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We are concerned with interior and global gradient estimates for solutions to a class of singular quasilinear elliptic equations with measure data, whose prototype is given by the p-Laplace equation -- Δp u = μ with p ∈ (1,2). The cases when p ∈ (2 - 1/n, 2) and p ∈ (3n-2/2n-1, 2 - 1/n] were studied in Duzaar and Mingione [J. Funct. Anal. 259 (2010), 379-418] and Nguyen and Phuc [J. Funct. Anal. 278 (2020), art. 108391] respectively. In this paper, we improve the results of Nguyen and Phuc and address the open case when p ∈ (1, 3n-2/2n-1]. Interior and global modulus of continuity estimates of the gradients of solutions are also established. [ABSTRACT FROM AUTHOR]

The molecular movement in single particle tracking (SPT) experiments shows a crucial role of diffusion in many biological processes such as signaling, cellular organization, transport mechanisms, and more. The SPT analysis detects not only classical Brownian motion but diffusion with other features. These include directed diffusion and confined motion. The behavior remains a challenging problem for several reasons. Due to the action of many physical processes, random trajectories of cellular molecules are segmented in different diffusive modes. Often their study requires sophisticated algorithms for the analysis of statistical properties. In this paper we consider the segment analysis for trajectories of G proteins and coupled-receptors in living cells. Their movement is often transient and switches among free diffusion, confined diffusion, directed diffusion, and immobility. Moreover, the confined segments can have both Gaussian and non-Gaussian statistics. The types of alternation of diffusive modes along the trajectories of G proteins and coupled-receptors are analyzed. [ABSTRACT FROM AUTHOR]

Renewable integration in utility grid is crucial in the current energy scenario. Optimized utilization of renewable energy can minimize the energy consumption from the grid. This demands accurate forecasting of renewable contribution and planning. Most of the researches aim to find a suitable forecasting model in terms of accuracy and error metrics. However, the uncertainty and variability in these forecasts are also significant. This work combines point forecast with interval forecast to provide comprehensive information about the forecast uncertainty. In this work, solar irradiance forecasting is carried out using artificial intelligence (AI) techniques. Forecasting is done using seasonal auto-regressive moving average with exogenous factors (SARIMAX), support vector regression (SVR), long short term memory (LSTM) techniques and performance is evaluated. SVR model exhibited the best performance with R 2 values of 0.97 and 0.96 for winter and summer respectively and 0.85 for monsoon and post-monsoon seasons. This is followed by forecast error distribution studies and uncertainty analysis. For this, SVR forecast error data is fitted using laplace distribution. Uncertainty study is carried out using confidence intervals and coverage rates. Excellent coverage rates are obtained for various confidence levels for all seasons, indicating the appropriate fitting of error distribution. For the narrow 85% confidence band, coverage rates of 89%, 95%, 90%, and 88% are obtained for winter, summer, monsoon and post-monsoon respectively. The work emphasizes the need for error-distribution studies, modeling of forecast errors and their application in providing reliable forecast intervals with the perspective of enhancing system reliability. [ABSTRACT FROM AUTHOR]

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using a generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated "peaks" and "fat" tails is also discussed. [ABSTRACT FROM AUTHOR]

The estimation of the slope (b -value) of the frequency–magnitude distribution of earthquakes is based on a formula derived by Aki decades ago, assuming a continuous exponential distribution. However, as the magnitude is usually provided with a limited resolution, its distribution is not continuous but discrete. In the literature, this problem was initially solved by an empirical correction (due to Utsu) to the minimum magnitude, and later by providing an exact formula such as that by Tinti and Mulargia, based on the geometric distribution theory. A recent paper by van der Elst showed that the b -value can be estimated also by considering the magnitude differences (which are proven to follow an exponential discrete Laplace distribution) and that in this case the estimator is more resilient to the incompleteness of the magnitude data set. In this work, we provide the complete theoretical formulation including (i) the derivation of the means and standard deviations of the discrete exponential and Laplace distributions; (ii) the estimators of the decay parameter of the discrete exponential and trimmed Laplace distributions and (iii) the corresponding formulas for the parameter b. We deduce (iv) the standard 1 σ intervals for the estimated b. Moreover, we are able (v) to quantify the error associated with the Utsu minimum-magnitude correction. Furthermore, we have discussed the formulas to produce statistically independent magnitude differences. We tested extensively the b -value estimators on simulated synthetic data sets including complete catalogues as well as catalogues affected by a strong incompleteness degree such as aftershock sequences where the incompleteness is made to vary from one event to the next. We have also analysed the real aftershock sequence of the 30/10/2016 Norcia (central Italy) to integrate the finding of the simulations. To judge the performance of the various estimators we have introduced an index p that can be seen as a non-parametric extension of the Student's t index. The main outcomes of this paper are that (1) the b -value estimators devised for continuous magnitude data are not adequate for binned magnitudes, (2) for complete data sets, estimators based on magnitudes and on magnitude differences provide substantially equivalent results, (3) for incomplete magnitude data sets, estimators based on magnitude differences provide better results and (4) for incomplete aftershock sequences there is no evidence that methods based on positive magnitude differences are superior than other methods using differences. This conclusion is further confirmed by our analysis of the above-mentioned Norcia seismic sequence. This last finding contrasts with the van der Elst's claim that the so called |${{b}_ + }$| method is the most adequate to treat real aftershock sequences. [ABSTRACT FROM AUTHOR]

A semi-analytical solution is proposed for the biohe- at equation, which includes the epidermis, dermis, and hypodermis layers in the presence of a surface pulsed heat source. A switching time sur- face heating/cooling source, which has therapeutic applications in hu- man tissue burning, is used. The interface temperature is calculated by matching the temperature and heat ux between two adjacent layers. A high-performance computing algorithm is designed and implemented by combining semigroups theory, Laplace transform, and convolution opera- tors in each layer. It is proved that the proposed solution is consistent, convergent and stable. The reliability, performance and eficiency of semi- analytical solutions are compared using the bioheat transfer module of COMSOL software based on standard finite element methods. Numerical results for three difierent medical examples are given. In uences of blood pressure on temperature along the layered skin for difierent switching and final times are discussed. [ABSTRACT FROM AUTHOR]

Abstract The molecular movement in single particle tracking (SPT) experiments shows a crucial role of diffusion in many biological processes such as signaling, cellular organization, transport mechanisms, and more. The SPT analysis detects not only classical Brownian motion but diffusion with other features. These include directed diffusion and confined motion. The behavior remains a challenging problem for several reasons. Due to the action of many physical processes, random trajectories of cellular molecules are segmented in different diffusive modes. Often their study requires sophisticated algorithms for the analysis of statistical properties. In this paper we consider the segment analysis for trajectories of G proteins and coupled-receptors in living cells. Their movement is often transient and switches among free diffusion, confined diffusion, directed diffusion, and immobility. Moreover, the confined segments can have both Gaussian and non-Gaussian statistics. The types of alternation of diffusive modes along the trajectories of G proteins and coupled-receptors are analyzed.

Aiming to address soft sensing model degradation under changing working conditions, and to accommodate dynamic, nonlinear, and multimodal data characteristics, this paper proposes a nonlinear dynamic transfer soft sensor algorithm. The approach leverages time-delay data augmentation to capture dynamics and projects the augmented data into a latent space for constructing a nonlinear regression model. Two regular terms, distribution alignment regularity and first-order difference regularity, are introduced during data projection to address data distribution disparities. Laplace regularity is incorporated into the nonlinear regression model to ensure geometric structure preservation. The final optimization objective is formulated within the framework of partial least squares, and hyperparameters are determined using Bayesian optimization. The effectiveness of the proposed algorithm is demonstrated through experiments on three public datasets. • Adaptive soft sensor combines unsupervised domain adaptation and dynamic PLS for variable conditions. • Leverages time-delay data augmentation to capture dynamics and constructs a nonlinear regression model in a latent space. • Introduces regular terms for distribution alignment and first-order differences, and incorporates Laplace regularity for geometric structure preservation. • Optimization within partial least squares framework, hyperparameters tuned by Bayesian optimization. [ABSTRACT FROM AUTHOR]

Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-Risk (EVaR) measure for Poisson, compound Poisson, Gamma, Laplace, exponential, chi-squared, inverse Gaussian distribution and normal inverse Gaussian distribution with the help of Lambert function that is a special function, generally speaking, with two branches.

The main finding of this study is the derivation of a new probability distribution that reveals interesting properties, especially with various asymmetry and kurtosi; behavior. We call this distribution the asymmetric generalized error distribution (AGED). AGED is a new contribution to the field of statistical theory, offering more flexible probability density functions, cumulative distribution functions and hazard functions than the base distribution. The AGED also includes normal uniform, Laplace, asymmetric Laplace, and generalized error distribution (GED as special cases. The mathematical and statistical features of the distribution are derived and discussed. Estimators of the parameters of the distribution are obtained using the maximum likelihood approach. In a simulation study, random samples are generated from the new probability distribution to illustrate wha ideal data looks like. Using real data from diverse applications such as health industry, and cybersecurity domains, the performance of the new distribution is compared to that of other distributions. The new distribution is found to be #AKC better fit for the data, showing great adaptability in the context of real data analysis. We expect the distribution to be applied to many more real data, anc the findings of the study can be used as a basis for future research in the field. [ABSTRACT FROM AUTHOR]

In this study, we introduce a matrix variate skew Laplace distribution as a variance-mean mixture of the matrix variate normal and the scale inverse gamma distribution. The proposed distribution is a generalization of the multivariate skew Laplace distribution studied by [1]. We explore some distributional properties of the proposed distribution such as the probability density function and the characteristic function. Also, we study the estimation of the parameters and give an EM algorithm to obtain the estimates of the parameters. Then, we give a small simulation study to illustrate the performance of the proposed EM algorithm for finding the estimates. [ABSTRACT FROM AUTHOR]

The simultaneous estimation of multiple quantiles is a crucial statistical task that enables a thorough understanding of data distribution for robust analysis and decision-making. In this study, we adopt a Bayesian approach to tackle this critical task, employing the asymmetric Laplace distribution (ALD) as a flexible framework for quantile modeling. Our methodology implementation involves the Hamiltonian Monte Carlo (HMC) algorithm, building on the foundation laid in prior work, where the error term is assumed to follow an ALD. Capitalizing on the interplay between two distinct quantiles of this distribution, we endorse a straightforward and fully Bayesian method that adheres to the non-crossing property of quantiles. Illustrated through simulated scenarios, we showcase the effectiveness of our approach in quantile estimation, enhancing precision via the HMC algorithm. The proposed method proves versatile, finding application in finance, environmental science, healthcare, and manufacturing, and contributing to sustainable development goals by fostering innovation and enhancing decision-making in diverse fields. [ABSTRACT FROM AUTHOR]

Investing in stocks and shares is a common strategy to pursue potential gains while considering future financial needs, such as retirement and children's education. Effectively managing investment risk requires thoroughly analyzing stock market returns and making informed predictions. Traditional models often utilize normal variance distributions to describe these returns. However, stock market returns often deviate from normality, exhibiting skewness, higher kurtosis, heavier tails, and a more pronounced center. This paper investigates the Laplace distribution and its generalized forms, including asymmetric Laplace, skewed Laplace, and the Kumaraswamy Laplace distribution, for modeling stock market returns. Our analysis involves a comparative study with the widely-used Variance-Gamma distribution, assessing their fit with the weekly returns of the S&P 500 Index and its eleven business sectors, drawing parallel inferences from international stock market indices like IBOVESPA and KOSPI for emerging and developed economies, as well as the 20+ Years Treasury Bond ETFs and individual stocks across varied time horizons. The empirical findings indicate the superior performance of the Kumaraswamy Laplace distribution, which establishes it as a robust alternative for precise return predictions and efficient risk mitigation in investments. [ABSTRACT FROM AUTHOR]

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]

Unidirectional liquid transport (UDLT) has been widely used in various fields as an important process for transferring both mass and energy. However, UDLT driven by a structural gradient has been witnessed for a long time only in wettable liquids. For nonwettable liquids, UDLT can hardly proceed merely by a structural gradient. Herein, we propose an asymmetrically concave structured surface (AMC-surface), featuring tip-to-base periodically arranged pyramid-shaped concave structures with a certain degree of overlap, which enables the UDLT of both wettable and nonwettable liquids. For wettable liquids, the capillary force along each corner leads to the UDLT pointing toward the base side of the concave pyramid, while for nonwettable liquids, the UDLT is attributable to the static liquid pressure overwhelming the repulsive Laplace pressure induced by the asymmetric grooves and overlapping part. As a result, both wettable and nonwettable liquids transport spontaneously and unidirectionally on the AMC-surface with no energy input. Moreover, the concave structure endows good mechanical stability and can be easily prepared using a facile nail-punching approach over a large area. We also demonstrated its application in a continuous chemical reaction in a confined area. We envision that the unique UDLT behavior on the as-developed AMC-surface will shed new light on the programmable manipulation of various liquids. [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]

Lithium-ion batteries are currently used as a key energy source in various industrial facilities, electronics, and automotive industries. However, due to the frequent charging and discharging of batteries, overcharging and overdischarging can occur, leading to fire and safety accidents as well as additional financial damages due to equipment failure. Therefore, accurately estimating the battery state of charge (SOC) is very important. In this paper, the robustness of estimation models was analyzed in relation to data collected amidst sensor failures. This analysis was especially pertinent during the battery SOC estimation process, when voltage and current sensors were prone to failure. The impact of these sensor failures on the accuracy and reliability of the SOC estimation models was rigorously scrutinized. Normal data was trained as training data, and Gaussian distribution, Laplace and chi-square combined distribution, Add bias distribution were employed as the test data. Herein, multilayer neural network, long short-term memory, gated recurrent unit, gradient boosting machine (GBM) were used as neural networks, the failure signal processing performance of each estimation algorithm was compared and analyzed, and the failure diagnosis was performed using support vector machine and GBM. [ABSTRACT FROM AUTHOR]

This research delves into the exploration of a statistical testing approach grounded in Laplace transform techniques specifically tailored for the New Better than Used Laplace transform order (NBUL) class of life distributions. The developed test exhibits versatility, accommodating both complete and censored data, and critical values are systematically calculated for its application. Beyond the methodological presentation, our study investigates the test's statistical power and explores Pitman's asymptotic efficiency concerning various alternative distributions. Comparative analyses with other tests within the same class contribute to a comprehensive understanding of the proposed approach. To demonstrate practical applicability, we apply this novel testing technique to authentic engineering and medical datasets. The outcomes of these applications serve as illustrative examples, showcasing the effectiveness and relevance of the proposed methodology in real-world scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we study a Cauchy problem for a space–time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp - Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp (Rd) and a time weighted Lr (Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space. [ABSTRACT FROM AUTHOR]

Seismic b-value is one of the most important parameters for seismological research and seismic hazards assessment, while the accuracy of the b-value largely depended on the completeness of seismic catalog. This article compares eight methods for estimating the minimum magnitude of completeness (Mc). The results indicate that the modified maximum curvature method (MMAXC), exhibits greater stability and accuracy, closely approximating the standard M[sub c] obtained from the synthetic seismic catalogs. We then calculate the b-value using the instrumental seismic catalog from 2000-2023 in the eastern Tibetan Plateau. The results indicate that the five major earthquakes occur in regions with lower b-value. In addition, the temporal evolution of b-value before and after major earthquakes exhibits a common trend of decreasing before earthquakes, and increasing after earthquakes, which may reflect the stress accumulation and release during earthquakes. Combining the results of maximum shear strain rate and b-value, we identify five regions characterized by low b-value and high shear strain rate, indicating a higher potential seismic hazard in the future. [ABSTRACT FROM AUTHOR]

We investigate the stochastic unstable nonlinear Schrödinger equation through bi-random sources. Specifically, we solve this equation via Itô sense, with the parameter following Laplace and Gumbel distributions. We provide vital stochastic solutions in applied sciences. We employ He's semi-inverse technique in order to provide these solutions in a unified way. Actually, this is the first time that the same model has been taken into account in these circumstances. In order to investigate the real relevance of the stochastic unstable nonlinear Schrödinger equation, we provide the simulations for some of the collected solutions using the appropriate parameter settings provided by the MATLAB software. Finally, our renewed drive might expand to incorporate further emerging natural science models. [ABSTRACT FROM AUTHOR]

The discrete Weibull model can be adapted to capture different levels of dispersion in the count data. This paper takes into account the direct relationship between explanatory variables and the median of discrete Weibull response variable. Additionally, it provides the Bayesian estimate of the discrete Weibull regression model using the random walk Metropolis algorithm. The prior distributions of the coeficient predictors were carried out based on the uniform non-informative, normal and Laplace distributions. The performance of the Bayes estimators was also compared with the maximum likelihood estimator in terms of the mean square error and the coverage probability through the Monte Carlo simulation study. Meanwhile, a real data set was analyzed to show how the proposed model and the methods work in practice. [ABSTRACT FROM AUTHOR]

Snapping Shrimps (SSs) live in a warm ocean except the North and South Poles, and they are characterized by generating strong shock waves underwater using large claws. Shock waves generated by these SSs are used for marine noise research as a signal and as a noise source, because they cause a decrease in the Signal-to-Noise Ratio (SNR), acting as one of the disruptors in fields such as sonar for target detection and underwater communication. A state-of-the-art technique to detect Snapping Shrimp Noise (SSN) is Linear Prediction (LP) analysis. Using the feature where SSN occurs for a very short time, the SSN interval was detected based on the phenomenon where the residuals appear large in the SSN interval when the LP analysis is used. In this paper, we propose an SSN interval detection technique using the Likelihood Ratio (LR) as a follow-up study to the LP-analysis-based method for further performance improvements. The proposed method was used to analyze the statistical distribution characteristics of the LP residual of SSNs compared to Gaussian, Laplace, and Gamma distributions through the Goodness-Of-Fit test. Based on this, the statistical-model-based LRs of the three distributions were computed to detect the SSN interval. Comparing the proposed method with the state-of-the-art method, the proposed method achieved 0.0620, 0.0675, and 0.0662 improvements in Gaussian, Laplace, and Gamma distributions in the Receiver Operating Characteristic curve and Area Under Curve, respectively. The study results confirmed that the proposed method can operate effectively in the marine acoustic environment. This can help find accurate intervals for the automatic labeling of or reduction in SSN. [ABSTRACT FROM AUTHOR]

In this paper, we study a Cauchy problem for a space-time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp(Rd) and a time weighted Lr(Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space. [ABSTRACT FROM AUTHOR]

Let s ∈ be an open bounded set. In this work we study the existence of solutions to problems (E±) Lu ± g(u) = μ and u = 0 a.e. in ℝN \ Ω, where g ∈ C(ℝ) is a nondecreasing function, μ is a bounded Radon measure on and Ω is an integro-differential operator with order of differentiability s ∈ (0, 1) and summability ... More precisely, L is a fractional p-Laplace type operator. We establish sufficient conditions for the solvability of problems (E±). In the particular case ..., these conditions are expressed in terms of Bessel capacities. [ABSTRACT FROM AUTHOR]

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using a generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated “peaks” and “fat” tails is also discussed.

In view of the unstable electromagnetic performance of the air gap magnetic field caused by the torque ripple and harmonic interference of a multi-slot and multi-pole low-speed, high-torque permanent magnet synchronous motor, we propose a simplified model of double-layer permanent magnets. The model is divided into an upper and a lower subdomain, with the upper subdomain being an ideal circular ring and the lower subdomain being a segmented sector ring. Moreover, we develop an exact analytical model of the motor that predicts the magnetic field distribution based on Laplace's and Poisson's equations, which is solved using the method of separating variables. Taking a 40p168s low-speed, high-torque permanent magnet synchronous motor as an example, the accuracy of the model is verified by comparison with an ideal circular ring model, a segmented sector ring model, and the finite element method. Based on the proposed simplified model, three combined permanent magnets considering both edge-cutting and polar arc cutting structures are proposed, which are chamfered, rounded, and rectangular combinations. Under the premise of a consistent edge-cutting amount, the electromagnetic characteristics of the three combination types of permanent magnets are compared using the finite element method. The results show that the electromagnetic characteristics of the chamfered combination PM are superior to those of the other two combinations. Finally, a prototype is manufactured and tested to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GAL) distributions can be seen as skewed and semi-heavy-tailed extensions of the Gaussian distribution. Models driven by these more flexible noise distributions are then regarded as flexible extensions of simpler Gaussian models. Inferential procedures tend to overestimate the degree of non-Gaussianity in the data and therefore we propose controlling the flexibility of these non-Gaussian models by adding sensible priors in the inferential framework that contract the model towards Gaussianity. In our venture to derive sensible priors, we also propose a new intuitive parameterization of the non-Gaussian models and discuss how to implement them efficiently in Stan. The methods are derived for a generic class of non-Gaussian models that include spatial Mat´ern fields, autoregressive models for time series, and simultaneous autoregressive models for aerial data. The results are illustrated with a simulation study and geostatistics application, where priors that penalize model complexity were shown to lead to more robust estimation and give preference to the Gaussian model, while at the same time allowing for non-Gaussianity if there is sufficient evidence in the data. [ABSTRACT FROM AUTHOR]

Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their certain fixed point. We consider the motion of a subdiffusive particle with a constant drift under Poissonian resetting. In this model the stochastic process is Brownian motion subordinated by an inverse infinitely divisible process (subordinator). Although this approach includes a wide class of subdiffusive system with Poissonian resetting by using different subordinators, each of such systems has a stationary state with the asymmetric Laplace distribution in which the scale and asymmetric parameters depend on the Laplace exponent of the subordinators used. Moreover, the mean time for the particle to reach a target is finite and has a minimum, optimal with respect to the resetting rate. Features of Lévy motion under this resetting and the effect of a linear potential are discussed. [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]

In this work, a procedure to obtain two-port admittance models of buried cables illuminated by incident electromagnetic fields for the analysis of transients in the frequency domain is presented. The procedure is based on cascading two-port admittance models of various cable segments, avoiding the numerical problems that chain matrix representations may have. To obtain results in the time domain, the Numerical Laplace Transform method is used. [ABSTRACT FROM AUTHOR]

An internal heat source is assumed to act on a cylindrical body with radiation-like boundary conditions to explore the memory-dependent thermoelastic response of a solid object. The top and bottom surfaces of the solid cylinder are subjected to additional heating conditions. To obtain the thermal behaviour of the considered medium, the integral transform method is used, while the inversion solution of the heat transfer equation, the thermoelastic displacement and stress functions are presented in the Laplace domain due to the complexity of the calculation. To understand the numerical calculations, the material properties of aluminium metal are taken into account, and all the obtained results are presented graphically. [ABSTRACT FROM AUTHOR]

Introduction: Epidemiological modelling of infectious diseases plays an important role in driving public health policy. Commonly used models are described, including those based on exponential growth (Laplace and related distributions); susceptible-infected-removed; the Gompertz distribution; and the skew-reflected-Gompertz distribution. These are all sensitive to the timing of peak infection. The development of a novel method for forecasting the number of deaths occurring during epidemics of infectious diseases is described.Methods: The mathematical development of the authors' novel asymmetric difference model is detailed in this paper. Its predictions for mortality rates associated with the COVID-19 pandemic for 14 countries were compared with the corresponding published mortality data.Results: Forecasts by the asymmetric difference model of deaths from SARS-CoV-2 in different countries, actual recorded deaths to 30th June 2020, and corresponding errors included UK (42,700; 55,904; − 24%); Poland (1490; 1444; +3%); Denmark (580; 605; − 4%); Netherlands (6510; 6189; +5%); France (34,280; 29,836; +15%); Canada (1500; 8591; − 78%); USA (44,540; 124,734; − 64%); and Italy (22,020; 34,980; − 37%). The model output was dependent upon forecast date accuracy for the peak of the disease outbreak. For Spain, the forecast date was one day early and for 10 (71%) countries the forecast peak occurred within seven days (inclusive) of the actual date.Discussion: Mortality prediction by the asymmetric difference model is relatively accurate. Furthermore, this new model does not appear to be as unduly sensitive to the timing of peak infection as other models. Indeed, its prediction of peak infection also appears to be relatively accurate. [ABSTRACT FROM AUTHOR]

The Laplace distribution, also known as the double exponential distribution, is a continuous probability distribution that is often used for modelling the data having heavy tails. In this paper, we proposed the Neutrosophic Laplace distribution which is the extension of the classical Laplace Distribution. We derived various statistical properties of the Neutrosophic Laplace Distribution such as mean, variance, skewness, rth moment, quartiles, and moment-generating function. The expressions for the estimation of the parameters are also derived using the maximum likelihood function of the distribution. A simulation study has been done to evaluate the performance of estimates. An application of the Neutrosophic Laplace Distribution is discussed to study the daily return of the NIFTY50 from Indian Stock Market. The analysis shows that the neutrosophic Laplace Model is acceptable, effective, and adequate for dealing with uncertainty in an unpredictable context. [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]

Intelligent manufacturing workshop uses automatic guided vehicles as an important logistics and transportation carrier, and most of the existing research adopts the intelligent manufacturing workshop layout and Automated Guided Vehicle (AGV) path step-by-step optimization, which leads to problems such as low AGV operation efficiency and inability to achieve the optimal layout. For this reason, a smart manufacturing assembly line layout optimization model considering AGV path planning with the objective of minimizing the amount of material flow and the shortest AGV path is designed for the machining shop of a discrete manufacturing enterprise of a smart manufacturing company. Firstly, the information of the current node, the next node and the target node is added to the heuristic information, and the dynamic adjustment factor is added to make the heuristic information guiding in the early stage and the pheromone guiding in the later stage of iteration; secondly, the Laplace distribution is introduced to regulate the volatilization of the pheromone in the pheromone updating of the ant colony algorithm, which speeds up the speed of convergence; the path obtained by the ant colony algorithm is subjected to the deletion of the bi-directional redundant nodes, which enhances the path smoothing degree; and finally, the improved ant colony algorithm is fused with the improved dynamic window algorithm, so as to enable the robots to arrive at the end point safely. Simulation shows that in the same map environment, the ant colony algorithm compared with the basic ant colony algorithm reduces the path length by 40% to 67% compared to the basic ant colony algorithm and reduces the path inflection points by 34% to 60%, which is more suitable for complex environments. It also verifies the feasibility and superiority of the conflict-free path optimization strategy in solving the production scheduling problem of the flexible machining operation shop. [ABSTRACT FROM AUTHOR]

The proposed study is focused to introduce a novel integral transform operator, called Generalized Bivariate (GB) transform. The proposed transform includes the features of the recently introduced Shehu transform, ARA transform, and Formable transform. It expands the repertoire of existing Laplace-type bivariate transforms. The primary focus of the present work is to elaborate fashionable properties and convolution theorems for the proposed transform operator. The existence, inversion, and duality of the proposed transform have been established with other existing transforms. Implementation of the proposed transform has been demonstrated by applying it to different types of differential and integral equations. It validates the potential and trustworthiness of the GB transform as a mathematical tool. Furthermore, weighted norm inequalities for integral convolutions have been constructed for the proposed transform operator. [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]

The total electron content (TEC) derived from the Global Navigation Satellite System (GNSS) has been widely used to study the ionosphere. The evaluation of the derivation method is usually based on the fitting residuals, which are the difference between the estimate and observation. However, there are few studies on the statistical characteristics of fitting residuals. The characteristics of fitting residuals and estimation errors are studied with international reference ionosphere (IRI-2016) and GNSS observations. First, the systematic estimation errors caused by mathematical modeling and related assumptions are discussed with IRI-2016. The errors are 1 TECU and 0.5 TECU for slant TEC (STEC) and vertical TEC (vTEC), respectively. The fitting residuals of STEC observations (Δ STEC r ) are studied by different noise models, including independent and identically distributed (IID) Gaussian noise, independent and non identical distributed (INID) Gaussian noise and INID Laplace noise. The statistical analysis shows that the distribution of Δ STEC r for the whole observations of all receivers is Gaussian when the noise is IID Gaussian, while it is Laplace for INID Gaussian or Laplace noise. The Δ STEC r reflects the statistical characteristic of noise. The estimation error of STEC (Δ STEC), which is the difference between the estimate ( STEC e ) and the model STEC (STEC) is discussed with IRI-2016. The distribution of Δ STEC is neither Gaussian nor Laplace, and STEC e is a biased estimate of STEC. The distribution of estimation error of vTEC (Δ vTEC) is neither Gaussian nor Laplace. Finally, the Δ STEC r is studied with GNSS observations. The distribution of Δ STEC r is more consistent with Laplace than Gaussian, indicating that the noise of the GNSS observations should not be modeled as IID Gaussian distribution. [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]

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]

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]

In this research, we proposed coupling the Laplace transform method and the homotopy Perturbation Method (LHPM). We employed the fusion of the Laplace method to make up for the shortcomings of other semi-analytical approaches like the homotopy perturbation method, variation iteration method, and the Adomian decomposition method. We aim to obtain an approximate and semi-analytic solution of the n-dimensional system of nonlinear partial differential equations. N-dimensional partial differential equations with nonlinear terms are known as nonlinear partial differential equations. They have been used to solve mathematical problems like the Poincare conjecture and the Calabi-Yau conjecture and describe physical systems, from gravity to fluid dynamics. Therefore, we proffer a semi-analytic solution in the form of a Taylor multivariate series of displacements x, y, and time t using the proposed method. A sideby-side comparison was carried out to compare the exact solution with the new solution using 3-dimensional graphs, and thus the graph analysis followed. Results show excellent agreement, and the emergence of this method as a viable alternative demonstrates its viability by requiring fewer computations and being much easier and more convenient than others, making it suitable for widespread use in engineering as well. [ABSTRACT FROM AUTHOR]

This paper proposes new improved binary versions of the Sine Cosine Algorithm (SCA) for the Feature Selection (FS) problem. FS is an essential machine learning and data mining task of choosing a subset of highly discriminating features from noisy, irrelevant, high-dimensional, and redundant features to best represent a dataset. SCA is a recent metaheuristic algorithm established to emulate a model based on sine and cosine trigonometric functions. It was initially proposed to tackle problems in the continuous domain. The SCA has been modified to Binary SCA (BSCA) to deal with the binary domain of the FS problem. To improve the performance of BSCA, three accumulative improved variations are proposed (i.e., IBSCA1, IBSCA2, and IBSCA3) where the last version has the best performance. IBSCA1 employs Opposition Based Learning (OBL) to help ensure a diverse population of candidate solutions. IBSCA2 improves IBSCA1 by adding Variable Neighborhood Search (VNS) and Laplace distribution to support several mutation methods. IBSCA3 improves IBSCA2 by optimizing the best candidate solution using Refraction Learning (RL), a novel OBL approach based on light refraction. For performance evaluation, 19 real-wold datasets, including a COVID-19 dataset, were selected with different numbers of features, classes, and instances. Three performance measurements have been used to test the IBSCA versions: classification accuracy, number of features, and fitness values. Furthermore, the performance of the last variation of IBSCA3 is compared against 28 existing popular algorithms. Interestingly, IBCSA3 outperformed almost all comparative methods in terms of classification accuracy and fitness values. At the same time, it was ranked 15 out of 19 in terms of number of features. The overall simulation and statistical results indicate that IBSCA3 performs better than the other algorithms. [ABSTRACT FROM AUTHOR]

By using a Gaussian process prior and a location-scale mixture representation of the asymmetric Laplace distribution, we develop a Bayesian analysis for the composite quantile single-index regression model. The posterior distributions for the unknown parameters are derived, and the Markov chain Monte Carlo sampling algorithms are also given. The proposed method is illustrated by three simulation examples and a real dataset. [ABSTRACT FROM AUTHOR]

We prove local Calderón-Zygmund type estimates for the gradient of weak solutions to degenerate or singular parabolic equations of p-Laplacian type with p > 2n/n+2 in weighted Lebesgue spaces Lqw. We introduce a new condition on the weight w which depends on the intrinsic geometry concerned with the parabolic p-Laplace problems. Our condition is weaker than the one in [13], where similar estimates were obtained. In particular, in the case p = 2, it is the same as the condition of the usual parabolic Aq weight. [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]

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]

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]