optimum electrode designs improving a standard electrode in both objectives, as designs with better focalization allow to include extra electrodes in the cochlear implant, and designs with lower power consumption extend the length of the battery. [ABSTRACT FROM AUTHOR]

Abstract: The Asian longhorned beetle Anoplophora glabripennis (Motschulsky) (Coleoptera: Cerambycidae) is one of the most dangerous xylophagous pests affecting broadleaf trees in the world. Eradication programmes are undertaken in non‐native regions, requiring extensive resources and involving high costs. An adapted strategy must be set up to optimize the ratio cost/probability of success. We developed a method to generate a risk index of A. glabripennis presence at a local scale, in the surrounding area of an infestation, using field observations (counts of adult insects, exit holes and infested trees). The method, mathematically based on the bivariate symmetric Laplace distribution, has thus reasonable input requirements. The output risk map is easy to interpret and can be directly used by decision‐makers. We used our approach in three infestations in Switzerland. The risk map represented well the insect pressure (beetle population density). We highlighted the fact that survey boundaries, commonly chosen using constant distances from the infestation, should be selected regarding the spatial distribution of the insect pressure, to prioritize monitoring activities. The risk map provides a helpful instrument for advanced survey planning after a first overview, for example to decide which area and which host trees should be inspected for infestations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider parabolic Q‐quasiminimizers related to the p‐Laplace equation in Ω T : = Ω × ( 0 , T ). In particular, we focus on the stability problem with respect to the parameters p and Q. It is known that, if Q → 1, then parabolic quasiminimizers with fixed initial‐boundary data on Ω T converge to the parabolic minimizer strongly in L p ( 0 , T ; W 1 , p ( Ω ) ) under suitable further structural assumptions. Our concern is whether or not we can obtain even stronger convergence. We will show a fairly strong stability result. [ABSTRACT FROM AUTHOR]

Abstract: Crack is one of the most important pavement condition indicators that are immediately relevant to water ingress and pavement deterioration. In practices of pavement management, crack width has been extensively referenced by highway agencies to determine pavement crack severity. Accurate measurement of pavement crack width is meaningful for highway agencies in understanding the mechanism of crack formation, and in predicting crack propagation. This article presents a new automatic method for measuring crack width using the binary crack map images. The proposed method introduces a new crack width definition and formulates it using the Laplace's Equation so that crack width can be continuously and unambiguously measured. Two algorithms, including the crack blob extraction algorithm and the crack boundary extraction algorithm, are developed to implement the proposed formulation in an automated fashion. Experimental tests using both synthetic data and field data are conducted to demonstrate the accuracy and reliability of the proposed method. A case study on crack width propagation is also performed to demonstrate the practical capacity of the proposed method. The results of the experimental tests and the outcome of the case study have demonstrated that the proposed method, together with the existing crack map extraction algorithms, provides a promising means for consistent and unambiguous crack width measurement supporting automated pavement condition evaluation. [ABSTRACT FROM AUTHOR]

Recently, there has been much interest in the solution of differential equations on surfaces and manifolds, driven by many applications whose dynamics take place on such domains. Although increasingly powerful algorithms have been developed in this field, many straightforward questions remain, particularly in the area of coupling advanced discretizations with efficient linear solvers. In this paper, we develop a structured refinement algorithm for octahedral triangulations of the surface of the sphere. We explain the composite-grid finite-element discretization of the Laplace-Beltrami operator on such triangulations and extend the fast adaptive composite-grid scheme to provide an efficient solution of the resulting linear system. Supporting numerical examples are presented, including the recovery of second-order accuracy in the case of a nonsmooth solution. [ABSTRACT FROM AUTHOR]

This article describes statistical analyses pertaining to marketing data from a large multinational pharmaceutical firm. We describe models for monthly new prescription counts that are written by physicians for the firm's focal drug and for competing drugs, as functions of physician‐specific and time‐varying predictors. Modeling patterns in discrete‐valued time series, and specifically time series of counts, based on large datasets, is the focus of much recent research attention. We first provide a brief overview of Bayesian approaches we have employed for modeling multivariate count time series using Markov Chain Monte Carlo methods. We then discuss a flexible level correlated model framework, which enables us to combine different marginal count distributions and to build a hierarchical model for the vector time series of counts, while accounting for the association among the components of the response vector, as well as possible overdispersion. We employ the integrated nested Laplace approximation (INLA) for fast approximate Bayesian modeling using the R‐INLA package (r‐inla.org). To enhance computational speed, we first build a model for each physician, use features of the estimated trends in the time‐varying parameters in order to cluster the physicians into groups, and fit aggregate models for all physicians within each cluster. Our three‐stage analysis can provide useful guidance to the pharmaceutical firm on their marketing actions. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]