Search

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]

In the area of information retrieval, in order to improve search accuracy and reduce communication overhead, there is an increasing tendency to adopt ranked search in engines. Ranked search allows cloud servers to search for the top k most relevant documents based on the relevance score between the query keywords and the documents. Recently, with the increasing popularity of encrypted search technologies, ranked searchable encryption is proposed accordingly which focuses on solving ranked search problem over encrypted databases. However, recent studies show that some privacy protection methods commonly used in ranked searchable encryption, like order-preserving encryption (OPE), have some security problems. These problems may lead to the leakage of the relevant ranking privacy information. Meanwhile, most of the existing ranked searchable encryption schemes do not consider the problem of payment for outsourced services. In this paper, we propose a scheme called ranked searchable encryption based on differential privacy and blockchain (DPB-RSE). Specifically, we first add noise drawn from a Laplace distribution into the relevance score to disturb its value. Then we design a smart contract to verify the correctness of the results returned by the cloud server and realize payment fairness. The experiment results demonstrate that the accuracy of search results in this scheme can reach 94% in a small privacy budge. [ABSTRACT FROM AUTHOR]

Linear mixed models are traditionally used for jointly modeling (multivariate) longitudinal outcomes and event-time(s). However, when the outcomes are non-Gaussian a quantile regression model is more appropriate. In addition, in the presence of some time-varying covariates, it might be of interest to see how the effects of different covariates vary from one quantile level (of outcomes) to the other, and consequently how the event-time changes across different quantiles. For such analyses linear quantile mixed models can be used, and an efficient computational algorithm can be developed. We analyze a dataset from the Acute Lymphocytic Leukemia (ALL) maintenance study conducted by Tata Medical Center, Kolkata. In this study, the patients suffering from ALL were treated with two standard drugs (6MP and MTx) for the first two years, and three biomarkers (e.g. lymphocyte count, neutrophil count and platelet count) were longitudinally measured. After treatment the patients were followed nearly for the next three years, and the relapse-time (if any) for each patient was recorded. For this dataset we develop a Bayesian quantile joint model for the three longitudinal biomarkers and time-to-relapse. We consider an Asymmetric Laplace Distribution (ALD) for each outcome, and exploit the mixture representation of the ALD for developing a Gibbs sampler algorithm to estimate the regression coefficients. Our proposed model allows different quantile levels for different biomarkers, but still simultaneously estimates the regression coefficients corresponding to a particular quantile combination. We infer that a higher lymphocyte count accelerates the chance of a relapse while a higher neutrophil count and a higher platelet count (jointly) reduce it. Also, we infer that across (almost) all quantiles 6MP reduces the lymphocyte count, while MTx increases the neutrophil count. Simulation studies are performed to assess the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

According to the Ray-Knight description, the Brownian local time in some conditional probability space is a diffusion process with respect to spatial variable. This diffusion has a local time. Thus the following definition of local time of the original Brownian local time seems to be natural: such a process is called the second-order Brownian local time. The paper studies the Laplace transform of the distribution of the Brownian local time of the second order. [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]

A family of parsimonious contaminated shifted asymmetric Laplace mixtures is developed for unsupervised classification of asymmetric clusters in the presence of outliers and noise. A series of constraints are applied to a modified factor analyzer structure of the component scale matrices, yielding a family of twelve models. Application of the modified factor analyzer structure and these parsimonious constraints makes these models effective for the analysis of high-dimensional data by reducing the number of free parameters that need to be estimated. A variant of the expectation-maximization algorithm is developed for parameter estimation with convergence issues being discussed and addressed. Popular model selection criteria like the Bayesian information criterion and the integrated complete likelihood (ICL) are utilized, and a novel modification to the ICL is also considered. Through a series of simulation studies and real data analyses, that includes comparisons to well-established methods, we demonstrate the improvements in classification performance found using the proposed family of models. [ABSTRACT FROM AUTHOR]

We present a novel depth from focus technique. Following prior work, our pipeline starts with a focal stack and an estimation of the amount of defocus as given by, for instance, the ring difference filter. To improve robustness to outliers while avoiding to rely on costly nonlinear optimizations, we propose an original scheme that linearly scans the profile over a fixed size window, searching for the best peak within each window using a linearized least-squares Laplace regression. As a post-process, depth estimates with low confidence are reconstructed though an adaptive moving least squares filter. We show how to objectively evaluate the performance of our approach by generating synthetic focal stacks from which the reconstructed depth maps can be compared to ground truth. Our results show that our method achieves higher accuracy than previous nonlinear Laplace regression technique, while being orders of magnitude faster. [ABSTRACT FROM AUTHOR]

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered. [ABSTRACT FROM AUTHOR]

Regression model is a popular and well-acknowledged technique for finding a relationship between random phenomena. In this context, the normality assumption on the error terms is one of the challenging issues in practical studies because many phenomena in the real world are prone to skewness, peakness, and outliers. In this paper, a new generalization of nonlinear regression models is postulated by considering asymmetric Laplace distribution on the error terms to cover the drawbacks of the normal-based model in accommodating skew data with peakness and mild outliers. We present three stochastic representations of the model which enables us to develop an expectation–maximization (EM) algorithm to computationally obtain the maximum-likelihood (ML) parameter estimates. The observed information matrix is computed by adopting an information-based approach. The Bayesian analysis for the proposed model is also investigated. Finally, experiments on the simulation and real-world datasets illustrate some computational and robust aspects of the proposed model. [ABSTRACT FROM AUTHOR]

In recent years, deep learning has been widely employed in the field of image compression, the most significant of which is the lossy image compression method on the basis of convolutional neural networks. And we study the application of convolutional neural networks to remote sensing image compression. Consequently, we implement an enhanced residual attention module (ERAM) on the primary and hyper coders. ERAM can apply a spatial attention mechanism to generate importance masks for potential features of the original image. And the importance mask can adaptively adjust the bit distribution and allocate more bits to substantial target regions and fewer bits to unimportant background regions. Additionally, ERAM has the capacity to lessen the channel redundancy of potential features. Furthermore, an accurate probability estimate of a potential feature can affect to a great degree the effectiveness of entropy coding and hence image compression. We propose to utilise the discrete mixed Laplace entropy model to parameterize the probability distribution of latent features, which can improve the compression efficiency of latent features in the entropy encoding process. In the field of remote sensing image compression, the experiments demonstrate that the algorithm described in this paper has good subjective effects as well as good objective effects. [ABSTRACT FROM AUTHOR]

We propose novel goodness-of-fit tests for the Weibull distribution with unknown parameters. These tests are based on an alternative characterizing representation of the Laplace transform related to the density approach in the context of Stein's method. Asymptotic theory of the tests is derived, including the limit null distribution, the behaviour under contiguous alternatives, the validity of the parametric bootstrap procedure, and consistency of the tests against a large class of alternatives. A Monte Carlo simulation study shows the competitiveness of the new procedure. Finally, the procedure is applied to real data examples taken from the materials science. [ABSTRACT FROM AUTHOR]

Various load balancing policies are known to achieve vanishing waiting times in the large-scale limit, that is, when the number of servers tends to infinity. These policies either require a communication overhead of one message per job or require job size information. Load balancing policies with an overhead below one message per job are called hyperscalable policies. While these policies often have bounded queue length in the large-scale limit and work well when the overhead is somewhat below one, they show poor performance when the communication overhead becomes small, that is, the mean response time tends to infinity when the overhead tends to zero even at low loads. In this paper, we introduce a hyperscalable load balancing policy, called Join-Up-To(m), that remains effective even when the communication overhead tends to zero. To study its performance under general job size distributions, we make use of the "queue at the cavity" approach. We provide explicit results for the first two moments of the response time, the generating function of the queue length distribution and the Laplace transform of the response time. These results show that the mean response time only depends on the first two moments of the job size distribution. [ABSTRACT FROM AUTHOR]

In a one-way design with unknown and unequal error variances, we are interested in testing the null hypothesis H 0 : μ 1 = μ 2 = ⋯ = μ k against the ordered alternative H 1 : μ 1 ≤ μ 2 ≤ ⋯ ≤ μ k (with at least one strict inequality). We propose the likelihood ratio test (LRT) as well as two Min-T tests (Min-T and AMin-T) and study their asymptotic behaviour. For better finite sample properties, a parametric bootstrap procedure is used. Asymptotic accuracy of the parametric bootstrap is established. Simulation results show that all the tests control the nominal level in case of small, moderate, and highly unbalanced sample sizes. This even holds for combinations with large variances. However, the asymptotic likelihood ratio test (ALRT) achieves the nominal size only for large samples and k = 3 . Power comparisons between LRT and Min-T test show that the LRT has more power than Min-T. However, the Min-T test is easier to use as it does not require evaluation of MLEs. Similar observations are made while comparing ALRT and AMin-T test. The robustness of these tests under departure from normality is also investigated by considering five non-normal distributions (t-distribution, Laplace, exponential, Weibull, and lognormal). When high variances are combined with small or highly unbalanced sample sizes, the tests are observed to be robust only for symmetric distributions. If variances of groups are equal and sample sizes of each group are at least 10, the proposed tests perform satisfactorily for symmetric and skewed distributions. R packages are developed for all tests and a practical example is provided to illustrate their application. [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]

Despite the urgent need for an effective prediction model tailored to individual interests, existing models have mainly been developed for the mean outcome, targeting average people. Additionally, the direction and magnitude of covariates' effects on the mean outcome may not hold across different quantiles of the outcome distribution. To accommodate the heterogeneous characteristics of covariates and provide a flexible risk model, we propose a quantile forward regression model for high-dimensional survival data. Our method selects variables by maximizing the likelihood of the asymmetric Laplace distribution (ALD) and derives the final model based on the extended Bayesian Information Criterion (EBIC). We demonstrate that the proposed method enjoys a sure screening property and selection consistency. We apply it to the national health survey dataset to show the advantages of a quantile-specific prediction model. Finally, we discuss potential extensions of our approach, including the nonlinear model and the globally concerned quantile regression coefficients model. [ABSTRACT FROM AUTHOR]

The objective of this research is to propose a fuzzy solution for a specific type of uncertain fractional descriptor linear systems referred to as granular fractional descriptor linear systems (gr-FFDLSs). The coefficients, boundary conditions, and parameters in gr-FFDLSs are represented as fuzzy numbers. This type of system also encompasses the concept of fractional order granular Caputo (gr-Caputo) fuzzy derivative. To achieve this goal, the gr-Caputo fuzzy derivative of order n - 1 < β < n , where n is a natural number, is defined. Furthermore, the granular fuzzy Laplace transforms of the fractional order gr-Caputo fuzzy derivative and fractional order granular fuzzy integrals are introduced. Using the definition of fractional order gr-Caputo fuzzy derivative, fuzzy Drazin inverse matrix, and Laplace transformation, the solution to the state equation of granular descriptor fuzzy fractional linear systems is obtained. Two techniques, the fuzzy shuffle algorithm and the fuzzy Drazin inverse method, are presented to find the fuzzy solution of gr-FFDLSs. To demonstrate the effectiveness of these techniques, two examples are provided to show that they can produce accurate solutions for gr-FFDLSs. [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]

In meta-analysis model, due to the appearance of publication bias or outliers, as well as the small sample size, the normal assumption is usually unreliable. Therefore, the exploration of more robust estimation, such quantile regression (QR) method, is extremely important in meta-analysis area. This paper studies the QR estimation method in random-effects meta-analysis model based on the reformulation by asymmetric Laplace distribution (ALD). The maximum likelihood estimation using Monte Carlo Expectation Maximization algorithm and the Bayesian estimation using Markov chain Monte Carlo (MCMC) algorithm are proposed for computation of the QR estimates. The significance tests of regression coefficients are suggested using likelihood ratio statistics. For MCMC algorithm, a simple and efficient Gibbs sampling algorithm is employed based on a location-scale mixture representation of the ALD, and information criterions are considered for choosing the hyper-parameters. Monte Carlo simulations are conducted to study the finite sample performance of the proposed methodology and analysis of two real data sets are presented for illustrations. Our results show that QR estimation methods perform very well, especially in case of non-normal assumption in meta-regression models. The detailed algorithms and software code are available for easy use in applications. [ABSTRACT FROM AUTHOR]

We study the parabolic equations involving local and nonlocal p-Laplace-type operators. Under the assumption that 2 < p < ∞ , an intrinsic Harnack inequality of nonnegative weak solutions to such problem is established by employing the energy estimates, De Giorgi lemma, and measure theoretical argument. [ABSTRACT FROM AUTHOR]

In this paper, we derive asymptotic crack tip fields during damage and tearing of a neo-Hookean sheet. The material damage near the crack tip is characterized by an exponential damage mode inspired by the damage distribution observed in a phase field model in Part I. The asymptotic governing equations consist of a quasi-linear eigenproblem for the deformed coordinates which reduce to the eigenproblem for a Laplace equation in the case of a purely elastic neo-Hookean sheet. The asymptotic fields are complemented by finite element results for a long-notched strip under uniaxial stretch. The asymptotic analysis indicates some interesting scaling relations and distribution features of the crack tip fields that are consistent with those observed in the phase field modelling. In particular, the stress component perpendicular to crack faces, σ 22 , vanishes at the crack tip instead of approaching infinity as observed in a purely elastic neo-Hookean sheet. Its magnitude is proportional to the critical energy release rate G f and inversely proportional to the internal length scale in a scaled coordinate (scaled by the internal length scale ℓ ), i.e., σ 22 ∼ G f ℓ . The near-tip crack faces become more blunted in comparison to a purely elastic neo-Hookean sheet. [ABSTRACT FROM AUTHOR]

In this paper, we propose a weighted extension of the family of multivariate Generalized Asymmetric Laplace (GAL) distributions. This extension is formed as a variance-mean mixture of the multivariate normal distribution and the weighted gamma distribution. By using the weighted gamma distribution as the mixing distribution, the resulting family of weighted GAL (WGAL) distributions gains an additional parameter to further regulate kurtosis and tail thickness; this is an advantage over the family of GAL distributions for modeling data sets. In particular, this new parameter provides great flexibility in adjusting the kurtosis and tail thickness for some members of the GAL distributions family, since these distributions are the widely used members of the GAL family without any shape parameter regulating kurtosis and tail thickness. After defining the multivariate WGAL distributions family and constructing the probability density function, we give some special cases of the new family and examine various properties of the new distributions, such as linear transformations, conditional distributions, and multivariate kurtosis measure. We study the maximum likelihood (ML) estimation to estimate the parameters and describe an algorithm based on the expectation maximization (EM) principle to obtain the ML estimates. We also provide simulation studies and real data examples to explore the modeling capacity of some distributions belonging to the newly proposed family of distributions. [ABSTRACT FROM AUTHOR]

The literature on variable selection for mean regression is quite rich, both in the classical as well as in the Bayesian setting. However, if the goal is to assess the effects of the predictors at different levels of the response variable then quantile regression is useful. In this paper, we develop a Bayesian variable selection method for longitudinal response at some prefixed quantile levels of the response. We consider an Asymmetric Laplace Distribution (ALD) for the longitudinal response, and develop a simple Gibbs sampler algorithm for variable selection at each quantile level. We analyze a dataset from the health and retirement study (HRS) conducted by the University of Michigan for understanding the relationship between the physical health and the financial health of the aged individuals. We consider the out-of-pocket medical expenses as our response variable since it summarizes the physical and the financial well-being of an aged individual. Our proposed approach efficiently selects the important predictors at different prefixed quantile levels. Simulation studies are performed to assess the practical usefulness of the proposed approach. We also compare the performance of the proposed approach to some other existing methods of variable selection in quantile regression. [ABSTRACT FROM AUTHOR]

The paper presents a three-dimensional hydrodynamic mathematical model that takes into account the processes of salt and heat transport in the Sea of Azov and makes it possible to obtain three-dimensional fields of water flow velocities, pressure, sea water density, salinity, and temperature. The model includes the Navier–Stokes equations of motion, the continuity equation in the case of variable density, and the equations of heat and salt transport. Boundary and initial conditions are specified. The diffusion–convection–reaction equation is approximated in time using weighted schemes. Approximation in spatial variables in the problem of determining the velocity field of the aquatic environment was performed by the balance method, taking into account the filling factors of the control regions. The initial distributions of salinity and temperature, which have a sufficient degree of smoothness at the points of setting their values, was performed using the Laplace equation. Maps of salinity and temperature of the Sea of Azov were obtained by interpolation and superimposing the boundaries of the region. Stationary regimes of heat and salt transfer have been studied. Based on the results of monitoring the water area, three-dimensional mathematical models of the movement of the aquatic environment were built, designed to predict possible scenarios for the development of the Azov Sea ecosystem, making it possible to study how anaerobic contamination areas emerge and take timely measures to localize them. To refine the input data of the mathematical model, an algorithm based on the Kalman filter was developed and implemented, which made it possible to obtain the minimum variance of the unbiased estimate of the state of the dynamic system. The elements of the software package are listed, making it possible to simulate hydrodynamic processes in shallow water bodies with complex spatial structures of currents with the transport of salts and heat. [ABSTRACT FROM AUTHOR]

This paper is devoted to study censored δ -shock models for both cases when the intershock times have discrete and continuous distributions. In particular, the distribution and moments of the system's lifetime are studied via probability generating functions and Laplace transforms. For discrete intershock time distributions, several recursions for evaluating the probability mass function, the survival function and the moments of the system's lifetime are given. As it is shown for the discrete case, the distribution of the system's lifetime is directly linked with matrix-geometric distributions for particular classes of intershock time distributions, such as phase-type distributions. Thus, matrix-based expressions are readily obtained for the exact distribution of the system's lifetime under discrete setup. Also, discrete uniform intershock time distributions are examined. For the case of continuous intershock time distributions, it is shown that the shifted lifetime has a compound geometric distribution, and based on this, the distribution of the system's lifetime is approximated via discrete mixture distributions having a mass at δ and matrix-exponential distributions for the continuous part. Both for the discrete and the continuous case, Lundberg-type bounds and asymptotics for the survival function of system's lifetime are given. To illustrate the results, some numerical examples, both for the discrete and the continuous case, are also given. [ABSTRACT FROM AUTHOR]

In this paper, we develop a joint quantile regression model for correlated mixed discrete and continuous data using Gaussian copula. Our approach entails specifying marginal quantile regression models for the responses, and combining them via a copula to form a joint model. For modeling the quantiles of continuous response an asymmetric Laplace (AL) distribution is assigned to the error terms in both continuous and discrete models. For modeling the discrete response an underlying latent variable model and the threshold concept are used. Quantile regression for discrete responses can be fitted using monotone equivariance property of quantiles. By assuming a latent variable framework to describe discrete responses, the applied proposed copula still uniquely determines the joint distribution. The likelihood function of the joint model have also a tractable form but it is not differentiable in some points of the parameter space. However, by using the stochastic representation of AL distribution, the maximum likelihood estimate of parameters are obtained using an EM algorithm and also in order to carry out inference about parameters Bootstrap confidence intervals are specified using a Monte Carlo technique. Some simulation studies are performed to illustrate the performance of the model. Finally, we illustrate applications of the proposed approach using burn injuries data. [ABSTRACT FROM AUTHOR]

A large amount of data and applications need to be shared with various parties and stakeholders in the cloud environment for storage, computation, and data utilization. Since a third party operates the cloud platform, owners cannot fully trust this environment. However, it has become a challenge to ensure privacy preservation when sharing data effectively among different parties. This paper proposes a novel model that partitions data into sensitive and non-sensitive parts, injects the noise into sensitive data, and performs classification tasks using k-anonymization, differential privacy, and machine learning approaches. It allows multiple owners to share their data in the cloud environment for various purposes. The model specifies communication protocol among involved multiple untrusted parties to process owners' data. The proposed model preserves actual data by providing a robust mechanism. The experiments are performed over Heart Disease, Arrhythmia, Hepatitis, Indian-liver-patient, and Framingham datasets for Support Vector Machine, K-Nearest Neighbor, Random Forest, Naive Bayes, and Artificial Neural Network classifiers to compute the efficiency in terms of accuracy, precision, recall, and F1-score of the proposed model. The achieved results provide high accuracy, precision, recall, and F1-score up to 93.75%, 94.11%, 100%, and 87.99% and improvement up to 16%, 29%, 12%, and 11%, respectively, compared to previous works. [ABSTRACT FROM AUTHOR]

In this paper, Chaotic implanted opposition-based-quantum equipoise state (CIOQES) and Ascidiacea (CIOQAA) algorithms are applied to solve the loss diminishing problem. In the projected process, the swapping of capricious data is done with the illogical statistics stimulated by Laplace distribution to augment the aid of the possibility of creation level inside the exploration area. Opposition-based learning is one of the persuasive methods to enhance the convergence swiftness of methods. The prospering application of the opposition-based learning involves appraisal of opposite populace and prevailing populace in the parallel generation to determine the greater entrant elucidation. Quantum mechanics has been combined with the algorithms to emulate the analogous performance with the certain stage as they route in a credible powdered of median. Chaotic sequences are integrated into algorithms to augment the exploration and exploitation. Tinkerbell chaotic map engendering standards are implemented. Chaotic implanted opposition-based-quantum equipoise state (CIOQES) algorithm is based on the idea of quantum mechanics about the quantity, inbound, exodus, and fabrication in the governor capacity. Equipoise state algorithm possesses elements as entrant elucidation, and element's location is designated as deliberation. Every element's aptness function is calculated to define the equipoise state of populaces for picking the preeminent solution. Chaotic implanted opposition-based-quantum Ascidiacea (CIOQAA) algorithm is designed to solve the problem. Probing attitudes of Ascidiacea for nutrition spring is imitated to formulate Ascidiacea algorithm. Single end of the Ascidiacea body is continuously resolutely attached to surface like rock or coral. Ascidiacea bottom is corrugated, and core-like postponements will clutch the shallow. Proposed chaotic implanted opposition based-quantum equipoise state (CIOQES) and Ascidiacea (CIOQAA) algorithms are corroborated in G01–G24 benchmark functions, IEEE 30, 57, 118, 300 and 354 bus test systems. Diminished power loss, curtailed power discrepancy, and increased power constancy have been achieved. [ABSTRACT FROM AUTHOR]

We introduce here the compound optimal design strategy to determine the Best Linear Unbiased Estimates (BLUEs) of location and scale parameters based on suitably chosen few order statistics. It is shown that the linear estimates of the parameters from any location-scale distribution, based on few optimally chosen ranks, obtained from the compound optimal design criterion is indeed the BLUE. Further extension of the strategy to Asymptotically Best Linear Unbiased Estimates (ABLUEs) is also discussed. The validation of the proposed strategy is justified through a numerical study for normal, Laplace and logistic distributions. Finally, a real-life data set is analyzed to illustrate the proposed strategy. [ABSTRACT FROM AUTHOR]

The paper focuses on deriving the macroscale viscoelastic constitutive laws using asymptotic expansion method. Both the differential and integral form of the linear viscoelastic constitutive relation of the phases is used in deriving the effective incremental potential and effective constitutive relation, respectively. The integral form is handled by considering the correspondence principle and the Laplace–Carson (LC) transform. A closed-form expression for the effective viscoelastic properties in LC domain is obtained by means of the asymptotic homogenization method (AHM). In addition, AHM coupled with finite element simulation of a representative volume element with periodic boundary conditions is used (AHM + FE). The last step in both approaches is the numerical inversion to the time domain. Solution in time domain is obtained with numerical Laplace inversion algorithms. In case of the differential form, using variational approach, the effective incremental potential in time domain is directly obtained using mean-field method. Different homogenization approaches are exemplified for evaluation of the effective relaxation behavior of composite (viscoelastic matrix reinforced by unidirectional elastic fibers), and they are compared. In the approaches based on LC transform, effective modulus and Poisson's ratio agree well with each other for any property contrast and fiber volume fraction. However, in case of relatively low property contrast, mean field overpredicts as compared to LC approaches in the fiber direction, whereas at relatively higher property contrast, it is vice versa. The difference increases at higher volume fractions due to synergistic effect of the error due to geometrical assumptions involved in the localization tensor and interaction effects of the fiber inclusions. A good agreement in all directions is observed among the three schemes at intermediate volume fractions and property contrast. This study serves as benchmark for further theoretical improvements and experimental investigations. [ABSTRACT FROM AUTHOR]

The B-meson light-cone distribution amplitude is an important non- perturbative quantity arising in the factorization of the amplitudes for many exclusive decays of B mesons, such as B− → γℓ− ν ¯ . We reconsider the renormalization-group (RG) equation satisfied by this function and present its solution at next-to-leading order (NLO) in RG-improved perturbation theory in Laplace space and, for the first time, in momentum space and the so-called diagonal (or dual) space. Since the information needed to describe the B decay processes at leading order in ΛQCD/mb is most directly contained in the distribution amplitude in Laplace space evaluated near the origin, we propose a convenient parameterization of this object in terms of a small set of uncorrelated hadronic parameters. Using recent results on the three-loop anomalous dimension for heavy-light current operators, we derive an expression for the convolution integral appearing in the B− → γℓ− ν ¯ factorization formula that is explicitly scale independent, and we evaluate this formula at (approximate) NNLO. [ABSTRACT FROM AUTHOR]

The cubature Kalman filter (CKF) and its square-root version, namely the square-root cubature Kalman filter (SCKF), are commonly used nonlinear estimators under Gaussian noises. Particularly, the latter has the added advantage of low computational complexity and guaranteed positive semi-definiteness. However, the estimation accuracy often degrades substantially when the measurements are contaminated by outliers. This paper proposes a robust Laplace ℓ 1 square-root cubature Kalman filter (LSCKF). The proposed filter employs the heavy-tailed Laplace distribution to model the measurement noises and solves the maximum posterior estimation using the majorization minimization (MM) approach and Gauss–Newton method. Besides, the filter is derived in square root and uses the orthogonal transformations to realize reliable computation of state estimates. Therefore, the new filter not only has good robustness against measurement outliers, but also retains the advantages of high numerical stability. Two numerical simulations are performed to test the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Time series forecasting is ubiquitous in various scientific and industrial domains. Powered by recurrent and convolutional and self-attention mechanism, deep learning exhibits high efficacy in time series forecasting. However, the existing forecasting methods are suffering some limitations. For example, recurrent neural networks are limited by the gradient vanishing problem, convolutional neural networks cost more parameters, and self-attention has a defect in capturing local dependencies. What's more, they all rely on time invariant or stationary since they leverage parameter sharing by repeating a set of fixed architectures with fixed parameters over time or space. To address the above issues, in this paper we propose a novel time-variant framework named Self-Attention-based Time-Variant Neural Networks (SATVNN), generally capable of capturing dynamic changes of time series on different scales more accurately with its time-variant structure and consisting of self-attention blocks that seek to better capture the dynamic changes of recent data, with the help of Gaussian distribution, Laplace distribution and a novel Cauchy distribution, respectively. SATVNN obviously outperforms the classical time series prediction methods and the state-of-the-art deep learning models on lots of widely used real-world datasets. [ABSTRACT FROM AUTHOR]

Growth mixture modeling is a common tool for longitudinal data analysis. One of the key assumptions of traditional growth mixture modeling is that repeated measures within each class are normally distributed. When this normality assumption is violated, traditional growth mixture modeling may provide misleading model estimation results and suffer from nonconvergence. In this article, we propose a robust approach to growth mixture modeling based on conditional medians and use Bayesian methods for model estimation and inferences. A simulation study is conducted to evaluate the performance of this approach. It is found that the new approach has a higher convergence rate and less biased parameter estimation than the traditional growth mixture modeling approach when data are skewed or have outliers. An empirical data analysis is also provided to illustrate how the proposed method can be applied in practice. [ABSTRACT FROM AUTHOR]

The paper deals with the analysis of the empirical distribution of returns of selected market indices of developed and developing markets in relation to applications in the field of financial risks. The probability distribution of returns plays a key role for both the theoretical and practical part of financial theory. The assumption of a normal distribution of returns, which is crucial for several financial theories, is rejected in line with our analysis of the daily returns of 30 markets. From the perspective of financial risk assessment, the choice of an appropriate distribution is key to the accuracy of the achieved results. In this paper, we examine the possibility of applying alternative distributions, in order to better capture the observed leptokurtic behavior of the empirical distribution of daily returns as compared to the assumption of normality. We perform the analysis on the daily returns of stock market indices in order to examine the possible differences between the empirical distribution of developed and emerging markets. We investigate the suitability and relative performance of these alternative distributions: the generalized skewed t distribution (sgt), the generalized lambda distribution (gld), the exponential power distribution (GED), the Hansen's skewed t distribution and the Laplace distribution. The best relative performance of fit for market index returns providing the sgt_2 and gld distributions, with gld appearing to be a more prominent adept than with the perspective of relative stability of quality of fit and also quality of risk estimation. [ABSTRACT FROM AUTHOR]

The application of the potential method to finding the stationary distribution of the number of customers in the Mn/Gn/1/r and Mn/Gn/1/∞ queueing systems with threshold operation strateges is proposed. The dependences of the input flow intensity on the number of customers are considered, which are characteristic both for closed systems, which are models of the reliability theory, and for queueing systems with random rarefaction of the input flow. Service intensity control strategies are constructed on the assumption that the intensity can vary at the time when servicing starts. Formulas to determine Laplace transforms of the distribution of the number of customers in the system during the busy period and for calculating the average duration of the busy period are obtained. [ABSTRACT FROM AUTHOR]

When querying databases containing sensitive information, the privacy of individuals stored in the database has to be guaranteed. Such guarantees are provided by differentially private mechanisms which add controlled noise to the query responses. However, most such mechanisms do not take into consideration the valid range of the query being posed. Thus, noisy responses that fall outside of this range may potentially be produced. To rectify this and therefore improve the utility of the mechanism, the commonly-used Laplace distribution can be truncated to the valid range of the query and then normalized. However, such a data-dependent operation of normalization leaks additional information about the true query response, thereby violating the differential privacy guarantee. Here, we propose a new method which preserves the differential privacy guarantee through a careful determination of an appropriate scaling parameter for the Laplace distribution. We adapt the privacy guarantee in the context of the Laplace distribution to account for data-dependent normalization factors and study this guarantee for different classes of range constraint configurations. We provide derivations of the optimal scaling parameter (i.e., the minimal value that preserves differential privacy) for each class or provide an approximation thereof. As a result of this work, one can use the Laplace distribution to answer queries in a range-adherent and differentially private manner. To demonstrate the benefits of our proposed method of normalization, we present an experimental comparison against other range-adherent mechanisms. We show that our proposed approach is able to provide improved utility over the alternative mechanisms. [ABSTRACT FROM AUTHOR]

As a part of the multi-source cooperative navigation scheme, data fusion has a significant impact on the quality of state estimation. Particle filtering has gradually become the focus of many fusion methods due to its unique theoretical advantages in nonlinear non-Gaussian systems. However, the particle degradation and the resulting sample impoverishment restrict its application in complex engineering scenarios. In this paper, a robust cubature fission particle filter (RCFPF) is proposed to deal with these problems. First, in the framework of cubature rule, Huber function is used to combine the L2 norm and L1 norm to improve the importance density function(IDF), suppress the observation noise. Meanwhile, the proposed distribution(PD) is further optimized by combining the Gaussian distribution with Laplace distribution to alleviate particle degradation. Second, the particle swarm is fissioned before resampling, and the particle weight is reconstructed by fission of high weight particles and covering low weight particles to inhibit sample impoverishment. The vehicle experiments of multi-source cooperative navigation show that the proposed algorithm achieves better test results in accuracy and robustness than extended Kalman filter (EKF), strong tracking particle filter (STPF), and cubature particle filter (CPF). [ABSTRACT FROM AUTHOR]

This study examines the problem of robust spectral analysis of long-memory processes. We investigate the possibility of using Laplace and quantile periodograms for a non-Gaussian distribution structure. The Laplace periodogram, derived by the least absolute deviations in the harmonic regression procedure, demonstrates its superiority in handling heavy-tailed noise and nonlinear distortion. In this study, we discuss an asymptotic distribution of the Laplace periodogram for long-memory processes. We also derive an asymptotic distribution of the quantile periodogram. Through numerical experiments, we demonstrate the robustness of the Laplace periodogram and the usefulness of the quantile periodogram in detecting the hidden frequency for the spectral analysis of the long-memory process under non-Gaussian distribution. Moreover, as an application of robust periodograms under the long-memory process, we discuss the long-memory parameter estimation based on a log periodogram regression approach. [ABSTRACT FROM AUTHOR]

Computational methods are increasingly being incorporated into the exploitation of microstructure–property relationships for microstructure-sensitive design of materials. In the present work, we propose non-intrusive materials informatics methods for the high-throughput exploration and analysis of a synthetic microstructure space using a machine learning-reinforced multi-phase-field modeling scheme. We specifically study the interface energy space as one of the most uncertain inputs in phase-field modeling and its impact on the shape and contact angle of a growing phase during heterogeneous solidification of secondary phase between solid and liquid phases. We evaluate and discuss methods for the study of sensitivity and propagation of uncertainty in these input parameters as reflected on the shape of the Cu6Sn5 intermetallic during growth over the Cu substrate inside the liquid Sn solder due to uncertain interface energies. The sensitivity results rank σSI,σIL, and σIL, respectively, as the most influential parameters on the shape of the intermetallic. Furthermore, we use variational autoencoder, a deep generative neural network method, and label spreading, a semi-supervised machine learning method for establishing correlations between inputs of outputs of the computational model. We clustered the microstructures into three categories ("wetting", "dewetting", and "invariant") using the label spreading method and compared it with the trend observed in the Young-Laplace equation. On the other hand, a structure map in the interface energy space is developed that shows σSI and σSL alter the shape of the intermetallic synchronously where an increase in the latter and decrease in the former changes the shape from dewetting structures to wetting structures. The study shows that the machine learning-reinforced phase-field method is a convenient approach to analyze microstructure design space in the framework of the ICME. [ABSTRACT FROM AUTHOR]

Trapping and transmission of waves through an acoustic waveguide with a set of perforated cross-walls are studied. Eigenvalues of the corresponding spectral Neumann problem for the Laplace operator are found under geometric symmetry conditions. Almost complete transmission of the piston wave through a system of small holes (an inverted Weinstein anomaly) is achieved by fine tuning of the distance between the cross-walls with a diverse configuration of the connecting holes. A criterion for the possibility of this anomaly is obtained. Related topics—in particular, primitive wave filters and the pinhole-camera effect—are discussed. [ABSTRACT FROM AUTHOR]

Estimation of low or high conditional quantiles is called for in many applications, but commonly encountered data sparsity at the tails of distributions makes this a challenging task. We develop a Bayesian joint-quantile regression method to borrow information across tail quantiles through a linear approximation of quantile coefficients. Motivated by a working likelihood linked to the asymmetric Laplace distributions, we propose a new Bayesian estimator for high quantiles by using a delayed rejection and adaptive Metropolis and Gibbs algorithm. We demonstrate through numerical studies that the proposed estimator is generally more stable and efficient than conventional methods for estimating tail quantiles, especially at small and modest sample sizes. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) is a powerful methodology employed in estimating subsurface physical parameters. FWI is classically formulated as a data-fitting problem based on minimizing the squared l 2 -norm of the difference between the observed data and modeled data (i.e., the data residuals or errors). The FWI based on l 2 -norm (hereafter classical FWI) stems from the assumption that the errors follow a Gaussian probability distribution. However, since, in most cases the error is non-Gaussian for non-linear problems and therefore, the classical FWI tends to fail. In this work, we consider the Tsallis q-deformation of the exponential function, which is widely used in the field of statistical physics, to derive an alternative misfit function to mitigate the FWI sensitivity to spurious measurements (outliers). In this regard, we formulated the FWI from a q-generalization of the Laplace probability distribution (or q-Laplace distribution). Application on a typical Brazilian pre-salt velocity model with an acoustic synthetic noisy-data is presented, in which we compare the performance of our proposal against the classical FWI. In addition, we compare also our methodology with the robust misfit function based on l 1 -norm, which is based on the Laplace distribution. The results show that our proposal outperforms classical FWI, and also the robust FWI based on l 1 -norm. The results also reveal that our proposal accelerates the data inversion process when the data is polluted by outliers. [ABSTRACT FROM AUTHOR]

In order to protect privacy, random noise was added using an automated Laplace mechanism ( I i , I i )-differential privacy, with I i = 0.66 and I i = 2.1 × 10 SP -29 sp . B replying to b F. Houssiau et al. I Nature Communications i https://doi.org/10.1038/s41467-021-27566-0 (2021) In the work developed in Bassolas et al.[1], we studied the structure of cities and their impact in city livability using a highly aggregated mobility dataset. [Extracted from the article]